diff --git a/2022.12/changelog.html b/2022.12/changelog.html
index c878e4120..c0584be9d 100644
--- a/2022.12/changelog.html
+++ b/2022.12/changelog.html
@@ -701,18 +701,18 @@ <h5 id="id4">APIs<a class="headerlink" href="#id4" title="Link to this heading">
 <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this heading">¶</a></h4>
 <p>The following is a list of fixes and points of clarification with regard to the previous version of the specification:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__bool__</span></code>: fix typo in special case notes (<a class="reference external" href="https://github.com/data-apis/array-api/pull/785">gh-785</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__dlpack__</span></code>: resolve conflicting exception guidance (<a class="reference external" href="https://github.com/data-apis/array-api/pull/887">gh-887</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__getitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify broadcast behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/888">gh-888</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify required exception behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/897">gh-897</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">clip</span></code>: clarify that the operation is only defined when elements in <code class="docutils literal notranslate"><span class="pre">min</span></code> and <code class="docutils literal notranslate"><span class="pre">max</span></code> are inside the bounds of the input array data type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/814">gh-814</a>)</p></li>
@@ -726,7 +726,7 @@ <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this h
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.irfftn</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.hfft</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">linalg.solve</span></code>: clarify broadcasting semantics and output shape (<a class="reference external" href="https://github.com/data-apis/array-api/pull/810">gh-810</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-https://github.com/data-apis/array-api/pull/904</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-904</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">searchsorted</span></code>: fix incorrect boundary conditions (<a class="reference external" href="https://github.com/data-apis/array-api/pull/898">gh-898</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">sign</span></code>: fix equation in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/844">gh-844</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">tile</span></code>: fix missing return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/798">gh-798</a>)</p></li>
diff --git a/2022.12/searchindex.js b/2022.12/searchindex.js
index acb9bb10d..9b94b4f9c 100644
--- a/2022.12/searchindex.js
+++ b/2022.12/searchindex.js
@@ -1 +1 @@
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5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 25, 26, 31, 33, 35, 37, 39, 44, 56, 58, 60, 61, 62, 63, 64, 65, 66, 73, 76, 78, 81, 85, 87, 90, 91, 92, 93, 94, 95, 97, 98, 100, 102, 103, 104, 105, 107, 108, 110, 111, 112, 113, 115, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 141, 142, 143, 144, 146, 147, 148, 149, 151, 152, 154, 155, 157, 158, 161, 162, 163, 166, 167, 172, 178, 180, 191, 193, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 215, 216, 217, 221, 225, 226, 227, 228, 231, 235, 239, 240], "dimens": [0, 1, 13, 14, 16, 17, 19, 40, 55, 56, 57, 58, 77, 92, 96, 122, 123, 124, 125, 127, 130, 134, 137, 140, 142, 150, 151, 152, 154, 155, 158, 159, 160, 162, 163, 164, 165, 166, 167, 172, 180, 185, 197, 199, 200, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 239], "where": [0, 1, 13, 14, 15, 47, 57, 65, 84, 85, 87, 91, 93, 94, 98, 100, 101, 114, 115, 116, 126, 128, 130, 134, 136, 144, 145, 146, 151, 152, 156, 157, 166, 167, 171, 172, 180, 185, 186, 188, 191, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 215, 216, 217, 219, 221, 224, 225, 226, 227, 228, 229, 231, 235, 239, 240, 241], "greater": [0, 10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 87, 97, 98, 113, 115, 136, 139, 144, 146, 148, 150, 157, 171, 172, 185, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 220], "than": [0, 10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 87, 95, 96, 97, 98, 113, 114, 115, 116, 122, 128, 136, 137, 139, 144, 146, 148, 150, 152, 154, 155, 157, 161, 162, 163, 164, 165, 166, 172, 180, 183, 186, 189, 192, 194, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 219, 220, 221, 224, 231, 233, 235, 236, 239, 241], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 85, 86, 91, 93, 94, 100, 101, 106, 108, 113, 114, 115, 116, 125, 130, 131, 132, 133, 136, 137, 143, 146, 147, 148, 152, 154, 155, 157, 158, 162, 163, 164, 165, 166, 171, 172, 178, 185, 188, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 220, 221, 224, 225, 226, 227, 231, 239], "zero": [0, 5, 13, 14, 16, 17, 24, 25, 29, 30, 34, 35, 40, 41, 47, 63, 65, 69, 87, 92, 93, 94, 98, 115, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 130, 132, 133, 136, 137, 139, 152, 154, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 178, 180, 185, 186, 188, 191, 197, 199, 200, 201, 202, 203, 205, 206, 207, 208, 210, 213, 220, 221, 224, 225, 226, 233, 241], "dimension": [0, 13, 14, 15, 16, 17, 19, 24, 25, 29, 34, 35, 40, 94, 112, 122, 124, 125, 126, 127, 130, 137, 152, 154, 155, 166, 167, 172, 180, 185, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 213, 216, 217, 221, 223, 224, 233, 235, 239], "apart": 0, "from": [0, 13, 14, 15, 19, 44, 59, 60, 75, 77, 89, 96, 98, 99, 100, 101, 112, 113, 115, 126, 129, 133, 136, 137, 140, 141, 148, 150, 152, 154, 155, 157, 162, 164, 166, 167, 168, 170, 172, 180, 183, 185, 186, 187, 188, 191, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 215, 226, 228, 231, 235, 236, 238, 239, 240, 241, 242], "ndim": [0, 171, 225, 228, 229], "devic": [0, 5, 15, 26, 27, 59, 60, 88, 89, 94, 100, 101, 112, 132, 133, 159, 160, 169, 170, 171, 172, 185, 191, 193, 198, 209, 225, 235, 239, 241], "dtype": [0, 5, 15, 26, 60, 63, 73, 75, 86, 88, 89, 94, 95, 100, 101, 104, 106, 112, 132, 133, 137, 141, 154, 169, 170, 171, 180, 183, 185, 191, 195, 231, 239, 240, 241], "all": [0, 5, 15, 19, 23, 26, 60, 63, 85, 87, 94, 96, 128, 142, 146, 157, 159, 160, 167, 171, 172, 183, 185, 186, 188, 189, 190, 191, 192, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 212, 224, 226, 227, 233, 234, 235, 238, 239, 241, 242], "thi": [0, 1, 5, 7, 15, 19, 26, 34, 58, 59, 63, 71, 77, 93, 98, 106, 112, 115, 118, 119, 120, 121, 125, 130, 136, 137, 139, 151, 152, 155, 162, 163, 164, 165, 166, 171, 172, 178, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 199, 200, 202, 203, 206, 207, 208, 210, 225, 226, 227, 228, 234, 235, 236, 238, 240, 241, 242], "return": [0, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 178, 185, 186, 187, 189, 191, 192, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 241], "tupl": [0, 1, 13, 14, 27, 32, 49, 57, 74, 77, 88, 96, 100, 106, 124, 125, 127, 130, 132, 134, 137, 140, 142, 150, 151, 152, 154, 158, 162, 163, 164, 166, 169, 172, 183, 215, 225, 226, 228, 230, 233, 239], "includ": [0, 1, 9, 13, 14, 15, 16, 17, 20, 21, 23, 28, 30, 40, 41, 42, 43, 47, 51, 106, 108, 112, 122, 124, 125, 127, 137, 148, 152, 154, 166, 171, 172, 180, 185, 186, 187, 188, 189, 190, 192, 194, 219, 233, 235, 236, 238, 240, 241], "those": [0, 5, 7, 15, 23, 87, 128, 130, 180, 185, 188, 189, 192, 225, 228, 229, 234, 235, 236, 239, 240, 241], "mean": [0, 26, 171, 183, 185, 189, 191, 192, 195, 236, 239], "var": [0, 171], "std": [0, 171], "which": [0, 1, 5, 7, 8, 13, 14, 15, 16, 17, 18, 19, 26, 30, 40, 41, 44, 59, 60, 63, 75, 77, 82, 88, 89, 92, 94, 95, 96, 98, 100, 101, 104, 112, 122, 124, 125, 127, 129, 130, 132, 133, 137, 139, 142, 147, 151, 152, 154, 155, 156, 159, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 185, 186, 187, 188, 189, 190, 191, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 219, 227, 228, 229, 231, 233, 234, 235, 236, 239, 240, 241], "some": [0, 93, 98, 115, 172, 186, 187, 188, 189, 192, 195, 239, 241, 242], "common": [0, 172, 180, 183, 192, 194, 235, 239, 240, 241], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 87, 93, 98, 106, 112, 115, 118, 119, 120, 121, 124, 125, 127, 130, 152, 157, 162, 163, 164, 165, 166, 171, 172, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 211, 215, 216, 225, 227, 234, 235, 236, 239, 240, 241, 242], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 87, 105, 106, 112, 124, 127, 128, 130, 137, 138, 141, 143, 154, 162, 163, 164, 165, 172, 178, 180, 185, 186, 187, 188, 189, 190, 191, 192, 201, 205, 206, 207, 208, 210, 215, 216, 219, 226, 228, 229, 231, 233, 234, 235, 236, 239, 240, 241], "numpi": [0, 19, 63, 172, 183, 188, 189, 191, 192, 235, 239, 240, 241, 242], "scalar": [0, 2, 49, 60, 171, 172, 233, 241], "valu": [0, 1, 2, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 84, 85, 86, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 125, 127, 128, 130, 131, 132, 136, 137, 139, 143, 144, 145, 146, 147, 148, 152, 154, 155, 156, 157, 161, 162, 163, 164, 165, 166, 167, 169, 171, 178, 180, 183, 185, 187, 189, 190, 195, 198, 201, 205, 206, 207, 208, 209, 210, 211, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 241], "rational": [0, 7, 172, 191, 192, 234, 236, 239], "alwai": [0, 12, 42, 60, 63, 95, 128, 140, 172, 183, 188, 189, 192, 215], "necessari": [0, 26, 60, 87, 128, 140, 172, 189, 239], "1": [0, 1, 7, 10, 11, 13, 14, 15, 18, 25, 26, 27, 29, 35, 40, 61, 62, 63, 64, 65, 66, 84, 85, 91, 92, 93, 94, 95, 98, 112, 113, 114, 115, 116, 122, 132, 133, 134, 136, 137, 140, 144, 147, 151, 152, 156, 157, 158, 159, 160, 166, 167, 172, 188, 189, 194, 197, 198, 199, 201, 202, 203, 205, 206, 207, 208, 209, 210, 212, 215, 217, 219, 227, 228, 229, 232, 233], "acceler": [0, 5, 183, 191], "non": [0, 1, 13, 14, 16, 17, 63, 118, 119, 120, 121, 124, 125, 127, 130, 137, 152, 158, 166, 167, 172, 180, 185, 186, 192, 197, 199, 202, 203, 206, 207, 208, 210, 212, 213, 215, 219, 221, 228, 233, 241], "could": [0, 26, 162, 163, 164, 165, 183, 189, 194, 235, 239, 241], "forc": 0, "synchron": [0, 26, 59, 239], "2": [0, 1, 5, 7, 9, 10, 11, 26, 27, 40, 61, 62, 64, 65, 66, 79, 84, 85, 87, 113, 115, 116, 122, 146, 149, 156, 157, 158, 172, 188, 189, 195, 198, 201, 205, 206, 207, 208, 209, 210, 219, 221, 224, 225, 226, 227, 228, 229, 230, 231, 233], "delai": [0, 183, 239], "execut": [0, 180, 183, 192, 194, 239, 241], "model": [0, 57, 58, 87, 128, 188, 241], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 85, 87, 98, 126, 128, 146, 156, 157, 185, 187, 192, 226, 240, 241], "futur": [0, 26, 184, 188, 189, 192, 194, 195, 215, 216, 237, 239, 241], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 98, 139, 171, 172, 183, 185, 188, 191, 194, 195, 236, 238, 239, 240], "x": [0, 1, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 61, 62, 63, 64, 65, 66, 68, 74, 76, 78, 84, 85, 89, 91, 92, 93, 96, 97, 99, 101, 105, 107, 108, 109, 113, 114, 115, 116, 119, 123, 124, 125, 127, 129, 130, 133, 134, 135, 137, 138, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 170, 172, 188, 189, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 222, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 241], "__pos__": [0, 171, 185], "po": 0, "__neg__": [0, 171, 185], "neg": [0, 13, 14, 15, 44, 47, 65, 77, 87, 92, 94, 96, 98, 108, 113, 115, 128, 136, 139, 142, 148, 155, 167, 171, 172, 185, 188, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 233, 239], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 139, 153, 158, 167, 168, 185, 212, 218, 223, 227, 230, 232], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 139, 153, 158, 167, 168, 185, 212, 218, 223, 227, 230, 232], "__add__": [0, 50, 171, 185], "add": [0, 5, 7, 21, 153, 154, 171, 172, 185, 186, 187, 192, 231], "__sub__": [0, 171, 185], "sub": [0, 172], "__mul__": [0, 171, 185], "mul": 0, "__truediv__": [0, 171, 185], "truediv": 0, "__floordiv__": [0, 171], "floordiv": 0, "__mod__": [0, 171], "mod": 0, "__pow__": [0, 171, 185], "pow": [0, 47, 171, 185, 187], "should": [0, 1, 5, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 78, 84, 85, 87, 91, 93, 95, 97, 98, 102, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 135, 136, 137, 138, 139, 143, 144, 145, 146, 147, 148, 149, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 178, 185, 186, 187, 188, 191, 192, 195, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 213, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 234, 235, 239, 241, 242], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 78, 87, 98, 100, 101, 112, 124, 125, 127, 128, 139, 144, 148, 149, 152, 159, 160, 166, 167, 171, 178, 185, 187, 188, 195, 199, 200, 203, 204, 207, 210, 211, 215, 216, 217, 224, 225, 227, 235, 240, 241, 242], "real": [0, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 84, 85, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 139, 143, 144, 145, 146, 147, 148, 152, 154, 156, 157, 161, 166, 167, 169, 171, 180, 185, 188, 198, 201, 205, 206, 207, 208, 209, 210, 211, 215, 216, 217, 219, 221, 224, 225, 226, 227, 228, 229, 231, 233, 236], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 171, 180, 183, 186, 188, 189, 192, 193, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 236, 237, 238, 239, 242], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 183, 186, 188, 189, 191, 193, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 236, 239, 240], "__matmul__": [0, 171, 185], "matmul": [0, 40, 171, 180, 185, 235], "The": [0, 1, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 84, 85, 87, 90, 91, 93, 96, 97, 98, 99, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139, 143, 144, 145, 146, 147, 148, 149, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 180, 183, 185, 186, 187, 189, 190, 191, 192, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 234, 235, 236, 238, 239, 240, 241, 242], "__invert__": [0, 171], "inv": [0, 185, 235], "invert": [0, 68, 217, 220, 227], "__inv__": 0, "__and__": [0, 171], "__or__": [0, 171], "__xor__": [0, 171], "xor": [0, 72, 121], "__lshift__": [0, 171], "lshift": 0, "__rshift__": [0, 171], "rshift": 0, "integ": [0, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 87, 97, 98, 100, 101, 104, 106, 112, 124, 125, 127, 129, 136, 137, 139, 141, 143, 152, 154, 155, 158, 161, 166, 167, 171, 172, 185, 187, 188, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 220, 221, 231, 233, 239], "boolean": [0, 22, 24, 25, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 86, 100, 101, 106, 112, 118, 119, 120, 121, 130, 140, 168, 171, 180, 185], "__lt__": [0, 171, 185], "lt": 0, "__le__": [0, 171, 185], "le": 0, "__gt__": [0, 171, 185], "gt": [0, 225, 228], "__ge__": [0, 171, 185], "ge": 0, "__eq__": [0, 171, 185, 192], "eq": 0, "__ne__": [0, 171, 185], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 26, 27, 40, 49, 55, 58, 60, 84, 86, 87, 91, 94, 95, 96, 98, 112, 118, 119, 120, 121, 122, 128, 130, 136, 142, 143, 145, 156, 157, 162, 164, 167, 172, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 209, 210, 212, 215, 216, 221, 224, 225, 228, 234, 235, 236, 239, 240, 241, 242], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 96, 106, 112, 118, 119, 120, 121, 122, 125, 152, 166, 171, 172, 180, 183, 185, 186, 188, 189, 191, 192, 195, 200, 217, 224, 225, 227, 235, 236, 239, 240, 241, 242], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 86, 87, 93, 98, 115, 128, 152, 166, 172, 183, 185, 187, 188, 189, 190, 191, 192, 195, 224, 234, 235, 238, 239, 241], "ani": [0, 1, 9, 10, 11, 23, 26, 28, 43, 59, 61, 62, 66, 86, 90, 107, 108, 131, 148, 171, 172, 180, 185, 188, 189, 191, 195, 228, 236, 238, 239, 242], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 78, 84, 85, 87, 90, 91, 93, 97, 98, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 124, 126, 127, 128, 129, 131, 136, 137, 139, 143, 144, 145, 146, 147, 148, 149, 151, 154, 156, 157, 161, 162, 163, 164, 165, 172, 178, 183, 187, 188, 190, 192, 198, 207, 209, 226, 228, 229, 231, 239, 241, 242], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 102, 103, 110, 111, 112, 124, 127, 139, 147, 167, 172, 185, 188, 189, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 239], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 87, 90, 98, 102, 103, 110, 111, 112, 117, 118, 120, 121, 122, 124, 125, 127, 128, 131, 136, 137, 139, 140, 147, 152, 153, 154, 166, 167, 168, 180, 185, 188, 189, 212, 219, 221, 224, 227, 233, 239, 241], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 86, 87, 90, 98, 99, 102, 103, 106, 110, 111, 112, 118, 119, 120, 121, 124, 125, 127, 128, 130, 131, 147, 152, 157, 162, 163, 164, 165, 166, 171, 172, 178, 180, 183, 185, 186, 187, 188, 189, 190, 192, 194, 195, 215, 225, 226, 228, 234, 235, 239, 240, 241], "complex": [0, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 78, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 122, 124, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 147, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 171, 180, 187, 191, 192, 193, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 240], "howev": [0, 5, 7, 16, 17, 18, 31, 33, 37, 39, 57, 98, 102, 103, 106, 110, 111, 112, 124, 127, 147, 155, 156, 157, 183, 186, 187, 188, 189, 190, 192, 235, 236, 239, 241], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 102, 103, 110, 111, 124, 127, 147], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 85, 87, 91, 93, 98, 100, 101, 102, 103, 110, 111, 112, 124, 127, 136, 139, 146, 147, 148, 151, 157, 172, 178, 180, 185, 199, 200, 203, 204, 207, 210, 215, 216, 239], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 98, 100, 101, 102, 103, 110, 111, 112, 124, 127, 136, 139, 147, 156, 157, 178, 187, 188, 199, 200, 203, 204, 207, 210, 215, 216, 228, 235], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 84, 85, 87, 91, 93, 102, 103, 110, 111, 112, 113, 114, 115, 116, 124, 127, 128, 129, 136, 145, 146, 147, 156, 157, 168, 178, 180, 187, 188, 191, 193, 195, 215, 216, 225, 226, 227, 228, 235, 239, 241, 242], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 87, 90, 93, 98, 99, 101, 102, 103, 110, 111, 113, 115, 117, 118, 120, 121, 122, 124, 125, 127, 128, 130, 131, 136, 137, 139, 141, 144, 147, 148, 149, 152, 153, 154, 162, 163, 164, 165, 166, 167, 168, 171, 172, 180, 182, 183, 186, 188, 190, 191, 192, 195, 212, 219, 221, 224, 227, 233, 234, 239, 240, 241, 242], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 86, 96, 98, 102, 103, 110, 111, 124, 127, 130, 147, 156, 157, 158, 162, 163, 164, 165, 172, 178, 180, 185, 187, 190, 191, 206, 207, 215, 216, 219, 228, 229, 233, 235, 236, 239, 240], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 140, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 183, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 236, 239, 241, 242], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 77, 88, 89, 92, 96, 100, 101, 122, 123, 126, 132, 133, 140, 142, 147, 151, 155, 158, 159, 160, 167, 169, 170, 171, 185, 193, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 239, 241], "result": [0, 1, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 78, 84, 85, 87, 90, 91, 93, 97, 98, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 125, 127, 128, 129, 131, 135, 136, 137, 138, 139, 141, 143, 144, 145, 146, 148, 149, 151, 152, 153, 154, 156, 157, 158, 161, 162, 166, 172, 178, 180, 185, 187, 188, 189, 211, 212, 214, 219, 220, 226, 227, 233, 239, 240, 241, 242], "promot": [0, 1, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 84, 85, 87, 91, 93, 98, 101, 112, 113, 114, 115, 116, 117, 122, 125, 128, 129, 136, 139, 141, 145, 146, 148, 149, 151, 152, 153, 156, 157, 158, 166, 167, 168, 171, 185, 211, 212, 217, 219, 220, 221, 223, 224, 225, 226, 227, 233, 235], "rule": [0, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 84, 85, 87, 91, 93, 98, 100, 101, 112, 113, 114, 115, 116, 117, 122, 128, 129, 136, 139, 141, 144, 145, 146, 148, 149, 151, 153, 156, 157, 158, 167, 168, 171, 172, 185, 188, 191, 211, 212, 217, 219, 220, 221, 223, 224, 225, 226, 227, 233, 235, 239, 241], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 122, 124, 125, 127, 128, 131, 136, 137, 139, 152, 153, 154, 158, 166, 167, 168, 171, 185, 212, 219, 221, 224, 227, 233, 239], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 87, 89, 92, 95, 96, 97, 98, 101, 105, 122, 123, 124, 125, 126, 127, 128, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 147, 150, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 172, 180, 183, 185, 188, 189, 191, 192, 195, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 213, 214, 215, 217, 220, 224, 225, 226, 228, 229, 231, 234, 235, 239, 241], "behavior": [0, 5, 47, 49, 60, 63, 87, 98, 100, 101, 112, 128, 136, 139, 162, 163, 164, 165, 171, 172, 180, 183, 185, 187, 188, 194, 199, 200, 203, 204, 207, 210, 235, 236, 239, 240, 241, 242], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 125, 127, 128, 131, 136, 137, 139, 143, 144, 145, 146, 148, 149, 152, 154, 156, 157, 161, 166, 185, 186, 188, 226, 231], "case": [0, 1, 5, 9, 10, 11, 12, 15, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 125, 126, 127, 128, 131, 136, 137, 139, 140, 143, 144, 145, 146, 148, 149, 152, 154, 156, 157, 161, 166, 172, 183, 185, 186, 187, 188, 189, 192, 225, 226, 228, 231, 235, 237, 239, 242], "its": [0, 5, 26, 40, 73, 87, 95, 122, 128, 140, 142, 187, 188, 192, 234, 239, 240, 241], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 85, 87, 90, 98, 102, 103, 110, 111, 112, 117, 118, 120, 121, 126, 128, 131, 139, 146, 153, 156, 157, 158, 167, 185, 187, 190, 192, 212, 215, 225, 228], "binari": [0, 5, 67, 70, 72, 156, 157, 186], "two": [0, 1, 15, 19, 40, 55, 65, 71, 94, 122, 123, 126, 143, 158, 159, 160, 162, 163, 164, 165, 167, 172, 180, 191, 192, 194, 199, 200, 203, 204, 207, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 235, 239, 240, 241, 242], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 127, 128, 131, 136, 137, 139, 143, 144, 145, 146, 148, 149, 154, 156, 157, 161, 180, 185, 187, 226, 231], "assign": [0, 189], "exampl": [0, 5, 12, 23, 106, 151, 171, 172, 183, 188, 189, 190, 192, 194, 195, 231, 235, 239, 241, 242], "after": [0, 1, 40, 122, 148], "addit": [0, 5, 7, 12, 50, 59, 153, 171, 172, 180, 186, 188, 191, 235, 239, 240, 242], "modifi": [0, 189, 238], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 98, 118, 119, 120, 121, 139, 143, 155, 172, 180, 185, 188, 189, 221, 224, 227, 233, 239], "discuss": [0, 90, 131, 185, 191, 192, 194, 239, 240, 241], "copi": [0, 1, 59, 60, 63, 99, 140, 147, 185, 186, 191, 192, 193, 238, 239], "view": [0, 99, 193], "behaviour": [0, 193, 239, 241], "mutabl": [0, 193], "via": [0, 26, 98, 155, 172, 186, 191, 192, 194, 196, 224, 234, 235, 236, 239], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 87, 128, 141, 143, 151, 158, 172, 180, 183, 188, 197, 199, 202, 203, 206, 207, 208, 210, 221, 224, 235, 239, 241], "match": [0, 1, 5, 9, 20, 63, 98, 139, 158, 201, 205, 206, 207, 208, 210, 215, 216, 219, 233, 241], "op": [0, 180], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 82, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 240, 242], "refer": [1, 13, 14, 93, 94, 115, 152, 166, 167, 172, 188, 189, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 227], "automat": [1, 239], "implicit": [1, 192, 239], "expans": [1, 239], "size": [1, 13, 14, 92, 112, 130, 142, 150, 155, 158, 167, 171, 172, 190, 194, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 223, 225, 228, 239], "without": [1, 7, 26, 57, 130, 140, 162, 163, 164, 165, 183, 186, 187, 190, 238, 239, 241], "purpos": [1, 5, 93, 115, 183, 226, 235, 237, 238, 241], "make": [1, 7, 183, 186, 187, 189, 191, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 234, 236, 239], "differ": [1, 12, 49, 50, 77, 87, 95, 98, 128, 137, 151, 153, 154, 172, 183, 185, 189, 192, 204, 215, 225, 226, 228, 231, 235, 239, 240, 241], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 78, 84, 85, 87, 90, 91, 93, 94, 96, 97, 98, 100, 101, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 127, 128, 129, 130, 131, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 148, 149, 150, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 168, 171, 172, 185, 187, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 215, 224, 225, 226, 228, 231, 239], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 78, 87, 90, 98, 102, 103, 105, 110, 111, 117, 118, 119, 120, 121, 128, 131, 136, 138, 139, 153, 171, 185, 187, 239], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 84, 87, 98, 114, 116, 122, 128, 136, 137, 139, 141, 145, 149, 154, 156, 158, 171, 172, 177, 180, 185, 188, 189, 190, 191, 192, 231, 235, 236, 239, 240, 241], "facilit": [1, 178, 183], "user": [1, 7, 157, 183, 186, 187, 189, 192, 194, 235, 239, 240, 241], "ergonom": 1, "encourag": [1, 239, 240], "avoid": [1, 9, 63, 87, 93, 98, 115, 128, 186, 189, 192, 235, 239, 241], "unnecessari": [1, 235], "can": [1, 7, 26, 60, 75, 106, 172, 180, 183, 186, 188, 189, 191, 192, 195, 224, 225, 228, 234, 235, 239, 240, 241, 242], "potenti": [1, 26, 93, 115, 189, 239], "enabl": [1, 192, 194, 195, 239], "more": [1, 7, 15, 19, 26, 40, 58, 60, 63, 73, 93, 96, 98, 115, 122, 130, 136, 155, 162, 163, 164, 165, 172, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 199, 200, 203, 204, 207, 210, 226, 235, 236, 239, 240, 242], "memori": [1, 26, 60, 140, 183, 189, 190, 192, 239, 241], "effici": [1, 183, 189], "through": [1, 60, 65, 234, 236, 240, 241], "vector": [1, 40, 122, 126, 167, 212, 223, 228, 229, 233, 235, 239], "reduc": [1, 13, 14, 16, 17, 124, 125, 127, 137, 152, 154, 166, 172, 225, 228, 235, 240, 241], "consumpt": [1, 26, 240], "cach": 1, "local": [1, 192], "given": [1, 23, 59, 96, 112, 142, 180, 185, 188, 189, 192, 195, 216, 226, 235, 236, 239, 241], "involv": [1, 12, 87, 98, 128, 136, 141, 180, 185, 187, 188, 192, 194], "singleton": [1, 13, 14, 16, 17, 92, 124, 125, 127, 137, 150, 152, 154, 166, 219, 233, 239], "whose": [1, 5, 9, 11, 19, 20, 47, 55, 62, 66, 84, 85, 94, 96, 123, 136, 142, 145, 146, 155, 156, 157, 158, 159, 160, 162, 163, 164, 172, 189, 201, 205, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 239, 241], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 87, 92, 94, 96, 98, 106, 112, 122, 126, 128, 130, 132, 133, 150, 155, 162, 163, 164, 165, 167, 172, 183, 185, 186, 188, 189, 191, 192, 194, 195, 197, 199, 201, 202, 203, 204, 205, 206, 207, 208, 210, 223, 224, 225, 233, 235, 236, 239, 241], "virtual": 1, "repeat": [1, 172, 185, 241], "across": [1, 5, 87, 98, 128, 157, 185, 187, 188, 192, 234, 239], "correspond": [1, 16, 17, 23, 47, 65, 73, 136, 137, 140, 142, 152, 154, 158, 162, 163, 164, 165, 166, 167, 172, 185, 187, 199, 203, 207, 210, 212, 215, 219, 231, 238, 239], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 172, 186, 188, 192, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 231, 233, 234, 235, 239, 241], "unequ": 1, "lower": [1, 94, 159, 211], "higher": [1, 172, 186, 235, 240], "prepend": [1, 40, 92, 122], "until": 1, "store": [1, 192, 231], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 84, 85, 87, 91, 93, 98, 107, 108, 109, 113, 114, 115, 116, 117, 122, 128, 129, 136, 139, 145, 146, 148, 149, 153, 155, 156, 157, 158, 162, 163, 164, 165, 167, 168, 180, 185, 188, 191, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 213, 214, 217, 219, 220, 221, 223, 224, 225, 226, 227, 231, 233, 235, 239], "let": [1, 9, 10, 11, 12, 62, 66, 85, 90, 91, 93, 107, 108, 109, 112, 113, 115, 125, 131, 137, 144, 146, 148, 152, 154, 157, 166, 167, 172, 194, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 215, 216, 217, 225, 227, 228, 231], "b": [1, 9, 10, 11, 12, 57, 62, 66, 85, 87, 90, 91, 93, 98, 107, 108, 109, 112, 113, 115, 128, 131, 144, 146, 148, 151, 157, 167, 172, 185, 188, 189, 224, 227, 241], "both": [1, 40, 44, 47, 51, 65, 87, 95, 98, 112, 122, 129, 136, 137, 154, 157, 158, 167, 172, 185, 188, 189, 191, 195, 212, 231, 235, 239, 240], "shape1": 1, "describ": [1, 5, 12, 87, 90, 106, 128, 131, 136, 137, 154, 180, 185, 188, 191, 198, 209, 231, 239], "shape2": 1, "n1": [1, 126], "len": [1, 126], "n2": [1, 126], "maximum": [1, 16, 112, 124, 127, 185, 187, 219], "max": [1, 95, 104, 171, 172, 185, 219, 221, 224], "temporari": 1, "list": [1, 73, 77, 126, 151, 172, 183, 185, 192, 239, 241], "length": [1, 15, 126, 140, 158, 172, 198, 200, 201, 204, 209, 228, 229], "while": [1, 98, 112, 118, 119, 120, 121, 125, 152, 162, 163, 166, 171, 172, 178, 183, 185, 188, 189, 190, 192, 224, 235, 240, 241, 242], "0": [1, 5, 9, 10, 11, 12, 15, 24, 25, 26, 29, 35, 38, 48, 57, 61, 62, 63, 64, 65, 66, 69, 71, 76, 77, 84, 85, 87, 90, 91, 92, 93, 94, 95, 97, 98, 113, 114, 115, 116, 125, 128, 134, 136, 137, 139, 143, 144, 145, 146, 148, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 172, 178, 180, 188, 189, 198, 200, 209, 214, 219, 226, 228, 229, 231, 233, 239, 241], "d1": 1, "els": [1, 183, 240], "d2": 1, "set": [1, 18, 49, 65, 147, 152, 159, 160, 162, 164, 165, 166, 171, 172, 185, 186, 187, 188, 189, 192, 194, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 215, 216, 217, 221, 224, 225, 227, 228, 234, 235, 239, 241, 242], "th": [1, 94, 172, 185, 199, 203, 207, 210], "throw": 1, "except": [1, 13, 14, 74, 77, 92, 94, 112, 130, 151, 155, 172, 180, 183, 185, 187, 189, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 224, 236, 239, 240, 241], "demonstr": 1, "applic": [1, 137, 154, 180, 185, 231, 235, 239, 240], "4d": 1, "8": [1, 5, 7, 27, 180, 183], "6": [1, 7], "3d": 1, "7": [1, 7, 27, 195], "5": [1, 172, 239], "2d": 1, "4": [1, 5, 10, 11, 27, 62, 65, 113, 115, 172, 194, 240], "1d": 1, "15": 1, "3": [1, 5, 7, 27, 83, 155, 183, 188, 189, 192, 212], "do": [1, 26, 87, 128, 139, 178, 183, 185, 186, 188, 189, 191, 192, 235, 236, 238, 239, 241, 242], "doe": [1, 15, 131, 172, 180, 183, 186, 187, 188, 189, 190, 192, 195, 235, 239, 241, 242], "second": [1, 12, 65, 67, 69, 70, 71, 72, 90, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 151, 153, 158, 162, 163, 164, 167, 168, 212, 215, 223, 225, 226, 228, 229, 239], "append": [1, 40, 69, 92, 122, 214], "As": [1, 112, 136, 162, 163, 164, 165, 183, 191, 195, 241], "impli": [1, 162, 163, 164, 165, 238, 239], "__setitem__": [1, 155, 171, 185], "Such": [1, 187, 235], "right": [1, 69, 71, 148, 186, 228, 238], "hand": [1, 180], "left": [1, 5, 7, 60, 69, 98, 100, 172, 180, 215, 216, 228, 239], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 82, 94, 126, 130, 151, 155, 162, 163, 164, 171, 185, 199, 203, 207, 210, 239, 241], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 87, 122, 128, 158, 172, 186, 187, 188, 189, 190, 191, 197, 199, 202, 203, 204, 206, 207, 208, 210, 228, 229, 235, 239, 240, 241], "empti": [1, 13, 14, 15, 137, 154, 171, 172, 185, 231, 239], "ok": 1, "allow": [1, 26, 136, 140, 172, 185, 186, 187, 189, 192, 194, 235, 241], "NOT": [1, 119, 238], "adher": [2, 7, 8, 171, 172, 183, 234, 239], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 113, 115, 122, 136, 148, 171, 172, 178, 188, 192, 234, 235, 240], "each": [2, 9, 10, 11, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 84, 85, 87, 90, 91, 93, 97, 98, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 126, 128, 129, 130, 131, 135, 136, 138, 139, 142, 143, 144, 145, 146, 148, 149, 151, 153, 156, 157, 158, 161, 162, 163, 172, 183, 185, 187, 191, 195, 207, 211, 212, 213, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 234, 235, 239, 240, 241], "float": [2, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 122, 124, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 141, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 161, 162, 163, 164, 165, 166, 167, 169, 171, 178, 185, 187, 188, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 240], "point": [2, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 122, 124, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 141, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 161, 162, 163, 164, 165, 166, 167, 169, 171, 178, 185, 187, 188, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 241], "creat": [3, 15, 60, 88, 89, 94, 100, 101, 112, 132, 133, 169, 170, 177, 183, 192, 198, 209, 235, 239], "true": [5, 13, 14, 16, 17, 18, 24, 25, 29, 35, 60, 63, 75, 90, 95, 98, 107, 108, 109, 112, 118, 119, 120, 121, 124, 125, 127, 130, 131, 137, 140, 147, 152, 154, 162, 163, 164, 165, 166, 168, 172, 185, 211, 219, 228, 233, 235], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 29, 35, 60, 63, 75, 90, 107, 108, 109, 112, 118, 119, 120, 121, 124, 125, 127, 131, 137, 140, 147, 152, 154, 162, 163, 164, 165, 166, 172, 211, 219, 228, 233], "bit": [5, 68, 69, 71, 95, 104, 137, 154, 180, 185, 187, 231], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 91, 93, 98, 106, 113, 115, 128, 129, 136, 137, 139, 146, 148, 154, 157, 162, 163, 164, 165, 171, 178, 185, 188, 225, 226, 231], "exist": [5, 7, 60, 77, 140, 183, 185, 188, 191, 192, 217, 236, 239, 240], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 112, 113, 115, 151, 159, 160, 167, 172, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 236], "128": 5, "127": 5, "16": [5, 180], "32": [5, 180], "767": 5, "147": 5, "483": 5, "647": 5, "64": [5, 180], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "unsign": [5, 106, 137, 154, 171, 231], "255": 5, "65": 5, "535": [5, 185], "294": 5, "967": 5, "295": 5, "18": 5, "446": [5, 185], "744": [5, 185], "073": 5, "709": [5, 185], "551": [5, 185], "615": 5, "ieee": [5, 12, 65, 79, 80, 81, 83, 87, 93, 95, 115, 128, 139, 148, 156, 157, 171, 178, 185, 187, 188, 239], "754": [5, 12, 65, 79, 80, 81, 83, 87, 93, 95, 115, 128, 139, 148, 156, 157, 171, 178, 185, 187, 188, 239], "singl": [5, 7, 24, 25, 29, 34, 35, 162, 163, 171, 180, 185, 186, 188, 191, 192, 195, 235, 239, 240, 241], "precis": [5, 9, 20, 42, 60, 95, 100, 101, 105, 128, 138, 148, 180, 185, 187, 201, 205, 206, 207, 208, 210, 215, 216, 219, 226, 228, 229, 233, 239], "2019": [5, 12, 87, 93, 115, 128, 171, 187, 239, 241], "doubl": [5, 158, 180, 185], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 78, 85, 87, 90, 91, 93, 95, 105, 113, 115, 128, 129, 130, 131, 132, 133, 136, 143, 146, 148, 157, 185, 188], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 78, 85, 87, 90, 91, 93, 95, 105, 113, 115, 128, 129, 130, 131, 132, 133, 136, 138, 143, 146, 148, 156, 157, 162, 163, 164, 165, 185, 188, 200, 209], "requir": [5, 10, 11, 59, 61, 62, 63, 64, 66, 106, 148, 151, 155, 157, 171, 172, 178, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 195, 234, 235, 239, 240, 241], "subnorm": 5, "k": [5, 40, 94, 122, 130, 159, 160, 172, 211, 215, 216, 217, 225, 227, 228, 229, 231, 239], "denorm": 5, "us": [5, 7, 19, 26, 27, 59, 60, 82, 95, 112, 114, 116, 142, 162, 164, 172, 180, 185, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 234, 235, 236, 237, 238, 239, 242], "gradual": [5, 239], "underflow": [5, 9, 87, 98, 226], "hardwar": [5, 53, 187, 191, 192, 215, 228, 235, 239], "univers": [5, 186, 192, 235, 239], "mani": [5, 239, 241], "platform": 5, "compil": [5, 157, 183, 186, 190, 239], "toggl": 5, "daz": 5, "flush": 5, "ftz": 5, "increas": [5, 187, 240], "guard": 5, "against": [5, 40, 73, 122, 157, 172, 221, 224, 242], "time": [5, 7, 16, 17, 162, 163, 183, 185, 190, 191, 194, 211, 215, 216, 217, 225, 227, 228, 235, 239, 241], "attack": 5, "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 87, 93, 98, 112, 113, 115, 124, 125, 126, 127, 128, 130, 137, 148, 152, 154, 162, 163, 164, 165, 166, 172, 180, 187, 188, 189, 190, 192, 219, 225, 233, 235], "vari": [5, 157, 162, 163, 164, 165, 180, 187], "beyond": [5, 142, 180, 185, 239], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 77, 88, 92, 95, 96, 100, 106, 112, 132, 137, 139, 142, 150, 151, 154, 155, 158, 159, 160, 162, 163, 164, 165, 167, 169, 172, 180, 185, 187, 188, 189, 191, 192, 195, 197, 199, 200, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 231, 233, 235, 236, 239, 241, 242], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 77, 84, 85, 91, 93, 96, 106, 112, 113, 115, 118, 119, 120, 121, 122, 125, 130, 136, 139, 140, 144, 145, 146, 147, 148, 151, 152, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 171, 183, 185, 186, 188, 189, 190, 191, 192, 194, 195, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 215, 216, 217, 221, 224, 225, 226, 227, 228, 229, 234, 235, 236, 239, 240, 241], "attribut": [5, 23, 95, 104, 171, 182, 185, 236, 239, 240, 241], "wai": [5, 63, 183, 186, 192, 236, 239, 240, 241, 242], "f4": [5, 180], "ensur": [5, 26, 183, 187, 235, 239, 240, 241], "portabl": [5, 59, 112, 187, 189, 192, 239], "consum": [5, 26, 63, 183, 188, 189, 195, 234, 239, 240], "recommend": [5, 7, 19, 23, 26, 112, 118, 119, 120, 121, 125, 139, 152, 166, 178, 185, 187, 191, 192, 239], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 85, 87, 90, 91, 93, 95, 98, 99, 106, 107, 108, 112, 113, 114, 115, 116, 117, 122, 128, 137, 139, 144, 145, 148, 154, 156, 157, 158, 172, 187, 188, 189, 195, 226, 231, 239, 240, 242], "whether": [5, 13, 14, 59, 60, 63, 86, 106, 109, 112, 140, 185, 192, 211, 215, 216, 225, 227, 234, 238, 239, 241], "otherwis": [5, 13, 14, 15, 16, 17, 59, 60, 63, 75, 124, 125, 127, 137, 140, 144, 152, 154, 166, 167, 168, 171, 172, 183, 192, 211, 213, 219, 226, 227, 233, 238], "note": [5, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 45, 47, 50, 51, 61, 62, 63, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 94, 95, 97, 98, 100, 101, 106, 107, 108, 109, 113, 114, 115, 116, 117, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 161, 162, 163, 164, 165, 166, 167, 171, 172, 185, 191, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 239, 240, 241, 242], "possibl": [5, 60, 98, 124, 127, 140, 156, 157, 183, 186, 187, 188, 189, 191, 192, 195, 235, 239, 240, 241, 242], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 122, 124, 125, 127, 128, 129, 137, 152, 154, 166, 172, 183, 186, 188, 191, 192, 194, 195, 216, 217, 235, 236, 239, 241], "In": [5, 12, 19, 59, 87, 90, 98, 106, 108, 109, 128, 131, 139, 144, 171, 172, 180, 187, 188, 191, 192, 206, 207, 225, 226, 228, 235, 236, 240, 241, 242], "clearli": [5, 59, 106, 178, 188, 235, 236], "warn": 5, "about": [5, 7, 26, 95, 104, 189, 235, 239, 241, 242], "document": [5, 7, 59, 98, 106, 178, 186, 188, 191, 234, 236, 238, 240, 241, 242], "": [5, 29, 32, 49, 58, 59, 60, 79, 98, 126, 139, 152, 159, 160, 166, 172, 178, 183, 185, 186, 187, 188, 189, 191, 192, 195, 199, 203, 207, 210, 224, 228, 229, 235, 236, 239, 241], "organ": [5, 185, 235, 240, 241], "within": [5, 15, 27, 172, 180, 183, 185, 188, 192, 197, 199, 202, 203, 206, 207, 208, 210, 239], "accord": [5, 12, 60, 71, 75, 87, 95, 98, 100, 112, 128, 136, 144, 152, 166, 167, 172, 185, 187, 188, 212], "These": [5, 189, 215, 240], "intend": [5, 137, 154, 183, 231], "posit": [7, 9, 10, 11, 13, 14, 20, 26, 46, 62, 65, 66, 80, 87, 92, 94, 95, 98, 108, 113, 115, 128, 130, 139, 142, 146, 148, 157, 171, 172, 183, 185, 187, 195, 209, 211, 225, 240], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 183, 185, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235], "extern": [7, 241], "usabl": 7, "name": [7, 23, 98, 162, 163, 164, 172, 188, 215, 224, 225, 226, 228, 234, 239, 240], "when": [7, 12, 16, 17, 26, 47, 49, 63, 87, 93, 98, 112, 115, 124, 127, 128, 136, 140, 152, 157, 166, 168, 171, 172, 180, 185, 186, 188, 189, 190, 191, 194, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 215, 217, 221, 224, 225, 226, 227, 228, 229, 235, 239, 240, 241], "accept": [7, 26, 118, 119, 120, 121, 125, 139, 152, 166, 183, 236], "call": [7, 34, 191, 192, 226, 239, 240, 241], "argument": [7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 84, 113, 115, 122, 137, 141, 145, 148, 154, 156, 157, 158, 171, 180, 187, 189, 191, 192, 197, 199, 202, 203, 206, 207, 208, 210, 231, 235, 239, 240, 241], "map": [7, 188, 189], "base": [7, 47, 57, 58, 91, 92, 113, 114, 115, 116, 136, 162, 163, 164, 165, 172, 185, 189, 195, 235, 236, 239, 240, 241], "sole": [7, 172, 178, 235], "incompat": [7, 26, 74, 183, 236, 239], "normal": [7, 77, 151, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210], "practic": [7, 19, 172, 235, 240], "avail": [7, 183, 191, 234, 236, 240], "still": [7, 195, 235, 240, 241, 242], "consid": [7, 63, 118, 119, 120, 121, 162, 163, 164, 165, 188, 192, 209, 224, 235, 239, 241, 242], "compliant": [7, 51, 87, 93, 112, 115, 118, 119, 120, 121, 124, 125, 127, 152, 166, 187, 190, 192, 236, 239], "namespac": [7, 23, 183, 185, 196, 234, 235, 236, 239, 242], "altern": [7, 189, 191, 242], "thei": [7, 26, 180, 186, 191, 192, 194, 195, 234, 235, 236, 239, 241, 242], "guidanc": [7, 49, 185, 186, 239], "were": [7, 98, 185, 239], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 77, 88, 89, 94, 96, 100, 101, 112, 124, 125, 127, 132, 133, 137, 140, 142, 152, 154, 155, 166, 169, 170, 171, 185, 194, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 219, 221, 224, 231, 233, 235, 240, 241], "keyword": [7, 126, 137, 154, 171, 185, 189, 192, 194, 195, 231, 235, 236, 239, 240, 241], "lead": [7, 98, 188, 225, 228, 239], "readabl": [7, 180, 235, 240], "code": [7, 59, 180, 189, 190, 192, 195, 235, 239, 240, 241], "easier": [7, 183, 189, 235], "evolv": [7, 183, 235], "over": [7, 13, 14, 112, 124, 125, 127, 137, 152, 154, 155, 158, 166, 167, 187, 188, 189, 191, 192, 194, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 212, 231, 233, 235, 239], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 172, 184, 185, 186, 192, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 236], "worri": 7, "xi": [7, 126], "annot": [7, 185, 195, 239], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 185, 186, 189, 191, 194, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 238, 241], "themselv": [7, 192], "individu": [7, 192, 194, 195, 198, 209, 239, 240], "descript": [7, 185, 187, 219, 233], "aim": [7, 186, 195, 234, 235, 236, 239, 240, 241, 242], "strongli": [7, 189, 241], "look": [7, 241], "like": [7, 183, 186, 188, 189, 195, 236, 239, 240, 241], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 77, 82, 88, 89, 94, 96, 100, 101, 112, 124, 125, 127, 132, 133, 137, 140, 142, 152, 154, 155, 166, 169, 170, 172, 185, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 219, 221, 224, 231, 233, 239, 240, 242], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 88, 92, 94, 95, 96, 98, 100, 101, 104, 112, 124, 125, 127, 132, 134, 137, 140, 142, 147, 150, 151, 152, 154, 155, 158, 159, 160, 166, 167, 169, 172, 180, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 214, 219, 220, 230, 231, 232, 233, 240], "str": [7, 8, 23, 106, 126, 240], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 86, 185, 241], "yyyi": [8, 23, 236], "mm": [8, 23, 236], "string": [8, 23, 106, 185, 236, 239], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 104, 106, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 171, 183, 186, 192, 194, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 237, 239, 241], "calcul": [9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 84, 85, 87, 91, 93, 113, 114, 115, 116, 117, 124, 125, 127, 128, 136, 137, 145, 146, 148, 152, 153, 154, 156, 157, 166, 185, 226], "absolut": [9, 20, 144, 187, 189, 219, 220, 226, 235], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 78, 84, 85, 91, 93, 97, 105, 107, 108, 109, 113, 114, 115, 116, 119, 124, 125, 127, 129, 135, 138, 143, 144, 145, 146, 148, 149, 152, 156, 157, 161, 166], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 84, 85, 87, 89, 90, 91, 92, 93, 96, 97, 98, 99, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 178, 183, 185, 188, 190, 192, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 228, 229, 231, 233, 235, 239, 241], "ha": [9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 84, 85, 87, 91, 92, 93, 98, 101, 122, 125, 126, 128, 129, 130, 136, 137, 145, 146, 150, 152, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 172, 180, 183, 188, 191, 192, 194, 212, 219, 227, 228, 231, 233, 235, 236, 239, 241, 242], "magnitud": [9, 12, 20, 87, 98, 128, 185, 228, 229], "minimum": [9, 17, 20, 44, 124, 127, 129, 171, 185, 187], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 79, 80, 81, 83, 87, 95, 98, 104, 128, 129, 156, 157, 185, 187, 240], "known": [9, 144, 187, 190], "norm": [9, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 219, 233, 235], "modulu": [9, 139], "z": [9, 10, 11, 61, 62, 64, 66, 113, 188], "bj": [9, 12, 78, 87, 128], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 78, 86, 87, 90, 92, 98, 102, 103, 110, 111, 118, 119, 120, 121, 122, 124, 125, 127, 128, 129, 130, 131, 135, 137, 152, 154, 158, 162, 163, 164, 165, 166, 167, 172, 185, 187, 190, 197, 198, 199, 201, 202, 203, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 219, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239], "operatornam": [9, 10, 11, 61, 62, 64, 66, 84, 85, 144, 145, 146, 156, 157, 188, 215, 216, 226, 228], "sqrt": [9, 10, 11, 61, 62, 171, 185, 188, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 233], "take": [9, 113, 115, 136, 148, 171, 185, 192, 195, 239], "care": [9, 189, 235], "undu": [9, 190], "overflow": [9, 12, 87, 98, 112, 137, 154, 180, 226, 231, 235], "dure": [9, 40, 59, 122, 152, 166, 180, 183, 224, 239, 240], "intermedi": 9, "stage": [9, 236], "numer": [9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 87, 98, 106, 107, 108, 109, 122, 126, 128, 129, 135, 136, 137, 143, 144, 149, 153, 154, 158, 171, 180, 187, 197, 199, 202, 203, 206, 207, 208, 210, 212, 223, 224, 226, 231, 235, 239, 241], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 84, 85, 87, 88, 89, 90, 91, 93, 97, 98, 99, 102, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 172, 185, 187, 188, 189, 191, 194, 198, 199, 200, 203, 204, 207, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 239, 241], "complex128": [9, 20, 106, 171, 180, 185, 201, 205, 206, 207, 208, 210, 215, 216, 219, 233], "float64": [9, 20, 106, 171, 180, 201, 205, 206, 207, 208, 210, 215, 216, 219, 233], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 125, 127, 128, 131, 136, 139, 143, 144, 145, 146, 148, 152, 156, 157, 161, 162, 163, 164, 165, 166, 171, 178, 185, 188, 239], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 80, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 113, 114, 115, 116, 117, 124, 127, 128, 131, 136, 139, 143, 145, 146, 148, 156, 157, 161, 188, 226, 233], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 85, 90, 91, 93, 107, 108, 109, 112, 113, 115, 131, 143, 144, 146, 148, 157, 171, 185, 186, 239, 240, 241], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 85, 87, 90, 91, 93, 98, 107, 108, 113, 115, 128, 131, 136, 139, 146, 148, 157, 187], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 78, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 78, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 236], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 84, 85, 91, 93, 98, 113, 114, 115, 116, 136, 145, 146, 156, 157, 187, 221, 224], "princip": [10, 11, 61, 62, 64, 66, 113, 148, 188, 235], "invers": [10, 11, 61, 62, 64, 65, 66, 188, 197, 199, 202, 203, 204, 205, 206, 207, 208, 210, 217, 220, 224, 235], "cosin": [10, 11, 84, 85, 157], "express": [10, 61, 63, 64, 65, 84, 145, 156, 172, 180, 189, 235, 238], "radian": [10, 61, 64, 65, 84, 145, 156], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 84, 85, 87, 112, 114, 116, 144, 145, 146, 156, 157, 188, 226], "pi": [10, 11, 61, 62, 64, 66, 85, 113, 115, 146, 156, 157, 171], "j": [10, 11, 12, 25, 61, 62, 64, 66, 85, 87, 91, 93, 112, 113, 115, 128, 144, 145, 146, 148, 156, 157, 172, 188, 215, 228, 231], "ln": [10, 11, 61, 62, 64, 66, 113], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 85, 91, 93, 113, 114, 115, 116, 146, 148, 157, 171, 185], "multi": [10, 11, 61, 62, 64, 66, 171, 188, 191, 192, 212, 241], "branch": [10, 11, 61, 62, 64, 65, 66, 84, 85, 87, 91, 93, 113, 115, 128, 136, 145, 146, 148, 156, 157, 239], "cut": [10, 11, 61, 62, 64, 66, 84, 85, 91, 93, 113, 115, 136, 145, 146, 148, 156, 157, 239], "plane": [10, 11, 61, 62, 64, 66, 84, 85, 87, 91, 93, 128, 145, 146, 148, 156, 157, 239], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 113, 115, 124, 125, 127, 136, 137, 148, 152, 154, 166, 167, 187, 188, 212, 235, 240], "place": [10, 11, 15, 60, 61, 62, 64, 66, 88, 89, 94, 100, 101, 112, 132, 133, 142, 169, 170, 171, 178, 180, 185, 189, 192, 198, 209, 224], "line": [10, 11, 61, 62, 64, 66, 156, 157, 180, 188, 239, 240, 241, 242], "segment": [10, 11, 61, 62, 64, 66, 188], "infti": [10, 11, 61, 62, 64, 66, 84, 113, 115, 136, 148, 188], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 77, 92, 96, 113, 115, 124, 125, 127, 136, 137, 142, 147, 148, 150, 151, 152, 154, 155, 158, 166, 167, 171, 185, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 212, 219, 232, 233, 239], "rang": [10, 61, 62, 64, 66, 113, 115, 137, 148, 154, 172, 185, 231, 239], "strip": [10, 61, 62, 64, 66, 113, 115], "unbound": [10, 61, 62, 64, 66, 113, 115], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 77, 94, 96, 113, 115, 124, 125, 127, 137, 142, 147, 148, 151, 152, 154, 155, 156, 157, 166, 167, 172, 185, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 231, 233, 235], "c99": [10, 11, 61, 62, 64, 66, 87, 113, 115, 128, 136, 148, 188, 236], "provision": [10, 11, 61, 62, 64, 66, 113, 115, 136, 148, 188], "statu": [10, 11, 61, 62, 64, 66, 113, 115, 136, 148, 188], "less": [10, 11, 39, 47, 61, 65, 66, 76, 87, 98, 113, 114, 115, 116, 136, 139, 144, 148, 152, 166, 171, 172, 185, 189, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 219, 220, 221, 224, 233, 239], "\u03c0": [10, 64, 65, 83], "0j": [10, 11, 12, 25, 62, 63, 66, 85, 91, 93, 94, 113, 115, 132, 133, 144, 146, 148, 157, 188, 226], "nonzero": [10, 11, 12, 62, 66, 85, 87, 91, 93, 98, 128, 146, 157, 171, 172, 185, 224], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 84, 85, 145, 146, 156, 157, 188], "aco": [11, 61, 171, 185, 187], "simpli": [11, 93, 115, 186, 195, 239, 241], "upper": [11, 94, 160, 185, 211, 225], "half": [11, 15, 66, 112, 148, 172, 200], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 113, 115], "3\u03c0j": [11, 113, 115], "sum": [12, 21, 117, 171, 185, 219, 231, 233, 235], "x1_i": [12, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 128, 131, 136, 139, 153, 168, 185], "x2_i": [12, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 128, 131, 136, 139, 153, 168, 185], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 90, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 142, 151, 153, 156, 157, 158, 162, 163, 164, 167, 168, 172, 188, 212, 215, 223, 225, 226, 228, 229, 235, 239, 240, 241, 242], "remain": [12, 87, 90, 98, 106, 108, 109, 128, 131, 139, 140, 144, 172, 189, 210], "neither": [12, 40, 87, 98, 122, 128, 158, 228, 240], "nor": [12, 87, 98, 128, 228, 240], "mathemat": [12, 19, 65, 83, 84, 85, 87, 93, 98, 113, 115, 128, 145, 146, 156, 157, 171, 188, 219, 233], "round": [12, 15, 76, 87, 97, 98, 128, 148, 161, 171, 185, 187], "nearest": [12, 87, 128, 143, 161, 187], "mode": [12, 87, 128, 187, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 225], "too": [12, 87, 98, 128, 235, 239], "larg": [12, 87, 98, 128, 195, 226, 239], "appropri": [12, 26, 87, 98, 128, 188], "commut": 12, "associ": [12, 42, 128, 180, 221, 224, 227, 235, 238, 240], "tabl": [12, 87, 128, 171], "c": [12, 87, 90, 112, 128, 130, 131, 151, 152, 157, 166, 172, 185, 188, 191, 193, 211, 215, 216, 217, 225, 227, 228, 236, 238, 239, 241], "d": [12, 87, 90, 112, 128, 131, 180, 198, 209], "dj": [12, 87, 128], "independ": [12, 87, 128, 143, 172, 183, 191, 212, 225, 227, 235, 236, 239], "abov": [12, 87, 90, 113, 115, 128, 131, 136, 137, 148, 154, 159, 160, 172, 180, 188, 189, 191, 192, 214, 215, 231, 235, 238, 241], "similarli": [12, 57, 106, 126, 180, 211, 228], "henc": [12, 78, 92, 130, 162, 163, 164, 165, 172, 186, 188, 189, 190, 191, 194, 195, 239, 241], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 124, 125, 127, 137, 152, 154, 166, 219, 233], "bool": [13, 14, 16, 17, 18, 22, 24, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 86, 90, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 118, 119, 120, 121, 124, 125, 127, 131, 137, 140, 147, 152, 154, 166, 171, 180, 185, 211, 219, 228, 233], "test": [13, 14, 86, 107, 108, 109, 185, 187, 237, 239, 240, 241], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 91, 93, 113, 114, 115, 116, 129, 135, 144, 149, 183, 239], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 88, 95, 96, 100, 101, 104, 106, 112, 124, 125, 127, 132, 137, 141, 142, 150, 151, 152, 154, 158, 166, 169, 200, 204, 219, 221, 224, 233, 240], "ax": [13, 14, 16, 17, 19, 55, 56, 96, 124, 125, 127, 134, 137, 142, 150, 152, 154, 158, 166, 167, 172, 185, 199, 200, 203, 204, 207, 210, 212, 219, 224, 227, 230, 233], "logic": [13, 14, 24, 87, 90, 118, 119, 120, 121, 128, 131, 192, 199, 203, 207, 210], "AND": [13, 67, 90, 118, 238], "reduct": [13, 14], "default": [13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 88, 89, 94, 96, 100, 101, 112, 124, 125, 126, 127, 130, 132, 133, 137, 140, 142, 147, 151, 152, 154, 158, 159, 160, 162, 163, 164, 166, 167, 169, 170, 171, 172, 185, 187, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 219, 221, 224, 225, 228, 231, 233], "entir": [13, 14, 84, 85, 91, 93, 124, 125, 127, 137, 145, 146, 152, 154, 166], "valid": [13, 14, 27, 92, 151, 158, 172, 187, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 215, 225, 228, 240], "count": [13, 14, 77, 96, 155, 162, 163, 167, 172, 185, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 216], "last": [13, 14, 18, 19, 55, 77, 96, 142, 147, 151, 155, 158, 167, 172, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 219, 225, 228, 231], "invalid": [13, 14, 23, 92, 167, 212, 239], "rais": [13, 14, 19, 23, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 87, 91, 92, 112, 122, 124, 127, 130, 136, 140, 150, 151, 167, 172, 180, 183, 185, 192, 212, 220, 239], "wa": [13, 14, 19, 98, 124, 125, 127, 137, 152, 154, 166, 180, 192, 195, 239, 241], "OR": [14, 24, 70, 120, 131, 238], "start": [15, 112, 172, 185, 195, 239, 241], "stop": [15, 112, 172, 185, 240], "step": [15, 112, 172, 240], "evenli": [15, 112], "space": [15, 112, 198, 200, 209], "open": [15, 112, 172], "inclus": [15, 172, 239], "end": [15, 65, 84, 112, 144, 145, 156, 157, 178, 189, 226, 239, 240, 241], "exclus": [15, 172], "distanc": 15, "between": [15, 26, 47, 51, 65, 77, 87, 90, 95, 112, 131, 136, 151, 162, 163, 164, 165, 180, 188, 189, 192, 198, 209, 235, 239, 241], "adjac": 15, "output": [15, 60, 77, 88, 89, 92, 94, 96, 100, 101, 112, 126, 132, 133, 140, 142, 150, 151, 155, 169, 170, 183, 185, 188, 189, 192, 193, 195, 197, 199, 201, 202, 203, 206, 207, 208, 210, 231, 239], "infer": [15, 60, 89, 100, 101, 133, 140, 170, 190, 235, 240], "cannot": [15, 26, 57, 156, 157, 185, 188, 190, 239], "guarante": [15, 59, 162, 164, 183, 188, 192, 239, 241], "error": [15, 19, 23, 26, 51, 55, 87, 124, 127, 156, 157, 180, 187, 226, 239], "affect": [15, 49, 189, 192], "ceil": [15, 171], "indic": [16, 17, 18, 60, 86, 106, 112, 130, 140, 142, 144, 155, 159, 160, 162, 164, 172, 180, 185, 233, 239], "occur": [16, 17, 75, 156, 157, 162, 163, 164, 165, 188, 240], "occurr": [16, 17, 162], "comparison": [16, 17, 18, 31, 33, 37, 39, 90, 102, 103, 110, 111, 124, 127, 131, 147, 171, 185, 188, 236, 240], "search": [16, 17, 171], "flatten": [16, 17, 77, 142, 162, 163, 164, 165, 233, 235], "descend": [18, 147, 228, 229], "stabl": [18, 147, 191], "sort": [18, 171, 185, 215, 216, 228, 229], "ascend": [18, 147, 185], "stabil": [18, 147], "maintain": [18, 147, 186, 239, 241], "rel": [18, 19, 55, 96, 142, 147, 185, 214, 221, 224, 231], "compar": [18, 147, 162, 163, 164, 165, 187, 192, 240, 242], "properti": [19, 53, 54, 55, 56, 57, 58, 185, 188, 192, 195, 239], "transpos": [19, 40, 55, 122, 123, 158, 211, 215, 224, 228, 235], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 86, 180, 183, 185, 192], "permut": [19, 55, 134], "revers": [19, 55, 65, 96], "origin": [19, 55, 65, 140, 142, 185, 189, 197, 199, 202, 203, 206, 207, 208, 210, 239, 240], "limit": [19, 95, 104, 106, 187, 235, 238], "matric": [19, 40, 55, 122, 123, 126, 159, 160, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 235], "deviat": [19, 152, 187, 239, 241], "et": [19, 228, 229], "al": 19, "intent": [19, 65], "found": [19, 188, 191, 241, 242], "problemat": [19, 63, 186, 189], "conflict": [19, 185], "definit": [19, 84, 85, 145, 146, 156, 157, 185, 211, 240], "batch": [19, 233, 235], "cetera": [19, 228, 229], "permute_dim": [19, 171], "interfac": [19, 191, 235, 239, 241], "ab": [20, 136, 171, 185, 219, 233], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 171, 185], "api_vers": [23, 239], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 86, 95, 99, 104, 171, 172, 180, 183, 185, 189, 191, 192, 195, 234, 236, 240, 241], "form": [23, 40, 78, 122, 123, 159, 160, 189, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 236, 240], "2020": [23, 195, 236, 238, 239], "10": [23, 27, 114, 172, 239], "latest": [23, 191], "modul": [23, 183, 234, 236, 240, 241, 242], "It": [23, 26, 183, 189, 191, 239, 241, 242], "everi": [23, 100, 101, 225, 239], "top": [23, 183, 239, 241], "level": [23, 180, 186, 191, 192, 234, 235, 239, 240], "public": [23, 234, 240, 241], "well": [23, 186, 188, 191, 192, 225, 241, 242], "part": [23, 35, 159, 160, 180, 185, 191, 194, 236, 239, 241], "convert": [24, 25, 29, 34, 35, 60, 180, 185, 186, 188, 191, 239, 241], "handl": [24, 26, 61, 64, 84, 114, 116, 136, 137, 144, 145, 149, 154, 156, 185, 186, 188, 189, 192, 231, 239], "new": [25, 92, 95, 99, 100, 101, 104, 106, 132, 133, 138, 140, 151, 169, 170, 183, 185, 186, 189, 191, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 236, 239, 240, 241], "stream": [26, 59, 192], "pycapsul": 26, "export": [26, 185, 240], "from_dlpack": [26, 27, 171, 185, 191], "dlpack": [26, 27, 185], "capsul": 26, "pointer": 26, "produc": [26, 215, 225, 228, 241], "instruct": 26, "safe": [26, 112], "insert": [26, 92, 185], "wait": 26, "event": [26, 238], "signal": [26, 201, 205, 241], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 183, 186, 191, 192, 235, 239, 241], "queue": [26, 59, 192], "similar": [26, 139, 186, 188, 190, 239, 240, 241], "mechan": [26, 99, 183, 185, 186, 193, 234, 239], "most": [26, 183, 192, 215, 235, 239, 241], "yet": [26, 195, 239], "sycl": 26, "want": [26, 87, 128, 186, 190, 191, 239, 241, 242], "cl": 26, "agre": 26, "assum": [26, 84, 145, 156, 183, 188, 192, 234, 239], "legaci": 26, "per": [26, 186, 191, 237], "thread": [26, 239, 241], "disallow": 26, "due": [26, 42, 57, 58, 112, 128, 155, 187, 188, 235, 239], "ambigu": [26, 63, 98, 189], "explicitli": [26, 40, 63, 122, 158, 172, 183, 185, 211, 215, 216, 225, 227, 235, 239, 241], "prefer": [26, 98, 183, 235, 241], "develop": [26, 187, 239, 240, 241, 242], "who": [26, 187, 239, 240], "think": 26, "cost": 26, "interchang": [26, 99, 183, 186, 193, 239], "detail": [26, 32, 49, 99, 130, 162, 163, 164, 165, 171, 172, 182, 183, 190, 192, 194, 235, 239, 241], "buffererror": [26, 185], "stride": [26, 189], "fail": [26, 239], "reason": [26, 139, 157, 189, 235, 239, 240], "incorrect": [26, 185], "pass": [26, 65, 183, 187, 192], "enum": 27, "id": 27, "format": [27, 185, 236], "meant": 27, "device_typ": 27, "device_id": 27, "member": 27, "cuda": [27, 186, 191, 241], "cpu_pin": 27, "opencl": 27, "vulkan": 27, "metal": 27, "vpi": 27, "rocm": [27, 186], "truth": [28, 31, 33, 37, 39, 43, 86, 90, 102, 103, 110, 111, 131, 242], "cast": [29, 49, 60, 63, 75, 137, 154, 180, 188, 231, 239, 241], "outsid": [29, 151, 172, 180, 185, 191], "bound": [29, 172, 180, 185, 195], "typeerror": [29, 34, 35, 239, 241], "divis": [30, 41, 71, 87, 98, 139, 144, 188], "floor_divid": [30, 171, 185], "greater_equ": [31, 171, 185], "kei": [32, 49, 239], "slice": [32, 49, 171, 189], "ellipsi": [32, 49, 172], "semant": [32, 40, 49, 98, 122, 139, 155, 171, 172, 183, 185, 189, 191, 194, 235, 239, 240, 241], "access": [32, 172, 185, 191, 234, 236, 239], "method": [34, 99, 171, 183, 189, 191, 192, 194, 195, 239, 240, 241], "also": [34, 144, 180, 183, 188, 189, 190, 191, 195, 199, 203, 207, 210, 228, 234, 241], "pep": [34, 40, 98, 122, 191, 236], "357": 34, "overflowerror": 35, "valueerror": [35, 60, 140, 150, 241], "bitwise_invert": [36, 171], "less_equ": [37, 171, 185], "bitwise_left_shift": [38, 171, 185], "matrix": [40, 55, 122, 123, 126, 158, 159, 160, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 235, 239], "product": [40, 42, 58, 122, 128, 137, 158, 167, 185, 212, 223, 235], "built": [40, 122, 172, 180, 239], "465": [40, 122], "least": [40, 87, 106, 122, 128, 130, 162, 163, 164, 165, 186, 187, 224], "m": [40, 55, 122, 123, 126, 159, 160, 172, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231], "remov": [40, 122, 150, 172, 188, 214, 231], "innermost": [40, 122, 123, 159, 160, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231], "conjug": [40, 78, 122, 158, 167, 185, 211, 215, 228, 235], "transposit": [40, 122, 158], "desir": [40, 63, 75, 122, 158, 187, 188, 195], "prior": [40, 122, 158], "inner": [40, 122, 185, 215, 235], "stack": [40, 55, 122, 123, 159, 160, 171, 194, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 235], "l": [40, 122, 211, 231], "remaind": [41, 171, 172, 185], "multipli": [42, 137, 149, 171, 185, 187, 215, 228], "not_equ": [43, 171, 185], "negat": [44, 78, 129], "bitwise_or": [45, 171, 185], "exponenti": [47, 91, 93, 117, 136, 188], "power": [47, 71, 91, 136, 188, 220, 241], "expon": [47, 136, 220], "kind": [47, 51, 87, 95, 101, 104, 106, 136, 137, 154, 180, 185, 231, 235, 238], "versu": [47, 51, 63, 87, 128, 136, 185], "bitwise_right_shift": [48, 171, 185], "mix": [49, 112, 125, 141, 152, 166, 171, 185, 189, 192, 235, 239], "how": [49, 87, 128, 183, 187, 192, 194, 240, 241, 242], "govern": [50, 153, 180, 235, 236], "minuend": 50, "subtrahend": 50, "subtract": [50, 171, 185, 187], "choos": [51, 57, 59, 87, 98, 112, 118, 119, 120, 121, 124, 125, 127, 128, 130, 152, 162, 163, 164, 165, 166, 171, 172, 178, 188, 189, 190, 192, 239, 241], "divid": [51, 98, 144, 171, 172, 185, 187], "bitwise_xor": [52, 171, 185], "resid": [53, 59, 92, 172, 185, 239], "fewer": 55, "unknown": [57, 58], "graph": [57, 58, 130, 162, 163, 164, 165, 172, 190, 239], "static": [57, 190, 193], "resolv": [57, 60, 92, 98, 100, 101, 137, 154, 185, 199, 200, 203, 204, 207, 210, 231, 239], "know": [57, 130, 162, 163, 164, 165, 183, 186, 187, 190, 239, 241], "content": [57, 190, 238], "warrant": 57, "custom": [57, 186], "immut": 57, "retriev": [57, 172, 183, 196, 235, 241], "behav": [57, 188], "current": [59, 155, 178, 189, 192, 195, 239, 240, 241], "__dlpack__": [59, 99, 171, 185], "caveat": 59, "would": [59, 60, 140, 172, 185, 189, 235, 239, 241], "locat": [59, 185, 189], "enqueu": 59, "asynchron": 59, "safeti": 59, "explain": [59, 186], "obj": 60, "nestedsequ": 60, "supportsbufferprotocol": 60, "possibli": [60, 194, 239], "nest": [60, 194], "sequenc": [60, 77, 112, 151, 158, 172, 185, 199, 200, 203, 204, 207, 210, 230], "buffer": [60, 140, 189, 191], "protocol": [60, 183, 191, 195, 239, 241], "turn": [60, 183, 234], "memoryview": 60, "preced": [60, 188, 191, 192], "mixtur": 60, "convers": [60, 112, 185, 186, 239], "obei": [60, 112], "permit": [60, 63, 112, 190, 238], "To": [60, 98, 172, 185, 187, 188, 195, 239, 240, 242], "explicit": [60, 155, 158, 192, 241], "array_api": [60, 239], "astyp": [60, 171, 185], "exce": [60, 100, 101, 112], "never": [60, 140, 239], "reus": [60, 140, 189, 239], "sine": [61, 62, 145, 146, 157], "1j": [61, 64, 84, 85, 91, 93, 145, 146, 156], "asinh": [61, 171, 185, 187], "asin": [62, 171, 185, 187], "irrespect": [63, 188], "integr": [63, 106], "histor": [63, 157, 235], "discard": 63, "choic": [63, 152, 166, 183, 187, 188, 192, 194, 235, 236, 239, 241], "introduc": [63, 98, 142, 195, 240], "achiev": [63, 172, 187], "outcom": 63, "instead": [63, 188, 191, 240, 241], "clariti": 63, "newli": [63, 192], "alloc": [63, 159, 160, 190, 192], "tangent": [64, 65, 66, 156, 157], "atanh": [64, 171, 185, 187], "quotient": [65, 87, 98, 172], "domain": [65, 185, 187, 188, 239, 241], "notat": 65, "denot": [65, 167, 224], "pair": [65, 98, 212, 228], "codomain": 65, "quadrant": 65, "chosen": [65, 168, 191], "angl": [65, 85, 146, 157], "rai": 65, "role": 65, "y": [65, 188, 189, 241], "coordin": [65, 113, 126, 156, 157, 194, 239], "tradit": 65, "atan": [66, 171, 185, 187], "bitwis": [67, 70, 72, 171], "underli": [67, 70, 72, 187, 226, 235], "flip": [68, 171], "shift": [69, 71, 142, 200, 204], "arithmet": [71, 87, 125, 128, 171, 180, 188, 239], "propag": [71, 124, 125, 127, 152, 166, 187], "floor": [71, 98, 171], "anoth": [73, 75, 99, 172, 183, 185, 186, 188, 189, 191, 192, 215, 228, 239, 241], "from_": 75, "smallest": [76, 95, 104, 219], "closest": [76, 97, 98, 143], "alreadi": [76, 97, 128, 143, 161, 191, 236, 241], "join": [77, 151, 180], "befor": [77, 137, 154, 162, 163, 164, 165, 167, 185, 188, 212, 231, 239], "concaten": 77, "leav": [77, 151, 172, 178, 185, 187, 189, 224], "famili": [77, 151], "intxx": [77, 151, 180], "floatxx": [77, 151, 180], "versionad": [78, 105], "718281828459045": 79, "euler": 79, "constant": [79, 83, 171, 185], "71828182845904523536028747135266249775724709369995": 79, "Not": 81, "alia": [82, 185, 218, 222, 230, 232], "141592653589793": 83, "1415926535897932384626433": 83, "begin": [84, 144, 145, 156, 157, 172, 178, 226, 241], "align": [84, 145, 156, 157, 185, 187, 240], "sum_": [84, 167], "2n": [84, 113], "jx": [84, 145, 156], "cosh": [84, 157, 171, 185, 187], "period": [85, 146, 156, 157], "ci": [85, 91, 93, 146, 241], "v": [85, 91, 93, 146, 224, 228, 239], "co": [85, 91, 93, 146, 171, 185, 187], "sin": [85, 91, 93, 146, 171, 185, 187, 189, 195], "dividend": [87, 98, 139], "divisor": [87, 98, 139, 152, 166], "small": [87, 98, 128, 187, 221, 224, 226, 239, 241], "gener": [87, 112, 128, 139, 158, 183, 186, 188, 235, 239, 240], "textbook": [87, 128], "formula": [87, 114, 116, 128], "ac": [87, 128, 188], "bd": [87, 128], "bc": [87, 128, 188], "riemann": [87, 128, 188], "sphere": [87, 128, 188], "infinit": [87, 128, 148, 187, 188], "even": [87, 128, 136, 143, 187, 188, 189, 198, 200, 204, 209, 225, 235, 239, 241], "usual": [87, 128, 239], "interest": [87, 128, 187], "unlik": [87, 128, 236, 239], "consist": [87, 98, 106, 112, 128, 158, 172, 178, 188, 192, 195, 206, 207, 208, 210, 215, 224, 235, 239], "uniniti": [88, 89], "deriv": [89, 101, 133, 170, 172, 240], "natur": [91, 113, 114, 115, 116, 136, 226, 235], "logarithm": [91, 113, 114, 115, 116, 117, 136, 226, 235], "expand": [92, 172, 241], "close": [92, 93, 112, 115, 143, 172, 239, 241], "indexerror": [92, 172], "exp": [93, 117, 136, 171, 185, 187, 226], "accur": [93, 115, 187, 226], "fdlibm": [93, 115, 187], "n_row": 94, "n_col": 94, "ones": [94, 133, 171, 185, 189, 239], "diagon": [94, 159, 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"extension-name-and-usage"], [235, "extension-name-and-usage"]], "fft": [[197, "fft"]], "fftfreq": [[198, "fftfreq"]], "fftn": [[199, "fftn"]], "fftshift": [[200, "fftshift"]], "hfft": [[201, "hfft"]], "ifft": [[202, "ifft"]], "ifftn": [[203, "ifftn"]], "ifftshift": [[204, "ifftshift"]], "ihfft": [[205, "ihfft"]], "irfft": [[206, "irfft"]], "irfftn": [[207, "irfftn"]], "rfft": [[208, "rfft"]], "rfftfreq": [[209, "rfftfreq"]], "rfftn": [[210, "rfftn"]], "cholesky": [[211, "cholesky"]], "cross": [[212, "cross"]], "det": [[213, "det"]], "diagonal": [[214, "diagonal"]], "eigh": [[215, "eigh"]], "eigvalsh": [[216, "eigvalsh"]], "inv": [[217, "inv"]], "matrix_norm": [[219, "matrix-norm"]], "matrix_power": [[220, "matrix-power"]], "matrix_rank": [[221, "matrix-rank"]], "outer": [[223, "outer"]], "pinv": [[224, "pinv"]], "qr": [[225, "qr"]], "slogdet": [[226, "slogdet"]], "solve": [[227, "solve"]], "svd": [[228, "svd"]], "svdvals": [[229, "svdvals"]], "trace": [[231, "trace"]], "vector_norm": [[233, "vector-norm"]], "Linear Algebra Extension": [[235, "linear-algebra-extension"]], "Design Principles": [[235, "design-principles"]], "Future API standard evolution": [[236, "future-api-standard-evolution"]], "Scope extensions": [[236, "scope-extensions"]], "Versioning": [[236, "versioning"]], "Python array API standard": [[237, "python-array-api-standard"]], "Contents": [[237, "contents"]], "Context": [[237, null]], "API": [[237, null]], "Methodology and Usage": [[237, null]], "Other": [[237, null]], "License": [[238, "license"]], "Purpose and scope": [[239, "purpose-and-scope"]], "Introduction": [[239, "introduction"], [240, "introduction"]], "This API standard": [[239, "this-api-standard"]], "History": [[239, "history"]], "Scope (includes out-of-scope / non-goals)": [[239, "scope-includes-out-of-scope-non-goals"]], "In scope": [[239, "in-scope"]], "Out of scope": [[239, "out-of-scope"]], "Implications of in/out of scope": [[239, "implications-of-in-out-of-scope"]], "Stakeholders": [[239, "stakeholders"]], "How to read this document": [[239, "how-to-read-this-document"]], "How to adopt this API": [[239, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[239, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[239, "discoverability-of-conforming-implementations"]], "Optional feature": [[239, null]], "Conformance": [[239, "conformance"]], "Terms and Definitions": [[239, "terms-and-definitions"]], "Normative References": [[239, "normative-references"]], "Usage Data": [[240, "usage-data"]], "Design": [[240, "design"]], "Usage": [[240, "usage"]], "Use in Decision-Making": [[240, "use-in-decision-making"]], "Use cases": [[241, "use-cases"]], "Types of use cases": [[241, "types-of-use-cases"]], "Concrete use cases": [[241, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[241, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[241, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[241, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[241, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[242, "verification-test-suite"]], "Measuring conformance": [[242, "measuring-conformance"]], "Running the tests": [[242, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, 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"broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "concat() (in module array_api)": [[77, "array_api.concat"]], "conj() (in module array_api)": [[78, "array_api.conj"]], "e (in module array_api.constants)": [[79, "array_api.constants.e"]], "inf (in module array_api.constants)": [[80, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[81, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[82, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[83, "array_api.constants.pi"]], "cos() (in module array_api)": [[84, "array_api.cos"]], "cosh() (in module array_api)": [[85, "array_api.cosh"]], "__eq__() (in module array_api.data_types)": [[86, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[87, "array_api.divide"]], "empty() (in module array_api)": [[88, 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(in module array_api)": [[104, "array_api.iinfo"]], "imag() (in module array_api)": [[105, "array_api.imag"]], "isdtype() (in module array_api)": [[106, "array_api.isdtype"]], "isfinite() (in module array_api)": [[107, "array_api.isfinite"]], "isinf() (in module array_api)": [[108, "array_api.isinf"]], "isnan() (in module array_api)": [[109, "array_api.isnan"]], "less() (in module array_api)": [[110, "array_api.less"]], "less_equal() (in module array_api)": [[111, "array_api.less_equal"]], "linspace() (in module array_api)": [[112, "array_api.linspace"]], "log() (in module array_api)": [[113, "array_api.log"]], "log10() (in module array_api)": [[114, "array_api.log10"]], "log1p() (in module array_api)": [[115, "array_api.log1p"]], "log2() (in module array_api)": [[116, "array_api.log2"]], "logaddexp() (in module array_api)": [[117, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[118, "array_api.logical_and"]], "logical_not() (in module array_api)": [[119, "array_api.logical_not"]], "logical_or() (in module array_api)": [[120, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[121, "array_api.logical_xor"]], "matmul() (in module array_api)": [[122, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[123, "array_api.matrix_transpose"]], "max() (in module array_api)": [[124, "array_api.max"]], "mean() (in module array_api)": [[125, "array_api.mean"]], "meshgrid() (in module array_api)": [[126, "array_api.meshgrid"]], "min() (in module array_api)": [[127, "array_api.min"]], "multiply() (in module array_api)": [[128, "array_api.multiply"]], "negative() (in module array_api)": [[129, "array_api.negative"]], "nonzero() (in module array_api)": [[130, "array_api.nonzero"]], "not_equal() (in module array_api)": [[131, "array_api.not_equal"]], "ones() (in module array_api)": [[132, "array_api.ones"]], "ones_like() (in module array_api)": [[133, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[134, "array_api.permute_dims"]], "positive() (in module array_api)": [[135, "array_api.positive"]], "pow() (in module array_api)": [[136, "array_api.pow"]], "prod() (in module array_api)": [[137, "array_api.prod"]], "real() (in module array_api)": [[138, "array_api.real"]], "remainder() (in module array_api)": [[139, "array_api.remainder"]], "reshape() (in module array_api)": [[140, "array_api.reshape"]], "result_type() (in module array_api)": [[141, "array_api.result_type"]], "roll() (in module array_api)": [[142, "array_api.roll"]], "round() (in module array_api)": [[143, "array_api.round"]], "sign() (in module array_api)": [[144, "array_api.sign"]], "sin() (in module array_api)": [[145, "array_api.sin"]], "sinh() (in module array_api)": [[146, "array_api.sinh"]], "sort() (in module array_api)": [[147, "array_api.sort"]], "sqrt() (in module array_api)": [[148, "array_api.sqrt"]], "square() (in module array_api)": [[149, "array_api.square"]], "squeeze() (in module array_api)": [[150, "array_api.squeeze"]], "stack() (in module array_api)": [[151, "array_api.stack"]], "std() (in module array_api)": [[152, "array_api.std"]], "subtract() (in module array_api)": [[153, "array_api.subtract"]], "sum() (in module array_api)": [[154, "array_api.sum"]], "take() (in module array_api)": [[155, "array_api.take"]], "tan() (in module array_api)": [[156, "array_api.tan"]], "tanh() (in module array_api)": [[157, "array_api.tanh"]], "tensordot() (in module array_api)": [[158, "array_api.tensordot"]], "tril() (in module array_api)": [[159, "array_api.tril"]], "triu() (in module array_api)": [[160, "array_api.triu"]], "trunc() (in module array_api)": [[161, "array_api.trunc"]], "unique_all() (in module array_api)": [[162, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[163, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[164, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[165, "array_api.unique_values"]], "var() (in module array_api)": [[166, "array_api.var"]], "vecdot() (in module array_api)": [[167, "array_api.vecdot"]], "where() (in module array_api)": [[168, "array_api.where"]], "zeros() (in module array_api)": [[169, "array_api.zeros"]], "zeros_like() (in module array_api)": [[170, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[197, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[198, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[199, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[200, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[201, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[202, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[203, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[204, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[205, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[206, 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"array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[220, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[221, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[222, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[223, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[224, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[225, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[226, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[227, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[228, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[229, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[230, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[231, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[232, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[233, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file
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"tanh", "tensordot", "tril", "triu", "trunc", "unique_all", "unique_counts", "unique_inverse", "unique_values", "var", "vecdot", "where", "zeros", "zeros_like", "API specification", "Indexing", "Indexing Functions", "Linear Algebra Functions", "Manipulation Functions", "Searching Functions", "Set Functions", "Sorting Functions", "Statistical Functions", "Type Promotion Rules", "Utility Functions", "Version", "Assumptions", "Benchmark suite", "Changelog per API standard version", "C API", "Accuracy", "Complex Numbers", "Copy-view behaviour and mutability", "Data-dependent output shapes", "Data interchange mechanisms", "Device support", "Design topics &amp; constraints", "Parallelism", "Static typing", "Fourier transform Functions", "fft", "fftfreq", "fftn", "fftshift", "hfft", "ifft", "ifftn", "ifftshift", "ihfft", "irfft", "irfftn", "rfft", "rfftfreq", "rfftn", "cholesky", "cross", "det", "diagonal", "eigh", "eigvalsh", "inv", "matmul", "matrix_norm", "matrix_power", "matrix_rank", 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115, 116, 122, 132, 133, 134, 136, 137, 140, 144, 147, 151, 152, 156, 157, 158, 159, 160, 166, 167, 172, 188, 189, 194, 197, 198, 199, 201, 202, 203, 205, 206, 207, 208, 209, 210, 212, 215, 217, 219, 227, 228, 229, 232, 233], "acceler": [0, 5, 183, 191], "non": [0, 1, 13, 14, 16, 17, 63, 118, 119, 120, 121, 124, 125, 127, 130, 137, 152, 158, 166, 167, 172, 180, 185, 186, 192, 197, 199, 202, 203, 206, 207, 208, 210, 212, 213, 215, 219, 221, 228, 233, 241], "could": [0, 26, 162, 163, 164, 165, 183, 189, 194, 235, 239, 241], "forc": 0, "synchron": [0, 26, 59, 239], "2": [0, 1, 5, 7, 9, 10, 11, 26, 27, 40, 61, 62, 64, 65, 66, 79, 84, 85, 87, 113, 115, 116, 122, 146, 149, 156, 157, 158, 172, 188, 189, 195, 198, 201, 205, 206, 207, 208, 209, 210, 219, 221, 224, 225, 226, 227, 228, 229, 230, 231, 233], "delai": [0, 183, 239], "execut": [0, 180, 183, 192, 194, 239, 241], "model": [0, 57, 58, 87, 128, 188, 241], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 85, 87, 98, 126, 128, 146, 156, 157, 185, 187, 192, 226, 240, 241], "futur": [0, 26, 184, 188, 189, 192, 194, 195, 215, 216, 237, 239, 241], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 98, 139, 171, 172, 183, 185, 188, 191, 194, 195, 236, 238, 239, 240], "x": [0, 1, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 61, 62, 63, 64, 65, 66, 68, 74, 76, 78, 84, 85, 89, 91, 92, 93, 96, 97, 99, 101, 105, 107, 108, 109, 113, 114, 115, 116, 119, 123, 124, 125, 127, 129, 130, 133, 134, 135, 137, 138, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 170, 172, 188, 189, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 222, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 241], "__pos__": [0, 171, 185], "po": 0, "__neg__": [0, 171, 185], "neg": [0, 13, 14, 15, 44, 47, 65, 77, 87, 92, 94, 96, 98, 108, 113, 115, 128, 136, 139, 142, 148, 155, 167, 171, 172, 185, 188, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 233, 239], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 139, 153, 158, 167, 168, 185, 212, 218, 223, 227, 230, 232], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 139, 153, 158, 167, 168, 185, 212, 218, 223, 227, 230, 232], "__add__": [0, 50, 171, 185], "add": [0, 5, 7, 21, 153, 154, 171, 172, 185, 186, 187, 192, 231], "__sub__": [0, 171, 185], "sub": [0, 172], "__mul__": [0, 171, 185], "mul": 0, "__truediv__": [0, 171, 185], "truediv": 0, "__floordiv__": [0, 171], "floordiv": 0, "__mod__": [0, 171], "mod": 0, "__pow__": [0, 171, 185], "pow": [0, 47, 171, 185, 187], "should": [0, 1, 5, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 78, 84, 85, 87, 91, 93, 95, 97, 98, 102, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 135, 136, 137, 138, 139, 143, 144, 145, 146, 147, 148, 149, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 178, 185, 186, 187, 188, 191, 192, 195, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 213, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 234, 235, 239, 241, 242], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 78, 87, 98, 100, 101, 112, 124, 125, 127, 128, 139, 144, 148, 149, 152, 159, 160, 166, 167, 171, 178, 185, 187, 188, 195, 199, 200, 203, 204, 207, 210, 211, 215, 216, 217, 224, 225, 227, 235, 240, 241, 242], "real": [0, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 84, 85, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 139, 143, 144, 145, 146, 147, 148, 152, 154, 156, 157, 161, 166, 167, 169, 171, 180, 185, 188, 198, 201, 205, 206, 207, 208, 209, 210, 211, 215, 216, 217, 219, 221, 224, 225, 226, 227, 228, 229, 231, 233, 236], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 171, 180, 183, 186, 188, 189, 192, 193, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 236, 237, 238, 239, 242], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 183, 186, 188, 189, 191, 193, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 236, 239, 240], "__matmul__": [0, 171, 185], "matmul": [0, 40, 171, 180, 185, 235], "The": [0, 1, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 84, 85, 87, 90, 91, 93, 96, 97, 98, 99, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139, 143, 144, 145, 146, 147, 148, 149, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 180, 183, 185, 186, 187, 189, 190, 191, 192, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 234, 235, 236, 238, 239, 240, 241, 242], "__invert__": [0, 171], "inv": [0, 185, 235], "invert": [0, 68, 217, 220, 227], "__inv__": 0, "__and__": [0, 171], "__or__": [0, 171], "__xor__": [0, 171], "xor": [0, 72, 121], "__lshift__": [0, 171], "lshift": 0, "__rshift__": [0, 171], "rshift": 0, "integ": [0, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 87, 97, 98, 100, 101, 104, 106, 112, 124, 125, 127, 129, 136, 137, 139, 141, 143, 152, 154, 155, 158, 161, 166, 167, 171, 172, 185, 187, 188, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 220, 221, 231, 233, 239], "boolean": [0, 22, 24, 25, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 86, 100, 101, 106, 112, 118, 119, 120, 121, 130, 140, 168, 171, 180, 185], "__lt__": [0, 171, 185], "lt": 0, "__le__": [0, 171, 185], "le": 0, "__gt__": [0, 171, 185], "gt": [0, 225, 228], "__ge__": [0, 171, 185], "ge": 0, "__eq__": [0, 171, 185, 192], "eq": 0, "__ne__": [0, 171, 185], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 26, 27, 40, 49, 55, 58, 60, 84, 86, 87, 91, 94, 95, 96, 98, 112, 118, 119, 120, 121, 122, 128, 130, 136, 142, 143, 145, 156, 157, 162, 164, 167, 172, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 209, 210, 212, 215, 216, 221, 224, 225, 228, 234, 235, 236, 239, 240, 241, 242], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 96, 106, 112, 118, 119, 120, 121, 122, 125, 152, 166, 171, 172, 180, 183, 185, 186, 188, 189, 191, 192, 195, 200, 217, 224, 225, 227, 235, 236, 239, 240, 241, 242], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 86, 87, 93, 98, 115, 128, 152, 166, 172, 183, 185, 187, 188, 189, 190, 191, 192, 195, 224, 234, 235, 238, 239, 241], "ani": [0, 1, 9, 10, 11, 23, 26, 28, 43, 59, 61, 62, 66, 86, 90, 107, 108, 131, 148, 171, 172, 180, 185, 188, 189, 191, 195, 228, 236, 238, 239, 242], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 78, 84, 85, 87, 90, 91, 93, 97, 98, 102, 103, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 124, 126, 127, 128, 129, 131, 136, 137, 139, 143, 144, 145, 146, 147, 148, 149, 151, 154, 156, 157, 161, 162, 163, 164, 165, 172, 178, 183, 187, 188, 190, 192, 198, 207, 209, 226, 228, 229, 231, 239, 241, 242], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 102, 103, 110, 111, 112, 124, 127, 139, 147, 167, 172, 185, 188, 189, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 239], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 87, 90, 98, 102, 103, 110, 111, 112, 117, 118, 120, 121, 122, 124, 125, 127, 128, 131, 136, 137, 139, 140, 147, 152, 153, 154, 166, 167, 168, 180, 185, 188, 189, 212, 219, 221, 224, 227, 233, 239, 241], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 86, 87, 90, 98, 99, 102, 103, 106, 110, 111, 112, 118, 119, 120, 121, 124, 125, 127, 128, 130, 131, 147, 152, 157, 162, 163, 164, 165, 166, 171, 172, 178, 180, 183, 185, 186, 187, 188, 189, 190, 192, 194, 195, 215, 225, 226, 228, 234, 235, 239, 240, 241], "complex": [0, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 78, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 122, 124, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 147, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 171, 180, 187, 191, 192, 193, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 240], "howev": [0, 5, 7, 16, 17, 18, 31, 33, 37, 39, 57, 98, 102, 103, 106, 110, 111, 112, 124, 127, 147, 155, 156, 157, 183, 186, 187, 188, 189, 190, 192, 235, 236, 239, 241], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 102, 103, 110, 111, 124, 127, 147], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 85, 87, 91, 93, 98, 100, 101, 102, 103, 110, 111, 112, 124, 127, 136, 139, 146, 147, 148, 151, 157, 172, 178, 180, 185, 199, 200, 203, 204, 207, 210, 215, 216, 239], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 98, 100, 101, 102, 103, 110, 111, 112, 124, 127, 136, 139, 147, 156, 157, 178, 187, 188, 199, 200, 203, 204, 207, 210, 215, 216, 228, 235], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 84, 85, 87, 91, 93, 102, 103, 110, 111, 112, 113, 114, 115, 116, 124, 127, 128, 129, 136, 145, 146, 147, 156, 157, 168, 178, 180, 187, 188, 191, 193, 195, 215, 216, 225, 226, 227, 228, 235, 239, 241, 242], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 87, 90, 93, 98, 99, 101, 102, 103, 110, 111, 113, 115, 117, 118, 120, 121, 122, 124, 125, 127, 128, 130, 131, 136, 137, 139, 141, 144, 147, 148, 149, 152, 153, 154, 162, 163, 164, 165, 166, 167, 168, 171, 172, 180, 182, 183, 186, 188, 190, 191, 192, 195, 212, 219, 221, 224, 227, 233, 234, 239, 240, 241, 242], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 86, 96, 98, 102, 103, 110, 111, 124, 127, 130, 147, 156, 157, 158, 162, 163, 164, 165, 172, 178, 180, 185, 187, 190, 191, 206, 207, 215, 216, 219, 228, 229, 233, 235, 236, 239, 240], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 140, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 183, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 236, 239, 241, 242], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 77, 88, 89, 92, 96, 100, 101, 122, 123, 126, 132, 133, 140, 142, 147, 151, 155, 158, 159, 160, 167, 169, 170, 171, 185, 193, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 239, 241], "result": [0, 1, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 78, 84, 85, 87, 90, 91, 93, 97, 98, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 125, 127, 128, 129, 131, 135, 136, 137, 138, 139, 141, 143, 144, 145, 146, 148, 149, 151, 152, 153, 154, 156, 157, 158, 161, 162, 166, 172, 178, 180, 185, 187, 188, 189, 211, 212, 214, 219, 220, 226, 227, 233, 239, 240, 241, 242], "promot": [0, 1, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 84, 85, 87, 91, 93, 98, 101, 112, 113, 114, 115, 116, 117, 122, 125, 128, 129, 136, 139, 141, 145, 146, 148, 149, 151, 152, 153, 156, 157, 158, 166, 167, 168, 171, 185, 211, 212, 217, 219, 220, 221, 223, 224, 225, 226, 227, 233, 235], "rule": [0, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 84, 85, 87, 91, 93, 98, 100, 101, 112, 113, 114, 115, 116, 117, 122, 128, 129, 136, 139, 141, 144, 145, 146, 148, 149, 151, 153, 156, 157, 158, 167, 168, 171, 172, 185, 188, 191, 211, 212, 217, 219, 220, 221, 223, 224, 225, 226, 227, 233, 235, 239, 241], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 122, 124, 125, 127, 128, 131, 136, 137, 139, 152, 153, 154, 158, 166, 167, 168, 171, 185, 212, 219, 221, 224, 227, 233, 239], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 87, 89, 92, 95, 96, 97, 98, 101, 105, 122, 123, 124, 125, 126, 127, 128, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 147, 150, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 170, 172, 180, 183, 185, 188, 189, 191, 192, 195, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 213, 214, 215, 217, 220, 224, 225, 226, 228, 229, 231, 234, 235, 239, 241], "behavior": [0, 5, 47, 49, 60, 63, 87, 98, 100, 101, 112, 128, 136, 139, 162, 163, 164, 165, 171, 172, 180, 183, 185, 187, 188, 194, 199, 200, 203, 204, 207, 210, 235, 236, 239, 240, 241, 242], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 125, 127, 128, 131, 136, 137, 139, 143, 144, 145, 146, 148, 149, 152, 154, 156, 157, 161, 166, 185, 186, 188, 226, 231], "case": [0, 1, 5, 9, 10, 11, 12, 15, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 125, 126, 127, 128, 131, 136, 137, 139, 140, 143, 144, 145, 146, 148, 149, 152, 154, 156, 157, 161, 166, 172, 183, 185, 186, 187, 188, 189, 192, 225, 226, 228, 231, 235, 237, 239, 242], "its": [0, 5, 26, 40, 73, 87, 95, 122, 128, 140, 142, 187, 188, 192, 234, 239, 240, 241], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 85, 87, 90, 98, 102, 103, 110, 111, 112, 117, 118, 120, 121, 126, 128, 131, 139, 146, 153, 156, 157, 158, 167, 185, 187, 190, 192, 212, 215, 225, 228], "binari": [0, 5, 67, 70, 72, 156, 157, 186], "two": [0, 1, 15, 19, 40, 55, 65, 71, 94, 122, 123, 126, 143, 158, 159, 160, 162, 163, 164, 165, 167, 172, 180, 191, 192, 194, 199, 200, 203, 204, 207, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 235, 239, 240, 241, 242], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 127, 128, 131, 136, 137, 139, 143, 144, 145, 146, 148, 149, 154, 156, 157, 161, 180, 185, 187, 226, 231], "assign": [0, 189], "exampl": [0, 5, 12, 23, 106, 151, 171, 172, 183, 188, 189, 190, 192, 194, 195, 231, 235, 239, 241, 242], "after": [0, 1, 40, 122, 148], "addit": [0, 5, 7, 12, 50, 59, 153, 171, 172, 180, 186, 188, 191, 235, 239, 240, 242], "modifi": [0, 189, 238], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 98, 118, 119, 120, 121, 139, 143, 155, 172, 180, 185, 188, 189, 221, 224, 227, 233, 239], "discuss": [0, 90, 131, 185, 191, 192, 194, 239, 240, 241], "copi": [0, 1, 59, 60, 63, 99, 140, 147, 185, 186, 191, 192, 193, 238, 239], "view": [0, 99, 193], "behaviour": [0, 193, 239, 241], "mutabl": [0, 193], "via": [0, 26, 98, 155, 172, 186, 191, 192, 194, 196, 224, 234, 235, 236, 239], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 87, 128, 141, 143, 151, 158, 172, 180, 183, 188, 197, 199, 202, 203, 206, 207, 208, 210, 221, 224, 235, 239, 241], "match": [0, 1, 5, 9, 20, 63, 98, 139, 158, 201, 205, 206, 207, 208, 210, 215, 216, 219, 233, 241], "op": [0, 180], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 82, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 240, 242], "refer": [1, 13, 14, 93, 94, 115, 152, 166, 167, 172, 188, 189, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 227], "automat": [1, 239], "implicit": [1, 192, 239], "expans": [1, 239], "size": [1, 13, 14, 92, 112, 130, 142, 150, 155, 158, 167, 171, 172, 190, 194, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 223, 225, 228, 239], "without": [1, 7, 26, 57, 130, 140, 162, 163, 164, 165, 183, 186, 187, 190, 238, 239, 241], "purpos": [1, 5, 93, 115, 183, 226, 235, 237, 238, 241], "make": [1, 7, 183, 186, 187, 189, 191, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 234, 236, 239], "differ": [1, 12, 49, 50, 77, 87, 95, 98, 128, 137, 151, 153, 154, 172, 183, 185, 189, 192, 204, 215, 225, 226, 228, 231, 235, 239, 240, 241], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 78, 84, 85, 87, 90, 91, 93, 94, 96, 97, 98, 100, 101, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 127, 128, 129, 130, 131, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 148, 149, 150, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 168, 171, 172, 185, 187, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 215, 224, 225, 226, 228, 231, 239], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 78, 87, 90, 98, 102, 103, 105, 110, 111, 117, 118, 119, 120, 121, 128, 131, 136, 138, 139, 153, 171, 185, 187, 239], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 84, 87, 98, 114, 116, 122, 128, 136, 137, 139, 141, 145, 149, 154, 156, 158, 171, 172, 177, 180, 185, 188, 189, 190, 191, 192, 231, 235, 236, 239, 240, 241], "facilit": [1, 178, 183], "user": [1, 7, 157, 183, 186, 187, 189, 192, 194, 235, 239, 240, 241], "ergonom": 1, "encourag": [1, 239, 240], "avoid": [1, 9, 63, 87, 93, 98, 115, 128, 186, 189, 192, 235, 239, 241], "unnecessari": [1, 235], "can": [1, 7, 26, 60, 75, 106, 172, 180, 183, 186, 188, 189, 191, 192, 195, 224, 225, 228, 234, 235, 239, 240, 241, 242], "potenti": [1, 26, 93, 115, 189, 239], "enabl": [1, 192, 194, 195, 239], "more": [1, 7, 15, 19, 26, 40, 58, 60, 63, 73, 93, 96, 98, 115, 122, 130, 136, 155, 162, 163, 164, 165, 172, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 199, 200, 203, 204, 207, 210, 226, 235, 236, 239, 240, 242], "memori": [1, 26, 60, 140, 183, 189, 190, 192, 239, 241], "effici": [1, 183, 189], "through": [1, 60, 65, 234, 236, 240, 241], "vector": [1, 40, 122, 126, 167, 212, 223, 228, 229, 233, 235, 239], "reduc": [1, 13, 14, 16, 17, 124, 125, 127, 137, 152, 154, 166, 172, 225, 228, 235, 240, 241], "consumpt": [1, 26, 240], "cach": 1, "local": [1, 192], "given": [1, 23, 59, 96, 112, 142, 180, 185, 188, 189, 192, 195, 216, 226, 235, 236, 239, 241], "involv": [1, 12, 87, 98, 128, 136, 141, 180, 185, 187, 188, 192, 194], 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20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 136, 137, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 172, 186, 188, 192, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 231, 233, 234, 235, 239, 241], "unequ": 1, "lower": [1, 94, 159, 211], "higher": [1, 172, 186, 235, 240], "prepend": [1, 40, 92, 122], "until": 1, "store": [1, 192, 231], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 84, 85, 87, 91, 93, 98, 107, 108, 109, 113, 114, 115, 116, 117, 122, 128, 129, 136, 139, 145, 146, 148, 149, 153, 155, 156, 157, 158, 162, 163, 164, 165, 167, 168, 180, 185, 188, 191, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 212, 213, 214, 217, 219, 220, 221, 223, 224, 225, 226, 227, 231, 233, 235, 239], "let": [1, 9, 10, 11, 12, 62, 66, 85, 90, 91, 93, 107, 108, 109, 112, 113, 115, 125, 131, 137, 144, 146, 148, 152, 154, 157, 166, 167, 172, 194, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 215, 216, 217, 225, 227, 228, 231], "b": [1, 9, 10, 11, 12, 57, 62, 66, 85, 87, 90, 91, 93, 98, 107, 108, 109, 112, 113, 115, 128, 131, 144, 146, 148, 151, 157, 167, 172, 185, 188, 189, 224, 227, 241], "both": [1, 40, 44, 47, 51, 65, 87, 95, 98, 112, 122, 129, 136, 137, 154, 157, 158, 167, 172, 185, 188, 189, 191, 195, 212, 231, 235, 239, 240], "shape1": 1, "describ": [1, 5, 12, 87, 90, 106, 128, 131, 136, 137, 154, 180, 185, 188, 191, 198, 209, 231, 239], "shape2": 1, "n1": [1, 126], "len": [1, 126], "n2": [1, 126], "maximum": [1, 16, 112, 124, 127, 185, 187, 219], "max": [1, 95, 104, 171, 172, 185, 219, 221, 224], "temporari": 1, "list": [1, 73, 77, 126, 151, 172, 183, 185, 192, 239, 241], "length": [1, 15, 126, 140, 158, 172, 198, 200, 201, 204, 209, 228, 229], "while": [1, 98, 112, 118, 119, 120, 121, 125, 152, 162, 163, 166, 171, 172, 178, 183, 185, 188, 189, 190, 192, 224, 235, 240, 241, 242], "0": [1, 5, 9, 10, 11, 12, 15, 24, 25, 26, 29, 35, 38, 48, 57, 61, 62, 63, 64, 65, 66, 69, 71, 76, 77, 84, 85, 87, 90, 91, 92, 93, 94, 95, 97, 98, 113, 114, 115, 116, 125, 128, 134, 136, 137, 139, 143, 144, 145, 146, 148, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 172, 178, 180, 188, 189, 198, 200, 209, 214, 219, 226, 228, 229, 231, 233, 239, 241], "d1": 1, "els": [1, 183, 240], "d2": 1, "set": [1, 18, 49, 65, 147, 152, 159, 160, 162, 164, 165, 166, 171, 172, 185, 186, 187, 188, 189, 192, 194, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 215, 216, 217, 221, 224, 225, 227, 228, 234, 235, 239, 241, 242], "th": [1, 94, 172, 185, 199, 203, 207, 210], "throw": 1, "except": [1, 13, 14, 74, 77, 92, 94, 112, 130, 151, 155, 172, 180, 183, 185, 187, 189, 192, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 224, 236, 239, 240, 241], "demonstr": 1, "applic": [1, 137, 154, 180, 185, 231, 235, 239, 240], "4d": 1, "8": [1, 5, 7, 27, 180, 183], "6": [1, 7], "3d": 1, "7": [1, 7, 27, 195], "5": [1, 172, 239], "2d": 1, "4": [1, 5, 10, 11, 27, 62, 65, 113, 115, 172, 194, 240], "1d": 1, "15": 1, "3": [1, 5, 7, 27, 83, 155, 183, 188, 189, 192, 212], "do": [1, 26, 87, 128, 139, 178, 183, 185, 186, 188, 189, 191, 192, 235, 236, 238, 239, 241, 242], "doe": [1, 15, 131, 172, 180, 183, 186, 187, 188, 189, 190, 192, 195, 235, 239, 241, 242], "second": [1, 12, 65, 67, 69, 70, 71, 72, 90, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 151, 153, 158, 162, 163, 164, 167, 168, 212, 215, 223, 225, 226, 228, 229, 239], "append": [1, 40, 69, 92, 122, 214], "As": [1, 112, 136, 162, 163, 164, 165, 183, 191, 195, 241], "impli": [1, 162, 163, 164, 165, 238, 239], "__setitem__": [1, 155, 171, 185], "Such": [1, 187, 235], "right": [1, 69, 71, 148, 186, 228, 238], "hand": [1, 180], "left": [1, 5, 7, 60, 69, 98, 100, 172, 180, 215, 216, 228, 239], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 82, 94, 126, 130, 151, 155, 162, 163, 164, 171, 185, 199, 203, 207, 210, 239, 241], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 87, 122, 128, 158, 172, 186, 187, 188, 189, 190, 191, 197, 199, 202, 203, 204, 206, 207, 208, 210, 228, 229, 235, 239, 240, 241], "empti": [1, 13, 14, 15, 137, 154, 171, 172, 185, 231, 239], "ok": 1, "allow": [1, 26, 136, 140, 172, 185, 186, 187, 189, 192, 194, 235, 241], "NOT": [1, 119, 238], "adher": [2, 7, 8, 171, 172, 183, 234, 239], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 113, 115, 122, 136, 148, 171, 172, 178, 188, 192, 234, 235, 240], "each": [2, 9, 10, 11, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 84, 85, 87, 90, 91, 93, 97, 98, 102, 103, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 126, 128, 129, 130, 131, 135, 136, 138, 139, 142, 143, 144, 145, 146, 148, 149, 151, 153, 156, 157, 158, 161, 162, 163, 172, 183, 185, 187, 191, 195, 207, 211, 212, 213, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 234, 235, 239, 240, 241], "float": [2, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 122, 124, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 141, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 161, 162, 163, 164, 165, 166, 167, 169, 171, 178, 185, 187, 188, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 240], "point": [2, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 95, 97, 98, 100, 101, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 122, 124, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 141, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 161, 162, 163, 164, 165, 166, 167, 169, 171, 178, 185, 187, 188, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239, 241], "creat": [3, 15, 60, 88, 89, 94, 100, 101, 112, 132, 133, 169, 170, 177, 183, 192, 198, 209, 235, 239], "true": [5, 13, 14, 16, 17, 18, 24, 25, 29, 35, 60, 63, 75, 90, 95, 98, 107, 108, 109, 112, 118, 119, 120, 121, 124, 125, 127, 130, 131, 137, 140, 147, 152, 154, 162, 163, 164, 165, 166, 168, 172, 185, 211, 219, 228, 233, 235], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 29, 35, 60, 63, 75, 90, 107, 108, 109, 112, 118, 119, 120, 121, 124, 125, 127, 131, 137, 140, 147, 152, 154, 162, 163, 164, 165, 166, 172, 211, 219, 228, 233], "bit": [5, 68, 69, 71, 95, 104, 137, 154, 180, 185, 187, 231], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 91, 93, 98, 106, 113, 115, 128, 129, 136, 137, 139, 146, 148, 154, 157, 162, 163, 164, 165, 171, 178, 185, 188, 225, 226, 231], "exist": [5, 7, 60, 77, 140, 183, 185, 188, 191, 192, 217, 236, 239, 240], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 112, 113, 115, 151, 159, 160, 167, 172, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 236], "128": 5, "127": 5, "16": [5, 180], "32": [5, 180], "767": 5, "147": 5, "483": 5, "647": 5, "64": [5, 180], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "unsign": [5, 106, 137, 154, 171, 231], "255": 5, "65": 5, "535": [5, 185], "294": 5, "967": 5, "295": 5, "18": 5, "446": [5, 185], "744": [5, 185], "073": 5, "709": [5, 185], "551": [5, 185], "615": 5, "ieee": [5, 12, 65, 79, 80, 81, 83, 87, 93, 95, 115, 128, 139, 148, 156, 157, 171, 178, 185, 187, 188, 239], "754": [5, 12, 65, 79, 80, 81, 83, 87, 93, 95, 115, 128, 139, 148, 156, 157, 171, 178, 185, 187, 188, 239], "singl": [5, 7, 24, 25, 29, 34, 35, 162, 163, 171, 180, 185, 186, 188, 191, 192, 195, 235, 239, 240, 241], "precis": [5, 9, 20, 42, 60, 95, 100, 101, 105, 128, 138, 148, 180, 185, 187, 201, 205, 206, 207, 208, 210, 215, 216, 219, 226, 228, 229, 233, 239], "2019": [5, 12, 87, 93, 115, 128, 171, 187, 239, 241], "doubl": [5, 158, 180, 185], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 78, 85, 87, 90, 91, 93, 95, 105, 113, 115, 128, 129, 130, 131, 132, 133, 136, 143, 146, 148, 157, 185, 188], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 78, 85, 87, 90, 91, 93, 95, 105, 113, 115, 128, 129, 130, 131, 132, 133, 136, 138, 143, 146, 148, 156, 157, 162, 163, 164, 165, 185, 188, 200, 209], "requir": [5, 10, 11, 59, 61, 62, 63, 64, 66, 106, 148, 151, 155, 157, 171, 172, 178, 180, 183, 185, 186, 187, 188, 189, 190, 191, 192, 195, 234, 235, 239, 240, 241], "subnorm": 5, "k": [5, 40, 94, 122, 130, 159, 160, 172, 211, 215, 216, 217, 225, 227, 228, 229, 231, 239], "denorm": 5, "us": [5, 7, 19, 26, 27, 59, 60, 82, 95, 112, 114, 116, 142, 162, 164, 172, 180, 185, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 234, 235, 236, 237, 238, 239, 242], "gradual": [5, 239], "underflow": [5, 9, 87, 98, 226], "hardwar": [5, 53, 187, 191, 192, 215, 228, 235, 239], "univers": [5, 186, 192, 235, 239], "mani": [5, 239, 241], "platform": 5, "compil": [5, 157, 183, 186, 190, 239], "toggl": 5, "daz": 5, "flush": 5, "ftz": 5, "increas": [5, 187, 240], "guard": 5, "against": [5, 40, 73, 122, 157, 172, 221, 224, 242], "time": [5, 7, 16, 17, 162, 163, 183, 185, 190, 191, 194, 211, 215, 216, 217, 225, 227, 228, 235, 239, 241], "attack": 5, "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 87, 93, 98, 112, 113, 115, 124, 125, 126, 127, 128, 130, 137, 148, 152, 154, 162, 163, 164, 165, 166, 172, 180, 187, 188, 189, 190, 192, 219, 225, 233, 235], "vari": [5, 157, 162, 163, 164, 165, 180, 187], "beyond": [5, 142, 180, 185, 239], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 77, 88, 92, 95, 96, 100, 106, 112, 132, 137, 139, 142, 150, 151, 154, 155, 158, 159, 160, 162, 163, 164, 165, 167, 169, 172, 180, 185, 187, 188, 189, 191, 192, 195, 197, 199, 200, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 231, 233, 235, 236, 239, 241, 242], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 77, 84, 85, 91, 93, 96, 106, 112, 113, 115, 118, 119, 120, 121, 122, 125, 130, 136, 139, 140, 144, 145, 146, 147, 148, 151, 152, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 171, 183, 185, 186, 188, 189, 190, 191, 192, 194, 195, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 215, 216, 217, 221, 224, 225, 226, 227, 228, 229, 234, 235, 236, 239, 240, 241], "attribut": [5, 23, 95, 104, 171, 182, 185, 236, 239, 240, 241], "wai": [5, 63, 183, 186, 192, 236, 239, 240, 241, 242], "f4": [5, 180], "ensur": [5, 26, 183, 187, 235, 239, 240, 241], "portabl": [5, 59, 112, 187, 189, 192, 239], "consum": [5, 26, 63, 183, 188, 189, 195, 234, 239, 240], "recommend": [5, 7, 19, 23, 26, 112, 118, 119, 120, 121, 125, 139, 152, 166, 178, 185, 187, 191, 192, 239], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 85, 87, 90, 91, 93, 95, 98, 99, 106, 107, 108, 112, 113, 114, 115, 116, 117, 122, 128, 137, 139, 144, 145, 148, 154, 156, 157, 158, 172, 187, 188, 189, 195, 226, 231, 239, 240, 242], "whether": [5, 13, 14, 59, 60, 63, 86, 106, 109, 112, 140, 185, 192, 211, 215, 216, 225, 227, 234, 238, 239, 241], "otherwis": [5, 13, 14, 15, 16, 17, 59, 60, 63, 75, 124, 125, 127, 137, 140, 144, 152, 154, 166, 167, 168, 171, 172, 183, 192, 211, 213, 219, 226, 227, 233, 238], "note": [5, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 35, 40, 42, 43, 44, 45, 47, 50, 51, 61, 62, 63, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 94, 95, 97, 98, 100, 101, 106, 107, 108, 109, 113, 114, 115, 116, 117, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 161, 162, 163, 164, 165, 166, 167, 171, 172, 185, 191, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 239, 240, 241, 242], "possibl": [5, 60, 98, 124, 127, 140, 156, 157, 183, 186, 187, 188, 189, 191, 192, 195, 235, 239, 240, 241, 242], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 122, 124, 125, 127, 128, 129, 137, 152, 154, 166, 172, 183, 186, 188, 191, 192, 194, 195, 216, 217, 235, 236, 239, 241], "In": [5, 12, 19, 59, 87, 90, 98, 106, 108, 109, 128, 131, 139, 144, 171, 172, 180, 187, 188, 191, 192, 206, 207, 225, 226, 228, 235, 236, 240, 241, 242], "clearli": [5, 59, 106, 178, 188, 235, 236], "warn": 5, "about": [5, 7, 26, 95, 104, 189, 235, 239, 241, 242], "document": [5, 7, 59, 98, 106, 178, 186, 188, 191, 234, 236, 238, 240, 241, 242], "": [5, 29, 32, 49, 58, 59, 60, 79, 98, 126, 139, 152, 159, 160, 166, 172, 178, 183, 185, 186, 187, 188, 189, 191, 192, 195, 199, 203, 207, 210, 224, 228, 229, 235, 236, 239, 241], "organ": [5, 185, 235, 240, 241], "within": [5, 15, 27, 172, 180, 183, 185, 188, 192, 197, 199, 202, 203, 206, 207, 208, 210, 239], "accord": [5, 12, 60, 71, 75, 87, 95, 98, 100, 112, 128, 136, 144, 152, 166, 167, 172, 185, 187, 188, 212], "These": [5, 189, 215, 240], "intend": [5, 137, 154, 183, 231], "posit": [7, 9, 10, 11, 13, 14, 20, 26, 46, 62, 65, 66, 80, 87, 92, 94, 95, 98, 108, 113, 115, 128, 130, 139, 142, 146, 148, 157, 171, 172, 183, 185, 187, 195, 209, 211, 225, 240], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 183, 185, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 235], "extern": [7, 241], "usabl": 7, "name": [7, 23, 98, 162, 163, 164, 172, 188, 215, 224, 225, 226, 228, 234, 239, 240], "when": [7, 12, 16, 17, 26, 47, 49, 63, 87, 93, 98, 112, 115, 124, 127, 128, 136, 140, 152, 157, 166, 168, 171, 172, 180, 185, 186, 188, 189, 190, 191, 194, 195, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 215, 217, 221, 224, 225, 226, 227, 228, 229, 235, 239, 240, 241], "accept": [7, 26, 118, 119, 120, 121, 125, 139, 152, 166, 183, 236], "call": [7, 34, 191, 192, 226, 239, 240, 241], "argument": [7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 84, 113, 115, 122, 137, 141, 145, 148, 154, 156, 157, 158, 171, 180, 187, 189, 191, 192, 197, 199, 202, 203, 206, 207, 208, 210, 231, 235, 239, 240, 241], "map": [7, 188, 189], "base": [7, 47, 57, 58, 91, 92, 113, 114, 115, 116, 136, 162, 163, 164, 165, 172, 185, 189, 195, 235, 236, 239, 240, 241], "sole": [7, 172, 178, 235], "incompat": [7, 26, 74, 183, 236, 239], "normal": [7, 77, 151, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210], "practic": [7, 19, 172, 235, 240], "avail": [7, 183, 191, 234, 236, 240], "still": [7, 195, 235, 240, 241, 242], "consid": [7, 63, 118, 119, 120, 121, 162, 163, 164, 165, 188, 192, 209, 224, 235, 239, 241, 242], "compliant": [7, 51, 87, 93, 112, 115, 118, 119, 120, 121, 124, 125, 127, 152, 166, 187, 190, 192, 236, 239], "namespac": [7, 23, 183, 185, 196, 234, 235, 236, 239, 242], "altern": [7, 189, 191, 242], "thei": [7, 26, 180, 186, 191, 192, 194, 195, 234, 235, 236, 239, 241, 242], "guidanc": [7, 49, 185, 186, 239], "were": [7, 98, 185, 239], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 77, 88, 89, 94, 96, 100, 101, 112, 124, 125, 127, 132, 133, 137, 140, 142, 152, 154, 155, 166, 169, 170, 171, 185, 194, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 219, 221, 224, 231, 233, 235, 240, 241], "keyword": [7, 126, 137, 154, 171, 185, 189, 192, 194, 195, 231, 235, 236, 239, 240, 241], "lead": [7, 98, 188, 225, 228, 239], "readabl": [7, 180, 235, 240], "code": [7, 59, 180, 189, 190, 192, 195, 235, 239, 240, 241], "easier": [7, 183, 189, 235], "evolv": [7, 183, 235], "over": [7, 13, 14, 112, 124, 125, 127, 137, 152, 154, 155, 158, 166, 167, 187, 188, 189, 191, 192, 194, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 212, 231, 233, 235, 239], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 172, 184, 185, 186, 192, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 236], "worri": 7, "xi": [7, 126], "annot": [7, 185, 195, 239], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 185, 186, 189, 191, 194, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 238, 241], "themselv": [7, 192], "individu": [7, 192, 194, 195, 198, 209, 239, 240], "descript": [7, 185, 187, 219, 233], "aim": [7, 186, 195, 234, 235, 236, 239, 240, 241, 242], "strongli": [7, 189, 241], "look": [7, 241], "like": [7, 183, 186, 188, 189, 195, 236, 239, 240, 241], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 77, 82, 88, 89, 94, 96, 100, 101, 112, 124, 125, 127, 132, 133, 137, 140, 142, 152, 154, 155, 166, 169, 170, 172, 185, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 219, 221, 224, 231, 233, 239, 240, 242], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 88, 92, 94, 95, 96, 98, 100, 101, 104, 112, 124, 125, 127, 132, 134, 137, 140, 142, 147, 150, 151, 152, 154, 155, 158, 159, 160, 166, 167, 169, 172, 180, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 214, 219, 220, 230, 231, 232, 233, 240], "str": [7, 8, 23, 106, 126, 240], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 86, 185, 241], "yyyi": [8, 23, 236], "mm": [8, 23, 236], "string": [8, 23, 106, 185, 236, 239], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 104, 106, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 171, 183, 186, 192, 194, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 237, 239, 241], "calcul": [9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 84, 85, 87, 91, 93, 113, 114, 115, 116, 117, 124, 125, 127, 128, 136, 137, 145, 146, 148, 152, 153, 154, 156, 157, 166, 185, 226], "absolut": [9, 20, 144, 187, 189, 219, 220, 226, 235], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 78, 84, 85, 91, 93, 97, 105, 107, 108, 109, 113, 114, 115, 116, 119, 124, 125, 127, 129, 135, 138, 143, 144, 145, 146, 148, 149, 152, 156, 157, 161, 166], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 84, 85, 87, 89, 90, 91, 92, 93, 96, 97, 98, 99, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 178, 183, 185, 188, 190, 192, 195, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 228, 229, 231, 233, 235, 239, 241], "ha": [9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 84, 85, 87, 91, 92, 93, 98, 101, 122, 125, 126, 128, 129, 130, 136, 137, 145, 146, 150, 152, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 172, 180, 183, 188, 191, 192, 194, 212, 219, 227, 228, 231, 233, 235, 236, 239, 241, 242], "magnitud": [9, 12, 20, 87, 98, 128, 185, 228, 229], "minimum": [9, 17, 20, 44, 124, 127, 129, 171, 185, 187], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 79, 80, 81, 83, 87, 95, 98, 104, 128, 129, 156, 157, 185, 187, 240], "known": [9, 144, 187, 190], "norm": [9, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 219, 233, 235], "modulu": [9, 139], "z": [9, 10, 11, 61, 62, 64, 66, 113, 188], "bj": [9, 12, 78, 87, 128], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 78, 86, 87, 90, 92, 98, 102, 103, 110, 111, 118, 119, 120, 121, 122, 124, 125, 127, 128, 129, 130, 131, 135, 137, 152, 154, 158, 162, 163, 164, 165, 166, 167, 172, 185, 187, 190, 197, 198, 199, 201, 202, 203, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 219, 221, 224, 225, 226, 227, 228, 229, 231, 233, 235, 239], "operatornam": [9, 10, 11, 61, 62, 64, 66, 84, 85, 144, 145, 146, 156, 157, 188, 215, 216, 226, 228], "sqrt": [9, 10, 11, 61, 62, 171, 185, 188, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 233], "take": [9, 113, 115, 136, 148, 171, 185, 192, 195, 239], "care": [9, 189, 235], "undu": [9, 190], "overflow": [9, 12, 87, 98, 112, 137, 154, 180, 226, 231, 235], "dure": [9, 40, 59, 122, 152, 166, 180, 183, 224, 239, 240], "intermedi": 9, "stage": [9, 236], "numer": [9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 87, 98, 106, 107, 108, 109, 122, 126, 128, 129, 135, 136, 137, 143, 144, 149, 153, 154, 158, 171, 180, 187, 197, 199, 202, 203, 206, 207, 208, 210, 212, 223, 224, 226, 231, 235, 239, 241], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 84, 85, 87, 88, 89, 90, 91, 93, 97, 98, 99, 102, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144, 145, 146, 148, 149, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 172, 185, 187, 188, 189, 191, 194, 198, 199, 200, 203, 204, 207, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 239, 241], "complex128": [9, 20, 106, 171, 180, 185, 201, 205, 206, 207, 208, 210, 215, 216, 219, 233], "float64": [9, 20, 106, 171, 180, 201, 205, 206, 207, 208, 210, 215, 216, 219, 233], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 109, 113, 114, 115, 116, 117, 124, 125, 127, 128, 131, 136, 139, 143, 144, 145, 146, 148, 152, 156, 157, 161, 162, 163, 164, 165, 166, 171, 178, 185, 188, 239], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 80, 84, 85, 87, 90, 91, 93, 97, 98, 107, 108, 113, 114, 115, 116, 117, 124, 127, 128, 131, 136, 139, 143, 145, 146, 148, 156, 157, 161, 188, 226, 233], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 85, 90, 91, 93, 107, 108, 109, 112, 113, 115, 131, 143, 144, 146, 148, 157, 171, 185, 186, 239, 240, 241], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 85, 87, 90, 91, 93, 98, 107, 108, 113, 115, 128, 131, 136, 139, 146, 148, 157, 187], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 78, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 47, 50, 51, 60, 61, 62, 63, 64, 66, 78, 84, 85, 87, 90, 91, 93, 94, 95, 100, 101, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 122, 126, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 143, 144, 145, 146, 148, 149, 153, 154, 156, 157, 158, 162, 163, 164, 165, 167, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 233, 236], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 84, 85, 91, 93, 98, 113, 114, 115, 116, 136, 145, 146, 156, 157, 187, 221, 224], "princip": [10, 11, 61, 62, 64, 66, 113, 148, 188, 235], "invers": [10, 11, 61, 62, 64, 65, 66, 188, 197, 199, 202, 203, 204, 205, 206, 207, 208, 210, 217, 220, 224, 235], "cosin": [10, 11, 84, 85, 157], "express": [10, 61, 63, 64, 65, 84, 145, 156, 172, 180, 189, 235, 238], "radian": [10, 61, 64, 65, 84, 145, 156], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 84, 85, 87, 112, 114, 116, 144, 145, 146, 156, 157, 188, 226], "pi": [10, 11, 61, 62, 64, 66, 85, 113, 115, 146, 156, 157, 171], "j": [10, 11, 12, 25, 61, 62, 64, 66, 85, 87, 91, 93, 112, 113, 115, 128, 144, 145, 146, 148, 156, 157, 172, 188, 215, 228, 231], "ln": [10, 11, 61, 62, 64, 66, 113], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 85, 91, 93, 113, 114, 115, 116, 146, 148, 157, 171, 185], "multi": [10, 11, 61, 62, 64, 66, 171, 188, 191, 192, 212, 241], "branch": [10, 11, 61, 62, 64, 65, 66, 84, 85, 87, 91, 93, 113, 115, 128, 136, 145, 146, 148, 156, 157, 239], "cut": [10, 11, 61, 62, 64, 66, 84, 85, 91, 93, 113, 115, 136, 145, 146, 148, 156, 157, 239], "plane": [10, 11, 61, 62, 64, 66, 84, 85, 87, 91, 93, 128, 145, 146, 148, 156, 157, 239], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 113, 115, 124, 125, 127, 136, 137, 148, 152, 154, 166, 167, 187, 188, 212, 235, 240], "place": [10, 11, 15, 60, 61, 62, 64, 66, 88, 89, 94, 100, 101, 112, 132, 133, 142, 169, 170, 171, 178, 180, 185, 189, 192, 198, 209, 224], "line": [10, 11, 61, 62, 64, 66, 156, 157, 180, 188, 239, 240, 241, 242], "segment": [10, 11, 61, 62, 64, 66, 188], "infti": [10, 11, 61, 62, 64, 66, 84, 113, 115, 136, 148, 188], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 77, 92, 96, 113, 115, 124, 125, 127, 136, 137, 142, 147, 148, 150, 151, 152, 154, 155, 158, 166, 167, 171, 185, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 212, 219, 232, 233, 239], "rang": [10, 61, 62, 64, 66, 113, 115, 137, 148, 154, 172, 185, 231, 239], "strip": [10, 61, 62, 64, 66, 113, 115], "unbound": [10, 61, 62, 64, 66, 113, 115], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 77, 94, 96, 113, 115, 124, 125, 127, 137, 142, 147, 148, 151, 152, 154, 155, 156, 157, 166, 167, 172, 185, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 231, 233, 235], "c99": [10, 11, 61, 62, 64, 66, 87, 113, 115, 128, 136, 148, 188, 236], "provision": [10, 11, 61, 62, 64, 66, 113, 115, 136, 148, 188], "statu": [10, 11, 61, 62, 64, 66, 113, 115, 136, 148, 188], "less": [10, 11, 39, 47, 61, 65, 66, 76, 87, 98, 113, 114, 115, 116, 136, 139, 144, 148, 152, 166, 171, 172, 185, 189, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 219, 220, 221, 224, 233, 239], "\u03c0": [10, 64, 65, 83], "0j": [10, 11, 12, 25, 62, 63, 66, 85, 91, 93, 94, 113, 115, 132, 133, 144, 146, 148, 157, 188, 226], "nonzero": [10, 11, 12, 62, 66, 85, 87, 91, 93, 98, 128, 146, 157, 171, 172, 185, 224], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 84, 85, 145, 146, 156, 157, 188], "aco": [11, 61, 171, 185, 187], "simpli": [11, 93, 115, 186, 195, 239, 241], "upper": [11, 94, 160, 185, 211, 225], "half": [11, 15, 66, 112, 148, 172, 200], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 113, 115], "3\u03c0j": [11, 113, 115], "sum": [12, 21, 117, 171, 185, 219, 231, 233, 235], "x1_i": [12, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 128, 131, 136, 139, 153, 168, 185], "x2_i": [12, 65, 67, 69, 70, 71, 72, 87, 90, 98, 102, 103, 110, 111, 117, 118, 120, 121, 128, 131, 136, 139, 153, 168, 185], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 90, 102, 103, 110, 111, 117, 118, 120, 121, 122, 128, 131, 136, 142, 151, 153, 156, 157, 158, 162, 163, 164, 167, 168, 172, 188, 212, 215, 223, 225, 226, 228, 229, 235, 239, 240, 241, 242], "remain": [12, 87, 90, 98, 106, 108, 109, 128, 131, 139, 140, 144, 172, 189, 210], "neither": [12, 40, 87, 98, 122, 128, 158, 228, 240], "nor": [12, 87, 98, 128, 228, 240], "mathemat": [12, 19, 65, 83, 84, 85, 87, 93, 98, 113, 115, 128, 145, 146, 156, 157, 171, 188, 219, 233], "round": [12, 15, 76, 87, 97, 98, 128, 148, 161, 171, 185, 187], "nearest": [12, 87, 128, 143, 161, 187], "mode": [12, 87, 128, 187, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 225], "too": [12, 87, 98, 128, 235, 239], "larg": [12, 87, 98, 128, 195, 226, 239], "appropri": [12, 26, 87, 98, 128, 188], "commut": 12, "associ": [12, 42, 128, 180, 221, 224, 227, 235, 238, 240], "tabl": [12, 87, 128, 171], "c": [12, 87, 90, 112, 128, 130, 131, 151, 152, 157, 166, 172, 185, 188, 191, 193, 211, 215, 216, 217, 225, 227, 228, 236, 238, 239, 241], "d": [12, 87, 90, 112, 128, 131, 180, 198, 209], "dj": [12, 87, 128], "independ": [12, 87, 128, 143, 172, 183, 191, 212, 225, 227, 235, 236, 239], "abov": [12, 87, 90, 113, 115, 128, 131, 136, 137, 148, 154, 159, 160, 172, 180, 188, 189, 191, 192, 214, 215, 231, 235, 238, 241], "similarli": [12, 57, 106, 126, 180, 211, 228], "henc": [12, 78, 92, 130, 162, 163, 164, 165, 172, 186, 188, 189, 190, 191, 194, 195, 239, 241], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 124, 125, 127, 137, 152, 154, 166, 219, 233], "bool": [13, 14, 16, 17, 18, 22, 24, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 86, 90, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 118, 119, 120, 121, 124, 125, 127, 131, 137, 140, 147, 152, 154, 166, 171, 180, 185, 211, 219, 228, 233], "test": [13, 14, 86, 107, 108, 109, 185, 187, 237, 239, 240, 241], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 91, 93, 113, 114, 115, 116, 129, 135, 144, 149, 183, 239], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 88, 95, 96, 100, 101, 104, 106, 112, 124, 125, 127, 132, 137, 141, 142, 150, 151, 152, 154, 158, 166, 169, 200, 204, 219, 221, 224, 233, 240], "ax": [13, 14, 16, 17, 19, 55, 56, 96, 124, 125, 127, 134, 137, 142, 150, 152, 154, 158, 166, 167, 172, 185, 199, 200, 203, 204, 207, 210, 212, 219, 224, 227, 230, 233], "logic": [13, 14, 24, 87, 90, 118, 119, 120, 121, 128, 131, 192, 199, 203, 207, 210], "AND": [13, 67, 90, 118, 238], "reduct": [13, 14], "default": [13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 88, 89, 94, 96, 100, 101, 112, 124, 125, 126, 127, 130, 132, 133, 137, 140, 142, 147, 151, 152, 154, 158, 159, 160, 162, 163, 164, 166, 167, 169, 170, 171, 172, 185, 187, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 219, 221, 224, 225, 228, 231, 233], "entir": [13, 14, 84, 85, 91, 93, 124, 125, 127, 137, 145, 146, 152, 154, 166], "valid": [13, 14, 27, 92, 151, 158, 172, 187, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 215, 225, 228, 240], "count": [13, 14, 77, 96, 155, 162, 163, 167, 172, 185, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 216], "last": [13, 14, 18, 19, 55, 77, 96, 142, 147, 151, 155, 158, 167, 172, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 212, 214, 219, 225, 228, 231], "invalid": [13, 14, 23, 92, 167, 212, 239], "rais": [13, 14, 19, 23, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 87, 91, 92, 112, 122, 124, 127, 130, 136, 140, 150, 151, 167, 172, 180, 183, 185, 192, 212, 220, 239], "wa": [13, 14, 19, 98, 124, 125, 127, 137, 152, 154, 166, 180, 192, 195, 239, 241], "OR": [14, 24, 70, 120, 131, 238], "start": [15, 112, 172, 185, 195, 239, 241], "stop": [15, 112, 172, 185, 240], "step": [15, 112, 172, 240], "evenli": [15, 112], "space": [15, 112, 198, 200, 209], "open": [15, 112, 172], "inclus": [15, 172, 239], "end": [15, 65, 84, 112, 144, 145, 156, 157, 178, 189, 226, 239, 240, 241], "exclus": [15, 172], "distanc": 15, "between": [15, 26, 47, 51, 65, 77, 87, 90, 95, 112, 131, 136, 151, 162, 163, 164, 165, 180, 188, 189, 192, 198, 209, 235, 239, 241], "adjac": 15, "output": [15, 60, 77, 88, 89, 92, 94, 96, 100, 101, 112, 126, 132, 133, 140, 142, 150, 151, 155, 169, 170, 183, 185, 188, 189, 192, 193, 195, 197, 199, 201, 202, 203, 206, 207, 208, 210, 231, 239], "infer": [15, 60, 89, 100, 101, 133, 140, 170, 190, 235, 240], "cannot": [15, 26, 57, 156, 157, 185, 188, 190, 239], "guarante": [15, 59, 162, 164, 183, 188, 192, 239, 241], "error": [15, 19, 23, 26, 51, 55, 87, 124, 127, 156, 157, 180, 187, 226, 239], "affect": [15, 49, 189, 192], "ceil": [15, 171], "indic": [16, 17, 18, 60, 86, 106, 112, 130, 140, 142, 144, 155, 159, 160, 162, 164, 172, 180, 185, 233, 239], "occur": [16, 17, 75, 156, 157, 162, 163, 164, 165, 188, 240], "occurr": [16, 17, 162], "comparison": [16, 17, 18, 31, 33, 37, 39, 90, 102, 103, 110, 111, 124, 127, 131, 147, 171, 185, 188, 236, 240], "search": [16, 17, 171], "flatten": [16, 17, 77, 142, 162, 163, 164, 165, 233, 235], "descend": [18, 147, 228, 229], "stabl": [18, 147, 191], "sort": [18, 171, 185, 215, 216, 228, 229], "ascend": [18, 147, 185], "stabil": [18, 147], "maintain": [18, 147, 186, 239, 241], "rel": [18, 19, 55, 96, 142, 147, 185, 214, 221, 224, 231], "compar": [18, 147, 162, 163, 164, 165, 187, 192, 240, 242], "properti": [19, 53, 54, 55, 56, 57, 58, 185, 188, 192, 195, 239], "transpos": [19, 40, 55, 122, 123, 158, 211, 215, 224, 228, 235], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 86, 180, 183, 185, 192], "permut": [19, 55, 134], "revers": [19, 55, 65, 96], "origin": [19, 55, 65, 140, 142, 185, 189, 197, 199, 202, 203, 206, 207, 208, 210, 239, 240], "limit": [19, 95, 104, 106, 187, 235, 238], "matric": [19, 40, 55, 122, 123, 126, 159, 160, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 235], "deviat": [19, 152, 187, 239, 241], "et": [19, 228, 229], "al": 19, "intent": [19, 65], "found": [19, 188, 191, 241, 242], "problemat": [19, 63, 186, 189], "conflict": [19, 185], "definit": [19, 84, 85, 145, 146, 156, 157, 185, 211, 240], "batch": [19, 233, 235], "cetera": [19, 228, 229], "permute_dim": [19, 171], "interfac": [19, 191, 235, 239, 241], "ab": [20, 136, 171, 185, 219, 233], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 171, 185], "api_vers": [23, 239], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 86, 95, 99, 104, 171, 172, 180, 183, 185, 189, 191, 192, 195, 234, 236, 240, 241], "form": [23, 40, 78, 122, 123, 159, 160, 189, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 236, 240], "2020": [23, 195, 236, 238, 239], "10": [23, 27, 114, 172, 239], "latest": [23, 191], "modul": [23, 183, 234, 236, 240, 241, 242], "It": [23, 26, 183, 189, 191, 239, 241, 242], "everi": [23, 100, 101, 225, 239], "top": [23, 183, 239, 241], "level": [23, 180, 186, 191, 192, 234, 235, 239, 240], "public": [23, 234, 240, 241], "well": [23, 186, 188, 191, 192, 225, 241, 242], "part": [23, 35, 159, 160, 180, 185, 191, 194, 236, 239, 241], "convert": [24, 25, 29, 34, 35, 60, 180, 185, 186, 188, 191, 239, 241], "handl": [24, 26, 61, 64, 84, 114, 116, 136, 137, 144, 145, 149, 154, 156, 185, 186, 188, 189, 192, 231, 239], "new": [25, 92, 95, 99, 100, 101, 104, 106, 132, 133, 138, 140, 151, 169, 170, 183, 185, 186, 189, 191, 192, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 236, 239, 240, 241], "stream": [26, 59, 192], "pycapsul": 26, "export": [26, 185, 240], "from_dlpack": [26, 27, 171, 185, 191], "dlpack": [26, 27, 185], "capsul": 26, "pointer": 26, "produc": [26, 215, 225, 228, 241], "instruct": 26, "safe": [26, 112], "insert": [26, 92, 185], "wait": 26, "event": [26, 238], "signal": [26, 201, 205, 241], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 183, 186, 191, 192, 235, 239, 241], "queue": [26, 59, 192], "similar": [26, 139, 186, 188, 190, 239, 240, 241], "mechan": [26, 99, 183, 185, 186, 193, 234, 239], "most": [26, 183, 192, 215, 235, 239, 241], "yet": [26, 195, 239], "sycl": 26, "want": [26, 87, 128, 186, 190, 191, 239, 241, 242], "cl": 26, "agre": 26, "assum": [26, 84, 145, 156, 183, 188, 192, 234, 239], "legaci": 26, "per": [26, 186, 191, 237], "thread": [26, 239, 241], "disallow": 26, "due": [26, 42, 57, 58, 112, 128, 155, 187, 188, 235, 239], "ambigu": [26, 63, 98, 189], "explicitli": [26, 40, 63, 122, 158, 172, 183, 185, 211, 215, 216, 225, 227, 235, 239, 241], "prefer": [26, 98, 183, 235, 241], "develop": [26, 187, 239, 240, 241, 242], "who": [26, 187, 239, 240], "think": 26, "cost": 26, "interchang": [26, 99, 183, 186, 193, 239], "detail": [26, 32, 49, 99, 130, 162, 163, 164, 165, 171, 172, 182, 183, 190, 192, 194, 235, 239, 241], "buffererror": [26, 185], "stride": [26, 189], "fail": [26, 239], "reason": [26, 139, 157, 189, 235, 239, 240], "incorrect": [26, 185], "pass": [26, 65, 183, 187, 192], "enum": 27, "id": 27, "format": [27, 185, 236], "meant": 27, "device_typ": 27, "device_id": 27, "member": 27, "cuda": [27, 186, 191, 241], "cpu_pin": 27, "opencl": 27, "vulkan": 27, "metal": 27, "vpi": 27, "rocm": [27, 186], "truth": [28, 31, 33, 37, 39, 43, 86, 90, 102, 103, 110, 111, 131, 242], "cast": [29, 49, 60, 63, 75, 137, 154, 180, 188, 231, 239, 241], "outsid": [29, 151, 172, 180, 185, 191], "bound": [29, 172, 180, 185, 195], "typeerror": [29, 34, 35, 239, 241], "divis": [30, 41, 71, 87, 98, 139, 144, 188], "floor_divid": [30, 171, 185], "greater_equ": [31, 171, 185], "kei": [32, 49, 239], "slice": [32, 49, 171, 189], "ellipsi": [32, 49, 172], "semant": [32, 40, 49, 98, 122, 139, 155, 171, 172, 183, 185, 189, 191, 194, 235, 239, 240, 241], "access": [32, 172, 185, 191, 234, 236, 239], "method": [34, 99, 171, 183, 189, 191, 192, 194, 195, 239, 240, 241], "also": [34, 144, 180, 183, 188, 189, 190, 191, 195, 199, 203, 207, 210, 228, 234, 241], "pep": [34, 40, 98, 122, 191, 236], "357": 34, "overflowerror": 35, "valueerror": [35, 60, 140, 150, 241], "bitwise_invert": [36, 171], "less_equ": [37, 171, 185], "bitwise_left_shift": [38, 171, 185], "matrix": [40, 55, 122, 123, 126, 158, 159, 160, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231, 235, 239], "product": [40, 42, 58, 122, 128, 137, 158, 167, 185, 212, 223, 235], "built": [40, 122, 172, 180, 239], "465": [40, 122], "least": [40, 87, 106, 122, 128, 130, 162, 163, 164, 165, 186, 187, 224], "m": [40, 55, 122, 123, 126, 159, 160, 172, 197, 199, 201, 202, 203, 205, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 219, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231], "remov": [40, 122, 150, 172, 188, 214, 231], "innermost": [40, 122, 123, 159, 160, 211, 213, 214, 215, 216, 217, 219, 220, 221, 224, 225, 226, 227, 228, 229, 231], 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160, 215, 224, 225, 231, 235], "elsewher": [94, 168, 188], "row": [94, 130, 172, 219, 225, 227, 228], "column": [94, 215, 219, 225, 227, 228, 239], "main": [94, 159, 160, 186, 191, 214, 231, 234, 241], "finfo_object": [95, 185], "machin": [95, 104, 221, 224, 239], "get": [95, 104, 186, 189, 191, 192], "inform": [95, 104, 239, 240, 241, 242], "so": [95, 172, 178, 191, 235, 238, 239, 242], "occupi": [95, 104], "ep": [95, 221, 224, 239], "next": [95, 185, 239], "larger": [95, 142, 152, 166, 224], "largest": [95, 104, 219, 228, 229], "min": [95, 104, 159, 160, 171, 185, 219, 225, 228, 229, 233], "smallest_norm": 95, "full": [95, 171, 185, 189, 225, 227, 228, 241], "preserv": [96, 172, 185, 188, 192], "reorder": 96, "greatest": [97, 98], "238": 98, "goal": [98, 186, 189, 235, 241], "disambigu": 98, "toward": [98, 142, 187, 235, 240], "former": [98, 172, 188, 240], "latter": [98, 172, 183, 188, 191, 240], "overload": [98, 235], "led": 98, "subtl": 98, "bug": [98, 241, 242], "expect": [98, 157, 180, 185, 187, 188, 190, 191, 192, 195, 239], "design": [98, 185, 187, 237, 239, 241, 242], "ill": [98, 235], "below": [98, 159, 160, 191, 192, 214, 231], "diverg": [98, 242], "strictli": 98, "relat": [98, 172, 188, 192, 194, 235, 239, 241], "surpris": [98, 188], "unexpect": [98, 188, 239], "fill_valu": [100, 101], "fill": [100, 101, 132, 133, 169, 170, 185], "iinfo_object": [104, 185], "complex64": [105, 106, 138, 171, 180, 185, 226, 228, 229], "float32": [105, 106, 138, 171, 180, 226, 228, 229], "int8": [106, 171, 180], "int16": [106, 137, 154, 171, 180, 231], "int32": [106, 137, 154, 171, 180, 231], "int64": [106, 137, 154, 171, 180, 231], "uint8": [106, 171, 180], "uint16": [106, 137, 154, 171, 180, 231], "uint32": [106, 137, 154, 171, 180, 231], "uint64": [106, 137, 154, 171, 180, 231], "shorthand": [106, 172], "belong": [106, 189], "float16": 106, "bfloat16": [106, 239], "int128": 106, "short": [106, 188, 239, 240], "extend": [106, 172, 188, 239], "extens": [106, 237, 241], 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165, 172, 189, 190, 194, 239, 240, 241], "etc": [130, 162, 163, 164, 165, 172, 190, 236], "find": [130, 162, 163, 164, 165, 172, 185, 190, 239, 240], "difficult": [130, 162, 163, 164, 165, 172, 187, 190, 239], "omit": [130, 162, 163, 164, 165, 172, 190], "section": [130, 162, 163, 164, 165, 172, 185, 186, 190, 191, 192, 195, 239, 241], "total": [130, 152, 166, 188], "major": [130, 172, 236], "style": [130, 172], "odd": [136, 198, 204, 206, 207, 209], "treat": 136, "carefulli": 136, "smaller": [137, 142, 154, 231, 241], "help": [137, 154, 186, 187, 194, 231], "prevent": [137, 154, 231], "success": [137, 154, 231], "That": [139, 172, 183, 195, 239], "primarili": 139, "One": [140, 239, 242], "arrays_and_dtyp": 141, "re": [142, 186, 189, 195, 241], "restor": 142, "counterpart": 143, "signum": 144, "2j": 145, "sinh": [145, 157, 171, 185, 187], "squar": [148, 171, 185, 188, 211, 213, 215, 216, 217, 220, 224, 226, 227, 235], "root": [148, 185, 188, 216], "indistinguish": [148, 172, 187], 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163, 164, 215, 225, 226, 228, 235], "field": [162, 163, 164, 188, 215, 225, 226, 228, 239], "third": [162, 228], "fourth": 162, "varianc": 166, "unbias": 166, "mathbf": 167, "overlin": [167, 224], "a_i": 167, "b_i": 167, "ident": [167, 188, 204, 216, 217, 220, 239], "condit": [168, 185, 238], "yield": [168, 188], "signatur": [171, 183, 195, 239, 240], "subset": [171, 187, 240, 241], "categori": 171, "satisfi": [171, 172, 187, 188, 240], "accuraci": [171, 185, 193, 197, 199, 202, 203, 206, 207, 208, 210], "reflect": 171, "mt": 171, "t": [171, 186, 189, 192, 194, 195, 239, 241], "__abs__": [171, 185], "__array_namespace__": [171, 196, 235, 239], "__bool__": [171, 185], "__complex__": [171, 185], "__dlpack_device__": 171, "__float__": [171, 185], "__getitem__": [171, 172, 185], "__index__": [171, 185], "__int__": [171, 185], "to_devic": [171, 185, 192], "overview": 171, "algorithm": [171, 187, 226, 241], "inf": [171, 219, 233, 239], "newaxi": [171, 185], "creation": [171, 183, 192, 239], 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[[16, "argmax"]], "argmin": [[17, "argmin"]], "argsort": [[18, "argsort"]], "T": [[19, "t"]], "__abs__": [[20, "abs"]], "__add__": [[21, "add"]], "__and__": [[22, "and"]], "__array_namespace__": [[23, "array-namespace"]], "__bool__": [[24, "bool"]], "__complex__": [[25, "complex"]], "__dlpack__": [[26, "dlpack"]], "CUDA": [[26, null]], "ROCm": [[26, null]], "Tip": [[26, null], [60, null]], "__dlpack_device__": [[27, "dlpack-device"]], "__eq__": [[28, "eq"], [86, "eq"]], "__float__": [[29, "float"]], "__floordiv__": [[30, "floordiv"]], "__ge__": [[31, "ge"]], "__getitem__": [[32, "getitem"]], "__gt__": [[33, "gt"]], "__index__": [[34, "index"]], "__int__": [[35, "int"]], "__invert__": [[36, "invert"]], "__le__": [[37, "le"]], "__lshift__": [[38, "lshift"]], "__lt__": [[39, "lt"]], "__matmul__": [[40, "matmul"]], "__mod__": [[41, "mod"]], "__mul__": [[42, "mul"]], "__ne__": [[43, "ne"]], "__neg__": [[44, "neg"]], "__or__": [[45, "or"]], "__pos__": [[46, "pos"]], "__pow__": [[47, "pow"]], "__rshift__": [[48, "rshift"]], "__setitem__": [[49, "setitem"]], "__sub__": [[50, "sub"]], "__truediv__": [[51, "truediv"]], "__xor__": [[52, "xor"]], "device": [[53, "device"]], "dtype": [[54, "dtype"]], "mT": [[55, "mt"]], "ndim": [[56, "ndim"]], "shape": [[57, "shape"]], "size": [[58, "size"]], "to_device": [[59, "to-device"]], "asarray": [[60, "asarray"]], "Note": [[60, null], [99, null], [112, null]], "asin": [[61, "asin"]], "asinh": [[62, "asinh"]], "astype": [[63, "astype"]], "atan": [[64, "atan"]], "atan2": [[65, "atan2"]], "atanh": [[66, "atanh"]], "bitwise_and": [[67, "bitwise-and"]], "bitwise_invert": [[68, "bitwise-invert"]], "bitwise_left_shift": [[69, "bitwise-left-shift"]], "bitwise_or": [[70, "bitwise-or"]], "bitwise_right_shift": [[71, "bitwise-right-shift"]], "bitwise_xor": [[72, "bitwise-xor"]], "broadcast_arrays": [[73, "broadcast-arrays"]], "broadcast_to": [[74, "broadcast-to"]], "can_cast": [[75, "can-cast"]], "ceil": [[76, "ceil"]], "concat": [[77, "concat"]], "conj": [[78, "conj"]], "e": [[79, "e"]], "inf": [[80, "inf"]], "nan": [[81, "nan"]], "newaxis": [[82, "newaxis"]], "pi": [[83, "pi"]], "cos": [[84, "cos"]], "cosh": [[85, "cosh"]], "divide": [[87, "divide"]], "empty": [[88, "empty"]], "empty_like": [[89, "empty-like"]], "equal": [[90, "equal"]], "exp": [[91, "exp"]], "expand_dims": [[92, "expand-dims"]], "expm1": [[93, "expm1"]], "eye": [[94, "eye"]], "finfo": [[95, "finfo"]], "flip": [[96, "flip"]], "floor": [[97, "floor"]], "floor_divide": [[98, "floor-divide"]], "from_dlpack": [[99, "from-dlpack"]], "full": [[100, "full"]], "full_like": [[101, "full-like"]], "greater": [[102, "greater"]], "greater_equal": [[103, "greater-equal"]], "iinfo": [[104, "iinfo"]], "imag": [[105, "imag"]], "isdtype": [[106, "isdtype"]], "isfinite": [[107, "isfinite"]], "isinf": [[108, "isinf"]], "isnan": [[109, "isnan"]], "less": [[110, "less"]], "less_equal": [[111, "less-equal"]], "linspace": [[112, "linspace"]], "log": [[113, "log"]], "log10": [[114, 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"Indexing": [[172, "indexing"]], "Single-axis Indexing": [[172, "single-axis-indexing"]], "Slice Syntax": [[172, "slice-syntax"]], "Multi-axis Indexing": [[172, "multi-axis-indexing"]], "Boolean Array Indexing": [[172, "boolean-array-indexing"]], "Return Values": [[172, "return-values"]], "Indexing Functions": [[173, "indexing-functions"]], "Linear Algebra Functions": [[174, "linear-algebra-functions"]], "Manipulation Functions": [[175, "manipulation-functions"]], "Searching Functions": [[176, "searching-functions"]], "Set Functions": [[177, "set-functions"]], "Sorting Functions": [[178, "sorting-functions"]], "Statistical Functions": [[179, "statistical-functions"], [187, "statistical-functions"]], "Type Promotion Rules": [[180, "type-promotion-rules"]], "Rules": [[180, "rules"]], "Signed integer type promotion table": [[180, "signed-integer-type-promotion-table"]], "Unsigned integer type promotion table": [[180, "unsigned-integer-type-promotion-table"]], "Mixed unsigned and signed integer type promotion table": [[180, "mixed-unsigned-and-signed-integer-type-promotion-table"]], "Floating-point type promotion table": [[180, "floating-point-type-promotion-table"]], "Notes": [[180, "notes"]], "Mixing arrays with Python scalars": [[180, "mixing-arrays-with-python-scalars"]], "Utility Functions": [[181, "utility-functions"]], "Version": [[182, "version"]], "Assumptions": [[183, "assumptions"]], "Hardware and software environments": [[183, "hardware-and-software-environments"]], "Dependencies": [[183, "dependencies"]], "Backwards compatibility": [[183, "backwards-compatibility"], [236, "backwards-compatibility"]], "Production code & interactive use": [[183, "production-code-interactive-use"]], "Benchmark suite": [[184, "benchmark-suite"]], "Changelog per API standard version": [[185, "changelog-per-api-standard-version"]], "Changelog": [[185, "changelog"]], "v2024.12": [[185, "v2024-12"]], "Updates": [[185, "updates"], [185, "id5"], [185, "id15"]], "Normative": [[185, "normative"], [185, "id1"], [185, "id3"], [185, "id6"]], "APIs": [[185, "apis"], [185, "id2"], [185, "id4"], [185, "id7"], [185, "id10"], [185, "id16"], [185, "id20"]], "Scalar Argument Support": [[185, "scalar-argument-support"]], "Extensions": [[185, "extensions"], [185, "id8"], [185, "id13"], [185, "id17"], [185, "id21"], [234, "extensions"], [234, "id2"]], "Additions": [[185, "additions"], [185, "id9"], [185, "id19"]], "Inspection APIs": [[185, "inspection-apis"], [185, "id11"]], "Breaking Changes": [[185, "breaking-changes"], [185, "id12"]], "Errata": [[185, "errata"], [185, "id14"], [185, "id22"]], "v2023.12": [[185, "v2023-12"]], "v2022.12": [[185, "v2022-12"]], "Complex Number Support": [[185, "complex-number-support"], [185, "id18"]], "C API": [[186, "c-api"]], "Example situations for C/Cython usage": [[186, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[186, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[186, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[186, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[186, "device-support"], [192, "device-support"]], "Other longer-term approaches": [[186, "other-longer-term-approaches"]], "Further Python API standardization": [[186, "further-python-api-standardization"]], "HPy": [[186, "hpy"]], "Accuracy": [[187, "accuracy"]], "Arithmetic Operations": [[187, "arithmetic-operations"]], "Mathematical Functions": [[187, "mathematical-functions"]], "Linear Algebra": [[187, "linear-algebra"]], "Complex Numbers": [[188, "complex-numbers"]], "The Complex Plane": [[188, "the-complex-plane"]], "Branch Cuts": [[188, "branch-cuts"]], "Complex Number Ordering": [[188, "complex-number-ordering"]], "Valued-based Promotion": [[188, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[189, "copy-view-behaviour-and-mutability"]], "Mutating views": [[189, null]], "Data-dependent output shapes": [[190, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[191, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[191, "dlpack-an-in-memory-tensor-structure"]], "Intended usage": [[192, "intended-usage"]], "Syntax for device assignment": [[192, "syntax-for-device-assignment"]], "Semantics": [[192, "semantics"]], "Out of scope for device support": [[192, "out-of-scope-for-device-support"]], "Design topics & constraints": [[193, "design-topics-constraints"], [193, null]], "Parallelism": [[194, "parallelism"]], "Static typing": [[195, "static-typing"]], "Fourier transform Functions": [[196, "fourier-transform-functions"]], "Extension name and usage": [[196, "extension-name-and-usage"], [235, "extension-name-and-usage"]], "fft": [[197, "fft"]], "fftfreq": [[198, "fftfreq"]], "fftn": [[199, "fftn"]], "fftshift": [[200, "fftshift"]], "hfft": [[201, "hfft"]], "ifft": [[202, "ifft"]], "ifftn": [[203, "ifftn"]], "ifftshift": [[204, "ifftshift"]], "ihfft": [[205, "ihfft"]], "irfft": [[206, "irfft"]], "irfftn": [[207, "irfftn"]], "rfft": [[208, "rfft"]], "rfftfreq": [[209, "rfftfreq"]], "rfftn": [[210, "rfftn"]], "cholesky": [[211, "cholesky"]], "cross": [[212, "cross"]], "det": [[213, "det"]], "diagonal": [[214, "diagonal"]], "eigh": [[215, "eigh"]], "eigvalsh": [[216, "eigvalsh"]], "inv": [[217, "inv"]], "matrix_norm": [[219, "matrix-norm"]], "matrix_power": [[220, "matrix-power"]], "matrix_rank": [[221, "matrix-rank"]], "outer": [[223, "outer"]], "pinv": [[224, "pinv"]], "qr": [[225, "qr"]], "slogdet": [[226, "slogdet"]], "solve": [[227, "solve"]], "svd": [[228, "svd"]], "svdvals": [[229, "svdvals"]], "trace": [[231, "trace"]], "vector_norm": [[233, "vector-norm"]], "Linear Algebra Extension": [[235, "linear-algebra-extension"]], "Design Principles": [[235, "design-principles"]], "Future API standard evolution": [[236, "future-api-standard-evolution"]], "Scope extensions": [[236, "scope-extensions"]], "Versioning": [[236, "versioning"]], "Python array API standard": [[237, "python-array-api-standard"]], "Contents": [[237, "contents"]], "Context": [[237, null]], "API": [[237, null]], "Methodology and Usage": [[237, null]], "Other": [[237, null]], "License": [[238, "license"]], "Purpose and scope": [[239, "purpose-and-scope"]], "Introduction": [[239, "introduction"], [240, "introduction"]], "This API standard": [[239, "this-api-standard"]], "History": [[239, "history"]], "Scope (includes out-of-scope / non-goals)": [[239, "scope-includes-out-of-scope-non-goals"]], "In scope": [[239, "in-scope"]], "Out of scope": [[239, "out-of-scope"]], "Implications of in/out of scope": [[239, "implications-of-in-out-of-scope"]], "Stakeholders": [[239, "stakeholders"]], "How to read this document": [[239, "how-to-read-this-document"]], "How to adopt this API": [[239, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[239, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[239, "discoverability-of-conforming-implementations"]], "Optional feature": [[239, null]], "Conformance": [[239, "conformance"]], "Terms and Definitions": [[239, "terms-and-definitions"]], "Normative References": [[239, "normative-references"]], "Usage Data": [[240, "usage-data"]], "Design": [[240, "design"]], "Usage": [[240, "usage"]], "Use in Decision-Making": [[240, "use-in-decision-making"]], "Use cases": [[241, "use-cases"]], "Types of use cases": [[241, "types-of-use-cases"]], "Concrete use cases": [[241, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[241, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[241, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[241, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[241, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[242, "verification-test-suite"]], "Measuring conformance": [[242, "measuring-conformance"]], "Running the tests": [[242, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "concat() (in module array_api)": [[77, "array_api.concat"]], "conj() (in module array_api)": [[78, "array_api.conj"]], "e (in module array_api.constants)": [[79, "array_api.constants.e"]], "inf (in module array_api.constants)": [[80, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[81, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[82, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[83, "array_api.constants.pi"]], "cos() (in module array_api)": [[84, "array_api.cos"]], "cosh() (in module array_api)": [[85, "array_api.cosh"]], "__eq__() (in module array_api.data_types)": [[86, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[87, "array_api.divide"]], "empty() (in module array_api)": [[88, 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diff --git a/2023.12/changelog.html b/2023.12/changelog.html
index af05091a5..024469843 100644
--- a/2023.12/changelog.html
+++ b/2023.12/changelog.html
@@ -701,18 +701,18 @@ <h5 id="id4">APIs<a class="headerlink" href="#id4" title="Link to this heading">
 <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this heading">¶</a></h4>
 <p>The following is a list of fixes and points of clarification with regard to the previous version of the specification:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__bool__</span></code>: fix typo in special case notes (<a class="reference external" href="https://github.com/data-apis/array-api/pull/785">gh-785</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__dlpack__</span></code>: resolve conflicting exception guidance (<a class="reference external" href="https://github.com/data-apis/array-api/pull/887">gh-887</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__getitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify broadcast behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/888">gh-888</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify required exception behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/897">gh-897</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">clip</span></code>: clarify that the operation is only defined when elements in <code class="docutils literal notranslate"><span class="pre">min</span></code> and <code class="docutils literal notranslate"><span class="pre">max</span></code> are inside the bounds of the input array data type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/814">gh-814</a>)</p></li>
@@ -726,7 +726,7 @@ <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this h
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.irfftn</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.hfft</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">linalg.solve</span></code>: clarify broadcasting semantics and output shape (<a class="reference external" href="https://github.com/data-apis/array-api/pull/810">gh-810</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-https://github.com/data-apis/array-api/pull/904</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-904</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">searchsorted</span></code>: fix incorrect boundary conditions (<a class="reference external" href="https://github.com/data-apis/array-api/pull/898">gh-898</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">sign</span></code>: fix equation in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/844">gh-844</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">tile</span></code>: fix missing return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/798">gh-798</a>)</p></li>
diff --git a/2023.12/searchindex.js b/2023.12/searchindex.js
index a3de01d77..d791dae7d 100644
--- a/2023.12/searchindex.js
+++ b/2023.12/searchindex.js
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229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "tupl": [0, 1, 13, 14, 26, 27, 32, 49, 57, 74, 78, 91, 99, 103, 115, 116, 134, 136, 138, 140, 143, 145, 147, 150, 154, 156, 166, 167, 168, 170, 174, 175, 179, 180, 181, 183, 184, 187, 190, 202, 236, 246, 247, 249, 251, 254, 260], "includ": [0, 1, 7, 9, 13, 14, 15, 16, 17, 20, 21, 23, 28, 30, 40, 41, 42, 43, 47, 51, 88, 107, 111, 115, 116, 118, 122, 132, 134, 136, 138, 150, 153, 164, 168, 170, 184, 189, 190, 199, 204, 205, 206, 207, 208, 209, 210, 211, 215, 240, 254, 256, 257, 259, 261, 262], "those": [0, 5, 7, 15, 23, 88, 90, 113, 115, 141, 143, 150, 153, 170, 199, 204, 207, 208, 211, 212, 214, 246, 249, 250, 252, 255, 256, 257, 260, 261, 262], "mean": [0, 26, 189, 202, 204, 208, 210, 211, 216, 257, 260], "var": [0, 189], "std": [0, 189], "which": [0, 1, 5, 7, 8, 13, 14, 15, 16, 17, 18, 19, 26, 30, 40, 41, 44, 59, 60, 63, 75, 77, 78, 83, 88, 91, 92, 95, 97, 98, 99, 101, 102, 103, 104, 107, 108, 111, 113, 114, 115, 122, 132, 134, 136, 138, 142, 143, 145, 146, 150, 152, 153, 156, 158, 163, 167, 168, 170, 171, 172, 176, 177, 179, 180, 181, 182, 183, 184, 185, 187, 188, 190, 204, 205, 206, 207, 208, 209, 210, 211, 212, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 240, 248, 249, 250, 252, 254, 255, 256, 257, 260, 261, 262], "some": [0, 96, 101, 113, 115, 125, 190, 205, 206, 207, 208, 211, 216, 260, 262, 263], "common": [0, 190, 199, 202, 211, 214, 215, 256, 260, 261, 262], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 90, 96, 101, 102, 111, 113, 115, 116, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 143, 153, 158, 168, 173, 179, 180, 181, 182, 184, 189, 190, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 232, 236, 237, 246, 248, 255, 256, 257, 260, 261, 262, 263], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 77, 88, 90, 102, 107, 109, 115, 116, 122, 134, 138, 141, 143, 150, 151, 153, 155, 157, 170, 175, 179, 180, 181, 182, 190, 197, 199, 204, 205, 206, 207, 208, 209, 210, 211, 214, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 252, 254, 255, 256, 257, 260, 261, 262], "numpi": [0, 19, 63, 190, 202, 207, 208, 210, 211, 256, 260, 261, 262, 263], "scalar": [0, 2, 49, 60, 189, 190, 214, 254, 262], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 105, 106, 107, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 145, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 171, 172, 173, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 199, 202, 204, 206, 208, 209, 210, 214, 216, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "rational": [0, 7, 88, 150, 170, 190, 210, 211, 252, 255, 257, 260], "alwai": [0, 12, 26, 42, 60, 63, 98, 102, 141, 154, 190, 202, 207, 208, 211, 236], "necessari": [0, 26, 60, 90, 102, 141, 154, 175, 190, 208, 260], "acceler": [0, 5, 107, 153, 202, 210], "where": [0, 1, 7, 13, 14, 15, 26, 47, 57, 65, 86, 87, 90, 94, 96, 97, 101, 103, 104, 124, 125, 126, 137, 141, 143, 147, 149, 153, 158, 159, 161, 162, 167, 168, 172, 173, 175, 183, 184, 185, 189, 190, 199, 204, 205, 207, 210, 211, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "non": [0, 1, 7, 13, 14, 16, 17, 63, 128, 129, 130, 131, 134, 136, 138, 143, 150, 168, 174, 184, 185, 190, 199, 204, 205, 211, 218, 220, 223, 224, 227, 228, 229, 231, 233, 234, 236, 240, 242, 249, 254, 262], "could": [0, 26, 179, 180, 181, 182, 202, 208, 215, 256, 260, 262], "forc": 0, "synchron": [0, 26, 59, 153, 260], "delai": [0, 24, 25, 29, 34, 35, 202, 214, 260], "execut": [0, 199, 202, 211, 213, 215, 260, 262], "model": [0, 57, 58, 90, 141, 207, 214, 262], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 90, 101, 137, 141, 162, 172, 173, 204, 206, 210, 211, 247, 261, 262], "futur": [0, 26, 102, 203, 207, 208, 211, 215, 216, 236, 237, 258, 260, 262], "python": [0, 2, 5, 7, 24, 25, 26, 29, 34, 35, 49, 60, 101, 102, 152, 189, 190, 202, 204, 207, 210, 212, 214, 215, 216, 257, 259, 260, 261], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 92, 94, 95, 96, 99, 100, 102, 104, 109, 117, 118, 119, 123, 124, 125, 126, 129, 133, 134, 136, 138, 140, 142, 143, 146, 147, 148, 150, 151, 153, 154, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 188, 190, 207, 208, 216, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 243, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "__pos__": [0, 189, 204], "po": 0, "__neg__": [0, 189, 204], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 88, 90, 95, 97, 99, 101, 118, 123, 125, 141, 149, 152, 156, 160, 164, 171, 174, 185, 189, 190, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 254, 260], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 152, 158, 169, 174, 185, 186, 204, 233, 239, 244, 248, 251, 253], "__add__": [0, 50, 189, 204], "add": [0, 7, 21, 88, 169, 170, 189, 190, 204, 205, 206, 211, 252], "__sub__": [0, 189, 204], "sub": [0, 190], "__mul__": [0, 189, 204], "mul": 0, "__truediv__": [0, 189, 204], "truediv": 0, "__floordiv__": [0, 189], "floordiv": 0, "__mod__": [0, 189], "mod": 0, "__pow__": [0, 189, 204], "pow": [0, 47, 189, 204, 206], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 79, 85, 86, 87, 88, 90, 94, 95, 96, 98, 100, 101, 102, 105, 106, 107, 109, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 141, 142, 148, 149, 150, 151, 152, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 197, 204, 205, 206, 207, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 260, 262, 263], "defin": [0, 5, 12, 23, 30, 41, 49, 60, 65, 79, 90, 101, 103, 104, 115, 122, 134, 135, 136, 138, 139, 140, 141, 152, 159, 164, 165, 168, 176, 177, 184, 185, 189, 192, 197, 204, 206, 207, 216, 220, 221, 224, 225, 228, 231, 232, 236, 237, 238, 245, 246, 248, 256, 261, 262, 263], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 152, 157, 158, 159, 160, 161, 162, 163, 164, 168, 170, 172, 173, 178, 184, 185, 187, 189, 199, 204, 207, 219, 222, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 257], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 184, 185, 186, 187, 188, 189, 192, 199, 202, 205, 207, 208, 211, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 258, 259, 260, 263], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 202, 205, 207, 208, 210, 212, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 260, 261], "__matmul__": [0, 189, 204], "matmul": [0, 40, 189, 199, 204, 256], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 199, 202, 204, 205, 206, 208, 209, 210, 211, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 257, 259, 260, 261, 262, 263], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 148, 149, 150, 157, 159, 165, 169, 170, 174, 199, 206, 218, 220, 223, 224, 227, 228, 229, 231, 233, 244, 245, 247, 252, 256, 260, 262], "__invert__": [0, 189], "inv": [0, 204, 256], "invert": [0, 68, 238, 241, 248], "__inv__": 0, "__and__": [0, 189], "__or__": [0, 189], "__xor__": [0, 189], "xor": [0, 72, 131], "__lshift__": [0, 189], "lshift": 0, "__rshift__": [0, 189], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 115, 116, 122, 134, 136, 138, 142, 149, 150, 152, 153, 155, 157, 158, 168, 170, 171, 178, 184, 185, 189, 190, 204, 206, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241, 242, 252, 254, 260], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 143, 186, 189, 199, 204], "__lt__": [0, 189, 204], "lt": 0, "__le__": [0, 189, 204], "le": 0, "__gt__": [0, 189, 204], "gt": [0, 246, 249], "__ge__": [0, 189, 204], "ge": 0, "__eq__": [0, 189, 204, 211], "eq": 0, "__ne__": [0, 189, 204], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 143, 149, 153, 156, 157, 161, 172, 173, 175, 179, 181, 185, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 218, 219, 220, 221, 223, 224, 225, 227, 228, 229, 230, 231, 233, 236, 237, 242, 245, 246, 249, 255, 256, 257, 260, 261, 262, 263], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 168, 184, 185, 189, 190, 199, 202, 204, 205, 207, 208, 210, 211, 212, 214, 216, 221, 233, 238, 245, 246, 248, 256, 257, 260, 261, 262, 263], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 168, 184, 190, 192, 202, 204, 206, 207, 208, 209, 210, 211, 212, 216, 233, 245, 255, 256, 259, 260, 262], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 144, 164, 189, 190, 199, 204, 207, 208, 210, 216, 249, 257, 259, 260, 263], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 144, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 170, 172, 173, 178, 179, 180, 181, 182, 190, 197, 202, 206, 207, 209, 211, 214, 219, 228, 230, 247, 249, 250, 252, 260, 262, 263], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 152, 163, 185, 190, 204, 207, 208, 212, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 260], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 154, 163, 168, 169, 170, 184, 185, 186, 199, 204, 207, 208, 212, 233, 240, 242, 245, 248, 254, 260, 262], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 153, 154, 158, 163, 168, 173, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 236, 246, 247, 249, 255, 256, 260, 261, 262], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 163, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 199, 206, 210, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 153, 158, 163, 171, 172, 173, 202, 205, 206, 207, 208, 209, 211, 256, 257, 260, 262], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 163], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 162, 163, 164, 167, 171, 173, 190, 197, 199, 204, 220, 221, 224, 225, 228, 231, 236, 237, 260], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 163, 172, 173, 190, 197, 206, 207, 220, 221, 224, 225, 228, 231, 236, 237, 249, 256], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 149, 158, 161, 162, 163, 172, 173, 186, 197, 199, 206, 207, 210, 213, 214, 216, 236, 237, 246, 247, 248, 249, 256, 260, 262, 263], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 110, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 149, 150, 152, 153, 155, 158, 159, 163, 164, 165, 168, 169, 170, 179, 180, 181, 182, 184, 185, 186, 189, 190, 199, 201, 202, 205, 207, 209, 210, 211, 216, 233, 240, 242, 245, 248, 254, 255, 260, 261, 262, 263], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 143, 153, 158, 163, 172, 173, 174, 179, 180, 181, 182, 190, 197, 199, 204, 206, 209, 210, 212, 227, 228, 236, 237, 240, 249, 250, 254, 256, 257, 260, 261], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 202, 218, 219, 220, 222, 223, 224, 227, 228, 230, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257, 260, 262, 263], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 145, 146, 154, 156, 158, 163, 167, 171, 174, 175, 176, 177, 183, 185, 187, 188, 189, 204, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 260, 262], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 157, 158, 159, 160, 161, 162, 164, 165, 167, 168, 169, 170, 172, 173, 174, 178, 179, 184, 190, 197, 199, 204, 206, 207, 208, 214, 232, 233, 235, 240, 241, 247, 248, 254, 260, 261, 262, 263], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 149, 152, 155, 161, 162, 164, 165, 167, 168, 169, 172, 173, 174, 184, 185, 186, 189, 204, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 155, 159, 161, 162, 164, 165, 167, 169, 172, 173, 174, 185, 186, 189, 190, 204, 207, 210, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256, 260, 262], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 168, 169, 170, 174, 184, 185, 186, 189, 204, 233, 240, 242, 245, 248, 254, 260], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 166, 167, 168, 169, 170, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 190, 199, 202, 204, 207, 208, 210, 211, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 238, 241, 245, 246, 247, 249, 250, 252, 255, 256, 260, 262], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 149, 152, 158, 171, 179, 180, 181, 182, 189, 190, 192, 199, 202, 204, 206, 207, 214, 215, 220, 221, 224, 225, 228, 231, 256, 257, 260, 261, 262, 263], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 204, 205, 207, 247, 252], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 190, 202, 204, 205, 206, 207, 208, 211, 212, 214, 246, 247, 249, 252, 256, 258, 260, 263], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 154, 156, 206, 207, 210, 211, 255, 260, 261, 262], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 144, 152, 162, 169, 172, 173, 174, 179, 180, 185, 204, 206, 209, 211, 236, 246, 249], "binari": [0, 5, 67, 70, 72, 172, 173, 205], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 157, 174, 176, 177, 179, 180, 181, 182, 185, 190, 199, 210, 211, 214, 215, 220, 221, 224, 225, 228, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262, 263], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 170, 172, 173, 178, 199, 204, 206, 247, 252], "assign": [0, 208], "exampl": [0, 5, 12, 23, 26, 115, 116, 167, 189, 190, 202, 207, 208, 209, 211, 214, 215, 216, 252, 256, 260, 262, 263], "after": [0, 1, 26, 40, 132, 164, 175], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 169, 189, 190, 199, 205, 207, 210, 256, 260, 261, 263], "modifi": [0, 26, 208, 259], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 143, 144, 145, 146, 149, 150, 157, 162, 163, 164, 168, 170, 171, 173, 174, 175, 179, 180, 181, 182, 184, 189, 190, 197, 204, 207, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 241, 242, 245, 246, 247, 248, 252, 260], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 152, 157, 171, 190, 199, 204, 207, 208, 242, 245, 248, 254, 260], "discuss": [0, 93, 144, 204, 210, 211, 215, 260, 261, 262], "copi": [0, 1, 26, 59, 60, 63, 102, 154, 163, 204, 205, 210, 211, 213, 259, 260], "view": [0, 102, 213], "behaviour": [0, 213, 260, 262], "mutabl": [0, 213], "via": [0, 26, 101, 102, 171, 190, 205, 210, 211, 215, 217, 245, 255, 256, 257, 260], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 155, 157, 167, 174, 190, 199, 202, 207, 218, 220, 223, 224, 227, 228, 229, 231, 242, 245, 256, 260, 262], "match": [0, 1, 5, 9, 20, 26, 63, 101, 152, 174, 179, 180, 212, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254, 262], "op": [0, 199], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 261, 263], "refer": [1, 13, 14, 96, 97, 125, 158, 168, 174, 175, 184, 185, 190, 207, 208, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 248], "automat": [1, 260], "implicit": [1, 210, 211, 214, 260], "expans": [1, 260], "size": [1, 13, 14, 88, 95, 122, 143, 156, 166, 171, 174, 185, 189, 190, 209, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 244, 246, 249, 260], "without": [1, 7, 26, 57, 102, 113, 115, 143, 153, 154, 179, 180, 181, 182, 202, 205, 206, 209, 259, 260, 262], "purpos": [1, 5, 96, 107, 125, 202, 247, 256, 258, 259, 262], "make": [1, 7, 202, 205, 206, 208, 210, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 257, 260], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 150, 167, 169, 170, 190, 202, 204, 208, 211, 212, 214, 225, 236, 246, 247, 249, 252, 256, 260, 261, 262], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 204, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 245, 246, 247, 249, 252, 260], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 144, 149, 151, 152, 169, 189, 204, 206, 260], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 149, 150, 152, 155, 161, 165, 170, 172, 174, 189, 190, 196, 199, 204, 207, 208, 209, 210, 211, 252, 256, 257, 260, 261, 262], "facilit": [1, 197, 202], "user": [1, 7, 26, 110, 173, 202, 205, 206, 208, 211, 215, 256, 260, 261, 262], "ergonom": 1, "encourag": [1, 260, 261], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 154, 205, 208, 211, 214, 256, 260, 262], "unnecessari": [1, 256], "can": [1, 7, 26, 60, 75, 110, 114, 116, 190, 199, 202, 205, 207, 208, 210, 211, 216, 245, 246, 249, 255, 256, 260, 261, 262, 263], "potenti": [1, 26, 96, 125, 153, 208, 260], "enabl": [1, 26, 102, 211, 215, 216, 260], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 143, 149, 153, 171, 179, 180, 181, 182, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 220, 221, 224, 225, 228, 231, 247, 256, 257, 260, 261, 263], "memori": [1, 26, 60, 102, 202, 208, 209, 211, 260, 262], "effici": [1, 202, 208], "through": [1, 60, 65, 255, 257, 261, 262], "vector": [1, 40, 132, 137, 185, 233, 244, 249, 250, 254, 256, 260], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 190, 246, 249, 256, 261, 262], "consumpt": [1, 26, 261], "cach": 1, "local": [1, 211], "given": [1, 23, 99, 122, 156, 158, 183, 199, 204, 207, 208, 211, 212, 216, 237, 247, 256, 257, 260, 262], "involv": [1, 12, 90, 101, 141, 149, 155, 199, 204, 206, 207, 211, 215], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 150, 166, 168, 170, 175, 184, 240, 254, 260], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 149, 156, 160, 161, 162, 171, 172, 173, 174, 176, 177, 179, 180, 181, 190, 208, 222, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 143, 145, 146, 153, 158, 166, 171, 179, 180, 181, 182, 185, 190, 202, 204, 205, 207, 208, 210, 211, 214, 215, 216, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 231, 244, 245, 246, 254, 256, 257, 260, 262], "virtual": 1, "repeat": [1, 189, 190, 204, 262], "across": [1, 5, 90, 101, 141, 173, 204, 206, 207, 211, 255, 260], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 149, 154, 156, 158, 168, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 220, 224, 228, 231, 233, 236, 240, 259, 260], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 187, 188, 190, 205, 207, 211, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 252, 254, 255, 256, 260, 262], "unequ": 1, "lower": [1, 77, 97, 176, 232], "higher": [1, 5, 26, 190, 205, 256, 261], "prepend": [1, 40, 95, 132, 175], "until": [1, 26, 175], "store": [1, 26, 211, 252], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 160, 161, 162, 164, 165, 169, 171, 172, 173, 174, 179, 180, 181, 182, 185, 186, 199, 204, 207, 210, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 235, 238, 240, 241, 242, 244, 245, 246, 247, 248, 252, 254, 256, 260], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 144, 150, 153, 158, 159, 162, 164, 168, 170, 173, 175, 184, 185, 190, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 246, 248, 249, 252], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 144, 159, 162, 164, 167, 173, 185, 190, 204, 207, 208, 212, 245, 248, 262], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 149, 150, 170, 173, 174, 185, 190, 204, 207, 208, 210, 214, 216, 233, 252, 256, 260, 261], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 144, 149, 150, 170, 192, 199, 204, 207, 210, 214, 219, 230, 252, 260], "shape2": 1, "n1": [1, 137], "len": [1, 137, 175], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 175, 189, 190, 204, 240, 242, 245], "temporari": 1, "list": [1, 73, 78, 110, 114, 137, 167, 190, 202, 204, 211, 260, 262], "length": [1, 15, 107, 137, 154, 174, 190, 219, 221, 222, 225, 230, 249, 250], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 158, 168, 179, 180, 184, 189, 190, 197, 202, 204, 207, 208, 209, 211, 214, 245, 256, 261, 262, 263], "d1": 1, "els": [1, 26, 202, 261], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 160, 163, 168, 176, 177, 179, 181, 182, 184, 189, 190, 204, 205, 206, 207, 208, 211, 212, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 242, 245, 246, 248, 249, 255, 256, 260, 262, 263], "th": [1, 97, 175, 190, 204, 220, 224, 228, 231], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 143, 153, 167, 171, 183, 190, 199, 202, 204, 206, 208, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 245, 257, 260, 261, 262], "demonstr": 1, "applic": [1, 26, 88, 150, 153, 170, 199, 204, 252, 256, 260, 261], "4d": 1, "8": [1, 5, 7, 27, 175, 199, 202], "6": [1, 7, 175], "3d": 1, "7": [1, 7, 27, 216], "5": [1, 190, 260], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 152, 197, 202, 204, 205, 207, 208, 210, 211, 212, 256, 257, 259, 260, 262, 263], "doe": [1, 15, 26, 102, 144, 171, 190, 199, 202, 205, 206, 207, 208, 209, 211, 212, 214, 216, 256, 260, 262, 263], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 167, 169, 174, 179, 180, 181, 185, 186, 233, 236, 244, 246, 247, 249, 250, 260], "append": [1, 40, 69, 95, 132, 235], "As": [1, 122, 149, 179, 180, 181, 182, 202, 210, 216, 262], "impli": [1, 179, 180, 181, 182, 259, 260], "__setitem__": [1, 171, 189, 204], "Such": [1, 206, 256], "right": [1, 69, 71, 107, 158, 164, 205, 249, 259], "hand": [1, 199], "left": [1, 5, 60, 69, 101, 103, 158, 171, 190, 199, 236, 237, 249, 260], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 143, 158, 167, 171, 174, 179, 180, 181, 189, 204, 220, 224, 228, 231, 260, 262], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 153, 174, 190, 205, 206, 207, 208, 209, 210, 218, 220, 223, 224, 225, 227, 228, 229, 231, 249, 250, 256, 260, 261, 262], "empti": [1, 13, 14, 15, 150, 170, 189, 190, 204, 252, 260], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 149, 154, 174, 190, 204, 205, 206, 208, 211, 214, 215, 256, 262], "NOT": [1, 129, 259], "adher": [2, 7, 8, 189, 190, 202, 255, 260], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 149, 164, 189, 190, 197, 207, 211, 255, 256, 261], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 148, 149, 151, 152, 153, 156, 157, 158, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 178, 179, 180, 190, 202, 204, 206, 210, 214, 216, 228, 232, 233, 234, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 255, 256, 260, 261, 262], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 145, 146, 187, 188, 196, 202, 211, 219, 230, 256, 260], "main": [5, 97, 176, 177, 205, 210, 235, 252, 255, 262], "namespac": [5, 7, 23, 110, 192, 202, 204, 217, 255, 256, 257, 260, 263], "under": [5, 255, 259, 260], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 145, 150, 152, 153, 156, 166, 167, 170, 171, 175, 176, 177, 179, 180, 181, 182, 185, 187, 190, 199, 204, 206, 207, 208, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 235, 252, 254, 256, 257, 260, 262, 263], "name": [5, 7, 23, 26, 101, 115, 179, 180, 181, 190, 207, 236, 245, 246, 247, 249, 255, 260, 261], "descript": [5, 7, 204, 206, 240, 254], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 184, 199, 204, 214, 232, 240, 249, 254], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 143, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 186, 190, 204, 232, 240, 249, 254, 256], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 190, 232, 240, 249, 254], "int8": [5, 115, 116, 199], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 150, 160, 170, 199, 204, 206, 252], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 149, 150, 152, 158, 160, 162, 164, 170, 173, 179, 180, 181, 182, 189, 197, 204, 207, 246, 247, 252], "exist": [5, 7, 26, 60, 78, 102, 202, 204, 207, 210, 211, 212, 238, 257, 260, 261], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 167, 174, 176, 177, 183, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 257], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 150, 170, 199, 252], "16": [5, 199], "32": [5, 199], "767": 5, "int32": [5, 88, 115, 116, 150, 170, 199, 252], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 150, 170, 199, 252], "64": [5, 199], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 199], "unsign": [5, 88, 115, 116, 150, 170, 189, 252], "255": 5, "uint16": [5, 88, 115, 116, 150, 170, 199, 252], "65": 5, "535": [5, 204], "uint32": [5, 88, 115, 116, 150, 170, 199, 252], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 199], "18": 5, "446": [5, 204], "744": [5, 204], "073": 5, "709": [5, 204], "551": [5, 204], "615": 5, "float32": [5, 109, 115, 116, 151, 199, 247, 249, 250], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 204, 206, 207, 260], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 204, 206, 207, 260], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 179, 180, 189, 199, 204, 205, 207, 210, 211, 216, 256, 260, 261, 262], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 151, 164, 199, 204, 206, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 254, 260], "2019": [5, 12, 90, 96, 107, 125, 141, 189, 206, 260, 262], "float64": [5, 9, 20, 115, 116, 199, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "doubl": [5, 174, 199, 204], "complex64": [5, 109, 115, 116, 151, 199, 204, 247, 249, 250], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 157, 162, 164, 173, 204, 207], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 151, 157, 162, 164, 172, 173, 179, 180, 181, 182, 204, 207, 221, 230], "complex128": [5, 9, 20, 115, 116, 199, 204, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "method": [5, 26, 34, 102, 189, 192, 202, 208, 210, 211, 214, 215, 216, 260, 261, 262], "attribut": [5, 23, 98, 108, 189, 201, 204, 257, 260, 261, 262], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 150, 164, 167, 170, 171, 173, 179, 180, 182, 183, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252, 255, 256, 260, 261, 262], "beyond": [5, 156, 199, 204, 260], "It": [5, 23, 26, 102, 202, 208, 210, 260, 262, 263], "also": [5, 7, 26, 34, 102, 107, 159, 199, 202, 207, 208, 209, 210, 216, 220, 224, 228, 231, 249, 255, 262], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 143, 176, 177, 190, 232, 236, 237, 238, 246, 248, 249, 250, 252, 260], "denorm": [5, 107], "gradual": [5, 107, 260], "underflow": [5, 9, 90, 101, 107, 247], "hardwar": [5, 53, 107, 153, 206, 210, 211, 236, 249, 256, 260], "univers": [5, 107, 205, 211, 256, 260], "mani": [5, 107, 175, 260, 262], "platform": [5, 26, 107], "compil": [5, 107, 173, 202, 205, 209, 260], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 206, 261], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 173, 190, 242, 245, 263], "time": [5, 7, 16, 17, 26, 107, 153, 179, 180, 202, 204, 209, 210, 215, 232, 236, 237, 238, 246, 248, 249, 256, 260, 262], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 143, 150, 153, 158, 164, 168, 170, 179, 180, 181, 182, 184, 190, 199, 206, 207, 208, 209, 211, 240, 246, 254, 256], "vari": [5, 107, 158, 173, 179, 180, 181, 182, 199, 206], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 143, 149, 150, 152, 153, 154, 159, 161, 162, 163, 164, 167, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 184, 185, 189, 192, 202, 204, 205, 207, 208, 209, 210, 211, 214, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 242, 245, 246, 247, 248, 249, 250, 252, 255, 256, 257, 260, 261, 262], "access": [5, 26, 32, 102, 110, 190, 204, 210, 255, 257, 260], "variou": [5, 204], "cast": [5, 29, 49, 60, 63, 75, 88, 150, 170, 199, 207, 252, 260, 262], "introspect": 5, "isdtyp": [5, 189, 204], "integr": [5, 63, 77, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 150, 170, 189, 204, 208, 211, 215, 216, 252, 256, 257, 260, 261, 262], "affect": [5, 15, 49, 208, 211], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 149, 150, 161, 162, 164, 168, 169, 170, 172, 173, 184, 204, 247], "implementor": [5, 255], "free": [5, 211, 259], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 149, 150, 153, 154, 158, 168, 170, 173, 184, 186, 189, 190, 199, 204, 205, 207, 208, 209, 210, 212, 214, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 238, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 216], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 143, 149, 150, 161, 162, 166, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 184, 190, 199, 202, 207, 210, 211, 214, 215, 233, 240, 248, 249, 252, 254, 256, 257, 260, 262, 263], "wai": [5, 26, 63, 102, 202, 205, 211, 212, 257, 260, 261, 262, 263], "f4": [5, 199], "ensur": [5, 26, 158, 202, 206, 256, 260, 261, 262], "portabl": [5, 59, 122, 206, 208, 211, 212, 260], "consum": [5, 26, 63, 113, 115, 202, 207, 208, 216, 255, 260, 261], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 152, 168, 184, 197, 204, 206, 210, 211, 260], "guidanc": [5, 7, 49, 204, 205, 212, 260], "govern": [5, 50, 169, 199, 256, 257], "interact": [5, 207], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 150, 152, 159, 160, 161, 164, 170, 172, 173, 174, 190, 206, 207, 208, 212, 216, 247, 252, 260, 261, 263], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 154, 160, 204, 211, 232, 236, 237, 246, 248, 255, 259, 260, 262], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 150, 153, 154, 158, 159, 168, 170, 184, 185, 186, 189, 190, 202, 211, 232, 234, 240, 247, 248, 254, 259], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 189, 190, 204, 210, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 261, 262, 263], "possibl": [5, 26, 60, 101, 102, 134, 138, 154, 172, 173, 202, 205, 206, 207, 208, 210, 211, 212, 214, 216, 256, 260, 261, 262, 263], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 150, 168, 170, 184, 190, 202, 205, 207, 210, 211, 215, 216, 237, 238, 256, 257, 260, 262], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 144, 150, 152, 159, 170, 189, 190, 192, 199, 206, 207, 210, 212, 227, 228, 246, 247, 249, 252, 256, 257, 261, 262, 263], "clearli": [5, 59, 116, 197, 207, 256, 257], "warn": [5, 153, 212], "about": [5, 7, 26, 98, 108, 208, 256, 260, 262, 263], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 152, 168, 175, 176, 177, 184, 190, 197, 202, 204, 205, 206, 207, 208, 210, 211, 214, 216, 220, 224, 228, 231, 245, 249, 250, 256, 257, 260, 262], "organ": [5, 204, 256, 261, 262], "within": [5, 15, 27, 190, 199, 202, 204, 207, 211, 218, 220, 223, 224, 227, 228, 229, 231, 260], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 149, 158, 159, 168, 184, 185, 190, 204, 206, 207], "These": [5, 208, 236, 261], "intend": [5, 88, 150, 170, 202, 252], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 143, 152, 156, 160, 162, 164, 173, 189, 190, 202, 204, 206, 216, 230, 232, 246, 261], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 202, 204, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256], "extern": [7, 262], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 152, 168, 184, 202, 257], "call": [7, 34, 210, 211, 214, 247, 260, 261, 262], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 150, 155, 158, 161, 164, 170, 172, 173, 174, 189, 199, 206, 208, 210, 211, 218, 220, 223, 224, 227, 228, 229, 231, 252, 256, 260, 261, 262], "map": [7, 207, 208], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 149, 179, 180, 181, 182, 190, 204, 208, 214, 216, 256, 257, 260, 261, 262], "sole": [7, 190, 197, 256], "incompat": [7, 26, 74, 102, 202, 257, 260], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 156, 179, 181, 189, 190, 199, 204, 206, 207, 208, 209, 211, 212, 215, 216, 217, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 256, 257, 258, 259, 260, 263], "normal": [7, 78, 167, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231], "practic": [7, 19, 190, 256, 261], "avail": [7, 102, 114, 202, 210, 255, 257, 261], "still": [7, 26, 216, 256, 261, 262, 263], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 179, 180, 181, 182, 207, 211, 230, 245, 256, 260, 262, 263], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 168, 184, 206, 209, 211, 257, 260], "altern": [7, 208, 210, 263], "thei": [7, 26, 199, 205, 210, 211, 215, 216, 255, 256, 257, 260, 262, 263], "were": [7, 101, 153, 158, 204, 260], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 189, 204, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 256, 261, 262], "lead": [7, 101, 207, 246, 249, 260], "readabl": [7, 199, 256, 261], "code": [7, 59, 199, 208, 209, 211, 214, 216, 256, 260, 261, 262], "easier": [7, 202, 208, 256], "evolv": [7, 202, 256], "over": [7, 13, 14, 26, 122, 134, 136, 138, 150, 168, 170, 171, 174, 184, 185, 206, 207, 208, 210, 211, 215, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 252, 254, 256, 260], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 157, 159, 161, 162, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 190, 203, 204, 205, 211, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "worri": 7, "xi": [7, 137], "annot": [7, 204, 216, 260], "individu": [7, 211, 214, 215, 216, 219, 230, 260, 261], "aim": [7, 205, 216, 255, 256, 257, 260, 261, 262, 263], "strongli": [7, 208, 262], "look": [7, 262], "like": [7, 202, 205, 207, 208, 214, 216, 257, 260, 261, 262], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 190, 204, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 260, 261, 263], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 204, 205, 208, 210, 214, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 259, 262], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 145, 147, 150, 153, 154, 156, 163, 166, 167, 168, 170, 171, 174, 175, 176, 177, 183, 184, 185, 187, 190, 199, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 240, 241, 251, 252, 253, 254, 261], "str": [7, 8, 23, 115, 116, 137, 261], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 204, 262], "few": [7, 206, 214, 260, 262], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 143, 145, 146, 150, 153, 154, 156, 158, 163, 167, 168, 170, 174, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 204, 206, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 240, 242, 245, 246, 249, 252, 254], "form": [7, 23, 26, 40, 79, 132, 133, 176, 177, 208, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 257, 261], "question": [7, 205, 260], "commonli": [7, 168, 184, 205, 207, 209, 255, 256, 260, 261], "written": [7, 202, 260, 262], "yyyi": [8, 23, 257], "mm": [8, 23, 257], "string": [8, 23, 115, 116, 204, 257, 260], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 189, 202, 205, 211, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 258, 260, 262], "absolut": [9, 20, 85, 159, 206, 208, 240, 241, 247, 256], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 148, 151, 157, 159, 160, 161, 162, 164, 165, 168, 172, 173, 178, 184], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 197, 202, 204, 207, 209, 211, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 249, 250, 252, 254, 256, 260, 262], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 204, 249, 250], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 172, 173, 204, 206, 210, 261], "known": [9, 159, 206, 209, 210], "norm": [9, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 254, 256], "modulu": [9, 152], "z": [9, 10, 11, 61, 62, 64, 66, 123, 207], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 150, 153, 168, 170, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 209, 214, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 159, 161, 162, 172, 173, 207, 236, 237, 247, 249], "sqrt": [9, 10, 11, 61, 62, 189, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 254], "take": [9, 123, 125, 149, 164, 189, 204, 211, 216, 260], "care": [9, 208, 256], "undu": [9, 209], "overflow": [9, 12, 88, 90, 101, 107, 122, 150, 170, 199, 247, 252, 256], "dure": [9, 40, 59, 107, 132, 168, 184, 199, 202, 245, 260, 261], "stage": [9, 107, 257], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 187, 190, 204, 206, 207, 208, 210, 214, 215, 219, 220, 221, 224, 225, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 152, 157, 158, 159, 160, 161, 162, 164, 168, 172, 173, 178, 179, 180, 181, 182, 184, 189, 197, 204, 207, 260], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 144, 149, 152, 157, 160, 161, 162, 164, 172, 173, 178, 207, 247, 254], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 144, 157, 159, 162, 164, 173, 189, 204, 205, 260, 261, 262], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 117, 118, 123, 125, 141, 144, 149, 152, 160, 162, 164, 173, 206], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 149, 161, 162, 172, 173, 206, 242, 245], "princip": [10, 11, 61, 62, 64, 66, 123, 164, 207, 256], "invers": [10, 11, 61, 62, 64, 65, 66, 207, 218, 220, 223, 224, 225, 226, 227, 228, 229, 231, 238, 241, 245, 256], "cosin": [10, 11, 86, 87, 173], "express": [10, 61, 63, 64, 65, 86, 161, 172, 190, 199, 208, 256, 259], "radian": [10, 61, 64, 65, 86, 161, 172], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 159, 161, 162, 172, 173, 207, 247], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 162, 172, 173, 189], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 158, 159, 161, 162, 164, 172, 173, 190, 207, 236, 249, 252], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 162, 164, 173, 189, 204], "multi": [10, 11, 61, 62, 64, 66, 189, 207, 210, 211, 233, 262], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 149, 161, 162, 164, 172, 173, 260], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 149, 161, 162, 164, 172, 173, 260], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 161, 162, 164, 172, 173, 260], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 149, 150, 164, 168, 170, 184, 185, 206, 207, 233, 256, 261], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 145, 146, 156, 187, 188, 189, 197, 199, 204, 208, 211, 219, 230, 245], "line": [10, 11, 61, 62, 64, 66, 172, 173, 199, 207, 260, 261, 262, 263], "segment": [10, 11, 61, 62, 64, 66, 207], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 149, 164, 207], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 149, 150, 153, 156, 163, 164, 166, 167, 168, 170, 171, 174, 175, 183, 184, 185, 189, 204, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 240, 253, 254, 260], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 150, 164, 170, 190, 204, 210, 252, 260], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 150, 153, 156, 163, 164, 167, 168, 170, 171, 172, 173, 175, 183, 184, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 252, 254, 256], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 149, 164, 207, 257], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 149, 152, 158, 159, 160, 162, 164, 166, 173, 189, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 149, 150, 152, 158, 159, 160, 162, 164, 166, 168, 170, 171, 173, 178, 179, 180, 181, 182, 184, 190, 199, 202, 205, 208, 211, 212, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 240, 241, 242, 245, 252, 254, 256, 257, 260, 262], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 149, 152, 158, 159, 160, 164, 168, 184, 189, 190, 204, 208, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 241, 242, 245, 254, 260], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 145, 146, 159, 162, 164, 173, 207, 247], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 162, 173, 189, 190, 204, 245], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 161, 162, 172, 173, 207], "aco": [11, 61, 189, 204, 206], "simpli": [11, 96, 125, 205, 216, 260, 262], "upper": [11, 77, 97, 177, 204, 232, 246], "half": [11, 15, 66, 122, 140, 164, 174, 190, 221], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 150, 189, 204, 240, 252, 254, 256], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 156, 167, 169, 172, 173, 174, 179, 180, 181, 185, 186, 190, 207, 233, 236, 244, 246, 247, 249, 250, 256, 260, 261, 262, 263], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 144, 152, 154, 159, 190, 208, 231], "neither": [12, 40, 90, 101, 132, 141, 174, 249, 261], "nor": [12, 90, 101, 141, 249, 261], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 161, 162, 172, 173, 189, 207, 240, 254], "round": [12, 15, 76, 90, 100, 101, 141, 164, 178, 189, 204, 206], "nearest": [12, 90, 141, 157, 178, 206], "mode": [12, 90, 141, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 246], "too": [12, 26, 90, 101, 141, 256, 260], "larg": [12, 90, 101, 141, 210, 216, 247, 260], "appropri": [12, 26, 90, 101, 141, 207, 212], "commut": 12, "associ": [12, 42, 141, 192, 199, 242, 245, 248, 256, 259, 261], "tabl": [12, 90, 141, 189], "c": [12, 90, 93, 122, 141, 143, 144, 153, 167, 168, 173, 184, 190, 204, 207, 210, 213, 232, 236, 237, 238, 246, 248, 249, 257, 259, 260, 262], "d": [12, 90, 93, 122, 141, 144, 199, 219, 230], "dj": [12, 90, 141], "independ": [12, 90, 141, 157, 190, 202, 210, 233, 246, 248, 256, 257, 260], "abov": [12, 88, 90, 93, 123, 125, 141, 144, 149, 150, 164, 170, 176, 177, 190, 199, 207, 208, 210, 211, 214, 235, 236, 252, 256, 259, 262], "similarli": [12, 57, 116, 137, 199, 232, 249], "henc": [12, 79, 95, 143, 153, 179, 180, 181, 182, 190, 205, 207, 208, 209, 210, 214, 215, 216, 260, 262], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 240, 254], "test": [13, 14, 89, 117, 118, 119, 204, 206, 258, 260, 261, 262], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 148, 159, 160, 165, 202, 260], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 145, 150, 153, 155, 156, 166, 167, 168, 170, 174, 184, 187, 221, 225, 240, 242, 245, 254, 261], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 147, 150, 156, 166, 168, 170, 174, 175, 184, 185, 190, 204, 220, 221, 224, 225, 228, 231, 233, 240, 245, 248, 251, 254], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 144, 211, 214, 220, 224, 228, 231], "AND": [13, 67, 93, 128, 259], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 150, 161, 162, 168, 170, 184], "valid": [13, 14, 26, 27, 95, 114, 140, 158, 167, 174, 183, 190, 206, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 236, 246, 249, 261], "count": [13, 14, 78, 88, 99, 171, 179, 180, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 237], "last": [13, 14, 18, 19, 55, 78, 88, 99, 156, 163, 167, 171, 174, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 240, 246, 249, 252], "invalid": [13, 14, 23, 95, 212, 260], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 143, 149, 154, 166, 167, 183, 185, 190, 199, 202, 204, 210, 211, 212, 214, 233, 241, 260], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 150, 168, 170, 184, 199, 211, 216, 260, 262], "OR": [14, 24, 70, 130, 144, 259], "start": [15, 122, 190, 204, 216, 260, 262], "stop": [15, 122, 190, 204, 261], "step": [15, 122, 190, 261], "evenli": [15, 122], "space": [15, 122, 219, 221, 230], "open": [15, 122, 140, 174, 190], "inclus": [15, 190, 260], "end": [15, 65, 86, 122, 159, 161, 172, 173, 197, 208, 247, 260, 261, 262], "exclus": [15, 190], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 144, 149, 167, 179, 180, 181, 182, 199, 207, 208, 211, 219, 230, 256, 260, 262], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 145, 146, 154, 156, 158, 166, 167, 171, 175, 187, 188, 202, 204, 207, 208, 211, 213, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 229, 230, 231, 252, 260], "infer": [15, 60, 63, 92, 103, 104, 146, 154, 188, 209, 256, 261], "cannot": [15, 26, 57, 102, 172, 173, 204, 207, 209, 260], "guarante": [15, 59, 179, 181, 202, 207, 211, 260, 262], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 172, 173, 199, 206, 247, 260], "ceil": [15, 189], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 143, 156, 158, 159, 171, 174, 176, 177, 179, 181, 190, 199, 204, 254, 260], "occur": [16, 17, 75, 107, 172, 173, 179, 180, 181, 182, 207, 261], "occurr": [16, 17, 179], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 144, 163, 189, 204, 207, 257, 261], "search": [16, 17, 158, 189], "flatten": [16, 17, 78, 153, 156, 179, 180, 181, 182, 254, 256], "descend": [18, 163, 249, 250], "stabl": [18, 163, 210], "sort": [18, 158, 189, 204, 236, 237, 249, 250], "ascend": [18, 158, 163, 204], "stabil": [18, 163], "maintain": [18, 163, 205, 260, 262], "rel": [18, 19, 55, 99, 135, 139, 156, 163, 204, 235, 242, 245, 252], "compar": [18, 163, 179, 180, 181, 182, 206, 211, 261, 263], "properti": [19, 53, 54, 55, 56, 57, 58, 115, 204, 207, 211, 216, 260], "transpos": [19, 40, 55, 132, 133, 174, 232, 236, 245, 249, 256], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 89, 199, 202, 204, 211], "permut": [19, 55, 147], "revers": [19, 55, 65, 99], "origin": [19, 55, 65, 107, 140, 154, 156, 204, 208, 218, 220, 223, 224, 227, 228, 229, 231, 260, 261], "limit": [19, 98, 108, 116, 206, 256, 259], "matric": [19, 40, 55, 132, 133, 137, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "deviat": [19, 168, 206, 212, 260, 262], "et": [19, 249, 250], "al": 19, "intent": [19, 65], "found": [19, 207, 210, 262, 263], "problemat": [19, 63, 205, 208], "conflict": [19, 204], "definit": [19, 86, 87, 161, 162, 172, 173, 204, 232, 261], "batch": [19, 254, 256], "cetera": [19, 249, 250], "permute_dim": [19, 189], "interfac": [19, 210, 256, 260, 262], "ab": [20, 107, 149, 189, 204, 240, 254], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 189, 204], "api_vers": [23, 260], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 189, 190, 199, 202, 204, 208, 210, 211, 214, 216, 255, 257, 261, 262], "2020": [23, 216, 257, 259, 260], "10": [23, 27, 124, 190, 260], "latest": [23, 210], "modul": [23, 202, 257, 261, 262, 263], "everi": [23, 103, 104, 246, 260], "top": [23, 202, 260, 262], "level": [23, 199, 205, 210, 211, 255, 256, 260, 261], "public": [23, 255, 261, 262], "well": [23, 205, 207, 210, 211, 246, 262, 263], "part": [23, 35, 176, 177, 199, 204, 210, 215, 257, 260, 262], "convert": [24, 25, 29, 34, 35, 60, 102, 199, 204, 205, 207, 210, 260, 262], "handl": [24, 26, 61, 64, 86, 88, 102, 124, 126, 149, 150, 159, 161, 165, 170, 172, 204, 205, 207, 208, 211, 212, 252, 260], "lazi": [24, 25, 29, 34, 35, 202, 204, 213, 262], "languag": [24, 25, 29, 34, 35, 208, 212, 214, 256, 260, 262], "therefor": [24, 25, 29, 34, 35, 202, 210, 211, 212, 214, 216, 257, 260, 262], "abl": [24, 25, 29, 34, 35, 102, 208, 210, 211, 260, 262], "kind": [24, 25, 26, 29, 34, 35, 47, 51, 77, 90, 98, 102, 104, 108, 113, 115, 116, 149, 199, 204, 214, 256, 259], "here": [24, 25, 26, 29, 34, 35, 190, 199, 208, 210, 215, 216, 262], "valueerror": [24, 25, 29, 34, 35, 60, 102, 154, 166, 262], "instead": [24, 25, 29, 34, 35, 63, 207, 210, 214, 261, 262], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 88, 102, 107, 134, 135, 138, 139, 140, 150, 153, 158, 160, 170, 171, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252], "new": [25, 26, 77, 79, 85, 88, 95, 98, 102, 103, 104, 107, 108, 109, 116, 135, 139, 140, 145, 146, 151, 153, 154, 158, 160, 167, 171, 175, 183, 187, 188, 202, 204, 205, 208, 210, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 257, 260, 261, 262], "stream": [26, 59, 211], "max_vers": [26, 204], "dl_devic": [26, 204], "enum": [26, 27], "pycapsul": 26, "export": [26, 102, 204, 210, 261], "from_dlpack": [26, 27, 189, 204, 210], "dlpack": [26, 27, 102, 204], "capsul": 26, "cuda": [26, 27, 205, 210, 262], "rocm": [26, 27, 205], "pointer": 26, "produc": [26, 236, 246, 249, 262], "instruct": 26, "safe": [26, 122], "insert": [26, 95, 158, 204], "wait": 26, "event": [26, 259], "larger": [26, 98, 156, 168, 184, 245], "below": [26, 101, 102, 176, 177, 192, 210, 211, 235, 252], "signal": [26, 222, 226, 262], "ownership": 26, "stai": 26, "On": 26, "cpu": [26, 27, 202, 205, 210, 211, 256, 260, 262], "queue": [26, 59, 211], "similar": [26, 152, 190, 205, 207, 209, 260, 261, 262], "mechan": [26, 102, 202, 204, 205, 213, 255, 260], "most": [26, 202, 211, 236, 256, 260, 262], "yet": [26, 216, 260], "sycl": 26, "want": [26, 90, 141, 205, 209, 210, 260, 262, 263], "cl": 26, "agre": 26, "assum": [26, 86, 102, 161, 172, 202, 207, 211, 255, 260], "legaci": 26, "per": [26, 153, 205, 210, 258], "thread": [26, 260, 262], "disallow": 26, "due": [26, 42, 57, 58, 122, 141, 153, 171, 206, 207, 256, 260], "ambigu": [26, 63, 101, 208], "construct": [26, 175, 202, 204, 205, 214, 260], "particular": [26, 190, 205, 207, 210, 211, 216, 256, 259, 260, 262, 263], "kdlcpu": 26, "safeti": [26, 59], "prefer": [26, 101, 202, 256, 262], "develop": [26, 206, 260, 261, 262, 263], "who": [26, 206, 260, 261], "think": 26, "cost": 26, "caller": 26, "major": [26, 143, 153, 190, 257], "minor": [26, 257], "verifi": [26, 260], "even": [26, 90, 141, 149, 157, 206, 207, 208, 219, 221, 225, 230, 246, 256, 260, 262], "pass": [26, 65, 202, 206, 211], "format": [26, 27, 204, 257], "__dlpack_device__": [26, 102, 189, 210], "buffererror": [26, 102, 204, 210], "v2023": [26, 102], "mandat": [26, 102, 260], "offer": [26, 102, 205, 210, 211, 215, 260, 262], "referenc": [26, 260], "underli": [26, 67, 70, 72, 102, 206, 247, 256], "interpret": [26, 102, 107, 207, 208, 263], "enumer": 26, "made": [26, 102, 202, 207, 255, 257, 260, 262], "never": [26, 60, 102, 154, 210, 260], "deem": [26, 102], "cross": [26, 102, 204, 211, 256, 260], "movement": [26, 102], "request": [26, 102, 260], "reus": [26, 60, 102, 208, 260], "buffer": [26, 60, 102, 208, 210], "happen": [26, 102, 208, 211, 214, 256], "dlpack_flag_bitmask_is_copi": 26, "flag": 26, "understood": [26, 199], "interchang": [26, 102, 202, 205, 213, 260], "detail": [26, 32, 49, 102, 143, 153, 179, 180, 181, 182, 189, 190, 201, 202, 209, 211, 215, 256, 260, 262], "stride": [26, 102, 208, 210], "fail": [26, 102, 260], "reason": [26, 102, 152, 173, 208, 210, 212, 256, 260, 261], "incorrect": [26, 204], "scheme": [26, 257], "semver": 26, "abi": [26, 205, 210], "break": [26, 212], "introduc": [26, 63, 101, 156, 216, 261], "goe": 26, "togeth": [26, 199, 210], "dlmanagedtensorvers": 26, "struct": 26, "later": 26, "introduct": 26, "becaus": [26, 199, 205, 208, 211, 212, 214, 216, 236, 249, 260, 262, 263], "keep": [26, 199, 205, 260], "march": 26, "2025": [26, 259], "onward": 26, "ideal": [26, 256], "late": 26, "okai": 26, "we": [26, 207, 249, 260], "get": [26, 98, 108, 205, 208, 210, 211], "now": [26, 102, 214, 260, 262], "our_own_dlpack_vers": 26, "fill": [26, 103, 104, 145, 146, 187, 188, 204], "field": [26, 179, 180, 181, 207, 236, 246, 247, 249, 260], "understand": [26, 245, 260, 261], "u": [26, 232, 245, 249], "just": [26, 260, 262], "our": 26, "elif": 26, "fine": [26, 216, 260], "own": [26, 202, 208, 260], "re": [26, 156, 205, 208, 216, 262], "intern": [26, 262], "did": 26, "older": [26, 173, 210, 257, 260], "around": [26, 261], "y": [26, 65, 102, 207, 208, 262], "dlmanagedtensor": 26, "so": [26, 98, 102, 110, 190, 197, 210, 256, 259, 260, 263], "tell": 26, "old": 26, "exchang": [26, 102, 210], "And": [26, 190, 211], "try": [26, 216, 260], "succe": 26, "info": [26, 110], "dltensor_vers": 26, "need": [26, 190, 205, 206, 208, 210, 212, 216, 256, 257, 260, 261, 262, 263], "used_dltensor_vers": 26, "done": [26, 202], "typeerror": [26, 29, 34, 35, 260, 262], "read": [26, 204, 208], "dlpack_flag_bitmask_read_onli": 26, "ignor": [26, 137, 256], "respons": 26, "isn": [26, 205], "t": [26, 189, 205, 208, 211, 215, 216, 260, 262], "id": 27, "meant": 27, "device_typ": 27, "device_id": 27, "member": 27, "cpu_pin": 27, "opencl": 27, "vulkan": 27, "metal": 27, "vpi": 27, "cuda_manag": 27, "13": 27, "one_api": 27, "14": [27, 257], "truth": [28, 31, 33, 37, 39, 43, 89, 93, 105, 106, 120, 121, 144, 263], "outsid": [29, 77, 167, 183, 190, 199, 204, 210], "bound": [29, 77, 171, 190, 199, 204, 216], "divis": [30, 41, 71, 90, 101, 152, 159, 207], "floor_divid": [30, 189, 204], "greater_equ": [31, 189, 204], "kei": [32, 49, 111, 113, 115, 260], "slice": [32, 49, 183, 189, 208], "ellipsi": [32, 49, 190], "semant": [32, 40, 49, 101, 132, 152, 171, 189, 190, 202, 204, 208, 210, 212, 214, 215, 256, 260, 261, 262], "pep": [34, 40, 101, 132, 210, 257], "357": 34, "overflowerror": 35, "bitwise_invert": [36, 189], "less_equ": [37, 189, 204], "bitwise_left_shift": [38, 189, 204], "matrix": [40, 55, 132, 133, 137, 174, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260], "product": [40, 42, 58, 132, 141, 150, 174, 185, 204, 233, 244, 256], "built": [40, 132, 190, 199, 260], "465": [40, 132], "least": [40, 90, 115, 116, 132, 141, 143, 179, 180, 181, 182, 205, 206, 245], "m": [40, 55, 132, 133, 137, 153, 158, 174, 175, 176, 177, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252], "remov": [40, 132, 166, 190, 207, 235, 252], "innermost": [40, 132, 133, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252], "conjug": [40, 79, 132, 174, 185, 204, 232, 236, 249, 256], "transposit": [40, 132, 174], "desir": [40, 63, 75, 132, 140, 174, 206, 207, 210, 216], "prior": [40, 132, 174], "inner": [40, 132, 204, 236, 256], "stack": [40, 55, 132, 133, 176, 177, 189, 215, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "l": [40, 132, 232, 252], 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[153, null], [179, null], [180, null], [181, null], [182, null], [190, null], [209, null]], "not_equal": [[144, "not-equal"]], "ones": [[145, "ones"]], "ones_like": [[146, "ones-like"]], "permute_dims": [[147, "permute-dims"]], "positive": [[148, "positive"]], "pow": [[149, "pow"]], "prod": [[150, "prod"]], "real": [[151, "real"]], "remainder": [[152, "remainder"]], "repeat": [[153, "repeat"]], "reshape": [[154, "reshape"]], "result_type": [[155, "result-type"]], "roll": [[156, "roll"]], "round": [[157, "round"]], "searchsorted": [[158, "searchsorted"]], "sign": [[159, "sign"]], "signbit": [[160, "signbit"]], "sin": [[161, "sin"]], "sinh": [[162, "sinh"]], "sort": [[163, "sort"]], "sqrt": [[164, "sqrt"]], "square": [[165, "square"]], "squeeze": [[166, "squeeze"]], "stack": [[167, "stack"]], "std": [[168, "std"]], "subtract": [[169, "subtract"]], "sum": [[170, "sum"]], "take": [[171, "take"]], "tan": [[172, "tan"]], "tanh": [[173, "tanh"]], "tensordot": [[174, "tensordot"], [251, "tensordot"]], "tile": [[175, "tile"]], "tril": [[176, "tril"]], "triu": [[177, "triu"]], "trunc": [[178, "trunc"]], "unique_all": [[179, "unique-all"]], "unique_counts": [[180, "unique-counts"]], "unique_inverse": [[181, "unique-inverse"]], "unique_values": [[182, "unique-values"]], "unstack": [[183, "unstack"]], "var": [[184, "var"]], "vecdot": [[185, "vecdot"], [253, "vecdot"]], "where": [[186, "where"]], "zeros": [[187, "zeros"]], "zeros_like": [[188, "zeros-like"]], "API specification": [[189, "api-specification"], [189, null]], "Indexing": [[190, "indexing"]], "Single-axis Indexing": [[190, "single-axis-indexing"]], "Slice Syntax": [[190, "slice-syntax"]], "Multi-axis Indexing": [[190, "multi-axis-indexing"]], "Boolean Array Indexing": [[190, "boolean-array-indexing"]], "Return Values": [[190, "return-values"]], "Indexing Functions": [[191, "indexing-functions"]], "Inspection": [[192, "inspection"]], "Inspection APIs": [[192, "inspection-apis"], [204, "inspection-apis"], [204, "id11"]], "Linear Algebra Functions": [[193, "linear-algebra-functions"]], "Manipulation Functions": [[194, "manipulation-functions"]], "Searching Functions": [[195, "searching-functions"]], "Set Functions": [[196, "set-functions"]], "Sorting Functions": [[197, "sorting-functions"]], "Statistical Functions": [[198, "statistical-functions"], [206, "statistical-functions"]], "Type Promotion Rules": [[199, "type-promotion-rules"]], "Rules": [[199, "rules"]], "Signed integer type promotion table": [[199, "signed-integer-type-promotion-table"]], "Unsigned integer type promotion table": [[199, "unsigned-integer-type-promotion-table"]], "Mixed unsigned and signed integer type promotion table": [[199, "mixed-unsigned-and-signed-integer-type-promotion-table"]], "Floating-point type promotion table": [[199, "floating-point-type-promotion-table"]], "Notes": [[199, "notes"]], "Mixing arrays with Python scalars": [[199, "mixing-arrays-with-python-scalars"]], "Utility Functions": [[200, "utility-functions"]], "Version": [[201, "version"]], "Assumptions": [[202, "assumptions"]], "Hardware and software environments": [[202, "hardware-and-software-environments"]], "Dependencies": [[202, "dependencies"]], "Backwards compatibility": [[202, "backwards-compatibility"], [257, "backwards-compatibility"]], "Production code & interactive use": [[202, "production-code-interactive-use"]], "Benchmark suite": [[203, "benchmark-suite"]], "Changelog per API standard version": [[204, "changelog-per-api-standard-version"]], "Changelog": [[204, "changelog"]], "v2024.12": [[204, "v2024-12"]], "Updates": [[204, "updates"], [204, "id5"], [204, "id15"]], "Normative": [[204, "normative"], [204, "id1"], [204, "id3"], [204, "id6"]], "APIs": [[204, "apis"], [204, "id2"], [204, "id4"], [204, "id7"], [204, "id10"], [204, "id16"], [204, "id20"]], "Scalar Argument Support": [[204, "scalar-argument-support"]], "Extensions": [[204, "extensions"], [204, "id8"], [204, "id13"], [204, "id17"], [204, "id21"], [255, "extensions"]], "Additions": [[204, "additions"], [204, "id9"], [204, "id19"]], "Breaking Changes": [[204, "breaking-changes"], [204, "id12"]], "Errata": [[204, "errata"], [204, "id14"], [204, "id22"]], "v2023.12": [[204, "v2023-12"]], "v2022.12": [[204, "v2022-12"]], "Complex Number Support": [[204, "complex-number-support"], [204, "id18"]], "C API": [[205, "c-api"]], "Example situations for C/Cython usage": [[205, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[205, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[205, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[205, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[205, "device-support"], [211, "device-support"]], "Other longer-term approaches": [[205, "other-longer-term-approaches"]], "Further Python API standardization": [[205, "further-python-api-standardization"]], "HPy": [[205, "hpy"]], "Accuracy": [[206, "accuracy"]], "Arithmetic Operations": [[206, "arithmetic-operations"]], "Mathematical Functions": [[206, "mathematical-functions"]], "Linear Algebra": [[206, "linear-algebra"]], "Complex Numbers": [[207, "complex-numbers"]], "The Complex Plane": [[207, "the-complex-plane"]], "Branch Cuts": [[207, "branch-cuts"]], "Complex Number Ordering": [[207, "complex-number-ordering"]], "Valued-based Promotion": [[207, "valued-based-promotion"]], "Copy-view behaviour and mutability": [[208, "copy-view-behaviour-and-mutability"]], "Mutating views": [[208, null]], "Data-dependent output shapes": [[209, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[210, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[210, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[210, "non-supported-use-cases"]], "Intended usage": [[211, "intended-usage"]], "Syntax for device assignment": [[211, "syntax-for-device-assignment"]], "Semantics": [[211, "semantics"]], "Out of scope for device support": [[211, "out-of-scope-for-device-support"]], "Exceptions": [[212, "exceptions"]], "Design topics & constraints": [[213, "design-topics-constraints"], [213, null]], "Lazy vs. eager execution": [[214, "lazy-vs-eager-execution"]], "Parallelism": [[215, "parallelism"]], "Static typing": [[216, "static-typing"]], "Fourier transform Functions": [[217, "fourier-transform-functions"]], "Extension name and usage": [[217, "extension-name-and-usage"], [256, "extension-name-and-usage"]], "fft": [[218, "fft"]], "fftfreq": [[219, "fftfreq"]], "fftn": [[220, "fftn"]], "fftshift": [[221, "fftshift"]], "hfft": [[222, "hfft"]], "ifft": [[223, "ifft"]], "ifftn": [[224, "ifftn"]], "ifftshift": [[225, "ifftshift"]], "ihfft": [[226, "ihfft"]], "irfft": [[227, "irfft"]], "irfftn": [[228, "irfftn"]], "rfft": [[229, "rfft"]], "rfftfreq": [[230, "rfftfreq"]], "rfftn": [[231, "rfftn"]], "cholesky": [[232, "cholesky"]], "cross": [[233, "cross"]], "det": [[234, "det"]], "diagonal": [[235, "diagonal"]], "eigh": [[236, "eigh"]], "eigvalsh": [[237, "eigvalsh"]], "inv": [[238, "inv"]], "matrix_norm": [[240, "matrix-norm"]], "matrix_power": [[241, "matrix-power"]], "matrix_rank": [[242, "matrix-rank"]], "outer": [[244, "outer"]], "pinv": [[245, "pinv"]], "qr": [[246, "qr"]], "slogdet": [[247, "slogdet"]], "solve": [[248, "solve"]], "svd": [[249, "svd"]], "svdvals": [[250, "svdvals"]], "trace": [[252, "trace"]], "vector_norm": [[254, "vector-norm"]], "Extension modules:": [[255, null]], "Linear Algebra Extension": [[256, "linear-algebra-extension"]], "Design Principles": [[256, "design-principles"]], "Future API standard evolution": [[257, "future-api-standard-evolution"]], "Scope extensions": [[257, "scope-extensions"]], "Versioning": [[257, "versioning"]], "Python array API standard": [[258, "python-array-api-standard"]], "Contents": [[258, "contents"]], "Context": [[258, null]], "API": [[258, null]], "Methodology and Usage": [[258, null]], "Other": [[258, null]], "License": [[259, "license"]], "Purpose and scope": [[260, "purpose-and-scope"]], "Introduction": [[260, "introduction"], [261, "introduction"]], "This API standard": [[260, "this-api-standard"]], "History": [[260, "history"]], "Scope (includes out-of-scope / non-goals)": [[260, "scope-includes-out-of-scope-non-goals"]], "In scope": [[260, "in-scope"]], "Out of scope": [[260, "out-of-scope"]], "Implications of in/out of scope": [[260, "implications-of-in-out-of-scope"]], "Stakeholders": [[260, "stakeholders"]], "How to read this document": [[260, "how-to-read-this-document"]], "How to adopt this API": [[260, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[260, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[260, "discoverability-of-conforming-implementations"]], "Optional feature": [[260, null]], "Conformance": [[260, "conformance"]], "Terms and Definitions": [[260, "terms-and-definitions"]], "Normative References": [[260, "normative-references"]], "Usage Data": [[261, "usage-data"]], "Design": [[261, "design"]], "Usage": [[261, "usage"]], "Use in Decision-Making": [[261, "use-in-decision-making"]], "Use cases": [[262, "use-cases"]], "Types of use cases": [[262, "types-of-use-cases"]], "Concrete use cases": [[262, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[262, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[262, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[262, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[262, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[263, "verification-test-suite"]], "Measuring conformance": [[263, "measuring-conformance"]], "Running the tests": [[263, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "cumulative_sum() (in module array_api)": [[88, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[89, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[90, "array_api.divide"]], "empty() (in module array_api)": [[91, "array_api.empty"]], "empty_like() (in module array_api)": [[92, "array_api.empty_like"]], "equal() (in module array_api)": [[93, "array_api.equal"]], "exp() (in module array_api)": [[94, "array_api.exp"]], "expand_dims() (in module array_api)": [[95, "array_api.expand_dims"]], "expm1() (in module array_api)": [[96, "array_api.expm1"]], "eye() (in module array_api)": [[97, "array_api.eye"]], "finfo() (in module array_api)": [[98, "array_api.finfo"]], "flip() (in module array_api)": [[99, "array_api.flip"]], "floor() (in module array_api)": [[100, "array_api.floor"]], "floor_divide() (in module array_api)": [[101, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[102, "array_api.from_dlpack"]], "full() (in module array_api)": [[103, "array_api.full"]], "full_like() (in module array_api)": [[104, "array_api.full_like"]], "greater() (in module array_api)": [[105, "array_api.greater"]], "greater_equal() (in module array_api)": [[106, "array_api.greater_equal"]], "hypot() (in module array_api)": [[107, "array_api.hypot"]], "iinfo() (in module array_api)": [[108, "array_api.iinfo"]], "imag() (in module array_api)": [[109, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[110, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[111, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[112, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[113, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[114, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[115, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[116, "array_api.isdtype"]], "isfinite() (in module array_api)": [[117, "array_api.isfinite"]], "isinf() (in module array_api)": [[118, "array_api.isinf"]], "isnan() (in module array_api)": [[119, "array_api.isnan"]], "less() (in module array_api)": [[120, "array_api.less"]], "less_equal() (in module array_api)": [[121, 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57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 184, 185, 186, 187, 188, 189, 192, 199, 202, 205, 207, 208, 211, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 258, 259, 260, 263], "type": [0, 2, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190, 192, 202, 205, 207, 208, 210, 212, 213, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 257, 260, 261], "__matmul__": [0, 189, 204], "matmul": [0, 40, 189, 199, 204, 256], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 190, 199, 202, 204, 205, 206, 208, 209, 210, 211, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 255, 256, 257, 259, 260, 261, 262, 263], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 88, 90, 101, 115, 116, 117, 118, 119, 132, 137, 141, 142, 148, 149, 150, 157, 159, 165, 169, 170, 174, 199, 206, 218, 220, 223, 224, 227, 228, 229, 231, 233, 244, 245, 247, 252, 256, 260, 262], "__invert__": [0, 189], "inv": [0, 204, 256], "invert": [0, 68, 238, 241, 248], "__inv__": 0, "__and__": [0, 189], "__or__": [0, 189], "__xor__": [0, 189], "xor": [0, 72, 131], "__lshift__": [0, 189], "lshift": 0, "__rshift__": [0, 189], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 90, 100, 101, 103, 104, 108, 115, 116, 122, 134, 136, 138, 142, 149, 150, 152, 153, 155, 157, 158, 168, 170, 171, 178, 184, 185, 189, 190, 204, 206, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241, 242, 252, 254, 260], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 102, 103, 104, 111, 115, 116, 122, 128, 129, 130, 131, 143, 186, 189, 199, 204], "__lt__": [0, 189, 204], "lt": 0, "__le__": [0, 189, 204], "le": 0, "__gt__": [0, 189, 204], "gt": [0, 246, 249], "__ge__": [0, 189, 204], "ge": 0, "__eq__": [0, 189, 204, 211], "eq": 0, "__ne__": [0, 189, 204], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 29, 34, 35, 40, 49, 55, 58, 60, 77, 85, 86, 89, 90, 94, 97, 98, 99, 101, 102, 107, 114, 115, 122, 128, 129, 130, 131, 132, 141, 143, 149, 153, 156, 157, 161, 172, 173, 175, 179, 181, 185, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 218, 219, 220, 221, 223, 224, 225, 227, 228, 229, 230, 231, 233, 236, 237, 242, 245, 246, 249, 255, 256, 257, 260, 261, 262, 263], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 99, 102, 107, 113, 115, 116, 122, 128, 129, 130, 131, 132, 136, 168, 184, 185, 189, 190, 199, 202, 204, 205, 207, 208, 210, 211, 212, 214, 216, 221, 233, 238, 245, 246, 248, 256, 257, 260, 261, 262, 263], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 89, 90, 96, 101, 102, 125, 140, 141, 168, 184, 190, 192, 202, 204, 206, 207, 208, 209, 210, 211, 212, 216, 233, 245, 255, 256, 259, 260, 262], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 89, 93, 107, 117, 118, 144, 164, 189, 190, 199, 204, 207, 208, 210, 216, 249, 257, 259, 260, 263], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 79, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 105, 106, 107, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 137, 138, 139, 141, 142, 144, 149, 150, 152, 153, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 170, 172, 173, 178, 179, 180, 181, 182, 190, 197, 202, 206, 207, 209, 211, 214, 219, 228, 230, 247, 249, 250, 252, 260, 262, 263], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 122, 134, 135, 138, 139, 152, 163, 185, 190, 204, 207, 208, 212, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 260], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 122, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 154, 163, 168, 169, 170, 184, 185, 186, 199, 204, 207, 208, 212, 233, 240, 242, 245, 248, 254, 260, 262], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 89, 90, 93, 101, 102, 105, 106, 107, 110, 115, 116, 120, 121, 122, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 143, 144, 153, 154, 158, 163, 168, 173, 179, 180, 181, 182, 184, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 214, 215, 216, 236, 246, 247, 249, 255, 256, 260, 261, 262], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 90, 93, 94, 96, 97, 98, 103, 104, 105, 106, 107, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 163, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 199, 206, 210, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 88, 101, 105, 106, 107, 116, 120, 121, 122, 134, 135, 138, 139, 153, 158, 163, 171, 172, 173, 202, 205, 206, 207, 208, 209, 211, 256, 257, 260, 262], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 105, 106, 120, 121, 134, 135, 138, 139, 163], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 51, 60, 62, 66, 77, 78, 87, 90, 94, 96, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 162, 163, 164, 167, 171, 173, 190, 197, 199, 204, 220, 221, 224, 225, 228, 231, 236, 237, 260], "thu": [0, 5, 16, 17, 18, 30, 31, 33, 37, 39, 41, 47, 57, 60, 71, 77, 101, 103, 104, 105, 106, 120, 121, 122, 134, 135, 138, 139, 149, 152, 158, 163, 172, 173, 190, 197, 206, 207, 220, 221, 224, 225, 228, 231, 236, 237, 249, 256], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 29, 31, 33, 37, 39, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 90, 94, 96, 105, 106, 111, 120, 121, 122, 123, 124, 125, 126, 141, 142, 149, 158, 161, 162, 163, 172, 173, 186, 197, 199, 206, 207, 210, 213, 214, 216, 236, 237, 246, 247, 248, 249, 256, 260, 262, 263], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 77, 85, 90, 93, 96, 101, 102, 104, 105, 106, 107, 110, 111, 114, 120, 121, 123, 125, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 143, 144, 149, 150, 152, 153, 155, 158, 159, 163, 164, 165, 168, 169, 170, 179, 180, 181, 182, 184, 185, 186, 189, 190, 199, 201, 202, 205, 207, 209, 210, 211, 216, 233, 240, 242, 245, 248, 254, 255, 260, 261, 262, 263], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 89, 99, 101, 102, 105, 106, 120, 121, 134, 135, 138, 139, 143, 153, 158, 163, 172, 173, 174, 179, 180, 181, 182, 190, 197, 199, 204, 206, 209, 210, 212, 227, 228, 236, 237, 240, 249, 250, 254, 256, 257, 260, 261], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 148, 149, 150, 154, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 202, 218, 219, 220, 222, 223, 224, 227, 228, 230, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257, 260, 262, 263], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 88, 91, 92, 95, 99, 103, 104, 111, 132, 133, 137, 145, 146, 154, 156, 158, 163, 167, 171, 174, 175, 176, 177, 183, 185, 187, 188, 189, 204, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 260, 262], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 138, 139, 141, 142, 144, 148, 149, 150, 151, 152, 153, 155, 157, 158, 159, 160, 161, 162, 164, 165, 167, 168, 169, 170, 172, 173, 174, 178, 179, 184, 190, 197, 199, 204, 206, 207, 208, 214, 232, 233, 235, 240, 241, 247, 248, 254, 260, 261, 262, 263], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 90, 94, 96, 101, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 136, 139, 141, 142, 149, 152, 155, 161, 162, 164, 165, 167, 168, 169, 172, 173, 174, 184, 185, 186, 189, 204, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 30, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 103, 104, 107, 122, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 155, 159, 161, 162, 164, 165, 167, 169, 172, 173, 174, 185, 186, 189, 190, 204, 207, 210, 232, 233, 238, 240, 241, 242, 244, 245, 246, 247, 248, 254, 256, 260, 262], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 153, 168, 169, 170, 174, 184, 185, 186, 189, 204, 233, 240, 242, 245, 248, 254, 260], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 88, 90, 92, 95, 98, 99, 100, 101, 102, 104, 109, 132, 133, 134, 136, 137, 138, 140, 141, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 163, 166, 167, 168, 169, 170, 171, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 188, 190, 199, 202, 204, 207, 208, 210, 211, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 234, 235, 236, 238, 241, 245, 246, 247, 249, 250, 252, 255, 256, 260, 262], "behavior": [0, 5, 47, 49, 59, 60, 63, 77, 90, 101, 103, 104, 107, 122, 141, 149, 152, 158, 171, 179, 180, 181, 182, 189, 190, 192, 199, 202, 204, 206, 207, 214, 215, 220, 221, 224, 225, 228, 231, 256, 257, 260, 261, 262, 263], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 204, 205, 207, 247, 252], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 102, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 168, 170, 172, 173, 178, 184, 190, 202, 204, 205, 206, 207, 208, 211, 212, 214, 246, 247, 249, 252, 256, 258, 260, 263], "its": [0, 5, 26, 40, 73, 90, 98, 132, 141, 154, 156, 206, 207, 210, 211, 255, 260, 261, 262], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 90, 93, 101, 105, 106, 107, 113, 120, 121, 122, 127, 128, 130, 131, 135, 137, 139, 140, 141, 144, 152, 162, 169, 172, 173, 174, 179, 180, 185, 204, 206, 209, 211, 236, 246, 249], "binari": [0, 5, 67, 70, 72, 172, 173, 205], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 97, 102, 132, 133, 137, 157, 174, 176, 177, 179, 180, 181, 182, 185, 190, 199, 210, 211, 214, 215, 220, 221, 224, 225, 228, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262, 263], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 85, 86, 87, 88, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 138, 139, 141, 144, 149, 150, 152, 157, 159, 160, 161, 162, 164, 165, 170, 172, 173, 178, 199, 204, 206, 247, 252], "assign": [0, 208], "exampl": [0, 5, 12, 23, 26, 115, 116, 167, 189, 190, 202, 207, 208, 209, 211, 214, 215, 216, 252, 256, 260, 262, 263], "after": [0, 1, 26, 40, 132, 164, 175], "addit": [0, 5, 7, 12, 26, 50, 59, 88, 115, 169, 189, 190, 199, 205, 207, 210, 256, 260, 261, 263], "modifi": [0, 26, 208, 259], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 89, 94, 96, 97, 103, 104, 107, 116, 118, 123, 124, 125, 126, 136, 143, 144, 145, 146, 149, 150, 157, 162, 163, 164, 168, 170, 171, 173, 174, 175, 179, 180, 181, 182, 184, 189, 190, 197, 204, 207, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 241, 242, 245, 246, 247, 248, 252, 260], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 101, 107, 128, 129, 130, 131, 152, 157, 171, 190, 199, 204, 207, 208, 242, 245, 248, 254, 260], "discuss": [0, 93, 144, 204, 210, 211, 215, 260, 261, 262], "copi": [0, 1, 26, 59, 60, 63, 102, 154, 163, 204, 205, 210, 211, 213, 259, 260], "view": [0, 102, 213], "behaviour": [0, 213, 260, 262], "mutabl": [0, 213], "via": [0, 26, 101, 102, 171, 190, 205, 210, 211, 215, 217, 245, 255, 256, 257, 260], "__iadd__": 0, "__isub__": 0, "__imul__": 0, "__itruediv__": 0, "__ifloordiv__": 0, "__ipow__": 0, "__imod__": 0, "__imatmul__": 0, "__iand__": 0, "__ior__": 0, "__ixor__": 0, "__ilshift__": 0, "__irshift__": 0, "appli": [0, 12, 77, 78, 85, 90, 141, 155, 157, 167, 174, 190, 199, 202, 207, 218, 220, 223, 224, 227, 228, 229, 231, 242, 245, 256, 260, 262], "match": [0, 1, 5, 9, 20, 26, 63, 101, 152, 174, 179, 180, 212, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254, 262], "op": [0, 199], "__radd__": 0, "__rsub__": 0, "__rmul__": 0, "__rtruediv__": 0, "__rfloordiv__": 0, "__rpow__": 0, "__rmod__": 0, "__rmatmul__": 0, "__rand__": 0, "__ror__": 0, "__rxor__": 0, "__rlshift__": 0, "__rrshift__": 0, "arrai": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 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223, 224, 226, 227, 228, 229, 231, 233, 235, 244, 246, 249, 260], "without": [1, 7, 26, 57, 102, 113, 115, 143, 153, 154, 179, 180, 181, 182, 202, 205, 206, 209, 259, 260, 262], "purpos": [1, 5, 96, 107, 125, 202, 247, 256, 258, 259, 262], "make": [1, 7, 202, 205, 206, 208, 210, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 257, 260], "differ": [1, 12, 26, 49, 50, 77, 78, 88, 90, 98, 101, 102, 141, 150, 167, 169, 170, 190, 202, 204, 208, 211, 212, 214, 225, 236, 246, 247, 249, 252, 256, 260, 261, 262], "element": [1, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 105, 106, 107, 109, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 184, 186, 189, 190, 204, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 236, 245, 246, 247, 249, 252, 260], "wise": [1, 9, 10, 12, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 64, 65, 67, 68, 69, 70, 71, 72, 77, 79, 85, 90, 93, 101, 105, 106, 107, 109, 120, 121, 127, 128, 129, 130, 131, 135, 139, 141, 144, 149, 151, 152, 169, 189, 204, 206, 260], "oper": [1, 12, 19, 24, 26, 34, 40, 57, 58, 59, 61, 64, 71, 86, 88, 90, 101, 124, 126, 132, 141, 149, 150, 152, 155, 161, 165, 170, 172, 174, 189, 190, 196, 199, 204, 207, 208, 209, 210, 211, 252, 256, 257, 260, 261, 262], "facilit": [1, 197, 202], "user": [1, 7, 26, 110, 173, 202, 205, 206, 208, 211, 215, 256, 260, 261, 262], "ergonom": 1, "encourag": [1, 260, 261], "avoid": [1, 9, 63, 90, 96, 101, 107, 125, 141, 154, 205, 208, 211, 214, 256, 260, 262], "unnecessari": [1, 256], "can": [1, 7, 26, 60, 75, 110, 114, 116, 190, 199, 202, 205, 207, 208, 210, 211, 216, 245, 246, 249, 255, 256, 260, 261, 262, 263], "potenti": [1, 26, 96, 125, 153, 208, 260], "enabl": [1, 26, 102, 211, 215, 216, 260], "more": [1, 5, 7, 15, 19, 26, 40, 58, 60, 63, 73, 88, 96, 99, 101, 125, 132, 143, 149, 153, 171, 179, 180, 181, 182, 190, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 215, 216, 220, 221, 224, 225, 228, 231, 247, 256, 257, 260, 261, 263], "memori": [1, 26, 60, 102, 202, 208, 209, 211, 260, 262], "effici": [1, 202, 208], "through": [1, 60, 65, 255, 257, 261, 262], "vector": [1, 40, 132, 137, 185, 233, 244, 249, 250, 254, 256, 260], "reduc": [1, 13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 190, 246, 249, 256, 261, 262], "consumpt": [1, 26, 261], "cach": 1, "local": [1, 211], "given": [1, 23, 99, 122, 156, 158, 183, 199, 204, 207, 208, 211, 212, 216, 237, 247, 256, 257, 260, 262], "involv": [1, 12, 90, 101, 141, 149, 155, 199, 204, 206, 207, 211, 215], "singleton": [1, 13, 14, 16, 17, 95, 134, 136, 138, 150, 166, 168, 170, 175, 184, 240, 254, 260], "whose": [1, 5, 9, 11, 19, 20, 26, 47, 55, 62, 66, 85, 86, 87, 97, 99, 102, 133, 149, 156, 160, 161, 162, 171, 172, 173, 174, 176, 177, 179, 180, 181, 190, 208, 222, 226, 227, 228, 229, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "one": [1, 15, 19, 26, 40, 51, 58, 60, 63, 73, 75, 88, 90, 95, 97, 99, 101, 102, 115, 116, 122, 132, 137, 141, 143, 145, 146, 153, 158, 166, 171, 179, 180, 181, 182, 185, 190, 202, 204, 205, 207, 208, 210, 211, 214, 215, 216, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 231, 244, 245, 246, 254, 256, 257, 260, 262], "virtual": 1, "repeat": [1, 189, 190, 204, 262], "across": [1, 5, 90, 101, 141, 173, 204, 206, 207, 211, 255, 260], "correspond": [1, 16, 17, 23, 47, 59, 65, 73, 77, 102, 111, 112, 113, 149, 154, 156, 158, 168, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 220, 224, 228, 231, 233, 236, 240, 259, 260], "If": [1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 111, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 149, 150, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 187, 188, 190, 205, 207, 211, 217, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 252, 254, 255, 256, 260, 262], "unequ": 1, "lower": [1, 77, 97, 176, 232], "higher": [1, 5, 26, 190, 205, 256, 261], "prepend": [1, 40, 95, 132, 175], "until": [1, 26, 175], "store": [1, 26, 211, 252], "determin": [1, 10, 11, 12, 13, 14, 21, 22, 26, 30, 40, 41, 42, 44, 45, 47, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 78, 85, 86, 87, 88, 90, 94, 96, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 132, 135, 139, 141, 142, 149, 152, 160, 161, 162, 164, 165, 169, 171, 172, 173, 174, 179, 180, 181, 182, 185, 186, 199, 204, 207, 210, 211, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 235, 238, 240, 241, 242, 244, 245, 246, 247, 248, 252, 254, 256, 260], "let": [1, 9, 10, 11, 12, 62, 66, 85, 87, 88, 93, 94, 96, 102, 117, 118, 119, 122, 123, 125, 136, 144, 150, 153, 158, 159, 162, 164, 168, 170, 173, 175, 184, 185, 190, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 246, 248, 249, 252], "b": [1, 9, 10, 11, 12, 57, 62, 66, 87, 90, 93, 94, 96, 101, 117, 118, 119, 122, 123, 125, 141, 144, 159, 162, 164, 167, 173, 185, 190, 204, 207, 208, 212, 245, 248, 262], "both": [1, 40, 44, 47, 51, 65, 77, 88, 90, 98, 101, 102, 107, 122, 132, 142, 149, 150, 170, 173, 174, 185, 190, 204, 207, 208, 210, 214, 216, 233, 252, 256, 260, 261], "shape1": 1, "describ": [1, 5, 12, 88, 90, 93, 115, 116, 141, 144, 149, 150, 170, 192, 199, 204, 207, 210, 214, 219, 230, 252, 260], "shape2": 1, "n1": [1, 137], "len": [1, 137, 175], "n2": [1, 137], "max": [1, 26, 77, 98, 108, 175, 189, 190, 204, 240, 242, 245], "temporari": 1, "list": [1, 73, 78, 110, 114, 137, 167, 190, 202, 204, 211, 260, 262], "length": [1, 15, 107, 137, 154, 174, 190, 219, 221, 222, 225, 230, 249, 250], "while": [1, 101, 115, 122, 128, 129, 130, 131, 136, 140, 158, 168, 179, 180, 184, 189, 190, 197, 202, 204, 207, 208, 209, 211, 214, 245, 256, 261, 262, 263], "d1": 1, "els": [1, 26, 202, 261], "d2": 1, "set": [1, 18, 26, 49, 65, 102, 160, 163, 168, 176, 177, 179, 181, 182, 184, 189, 190, 204, 205, 206, 207, 208, 211, 212, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 237, 238, 242, 245, 246, 248, 249, 255, 256, 260, 262, 263], "th": [1, 97, 175, 190, 204, 220, 224, 228, 231], "throw": 1, "except": [1, 7, 13, 14, 26, 74, 78, 88, 97, 102, 122, 143, 153, 167, 171, 183, 190, 199, 202, 204, 206, 208, 211, 213, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 245, 257, 260, 261, 262], "demonstr": 1, "applic": [1, 26, 88, 150, 153, 170, 199, 204, 252, 256, 260, 261], "4d": 1, "8": [1, 5, 7, 27, 175, 199, 202], "6": [1, 7, 175], "3d": 1, "7": [1, 7, 27, 216], "5": [1, 190, 260], "2d": 1, "1d": 1, "15": 1, "do": [1, 26, 90, 141, 152, 197, 202, 204, 205, 207, 208, 210, 211, 212, 256, 257, 259, 260, 262, 263], "doe": [1, 15, 26, 102, 144, 171, 190, 199, 202, 205, 206, 207, 208, 209, 211, 212, 214, 216, 256, 260, 262, 263], "second": [1, 12, 65, 67, 69, 70, 71, 72, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 167, 169, 174, 179, 180, 181, 185, 186, 233, 236, 244, 246, 247, 249, 250, 260], "append": [1, 40, 69, 95, 132, 235], "As": [1, 122, 149, 179, 180, 181, 182, 202, 210, 216, 262], "impli": [1, 179, 180, 181, 182, 259, 260], "__setitem__": [1, 171, 189, 204], "Such": [1, 206, 256], "right": [1, 69, 71, 107, 158, 164, 205, 249, 259], "hand": [1, 199], "left": [1, 5, 60, 69, 101, 103, 158, 171, 190, 199, 236, 237, 249, 260], "index": [1, 5, 16, 17, 18, 32, 34, 49, 57, 83, 97, 111, 113, 137, 140, 143, 158, 167, 171, 174, 179, 180, 181, 189, 204, 220, 224, 228, 231, 260, 262], "perform": [1, 5, 13, 14, 26, 40, 59, 60, 90, 107, 132, 141, 153, 174, 190, 205, 206, 207, 208, 209, 210, 218, 220, 223, 224, 225, 227, 228, 229, 231, 249, 250, 256, 260, 261, 262], "empti": [1, 13, 14, 15, 150, 170, 189, 190, 204, 252, 260], "ok": 1, "allow": [1, 24, 25, 26, 29, 34, 35, 113, 115, 149, 154, 174, 190, 204, 205, 206, 208, 211, 214, 215, 256, 262], "NOT": [1, 129, 259], "adher": [2, 7, 8, 189, 190, 202, 255, 260], "convent": [2, 7, 10, 11, 26, 40, 61, 62, 64, 65, 66, 88, 123, 125, 132, 149, 164, 189, 190, 197, 207, 211, 255, 256, 261], "each": [2, 9, 10, 11, 12, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 85, 86, 87, 90, 93, 94, 96, 100, 101, 105, 106, 107, 109, 114, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 137, 139, 140, 141, 142, 143, 144, 148, 149, 151, 152, 153, 156, 157, 158, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 178, 179, 180, 190, 202, 204, 206, 210, 214, 216, 228, 232, 233, 234, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 255, 256, 260, 261, 262], "float": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 21, 24, 25, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 47, 49, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 261], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 113, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 145, 146, 149, 150, 151, 152, 155, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 178, 179, 180, 181, 182, 184, 185, 187, 189, 197, 204, 206, 207, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260, 262], "creat": [3, 15, 60, 91, 92, 97, 102, 103, 104, 122, 145, 146, 187, 188, 196, 202, 211, 219, 230, 256, 260], "main": [5, 97, 176, 177, 205, 210, 235, 252, 255, 262], "namespac": [5, 7, 23, 110, 192, 202, 204, 217, 255, 256, 257, 260, 263], "under": [5, 255, 259, 260], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 91, 95, 98, 99, 103, 113, 115, 116, 122, 145, 150, 152, 153, 156, 166, 167, 170, 171, 175, 176, 177, 179, 180, 181, 182, 185, 187, 190, 199, 204, 206, 207, 208, 210, 211, 212, 216, 218, 220, 221, 222, 223, 224, 226, 227, 228, 229, 231, 235, 252, 254, 256, 257, 260, 262, 263], "name": [5, 7, 23, 26, 101, 115, 179, 180, 181, 190, 207, 236, 245, 246, 247, 249, 255, 260, 261], "descript": [5, 7, 204, 206, 240, 254], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 75, 88, 89, 93, 102, 103, 104, 105, 106, 115, 116, 117, 118, 119, 120, 121, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 184, 199, 204, 214, 232, 240, 249, 254], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 98, 101, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 143, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 186, 190, 204, 232, 240, 249, 254, 256], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 93, 102, 111, 117, 118, 119, 122, 128, 129, 130, 131, 134, 136, 138, 144, 150, 154, 160, 163, 168, 170, 179, 180, 181, 182, 184, 190, 232, 240, 249, 254], "int8": [5, 115, 116, 199], "bit": [5, 68, 69, 71, 85, 88, 98, 108, 150, 160, 170, 199, 204, 206, 252], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 88, 90, 94, 96, 101, 115, 116, 123, 125, 134, 135, 138, 139, 141, 142, 149, 150, 152, 158, 160, 162, 164, 170, 173, 179, 180, 181, 182, 189, 197, 204, 207, 246, 247, 252], "exist": [5, 7, 26, 60, 78, 102, 202, 204, 207, 210, 211, 212, 238, 257, 260, 261], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 95, 122, 123, 125, 140, 167, 174, 176, 177, 183, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 257], "128": 5, "127": 5, "int16": [5, 88, 115, 116, 150, 170, 199, 252], "16": [5, 199], "32": [5, 199], "767": 5, "int32": [5, 88, 115, 116, 150, 170, 199, 252], "147": 5, "483": 5, "647": 5, "int64": [5, 88, 115, 116, 150, 170, 199, 252], "64": [5, 199], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 115, 116, 199], "unsign": [5, 88, 115, 116, 150, 170, 189, 252], "255": 5, "uint16": [5, 88, 115, 116, 150, 170, 199, 252], "65": 5, "535": [5, 204], "uint32": [5, 88, 115, 116, 150, 170, 199, 252], "294": 5, "967": 5, "295": 5, "uint64": [5, 115, 116, 199], "18": 5, "446": [5, 204], "744": [5, 204], "073": 5, "709": [5, 204], "551": [5, 204], "615": 5, "float32": [5, 109, 115, 116, 151, 199, 247, 249, 250], "ieee": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 204, 206, 207, 260], "754": [5, 12, 65, 80, 81, 82, 84, 90, 96, 98, 107, 125, 141, 152, 164, 172, 173, 189, 197, 204, 206, 207, 260], "singl": [5, 7, 24, 25, 29, 34, 35, 113, 115, 179, 180, 189, 199, 204, 205, 207, 210, 211, 216, 256, 260, 261, 262], "precis": [5, 9, 20, 42, 60, 98, 103, 104, 109, 141, 151, 164, 199, 204, 206, 222, 226, 227, 228, 229, 231, 236, 237, 240, 247, 249, 250, 254, 260], "2019": [5, 12, 90, 96, 107, 125, 141, 189, 206, 260, 262], "float64": [5, 9, 20, 115, 116, 199, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "doubl": [5, 174, 199, 204], "complex64": [5, 109, 115, 116, 151, 199, 204, 247, 249, 250], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 157, 162, 164, 173, 204, 207], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 90, 93, 94, 96, 98, 109, 123, 125, 141, 142, 143, 144, 145, 146, 149, 151, 157, 162, 164, 172, 173, 179, 180, 181, 182, 204, 207, 221, 230], "complex128": [5, 9, 20, 115, 116, 199, 204, 222, 226, 227, 228, 229, 231, 236, 237, 240, 254], "method": [5, 26, 34, 102, 189, 192, 202, 208, 210, 211, 214, 215, 216, 260, 261, 262], "attribut": [5, 23, 98, 108, 189, 201, 204, 257, 260, 261, 262], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 88, 102, 107, 116, 150, 164, 167, 170, 171, 173, 179, 180, 182, 183, 189, 190, 197, 199, 202, 204, 205, 206, 207, 208, 209, 210, 211, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 230, 233, 252, 255, 256, 260, 261, 262], "beyond": [5, 156, 199, 204, 260], "It": [5, 23, 26, 102, 202, 208, 210, 260, 262, 263], "also": [5, 7, 26, 34, 102, 107, 159, 199, 202, 207, 208, 209, 210, 216, 220, 224, 228, 231, 249, 255, 262], "subnorm": [5, 107], "k": [5, 40, 97, 107, 132, 143, 176, 177, 190, 232, 236, 237, 238, 246, 248, 249, 250, 252, 260], "denorm": [5, 107], "gradual": [5, 107, 260], "underflow": [5, 9, 90, 101, 107, 247], "hardwar": [5, 53, 107, 153, 206, 210, 211, 236, 249, 256, 260], "univers": [5, 107, 205, 211, 256, 260], "mani": [5, 107, 175, 260, 262], "platform": [5, 26, 107], "compil": [5, 107, 173, 202, 205, 209, 260], "toggl": [5, 107], "daz": [5, 107], "flush": [5, 107], "ftz": [5, 107], "increas": [5, 107, 206, 261], "guard": [5, 107], "against": [5, 40, 73, 107, 132, 173, 190, 242, 245, 263], "time": [5, 7, 16, 17, 26, 107, 153, 179, 180, 202, 204, 209, 210, 215, 232, 236, 237, 238, 246, 248, 249, 256, 260, 262], "attack": [5, 107], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 90, 96, 101, 107, 122, 123, 125, 134, 136, 137, 138, 141, 143, 150, 153, 158, 164, 168, 170, 179, 180, 181, 182, 184, 190, 199, 206, 207, 208, 209, 211, 240, 246, 254, 256], "vari": [5, 107, 158, 173, 179, 180, 181, 182, 199, 206], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 78, 86, 87, 88, 94, 96, 99, 102, 107, 114, 115, 116, 122, 123, 125, 128, 129, 130, 131, 132, 136, 143, 149, 150, 152, 153, 154, 159, 161, 162, 163, 164, 167, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 184, 185, 189, 192, 202, 204, 205, 207, 208, 209, 210, 211, 214, 215, 216, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 232, 233, 236, 237, 238, 242, 245, 246, 247, 248, 249, 250, 252, 255, 256, 257, 260, 261, 262], "access": [5, 26, 32, 102, 110, 190, 204, 210, 255, 257, 260], "variou": [5, 204], "cast": [5, 29, 49, 60, 63, 75, 88, 150, 170, 199, 207, 252, 260, 262], "introspect": 5, "isdtyp": [5, 189, 204], "integr": [5, 63, 77, 113, 115, 116], "keyword": [5, 7, 26, 63, 88, 114, 137, 150, 170, 189, 204, 208, 211, 215, 216, 252, 256, 257, 260, 261, 262], "affect": [5, 15, 49, 208, 211], "intermedi": [5, 9, 107], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 88, 90, 94, 96, 123, 124, 125, 126, 127, 134, 136, 138, 141, 149, 150, 161, 162, 164, 168, 169, 170, 172, 173, 184, 204, 247], "implementor": [5, 255], "free": [5, 211, 259], "when": [5, 7, 12, 16, 17, 26, 47, 49, 59, 63, 90, 96, 101, 102, 107, 113, 115, 122, 125, 134, 135, 138, 139, 141, 149, 150, 153, 154, 158, 168, 170, 173, 184, 186, 189, 190, 199, 204, 205, 207, 208, 209, 210, 212, 214, 215, 216, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 232, 236, 238, 242, 245, 246, 247, 248, 249, 250, 252, 256, 260, 261, 262], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 110, 216], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 90, 94, 95, 96, 101, 104, 132, 136, 137, 140, 141, 142, 143, 149, 150, 161, 162, 166, 168, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 184, 190, 199, 202, 207, 210, 211, 214, 215, 233, 240, 248, 249, 252, 254, 256, 257, 260, 262, 263], "wai": [5, 26, 63, 102, 202, 205, 211, 212, 257, 260, 261, 262, 263], "f4": [5, 199], "ensur": [5, 26, 158, 202, 206, 256, 260, 261, 262], "portabl": [5, 59, 122, 206, 208, 211, 212, 260], "consum": [5, 26, 63, 113, 115, 202, 207, 208, 216, 255, 260, 261], "recommend": [5, 7, 19, 23, 26, 122, 128, 129, 130, 131, 136, 152, 168, 184, 197, 204, 206, 210, 211, 260], "guidanc": [5, 7, 49, 204, 205, 212, 260], "govern": [5, 50, 169, 199, 256, 257], "interact": [5, 207], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 88, 90, 93, 94, 96, 98, 101, 102, 107, 110, 116, 117, 118, 122, 123, 124, 125, 126, 127, 132, 134, 135, 138, 139, 141, 150, 152, 159, 160, 161, 164, 170, 172, 173, 174, 190, 206, 207, 208, 212, 216, 247, 252, 260, 261, 263], "whether": [5, 13, 14, 26, 59, 60, 63, 88, 89, 102, 111, 116, 119, 122, 154, 160, 204, 211, 232, 236, 237, 246, 248, 255, 259, 260, 262], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 102, 111, 113, 115, 134, 136, 138, 150, 153, 154, 158, 159, 168, 170, 184, 185, 186, 189, 190, 202, 211, 232, 234, 240, 247, 248, 254, 259], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 100, 101, 103, 104, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 125, 126, 127, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 171, 172, 173, 174, 175, 178, 179, 180, 181, 182, 183, 184, 185, 189, 190, 204, 210, 214, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 261, 262, 263], "possibl": [5, 26, 60, 101, 102, 134, 138, 154, 172, 173, 202, 205, 206, 207, 208, 210, 211, 212, 214, 216, 256, 260, 261, 262, 263], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 132, 134, 136, 138, 141, 142, 150, 168, 170, 184, 190, 202, 205, 207, 210, 211, 215, 216, 237, 238, 256, 257, 260, 262], "In": [5, 12, 19, 26, 59, 88, 90, 93, 101, 116, 118, 119, 141, 144, 150, 152, 159, 170, 189, 190, 192, 199, 206, 207, 210, 212, 227, 228, 246, 247, 249, 252, 256, 257, 261, 262, 263], "clearli": [5, 59, 116, 197, 207, 256, 257], "warn": [5, 153, 212], "about": [5, 7, 26, 98, 108, 208, 256, 260, 262, 263], "": [5, 26, 29, 32, 49, 58, 59, 60, 80, 101, 102, 137, 152, 168, 175, 176, 177, 184, 190, 197, 202, 204, 205, 206, 207, 208, 210, 211, 214, 216, 220, 224, 228, 231, 245, 249, 250, 256, 257, 260, 262], "organ": [5, 204, 256, 261, 262], "within": [5, 15, 27, 190, 199, 202, 204, 207, 211, 218, 220, 223, 224, 227, 228, 229, 231, 260], "accord": [5, 12, 60, 71, 75, 88, 90, 98, 101, 103, 122, 141, 149, 158, 159, 168, 184, 185, 190, 204, 206, 207], "These": [5, 208, 236, 261], "intend": [5, 88, 150, 170, 202, 252], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 90, 95, 97, 98, 101, 118, 123, 125, 140, 141, 143, 152, 156, 160, 162, 164, 173, 189, 190, 202, 204, 206, 216, 230, 232, 246, 261], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 202, 204, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 256], "extern": [7, 262], "usabl": 7, "accept": [7, 26, 128, 129, 130, 131, 136, 152, 168, 184, 202, 257], "call": [7, 34, 210, 211, 214, 247, 260, 261, 262], "argument": [7, 10, 11, 26, 40, 61, 62, 63, 64, 65, 66, 86, 88, 107, 114, 123, 125, 132, 150, 155, 158, 161, 164, 170, 172, 173, 174, 189, 199, 206, 208, 210, 211, 218, 220, 223, 224, 227, 228, 229, 231, 252, 256, 260, 261, 262], "map": [7, 207, 208], "base": [7, 47, 57, 58, 94, 95, 123, 124, 125, 126, 149, 179, 180, 181, 182, 190, 204, 208, 214, 216, 256, 257, 260, 261, 262], "sole": [7, 190, 197, 256], "incompat": [7, 26, 74, 102, 202, 257, 260], "us": [7, 19, 26, 27, 59, 60, 83, 98, 102, 107, 122, 124, 126, 156, 179, 181, 189, 190, 199, 204, 206, 207, 208, 209, 211, 212, 215, 216, 217, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 255, 256, 257, 258, 259, 260, 263], "normal": [7, 78, 167, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231], "practic": [7, 19, 190, 256, 261], "avail": [7, 102, 114, 202, 210, 255, 257, 261], "still": [7, 26, 216, 256, 261, 262, 263], "consid": [7, 26, 63, 102, 128, 129, 130, 131, 179, 180, 181, 182, 207, 211, 230, 245, 256, 260, 262, 263], "compliant": [7, 26, 51, 90, 96, 102, 122, 125, 128, 129, 130, 131, 134, 135, 136, 138, 139, 168, 184, 206, 209, 211, 257, 260], "altern": [7, 208, 210, 263], "thei": [7, 26, 199, 205, 210, 211, 215, 216, 255, 256, 257, 260, 262, 263], "were": [7, 101, 153, 158, 204, 260], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 189, 204, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 256, 261, 262], "lead": [7, 101, 207, 246, 249, 260], "readabl": [7, 199, 256, 261], "code": [7, 59, 199, 208, 209, 211, 214, 216, 256, 260, 261, 262], "easier": [7, 202, 208, 256], "evolv": [7, 202, 256], "over": [7, 13, 14, 26, 122, 134, 136, 138, 150, 168, 170, 171, 174, 184, 185, 206, 207, 208, 210, 211, 215, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 252, 254, 256, 260], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 86, 87, 90, 93, 94, 96, 97, 98, 102, 103, 104, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 157, 159, 161, 162, 164, 165, 169, 170, 172, 173, 174, 179, 180, 181, 182, 185, 190, 203, 204, 205, 211, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "worri": 7, "xi": [7, 137], "annot": [7, 204, 216, 260], "individu": [7, 211, 214, 215, 216, 219, 230, 260, 261], "aim": [7, 205, 216, 255, 256, 257, 260, 261, 262, 263], "strongli": [7, 208, 262], "look": [7, 262], "like": [7, 202, 205, 207, 208, 214, 216, 257, 260, 261, 262], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 91, 92, 97, 99, 102, 103, 104, 113, 115, 122, 134, 136, 138, 145, 146, 150, 153, 154, 156, 158, 168, 170, 171, 184, 187, 188, 190, 204, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 240, 242, 245, 252, 254, 260, 261, 263], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 204, 205, 208, 210, 214, 215, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 259, 262], "int": [7, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 74, 77, 78, 88, 91, 95, 97, 98, 99, 101, 103, 104, 108, 122, 134, 136, 138, 140, 145, 147, 150, 153, 154, 156, 163, 166, 167, 168, 170, 171, 174, 175, 176, 177, 183, 184, 185, 187, 190, 199, 214, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 235, 240, 241, 251, 252, 253, 254, 261], "str": [7, 8, 23, 115, 116, 137, 261], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 89, 204, 262], "few": [7, 206, 214, 260, 262], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 91, 92, 97, 99, 102, 103, 104, 112, 113, 115, 122, 134, 136, 137, 138, 143, 145, 146, 150, 153, 154, 156, 158, 163, 167, 168, 170, 174, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 204, 206, 211, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 235, 240, 242, 245, 246, 249, 252, 254], "form": [7, 23, 26, 40, 79, 132, 133, 176, 177, 208, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 257, 261], "question": [7, 205, 260], "commonli": [7, 168, 184, 205, 207, 209, 255, 256, 260, 261], "written": [7, 202, 260, 262], "yyyi": [8, 23, 257], "mm": [8, 23, 257], "string": [8, 23, 115, 116, 204, 257, 260], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 189, 202, 205, 211, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 258, 260, 262], "absolut": [9, 20, 85, 159, 206, 208, 240, 241, 247, 256], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 94, 96, 100, 109, 117, 118, 119, 123, 124, 125, 126, 129, 134, 136, 138, 142, 148, 151, 157, 159, 160, 161, 162, 164, 165, 168, 172, 173, 178, 184], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 107, 109, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 197, 202, 204, 207, 209, 211, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 249, 250, 252, 254, 256, 260, 262], "magnitud": [9, 12, 20, 85, 90, 101, 107, 141, 204, 249, 250], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 90, 98, 101, 108, 141, 142, 172, 173, 204, 206, 210, 261], "known": [9, 159, 206, 209, 210], "norm": [9, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 254, 256], "modulu": [9, 152], "z": [9, 10, 11, 61, 62, 64, 66, 123, 207], "bj": [9, 12, 79, 90, 141], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 93, 95, 101, 105, 106, 107, 120, 121, 128, 129, 130, 131, 132, 134, 135, 136, 138, 139, 141, 142, 143, 144, 148, 150, 153, 168, 170, 174, 179, 180, 181, 182, 184, 185, 190, 204, 206, 209, 214, 218, 219, 220, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 236, 237, 238, 240, 242, 245, 246, 247, 248, 249, 250, 252, 254, 256, 260], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 159, 161, 162, 172, 173, 207, 236, 237, 247, 249], "sqrt": [9, 10, 11, 61, 62, 189, 204, 207, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 254], "take": [9, 123, 125, 149, 164, 189, 204, 211, 216, 260], "care": [9, 208, 256], "undu": [9, 209], "overflow": [9, 12, 88, 90, 101, 107, 122, 150, 170, 199, 247, 252, 256], "dure": [9, 40, 59, 107, 132, 168, 184, 199, 202, 245, 260, 261], "stage": [9, 107, 257], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 100, 101, 102, 105, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 158, 159, 160, 161, 162, 164, 165, 168, 169, 170, 172, 173, 174, 176, 177, 178, 179, 180, 181, 182, 184, 185, 187, 190, 204, 206, 207, 208, 210, 214, 215, 219, 220, 221, 224, 225, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 260, 262], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 119, 123, 124, 125, 126, 127, 134, 135, 136, 138, 139, 141, 144, 149, 152, 157, 158, 159, 160, 161, 162, 164, 168, 172, 173, 178, 179, 180, 181, 182, 184, 189, 197, 204, 207, 260], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 90, 93, 94, 96, 100, 101, 107, 117, 118, 123, 124, 125, 126, 127, 134, 138, 141, 144, 149, 152, 157, 160, 161, 162, 164, 172, 173, 178, 207, 247, 254], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 93, 94, 96, 117, 118, 119, 122, 123, 125, 144, 157, 159, 162, 164, 173, 189, 204, 205, 260, 261, 262], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 90, 93, 94, 96, 101, 107, 117, 118, 123, 125, 141, 144, 149, 152, 160, 162, 164, 173, 206], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 90, 93, 94, 96, 97, 98, 103, 104, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 137, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 157, 159, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 179, 180, 181, 182, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 34, 35, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 66, 77, 79, 85, 86, 87, 88, 90, 93, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 116, 117, 118, 119, 122, 123, 124, 125, 126, 132, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 153, 157, 158, 159, 160, 161, 162, 164, 165, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 182, 183, 185, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 254, 257], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 94, 96, 101, 123, 124, 125, 126, 149, 161, 162, 172, 173, 206, 242, 245], "princip": [10, 11, 61, 62, 64, 66, 123, 164, 207, 256], "invers": [10, 11, 61, 62, 64, 65, 66, 207, 218, 220, 223, 224, 225, 226, 227, 228, 229, 231, 238, 241, 245, 256], "cosin": [10, 11, 86, 87, 173], "express": [10, 61, 63, 64, 65, 86, 161, 172, 190, 199, 208, 256, 259], "radian": [10, 61, 64, 65, 86, 161, 172], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 90, 122, 124, 126, 159, 161, 162, 172, 173, 207, 247], "pi": [10, 11, 61, 62, 64, 66, 87, 123, 125, 162, 172, 173, 189], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 90, 94, 96, 122, 123, 125, 141, 158, 159, 161, 162, 164, 172, 173, 190, 207, 236, 249, 252], "ln": [10, 11, 61, 62, 64, 66, 123], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 94, 96, 123, 124, 125, 126, 162, 164, 173, 189, 204], "multi": [10, 11, 61, 62, 64, 66, 189, 207, 210, 211, 233, 262], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 90, 94, 96, 123, 125, 141, 149, 161, 162, 164, 172, 173, 260], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 94, 96, 123, 125, 149, 161, 162, 164, 172, 173, 260], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 90, 94, 96, 141, 161, 162, 164, 172, 173, 260], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 123, 125, 134, 136, 138, 149, 150, 164, 168, 170, 184, 185, 206, 207, 233, 256, 261], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 91, 92, 97, 102, 103, 104, 122, 145, 146, 156, 187, 188, 189, 197, 199, 204, 208, 211, 219, 230, 245], "line": [10, 11, 61, 62, 64, 66, 172, 173, 199, 207, 260, 261, 262, 263], "segment": [10, 11, 61, 62, 64, 66, 207], "infti": [10, 11, 61, 62, 64, 66, 86, 123, 125, 149, 164, 207], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 95, 99, 123, 125, 134, 136, 138, 140, 149, 150, 153, 156, 163, 164, 166, 167, 168, 170, 171, 174, 175, 183, 184, 185, 189, 204, 218, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 240, 253, 254, 260], "rang": [10, 61, 62, 64, 66, 77, 88, 123, 125, 150, 164, 170, 190, 204, 210, 252, 260], "strip": [10, 61, 62, 64, 66, 123, 125], "unbound": [10, 61, 62, 64, 66, 123, 125], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 97, 99, 123, 125, 134, 136, 138, 150, 153, 156, 163, 164, 167, 168, 170, 171, 172, 173, 175, 183, 184, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 252, 254, 256], "c99": [10, 11, 61, 62, 64, 66, 90, 123, 125, 141, 149, 164, 207, 257], "provision": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "statu": [10, 11, 61, 62, 64, 66, 123, 125, 149, 164, 207], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 90, 100, 101, 123, 125, 149, 152, 158, 159, 160, 162, 164, 166, 173, 189, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 241], "than": [10, 11, 19, 26, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 88, 90, 98, 99, 100, 101, 102, 123, 124, 125, 126, 132, 141, 149, 150, 152, 158, 159, 160, 162, 164, 166, 168, 170, 171, 173, 178, 179, 180, 181, 182, 184, 190, 199, 202, 205, 208, 211, 212, 215, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 240, 241, 242, 245, 252, 254, 256, 257, 260, 262], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 90, 101, 123, 124, 125, 126, 149, 152, 158, 159, 160, 164, 168, 184, 189, 190, 204, 208, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 240, 241, 242, 245, 254, 260], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 94, 96, 97, 123, 125, 145, 146, 159, 162, 164, 173, 207, 247], "nonzero": [10, 11, 12, 62, 66, 87, 90, 94, 96, 101, 141, 162, 173, 189, 190, 204, 245], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 161, 162, 172, 173, 207], "aco": [11, 61, 189, 204, 206], "simpli": [11, 96, 125, 205, 216, 260, 262], "upper": [11, 77, 97, 177, 204, 232, 246], "half": [11, 15, 66, 122, 140, 164, 174, 190, 221], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 123, 125], "3\u03c0j": [11, 123, 125], "sum": [12, 21, 88, 107, 127, 150, 189, 204, 240, 252, 254, 256], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 90, 93, 101, 105, 106, 107, 120, 121, 127, 128, 130, 131, 135, 139, 141, 144, 149, 152, 169, 186, 204], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 88, 93, 105, 106, 107, 120, 121, 127, 128, 130, 131, 132, 135, 139, 141, 144, 149, 156, 167, 169, 172, 173, 174, 179, 180, 181, 185, 186, 190, 207, 233, 236, 244, 246, 247, 249, 250, 256, 260, 261, 262, 263], "remain": [12, 90, 93, 101, 116, 118, 119, 141, 144, 152, 154, 159, 190, 208, 231], "neither": [12, 40, 90, 101, 132, 141, 174, 249, 261], "nor": [12, 90, 101, 141, 249, 261], "mathemat": [12, 19, 65, 84, 86, 87, 90, 96, 101, 123, 125, 141, 161, 162, 172, 173, 189, 207, 240, 254], "round": [12, 15, 76, 90, 100, 101, 141, 164, 178, 189, 204, 206], "nearest": [12, 90, 141, 157, 178, 206], "mode": [12, 90, 141, 206, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 246], "too": [12, 26, 90, 101, 141, 256, 260], "larg": [12, 90, 101, 141, 210, 216, 247, 260], "appropri": [12, 26, 90, 101, 141, 207, 212], "commut": 12, "associ": [12, 42, 141, 192, 199, 242, 245, 248, 256, 259, 261], "tabl": [12, 90, 141, 189], "c": [12, 90, 93, 122, 141, 143, 144, 153, 167, 168, 173, 184, 190, 204, 207, 210, 213, 232, 236, 237, 238, 246, 248, 249, 257, 259, 260, 262], "d": [12, 90, 93, 122, 141, 144, 199, 219, 230], "dj": [12, 90, 141], "independ": [12, 90, 141, 157, 190, 202, 210, 233, 246, 248, 256, 257, 260], "abov": [12, 88, 90, 93, 123, 125, 141, 144, 149, 150, 164, 170, 176, 177, 190, 199, 207, 208, 210, 211, 214, 235, 236, 252, 256, 259, 262], "similarli": [12, 57, 116, 137, 199, 232, 249], "henc": [12, 79, 95, 143, 153, 179, 180, 181, 182, 190, 205, 207, 208, 209, 210, 214, 215, 216, 260, 262], "z1": 12, "z2": 12, "keepdim": [13, 14, 16, 17, 134, 136, 138, 150, 168, 170, 184, 240, 254], "test": [13, 14, 89, 117, 118, 119, 204, 206, 258, 260, 261, 262], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 94, 96, 123, 124, 125, 126, 142, 148, 159, 160, 165, 202, 260], "union": [13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 75, 77, 78, 91, 98, 99, 103, 104, 108, 115, 116, 122, 134, 136, 138, 140, 145, 150, 153, 155, 156, 166, 167, 168, 170, 174, 184, 187, 221, 225, 240, 242, 245, 254, 261], "ax": [13, 14, 16, 17, 19, 55, 56, 99, 134, 136, 138, 140, 147, 150, 156, 166, 168, 170, 174, 175, 184, 185, 190, 204, 220, 221, 224, 225, 228, 231, 233, 240, 245, 248, 251, 254], "logic": [13, 14, 24, 26, 90, 93, 128, 129, 130, 131, 141, 144, 211, 214, 220, 224, 228, 231], "AND": [13, 67, 93, 128, 259], "entir": [13, 14, 86, 87, 94, 96, 134, 136, 138, 150, 161, 162, 168, 170, 184], "valid": [13, 14, 26, 27, 95, 114, 140, 158, 167, 174, 183, 190, 206, 214, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 236, 246, 249, 261], "count": [13, 14, 78, 88, 99, 171, 179, 180, 185, 190, 204, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 237], "last": [13, 14, 18, 19, 55, 78, 88, 99, 156, 163, 167, 171, 174, 185, 190, 218, 220, 222, 223, 224, 226, 227, 228, 229, 231, 233, 235, 240, 246, 249, 252], "invalid": [13, 14, 23, 95, 212, 260], "rais": [13, 14, 19, 23, 24, 25, 26, 29, 34, 35, 40, 47, 51, 55, 60, 74, 90, 94, 95, 102, 122, 132, 134, 138, 143, 149, 154, 166, 167, 183, 185, 190, 199, 202, 204, 210, 211, 212, 214, 233, 241, 260], "wa": [13, 14, 19, 26, 101, 134, 136, 138, 150, 168, 170, 184, 199, 211, 216, 260, 262], "OR": [14, 24, 70, 130, 144, 259], "start": [15, 122, 190, 204, 216, 260, 262], "stop": [15, 122, 190, 204, 261], "step": [15, 122, 190, 261], "evenli": [15, 122], "space": [15, 122, 219, 221, 230], "open": [15, 122, 140, 174, 190], "inclus": [15, 190, 260], "end": [15, 65, 86, 122, 159, 161, 172, 173, 197, 208, 247, 260, 261, 262], "exclus": [15, 190], "distanc": [15, 107], "between": [15, 26, 47, 51, 65, 78, 90, 93, 98, 122, 134, 135, 138, 139, 144, 149, 167, 179, 180, 181, 182, 199, 207, 208, 211, 219, 230, 256, 260, 262], "adjac": 15, "output": [15, 60, 63, 78, 88, 91, 92, 95, 97, 99, 102, 103, 104, 111, 122, 137, 145, 146, 154, 156, 158, 166, 167, 171, 175, 187, 188, 202, 204, 207, 208, 211, 213, 214, 216, 218, 219, 220, 222, 223, 224, 227, 228, 229, 230, 231, 252, 260], "infer": [15, 60, 63, 92, 103, 104, 146, 154, 188, 209, 256, 261], "cannot": [15, 26, 57, 102, 172, 173, 204, 207, 209, 260], "guarante": [15, 59, 179, 181, 202, 207, 211, 260, 262], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 90, 102, 134, 138, 172, 173, 199, 206, 247, 260], "ceil": [15, 189], "indic": [16, 17, 18, 26, 60, 88, 89, 102, 111, 116, 122, 140, 143, 156, 158, 159, 171, 174, 176, 177, 179, 181, 190, 199, 204, 254, 260], "occur": [16, 17, 75, 107, 172, 173, 179, 180, 181, 182, 207, 261], "occurr": [16, 17, 179], "comparison": [16, 17, 18, 31, 33, 37, 39, 93, 105, 106, 120, 121, 134, 135, 138, 139, 144, 163, 189, 204, 207, 257, 261], "search": [16, 17, 158, 189], "flatten": [16, 17, 78, 153, 156, 179, 180, 181, 182, 254, 256], "descend": [18, 163, 249, 250], "stabl": [18, 163, 210], "sort": [18, 158, 189, 204, 236, 237, 249, 250], "ascend": [18, 158, 163, 204], "stabil": [18, 163], "maintain": [18, 163, 205, 260, 262], "rel": [18, 19, 55, 99, 135, 139, 156, 163, 204, 235, 242, 245, 252], "compar": [18, 163, 179, 180, 181, 182, 206, 211, 261, 263], "properti": [19, 53, 54, 55, 56, 57, 58, 115, 204, 207, 211, 216, 260], "transpos": [19, 40, 55, 132, 133, 174, 232, 236, 245, 249, 256], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 89, 199, 202, 204, 211], "permut": [19, 55, 147], "revers": [19, 55, 65, 99], "origin": [19, 55, 65, 107, 140, 154, 156, 204, 208, 218, 220, 223, 224, 227, 228, 229, 231, 260, 261], "limit": [19, 98, 108, 116, 206, 256, 259], "matric": [19, 40, 55, 132, 133, 137, 176, 177, 232, 234, 235, 236, 237, 238, 240, 241, 242, 245, 246, 247, 248, 249, 250, 252, 256], "deviat": [19, 168, 206, 212, 260, 262], "et": [19, 249, 250], "al": 19, "intent": [19, 65], "found": [19, 207, 210, 262, 263], "problemat": [19, 63, 205, 208], "conflict": [19, 204], "definit": [19, 86, 87, 161, 162, 172, 173, 204, 232, 261], "batch": [19, 254, 256], "cetera": [19, 249, 250], "permute_dim": [19, 189], "interfac": [19, 210, 256, 260, 262], "ab": [20, 107, 149, 189, 204, 240, 254], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 189, 204], "api_vers": [23, 260], "object": [23, 24, 25, 26, 29, 34, 35, 53, 57, 59, 60, 89, 98, 102, 108, 110, 112, 113, 114, 189, 190, 199, 202, 204, 208, 210, 211, 214, 216, 255, 257, 261, 262], "2020": [23, 216, 257, 259, 260], "10": [23, 27, 124, 190, 260], "latest": [23, 210], "modul": [23, 202, 257, 261, 262, 263], "everi": [23, 103, 104, 246, 260], "top": [23, 202, 260, 262], "level": [23, 199, 205, 210, 211, 255, 256, 260, 261], "public": [23, 255, 261, 262], "well": [23, 205, 207, 210, 211, 246, 262, 263], "part": [23, 35, 176, 177, 199, 204, 210, 215, 257, 260, 262], "convert": [24, 25, 29, 34, 35, 60, 102, 199, 204, 205, 207, 210, 260, 262], "handl": [24, 26, 61, 64, 86, 88, 102, 124, 126, 149, 150, 159, 161, 165, 170, 172, 204, 205, 207, 208, 211, 212, 252, 260], "lazi": [24, 25, 29, 34, 35, 202, 204, 213, 262], "languag": [24, 25, 29, 34, 35, 208, 212, 214, 256, 260, 262], "therefor": [24, 25, 29, 34, 35, 202, 210, 211, 212, 214, 216, 257, 260, 262], "abl": [24, 25, 29, 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method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "cumulative_sum() (in module array_api)": [[88, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[89, "array_api.data_types.__eq__"]], "divide() (in module array_api)": [[90, "array_api.divide"]], "empty() (in module array_api)": [[91, "array_api.empty"]], "empty_like() (in module array_api)": [[92, "array_api.empty_like"]], "equal() (in module array_api)": [[93, "array_api.equal"]], "exp() (in module array_api)": [[94, "array_api.exp"]], "expand_dims() (in module array_api)": [[95, "array_api.expand_dims"]], "expm1() (in module array_api)": [[96, "array_api.expm1"]], "eye() (in module array_api)": [[97, "array_api.eye"]], "finfo() (in module array_api)": [[98, "array_api.finfo"]], "flip() (in module array_api)": [[99, "array_api.flip"]], "floor() (in module array_api)": [[100, "array_api.floor"]], "floor_divide() (in module array_api)": [[101, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[102, "array_api.from_dlpack"]], "full() (in module array_api)": [[103, "array_api.full"]], "full_like() (in module array_api)": [[104, "array_api.full_like"]], "greater() (in module array_api)": [[105, "array_api.greater"]], "greater_equal() (in module array_api)": [[106, "array_api.greater_equal"]], "hypot() (in module array_api)": [[107, "array_api.hypot"]], "iinfo() (in module array_api)": [[108, "array_api.iinfo"]], "imag() (in module array_api)": [[109, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[110, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[111, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[112, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[113, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[114, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[115, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[116, "array_api.isdtype"]], "isfinite() (in module array_api)": [[117, "array_api.isfinite"]], "isinf() (in module array_api)": [[118, "array_api.isinf"]], "isnan() (in module array_api)": [[119, "array_api.isnan"]], "less() (in module array_api)": [[120, "array_api.less"]], "less_equal() (in module array_api)": [[121, "array_api.less_equal"]], "linspace() (in module array_api)": [[122, "array_api.linspace"]], "log() (in module array_api)": [[123, "array_api.log"]], "log10() (in module array_api)": [[124, "array_api.log10"]], "log1p() (in module array_api)": [[125, "array_api.log1p"]], "log2() (in module array_api)": [[126, "array_api.log2"]], "logaddexp() (in module array_api)": [[127, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[128, "array_api.logical_and"]], "logical_not() (in module array_api)": [[129, "array_api.logical_not"]], "logical_or() (in module array_api)": [[130, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[131, "array_api.logical_xor"]], "matmul() (in module array_api)": [[132, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[133, "array_api.matrix_transpose"]], "max() (in module array_api)": [[134, "array_api.max"]], "maximum() (in module array_api)": [[135, "array_api.maximum"]], "mean() (in module array_api)": [[136, "array_api.mean"]], "meshgrid() (in module array_api)": [[137, "array_api.meshgrid"]], "min() (in module array_api)": [[138, "array_api.min"]], "minimum() (in module array_api)": [[139, "array_api.minimum"]], "moveaxis() (in module array_api)": [[140, "array_api.moveaxis"]], "multiply() (in module array_api)": [[141, "array_api.multiply"]], "negative() (in module array_api)": [[142, "array_api.negative"]], "nonzero() (in module array_api)": [[143, "array_api.nonzero"]], "not_equal() (in module array_api)": [[144, "array_api.not_equal"]], "ones() (in module array_api)": [[145, "array_api.ones"]], "ones_like() (in module array_api)": [[146, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[147, "array_api.permute_dims"]], "positive() (in module array_api)": [[148, "array_api.positive"]], "pow() (in module array_api)": [[149, "array_api.pow"]], "prod() (in module array_api)": [[150, "array_api.prod"]], "real() (in module array_api)": [[151, "array_api.real"]], "remainder() (in module array_api)": [[152, "array_api.remainder"]], "repeat() (in module array_api)": [[153, "array_api.repeat"]], "reshape() (in module array_api)": [[154, "array_api.reshape"]], "result_type() (in module array_api)": [[155, "array_api.result_type"]], "roll() (in module array_api)": [[156, "array_api.roll"]], "round() (in module array_api)": [[157, "array_api.round"]], "searchsorted() (in module array_api)": [[158, "array_api.searchsorted"]], "sign() (in module array_api)": [[159, "array_api.sign"]], "signbit() (in module array_api)": [[160, "array_api.signbit"]], "sin() (in module array_api)": [[161, "array_api.sin"]], "sinh() (in module array_api)": [[162, "array_api.sinh"]], "sort() (in module array_api)": [[163, "array_api.sort"]], "sqrt() (in module array_api)": [[164, "array_api.sqrt"]], "square() (in module array_api)": [[165, "array_api.square"]], "squeeze() (in module array_api)": [[166, "array_api.squeeze"]], "stack() (in module array_api)": [[167, "array_api.stack"]], "std() (in module array_api)": [[168, "array_api.std"]], "subtract() (in module array_api)": [[169, "array_api.subtract"]], "sum() (in module array_api)": [[170, "array_api.sum"]], "take() (in module array_api)": [[171, "array_api.take"]], "tan() (in module array_api)": [[172, "array_api.tan"]], "tanh() (in module array_api)": [[173, "array_api.tanh"]], "tensordot() (in module array_api)": [[174, "array_api.tensordot"]], "tile() (in module array_api)": [[175, "array_api.tile"]], "tril() (in module array_api)": [[176, "array_api.tril"]], "triu() (in module array_api)": [[177, "array_api.triu"]], "trunc() (in module array_api)": [[178, "array_api.trunc"]], "unique_all() (in module array_api)": [[179, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[180, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[181, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[182, "array_api.unique_values"]], "unstack() (in module array_api)": [[183, "array_api.unstack"]], "var() (in module array_api)": [[184, "array_api.var"]], "vecdot() (in module array_api)": [[185, "array_api.vecdot"]], "where() (in module array_api)": [[186, "array_api.where"]], "zeros() (in module array_api)": [[187, "array_api.zeros"]], "zeros_like() (in module array_api)": [[188, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[218, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[219, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[220, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[221, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[222, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[223, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[224, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[225, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[226, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[227, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[228, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[229, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[230, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[231, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[232, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[233, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[234, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[235, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[236, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[237, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[238, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[239, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[240, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[241, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[242, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[243, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[244, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[245, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[246, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[247, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[248, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[249, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[250, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[251, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[252, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[253, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[254, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file
diff --git a/2024.12/changelog.html b/2024.12/changelog.html
index afbf59d4a..ae7120be4 100644
--- a/2024.12/changelog.html
+++ b/2024.12/changelog.html
@@ -701,18 +701,18 @@ <h5 id="id4">APIs<a class="headerlink" href="#id4" title="Link to this heading">
 <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this heading">¶</a></h4>
 <p>The following is a list of fixes and points of clarification with regard to the previous version of the specification:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__bool__</span></code>: fix typo in special case notes (<a class="reference external" href="https://github.com/data-apis/array-api/pull/785">gh-785</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__dlpack__</span></code>: resolve conflicting exception guidance (<a class="reference external" href="https://github.com/data-apis/array-api/pull/887">gh-887</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__getitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify broadcast behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/888">gh-888</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify required exception behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/897">gh-897</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">clip</span></code>: clarify that the operation is only defined when elements in <code class="docutils literal notranslate"><span class="pre">min</span></code> and <code class="docutils literal notranslate"><span class="pre">max</span></code> are inside the bounds of the input array data type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/814">gh-814</a>)</p></li>
@@ -726,7 +726,7 @@ <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this h
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.irfftn</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.hfft</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">linalg.solve</span></code>: clarify broadcasting semantics and output shape (<a class="reference external" href="https://github.com/data-apis/array-api/pull/810">gh-810</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-https://github.com/data-apis/array-api/pull/904</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-904</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">searchsorted</span></code>: fix incorrect boundary conditions (<a class="reference external" href="https://github.com/data-apis/array-api/pull/898">gh-898</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">sign</span></code>: fix equation in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/844">gh-844</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">tile</span></code>: fix missing return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/798">gh-798</a>)</p></li>
diff --git a/2024.12/searchindex.js b/2024.12/searchindex.js
index 60ad5943a..c359eb2ce 100644
--- a/2024.12/searchindex.js
+++ b/2024.12/searchindex.js
@@ -1 +1 @@
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15, 19, 23, 26, 60, 63, 75, 87, 93, 100, 102, 105, 114, 118, 144, 160, 161, 163, 167, 179, 181, 182, 183, 189, 191, 195, 196, 208, 210, 211, 213, 214, 215, 216, 217, 218, 220, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 251, 253, 254, 260, 261, 262, 265, 266, 268, 269], "thi": [0, 1, 5, 7, 15, 19, 26, 32, 34, 49, 58, 59, 63, 71, 75, 77, 78, 99, 104, 105, 110, 114, 118, 119, 125, 128, 131, 132, 133, 134, 139, 147, 153, 157, 158, 160, 172, 173, 176, 177, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 227, 229, 230, 233, 234, 235, 237, 252, 253, 254, 255, 261, 262, 263, 265, 267, 268, 269], "return": [0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 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49, 60, 65, 67, 69, 70, 71, 72, 77, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 148, 153, 157, 160, 174, 192, 195, 196, 220, 260, 268], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 146, 147, 148, 149, 153, 154, 155, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 173, 175, 176, 177, 178, 179, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 205, 208, 210, 212, 214, 215, 216, 220, 222, 225, 228, 232, 233, 234, 235, 236, 237, 238, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "rational": [0, 7, 89, 90, 154, 175, 196, 216, 217, 258, 261, 263, 266], "alwai": 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253, 254, 255, 256, 258, 260, 262, 266, 268], "__pos__": [0, 195, 210], "po": 0, "__neg__": [0, 195, 210], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 89, 90, 92, 93, 98, 100, 102, 104, 121, 126, 128, 144, 153, 157, 161, 165, 169, 176, 177, 180, 191, 195, 196, 210, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 260, 266], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "__add__": [0, 50, 195, 210], "add": [0, 7, 21, 90, 174, 175, 195, 196, 210, 211, 212, 217, 258], "__sub__": [0, 195, 210], "sub": [0, 196], "__mul__": [0, 195, 210], "mul": 0, "__truediv__": [0, 195, 210], "truediv": 0, "__floordiv__": [0, 195], 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"The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 102, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 205, 208, 210, 211, 212, 214, 215, 216, 217, 220, 221, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 263, 265, 266, 267, 268, 269], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 79, 89, 90, 92, 93, 104, 118, 119, 120, 121, 122, 135, 140, 144, 145, 152, 153, 154, 155, 162, 164, 170, 174, 175, 180, 205, 212, 224, 226, 229, 230, 233, 234, 235, 237, 239, 250, 251, 253, 258, 262, 266, 268], "__invert__": [0, 195], "inv": [0, 210, 262], "invert": [0, 68, 244, 247, 254], "__inv__": 0, "__and__": [0, 195], "__or__": [0, 195], "__xor__": [0, 195], "xor": [0, 72, 134], "__lshift__": [0, 195], "lshift": 0, "__rshift__": [0, 195], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 49, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 89, 90, 92, 93, 103, 104, 106, 107, 111, 114, 118, 119, 125, 137, 139, 141, 145, 153, 154, 157, 158, 160, 162, 163, 173, 175, 176, 184, 190, 191, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247, 248, 258, 260, 266], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 90, 91, 105, 106, 107, 114, 118, 119, 125, 131, 132, 133, 134, 147, 192, 195, 205, 210], "__lt__": [0, 195, 210], "lt": 0, "__le__": [0, 195, 210], "le": 0, "__gt__": [0, 195, 210], "gt": [0, 252, 255], "__ge__": [0, 195, 210], "ge": 0, "__eq__": [0, 195, 210, 217], "eq": 0, "__ne__": [0, 195, 210], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 43, 49, 55, 58, 60, 77, 85, 86, 88, 91, 92, 93, 96, 97, 100, 101, 102, 104, 105, 108, 109, 110, 117, 118, 123, 124, 125, 131, 132, 133, 134, 135, 139, 144, 147, 148, 153, 158, 160, 161, 162, 166, 178, 179, 181, 185, 187, 191, 196, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 229, 230, 231, 233, 234, 235, 236, 237, 239, 242, 243, 248, 251, 252, 255, 261, 262, 263, 266, 267, 268, 269], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 77, 102, 105, 110, 116, 118, 119, 125, 131, 132, 133, 134, 135, 139, 173, 190, 191, 195, 196, 205, 208, 210, 211, 213, 214, 216, 217, 218, 220, 222, 227, 239, 244, 251, 252, 254, 262, 263, 266, 267, 268, 269], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 91, 93, 99, 104, 105, 128, 143, 144, 160, 173, 190, 196, 198, 208, 210, 212, 213, 214, 215, 216, 217, 218, 222, 239, 251, 261, 262, 265, 266, 268], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 91, 92, 96, 110, 120, 121, 148, 169, 195, 196, 205, 210, 213, 214, 216, 222, 255, 263, 265, 266, 269], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 77, 79, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 153, 154, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 175, 178, 179, 184, 185, 186, 187, 188, 196, 203, 208, 212, 213, 214, 215, 217, 220, 225, 234, 236, 253, 255, 256, 258, 266, 268, 269], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 92, 108, 109, 123, 124, 125, 137, 138, 141, 142, 157, 168, 191, 196, 210, 213, 214, 218, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 266], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 125, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 159, 168, 173, 174, 175, 177, 190, 191, 192, 196, 205, 210, 213, 214, 218, 239, 246, 248, 251, 254, 260, 266, 268], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 75, 91, 92, 93, 96, 104, 105, 108, 109, 110, 113, 118, 119, 123, 124, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 148, 158, 159, 160, 163, 168, 173, 179, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 242, 252, 253, 255, 261, 262, 266, 267, 268], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 89, 90, 93, 96, 97, 99, 100, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 160, 162, 164, 166, 167, 168, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 205, 216, 217, 219, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 89, 90, 104, 108, 109, 110, 119, 123, 124, 125, 137, 138, 141, 142, 158, 163, 168, 176, 178, 179, 196, 208, 211, 212, 213, 214, 215, 217, 262, 263, 266, 268], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 108, 109, 123, 124, 137, 138, 141, 142, 168], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 60, 62, 66, 77, 78, 79, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 167, 168, 169, 172, 176, 177, 179, 196, 203, 205, 210, 226, 227, 230, 231, 234, 237, 242, 243, 266], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 57, 60, 71, 77, 79, 89, 90, 92, 96, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 168, 176, 178, 179, 196, 203, 212, 213, 226, 227, 230, 231, 234, 237, 242, 243, 255, 262], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 93, 96, 97, 99, 108, 109, 114, 123, 124, 125, 126, 127, 128, 129, 144, 145, 148, 153, 160, 163, 166, 167, 168, 178, 179, 192, 203, 205, 212, 213, 216, 219, 220, 222, 242, 243, 252, 253, 254, 255, 262, 266, 268, 269], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 85, 88, 93, 96, 99, 104, 105, 107, 108, 109, 110, 113, 114, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 147, 148, 153, 154, 156, 157, 158, 159, 160, 163, 164, 168, 169, 170, 173, 174, 175, 177, 185, 186, 187, 188, 190, 191, 192, 195, 196, 205, 207, 208, 211, 213, 215, 216, 217, 222, 239, 246, 248, 251, 254, 260, 261, 266, 267, 268, 269], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 91, 92, 102, 104, 105, 108, 109, 123, 124, 137, 138, 141, 142, 147, 158, 163, 168, 178, 179, 180, 185, 186, 187, 188, 196, 203, 205, 210, 212, 214, 215, 216, 218, 233, 234, 242, 243, 246, 255, 256, 260, 262, 263, 266, 267], "discuss": [0, 96, 148, 210, 216, 217, 221, 266, 267, 268], "copi": [0, 1, 26, 59, 60, 63, 105, 159, 168, 210, 211, 216, 217, 219, 265, 266], "view": [0, 105, 219], "behavior": [0, 5, 26, 32, 47, 49, 59, 60, 63, 74, 77, 89, 90, 92, 93, 104, 106, 107, 110, 125, 144, 153, 157, 159, 160, 163, 176, 177, 185, 186, 187, 188, 195, 196, 198, 205, 208, 210, 212, 213, 219, 220, 221, 226, 227, 230, 231, 234, 237, 262, 263, 266, 267, 268, 269], "mutabl": [0, 219], "refer": [0, 1, 13, 14, 92, 99, 100, 128, 163, 173, 176, 177, 180, 181, 190, 191, 196, 213, 214, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 254], "what": [0, 163, 208, 216, 218, 222, 262, 266, 267, 268, 269], "call": [0, 7, 34, 92, 216, 217, 220, 253, 266, 267, 268], "http": [0, 210, 216, 263, 269], "doc": 0, "org": 0, "html": 0, "do": [0, 1, 26, 75, 93, 144, 157, 203, 208, 210, 211, 213, 214, 216, 217, 218, 262, 263, 265, 266, 268, 269], "mutat": [0, 176, 210], "choos": [0, 51, 57, 59, 92, 93, 104, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 158, 160, 173, 185, 186, 187, 188, 190, 195, 196, 203, 213, 214, 215, 217, 220, 266, 268], "when": [0, 5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 75, 77, 89, 90, 93, 99, 104, 105, 110, 116, 118, 125, 128, 137, 138, 139, 141, 142, 144, 153, 154, 158, 159, 163, 173, 175, 176, 179, 190, 192, 195, 196, 205, 210, 211, 213, 214, 215, 216, 218, 220, 221, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 244, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268], "doe": [0, 1, 15, 26, 105, 148, 176, 177, 196, 205, 208, 211, 212, 213, 214, 215, 217, 218, 220, 222, 262, 266, 268, 269], "correspond": [0, 1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 96, 105, 108, 109, 114, 115, 116, 123, 124, 148, 153, 159, 161, 163, 173, 177, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 226, 230, 234, 237, 239, 242, 246, 265, 266], "fall": 0, "back": [0, 268], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 77, 104, 110, 131, 132, 133, 134, 157, 162, 176, 196, 205, 210, 213, 214, 248, 251, 254, 260, 266], "binari": [0, 5, 67, 70, 72, 178, 179, 211], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 90, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 159, 160, 162, 163, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 192, 208, 224, 225, 226, 228, 229, 230, 233, 234, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263, 266, 268, 269], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 89, 90, 92, 94, 95, 98, 102, 106, 107, 114, 135, 136, 140, 149, 150, 159, 161, 163, 168, 172, 176, 177, 180, 181, 182, 183, 189, 191, 193, 194, 195, 210, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 266, 268], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 93, 96, 97, 99, 103, 104, 108, 109, 110, 112, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 173, 174, 175, 178, 179, 180, 184, 185, 190, 196, 203, 205, 210, 212, 213, 214, 220, 238, 239, 241, 246, 247, 253, 254, 260, 266, 267, 268, 269], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 92, 93, 96, 97, 99, 104, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 139, 142, 144, 145, 148, 153, 156, 157, 160, 166, 167, 169, 170, 172, 173, 174, 178, 179, 180, 190, 191, 192, 195, 210, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 142, 144, 145, 148, 153, 156, 157, 160, 164, 166, 167, 169, 170, 172, 174, 178, 179, 180, 191, 192, 195, 196, 210, 213, 216, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262, 266, 268], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 173, 174, 175, 177, 180, 190, 191, 192, 195, 196, 210, 239, 246, 248, 251, 254, 260, 266], "let": [0, 1, 9, 10, 11, 12, 62, 66, 85, 87, 89, 90, 92, 96, 97, 99, 105, 120, 121, 122, 125, 126, 128, 139, 148, 154, 158, 163, 164, 167, 169, 173, 175, 179, 181, 190, 191, 196, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 243, 244, 252, 254, 255, 258], "If": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 114, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 211, 213, 217, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 258, 260, 261, 262, 266, 268], "after": [0, 1, 26, 40, 135, 169, 181, 196], "appli": [0, 12, 77, 78, 85, 93, 139, 144, 160, 162, 172, 180, 196, 205, 208, 213, 224, 226, 229, 230, 233, 234, 235, 237, 248, 251, 262, 266, 268], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 175, 178, 179, 184, 205, 210, 212, 253, 258], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 88, 91, 97, 99, 100, 106, 107, 110, 119, 121, 126, 127, 128, 129, 139, 147, 148, 149, 150, 153, 154, 162, 167, 168, 169, 173, 175, 176, 177, 179, 180, 181, 185, 186, 187, 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169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 193, 195, 203, 210, 212, 213, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "creat": [3, 15, 60, 94, 95, 100, 105, 106, 107, 125, 149, 150, 193, 194, 202, 208, 217, 225, 236, 262, 266], "its": [5, 26, 40, 73, 93, 101, 135, 144, 159, 161, 212, 213, 216, 217, 261, 266, 267, 268], "main": [5, 100, 182, 183, 211, 216, 241, 258, 261, 268], "namespac": [5, 7, 23, 113, 198, 208, 210, 223, 261, 262, 263, 266, 269], "under": [5, 261, 265, 266], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 89, 90, 92, 94, 98, 101, 102, 106, 116, 118, 119, 125, 149, 154, 157, 158, 161, 171, 172, 175, 176, 177, 181, 182, 183, 185, 186, 187, 188, 191, 193, 196, 205, 210, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 232, 233, 234, 235, 237, 241, 258, 260, 262, 263, 266, 268, 269], "name": [5, 7, 23, 26, 104, 118, 185, 186, 187, 196, 213, 214, 242, 251, 252, 253, 255, 261, 266, 267], "descript": [5, 7, 210, 212, 246, 260], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 67, 70, 72, 75, 88, 89, 90, 91, 96, 105, 106, 107, 108, 109, 118, 119, 120, 121, 122, 123, 124, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 160, 165, 168, 173, 175, 190, 192, 205, 210, 220, 238, 246, 255, 260], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 101, 104, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 147, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 192, 196, 210, 214, 238, 246, 255, 260, 262], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 196, 238, 246, 255, 260], "int8": [5, 118, 119, 196, 205], "bit": [5, 68, 69, 71, 85, 89, 90, 101, 111, 154, 165, 175, 205, 210, 212, 258], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 89, 90, 93, 97, 99, 104, 118, 119, 126, 128, 137, 138, 141, 142, 144, 145, 153, 154, 157, 163, 165, 167, 169, 175, 179, 185, 186, 187, 188, 195, 203, 210, 213, 252, 253, 258], "exist": [5, 7, 26, 60, 78, 105, 208, 210, 213, 216, 217, 218, 244, 263, 266, 267], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 98, 125, 126, 128, 143, 172, 180, 182, 183, 189, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 263], "128": 5, "127": 5, "int16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "16": [5, 205], "32": [5, 205], "767": 5, "int32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "147": 5, "483": 5, "647": 5, "int64": [5, 89, 90, 118, 119, 154, 175, 205, 258], "64": [5, 205], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 118, 119, 196, 205], "unsign": [5, 89, 90, 118, 119, 154, 175, 195, 258], "255": 5, "uint16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "65": 5, "535": [5, 210], "uint32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "294": 5, "967": 5, "295": 5, "uint64": [5, 118, 119, 205], "18": 5, "446": [5, 210], "744": [5, 210], "073": 5, "709": [5, 210], "551": [5, 210], "615": 5, "float32": [5, 112, 118, 119, 155, 205, 253, 255, 256], "ieee": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "754": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "singl": [5, 7, 24, 25, 29, 34, 35, 116, 118, 185, 186, 195, 205, 210, 211, 213, 216, 217, 222, 262, 266, 267, 268], "2019": [5, 12, 93, 99, 110, 128, 144, 195, 212, 266, 268], "float64": [5, 9, 20, 118, 119, 205, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "doubl": [5, 180, 205, 210], "complex64": [5, 112, 118, 119, 155, 205, 210, 253, 255, 256], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 162, 167, 169, 179, 210, 213], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 155, 162, 167, 169, 178, 179, 185, 186, 187, 188, 210, 213, 227, 236], "complex128": [5, 9, 20, 118, 119, 205, 210, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "method": [5, 26, 34, 105, 195, 198, 208, 214, 216, 217, 220, 221, 222, 266, 267, 268], "attribut": [5, 23, 101, 111, 160, 195, 207, 210, 263, 266, 267, 268], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 75, 89, 90, 105, 110, 119, 154, 160, 169, 172, 175, 176, 177, 179, 185, 186, 188, 189, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 236, 239, 258, 261, 262, 266, 267, 268], "beyond": [5, 161, 205, 210, 266], "It": [5, 23, 26, 105, 208, 214, 216, 266, 268, 269], "also": [5, 7, 26, 32, 34, 105, 110, 164, 208, 213, 214, 215, 216, 222, 226, 230, 234, 237, 255, 261, 268], "subnorm": [5, 110, 212], "k": [5, 40, 100, 110, 135, 147, 182, 183, 196, 212, 238, 242, 243, 244, 252, 254, 255, 256, 258, 266], "denorm": [5, 110, 212], "gradual": [5, 110, 212, 266], "underflow": [5, 9, 93, 104, 110, 212, 253], "hardwar": [5, 53, 110, 158, 212, 216, 217, 242, 255, 262, 266], "univers": [5, 110, 211, 212, 217, 262, 266], "mani": [5, 110, 181, 212, 266, 268], "platform": [5, 26, 110, 212], "compil": [5, 110, 179, 208, 211, 212, 215, 266], "toggl": [5, 110, 212], "daz": [5, 110, 212], "flush": [5, 110, 212], "ftz": [5, 110, 212], "increas": [5, 110, 212, 267], "guard": [5, 110, 212], "against": [5, 40, 73, 110, 135, 179, 196, 212, 248, 251, 269], "time": [5, 7, 16, 17, 26, 92, 110, 158, 185, 186, 208, 210, 212, 215, 216, 221, 238, 242, 243, 244, 252, 254, 255, 262, 266, 268], "attack": [5, 110, 212], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 75, 88, 93, 99, 104, 110, 125, 126, 128, 137, 139, 140, 141, 144, 147, 154, 158, 160, 163, 169, 173, 175, 185, 186, 187, 188, 190, 196, 205, 212, 213, 214, 215, 217, 246, 252, 260, 262], "vari": [5, 110, 163, 179, 185, 186, 187, 188, 205, 212], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 75, 77, 78, 86, 87, 89, 90, 92, 97, 99, 102, 105, 110, 117, 118, 119, 125, 126, 128, 131, 132, 133, 134, 135, 139, 147, 153, 154, 157, 158, 159, 160, 164, 166, 167, 168, 169, 172, 173, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 195, 198, 208, 210, 211, 213, 214, 215, 216, 217, 220, 221, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 244, 248, 251, 252, 253, 254, 255, 256, 258, 261, 262, 263, 266, 267, 268], "access": [5, 26, 32, 105, 113, 196, 210, 216, 261, 263, 266], "variou": [5, 210], "introspect": 5, "isdtyp": [5, 195, 210], "integr": [5, 63, 77, 116, 118, 119], "keyword": [5, 7, 26, 60, 63, 89, 90, 117, 140, 154, 159, 175, 195, 210, 217, 221, 222, 225, 236, 258, 262, 263, 266, 267, 268], "affect": [5, 15, 49, 214, 217], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 89, 90, 92, 93, 97, 99, 126, 127, 128, 129, 130, 137, 139, 141, 144, 153, 154, 166, 167, 169, 173, 174, 175, 178, 179, 190, 210, 253], "implementor": [5, 261], "free": [5, 214, 217, 265], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 113, 222], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 89, 90, 93, 97, 98, 99, 104, 107, 135, 139, 140, 143, 144, 145, 147, 153, 154, 166, 167, 171, 173, 175, 176, 178, 179, 180, 181, 185, 186, 187, 188, 190, 196, 205, 208, 213, 216, 217, 220, 221, 239, 246, 254, 255, 258, 260, 262, 263, 266, 268, 269], "wai": [5, 26, 63, 105, 208, 211, 217, 218, 263, 266, 267, 268, 269], "f4": [5, 205], "recommend": [5, 7, 19, 23, 26, 125, 131, 132, 133, 134, 139, 157, 173, 190, 203, 210, 212, 214, 216, 217, 266], "guidanc": [5, 7, 26, 49, 210, 211, 218, 266], "govern": [5, 50, 174, 205, 262, 263], "interact": [5, 213], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 89, 90, 93, 96, 97, 99, 101, 104, 105, 110, 113, 119, 120, 121, 125, 126, 127, 128, 129, 130, 135, 137, 138, 141, 142, 144, 146, 154, 157, 164, 165, 166, 169, 175, 178, 179, 180, 192, 196, 212, 213, 214, 218, 222, 253, 258, 266, 267, 269], "exampl": [5, 12, 23, 26, 118, 119, 139, 172, 195, 196, 208, 213, 214, 215, 217, 220, 221, 222, 258, 262, 266, 268, 269], "whether": [5, 13, 14, 26, 59, 60, 63, 75, 79, 89, 90, 91, 105, 114, 119, 122, 125, 139, 155, 159, 165, 210, 217, 238, 242, 243, 252, 254, 261, 265, 266, 268], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 88, 105, 114, 116, 118, 137, 139, 141, 154, 158, 159, 163, 164, 173, 175, 190, 191, 192, 195, 196, 208, 217, 238, 240, 246, 253, 254, 260, 265], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 192, 195, 196, 210, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 267, 268, 269], "possibl": [5, 26, 60, 75, 104, 105, 137, 141, 159, 160, 178, 179, 208, 211, 212, 213, 214, 216, 217, 218, 220, 222, 262, 266, 267, 268, 269], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 88, 89, 135, 137, 139, 141, 144, 145, 154, 173, 175, 190, 196, 208, 211, 213, 216, 217, 221, 222, 243, 244, 262, 263, 266, 268], "In": [5, 12, 19, 26, 59, 89, 90, 93, 96, 104, 119, 121, 122, 139, 144, 148, 154, 157, 164, 175, 195, 196, 198, 205, 212, 213, 214, 216, 218, 233, 234, 252, 253, 255, 258, 262, 263, 267, 268, 269], "clearli": [5, 59, 119, 203, 213, 262, 263], "warn": [5, 158, 218], "about": [5, 7, 26, 101, 111, 214, 262, 266, 268, 269], "organ": [5, 210, 262, 267, 268], "within": [5, 15, 27, 196, 205, 208, 210, 213, 217, 224, 226, 229, 230, 233, 234, 235, 237, 266], "accord": [5, 12, 60, 71, 75, 89, 90, 93, 101, 104, 106, 125, 144, 153, 160, 163, 164, 173, 177, 190, 191, 192, 196, 210, 212, 213], "These": [5, 214, 242, 267], "intend": [5, 89, 90, 154, 175, 208, 258], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 93, 98, 100, 101, 104, 121, 126, 128, 143, 144, 147, 157, 161, 165, 167, 169, 179, 195, 196, 208, 210, 212, 222, 236, 238, 252, 267], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 208, 210, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262], "extern": [7, 268], "usabl": 7, "accept": [7, 26, 131, 132, 133, 134, 139, 157, 173, 190, 208, 263], "argument": [7, 10, 11, 12, 26, 40, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 85, 86, 89, 90, 93, 96, 104, 108, 109, 110, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 138, 142, 144, 148, 153, 154, 157, 159, 160, 163, 166, 169, 174, 175, 178, 179, 180, 192, 195, 205, 212, 216, 217, 224, 225, 226, 229, 230, 233, 234, 235, 236, 237, 258, 262, 266, 267, 268], "map": [7, 213, 214], "base": [7, 47, 57, 58, 97, 98, 126, 127, 128, 129, 153, 185, 186, 187, 188, 196, 210, 214, 220, 222, 262, 263, 266, 267, 268], "sole": [7, 196, 203, 262], "incompat": [7, 26, 74, 105, 208, 263, 266], "normal": [7, 78, 172, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237], "practic": [7, 19, 196, 262, 267], "avail": [7, 105, 117, 208, 216, 261, 263, 267], "still": [7, 26, 222, 262, 267, 268, 269], "consid": [7, 26, 63, 105, 131, 132, 133, 134, 185, 186, 187, 188, 213, 217, 236, 251, 262, 266, 268, 269], "compliant": [7, 26, 51, 93, 99, 105, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 173, 190, 212, 215, 217, 263, 266], "altern": [7, 214, 216, 269], "thei": [7, 26, 205, 211, 214, 216, 217, 221, 222, 261, 262, 263, 266, 268, 269], "were": [7, 104, 158, 163, 210, 266], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 195, 210, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 262, 267, 268], "lead": [7, 104, 213, 252, 255, 266], "readabl": [7, 205, 262, 267], "code": [7, 59, 205, 214, 215, 217, 220, 222, 262, 266, 267, 268], "easier": [7, 208, 214, 262], "evolv": [7, 208, 262], "over": [7, 13, 14, 26, 88, 125, 137, 139, 141, 154, 173, 175, 176, 180, 190, 191, 196, 212, 213, 214, 216, 217, 221, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 258, 260, 262, 266], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 77, 79, 85, 86, 87, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 138, 139, 140, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 160, 162, 164, 166, 167, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 196, 209, 210, 211, 217, 225, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "worri": 7, "xi": [7, 140], "annot": [7, 210, 222, 266], "individu": [7, 139, 196, 217, 220, 221, 222, 225, 236, 266, 267], "aim": [7, 211, 222, 261, 262, 263, 266, 267, 268, 269], "strongli": [7, 214, 268], "look": [7, 268], "like": [7, 196, 208, 211, 213, 220, 222, 263, 266, 267, 268], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 114, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 196, 210, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 266, 267, 269], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 210, 211, 214, 216, 220, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 265, 268], "int": [7, 12, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 74, 77, 78, 85, 88, 89, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 123, 124, 125, 130, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 151, 153, 154, 157, 158, 159, 160, 161, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 189, 190, 191, 192, 193, 196, 205, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 241, 246, 247, 257, 258, 259, 260, 267], "str": [7, 8, 23, 118, 119, 140, 267], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 91, 210, 268], "few": [7, 212, 220, 266, 268], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 115, 116, 118, 125, 137, 139, 140, 141, 147, 149, 150, 154, 158, 159, 161, 163, 168, 172, 173, 175, 177, 180, 182, 183, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 210, 212, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 246, 248, 251, 252, 255, 258, 260], "form": [7, 23, 26, 40, 79, 135, 136, 182, 183, 196, 214, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 263, 267], "question": [7, 211, 266], "commonli": [7, 173, 190, 196, 211, 213, 215, 261, 262, 266, 267], "written": [7, 208, 266, 268], "yyyi": [8, 23, 263], "mm": [8, 23, 263], "string": [8, 23, 118, 119, 210, 263, 266], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 195, 208, 211, 217, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 264, 266, 268], "absolut": [9, 20, 85, 164, 212, 214, 246, 247, 253, 262], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 97, 99, 103, 112, 120, 121, 122, 126, 127, 128, 129, 132, 137, 139, 141, 145, 152, 155, 156, 162, 164, 165, 166, 167, 169, 170, 173, 178, 179, 184, 190], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 110, 112, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 203, 208, 210, 213, 215, 217, 218, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 255, 256, 258, 260, 262, 266, 268], "magnitud": [9, 12, 20, 85, 93, 104, 110, 144, 210, 255, 256], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 93, 101, 104, 111, 144, 145, 146, 178, 179, 210, 216, 267], "known": [9, 164, 212, 215, 216], "norm": [9, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 260, 262], "modulu": [9, 157], "z": [9, 10, 11, 61, 62, 64, 66, 126, 213], "bj": [9, 12, 79, 93, 144], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 92, 93, 96, 98, 104, 108, 109, 110, 123, 124, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 144, 145, 147, 148, 152, 154, 158, 173, 175, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 215, 220, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 164, 166, 167, 178, 179, 213, 242, 243, 253, 255], "sqrt": [9, 10, 11, 61, 62, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 260], "take": [9, 126, 128, 153, 169, 195, 210, 217, 222, 266], "care": [9, 262], "undu": [9, 215], "overflow": [9, 12, 89, 90, 93, 104, 110, 125, 154, 175, 205, 253, 258, 262], "dure": [9, 40, 59, 110, 135, 173, 190, 205, 208, 251, 266, 267], "stage": [9, 110, 263], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 193, 196, 210, 212, 213, 214, 216, 220, 221, 225, 226, 227, 230, 231, 234, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 268], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 157, 162, 163, 164, 165, 166, 167, 169, 173, 178, 179, 184, 185, 186, 187, 188, 190, 195, 203, 210, 213, 266], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 126, 127, 128, 129, 130, 137, 141, 144, 148, 153, 157, 162, 165, 166, 167, 169, 178, 179, 184, 213, 253, 260], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 96, 97, 99, 120, 121, 122, 125, 126, 128, 139, 148, 162, 164, 167, 169, 179, 195, 210, 211, 266, 267, 268], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 93, 96, 97, 99, 104, 110, 114, 120, 121, 126, 128, 144, 148, 153, 157, 165, 167, 169, 179, 212], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 93, 96, 97, 99, 100, 101, 106, 107, 111, 112, 119, 120, 121, 122, 125, 126, 127, 128, 129, 135, 140, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 162, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 97, 99, 104, 126, 127, 128, 129, 153, 166, 167, 178, 179, 212, 248, 251], "princip": [10, 11, 61, 62, 64, 66, 126, 169, 213, 262], "invers": [10, 11, 61, 62, 64, 65, 66, 213, 224, 226, 229, 230, 231, 232, 233, 234, 235, 237, 244, 247, 251, 262], "cosin": [10, 11, 86, 87, 179], "express": [10, 61, 63, 64, 65, 86, 166, 178, 196, 205, 214, 262, 265], "radian": [10, 61, 64, 65, 86, 166, 178], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 93, 125, 127, 129, 164, 166, 167, 178, 179, 213, 253], "pi": [10, 11, 61, 62, 64, 66, 87, 126, 128, 167, 178, 179, 195], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 93, 97, 99, 125, 126, 128, 139, 144, 163, 164, 166, 167, 169, 178, 179, 196, 213, 242, 255, 258], "ln": [10, 11, 61, 62, 64, 66, 126], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 97, 99, 126, 127, 128, 129, 167, 169, 179, 195, 210], "multi": [10, 11, 61, 62, 64, 66, 195, 213, 216, 217, 239, 268], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 93, 97, 99, 126, 128, 144, 153, 166, 167, 169, 178, 179, 266], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 97, 99, 126, 128, 153, 166, 167, 169, 178, 179, 266], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 93, 97, 99, 144, 166, 167, 169, 178, 179, 266], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 89, 90, 126, 128, 137, 139, 141, 153, 154, 169, 173, 175, 190, 191, 212, 213, 239, 262, 267], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 94, 95, 100, 105, 106, 107, 125, 149, 150, 161, 193, 194, 195, 203, 205, 210, 214, 217, 225, 236, 251], "line": [10, 11, 61, 62, 64, 66, 178, 179, 205, 213, 266, 267, 268, 269], "segment": [10, 11, 61, 62, 64, 66, 213], "infti": [10, 11, 61, 62, 64, 66, 86, 126, 128, 153, 169, 213], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 98, 102, 126, 128, 137, 139, 141, 143, 153, 154, 158, 161, 168, 169, 171, 172, 173, 175, 176, 177, 180, 181, 189, 190, 191, 195, 210, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 246, 259, 260, 266], "rang": [10, 61, 62, 64, 66, 77, 89, 90, 126, 128, 154, 169, 175, 196, 210, 216, 258, 266], "strip": [10, 61, 62, 64, 66, 126, 128], "unbound": [10, 61, 62, 64, 66, 126, 128], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 100, 102, 126, 128, 137, 139, 141, 154, 158, 161, 168, 169, 172, 173, 175, 176, 177, 178, 179, 181, 189, 190, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 258, 260, 262], "c99": [10, 11, 61, 62, 64, 66, 93, 126, 128, 144, 153, 169, 213, 263], "provision": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "statu": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 93, 103, 104, 126, 128, 153, 157, 163, 164, 165, 167, 169, 171, 179, 195, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 89, 90, 92, 93, 101, 102, 103, 104, 105, 126, 127, 128, 129, 135, 139, 144, 153, 154, 157, 163, 164, 165, 167, 169, 171, 173, 175, 176, 179, 184, 185, 186, 187, 188, 190, 196, 205, 208, 211, 214, 217, 218, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 246, 247, 248, 251, 258, 260, 262, 263, 266, 268], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 93, 104, 126, 127, 128, 129, 153, 157, 163, 164, 165, 169, 173, 190, 195, 196, 210, 214, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 247, 248, 251, 260, 266], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 97, 99, 100, 126, 128, 149, 150, 164, 167, 169, 179, 213, 253], "nonzero": [10, 11, 12, 62, 66, 87, 93, 97, 99, 104, 144, 167, 179, 195, 196, 210, 251], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 166, 167, 178, 179, 213], "aco": [11, 61, 195, 210, 212], "simpli": [11, 99, 128, 211, 222, 266, 268], "upper": [11, 77, 100, 183, 210, 238, 252], "half": [11, 15, 66, 125, 143, 169, 180, 196, 227], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 126, 128], "3\u03c0j": [11, 126, 128], "sum": [12, 21, 90, 110, 130, 154, 195, 210, 246, 258, 260, 262], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "union": [12, 13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 65, 67, 69, 70, 71, 72, 75, 77, 78, 85, 88, 93, 94, 96, 101, 102, 104, 106, 107, 108, 109, 110, 111, 118, 119, 123, 124, 125, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 153, 154, 157, 158, 160, 161, 171, 172, 173, 174, 175, 180, 190, 192, 193, 227, 231, 246, 248, 251, 260, 267], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 89, 90, 92, 96, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 161, 172, 174, 178, 179, 180, 185, 186, 187, 191, 192, 196, 213, 239, 242, 250, 252, 253, 255, 256, 262, 266, 267, 268, 269], "At": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 160, 174, 192], "least": [12, 40, 65, 67, 69, 70, 71, 72, 85, 88, 93, 96, 104, 108, 109, 110, 118, 119, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 147, 148, 153, 157, 160, 174, 185, 186, 187, 188, 192, 196, 211, 212, 251], "remain": [12, 93, 96, 104, 119, 121, 122, 144, 148, 157, 159, 164, 196, 214, 237], "neither": [12, 40, 93, 104, 135, 144, 180, 255, 267], "nor": [12, 93, 104, 144, 255, 267], "mathemat": [12, 19, 65, 84, 86, 87, 93, 99, 104, 126, 128, 144, 166, 167, 178, 179, 195, 213, 246, 260], "round": [12, 15, 76, 93, 103, 104, 144, 169, 184, 195, 210, 212], "nearest": [12, 93, 144, 162, 184, 212], "mode": [12, 93, 144, 212, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 252], "too": [12, 26, 93, 104, 144, 262, 266], "larg": [12, 93, 104, 144, 216, 222, 253, 266], "appropri": [12, 26, 93, 104, 144, 213, 218], "commut": 12, "associ": [12, 42, 144, 198, 205, 248, 251, 254, 262, 265, 267], "tabl": [12, 93, 144, 195], "c": [12, 93, 96, 125, 144, 147, 148, 158, 172, 173, 179, 190, 196, 210, 213, 216, 219, 238, 242, 243, 244, 252, 254, 255, 263, 265, 266, 268], "d": [12, 93, 96, 125, 144, 148, 205, 225, 236], "dj": [12, 93, 144], "independ": [12, 93, 139, 144, 162, 196, 208, 216, 239, 252, 254, 262, 263, 266], "abov": [12, 89, 90, 93, 96, 126, 128, 144, 148, 153, 154, 169, 175, 182, 183, 196, 205, 213, 214, 216, 217, 220, 241, 242, 258, 262, 265, 268], "similarli": [12, 57, 119, 139, 140, 238, 255], "henc": [12, 77, 79, 98, 147, 158, 185, 186, 187, 188, 196, 211, 213, 215, 216, 220, 221, 222, 266, 268], "z1": 12, "z2": 12, "2024": [12, 26, 28, 31, 32, 33, 37, 39, 43, 65, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 88, 89, 90, 92, 93, 96, 104, 108, 109, 110, 114, 123, 124, 130, 131, 133, 134, 138, 139, 142, 144, 146, 148, 153, 155, 156, 157, 160, 163, 174, 176, 177, 192, 225, 236, 254], "keepdim": [13, 14, 16, 17, 88, 137, 139, 141, 154, 173, 175, 190, 246, 260], "test": [13, 14, 91, 120, 121, 122, 139, 210, 212, 264, 266, 267, 268], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 97, 99, 126, 127, 128, 129, 145, 152, 164, 165, 170, 208, 266], "ax": [13, 14, 16, 17, 19, 55, 56, 88, 89, 90, 102, 137, 139, 141, 143, 151, 154, 161, 171, 173, 175, 176, 180, 181, 190, 191, 196, 210, 226, 227, 230, 231, 234, 237, 239, 246, 251, 254, 257, 260], "logic": [13, 14, 24, 26, 93, 96, 131, 132, 133, 134, 144, 148, 217, 220, 226, 230, 234, 237], "AND": [13, 67, 96, 131, 265], "entir": [13, 14, 86, 87, 88, 97, 99, 137, 139, 141, 154, 166, 167, 173, 175, 190], "valid": [13, 14, 26, 27, 92, 98, 117, 143, 163, 172, 180, 189, 196, 212, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 242, 252, 255, 267], "count": [13, 14, 78, 88, 89, 90, 92, 102, 176, 177, 185, 186, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 243], "last": [13, 14, 18, 19, 55, 78, 89, 90, 92, 102, 161, 168, 172, 176, 177, 180, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 246, 252, 255, 258], "invalid": [13, 14, 23, 92, 98, 218, 266], "wa": [13, 14, 19, 26, 88, 104, 137, 139, 141, 154, 173, 175, 190, 205, 217, 222, 266, 268], "OR": [14, 24, 70, 133, 148, 265], "start": [15, 125, 196, 210, 222, 266, 268], "stop": [15, 125, 196, 210, 267], "step": [15, 125, 196, 267], "evenli": [15, 125], "space": [15, 125, 225, 227, 236], "open": [15, 125, 143, 180, 196], "inclus": [15, 196, 266], "end": [15, 65, 86, 125, 164, 166, 178, 179, 203, 214, 253, 266, 267, 268], "exclus": [15, 196], "distanc": [15, 110], "adjac": 15, "output": [15, 60, 63, 75, 78, 89, 90, 94, 95, 98, 100, 102, 105, 106, 107, 114, 125, 140, 149, 150, 159, 161, 163, 171, 172, 176, 181, 193, 194, 208, 210, 213, 214, 217, 219, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 235, 236, 237, 254, 258, 266], "infer": [15, 60, 63, 95, 106, 107, 150, 159, 194, 196, 215, 262, 267], "cannot": [15, 26, 57, 105, 178, 179, 210, 213, 215, 266], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 93, 105, 137, 141, 178, 179, 205, 212, 253, 266], "ceil": [15, 195], "indic": [16, 17, 18, 26, 60, 89, 90, 91, 105, 114, 119, 125, 143, 147, 161, 163, 164, 176, 177, 180, 182, 183, 185, 187, 196, 205, 210, 260, 266], "occur": [16, 17, 75, 110, 178, 179, 185, 186, 187, 188, 213, 267], "occurr": [16, 17, 185], "comparison": [16, 17, 18, 28, 31, 33, 37, 39, 43, 96, 108, 109, 123, 124, 137, 138, 141, 142, 148, 168, 195, 210, 213, 263, 267], "search": [16, 17, 163, 195], "flatten": [16, 17, 78, 158, 161, 185, 186, 187, 188, 260, 262], "descend": [18, 168, 255, 256], "stabl": [18, 168, 216], "sort": [18, 163, 195, 210, 242, 243, 255, 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"complex-number-ordering"]], "Valued-based Promotion": [[213, "valued-based-promotion"]], "Copy-view behavior and mutability": [[214, "copy-view-behavior-and-mutability"]], "Mutating views": [[214, null]], "Copy keyword argument behavior": [[214, "copy-keyword-argument-behavior"]], "Data-dependent output shapes": [[215, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[216, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[216, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[216, "non-supported-use-cases"]], "Intended usage": [[217, "intended-usage"]], "Syntax for device assignment": [[217, "syntax-for-device-assignment"]], "Semantics": [[217, "semantics"]], "Out of scope for device support": [[217, "out-of-scope-for-device-support"]], "Exceptions": [[218, "exceptions"]], "Design topics & constraints": [[219, "design-topics-constraints"], [219, null]], "Lazy vs. eager execution": [[220, "lazy-vs-eager-execution"]], "Parallelism": [[221, "parallelism"]], "Static typing": [[222, "static-typing"]], "Fourier transform Functions": [[223, "fourier-transform-functions"]], "Extension name and usage": [[223, "extension-name-and-usage"], [262, "extension-name-and-usage"]], "fft": [[224, "fft"]], "fftfreq": [[225, "fftfreq"]], "fftn": [[226, "fftn"]], "fftshift": [[227, "fftshift"]], "hfft": [[228, "hfft"]], "ifft": [[229, "ifft"]], "ifftn": [[230, "ifftn"]], "ifftshift": [[231, "ifftshift"]], "ihfft": [[232, "ihfft"]], "irfft": [[233, "irfft"]], "irfftn": [[234, "irfftn"]], "rfft": [[235, "rfft"]], "rfftfreq": [[236, "rfftfreq"]], "rfftn": [[237, "rfftn"]], "cholesky": [[238, "cholesky"]], "cross": [[239, "cross"]], "det": [[240, "det"]], "diagonal": [[241, "diagonal"]], "eigh": [[242, "eigh"]], "eigvalsh": [[243, "eigvalsh"]], "inv": [[244, "inv"]], "matrix_norm": [[246, "matrix-norm"]], "matrix_power": [[247, "matrix-power"]], "matrix_rank": [[248, "matrix-rank"]], "outer": [[250, "outer"]], "pinv": [[251, "pinv"]], "qr": [[252, "qr"]], "slogdet": [[253, "slogdet"]], "solve": [[254, "solve"]], "svd": [[255, "svd"]], "svdvals": [[256, "svdvals"]], "trace": [[258, "trace"]], "vector_norm": [[260, "vector-norm"]], "Extension modules:": [[261, null]], "Linear Algebra Extension": [[262, "linear-algebra-extension"]], "Design Principles": [[262, "design-principles"]], "Future API standard evolution": [[263, "future-api-standard-evolution"]], "Scope extensions": [[263, "scope-extensions"]], "Versioning": [[263, "versioning"]], "Python array API standard": [[264, "python-array-api-standard"]], "Contents": [[264, "contents"]], "Context": [[264, null]], "API": [[264, null]], "Methodology and Usage": [[264, null]], "Other": [[264, null]], "License": [[265, "license"]], "Purpose and scope": [[266, "purpose-and-scope"]], "Introduction": [[266, "introduction"], [267, "introduction"]], "This API standard": [[266, "this-api-standard"]], "History": [[266, "history"]], "Scope (includes out-of-scope / non-goals)": [[266, "scope-includes-out-of-scope-non-goals"]], "In scope": [[266, "in-scope"]], "Out of scope": [[266, "out-of-scope"]], "Implications of in/out of scope": [[266, "implications-of-in-out-of-scope"]], "Stakeholders": [[266, "stakeholders"]], "How to read this document": [[266, "how-to-read-this-document"]], "How to adopt this API": [[266, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[266, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[266, "discoverability-of-conforming-implementations"]], "Optional feature": [[266, null]], "Conformance": [[266, "conformance"]], "Terms and Definitions": [[266, "terms-and-definitions"]], "Normative References": [[266, "normative-references"]], "Usage Data": [[267, "usage-data"]], "Design": [[267, "design"]], "Usage": [[267, "usage"]], "Use in Decision-Making": [[267, "use-in-decision-making"]], "Use cases": [[268, "use-cases"]], "Types of use cases": [[268, "types-of-use-cases"]], "Concrete use cases": [[268, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[268, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[268, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[268, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[268, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[269, "verification-test-suite"]], "Measuring conformance": [[269, "measuring-conformance"]], "Running the tests": [[269, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "count_nonzero() (in module array_api)": [[88, "array_api.count_nonzero"]], "cumulative_prod() (in module array_api)": [[89, "array_api.cumulative_prod"]], "cumulative_sum() (in module array_api)": [[90, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[91, "array_api.data_types.__eq__"]], "diff() (in module array_api)": [[92, "array_api.diff"]], "divide() (in module array_api)": [[93, "array_api.divide"]], "empty() (in module array_api)": [[94, "array_api.empty"]], "empty_like() (in module array_api)": [[95, "array_api.empty_like"]], "equal() (in module array_api)": [[96, "array_api.equal"]], "exp() (in module array_api)": [[97, "array_api.exp"]], "expand_dims() (in module array_api)": [[98, "array_api.expand_dims"]], "expm1() (in module array_api)": [[99, "array_api.expm1"]], "eye() (in module array_api)": [[100, "array_api.eye"]], "finfo() (in module array_api)": [[101, "array_api.finfo"]], "flip() (in module array_api)": [[102, "array_api.flip"]], "floor() (in module array_api)": [[103, "array_api.floor"]], "floor_divide() (in module array_api)": [[104, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[105, "array_api.from_dlpack"]], "full() (in module array_api)": [[106, "array_api.full"]], "full_like() (in module array_api)": [[107, "array_api.full_like"]], "greater() (in module array_api)": [[108, "array_api.greater"]], "greater_equal() (in module array_api)": [[109, "array_api.greater_equal"]], "hypot() (in module array_api)": [[110, "array_api.hypot"]], "iinfo() (in module array_api)": [[111, "array_api.iinfo"]], "imag() (in module array_api)": [[112, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[113, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[114, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[115, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[116, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[117, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[118, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[119, "array_api.isdtype"]], "isfinite() (in module array_api)": [[120, "array_api.isfinite"]], "isinf() (in module array_api)": [[121, "array_api.isinf"]], "isnan() (in module array_api)": [[122, "array_api.isnan"]], "less() (in module array_api)": [[123, "array_api.less"]], "less_equal() (in module array_api)": [[124, "array_api.less_equal"]], "linspace() (in module array_api)": [[125, "array_api.linspace"]], "log() (in module array_api)": [[126, "array_api.log"]], "log10() (in module array_api)": [[127, "array_api.log10"]], "log1p() (in module array_api)": [[128, "array_api.log1p"]], "log2() (in module array_api)": [[129, "array_api.log2"]], "logaddexp() (in module array_api)": [[130, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[131, "array_api.logical_and"]], "logical_not() (in module array_api)": [[132, "array_api.logical_not"]], "logical_or() (in module array_api)": [[133, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[134, "array_api.logical_xor"]], "matmul() (in module array_api)": [[135, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[136, "array_api.matrix_transpose"]], "max() (in module array_api)": [[137, "array_api.max"]], "maximum() (in module array_api)": [[138, "array_api.maximum"]], "mean() (in module array_api)": [[139, "array_api.mean"]], "meshgrid() (in module array_api)": [[140, "array_api.meshgrid"]], "min() (in module array_api)": [[141, "array_api.min"]], "minimum() (in module array_api)": [[142, "array_api.minimum"]], "moveaxis() (in module array_api)": [[143, "array_api.moveaxis"]], "multiply() (in module array_api)": [[144, "array_api.multiply"]], "negative() (in module array_api)": [[145, "array_api.negative"]], "nextafter() (in module array_api)": [[146, "array_api.nextafter"]], "nonzero() (in module array_api)": [[147, "array_api.nonzero"]], "not_equal() (in module array_api)": [[148, "array_api.not_equal"]], "ones() (in module array_api)": [[149, "array_api.ones"]], "ones_like() (in module array_api)": [[150, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[151, "array_api.permute_dims"]], "positive() (in module array_api)": [[152, "array_api.positive"]], "pow() (in module array_api)": [[153, "array_api.pow"]], "prod() (in module array_api)": [[154, "array_api.prod"]], "real() (in module array_api)": [[155, "array_api.real"]], "reciprocal() (in module array_api)": [[156, "array_api.reciprocal"]], "remainder() (in module array_api)": [[157, "array_api.remainder"]], "repeat() (in module array_api)": [[158, "array_api.repeat"]], "reshape() (in module array_api)": [[159, "array_api.reshape"]], "result_type() (in module array_api)": [[160, "array_api.result_type"]], "roll() (in module array_api)": [[161, "array_api.roll"]], "round() (in module array_api)": [[162, "array_api.round"]], "searchsorted() (in module array_api)": [[163, "array_api.searchsorted"]], "sign() (in module array_api)": [[164, "array_api.sign"]], "signbit() (in module array_api)": [[165, "array_api.signbit"]], "sin() (in module array_api)": [[166, "array_api.sin"]], "sinh() (in module array_api)": [[167, "array_api.sinh"]], "sort() (in module array_api)": [[168, "array_api.sort"]], "sqrt() (in module array_api)": [[169, "array_api.sqrt"]], "square() (in module array_api)": [[170, "array_api.square"]], "squeeze() (in module array_api)": [[171, "array_api.squeeze"]], "stack() (in module array_api)": [[172, "array_api.stack"]], "std() (in module array_api)": [[173, "array_api.std"]], "subtract() (in module array_api)": [[174, "array_api.subtract"]], "sum() (in module array_api)": [[175, "array_api.sum"]], "take() (in module array_api)": [[176, "array_api.take"]], "take_along_axis() (in module array_api)": [[177, "array_api.take_along_axis"]], "tan() (in module array_api)": [[178, "array_api.tan"]], "tanh() (in module array_api)": [[179, "array_api.tanh"]], "tensordot() (in module array_api)": [[180, "array_api.tensordot"]], "tile() (in module array_api)": [[181, "array_api.tile"]], "tril() (in module array_api)": [[182, "array_api.tril"]], "triu() (in module array_api)": [[183, "array_api.triu"]], "trunc() (in module array_api)": [[184, "array_api.trunc"]], "unique_all() (in module array_api)": [[185, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[186, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[187, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[188, "array_api.unique_values"]], "unstack() (in module array_api)": [[189, "array_api.unstack"]], "var() (in module array_api)": [[190, "array_api.var"]], "vecdot() (in module array_api)": [[191, "array_api.vecdot"]], "where() (in module array_api)": [[192, "array_api.where"]], "zeros() (in module array_api)": [[193, "array_api.zeros"]], "zeros_like() (in module array_api)": [[194, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[224, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[225, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[226, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[227, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[228, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[229, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[230, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[231, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[232, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[233, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[234, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[235, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[236, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[237, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[238, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[239, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[240, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[241, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[242, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[243, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[244, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[245, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[246, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[247, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[248, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[249, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[250, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[251, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[252, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[253, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[254, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[255, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[256, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[257, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[258, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[259, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[260, 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15, 19, 23, 26, 60, 63, 75, 87, 93, 100, 102, 105, 114, 118, 144, 160, 161, 163, 167, 179, 181, 182, 183, 189, 191, 195, 196, 208, 210, 211, 213, 214, 215, 216, 217, 218, 220, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 251, 253, 254, 260, 261, 262, 265, 266, 268, 269], "thi": [0, 1, 5, 7, 15, 19, 26, 32, 34, 49, 58, 59, 63, 71, 75, 77, 78, 99, 104, 105, 110, 114, 118, 119, 125, 128, 131, 132, 133, 134, 139, 147, 153, 157, 158, 160, 172, 173, 176, 177, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 227, 229, 230, 233, 234, 235, 237, 252, 253, 254, 255, 261, 262, 263, 265, 267, 268, 269], "return": [0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 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235, 236, 237, 239, 246, 254, 255, 256, 258, 260, 261, 262, 263, 266, 267, 268], "some": [0, 99, 104, 116, 118, 128, 160, 196, 211, 212, 213, 214, 217, 222, 266, 268, 269], "common": [0, 196, 205, 208, 217, 220, 221, 262, 266, 267, 268], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 75, 93, 99, 104, 105, 114, 116, 118, 119, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 147, 158, 163, 173, 179, 185, 186, 187, 188, 190, 195, 196, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 238, 242, 243, 252, 254, 261, 262, 263, 266, 267, 268, 269], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 77, 89, 90, 92, 93, 105, 110, 112, 118, 119, 125, 137, 141, 144, 147, 154, 155, 158, 160, 162, 175, 181, 185, 186, 187, 188, 196, 203, 205, 210, 211, 212, 213, 214, 215, 216, 217, 220, 228, 232, 233, 234, 235, 237, 242, 243, 246, 253, 255, 256, 258, 260, 261, 262, 263, 266, 267, 268], "numpi": [0, 19, 63, 139, 196, 208, 213, 214, 216, 217, 262, 266, 267, 268, 269], "scalar": [0, 2, 12, 49, 60, 65, 67, 69, 70, 71, 72, 77, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 148, 153, 157, 160, 174, 192, 195, 196, 220, 260, 268], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 146, 147, 148, 149, 153, 154, 155, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 173, 175, 176, 177, 178, 179, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 205, 208, 210, 212, 214, 215, 216, 220, 222, 225, 228, 232, 233, 234, 235, 236, 237, 238, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "rational": [0, 7, 89, 90, 154, 175, 196, 216, 217, 258, 261, 263, 266], "alwai": 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268], "model": [0, 57, 58, 93, 144, 213, 220, 268], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 93, 104, 140, 144, 167, 178, 179, 210, 212, 216, 217, 253, 267, 268], "futur": [0, 26, 49, 105, 196, 209, 213, 214, 217, 221, 222, 242, 243, 264, 266, 268], "python": [0, 2, 5, 7, 24, 25, 26, 29, 32, 34, 35, 49, 60, 104, 105, 157, 192, 195, 196, 208, 210, 213, 216, 218, 220, 221, 222, 263, 265, 266, 267], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 32, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 95, 97, 98, 99, 102, 103, 105, 107, 112, 120, 121, 122, 126, 127, 128, 129, 132, 136, 137, 139, 141, 143, 145, 147, 150, 151, 152, 154, 155, 156, 158, 159, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 194, 196, 213, 214, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 249, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "__pos__": [0, 195, 210], "po": 0, "__neg__": [0, 195, 210], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 89, 90, 92, 93, 98, 100, 102, 104, 121, 126, 128, 144, 153, 157, 161, 165, 169, 176, 177, 180, 191, 195, 196, 210, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 260, 266], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "__add__": [0, 50, 195, 210], "add": [0, 7, 21, 90, 174, 175, 195, 196, 210, 211, 212, 217, 258], "__sub__": [0, 195, 210], "sub": [0, 196], "__mul__": [0, 195, 210], "mul": 0, "__truediv__": [0, 195, 210], "truediv": 0, "__floordiv__": [0, 195], "floordiv": 0, "__mod__": [0, 195], "mod": 0, "__pow__": [0, 195, 210], "pow": [0, 47, 195, 210, 212], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 85, 86, 87, 89, 90, 92, 93, 97, 98, 99, 101, 103, 104, 105, 108, 109, 110, 112, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 146, 152, 153, 154, 156, 157, 159, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 203, 210, 211, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 266, 268, 269], "defin": [0, 5, 12, 23, 30, 32, 41, 49, 60, 65, 77, 79, 89, 90, 92, 93, 104, 106, 107, 118, 125, 137, 138, 139, 141, 142, 143, 144, 155, 157, 160, 164, 169, 170, 173, 176, 182, 183, 190, 191, 195, 196, 198, 203, 210, 212, 213, 222, 226, 227, 230, 231, 234, 237, 238, 242, 243, 244, 251, 252, 254, 262, 267, 268, 269], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 162, 163, 164, 165, 166, 167, 168, 169, 173, 175, 178, 179, 184, 190, 191, 193, 195, 205, 210, 212, 213, 225, 228, 232, 233, 234, 235, 236, 237, 238, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 263], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 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31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 198, 208, 211, 213, 214, 216, 218, 219, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 263, 266, 267], "__matmul__": [0, 195, 210], "matmul": [0, 40, 195, 205, 210, 262], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 102, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 205, 208, 210, 211, 212, 214, 215, 216, 217, 220, 221, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 263, 265, 266, 267, 268, 269], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 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244, 251, 252, 254, 262, 263, 266, 267, 268, 269], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 91, 93, 99, 104, 105, 128, 143, 144, 160, 173, 190, 196, 198, 208, 210, 212, 213, 214, 215, 216, 217, 218, 222, 239, 251, 261, 262, 265, 266, 268], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 91, 92, 96, 110, 120, 121, 148, 169, 195, 196, 205, 210, 213, 214, 216, 222, 255, 263, 265, 266, 269], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 77, 79, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 153, 154, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 175, 178, 179, 184, 185, 186, 187, 188, 196, 203, 208, 212, 213, 214, 215, 217, 220, 225, 234, 236, 253, 255, 256, 258, 266, 268, 269], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 92, 108, 109, 123, 124, 125, 137, 138, 141, 142, 157, 168, 191, 196, 210, 213, 214, 218, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 266], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 125, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 159, 168, 173, 174, 175, 177, 190, 191, 192, 196, 205, 210, 213, 214, 218, 239, 246, 248, 251, 254, 260, 266, 268], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 75, 91, 92, 93, 96, 104, 105, 108, 109, 110, 113, 118, 119, 123, 124, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 148, 158, 159, 160, 163, 168, 173, 179, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 242, 252, 253, 255, 261, 262, 266, 267, 268], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 89, 90, 93, 96, 97, 99, 100, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 160, 162, 164, 166, 167, 168, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 205, 216, 217, 219, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 89, 90, 104, 108, 109, 110, 119, 123, 124, 125, 137, 138, 141, 142, 158, 163, 168, 176, 178, 179, 196, 208, 211, 212, 213, 214, 215, 217, 262, 263, 266, 268], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 108, 109, 123, 124, 137, 138, 141, 142, 168], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 60, 62, 66, 77, 78, 79, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 167, 168, 169, 172, 176, 177, 179, 196, 203, 205, 210, 226, 227, 230, 231, 234, 237, 242, 243, 266], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 57, 60, 71, 77, 79, 89, 90, 92, 96, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 168, 176, 178, 179, 196, 203, 212, 213, 226, 227, 230, 231, 234, 237, 242, 243, 255, 262], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 93, 96, 97, 99, 108, 109, 114, 123, 124, 125, 126, 127, 128, 129, 144, 145, 148, 153, 160, 163, 166, 167, 168, 178, 179, 192, 203, 205, 212, 213, 216, 219, 220, 222, 242, 243, 252, 253, 254, 255, 262, 266, 268, 269], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 85, 88, 93, 96, 99, 104, 105, 107, 108, 109, 110, 113, 114, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 147, 148, 153, 154, 156, 157, 158, 159, 160, 163, 164, 168, 169, 170, 173, 174, 175, 177, 185, 186, 187, 188, 190, 191, 192, 195, 196, 205, 207, 208, 211, 213, 215, 216, 217, 222, 239, 246, 248, 251, 254, 260, 261, 266, 267, 268, 269], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 91, 92, 102, 104, 105, 108, 109, 123, 124, 137, 138, 141, 142, 147, 158, 163, 168, 178, 179, 180, 185, 186, 187, 188, 196, 203, 205, 210, 212, 214, 215, 216, 218, 233, 234, 242, 243, 246, 255, 256, 260, 262, 263, 266, 267], "discuss": [0, 96, 148, 210, 216, 217, 221, 266, 267, 268], "copi": [0, 1, 26, 59, 60, 63, 105, 159, 168, 210, 211, 216, 217, 219, 265, 266], "view": [0, 105, 219], "behavior": [0, 5, 26, 32, 47, 49, 59, 60, 63, 74, 77, 89, 90, 92, 93, 104, 106, 107, 110, 125, 144, 153, 157, 159, 160, 163, 176, 177, 185, 186, 187, 188, 195, 196, 198, 205, 208, 210, 212, 213, 219, 220, 221, 226, 227, 230, 231, 234, 237, 262, 263, 266, 267, 268, 269], "mutabl": [0, 219], "refer": [0, 1, 13, 14, 92, 99, 100, 128, 163, 173, 176, 177, 180, 181, 190, 191, 196, 213, 214, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 254], "what": [0, 163, 208, 216, 218, 222, 262, 266, 267, 268, 269], "call": [0, 7, 34, 92, 216, 217, 220, 253, 266, 267, 268], "http": [0, 216, 263, 269], "doc": 0, "org": 0, "html": 0, "do": [0, 1, 26, 75, 93, 144, 157, 203, 208, 210, 211, 213, 214, 216, 217, 218, 262, 263, 265, 266, 268, 269], "mutat": [0, 176, 210], "choos": [0, 51, 57, 59, 92, 93, 104, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 158, 160, 173, 185, 186, 187, 188, 190, 195, 196, 203, 213, 214, 215, 217, 220, 266, 268], "when": [0, 5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 75, 77, 89, 90, 93, 99, 104, 105, 110, 116, 118, 125, 128, 137, 138, 139, 141, 142, 144, 153, 154, 158, 159, 163, 173, 175, 176, 179, 190, 192, 195, 196, 205, 210, 211, 213, 214, 215, 216, 218, 220, 221, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 244, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268], "doe": [0, 1, 15, 26, 105, 148, 176, 177, 196, 205, 208, 211, 212, 213, 214, 215, 217, 218, 220, 222, 262, 266, 268, 269], "correspond": [0, 1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 96, 105, 108, 109, 114, 115, 116, 123, 124, 148, 153, 159, 161, 163, 173, 177, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 226, 230, 234, 237, 239, 242, 246, 265, 266], "fall": 0, "back": [0, 268], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 77, 104, 110, 131, 132, 133, 134, 157, 162, 176, 196, 205, 210, 213, 214, 248, 251, 254, 260, 266], "binari": [0, 5, 67, 70, 72, 178, 179, 211], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 90, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 159, 160, 162, 163, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 192, 208, 224, 225, 226, 228, 229, 230, 233, 234, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263, 266, 268, 269], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 89, 90, 92, 94, 95, 98, 102, 106, 107, 114, 135, 136, 140, 149, 150, 159, 161, 163, 168, 172, 176, 177, 180, 181, 182, 183, 189, 191, 193, 194, 195, 210, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 266, 268], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 93, 96, 97, 99, 103, 104, 108, 109, 110, 112, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 173, 174, 175, 178, 179, 180, 184, 185, 190, 196, 203, 205, 210, 212, 213, 214, 220, 238, 239, 241, 246, 247, 253, 254, 260, 266, 267, 268, 269], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 92, 93, 96, 97, 99, 104, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 139, 142, 144, 145, 148, 153, 156, 157, 160, 166, 167, 169, 170, 172, 173, 174, 178, 179, 180, 190, 191, 192, 195, 210, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 142, 144, 145, 148, 153, 156, 157, 160, 164, 166, 167, 169, 170, 172, 174, 178, 179, 180, 191, 192, 195, 196, 210, 213, 216, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262, 266, 268], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 173, 174, 175, 177, 180, 190, 191, 192, 195, 196, 210, 239, 246, 248, 251, 254, 260, 266], "let": [0, 1, 9, 10, 11, 12, 62, 66, 85, 87, 89, 90, 92, 96, 97, 99, 105, 120, 121, 122, 125, 126, 128, 139, 148, 154, 158, 163, 164, 167, 169, 173, 175, 179, 181, 190, 191, 196, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 243, 244, 252, 254, 255, 258], "If": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 114, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 211, 213, 217, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 258, 260, 261, 262, 266, 268], "after": [0, 1, 26, 40, 135, 169, 181, 196], "appli": [0, 12, 77, 78, 85, 93, 139, 144, 160, 162, 172, 180, 196, 205, 208, 213, 224, 226, 229, 230, 233, 234, 235, 237, 248, 251, 262, 266, 268], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 175, 178, 179, 184, 205, 210, 212, 253, 258], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 88, 91, 97, 99, 100, 106, 107, 110, 119, 121, 126, 127, 128, 129, 139, 147, 148, 149, 150, 153, 154, 162, 167, 168, 169, 173, 175, 176, 177, 179, 180, 181, 185, 186, 187, 188, 190, 195, 196, 203, 210, 213, 217, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 247, 248, 251, 252, 253, 254, 258, 266], "left": [0, 1, 5, 28, 31, 33, 37, 39, 43, 60, 69, 90, 96, 104, 106, 108, 109, 123, 124, 148, 163, 176, 177, 196, 205, 242, 243, 255, 266], "hand": [0, 1, 205], "side": [0, 110, 163, 196, 214, 216], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 89, 90, 92, 93, 95, 98, 101, 102, 103, 104, 105, 107, 112, 135, 136, 137, 139, 140, 141, 143, 144, 146, 150, 151, 152, 153, 154, 155, 157, 158, 159, 161, 162, 163, 164, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 194, 196, 205, 208, 210, 213, 214, 216, 217, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 240, 241, 242, 244, 247, 251, 252, 253, 255, 256, 258, 261, 262, 266, 268], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 173, 175, 178, 179, 184, 190, 210, 211, 213, 253, 258], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 105, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 173, 175, 178, 179, 184, 190, 196, 208, 210, 211, 212, 213, 214, 217, 218, 220, 252, 253, 255, 258, 262, 264, 266, 269], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 93, 96, 104, 108, 109, 110, 116, 123, 124, 125, 130, 131, 133, 134, 138, 140, 142, 143, 144, 146, 148, 157, 167, 174, 178, 179, 180, 185, 186, 191, 196, 210, 212, 215, 217, 242, 252, 255], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 100, 105, 135, 136, 140, 160, 162, 180, 182, 183, 185, 186, 187, 188, 191, 196, 205, 216, 217, 220, 221, 226, 227, 230, 231, 234, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268, 269], "assign": [0, 214], "addit": [0, 5, 7, 12, 26, 50, 59, 90, 118, 174, 195, 196, 205, 211, 213, 216, 262, 266, 267, 269], "modifi": [0, 26, 214, 265], "differ": [0, 1, 12, 26, 49, 50, 75, 77, 78, 89, 90, 92, 93, 101, 104, 105, 144, 154, 160, 172, 174, 175, 196, 208, 210, 214, 217, 218, 220, 231, 242, 252, 253, 255, 258, 262, 266, 267, 268], "due": [0, 26, 42, 57, 58, 125, 144, 158, 176, 212, 213, 214, 262, 266], "cast": [0, 5, 29, 49, 60, 63, 75, 89, 90, 92, 154, 175, 205, 213, 258, 266, 268], "select": [0, 176, 177, 196, 266], "": [0, 5, 26, 29, 32, 49, 58, 59, 60, 80, 104, 105, 140, 157, 173, 181, 182, 183, 190, 196, 203, 208, 210, 211, 212, 213, 214, 216, 217, 220, 222, 226, 230, 234, 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88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 210, 212, 213, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 110, 112, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 193, 195, 203, 210, 212, 213, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "creat": [3, 15, 60, 94, 95, 100, 105, 106, 107, 125, 149, 150, 193, 194, 202, 208, 217, 225, 236, 262, 266], "its": [5, 26, 40, 73, 93, 101, 135, 144, 159, 161, 212, 213, 216, 217, 261, 266, 267, 268], "main": [5, 100, 182, 183, 211, 216, 241, 258, 261, 268], "namespac": [5, 7, 23, 113, 198, 208, 210, 223, 261, 262, 263, 266, 269], "under": [5, 261, 265, 266], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 89, 90, 92, 94, 98, 101, 102, 106, 116, 118, 119, 125, 149, 154, 157, 158, 161, 171, 172, 175, 176, 177, 181, 182, 183, 185, 186, 187, 188, 191, 193, 196, 205, 210, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 232, 233, 234, 235, 237, 241, 258, 260, 262, 263, 266, 268, 269], "name": [5, 7, 23, 26, 104, 118, 185, 186, 187, 196, 213, 214, 242, 251, 252, 253, 255, 261, 266, 267], "descript": [5, 7, 210, 212, 246, 260], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 67, 70, 72, 75, 88, 89, 90, 91, 96, 105, 106, 107, 108, 109, 118, 119, 120, 121, 122, 123, 124, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 160, 165, 168, 173, 175, 190, 192, 205, 210, 220, 238, 246, 255, 260], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 101, 104, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 147, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 192, 196, 210, 214, 238, 246, 255, 260, 262], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 196, 238, 246, 255, 260], "int8": [5, 118, 119, 196, 205], "bit": [5, 68, 69, 71, 85, 89, 90, 101, 111, 154, 165, 175, 205, 210, 212, 258], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 89, 90, 93, 97, 99, 104, 118, 119, 126, 128, 137, 138, 141, 142, 144, 145, 153, 154, 157, 163, 165, 167, 169, 175, 179, 185, 186, 187, 188, 195, 203, 210, 213, 252, 253, 258], "exist": [5, 7, 26, 60, 78, 105, 208, 210, 213, 216, 217, 218, 244, 263, 266, 267], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 98, 125, 126, 128, 143, 172, 180, 182, 183, 189, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 263], "128": 5, "127": 5, "int16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "16": [5, 205], "32": [5, 205], "767": 5, "int32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "147": 5, "483": 5, "647": 5, "int64": [5, 89, 90, 118, 119, 154, 175, 205, 258], "64": [5, 205], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 118, 119, 196, 205], "unsign": [5, 89, 90, 118, 119, 154, 175, 195, 258], "255": 5, "uint16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "65": 5, "535": [5, 210], "uint32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "294": 5, "967": 5, "295": 5, "uint64": [5, 118, 119, 205], "18": 5, "446": [5, 210], "744": [5, 210], "073": 5, "709": [5, 210], "551": [5, 210], "615": 5, "float32": [5, 112, 118, 119, 155, 205, 253, 255, 256], "ieee": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "754": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "singl": [5, 7, 24, 25, 29, 34, 35, 116, 118, 185, 186, 195, 205, 210, 211, 213, 216, 217, 222, 262, 266, 267, 268], "2019": [5, 12, 93, 99, 110, 128, 144, 195, 212, 266, 268], "float64": [5, 9, 20, 118, 119, 205, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "doubl": [5, 180, 205, 210], "complex64": [5, 112, 118, 119, 155, 205, 210, 253, 255, 256], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 162, 167, 169, 179, 210, 213], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 155, 162, 167, 169, 178, 179, 185, 186, 187, 188, 210, 213, 227, 236], "complex128": [5, 9, 20, 118, 119, 205, 210, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "method": [5, 26, 34, 105, 195, 198, 208, 214, 216, 217, 220, 221, 222, 266, 267, 268], "attribut": [5, 23, 101, 111, 160, 195, 207, 210, 263, 266, 267, 268], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 75, 89, 90, 105, 110, 119, 154, 160, 169, 172, 175, 176, 177, 179, 185, 186, 188, 189, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 236, 239, 258, 261, 262, 266, 267, 268], "beyond": [5, 161, 205, 210, 266], "It": [5, 23, 26, 105, 208, 214, 216, 266, 268, 269], "also": [5, 7, 26, 32, 34, 105, 110, 164, 208, 213, 214, 215, 216, 222, 226, 230, 234, 237, 255, 261, 268], "subnorm": [5, 110, 212], "k": [5, 40, 100, 110, 135, 147, 182, 183, 196, 212, 238, 242, 243, 244, 252, 254, 255, 256, 258, 266], "denorm": [5, 110, 212], "gradual": [5, 110, 212, 266], "underflow": [5, 9, 93, 104, 110, 212, 253], "hardwar": [5, 53, 110, 158, 212, 216, 217, 242, 255, 262, 266], "univers": [5, 110, 211, 212, 217, 262, 266], "mani": [5, 110, 181, 212, 266, 268], "platform": [5, 26, 110, 212], "compil": [5, 110, 179, 208, 211, 212, 215, 266], "toggl": [5, 110, 212], "daz": [5, 110, 212], "flush": [5, 110, 212], "ftz": [5, 110, 212], "increas": [5, 110, 212, 267], "guard": [5, 110, 212], "against": [5, 40, 73, 110, 135, 179, 196, 212, 248, 251, 269], "time": [5, 7, 16, 17, 26, 92, 110, 158, 185, 186, 208, 210, 212, 215, 216, 221, 238, 242, 243, 244, 252, 254, 255, 262, 266, 268], "attack": [5, 110, 212], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 75, 88, 93, 99, 104, 110, 125, 126, 128, 137, 139, 140, 141, 144, 147, 154, 158, 160, 163, 169, 173, 175, 185, 186, 187, 188, 190, 196, 205, 212, 213, 214, 215, 217, 246, 252, 260, 262], "vari": [5, 110, 163, 179, 185, 186, 187, 188, 205, 212], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 75, 77, 78, 86, 87, 89, 90, 92, 97, 99, 102, 105, 110, 117, 118, 119, 125, 126, 128, 131, 132, 133, 134, 135, 139, 147, 153, 154, 157, 158, 159, 160, 164, 166, 167, 168, 169, 172, 173, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 195, 198, 208, 210, 211, 213, 214, 215, 216, 217, 220, 221, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 244, 248, 251, 252, 253, 254, 255, 256, 258, 261, 262, 263, 266, 267, 268], "access": [5, 26, 32, 105, 113, 196, 210, 216, 261, 263, 266], "variou": [5, 210], "introspect": 5, "isdtyp": [5, 195, 210], "integr": [5, 63, 77, 116, 118, 119], "keyword": [5, 7, 26, 60, 63, 89, 90, 117, 140, 154, 159, 175, 195, 210, 217, 221, 222, 225, 236, 258, 262, 263, 266, 267, 268], "affect": [5, 15, 49, 214, 217], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 89, 90, 92, 93, 97, 99, 126, 127, 128, 129, 130, 137, 139, 141, 144, 153, 154, 166, 167, 169, 173, 174, 175, 178, 179, 190, 210, 253], "implementor": [5, 261], "free": [5, 214, 217, 265], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 113, 222], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 89, 90, 93, 97, 98, 99, 104, 107, 135, 139, 140, 143, 144, 145, 147, 153, 154, 166, 167, 171, 173, 175, 176, 178, 179, 180, 181, 185, 186, 187, 188, 190, 196, 205, 208, 213, 216, 217, 220, 221, 239, 246, 254, 255, 258, 260, 262, 263, 266, 268, 269], "wai": [5, 26, 63, 105, 208, 211, 217, 218, 263, 266, 267, 268, 269], "f4": [5, 205], "recommend": [5, 7, 19, 23, 26, 125, 131, 132, 133, 134, 139, 157, 173, 190, 203, 210, 212, 214, 216, 217, 266], "guidanc": [5, 7, 26, 49, 210, 211, 218, 266], "govern": [5, 50, 174, 205, 262, 263], "interact": [5, 213], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 89, 90, 93, 96, 97, 99, 101, 104, 105, 110, 113, 119, 120, 121, 125, 126, 127, 128, 129, 130, 135, 137, 138, 141, 142, 144, 146, 154, 157, 164, 165, 166, 169, 175, 178, 179, 180, 192, 196, 212, 213, 214, 218, 222, 253, 258, 266, 267, 269], "exampl": [5, 12, 23, 26, 118, 119, 139, 172, 195, 196, 208, 213, 214, 215, 217, 220, 221, 222, 258, 262, 266, 268, 269], "whether": [5, 13, 14, 26, 59, 60, 63, 75, 79, 89, 90, 91, 105, 114, 119, 122, 125, 139, 155, 159, 165, 210, 217, 238, 242, 243, 252, 254, 261, 265, 266, 268], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 88, 105, 114, 116, 118, 137, 139, 141, 154, 158, 159, 163, 164, 173, 175, 190, 191, 192, 195, 196, 208, 217, 238, 240, 246, 253, 254, 260, 265], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 192, 195, 196, 210, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 267, 268, 269], "possibl": [5, 26, 60, 75, 104, 105, 137, 141, 159, 160, 178, 179, 208, 211, 212, 213, 214, 216, 217, 218, 220, 222, 262, 266, 267, 268, 269], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 88, 89, 135, 137, 139, 141, 144, 145, 154, 173, 175, 190, 196, 208, 211, 213, 216, 217, 221, 222, 243, 244, 262, 263, 266, 268], "In": [5, 12, 19, 26, 59, 89, 90, 93, 96, 104, 119, 121, 122, 139, 144, 148, 154, 157, 164, 175, 195, 196, 198, 205, 212, 213, 214, 216, 218, 233, 234, 252, 253, 255, 258, 262, 263, 267, 268, 269], "clearli": [5, 59, 119, 203, 213, 262, 263], "warn": [5, 158, 218], "about": [5, 7, 26, 101, 111, 214, 262, 266, 268, 269], "organ": [5, 210, 262, 267, 268], "within": [5, 15, 27, 196, 205, 208, 210, 213, 217, 224, 226, 229, 230, 233, 234, 235, 237, 266], "accord": [5, 12, 60, 71, 75, 89, 90, 93, 101, 104, 106, 125, 144, 153, 160, 163, 164, 173, 177, 190, 191, 192, 196, 210, 212, 213], "These": [5, 214, 242, 267], "intend": [5, 89, 90, 154, 175, 208, 258], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 93, 98, 100, 101, 104, 121, 126, 128, 143, 144, 147, 157, 161, 165, 167, 169, 179, 195, 196, 208, 210, 212, 222, 236, 238, 252, 267], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 208, 210, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262], "extern": [7, 268], "usabl": 7, "accept": [7, 26, 131, 132, 133, 134, 139, 157, 173, 190, 208, 263], "argument": [7, 10, 11, 12, 26, 40, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 85, 86, 89, 90, 93, 96, 104, 108, 109, 110, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 138, 142, 144, 148, 153, 154, 157, 159, 160, 163, 166, 169, 174, 175, 178, 179, 180, 192, 195, 205, 212, 216, 217, 224, 225, 226, 229, 230, 233, 234, 235, 236, 237, 258, 262, 266, 267, 268], "map": [7, 213, 214], "base": [7, 47, 57, 58, 97, 98, 126, 127, 128, 129, 153, 185, 186, 187, 188, 196, 210, 214, 220, 222, 262, 263, 266, 267, 268], "sole": [7, 196, 203, 262], "incompat": [7, 26, 74, 105, 208, 263, 266], "normal": [7, 78, 172, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237], "practic": [7, 19, 196, 262, 267], "avail": [7, 105, 117, 208, 216, 261, 263, 267], "still": [7, 26, 222, 262, 267, 268, 269], "consid": [7, 26, 63, 105, 131, 132, 133, 134, 185, 186, 187, 188, 213, 217, 236, 251, 262, 266, 268, 269], "compliant": [7, 26, 51, 93, 99, 105, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 173, 190, 212, 215, 217, 263, 266], "altern": [7, 214, 216, 269], "thei": [7, 26, 205, 211, 214, 216, 217, 221, 222, 261, 262, 263, 266, 268, 269], "were": [7, 104, 158, 163, 210, 266], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 195, 210, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 262, 267, 268], "lead": [7, 104, 213, 252, 255, 266], "readabl": [7, 205, 262, 267], "code": [7, 59, 205, 214, 215, 217, 220, 222, 262, 266, 267, 268], "easier": [7, 208, 214, 262], "evolv": [7, 208, 262], "over": [7, 13, 14, 26, 88, 125, 137, 139, 141, 154, 173, 175, 176, 180, 190, 191, 196, 212, 213, 214, 216, 217, 221, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 258, 260, 262, 266], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 77, 79, 85, 86, 87, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 138, 139, 140, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 160, 162, 164, 166, 167, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 196, 209, 210, 211, 217, 225, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "worri": 7, "xi": [7, 140], "annot": [7, 210, 222, 266], "individu": [7, 139, 196, 217, 220, 221, 222, 225, 236, 266, 267], "aim": [7, 211, 222, 261, 262, 263, 266, 267, 268, 269], "strongli": [7, 214, 268], "look": [7, 268], "like": [7, 196, 208, 211, 213, 220, 222, 263, 266, 267, 268], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 114, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 196, 210, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 266, 267, 269], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 210, 211, 214, 216, 220, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 265, 268], "int": [7, 12, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 74, 77, 78, 85, 88, 89, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 123, 124, 125, 130, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 151, 153, 154, 157, 158, 159, 160, 161, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 189, 190, 191, 192, 193, 196, 205, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 241, 246, 247, 257, 258, 259, 260, 267], "str": [7, 8, 23, 118, 119, 140, 267], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 91, 210, 268], "few": [7, 212, 220, 266, 268], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 115, 116, 118, 125, 137, 139, 140, 141, 147, 149, 150, 154, 158, 159, 161, 163, 168, 172, 173, 175, 177, 180, 182, 183, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 210, 212, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 246, 248, 251, 252, 255, 258, 260], "form": [7, 23, 26, 40, 79, 135, 136, 182, 183, 196, 214, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 263, 267], "question": [7, 211, 266], "commonli": [7, 173, 190, 196, 211, 213, 215, 261, 262, 266, 267], "written": [7, 208, 266, 268], "yyyi": [8, 23, 263], "mm": [8, 23, 263], "string": [8, 23, 118, 119, 210, 263, 266], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 195, 208, 211, 217, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 264, 266, 268], "absolut": [9, 20, 85, 164, 212, 214, 246, 247, 253, 262], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 97, 99, 103, 112, 120, 121, 122, 126, 127, 128, 129, 132, 137, 139, 141, 145, 152, 155, 156, 162, 164, 165, 166, 167, 169, 170, 173, 178, 179, 184, 190], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 110, 112, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 203, 208, 210, 213, 215, 217, 218, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 255, 256, 258, 260, 262, 266, 268], "magnitud": [9, 12, 20, 85, 93, 104, 110, 144, 210, 255, 256], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 93, 101, 104, 111, 144, 145, 146, 178, 179, 210, 216, 267], "known": [9, 164, 212, 215, 216], "norm": [9, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 260, 262], "modulu": [9, 157], "z": [9, 10, 11, 61, 62, 64, 66, 126, 213], "bj": [9, 12, 79, 93, 144], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 92, 93, 96, 98, 104, 108, 109, 110, 123, 124, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 144, 145, 147, 148, 152, 154, 158, 173, 175, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 215, 220, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 164, 166, 167, 178, 179, 213, 242, 243, 253, 255], "sqrt": [9, 10, 11, 61, 62, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 260], "take": [9, 126, 128, 153, 169, 195, 210, 217, 222, 266], "care": [9, 262], "undu": [9, 215], "overflow": [9, 12, 89, 90, 93, 104, 110, 125, 154, 175, 205, 253, 258, 262], "dure": [9, 40, 59, 110, 135, 173, 190, 205, 208, 251, 266, 267], "stage": [9, 110, 263], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 193, 196, 210, 212, 213, 214, 216, 220, 221, 225, 226, 227, 230, 231, 234, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 268], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 157, 162, 163, 164, 165, 166, 167, 169, 173, 178, 179, 184, 185, 186, 187, 188, 190, 195, 203, 210, 213, 266], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 126, 127, 128, 129, 130, 137, 141, 144, 148, 153, 157, 162, 165, 166, 167, 169, 178, 179, 184, 213, 253, 260], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 96, 97, 99, 120, 121, 122, 125, 126, 128, 139, 148, 162, 164, 167, 169, 179, 195, 210, 211, 266, 267, 268], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 93, 96, 97, 99, 104, 110, 114, 120, 121, 126, 128, 144, 148, 153, 157, 165, 167, 169, 179, 212], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 93, 96, 97, 99, 100, 101, 106, 107, 111, 112, 119, 120, 121, 122, 125, 126, 127, 128, 129, 135, 140, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 162, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 97, 99, 104, 126, 127, 128, 129, 153, 166, 167, 178, 179, 212, 248, 251], "princip": [10, 11, 61, 62, 64, 66, 126, 169, 213, 262], "invers": [10, 11, 61, 62, 64, 65, 66, 213, 224, 226, 229, 230, 231, 232, 233, 234, 235, 237, 244, 247, 251, 262], "cosin": [10, 11, 86, 87, 179], "express": [10, 61, 63, 64, 65, 86, 166, 178, 196, 205, 214, 262, 265], "radian": [10, 61, 64, 65, 86, 166, 178], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 93, 125, 127, 129, 164, 166, 167, 178, 179, 213, 253], "pi": [10, 11, 61, 62, 64, 66, 87, 126, 128, 167, 178, 179, 195], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 93, 97, 99, 125, 126, 128, 139, 144, 163, 164, 166, 167, 169, 178, 179, 196, 213, 242, 255, 258], "ln": [10, 11, 61, 62, 64, 66, 126], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 97, 99, 126, 127, 128, 129, 167, 169, 179, 195, 210], "multi": [10, 11, 61, 62, 64, 66, 195, 213, 216, 217, 239, 268], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 93, 97, 99, 126, 128, 144, 153, 166, 167, 169, 178, 179, 266], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 97, 99, 126, 128, 153, 166, 167, 169, 178, 179, 266], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 93, 97, 99, 144, 166, 167, 169, 178, 179, 266], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 89, 90, 126, 128, 137, 139, 141, 153, 154, 169, 173, 175, 190, 191, 212, 213, 239, 262, 267], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 94, 95, 100, 105, 106, 107, 125, 149, 150, 161, 193, 194, 195, 203, 205, 210, 214, 217, 225, 236, 251], "line": [10, 11, 61, 62, 64, 66, 178, 179, 205, 213, 266, 267, 268, 269], "segment": [10, 11, 61, 62, 64, 66, 213], "infti": [10, 11, 61, 62, 64, 66, 86, 126, 128, 153, 169, 213], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 98, 102, 126, 128, 137, 139, 141, 143, 153, 154, 158, 161, 168, 169, 171, 172, 173, 175, 176, 177, 180, 181, 189, 190, 191, 195, 210, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 246, 259, 260, 266], "rang": [10, 61, 62, 64, 66, 77, 89, 90, 126, 128, 154, 169, 175, 196, 210, 216, 258, 266], "strip": [10, 61, 62, 64, 66, 126, 128], "unbound": [10, 61, 62, 64, 66, 126, 128], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 100, 102, 126, 128, 137, 139, 141, 154, 158, 161, 168, 169, 172, 173, 175, 176, 177, 178, 179, 181, 189, 190, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 258, 260, 262], "c99": [10, 11, 61, 62, 64, 66, 93, 126, 128, 144, 153, 169, 213, 263], "provision": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "statu": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 93, 103, 104, 126, 128, 153, 157, 163, 164, 165, 167, 169, 171, 179, 195, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 89, 90, 92, 93, 101, 102, 103, 104, 105, 126, 127, 128, 129, 135, 139, 144, 153, 154, 157, 163, 164, 165, 167, 169, 171, 173, 175, 176, 179, 184, 185, 186, 187, 188, 190, 196, 205, 208, 211, 214, 217, 218, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 246, 247, 248, 251, 258, 260, 262, 263, 266, 268], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 93, 104, 126, 127, 128, 129, 153, 157, 163, 164, 165, 169, 173, 190, 195, 196, 210, 214, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 247, 248, 251, 260, 266], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 97, 99, 100, 126, 128, 149, 150, 164, 167, 169, 179, 213, 253], "nonzero": [10, 11, 12, 62, 66, 87, 93, 97, 99, 104, 144, 167, 179, 195, 196, 210, 251], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 166, 167, 178, 179, 213], "aco": [11, 61, 195, 210, 212], "simpli": [11, 99, 128, 211, 222, 266, 268], "upper": [11, 77, 100, 183, 210, 238, 252], "half": [11, 15, 66, 125, 143, 169, 180, 196, 227], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 126, 128], "3\u03c0j": [11, 126, 128], "sum": [12, 21, 90, 110, 130, 154, 195, 210, 246, 258, 260, 262], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "union": [12, 13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 65, 67, 69, 70, 71, 72, 75, 77, 78, 85, 88, 93, 94, 96, 101, 102, 104, 106, 107, 108, 109, 110, 111, 118, 119, 123, 124, 125, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 153, 154, 157, 158, 160, 161, 171, 172, 173, 174, 175, 180, 190, 192, 193, 227, 231, 246, 248, 251, 260, 267], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 89, 90, 92, 96, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 161, 172, 174, 178, 179, 180, 185, 186, 187, 191, 192, 196, 213, 239, 242, 250, 252, 253, 255, 256, 262, 266, 267, 268, 269], "At": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 160, 174, 192], "least": [12, 40, 65, 67, 69, 70, 71, 72, 85, 88, 93, 96, 104, 108, 109, 110, 118, 119, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 147, 148, 153, 157, 160, 174, 185, 186, 187, 188, 192, 196, 211, 212, 251], "remain": [12, 93, 96, 104, 119, 121, 122, 144, 148, 157, 159, 164, 196, 214, 237], "neither": [12, 40, 93, 104, 135, 144, 180, 255, 267], "nor": [12, 93, 104, 144, 255, 267], "mathemat": [12, 19, 65, 84, 86, 87, 93, 99, 104, 126, 128, 144, 166, 167, 178, 179, 195, 213, 246, 260], "round": [12, 15, 76, 93, 103, 104, 144, 169, 184, 195, 210, 212], "nearest": [12, 93, 144, 162, 184, 212], "mode": [12, 93, 144, 212, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 252], "too": [12, 26, 93, 104, 144, 262, 266], "larg": [12, 93, 104, 144, 216, 222, 253, 266], "appropri": [12, 26, 93, 104, 144, 213, 218], "commut": 12, "associ": [12, 42, 144, 198, 205, 248, 251, 254, 262, 265, 267], "tabl": [12, 93, 144, 195], "c": [12, 93, 96, 125, 144, 147, 148, 158, 172, 173, 179, 190, 196, 210, 213, 216, 219, 238, 242, 243, 244, 252, 254, 255, 263, 265, 266, 268], "d": [12, 93, 96, 125, 144, 148, 205, 225, 236], "dj": [12, 93, 144], "independ": [12, 93, 139, 144, 162, 196, 208, 216, 239, 252, 254, 262, 263, 266], "abov": [12, 89, 90, 93, 96, 126, 128, 144, 148, 153, 154, 169, 175, 182, 183, 196, 205, 213, 214, 216, 217, 220, 241, 242, 258, 262, 265, 268], "similarli": [12, 57, 119, 139, 140, 238, 255], "henc": [12, 77, 79, 98, 147, 158, 185, 186, 187, 188, 196, 211, 213, 215, 216, 220, 221, 222, 266, 268], "z1": 12, "z2": 12, "2024": [12, 26, 28, 31, 32, 33, 37, 39, 43, 65, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 88, 89, 90, 92, 93, 96, 104, 108, 109, 110, 114, 123, 124, 130, 131, 133, 134, 138, 139, 142, 144, 146, 148, 153, 155, 156, 157, 160, 163, 174, 176, 177, 192, 225, 236, 254], "keepdim": [13, 14, 16, 17, 88, 137, 139, 141, 154, 173, 175, 190, 246, 260], "test": [13, 14, 91, 120, 121, 122, 139, 210, 212, 264, 266, 267, 268], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 97, 99, 126, 127, 128, 129, 145, 152, 164, 165, 170, 208, 266], "ax": [13, 14, 16, 17, 19, 55, 56, 88, 89, 90, 102, 137, 139, 141, 143, 151, 154, 161, 171, 173, 175, 176, 180, 181, 190, 191, 196, 210, 226, 227, 230, 231, 234, 237, 239, 246, 251, 254, 257, 260], "logic": [13, 14, 24, 26, 93, 96, 131, 132, 133, 134, 144, 148, 217, 220, 226, 230, 234, 237], "AND": [13, 67, 96, 131, 265], "entir": [13, 14, 86, 87, 88, 97, 99, 137, 139, 141, 154, 166, 167, 173, 175, 190], "valid": [13, 14, 26, 27, 92, 98, 117, 143, 163, 172, 180, 189, 196, 212, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 242, 252, 255, 267], "count": [13, 14, 78, 88, 89, 90, 92, 102, 176, 177, 185, 186, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 243], "last": [13, 14, 18, 19, 55, 78, 89, 90, 92, 102, 161, 168, 172, 176, 177, 180, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 246, 252, 255, 258], "invalid": [13, 14, 23, 92, 98, 218, 266], "wa": [13, 14, 19, 26, 88, 104, 137, 139, 141, 154, 173, 175, 190, 205, 217, 222, 266, 268], "OR": [14, 24, 70, 133, 148, 265], "start": [15, 125, 196, 210, 222, 266, 268], "stop": [15, 125, 196, 210, 267], "step": [15, 125, 196, 267], "evenli": [15, 125], "space": [15, 125, 225, 227, 236], "open": [15, 125, 143, 180, 196], "inclus": [15, 196, 266], "end": [15, 65, 86, 125, 164, 166, 178, 179, 203, 214, 253, 266, 267, 268], "exclus": [15, 196], "distanc": [15, 110], "adjac": 15, "output": [15, 60, 63, 75, 78, 89, 90, 94, 95, 98, 100, 102, 105, 106, 107, 114, 125, 140, 149, 150, 159, 161, 163, 171, 172, 176, 181, 193, 194, 208, 210, 213, 214, 217, 219, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 235, 236, 237, 254, 258, 266], "infer": [15, 60, 63, 95, 106, 107, 150, 159, 194, 196, 215, 262, 267], "cannot": [15, 26, 57, 105, 178, 179, 210, 213, 215, 266], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 93, 105, 137, 141, 178, 179, 205, 212, 253, 266], "ceil": [15, 195], "indic": [16, 17, 18, 26, 60, 89, 90, 91, 105, 114, 119, 125, 143, 147, 161, 163, 164, 176, 177, 180, 182, 183, 185, 187, 196, 205, 210, 260, 266], "occur": [16, 17, 75, 110, 178, 179, 185, 186, 187, 188, 213, 267], "occurr": [16, 17, 185], "comparison": [16, 17, 18, 28, 31, 33, 37, 39, 43, 96, 108, 109, 123, 124, 137, 138, 141, 142, 148, 168, 195, 210, 213, 263, 267], "search": [16, 17, 163, 195], "flatten": [16, 17, 78, 158, 161, 185, 186, 187, 188, 260, 262], "descend": [18, 168, 255, 256], "stabl": [18, 168, 216], "sort": [18, 163, 195, 210, 242, 243, 255, 256], "ascend": [18, 163, 168, 210], "stabil": [18, 168], "maintain": [18, 168, 211, 266, 268], "rel": [18, 19, 55, 102, 138, 142, 161, 168, 210, 241, 248, 251, 258], "compar": [18, 168, 185, 186, 187, 188, 212, 217, 267, 269], "properti": [19, 53, 54, 55, 56, 57, 58, 118, 210, 213, 217, 222, 266], "transpos": [19, 40, 55, 135, 136, 180, 238, 242, 251, 255, 262], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 91, 205, 208, 210, 217], "permut": [19, 55, 151], "revers": [19, 55, 65, 102], "origin": [19, 55, 65, 110, 143, 159, 161, 210, 214, 224, 226, 229, 230, 233, 234, 235, 237, 266, 267], "limit": [19, 101, 111, 119, 212, 262, 265], "matric": [19, 40, 55, 135, 136, 140, 182, 183, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 262], "deviat": [19, 139, 173, 212, 218, 266, 268], "et": [19, 196, 255, 256], "al": 19, "intent": [19, 65], "found": [19, 213, 216, 268, 269], "problemat": [19, 63, 211, 214], "conflict": [19, 26, 210], "definit": [19, 86, 87, 166, 167, 178, 179, 210, 238, 267], "batch": [19, 260, 262], "cetera": [19, 196, 255, 256], "permute_dim": [19, 195], "interfac": [19, 216, 262, 266, 268], "ab": [20, 110, 153, 195, 210, 246, 260], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 195, 210], "api_vers": [23, 266], "object": [23, 24, 25, 26, 29, 32, 34, 35, 53, 57, 59, 60, 91, 101, 105, 111, 113, 115, 116, 117, 195, 196, 205, 208, 210, 214, 216, 217, 220, 222, 261, 263, 267, 268], "2020": [23, 222, 263, 265, 266], "10": [23, 27, 127, 196, 266], "latest": [23, 216], "modul": [23, 208, 263, 267, 268, 269], "everi": [23, 106, 107, 252, 266], "top": [23, 208, 266, 268], "level": [23, 205, 211, 216, 217, 261, 262, 266, 267], "public": [23, 261, 267, 268], "well": [23, 211, 213, 216, 217, 252, 268, 269], "part": [23, 35, 182, 183, 205, 210, 216, 221, 263, 266, 268], "convert": [24, 25, 29, 34, 35, 60, 105, 205, 210, 211, 213, 216, 266, 268], "handl": [24, 26, 61, 64, 86, 89, 90, 105, 127, 129, 139, 153, 154, 156, 164, 166, 170, 175, 178, 210, 211, 213, 214, 217, 218, 258, 266], "lazi": [24, 25, 29, 34, 35, 208, 210, 219, 268], "languag": [24, 25, 29, 34, 35, 196, 218, 220, 262, 266, 268], "therefor": [24, 25, 29, 32, 34, 35, 208, 216, 217, 218, 220, 222, 263, 266, 268], "abl": [24, 25, 29, 34, 35, 105, 214, 216, 217, 266, 268], "kind": [24, 25, 26, 28, 29, 31, 33, 34, 35, 37, 39, 43, 47, 51, 77, 93, 96, 101, 105, 107, 108, 109, 111, 116, 118, 119, 123, 124, 148, 153, 160, 205, 210, 220, 262, 265], "here": [24, 25, 26, 29, 34, 35, 196, 205, 216, 221, 222, 268], "valueerror": [24, 25, 29, 34, 35, 60, 105, 159, 171, 268], "instead": [24, 25, 29, 34, 35, 63, 213, 216, 220, 267, 268], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 90, 105, 110, 137, 138, 141, 142, 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method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "count_nonzero() (in module array_api)": [[88, "array_api.count_nonzero"]], "cumulative_prod() (in module array_api)": [[89, "array_api.cumulative_prod"]], "cumulative_sum() (in module array_api)": [[90, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[91, "array_api.data_types.__eq__"]], "diff() (in module array_api)": [[92, "array_api.diff"]], "divide() (in module array_api)": [[93, "array_api.divide"]], "empty() (in module array_api)": [[94, "array_api.empty"]], "empty_like() (in module array_api)": [[95, "array_api.empty_like"]], "equal() (in module array_api)": [[96, "array_api.equal"]], "exp() (in module array_api)": [[97, "array_api.exp"]], "expand_dims() (in module array_api)": [[98, "array_api.expand_dims"]], "expm1() (in module array_api)": [[99, "array_api.expm1"]], "eye() (in module array_api)": [[100, "array_api.eye"]], "finfo() (in module array_api)": [[101, "array_api.finfo"]], "flip() (in module array_api)": [[102, "array_api.flip"]], "floor() (in module array_api)": [[103, "array_api.floor"]], "floor_divide() (in module array_api)": [[104, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[105, "array_api.from_dlpack"]], "full() (in module array_api)": [[106, "array_api.full"]], "full_like() (in module array_api)": [[107, "array_api.full_like"]], "greater() (in module array_api)": [[108, "array_api.greater"]], "greater_equal() (in module array_api)": [[109, "array_api.greater_equal"]], "hypot() (in module array_api)": [[110, "array_api.hypot"]], "iinfo() (in module array_api)": [[111, "array_api.iinfo"]], "imag() (in module array_api)": [[112, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[113, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[114, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[115, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[116, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[117, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[118, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[119, "array_api.isdtype"]], "isfinite() (in module array_api)": [[120, "array_api.isfinite"]], "isinf() (in module array_api)": [[121, "array_api.isinf"]], "isnan() (in module array_api)": [[122, "array_api.isnan"]], "less() (in module array_api)": [[123, "array_api.less"]], "less_equal() (in module array_api)": [[124, "array_api.less_equal"]], "linspace() (in module array_api)": [[125, "array_api.linspace"]], "log() (in module array_api)": [[126, "array_api.log"]], "log10() (in module array_api)": [[127, "array_api.log10"]], "log1p() (in module array_api)": [[128, "array_api.log1p"]], "log2() (in module array_api)": [[129, "array_api.log2"]], "logaddexp() (in module array_api)": [[130, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[131, "array_api.logical_and"]], "logical_not() (in module array_api)": [[132, "array_api.logical_not"]], "logical_or() (in module array_api)": [[133, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[134, "array_api.logical_xor"]], "matmul() (in module array_api)": [[135, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[136, "array_api.matrix_transpose"]], "max() (in module array_api)": [[137, "array_api.max"]], "maximum() (in module array_api)": [[138, "array_api.maximum"]], "mean() (in module array_api)": [[139, "array_api.mean"]], "meshgrid() (in module array_api)": [[140, "array_api.meshgrid"]], "min() (in module array_api)": [[141, "array_api.min"]], "minimum() (in module array_api)": [[142, "array_api.minimum"]], "moveaxis() (in module array_api)": [[143, "array_api.moveaxis"]], "multiply() (in module array_api)": [[144, "array_api.multiply"]], "negative() (in module array_api)": [[145, "array_api.negative"]], "nextafter() (in module array_api)": [[146, "array_api.nextafter"]], "nonzero() (in module array_api)": [[147, "array_api.nonzero"]], "not_equal() (in module array_api)": [[148, "array_api.not_equal"]], "ones() (in module array_api)": [[149, "array_api.ones"]], "ones_like() (in module array_api)": [[150, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[151, "array_api.permute_dims"]], "positive() (in module array_api)": [[152, "array_api.positive"]], "pow() (in module array_api)": [[153, "array_api.pow"]], "prod() (in module array_api)": [[154, "array_api.prod"]], "real() (in module array_api)": [[155, "array_api.real"]], "reciprocal() (in module array_api)": [[156, "array_api.reciprocal"]], "remainder() (in module array_api)": [[157, "array_api.remainder"]], "repeat() (in module array_api)": [[158, "array_api.repeat"]], "reshape() (in module array_api)": [[159, "array_api.reshape"]], "result_type() (in module array_api)": [[160, "array_api.result_type"]], "roll() (in module array_api)": [[161, "array_api.roll"]], "round() (in module array_api)": [[162, "array_api.round"]], "searchsorted() (in module array_api)": [[163, "array_api.searchsorted"]], "sign() (in module array_api)": [[164, "array_api.sign"]], "signbit() (in module array_api)": [[165, "array_api.signbit"]], "sin() (in module array_api)": [[166, "array_api.sin"]], "sinh() (in module array_api)": [[167, "array_api.sinh"]], "sort() (in module array_api)": [[168, "array_api.sort"]], "sqrt() (in module array_api)": [[169, "array_api.sqrt"]], "square() (in module array_api)": [[170, "array_api.square"]], "squeeze() (in module array_api)": [[171, "array_api.squeeze"]], "stack() (in module array_api)": [[172, "array_api.stack"]], "std() (in module array_api)": [[173, "array_api.std"]], "subtract() (in module array_api)": [[174, "array_api.subtract"]], "sum() (in module array_api)": [[175, "array_api.sum"]], "take() (in module array_api)": [[176, "array_api.take"]], "take_along_axis() (in module array_api)": [[177, "array_api.take_along_axis"]], "tan() (in module array_api)": [[178, "array_api.tan"]], "tanh() (in module array_api)": [[179, "array_api.tanh"]], "tensordot() (in module array_api)": [[180, "array_api.tensordot"]], "tile() (in module array_api)": [[181, "array_api.tile"]], "tril() (in module array_api)": [[182, "array_api.tril"]], "triu() (in module array_api)": [[183, "array_api.triu"]], "trunc() (in module array_api)": [[184, "array_api.trunc"]], "unique_all() (in module array_api)": [[185, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[186, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[187, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[188, "array_api.unique_values"]], "unstack() (in module array_api)": [[189, "array_api.unstack"]], "var() (in module array_api)": [[190, "array_api.var"]], "vecdot() (in module array_api)": [[191, "array_api.vecdot"]], "where() (in module array_api)": [[192, "array_api.where"]], "zeros() (in module array_api)": [[193, "array_api.zeros"]], "zeros_like() (in module array_api)": [[194, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[224, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[225, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[226, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[227, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[228, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[229, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[230, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[231, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[232, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[233, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[234, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[235, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[236, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[237, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[238, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[239, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[240, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[241, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[242, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[243, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[244, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[245, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[246, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[247, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[248, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[249, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[250, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[251, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[252, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[253, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[254, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[255, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[256, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[257, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[258, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[259, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[260, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file
diff --git a/draft/changelog.html b/draft/changelog.html
index d1ff514b9..64c241dee 100644
--- a/draft/changelog.html
+++ b/draft/changelog.html
@@ -701,18 +701,18 @@ <h5 id="id4">APIs<a class="headerlink" href="#id4" title="Link to this heading">
 <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this heading">¶</a></h4>
 <p>The following is a list of fixes and points of clarification with regard to the previous version of the specification:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__bool__</span></code>: fix typo in special case notes (<a class="reference external" href="https://github.com/data-apis/array-api/pull/785">gh-785</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__dlpack__</span></code>: resolve conflicting exception guidance (<a class="reference external" href="https://github.com/data-apis/array-api/pull/887">gh-887</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__getitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify broadcast behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/888">gh-888</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify required exception behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/897">gh-897</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">clip</span></code>: clarify that the operation is only defined when elements in <code class="docutils literal notranslate"><span class="pre">min</span></code> and <code class="docutils literal notranslate"><span class="pre">max</span></code> are inside the bounds of the input array data type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/814">gh-814</a>)</p></li>
@@ -726,7 +726,7 @@ <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this h
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.irfftn</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.hfft</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">linalg.solve</span></code>: clarify broadcasting semantics and output shape (<a class="reference external" href="https://github.com/data-apis/array-api/pull/810">gh-810</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-https://github.com/data-apis/array-api/pull/904</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-904</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">searchsorted</span></code>: fix incorrect boundary conditions (<a class="reference external" href="https://github.com/data-apis/array-api/pull/898">gh-898</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">sign</span></code>: fix equation in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/844">gh-844</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">tile</span></code>: fix missing return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/798">gh-798</a>)</p></li>
diff --git a/draft/searchindex.js b/draft/searchindex.js
index 60ad5943a..c359eb2ce 100644
--- a/draft/searchindex.js
+++ b/draft/searchindex.js
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15, 19, 23, 26, 60, 63, 75, 87, 93, 100, 102, 105, 114, 118, 144, 160, 161, 163, 167, 179, 181, 182, 183, 189, 191, 195, 196, 208, 210, 211, 213, 214, 215, 216, 217, 218, 220, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 251, 253, 254, 260, 261, 262, 265, 266, 268, 269], "thi": [0, 1, 5, 7, 15, 19, 26, 32, 34, 49, 58, 59, 63, 71, 75, 77, 78, 99, 104, 105, 110, 114, 118, 119, 125, 128, 131, 132, 133, 134, 139, 147, 153, 157, 158, 160, 172, 173, 176, 177, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 227, 229, 230, 233, 234, 235, 237, 252, 253, 254, 255, 261, 262, 263, 265, 267, 268, 269], "return": [0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 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49, 60, 65, 67, 69, 70, 71, 72, 77, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 148, 153, 157, 160, 174, 192, 195, 196, 220, 260, 268], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 146, 147, 148, 149, 153, 154, 155, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 173, 175, 176, 177, 178, 179, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 205, 208, 210, 212, 214, 215, 216, 220, 222, 225, 228, 232, 233, 234, 235, 236, 237, 238, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "rational": [0, 7, 89, 90, 154, 175, 196, 216, 217, 258, 261, 263, 266], "alwai": 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253, 254, 255, 256, 258, 260, 262, 266, 268], "__pos__": [0, 195, 210], "po": 0, "__neg__": [0, 195, 210], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 89, 90, 92, 93, 98, 100, 102, 104, 121, 126, 128, 144, 153, 157, 161, 165, 169, 176, 177, 180, 191, 195, 196, 210, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 260, 266], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "__add__": [0, 50, 195, 210], "add": [0, 7, 21, 90, 174, 175, 195, 196, 210, 211, 212, 217, 258], "__sub__": [0, 195, 210], "sub": [0, 196], "__mul__": [0, 195, 210], "mul": 0, "__truediv__": [0, 195, 210], "truediv": 0, "__floordiv__": [0, 195], 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"The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 102, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 205, 208, 210, 211, 212, 214, 215, 216, 217, 220, 221, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 263, 265, 266, 267, 268, 269], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 79, 89, 90, 92, 93, 104, 118, 119, 120, 121, 122, 135, 140, 144, 145, 152, 153, 154, 155, 162, 164, 170, 174, 175, 180, 205, 212, 224, 226, 229, 230, 233, 234, 235, 237, 239, 250, 251, 253, 258, 262, 266, 268], "__invert__": [0, 195], "inv": [0, 210, 262], "invert": [0, 68, 244, 247, 254], "__inv__": 0, "__and__": [0, 195], "__or__": [0, 195], "__xor__": [0, 195], "xor": [0, 72, 134], "__lshift__": [0, 195], "lshift": 0, "__rshift__": [0, 195], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 49, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 89, 90, 92, 93, 103, 104, 106, 107, 111, 114, 118, 119, 125, 137, 139, 141, 145, 153, 154, 157, 158, 160, 162, 163, 173, 175, 176, 184, 190, 191, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247, 248, 258, 260, 266], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 90, 91, 105, 106, 107, 114, 118, 119, 125, 131, 132, 133, 134, 147, 192, 195, 205, 210], "__lt__": [0, 195, 210], "lt": 0, "__le__": [0, 195, 210], "le": 0, "__gt__": [0, 195, 210], "gt": [0, 252, 255], "__ge__": [0, 195, 210], "ge": 0, "__eq__": [0, 195, 210, 217], "eq": 0, "__ne__": [0, 195, 210], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 43, 49, 55, 58, 60, 77, 85, 86, 88, 91, 92, 93, 96, 97, 100, 101, 102, 104, 105, 108, 109, 110, 117, 118, 123, 124, 125, 131, 132, 133, 134, 135, 139, 144, 147, 148, 153, 158, 160, 161, 162, 166, 178, 179, 181, 185, 187, 191, 196, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 229, 230, 231, 233, 234, 235, 236, 237, 239, 242, 243, 248, 251, 252, 255, 261, 262, 263, 266, 267, 268, 269], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 77, 102, 105, 110, 116, 118, 119, 125, 131, 132, 133, 134, 135, 139, 173, 190, 191, 195, 196, 205, 208, 210, 211, 213, 214, 216, 217, 218, 220, 222, 227, 239, 244, 251, 252, 254, 262, 263, 266, 267, 268, 269], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 91, 93, 99, 104, 105, 128, 143, 144, 160, 173, 190, 196, 198, 208, 210, 212, 213, 214, 215, 216, 217, 218, 222, 239, 251, 261, 262, 265, 266, 268], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 91, 92, 96, 110, 120, 121, 148, 169, 195, 196, 205, 210, 213, 214, 216, 222, 255, 263, 265, 266, 269], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 77, 79, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 153, 154, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 175, 178, 179, 184, 185, 186, 187, 188, 196, 203, 208, 212, 213, 214, 215, 217, 220, 225, 234, 236, 253, 255, 256, 258, 266, 268, 269], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 92, 108, 109, 123, 124, 125, 137, 138, 141, 142, 157, 168, 191, 196, 210, 213, 214, 218, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 266], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 125, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 159, 168, 173, 174, 175, 177, 190, 191, 192, 196, 205, 210, 213, 214, 218, 239, 246, 248, 251, 254, 260, 266, 268], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 75, 91, 92, 93, 96, 104, 105, 108, 109, 110, 113, 118, 119, 123, 124, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 148, 158, 159, 160, 163, 168, 173, 179, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 242, 252, 253, 255, 261, 262, 266, 267, 268], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 89, 90, 93, 96, 97, 99, 100, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 160, 162, 164, 166, 167, 168, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 205, 216, 217, 219, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 89, 90, 104, 108, 109, 110, 119, 123, 124, 125, 137, 138, 141, 142, 158, 163, 168, 176, 178, 179, 196, 208, 211, 212, 213, 214, 215, 217, 262, 263, 266, 268], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 108, 109, 123, 124, 137, 138, 141, 142, 168], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 60, 62, 66, 77, 78, 79, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 167, 168, 169, 172, 176, 177, 179, 196, 203, 205, 210, 226, 227, 230, 231, 234, 237, 242, 243, 266], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 57, 60, 71, 77, 79, 89, 90, 92, 96, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 168, 176, 178, 179, 196, 203, 212, 213, 226, 227, 230, 231, 234, 237, 242, 243, 255, 262], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 93, 96, 97, 99, 108, 109, 114, 123, 124, 125, 126, 127, 128, 129, 144, 145, 148, 153, 160, 163, 166, 167, 168, 178, 179, 192, 203, 205, 212, 213, 216, 219, 220, 222, 242, 243, 252, 253, 254, 255, 262, 266, 268, 269], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 85, 88, 93, 96, 99, 104, 105, 107, 108, 109, 110, 113, 114, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 147, 148, 153, 154, 156, 157, 158, 159, 160, 163, 164, 168, 169, 170, 173, 174, 175, 177, 185, 186, 187, 188, 190, 191, 192, 195, 196, 205, 207, 208, 211, 213, 215, 216, 217, 222, 239, 246, 248, 251, 254, 260, 261, 266, 267, 268, 269], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 91, 92, 102, 104, 105, 108, 109, 123, 124, 137, 138, 141, 142, 147, 158, 163, 168, 178, 179, 180, 185, 186, 187, 188, 196, 203, 205, 210, 212, 214, 215, 216, 218, 233, 234, 242, 243, 246, 255, 256, 260, 262, 263, 266, 267], "discuss": [0, 96, 148, 210, 216, 217, 221, 266, 267, 268], "copi": [0, 1, 26, 59, 60, 63, 105, 159, 168, 210, 211, 216, 217, 219, 265, 266], "view": [0, 105, 219], "behavior": [0, 5, 26, 32, 47, 49, 59, 60, 63, 74, 77, 89, 90, 92, 93, 104, 106, 107, 110, 125, 144, 153, 157, 159, 160, 163, 176, 177, 185, 186, 187, 188, 195, 196, 198, 205, 208, 210, 212, 213, 219, 220, 221, 226, 227, 230, 231, 234, 237, 262, 263, 266, 267, 268, 269], "mutabl": [0, 219], "refer": [0, 1, 13, 14, 92, 99, 100, 128, 163, 173, 176, 177, 180, 181, 190, 191, 196, 213, 214, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 254], "what": [0, 163, 208, 216, 218, 222, 262, 266, 267, 268, 269], "call": [0, 7, 34, 92, 216, 217, 220, 253, 266, 267, 268], "http": [0, 210, 216, 263, 269], "doc": 0, "org": 0, "html": 0, "do": [0, 1, 26, 75, 93, 144, 157, 203, 208, 210, 211, 213, 214, 216, 217, 218, 262, 263, 265, 266, 268, 269], "mutat": [0, 176, 210], "choos": [0, 51, 57, 59, 92, 93, 104, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 158, 160, 173, 185, 186, 187, 188, 190, 195, 196, 203, 213, 214, 215, 217, 220, 266, 268], "when": [0, 5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 75, 77, 89, 90, 93, 99, 104, 105, 110, 116, 118, 125, 128, 137, 138, 139, 141, 142, 144, 153, 154, 158, 159, 163, 173, 175, 176, 179, 190, 192, 195, 196, 205, 210, 211, 213, 214, 215, 216, 218, 220, 221, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 244, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268], "doe": [0, 1, 15, 26, 105, 148, 176, 177, 196, 205, 208, 211, 212, 213, 214, 215, 217, 218, 220, 222, 262, 266, 268, 269], "correspond": [0, 1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 96, 105, 108, 109, 114, 115, 116, 123, 124, 148, 153, 159, 161, 163, 173, 177, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 226, 230, 234, 237, 239, 242, 246, 265, 266], "fall": 0, "back": [0, 268], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 77, 104, 110, 131, 132, 133, 134, 157, 162, 176, 196, 205, 210, 213, 214, 248, 251, 254, 260, 266], "binari": [0, 5, 67, 70, 72, 178, 179, 211], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 90, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 159, 160, 162, 163, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 192, 208, 224, 225, 226, 228, 229, 230, 233, 234, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263, 266, 268, 269], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 89, 90, 92, 94, 95, 98, 102, 106, 107, 114, 135, 136, 140, 149, 150, 159, 161, 163, 168, 172, 176, 177, 180, 181, 182, 183, 189, 191, 193, 194, 195, 210, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 266, 268], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 93, 96, 97, 99, 103, 104, 108, 109, 110, 112, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 173, 174, 175, 178, 179, 180, 184, 185, 190, 196, 203, 205, 210, 212, 213, 214, 220, 238, 239, 241, 246, 247, 253, 254, 260, 266, 267, 268, 269], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 92, 93, 96, 97, 99, 104, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 139, 142, 144, 145, 148, 153, 156, 157, 160, 166, 167, 169, 170, 172, 173, 174, 178, 179, 180, 190, 191, 192, 195, 210, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 142, 144, 145, 148, 153, 156, 157, 160, 164, 166, 167, 169, 170, 172, 174, 178, 179, 180, 191, 192, 195, 196, 210, 213, 216, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262, 266, 268], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 173, 174, 175, 177, 180, 190, 191, 192, 195, 196, 210, 239, 246, 248, 251, 254, 260, 266], "let": [0, 1, 9, 10, 11, 12, 62, 66, 85, 87, 89, 90, 92, 96, 97, 99, 105, 120, 121, 122, 125, 126, 128, 139, 148, 154, 158, 163, 164, 167, 169, 173, 175, 179, 181, 190, 191, 196, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 243, 244, 252, 254, 255, 258], "If": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 114, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 211, 213, 217, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 258, 260, 261, 262, 266, 268], "after": [0, 1, 26, 40, 135, 169, 181, 196], "appli": [0, 12, 77, 78, 85, 93, 139, 144, 160, 162, 172, 180, 196, 205, 208, 213, 224, 226, 229, 230, 233, 234, 235, 237, 248, 251, 262, 266, 268], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 175, 178, 179, 184, 205, 210, 212, 253, 258], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 88, 91, 97, 99, 100, 106, 107, 110, 119, 121, 126, 127, 128, 129, 139, 147, 148, 149, 150, 153, 154, 162, 167, 168, 169, 173, 175, 176, 177, 179, 180, 181, 185, 186, 187, 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169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 193, 195, 203, 210, 212, 213, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "creat": [3, 15, 60, 94, 95, 100, 105, 106, 107, 125, 149, 150, 193, 194, 202, 208, 217, 225, 236, 262, 266], "its": [5, 26, 40, 73, 93, 101, 135, 144, 159, 161, 212, 213, 216, 217, 261, 266, 267, 268], "main": [5, 100, 182, 183, 211, 216, 241, 258, 261, 268], "namespac": [5, 7, 23, 113, 198, 208, 210, 223, 261, 262, 263, 266, 269], "under": [5, 261, 265, 266], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 89, 90, 92, 94, 98, 101, 102, 106, 116, 118, 119, 125, 149, 154, 157, 158, 161, 171, 172, 175, 176, 177, 181, 182, 183, 185, 186, 187, 188, 191, 193, 196, 205, 210, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 232, 233, 234, 235, 237, 241, 258, 260, 262, 263, 266, 268, 269], "name": [5, 7, 23, 26, 104, 118, 185, 186, 187, 196, 213, 214, 242, 251, 252, 253, 255, 261, 266, 267], "descript": [5, 7, 210, 212, 246, 260], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 67, 70, 72, 75, 88, 89, 90, 91, 96, 105, 106, 107, 108, 109, 118, 119, 120, 121, 122, 123, 124, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 160, 165, 168, 173, 175, 190, 192, 205, 210, 220, 238, 246, 255, 260], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 101, 104, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 147, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 192, 196, 210, 214, 238, 246, 255, 260, 262], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 196, 238, 246, 255, 260], "int8": [5, 118, 119, 196, 205], "bit": [5, 68, 69, 71, 85, 89, 90, 101, 111, 154, 165, 175, 205, 210, 212, 258], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 89, 90, 93, 97, 99, 104, 118, 119, 126, 128, 137, 138, 141, 142, 144, 145, 153, 154, 157, 163, 165, 167, 169, 175, 179, 185, 186, 187, 188, 195, 203, 210, 213, 252, 253, 258], "exist": [5, 7, 26, 60, 78, 105, 208, 210, 213, 216, 217, 218, 244, 263, 266, 267], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 98, 125, 126, 128, 143, 172, 180, 182, 183, 189, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 263], "128": 5, "127": 5, "int16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "16": [5, 205], "32": [5, 205], "767": 5, "int32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "147": 5, "483": 5, "647": 5, "int64": [5, 89, 90, 118, 119, 154, 175, 205, 258], "64": [5, 205], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 118, 119, 196, 205], "unsign": [5, 89, 90, 118, 119, 154, 175, 195, 258], "255": 5, "uint16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "65": 5, "535": [5, 210], "uint32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "294": 5, "967": 5, "295": 5, "uint64": [5, 118, 119, 205], "18": 5, "446": [5, 210], "744": [5, 210], "073": 5, "709": [5, 210], "551": [5, 210], "615": 5, "float32": [5, 112, 118, 119, 155, 205, 253, 255, 256], "ieee": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "754": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "singl": [5, 7, 24, 25, 29, 34, 35, 116, 118, 185, 186, 195, 205, 210, 211, 213, 216, 217, 222, 262, 266, 267, 268], "2019": [5, 12, 93, 99, 110, 128, 144, 195, 212, 266, 268], "float64": [5, 9, 20, 118, 119, 205, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "doubl": [5, 180, 205, 210], "complex64": [5, 112, 118, 119, 155, 205, 210, 253, 255, 256], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 162, 167, 169, 179, 210, 213], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 155, 162, 167, 169, 178, 179, 185, 186, 187, 188, 210, 213, 227, 236], "complex128": [5, 9, 20, 118, 119, 205, 210, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "method": [5, 26, 34, 105, 195, 198, 208, 214, 216, 217, 220, 221, 222, 266, 267, 268], "attribut": [5, 23, 101, 111, 160, 195, 207, 210, 263, 266, 267, 268], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 75, 89, 90, 105, 110, 119, 154, 160, 169, 172, 175, 176, 177, 179, 185, 186, 188, 189, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 236, 239, 258, 261, 262, 266, 267, 268], "beyond": [5, 161, 205, 210, 266], "It": [5, 23, 26, 105, 208, 214, 216, 266, 268, 269], "also": [5, 7, 26, 32, 34, 105, 110, 164, 208, 213, 214, 215, 216, 222, 226, 230, 234, 237, 255, 261, 268], "subnorm": [5, 110, 212], "k": [5, 40, 100, 110, 135, 147, 182, 183, 196, 212, 238, 242, 243, 244, 252, 254, 255, 256, 258, 266], "denorm": [5, 110, 212], "gradual": [5, 110, 212, 266], "underflow": [5, 9, 93, 104, 110, 212, 253], "hardwar": [5, 53, 110, 158, 212, 216, 217, 242, 255, 262, 266], "univers": [5, 110, 211, 212, 217, 262, 266], "mani": [5, 110, 181, 212, 266, 268], "platform": [5, 26, 110, 212], "compil": [5, 110, 179, 208, 211, 212, 215, 266], "toggl": [5, 110, 212], "daz": [5, 110, 212], "flush": [5, 110, 212], "ftz": [5, 110, 212], "increas": [5, 110, 212, 267], "guard": [5, 110, 212], "against": [5, 40, 73, 110, 135, 179, 196, 212, 248, 251, 269], "time": [5, 7, 16, 17, 26, 92, 110, 158, 185, 186, 208, 210, 212, 215, 216, 221, 238, 242, 243, 244, 252, 254, 255, 262, 266, 268], "attack": [5, 110, 212], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 75, 88, 93, 99, 104, 110, 125, 126, 128, 137, 139, 140, 141, 144, 147, 154, 158, 160, 163, 169, 173, 175, 185, 186, 187, 188, 190, 196, 205, 212, 213, 214, 215, 217, 246, 252, 260, 262], "vari": [5, 110, 163, 179, 185, 186, 187, 188, 205, 212], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 75, 77, 78, 86, 87, 89, 90, 92, 97, 99, 102, 105, 110, 117, 118, 119, 125, 126, 128, 131, 132, 133, 134, 135, 139, 147, 153, 154, 157, 158, 159, 160, 164, 166, 167, 168, 169, 172, 173, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 195, 198, 208, 210, 211, 213, 214, 215, 216, 217, 220, 221, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 244, 248, 251, 252, 253, 254, 255, 256, 258, 261, 262, 263, 266, 267, 268], "access": [5, 26, 32, 105, 113, 196, 210, 216, 261, 263, 266], "variou": [5, 210], "introspect": 5, "isdtyp": [5, 195, 210], "integr": [5, 63, 77, 116, 118, 119], "keyword": [5, 7, 26, 60, 63, 89, 90, 117, 140, 154, 159, 175, 195, 210, 217, 221, 222, 225, 236, 258, 262, 263, 266, 267, 268], "affect": [5, 15, 49, 214, 217], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 89, 90, 92, 93, 97, 99, 126, 127, 128, 129, 130, 137, 139, 141, 144, 153, 154, 166, 167, 169, 173, 174, 175, 178, 179, 190, 210, 253], "implementor": [5, 261], "free": [5, 214, 217, 265], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 113, 222], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 89, 90, 93, 97, 98, 99, 104, 107, 135, 139, 140, 143, 144, 145, 147, 153, 154, 166, 167, 171, 173, 175, 176, 178, 179, 180, 181, 185, 186, 187, 188, 190, 196, 205, 208, 213, 216, 217, 220, 221, 239, 246, 254, 255, 258, 260, 262, 263, 266, 268, 269], "wai": [5, 26, 63, 105, 208, 211, 217, 218, 263, 266, 267, 268, 269], "f4": [5, 205], "recommend": [5, 7, 19, 23, 26, 125, 131, 132, 133, 134, 139, 157, 173, 190, 203, 210, 212, 214, 216, 217, 266], "guidanc": [5, 7, 26, 49, 210, 211, 218, 266], "govern": [5, 50, 174, 205, 262, 263], "interact": [5, 213], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 89, 90, 93, 96, 97, 99, 101, 104, 105, 110, 113, 119, 120, 121, 125, 126, 127, 128, 129, 130, 135, 137, 138, 141, 142, 144, 146, 154, 157, 164, 165, 166, 169, 175, 178, 179, 180, 192, 196, 212, 213, 214, 218, 222, 253, 258, 266, 267, 269], "exampl": [5, 12, 23, 26, 118, 119, 139, 172, 195, 196, 208, 213, 214, 215, 217, 220, 221, 222, 258, 262, 266, 268, 269], "whether": [5, 13, 14, 26, 59, 60, 63, 75, 79, 89, 90, 91, 105, 114, 119, 122, 125, 139, 155, 159, 165, 210, 217, 238, 242, 243, 252, 254, 261, 265, 266, 268], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 88, 105, 114, 116, 118, 137, 139, 141, 154, 158, 159, 163, 164, 173, 175, 190, 191, 192, 195, 196, 208, 217, 238, 240, 246, 253, 254, 260, 265], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 192, 195, 196, 210, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 267, 268, 269], "possibl": [5, 26, 60, 75, 104, 105, 137, 141, 159, 160, 178, 179, 208, 211, 212, 213, 214, 216, 217, 218, 220, 222, 262, 266, 267, 268, 269], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 88, 89, 135, 137, 139, 141, 144, 145, 154, 173, 175, 190, 196, 208, 211, 213, 216, 217, 221, 222, 243, 244, 262, 263, 266, 268], "In": [5, 12, 19, 26, 59, 89, 90, 93, 96, 104, 119, 121, 122, 139, 144, 148, 154, 157, 164, 175, 195, 196, 198, 205, 212, 213, 214, 216, 218, 233, 234, 252, 253, 255, 258, 262, 263, 267, 268, 269], "clearli": [5, 59, 119, 203, 213, 262, 263], "warn": [5, 158, 218], "about": [5, 7, 26, 101, 111, 214, 262, 266, 268, 269], "organ": [5, 210, 262, 267, 268], "within": [5, 15, 27, 196, 205, 208, 210, 213, 217, 224, 226, 229, 230, 233, 234, 235, 237, 266], "accord": [5, 12, 60, 71, 75, 89, 90, 93, 101, 104, 106, 125, 144, 153, 160, 163, 164, 173, 177, 190, 191, 192, 196, 210, 212, 213], "These": [5, 214, 242, 267], "intend": [5, 89, 90, 154, 175, 208, 258], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 93, 98, 100, 101, 104, 121, 126, 128, 143, 144, 147, 157, 161, 165, 167, 169, 179, 195, 196, 208, 210, 212, 222, 236, 238, 252, 267], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 208, 210, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262], "extern": [7, 268], "usabl": 7, "accept": [7, 26, 131, 132, 133, 134, 139, 157, 173, 190, 208, 263], "argument": [7, 10, 11, 12, 26, 40, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 85, 86, 89, 90, 93, 96, 104, 108, 109, 110, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 138, 142, 144, 148, 153, 154, 157, 159, 160, 163, 166, 169, 174, 175, 178, 179, 180, 192, 195, 205, 212, 216, 217, 224, 225, 226, 229, 230, 233, 234, 235, 236, 237, 258, 262, 266, 267, 268], "map": [7, 213, 214], "base": [7, 47, 57, 58, 97, 98, 126, 127, 128, 129, 153, 185, 186, 187, 188, 196, 210, 214, 220, 222, 262, 263, 266, 267, 268], "sole": [7, 196, 203, 262], "incompat": [7, 26, 74, 105, 208, 263, 266], "normal": [7, 78, 172, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237], "practic": [7, 19, 196, 262, 267], "avail": [7, 105, 117, 208, 216, 261, 263, 267], "still": [7, 26, 222, 262, 267, 268, 269], "consid": [7, 26, 63, 105, 131, 132, 133, 134, 185, 186, 187, 188, 213, 217, 236, 251, 262, 266, 268, 269], "compliant": [7, 26, 51, 93, 99, 105, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 173, 190, 212, 215, 217, 263, 266], "altern": [7, 214, 216, 269], "thei": [7, 26, 205, 211, 214, 216, 217, 221, 222, 261, 262, 263, 266, 268, 269], "were": [7, 104, 158, 163, 210, 266], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 195, 210, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 262, 267, 268], "lead": [7, 104, 213, 252, 255, 266], "readabl": [7, 205, 262, 267], "code": [7, 59, 205, 214, 215, 217, 220, 222, 262, 266, 267, 268], "easier": [7, 208, 214, 262], "evolv": [7, 208, 262], "over": [7, 13, 14, 26, 88, 125, 137, 139, 141, 154, 173, 175, 176, 180, 190, 191, 196, 212, 213, 214, 216, 217, 221, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 258, 260, 262, 266], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 77, 79, 85, 86, 87, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 138, 139, 140, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 160, 162, 164, 166, 167, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 196, 209, 210, 211, 217, 225, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "worri": 7, "xi": [7, 140], "annot": [7, 210, 222, 266], "individu": [7, 139, 196, 217, 220, 221, 222, 225, 236, 266, 267], "aim": [7, 211, 222, 261, 262, 263, 266, 267, 268, 269], "strongli": [7, 214, 268], "look": [7, 268], "like": [7, 196, 208, 211, 213, 220, 222, 263, 266, 267, 268], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 114, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 196, 210, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 266, 267, 269], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 210, 211, 214, 216, 220, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 265, 268], "int": [7, 12, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 74, 77, 78, 85, 88, 89, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 123, 124, 125, 130, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 151, 153, 154, 157, 158, 159, 160, 161, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 189, 190, 191, 192, 193, 196, 205, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 241, 246, 247, 257, 258, 259, 260, 267], "str": [7, 8, 23, 118, 119, 140, 267], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 91, 210, 268], "few": [7, 212, 220, 266, 268], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 115, 116, 118, 125, 137, 139, 140, 141, 147, 149, 150, 154, 158, 159, 161, 163, 168, 172, 173, 175, 177, 180, 182, 183, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 210, 212, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 246, 248, 251, 252, 255, 258, 260], "form": [7, 23, 26, 40, 79, 135, 136, 182, 183, 196, 214, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 263, 267], "question": [7, 211, 266], "commonli": [7, 173, 190, 196, 211, 213, 215, 261, 262, 266, 267], "written": [7, 208, 266, 268], "yyyi": [8, 23, 263], "mm": [8, 23, 263], "string": [8, 23, 118, 119, 210, 263, 266], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 195, 208, 211, 217, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 264, 266, 268], "absolut": [9, 20, 85, 164, 212, 214, 246, 247, 253, 262], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 97, 99, 103, 112, 120, 121, 122, 126, 127, 128, 129, 132, 137, 139, 141, 145, 152, 155, 156, 162, 164, 165, 166, 167, 169, 170, 173, 178, 179, 184, 190], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 110, 112, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 203, 208, 210, 213, 215, 217, 218, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 255, 256, 258, 260, 262, 266, 268], "magnitud": [9, 12, 20, 85, 93, 104, 110, 144, 210, 255, 256], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 93, 101, 104, 111, 144, 145, 146, 178, 179, 210, 216, 267], "known": [9, 164, 212, 215, 216], "norm": [9, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 260, 262], "modulu": [9, 157], "z": [9, 10, 11, 61, 62, 64, 66, 126, 213], "bj": [9, 12, 79, 93, 144], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 92, 93, 96, 98, 104, 108, 109, 110, 123, 124, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 144, 145, 147, 148, 152, 154, 158, 173, 175, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 215, 220, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 164, 166, 167, 178, 179, 213, 242, 243, 253, 255], "sqrt": [9, 10, 11, 61, 62, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 260], "take": [9, 126, 128, 153, 169, 195, 210, 217, 222, 266], "care": [9, 262], "undu": [9, 215], "overflow": [9, 12, 89, 90, 93, 104, 110, 125, 154, 175, 205, 253, 258, 262], "dure": [9, 40, 59, 110, 135, 173, 190, 205, 208, 251, 266, 267], "stage": [9, 110, 263], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 193, 196, 210, 212, 213, 214, 216, 220, 221, 225, 226, 227, 230, 231, 234, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 268], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 157, 162, 163, 164, 165, 166, 167, 169, 173, 178, 179, 184, 185, 186, 187, 188, 190, 195, 203, 210, 213, 266], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 126, 127, 128, 129, 130, 137, 141, 144, 148, 153, 157, 162, 165, 166, 167, 169, 178, 179, 184, 213, 253, 260], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 96, 97, 99, 120, 121, 122, 125, 126, 128, 139, 148, 162, 164, 167, 169, 179, 195, 210, 211, 266, 267, 268], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 93, 96, 97, 99, 104, 110, 114, 120, 121, 126, 128, 144, 148, 153, 157, 165, 167, 169, 179, 212], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 93, 96, 97, 99, 100, 101, 106, 107, 111, 112, 119, 120, 121, 122, 125, 126, 127, 128, 129, 135, 140, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 162, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 97, 99, 104, 126, 127, 128, 129, 153, 166, 167, 178, 179, 212, 248, 251], "princip": [10, 11, 61, 62, 64, 66, 126, 169, 213, 262], "invers": [10, 11, 61, 62, 64, 65, 66, 213, 224, 226, 229, 230, 231, 232, 233, 234, 235, 237, 244, 247, 251, 262], "cosin": [10, 11, 86, 87, 179], "express": [10, 61, 63, 64, 65, 86, 166, 178, 196, 205, 214, 262, 265], "radian": [10, 61, 64, 65, 86, 166, 178], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 93, 125, 127, 129, 164, 166, 167, 178, 179, 213, 253], "pi": [10, 11, 61, 62, 64, 66, 87, 126, 128, 167, 178, 179, 195], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 93, 97, 99, 125, 126, 128, 139, 144, 163, 164, 166, 167, 169, 178, 179, 196, 213, 242, 255, 258], "ln": [10, 11, 61, 62, 64, 66, 126], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 97, 99, 126, 127, 128, 129, 167, 169, 179, 195, 210], "multi": [10, 11, 61, 62, 64, 66, 195, 213, 216, 217, 239, 268], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 93, 97, 99, 126, 128, 144, 153, 166, 167, 169, 178, 179, 266], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 97, 99, 126, 128, 153, 166, 167, 169, 178, 179, 266], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 93, 97, 99, 144, 166, 167, 169, 178, 179, 266], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 89, 90, 126, 128, 137, 139, 141, 153, 154, 169, 173, 175, 190, 191, 212, 213, 239, 262, 267], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 94, 95, 100, 105, 106, 107, 125, 149, 150, 161, 193, 194, 195, 203, 205, 210, 214, 217, 225, 236, 251], "line": [10, 11, 61, 62, 64, 66, 178, 179, 205, 213, 266, 267, 268, 269], "segment": [10, 11, 61, 62, 64, 66, 213], "infti": [10, 11, 61, 62, 64, 66, 86, 126, 128, 153, 169, 213], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 98, 102, 126, 128, 137, 139, 141, 143, 153, 154, 158, 161, 168, 169, 171, 172, 173, 175, 176, 177, 180, 181, 189, 190, 191, 195, 210, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 246, 259, 260, 266], "rang": [10, 61, 62, 64, 66, 77, 89, 90, 126, 128, 154, 169, 175, 196, 210, 216, 258, 266], "strip": [10, 61, 62, 64, 66, 126, 128], "unbound": [10, 61, 62, 64, 66, 126, 128], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 100, 102, 126, 128, 137, 139, 141, 154, 158, 161, 168, 169, 172, 173, 175, 176, 177, 178, 179, 181, 189, 190, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 258, 260, 262], "c99": [10, 11, 61, 62, 64, 66, 93, 126, 128, 144, 153, 169, 213, 263], "provision": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "statu": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 93, 103, 104, 126, 128, 153, 157, 163, 164, 165, 167, 169, 171, 179, 195, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 89, 90, 92, 93, 101, 102, 103, 104, 105, 126, 127, 128, 129, 135, 139, 144, 153, 154, 157, 163, 164, 165, 167, 169, 171, 173, 175, 176, 179, 184, 185, 186, 187, 188, 190, 196, 205, 208, 211, 214, 217, 218, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 246, 247, 248, 251, 258, 260, 262, 263, 266, 268], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 93, 104, 126, 127, 128, 129, 153, 157, 163, 164, 165, 169, 173, 190, 195, 196, 210, 214, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 247, 248, 251, 260, 266], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 97, 99, 100, 126, 128, 149, 150, 164, 167, 169, 179, 213, 253], "nonzero": [10, 11, 12, 62, 66, 87, 93, 97, 99, 104, 144, 167, 179, 195, 196, 210, 251], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 166, 167, 178, 179, 213], "aco": [11, 61, 195, 210, 212], "simpli": [11, 99, 128, 211, 222, 266, 268], "upper": [11, 77, 100, 183, 210, 238, 252], "half": [11, 15, 66, 125, 143, 169, 180, 196, 227], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 126, 128], "3\u03c0j": [11, 126, 128], "sum": [12, 21, 90, 110, 130, 154, 195, 210, 246, 258, 260, 262], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "union": [12, 13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 65, 67, 69, 70, 71, 72, 75, 77, 78, 85, 88, 93, 94, 96, 101, 102, 104, 106, 107, 108, 109, 110, 111, 118, 119, 123, 124, 125, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 153, 154, 157, 158, 160, 161, 171, 172, 173, 174, 175, 180, 190, 192, 193, 227, 231, 246, 248, 251, 260, 267], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 89, 90, 92, 96, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 161, 172, 174, 178, 179, 180, 185, 186, 187, 191, 192, 196, 213, 239, 242, 250, 252, 253, 255, 256, 262, 266, 267, 268, 269], "At": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 160, 174, 192], "least": [12, 40, 65, 67, 69, 70, 71, 72, 85, 88, 93, 96, 104, 108, 109, 110, 118, 119, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 147, 148, 153, 157, 160, 174, 185, 186, 187, 188, 192, 196, 211, 212, 251], "remain": [12, 93, 96, 104, 119, 121, 122, 144, 148, 157, 159, 164, 196, 214, 237], "neither": [12, 40, 93, 104, 135, 144, 180, 255, 267], "nor": [12, 93, 104, 144, 255, 267], "mathemat": [12, 19, 65, 84, 86, 87, 93, 99, 104, 126, 128, 144, 166, 167, 178, 179, 195, 213, 246, 260], "round": [12, 15, 76, 93, 103, 104, 144, 169, 184, 195, 210, 212], "nearest": [12, 93, 144, 162, 184, 212], "mode": [12, 93, 144, 212, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 252], "too": [12, 26, 93, 104, 144, 262, 266], "larg": [12, 93, 104, 144, 216, 222, 253, 266], "appropri": [12, 26, 93, 104, 144, 213, 218], "commut": 12, "associ": [12, 42, 144, 198, 205, 248, 251, 254, 262, 265, 267], "tabl": [12, 93, 144, 195], "c": [12, 93, 96, 125, 144, 147, 148, 158, 172, 173, 179, 190, 196, 210, 213, 216, 219, 238, 242, 243, 244, 252, 254, 255, 263, 265, 266, 268], "d": [12, 93, 96, 125, 144, 148, 205, 225, 236], "dj": [12, 93, 144], "independ": [12, 93, 139, 144, 162, 196, 208, 216, 239, 252, 254, 262, 263, 266], "abov": [12, 89, 90, 93, 96, 126, 128, 144, 148, 153, 154, 169, 175, 182, 183, 196, 205, 213, 214, 216, 217, 220, 241, 242, 258, 262, 265, 268], "similarli": [12, 57, 119, 139, 140, 238, 255], "henc": [12, 77, 79, 98, 147, 158, 185, 186, 187, 188, 196, 211, 213, 215, 216, 220, 221, 222, 266, 268], "z1": 12, "z2": 12, "2024": [12, 26, 28, 31, 32, 33, 37, 39, 43, 65, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 88, 89, 90, 92, 93, 96, 104, 108, 109, 110, 114, 123, 124, 130, 131, 133, 134, 138, 139, 142, 144, 146, 148, 153, 155, 156, 157, 160, 163, 174, 176, 177, 192, 225, 236, 254], "keepdim": [13, 14, 16, 17, 88, 137, 139, 141, 154, 173, 175, 190, 246, 260], "test": [13, 14, 91, 120, 121, 122, 139, 210, 212, 264, 266, 267, 268], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 97, 99, 126, 127, 128, 129, 145, 152, 164, 165, 170, 208, 266], "ax": [13, 14, 16, 17, 19, 55, 56, 88, 89, 90, 102, 137, 139, 141, 143, 151, 154, 161, 171, 173, 175, 176, 180, 181, 190, 191, 196, 210, 226, 227, 230, 231, 234, 237, 239, 246, 251, 254, 257, 260], "logic": [13, 14, 24, 26, 93, 96, 131, 132, 133, 134, 144, 148, 217, 220, 226, 230, 234, 237], "AND": [13, 67, 96, 131, 265], "entir": [13, 14, 86, 87, 88, 97, 99, 137, 139, 141, 154, 166, 167, 173, 175, 190], "valid": [13, 14, 26, 27, 92, 98, 117, 143, 163, 172, 180, 189, 196, 212, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 242, 252, 255, 267], "count": [13, 14, 78, 88, 89, 90, 92, 102, 176, 177, 185, 186, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 243], "last": [13, 14, 18, 19, 55, 78, 89, 90, 92, 102, 161, 168, 172, 176, 177, 180, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 246, 252, 255, 258], "invalid": [13, 14, 23, 92, 98, 218, 266], "wa": [13, 14, 19, 26, 88, 104, 137, 139, 141, 154, 173, 175, 190, 205, 217, 222, 266, 268], "OR": [14, 24, 70, 133, 148, 265], "start": [15, 125, 196, 210, 222, 266, 268], "stop": [15, 125, 196, 210, 267], "step": [15, 125, 196, 267], "evenli": [15, 125], "space": [15, 125, 225, 227, 236], "open": [15, 125, 143, 180, 196], "inclus": [15, 196, 266], "end": [15, 65, 86, 125, 164, 166, 178, 179, 203, 214, 253, 266, 267, 268], "exclus": [15, 196], "distanc": [15, 110], "adjac": 15, "output": [15, 60, 63, 75, 78, 89, 90, 94, 95, 98, 100, 102, 105, 106, 107, 114, 125, 140, 149, 150, 159, 161, 163, 171, 172, 176, 181, 193, 194, 208, 210, 213, 214, 217, 219, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 235, 236, 237, 254, 258, 266], "infer": [15, 60, 63, 95, 106, 107, 150, 159, 194, 196, 215, 262, 267], "cannot": [15, 26, 57, 105, 178, 179, 210, 213, 215, 266], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 93, 105, 137, 141, 178, 179, 205, 212, 253, 266], "ceil": [15, 195], "indic": [16, 17, 18, 26, 60, 89, 90, 91, 105, 114, 119, 125, 143, 147, 161, 163, 164, 176, 177, 180, 182, 183, 185, 187, 196, 205, 210, 260, 266], "occur": [16, 17, 75, 110, 178, 179, 185, 186, 187, 188, 213, 267], "occurr": [16, 17, 185], "comparison": [16, 17, 18, 28, 31, 33, 37, 39, 43, 96, 108, 109, 123, 124, 137, 138, 141, 142, 148, 168, 195, 210, 213, 263, 267], "search": [16, 17, 163, 195], "flatten": [16, 17, 78, 158, 161, 185, 186, 187, 188, 260, 262], "descend": [18, 168, 255, 256], "stabl": [18, 168, 216], "sort": [18, 163, 195, 210, 242, 243, 255, 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"complex-number-ordering"]], "Valued-based Promotion": [[213, "valued-based-promotion"]], "Copy-view behavior and mutability": [[214, "copy-view-behavior-and-mutability"]], "Mutating views": [[214, null]], "Copy keyword argument behavior": [[214, "copy-keyword-argument-behavior"]], "Data-dependent output shapes": [[215, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[216, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[216, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[216, "non-supported-use-cases"]], "Intended usage": [[217, "intended-usage"]], "Syntax for device assignment": [[217, "syntax-for-device-assignment"]], "Semantics": [[217, "semantics"]], "Out of scope for device support": [[217, "out-of-scope-for-device-support"]], "Exceptions": [[218, "exceptions"]], "Design topics & constraints": [[219, "design-topics-constraints"], [219, null]], "Lazy vs. eager execution": [[220, "lazy-vs-eager-execution"]], "Parallelism": [[221, "parallelism"]], "Static typing": [[222, "static-typing"]], "Fourier transform Functions": [[223, "fourier-transform-functions"]], "Extension name and usage": [[223, "extension-name-and-usage"], [262, "extension-name-and-usage"]], "fft": [[224, "fft"]], "fftfreq": [[225, "fftfreq"]], "fftn": [[226, "fftn"]], "fftshift": [[227, "fftshift"]], "hfft": [[228, "hfft"]], "ifft": [[229, "ifft"]], "ifftn": [[230, "ifftn"]], "ifftshift": [[231, "ifftshift"]], "ihfft": [[232, "ihfft"]], "irfft": [[233, "irfft"]], "irfftn": [[234, "irfftn"]], "rfft": [[235, "rfft"]], "rfftfreq": [[236, "rfftfreq"]], "rfftn": [[237, "rfftn"]], "cholesky": [[238, "cholesky"]], "cross": [[239, "cross"]], "det": [[240, "det"]], "diagonal": [[241, "diagonal"]], "eigh": [[242, "eigh"]], "eigvalsh": [[243, "eigvalsh"]], "inv": [[244, "inv"]], "matrix_norm": [[246, "matrix-norm"]], "matrix_power": [[247, "matrix-power"]], "matrix_rank": [[248, "matrix-rank"]], "outer": [[250, "outer"]], "pinv": [[251, "pinv"]], "qr": [[252, "qr"]], "slogdet": [[253, "slogdet"]], "solve": [[254, "solve"]], "svd": [[255, "svd"]], "svdvals": [[256, "svdvals"]], "trace": [[258, "trace"]], "vector_norm": [[260, "vector-norm"]], "Extension modules:": [[261, null]], "Linear Algebra Extension": [[262, "linear-algebra-extension"]], "Design Principles": [[262, "design-principles"]], "Future API standard evolution": [[263, "future-api-standard-evolution"]], "Scope extensions": [[263, "scope-extensions"]], "Versioning": [[263, "versioning"]], "Python array API standard": [[264, "python-array-api-standard"]], "Contents": [[264, "contents"]], "Context": [[264, null]], "API": [[264, null]], "Methodology and Usage": [[264, null]], "Other": [[264, null]], "License": [[265, "license"]], "Purpose and scope": [[266, "purpose-and-scope"]], "Introduction": [[266, "introduction"], [267, "introduction"]], "This API standard": [[266, "this-api-standard"]], "History": [[266, "history"]], "Scope (includes out-of-scope / non-goals)": [[266, "scope-includes-out-of-scope-non-goals"]], "In scope": [[266, "in-scope"]], "Out of scope": [[266, "out-of-scope"]], "Implications of in/out of scope": [[266, "implications-of-in-out-of-scope"]], "Stakeholders": [[266, "stakeholders"]], "How to read this document": [[266, "how-to-read-this-document"]], "How to adopt this API": [[266, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[266, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[266, "discoverability-of-conforming-implementations"]], "Optional feature": [[266, null]], "Conformance": [[266, "conformance"]], "Terms and Definitions": [[266, "terms-and-definitions"]], "Normative References": [[266, "normative-references"]], "Usage Data": [[267, "usage-data"]], "Design": [[267, "design"]], "Usage": [[267, "usage"]], "Use in Decision-Making": [[267, "use-in-decision-making"]], "Use cases": [[268, "use-cases"]], "Types of use cases": [[268, "types-of-use-cases"]], "Concrete use cases": [[268, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[268, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[268, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[268, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[268, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[269, "verification-test-suite"]], "Measuring conformance": [[269, "measuring-conformance"]], "Running the tests": [[269, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "count_nonzero() (in module array_api)": [[88, "array_api.count_nonzero"]], "cumulative_prod() (in module array_api)": [[89, "array_api.cumulative_prod"]], "cumulative_sum() (in module array_api)": [[90, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[91, "array_api.data_types.__eq__"]], "diff() (in module array_api)": [[92, "array_api.diff"]], "divide() (in module array_api)": [[93, "array_api.divide"]], "empty() (in module array_api)": [[94, "array_api.empty"]], "empty_like() (in module array_api)": [[95, "array_api.empty_like"]], "equal() (in module array_api)": [[96, "array_api.equal"]], "exp() (in module array_api)": [[97, "array_api.exp"]], "expand_dims() (in module array_api)": [[98, "array_api.expand_dims"]], "expm1() (in module array_api)": [[99, "array_api.expm1"]], "eye() (in module array_api)": [[100, "array_api.eye"]], "finfo() (in module array_api)": [[101, "array_api.finfo"]], "flip() (in module array_api)": [[102, "array_api.flip"]], "floor() (in module array_api)": [[103, "array_api.floor"]], "floor_divide() (in module array_api)": [[104, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[105, "array_api.from_dlpack"]], "full() (in module array_api)": [[106, "array_api.full"]], "full_like() (in module array_api)": [[107, "array_api.full_like"]], "greater() (in module array_api)": [[108, "array_api.greater"]], "greater_equal() (in module array_api)": [[109, "array_api.greater_equal"]], "hypot() (in module array_api)": [[110, "array_api.hypot"]], "iinfo() (in module array_api)": [[111, "array_api.iinfo"]], "imag() (in module array_api)": [[112, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[113, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[114, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[115, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[116, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[117, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[118, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[119, "array_api.isdtype"]], "isfinite() (in module array_api)": [[120, "array_api.isfinite"]], "isinf() (in module array_api)": [[121, "array_api.isinf"]], "isnan() (in module array_api)": [[122, "array_api.isnan"]], "less() (in module array_api)": [[123, "array_api.less"]], "less_equal() (in module array_api)": [[124, "array_api.less_equal"]], "linspace() (in module array_api)": [[125, "array_api.linspace"]], "log() (in module array_api)": [[126, "array_api.log"]], "log10() (in module array_api)": [[127, "array_api.log10"]], "log1p() (in module array_api)": [[128, "array_api.log1p"]], "log2() (in module array_api)": [[129, "array_api.log2"]], "logaddexp() (in module array_api)": [[130, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[131, "array_api.logical_and"]], "logical_not() (in module array_api)": [[132, "array_api.logical_not"]], "logical_or() (in module array_api)": [[133, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[134, "array_api.logical_xor"]], "matmul() (in module array_api)": [[135, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[136, "array_api.matrix_transpose"]], "max() (in module array_api)": [[137, "array_api.max"]], "maximum() (in module array_api)": [[138, "array_api.maximum"]], "mean() (in module array_api)": [[139, "array_api.mean"]], "meshgrid() (in module array_api)": [[140, "array_api.meshgrid"]], "min() (in module array_api)": [[141, "array_api.min"]], "minimum() (in module array_api)": [[142, "array_api.minimum"]], "moveaxis() (in module array_api)": [[143, "array_api.moveaxis"]], "multiply() (in module array_api)": [[144, "array_api.multiply"]], "negative() (in module array_api)": [[145, "array_api.negative"]], "nextafter() (in module array_api)": [[146, "array_api.nextafter"]], "nonzero() (in module array_api)": [[147, "array_api.nonzero"]], "not_equal() (in module array_api)": [[148, "array_api.not_equal"]], "ones() (in module array_api)": [[149, "array_api.ones"]], "ones_like() (in module array_api)": [[150, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[151, "array_api.permute_dims"]], "positive() (in module array_api)": [[152, "array_api.positive"]], "pow() (in module array_api)": [[153, "array_api.pow"]], "prod() (in module array_api)": [[154, "array_api.prod"]], "real() (in module array_api)": [[155, "array_api.real"]], "reciprocal() (in module array_api)": [[156, "array_api.reciprocal"]], "remainder() (in module array_api)": [[157, "array_api.remainder"]], "repeat() (in module array_api)": [[158, "array_api.repeat"]], "reshape() (in module array_api)": [[159, "array_api.reshape"]], "result_type() (in module array_api)": [[160, "array_api.result_type"]], "roll() (in module array_api)": [[161, "array_api.roll"]], "round() (in module array_api)": [[162, "array_api.round"]], "searchsorted() (in module array_api)": [[163, "array_api.searchsorted"]], "sign() (in module array_api)": [[164, "array_api.sign"]], "signbit() (in module array_api)": [[165, "array_api.signbit"]], "sin() (in module array_api)": [[166, "array_api.sin"]], "sinh() (in module array_api)": [[167, "array_api.sinh"]], "sort() (in module array_api)": [[168, "array_api.sort"]], "sqrt() (in module array_api)": [[169, "array_api.sqrt"]], "square() (in module array_api)": [[170, "array_api.square"]], "squeeze() (in module array_api)": [[171, "array_api.squeeze"]], "stack() (in module array_api)": [[172, "array_api.stack"]], "std() (in module array_api)": [[173, "array_api.std"]], "subtract() (in module array_api)": [[174, "array_api.subtract"]], "sum() (in module array_api)": [[175, "array_api.sum"]], "take() (in module array_api)": [[176, "array_api.take"]], "take_along_axis() (in module array_api)": [[177, "array_api.take_along_axis"]], "tan() (in module array_api)": [[178, "array_api.tan"]], "tanh() (in module array_api)": [[179, "array_api.tanh"]], "tensordot() (in module array_api)": [[180, "array_api.tensordot"]], "tile() (in module array_api)": [[181, "array_api.tile"]], "tril() (in module array_api)": [[182, "array_api.tril"]], "triu() (in module array_api)": [[183, "array_api.triu"]], "trunc() (in module array_api)": [[184, "array_api.trunc"]], "unique_all() (in module array_api)": [[185, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[186, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[187, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[188, "array_api.unique_values"]], "unstack() (in module array_api)": [[189, "array_api.unstack"]], "var() (in module array_api)": [[190, "array_api.var"]], "vecdot() (in module array_api)": [[191, "array_api.vecdot"]], "where() (in module array_api)": [[192, "array_api.where"]], "zeros() (in module array_api)": [[193, "array_api.zeros"]], "zeros_like() (in module array_api)": [[194, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[224, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[225, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[226, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[227, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[228, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[229, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[230, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[231, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[232, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[233, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[234, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[235, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[236, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[237, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[238, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[239, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[240, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[241, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[242, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[243, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[244, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[245, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[246, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[247, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[248, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[249, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[250, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[251, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[252, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[253, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[254, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[255, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[256, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[257, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[258, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[259, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[260, 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15, 19, 23, 26, 60, 63, 75, 87, 93, 100, 102, 105, 114, 118, 144, 160, 161, 163, 167, 179, 181, 182, 183, 189, 191, 195, 196, 208, 210, 211, 213, 214, 215, 216, 217, 218, 220, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 251, 253, 254, 260, 261, 262, 265, 266, 268, 269], "thi": [0, 1, 5, 7, 15, 19, 26, 32, 34, 49, 58, 59, 63, 71, 75, 77, 78, 99, 104, 105, 110, 114, 118, 119, 125, 128, 131, 132, 133, 134, 139, 147, 153, 157, 158, 160, 172, 173, 176, 177, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 227, 229, 230, 233, 234, 235, 237, 252, 253, 254, 255, 261, 262, 263, 265, 267, 268, 269], "return": [0, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 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235, 236, 237, 239, 246, 254, 255, 256, 258, 260, 261, 262, 263, 266, 267, 268], "some": [0, 99, 104, 116, 118, 128, 160, 196, 211, 212, 213, 214, 217, 222, 266, 268, 269], "common": [0, 196, 205, 208, 217, 220, 221, 262, 266, 267, 268], "librari": [0, 5, 7, 26, 51, 57, 58, 59, 60, 63, 75, 93, 99, 104, 105, 114, 116, 118, 119, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 147, 158, 163, 173, 179, 185, 186, 187, 188, 190, 195, 196, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 238, 242, 243, 252, 254, 261, 262, 263, 266, 267, 268, 269], "g": [0, 5, 9, 19, 20, 26, 47, 51, 57, 77, 89, 90, 92, 93, 105, 110, 112, 118, 119, 125, 137, 141, 144, 147, 154, 155, 158, 160, 162, 175, 181, 185, 186, 187, 188, 196, 203, 205, 210, 211, 212, 213, 214, 215, 216, 217, 220, 228, 232, 233, 234, 235, 237, 242, 243, 246, 253, 255, 256, 258, 260, 261, 262, 263, 266, 267, 268], "numpi": [0, 19, 63, 139, 196, 208, 213, 214, 216, 217, 262, 266, 267, 268, 269], "scalar": [0, 2, 12, 49, 60, 65, 67, 69, 70, 71, 72, 77, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 148, 153, 157, 160, 174, 192, 195, 196, 220, 260, 268], "valu": [0, 1, 2, 5, 7, 9, 10, 11, 12, 15, 16, 17, 18, 20, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 43, 49, 51, 57, 58, 60, 61, 62, 63, 64, 65, 66, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 146, 147, 148, 149, 153, 154, 155, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 173, 175, 176, 177, 178, 179, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 205, 208, 210, 212, 214, 215, 216, 220, 222, 225, 228, 232, 233, 234, 235, 236, 237, 238, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "rational": [0, 7, 89, 90, 154, 175, 196, 216, 217, 258, 261, 263, 266], "alwai": 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268], "model": [0, 57, 58, 93, 144, 213, 220, 268], "repres": [0, 8, 11, 12, 23, 24, 25, 26, 29, 34, 35, 62, 66, 87, 93, 104, 140, 144, 167, 178, 179, 210, 212, 216, 217, 253, 267, 268], "futur": [0, 26, 49, 105, 196, 209, 213, 214, 217, 221, 222, 242, 243, 264, 266, 268], "python": [0, 2, 5, 7, 24, 25, 26, 29, 32, 34, 35, 49, 60, 104, 105, 157, 192, 195, 196, 208, 210, 213, 216, 218, 220, 221, 222, 263, 265, 266, 267], "x": [0, 1, 5, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 26, 32, 61, 62, 63, 64, 65, 66, 68, 74, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 95, 97, 98, 99, 102, 103, 105, 107, 112, 120, 121, 122, 126, 127, 128, 129, 132, 136, 137, 139, 141, 143, 145, 147, 150, 151, 152, 154, 155, 156, 158, 159, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 194, 196, 213, 214, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 249, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "__pos__": [0, 195, 210], "po": 0, "__neg__": [0, 195, 210], "neg": [0, 13, 14, 15, 44, 47, 65, 78, 89, 90, 92, 93, 98, 100, 102, 104, 121, 126, 128, 144, 153, 157, 161, 165, 169, 176, 177, 180, 191, 195, 196, 210, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 260, 266], "x1": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "x2": [0, 7, 12, 40, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 157, 163, 174, 180, 191, 192, 210, 239, 245, 250, 254, 257, 259], "__add__": [0, 50, 195, 210], "add": [0, 7, 21, 90, 174, 175, 195, 196, 210, 211, 212, 217, 258], "__sub__": [0, 195, 210], "sub": [0, 196], "__mul__": [0, 195, 210], "mul": 0, "__truediv__": [0, 195, 210], "truediv": 0, "__floordiv__": [0, 195], "floordiv": 0, "__mod__": [0, 195], "mod": 0, "__pow__": [0, 195, 210], "pow": [0, 47, 195, 210, 212], "should": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 85, 86, 87, 89, 90, 92, 93, 97, 98, 99, 101, 103, 104, 105, 108, 109, 110, 112, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 146, 152, 153, 154, 156, 157, 159, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 203, 210, 211, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 266, 268, 269], "defin": [0, 5, 12, 23, 30, 32, 41, 49, 60, 65, 77, 79, 89, 90, 92, 93, 104, 106, 107, 118, 125, 137, 138, 139, 141, 142, 143, 144, 155, 157, 160, 164, 169, 170, 173, 176, 182, 183, 190, 191, 195, 196, 198, 203, 210, 212, 213, 222, 226, 227, 230, 231, 234, 237, 238, 242, 243, 244, 251, 252, 254, 262, 267, 268, 269], "real": [0, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24, 25, 29, 30, 31, 33, 35, 37, 39, 41, 44, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 79, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 162, 163, 164, 165, 166, 167, 168, 169, 173, 175, 178, 179, 184, 190, 191, 193, 195, 205, 210, 212, 213, 225, 228, 232, 233, 234, 235, 236, 237, 238, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 263], "data": [0, 1, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 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31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 198, 208, 211, 213, 214, 216, 218, 219, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 263, 266, 267], "__matmul__": [0, 195, 210], "matmul": [0, 40, 195, 205, 210, 262], "The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 102, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 205, 208, 210, 211, 212, 214, 215, 216, 217, 220, 221, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 263, 265, 266, 267, 268, 269], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 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244, 251, 252, 254, 262, 263, 266, 267, 268, 269], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 91, 93, 99, 104, 105, 128, 143, 144, 160, 173, 190, 196, 198, 208, 210, 212, 213, 214, 215, 216, 217, 218, 222, 239, 251, 261, 262, 265, 266, 268], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 91, 92, 96, 110, 120, 121, 148, 169, 195, 196, 205, 210, 213, 214, 216, 222, 255, 263, 265, 266, 269], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 77, 79, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 153, 154, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 175, 178, 179, 184, 185, 186, 187, 188, 196, 203, 208, 212, 213, 214, 215, 217, 220, 225, 234, 236, 253, 255, 256, 258, 266, 268, 269], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 92, 108, 109, 123, 124, 125, 137, 138, 141, 142, 157, 168, 191, 196, 210, 213, 214, 218, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 266], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 125, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 159, 168, 173, 174, 175, 177, 190, 191, 192, 196, 205, 210, 213, 214, 218, 239, 246, 248, 251, 254, 260, 266, 268], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 75, 91, 92, 93, 96, 104, 105, 108, 109, 110, 113, 118, 119, 123, 124, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 148, 158, 159, 160, 163, 168, 173, 179, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 242, 252, 253, 255, 261, 262, 266, 267, 268], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 89, 90, 93, 96, 97, 99, 100, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 160, 162, 164, 166, 167, 168, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 205, 216, 217, 219, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 89, 90, 104, 108, 109, 110, 119, 123, 124, 125, 137, 138, 141, 142, 158, 163, 168, 176, 178, 179, 196, 208, 211, 212, 213, 214, 215, 217, 262, 263, 266, 268], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 108, 109, 123, 124, 137, 138, 141, 142, 168], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 60, 62, 66, 77, 78, 79, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 167, 168, 169, 172, 176, 177, 179, 196, 203, 205, 210, 226, 227, 230, 231, 234, 237, 242, 243, 266], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 57, 60, 71, 77, 79, 89, 90, 92, 96, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 168, 176, 178, 179, 196, 203, 212, 213, 226, 227, 230, 231, 234, 237, 242, 243, 255, 262], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 93, 96, 97, 99, 108, 109, 114, 123, 124, 125, 126, 127, 128, 129, 144, 145, 148, 153, 160, 163, 166, 167, 168, 178, 179, 192, 203, 205, 212, 213, 216, 219, 220, 222, 242, 243, 252, 253, 254, 255, 262, 266, 268, 269], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 85, 88, 93, 96, 99, 104, 105, 107, 108, 109, 110, 113, 114, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 147, 148, 153, 154, 156, 157, 158, 159, 160, 163, 164, 168, 169, 170, 173, 174, 175, 177, 185, 186, 187, 188, 190, 191, 192, 195, 196, 205, 207, 208, 211, 213, 215, 216, 217, 222, 239, 246, 248, 251, 254, 260, 261, 266, 267, 268, 269], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 91, 92, 102, 104, 105, 108, 109, 123, 124, 137, 138, 141, 142, 147, 158, 163, 168, 178, 179, 180, 185, 186, 187, 188, 196, 203, 205, 210, 212, 214, 215, 216, 218, 233, 234, 242, 243, 246, 255, 256, 260, 262, 263, 266, 267], "discuss": [0, 96, 148, 210, 216, 217, 221, 266, 267, 268], "copi": [0, 1, 26, 59, 60, 63, 105, 159, 168, 210, 211, 216, 217, 219, 265, 266], "view": [0, 105, 219], "behavior": [0, 5, 26, 32, 47, 49, 59, 60, 63, 74, 77, 89, 90, 92, 93, 104, 106, 107, 110, 125, 144, 153, 157, 159, 160, 163, 176, 177, 185, 186, 187, 188, 195, 196, 198, 205, 208, 210, 212, 213, 219, 220, 221, 226, 227, 230, 231, 234, 237, 262, 263, 266, 267, 268, 269], "mutabl": [0, 219], "refer": [0, 1, 13, 14, 92, 99, 100, 128, 163, 173, 176, 177, 180, 181, 190, 191, 196, 213, 214, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 254], "what": [0, 163, 208, 216, 218, 222, 262, 266, 267, 268, 269], "call": [0, 7, 34, 92, 216, 217, 220, 253, 266, 267, 268], "http": [0, 216, 263, 269], "doc": 0, "org": 0, "html": 0, "do": [0, 1, 26, 75, 93, 144, 157, 203, 208, 210, 211, 213, 214, 216, 217, 218, 262, 263, 265, 266, 268, 269], "mutat": [0, 176, 210], "choos": [0, 51, 57, 59, 92, 93, 104, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 158, 160, 173, 185, 186, 187, 188, 190, 195, 196, 203, 213, 214, 215, 217, 220, 266, 268], "when": [0, 5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 75, 77, 89, 90, 93, 99, 104, 105, 110, 116, 118, 125, 128, 137, 138, 139, 141, 142, 144, 153, 154, 158, 159, 163, 173, 175, 176, 179, 190, 192, 195, 196, 205, 210, 211, 213, 214, 215, 216, 218, 220, 221, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 244, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268], "doe": [0, 1, 15, 26, 105, 148, 176, 177, 196, 205, 208, 211, 212, 213, 214, 215, 217, 218, 220, 222, 262, 266, 268, 269], "correspond": [0, 1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 96, 105, 108, 109, 114, 115, 116, 123, 124, 148, 153, 159, 161, 163, 173, 177, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 226, 230, 234, 237, 239, 242, 246, 265, 266], "fall": 0, "back": [0, 268], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 77, 104, 110, 131, 132, 133, 134, 157, 162, 176, 196, 205, 210, 213, 214, 248, 251, 254, 260, 266], "binari": [0, 5, 67, 70, 72, 178, 179, 211], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 90, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 159, 160, 162, 163, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 192, 208, 224, 225, 226, 228, 229, 230, 233, 234, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263, 266, 268, 269], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 89, 90, 92, 94, 95, 98, 102, 106, 107, 114, 135, 136, 140, 149, 150, 159, 161, 163, 168, 172, 176, 177, 180, 181, 182, 183, 189, 191, 193, 194, 195, 210, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 266, 268], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 93, 96, 97, 99, 103, 104, 108, 109, 110, 112, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 173, 174, 175, 178, 179, 180, 184, 185, 190, 196, 203, 205, 210, 212, 213, 214, 220, 238, 239, 241, 246, 247, 253, 254, 260, 266, 267, 268, 269], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 92, 93, 96, 97, 99, 104, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 139, 142, 144, 145, 148, 153, 156, 157, 160, 166, 167, 169, 170, 172, 173, 174, 178, 179, 180, 190, 191, 192, 195, 210, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 142, 144, 145, 148, 153, 156, 157, 160, 164, 166, 167, 169, 170, 172, 174, 178, 179, 180, 191, 192, 195, 196, 210, 213, 216, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262, 266, 268], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 173, 174, 175, 177, 180, 190, 191, 192, 195, 196, 210, 239, 246, 248, 251, 254, 260, 266], "let": [0, 1, 9, 10, 11, 12, 62, 66, 85, 87, 89, 90, 92, 96, 97, 99, 105, 120, 121, 122, 125, 126, 128, 139, 148, 154, 158, 163, 164, 167, 169, 173, 175, 179, 181, 190, 191, 196, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 243, 244, 252, 254, 255, 258], "If": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 114, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 211, 213, 217, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 258, 260, 261, 262, 266, 268], "after": [0, 1, 26, 40, 135, 169, 181, 196], "appli": [0, 12, 77, 78, 85, 93, 139, 144, 160, 162, 172, 180, 196, 205, 208, 213, 224, 226, 229, 230, 233, 234, 235, 237, 248, 251, 262, 266, 268], "operand": [0, 1, 9, 10, 11, 12, 24, 25, 29, 35, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 175, 178, 179, 184, 205, 210, 212, 253, 258], "equal": [0, 1, 9, 10, 11, 18, 20, 21, 22, 26, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 58, 61, 62, 63, 64, 65, 66, 69, 71, 77, 87, 88, 91, 97, 99, 100, 106, 107, 110, 119, 121, 126, 127, 128, 129, 139, 147, 148, 149, 150, 153, 154, 162, 167, 168, 169, 173, 175, 176, 177, 179, 180, 181, 185, 186, 187, 188, 190, 195, 196, 203, 210, 213, 217, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 247, 248, 251, 252, 253, 254, 258, 266], "left": [0, 1, 5, 28, 31, 33, 37, 39, 43, 60, 69, 90, 96, 104, 106, 108, 109, 123, 124, 148, 163, 176, 177, 196, 205, 242, 243, 255, 266], "hand": [0, 1, 205], "side": [0, 110, 163, 196, 214, 216], "same": [0, 5, 7, 9, 12, 15, 18, 19, 20, 26, 32, 36, 38, 40, 41, 46, 48, 50, 55, 59, 63, 68, 73, 74, 76, 77, 78, 79, 89, 90, 92, 93, 95, 98, 101, 102, 103, 104, 105, 107, 112, 135, 136, 137, 139, 140, 141, 143, 144, 146, 150, 151, 152, 153, 154, 155, 157, 158, 159, 161, 162, 163, 164, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 194, 196, 205, 208, 210, 213, 214, 216, 217, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 240, 241, 242, 244, 247, 251, 252, 253, 255, 256, 258, 261, 262, 266, 268], "special": [0, 9, 10, 11, 12, 20, 21, 24, 25, 28, 29, 30, 35, 41, 42, 43, 47, 51, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 173, 175, 178, 179, 184, 190, 210, 211, 213, 253, 258], "case": [0, 1, 5, 7, 9, 10, 11, 12, 15, 20, 21, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 47, 51, 60, 61, 62, 64, 65, 66, 76, 77, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 105, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 146, 148, 153, 154, 156, 157, 162, 164, 165, 166, 167, 169, 170, 173, 175, 178, 179, 184, 190, 196, 208, 210, 211, 212, 213, 214, 217, 218, 220, 252, 253, 255, 258, 262, 264, 266, 269], "respect": [0, 9, 12, 20, 21, 22, 28, 30, 31, 33, 37, 38, 39, 41, 42, 43, 45, 48, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 87, 93, 96, 104, 108, 109, 110, 116, 123, 124, 125, 130, 131, 133, 134, 138, 140, 142, 143, 144, 146, 148, 157, 167, 174, 178, 179, 180, 185, 186, 191, 196, 210, 212, 215, 217, 242, 252, 255], "two": [0, 1, 5, 15, 19, 40, 55, 65, 71, 100, 105, 135, 136, 140, 160, 162, 180, 182, 183, 185, 186, 187, 188, 191, 196, 205, 216, 217, 220, 221, 226, 227, 230, 231, 234, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268, 269], "assign": [0, 214], "addit": [0, 5, 7, 12, 26, 50, 59, 90, 118, 174, 195, 196, 205, 211, 213, 216, 262, 266, 267, 269], "modifi": [0, 26, 214, 265], "differ": [0, 1, 12, 26, 49, 50, 75, 77, 78, 89, 90, 92, 93, 101, 104, 105, 144, 154, 160, 172, 174, 175, 196, 208, 210, 214, 217, 218, 220, 231, 242, 252, 253, 255, 258, 262, 266, 267, 268], "due": [0, 26, 42, 57, 58, 125, 144, 158, 176, 212, 213, 214, 262, 266], "cast": [0, 5, 29, 49, 60, 63, 75, 89, 90, 92, 154, 175, 205, 213, 258, 266, 268], "select": [0, 176, 177, 196, 266], "": [0, 5, 26, 29, 32, 49, 58, 59, 60, 80, 104, 105, 140, 157, 173, 181, 182, 183, 190, 196, 203, 208, 210, 211, 212, 213, 214, 216, 217, 220, 222, 226, 230, 234, 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88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 210, 212, 213, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 110, 112, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 193, 195, 203, 210, 212, 213, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "creat": [3, 15, 60, 94, 95, 100, 105, 106, 107, 125, 149, 150, 193, 194, 202, 208, 217, 225, 236, 262, 266], "its": [5, 26, 40, 73, 93, 101, 135, 144, 159, 161, 212, 213, 216, 217, 261, 266, 267, 268], "main": [5, 100, 182, 183, 211, 216, 241, 258, 261, 268], "namespac": [5, 7, 23, 113, 198, 208, 210, 223, 261, 262, 263, 266, 269], "under": [5, 261, 265, 266], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 89, 90, 92, 94, 98, 101, 102, 106, 116, 118, 119, 125, 149, 154, 157, 158, 161, 171, 172, 175, 176, 177, 181, 182, 183, 185, 186, 187, 188, 191, 193, 196, 205, 210, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 232, 233, 234, 235, 237, 241, 258, 260, 262, 263, 266, 268, 269], "name": [5, 7, 23, 26, 104, 118, 185, 186, 187, 196, 213, 214, 242, 251, 252, 253, 255, 261, 266, 267], "descript": [5, 7, 210, 212, 246, 260], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 67, 70, 72, 75, 88, 89, 90, 91, 96, 105, 106, 107, 108, 109, 118, 119, 120, 121, 122, 123, 124, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 160, 165, 168, 173, 175, 190, 192, 205, 210, 220, 238, 246, 255, 260], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 101, 104, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 147, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 192, 196, 210, 214, 238, 246, 255, 260, 262], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 196, 238, 246, 255, 260], "int8": [5, 118, 119, 196, 205], "bit": [5, 68, 69, 71, 85, 89, 90, 101, 111, 154, 165, 175, 205, 210, 212, 258], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 89, 90, 93, 97, 99, 104, 118, 119, 126, 128, 137, 138, 141, 142, 144, 145, 153, 154, 157, 163, 165, 167, 169, 175, 179, 185, 186, 187, 188, 195, 203, 210, 213, 252, 253, 258], "exist": [5, 7, 26, 60, 78, 105, 208, 210, 213, 216, 217, 218, 244, 263, 266, 267], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 98, 125, 126, 128, 143, 172, 180, 182, 183, 189, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 263], "128": 5, "127": 5, "int16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "16": [5, 205], "32": [5, 205], "767": 5, "int32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "147": 5, "483": 5, "647": 5, "int64": [5, 89, 90, 118, 119, 154, 175, 205, 258], "64": [5, 205], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 118, 119, 196, 205], "unsign": [5, 89, 90, 118, 119, 154, 175, 195, 258], "255": 5, "uint16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "65": 5, "535": [5, 210], "uint32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "294": 5, "967": 5, "295": 5, "uint64": [5, 118, 119, 205], "18": 5, "446": [5, 210], "744": [5, 210], "073": 5, "709": [5, 210], "551": [5, 210], "615": 5, "float32": [5, 112, 118, 119, 155, 205, 253, 255, 256], "ieee": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "754": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "singl": [5, 7, 24, 25, 29, 34, 35, 116, 118, 185, 186, 195, 205, 210, 211, 213, 216, 217, 222, 262, 266, 267, 268], "2019": [5, 12, 93, 99, 110, 128, 144, 195, 212, 266, 268], "float64": [5, 9, 20, 118, 119, 205, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "doubl": [5, 180, 205, 210], "complex64": [5, 112, 118, 119, 155, 205, 210, 253, 255, 256], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 162, 167, 169, 179, 210, 213], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 155, 162, 167, 169, 178, 179, 185, 186, 187, 188, 210, 213, 227, 236], "complex128": [5, 9, 20, 118, 119, 205, 210, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "method": [5, 26, 34, 105, 195, 198, 208, 214, 216, 217, 220, 221, 222, 266, 267, 268], "attribut": [5, 23, 101, 111, 160, 195, 207, 210, 263, 266, 267, 268], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 75, 89, 90, 105, 110, 119, 154, 160, 169, 172, 175, 176, 177, 179, 185, 186, 188, 189, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 236, 239, 258, 261, 262, 266, 267, 268], "beyond": [5, 161, 205, 210, 266], "It": [5, 23, 26, 105, 208, 214, 216, 266, 268, 269], "also": [5, 7, 26, 32, 34, 105, 110, 164, 208, 213, 214, 215, 216, 222, 226, 230, 234, 237, 255, 261, 268], "subnorm": [5, 110, 212], "k": [5, 40, 100, 110, 135, 147, 182, 183, 196, 212, 238, 242, 243, 244, 252, 254, 255, 256, 258, 266], "denorm": [5, 110, 212], "gradual": [5, 110, 212, 266], "underflow": [5, 9, 93, 104, 110, 212, 253], "hardwar": [5, 53, 110, 158, 212, 216, 217, 242, 255, 262, 266], "univers": [5, 110, 211, 212, 217, 262, 266], "mani": [5, 110, 181, 212, 266, 268], "platform": [5, 26, 110, 212], "compil": [5, 110, 179, 208, 211, 212, 215, 266], "toggl": [5, 110, 212], "daz": [5, 110, 212], "flush": [5, 110, 212], "ftz": [5, 110, 212], "increas": [5, 110, 212, 267], "guard": [5, 110, 212], "against": [5, 40, 73, 110, 135, 179, 196, 212, 248, 251, 269], "time": [5, 7, 16, 17, 26, 92, 110, 158, 185, 186, 208, 210, 212, 215, 216, 221, 238, 242, 243, 244, 252, 254, 255, 262, 266, 268], "attack": [5, 110, 212], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 75, 88, 93, 99, 104, 110, 125, 126, 128, 137, 139, 140, 141, 144, 147, 154, 158, 160, 163, 169, 173, 175, 185, 186, 187, 188, 190, 196, 205, 212, 213, 214, 215, 217, 246, 252, 260, 262], "vari": [5, 110, 163, 179, 185, 186, 187, 188, 205, 212], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 75, 77, 78, 86, 87, 89, 90, 92, 97, 99, 102, 105, 110, 117, 118, 119, 125, 126, 128, 131, 132, 133, 134, 135, 139, 147, 153, 154, 157, 158, 159, 160, 164, 166, 167, 168, 169, 172, 173, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 195, 198, 208, 210, 211, 213, 214, 215, 216, 217, 220, 221, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 244, 248, 251, 252, 253, 254, 255, 256, 258, 261, 262, 263, 266, 267, 268], "access": [5, 26, 32, 105, 113, 196, 210, 216, 261, 263, 266], "variou": [5, 210], "introspect": 5, "isdtyp": [5, 195, 210], "integr": [5, 63, 77, 116, 118, 119], "keyword": [5, 7, 26, 60, 63, 89, 90, 117, 140, 154, 159, 175, 195, 210, 217, 221, 222, 225, 236, 258, 262, 263, 266, 267, 268], "affect": [5, 15, 49, 214, 217], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 89, 90, 92, 93, 97, 99, 126, 127, 128, 129, 130, 137, 139, 141, 144, 153, 154, 166, 167, 169, 173, 174, 175, 178, 179, 190, 210, 253], "implementor": [5, 261], "free": [5, 214, 217, 265], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 113, 222], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 89, 90, 93, 97, 98, 99, 104, 107, 135, 139, 140, 143, 144, 145, 147, 153, 154, 166, 167, 171, 173, 175, 176, 178, 179, 180, 181, 185, 186, 187, 188, 190, 196, 205, 208, 213, 216, 217, 220, 221, 239, 246, 254, 255, 258, 260, 262, 263, 266, 268, 269], "wai": [5, 26, 63, 105, 208, 211, 217, 218, 263, 266, 267, 268, 269], "f4": [5, 205], "recommend": [5, 7, 19, 23, 26, 125, 131, 132, 133, 134, 139, 157, 173, 190, 203, 210, 212, 214, 216, 217, 266], "guidanc": [5, 7, 26, 49, 210, 211, 218, 266], "govern": [5, 50, 174, 205, 262, 263], "interact": [5, 213], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 89, 90, 93, 96, 97, 99, 101, 104, 105, 110, 113, 119, 120, 121, 125, 126, 127, 128, 129, 130, 135, 137, 138, 141, 142, 144, 146, 154, 157, 164, 165, 166, 169, 175, 178, 179, 180, 192, 196, 212, 213, 214, 218, 222, 253, 258, 266, 267, 269], "exampl": [5, 12, 23, 26, 118, 119, 139, 172, 195, 196, 208, 213, 214, 215, 217, 220, 221, 222, 258, 262, 266, 268, 269], "whether": [5, 13, 14, 26, 59, 60, 63, 75, 79, 89, 90, 91, 105, 114, 119, 122, 125, 139, 155, 159, 165, 210, 217, 238, 242, 243, 252, 254, 261, 265, 266, 268], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 88, 105, 114, 116, 118, 137, 139, 141, 154, 158, 159, 163, 164, 173, 175, 190, 191, 192, 195, 196, 208, 217, 238, 240, 246, 253, 254, 260, 265], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 192, 195, 196, 210, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 267, 268, 269], "possibl": [5, 26, 60, 75, 104, 105, 137, 141, 159, 160, 178, 179, 208, 211, 212, 213, 214, 216, 217, 218, 220, 222, 262, 266, 267, 268, 269], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 88, 89, 135, 137, 139, 141, 144, 145, 154, 173, 175, 190, 196, 208, 211, 213, 216, 217, 221, 222, 243, 244, 262, 263, 266, 268], "In": [5, 12, 19, 26, 59, 89, 90, 93, 96, 104, 119, 121, 122, 139, 144, 148, 154, 157, 164, 175, 195, 196, 198, 205, 212, 213, 214, 216, 218, 233, 234, 252, 253, 255, 258, 262, 263, 267, 268, 269], "clearli": [5, 59, 119, 203, 213, 262, 263], "warn": [5, 158, 218], "about": [5, 7, 26, 101, 111, 214, 262, 266, 268, 269], "organ": [5, 210, 262, 267, 268], "within": [5, 15, 27, 196, 205, 208, 210, 213, 217, 224, 226, 229, 230, 233, 234, 235, 237, 266], "accord": [5, 12, 60, 71, 75, 89, 90, 93, 101, 104, 106, 125, 144, 153, 160, 163, 164, 173, 177, 190, 191, 192, 196, 210, 212, 213], "These": [5, 214, 242, 267], "intend": [5, 89, 90, 154, 175, 208, 258], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 93, 98, 100, 101, 104, 121, 126, 128, 143, 144, 147, 157, 161, 165, 167, 169, 179, 195, 196, 208, 210, 212, 222, 236, 238, 252, 267], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 208, 210, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262], "extern": [7, 268], "usabl": 7, "accept": [7, 26, 131, 132, 133, 134, 139, 157, 173, 190, 208, 263], "argument": [7, 10, 11, 12, 26, 40, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 85, 86, 89, 90, 93, 96, 104, 108, 109, 110, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 138, 142, 144, 148, 153, 154, 157, 159, 160, 163, 166, 169, 174, 175, 178, 179, 180, 192, 195, 205, 212, 216, 217, 224, 225, 226, 229, 230, 233, 234, 235, 236, 237, 258, 262, 266, 267, 268], "map": [7, 213, 214], "base": [7, 47, 57, 58, 97, 98, 126, 127, 128, 129, 153, 185, 186, 187, 188, 196, 210, 214, 220, 222, 262, 263, 266, 267, 268], "sole": [7, 196, 203, 262], "incompat": [7, 26, 74, 105, 208, 263, 266], "normal": [7, 78, 172, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237], "practic": [7, 19, 196, 262, 267], "avail": [7, 105, 117, 208, 216, 261, 263, 267], "still": [7, 26, 222, 262, 267, 268, 269], "consid": [7, 26, 63, 105, 131, 132, 133, 134, 185, 186, 187, 188, 213, 217, 236, 251, 262, 266, 268, 269], "compliant": [7, 26, 51, 93, 99, 105, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 173, 190, 212, 215, 217, 263, 266], "altern": [7, 214, 216, 269], "thei": [7, 26, 205, 211, 214, 216, 217, 221, 222, 261, 262, 263, 266, 268, 269], "were": [7, 104, 158, 163, 210, 266], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 195, 210, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 262, 267, 268], "lead": [7, 104, 213, 252, 255, 266], "readabl": [7, 205, 262, 267], "code": [7, 59, 205, 214, 215, 217, 220, 222, 262, 266, 267, 268], "easier": [7, 208, 214, 262], "evolv": [7, 208, 262], "over": [7, 13, 14, 26, 88, 125, 137, 139, 141, 154, 173, 175, 176, 180, 190, 191, 196, 212, 213, 214, 216, 217, 221, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 258, 260, 262, 266], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 77, 79, 85, 86, 87, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 138, 139, 140, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 160, 162, 164, 166, 167, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 196, 209, 210, 211, 217, 225, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "worri": 7, "xi": [7, 140], "annot": [7, 210, 222, 266], "individu": [7, 139, 196, 217, 220, 221, 222, 225, 236, 266, 267], "aim": [7, 211, 222, 261, 262, 263, 266, 267, 268, 269], "strongli": [7, 214, 268], "look": [7, 268], "like": [7, 196, 208, 211, 213, 220, 222, 263, 266, 267, 268], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 114, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 196, 210, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 266, 267, 269], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 210, 211, 214, 216, 220, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 265, 268], "int": [7, 12, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 74, 77, 78, 85, 88, 89, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 123, 124, 125, 130, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 151, 153, 154, 157, 158, 159, 160, 161, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 189, 190, 191, 192, 193, 196, 205, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 241, 246, 247, 257, 258, 259, 260, 267], "str": [7, 8, 23, 118, 119, 140, 267], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 91, 210, 268], "few": [7, 212, 220, 266, 268], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 115, 116, 118, 125, 137, 139, 140, 141, 147, 149, 150, 154, 158, 159, 161, 163, 168, 172, 173, 175, 177, 180, 182, 183, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 210, 212, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 246, 248, 251, 252, 255, 258, 260], "form": [7, 23, 26, 40, 79, 135, 136, 182, 183, 196, 214, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 263, 267], "question": [7, 211, 266], "commonli": [7, 173, 190, 196, 211, 213, 215, 261, 262, 266, 267], "written": [7, 208, 266, 268], "yyyi": [8, 23, 263], "mm": [8, 23, 263], "string": [8, 23, 118, 119, 210, 263, 266], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 195, 208, 211, 217, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 264, 266, 268], "absolut": [9, 20, 85, 164, 212, 214, 246, 247, 253, 262], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 97, 99, 103, 112, 120, 121, 122, 126, 127, 128, 129, 132, 137, 139, 141, 145, 152, 155, 156, 162, 164, 165, 166, 167, 169, 170, 173, 178, 179, 184, 190], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 110, 112, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 203, 208, 210, 213, 215, 217, 218, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 255, 256, 258, 260, 262, 266, 268], "magnitud": [9, 12, 20, 85, 93, 104, 110, 144, 210, 255, 256], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 93, 101, 104, 111, 144, 145, 146, 178, 179, 210, 216, 267], "known": [9, 164, 212, 215, 216], "norm": [9, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 260, 262], "modulu": [9, 157], "z": [9, 10, 11, 61, 62, 64, 66, 126, 213], "bj": [9, 12, 79, 93, 144], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 92, 93, 96, 98, 104, 108, 109, 110, 123, 124, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 144, 145, 147, 148, 152, 154, 158, 173, 175, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 215, 220, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 164, 166, 167, 178, 179, 213, 242, 243, 253, 255], "sqrt": [9, 10, 11, 61, 62, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 260], "take": [9, 126, 128, 153, 169, 195, 210, 217, 222, 266], "care": [9, 262], "undu": [9, 215], "overflow": [9, 12, 89, 90, 93, 104, 110, 125, 154, 175, 205, 253, 258, 262], "dure": [9, 40, 59, 110, 135, 173, 190, 205, 208, 251, 266, 267], "stage": [9, 110, 263], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 193, 196, 210, 212, 213, 214, 216, 220, 221, 225, 226, 227, 230, 231, 234, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 268], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 157, 162, 163, 164, 165, 166, 167, 169, 173, 178, 179, 184, 185, 186, 187, 188, 190, 195, 203, 210, 213, 266], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 126, 127, 128, 129, 130, 137, 141, 144, 148, 153, 157, 162, 165, 166, 167, 169, 178, 179, 184, 213, 253, 260], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 96, 97, 99, 120, 121, 122, 125, 126, 128, 139, 148, 162, 164, 167, 169, 179, 195, 210, 211, 266, 267, 268], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 93, 96, 97, 99, 104, 110, 114, 120, 121, 126, 128, 144, 148, 153, 157, 165, 167, 169, 179, 212], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 93, 96, 97, 99, 100, 101, 106, 107, 111, 112, 119, 120, 121, 122, 125, 126, 127, 128, 129, 135, 140, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 162, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 97, 99, 104, 126, 127, 128, 129, 153, 166, 167, 178, 179, 212, 248, 251], "princip": [10, 11, 61, 62, 64, 66, 126, 169, 213, 262], "invers": [10, 11, 61, 62, 64, 65, 66, 213, 224, 226, 229, 230, 231, 232, 233, 234, 235, 237, 244, 247, 251, 262], "cosin": [10, 11, 86, 87, 179], "express": [10, 61, 63, 64, 65, 86, 166, 178, 196, 205, 214, 262, 265], "radian": [10, 61, 64, 65, 86, 166, 178], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 93, 125, 127, 129, 164, 166, 167, 178, 179, 213, 253], "pi": [10, 11, 61, 62, 64, 66, 87, 126, 128, 167, 178, 179, 195], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 93, 97, 99, 125, 126, 128, 139, 144, 163, 164, 166, 167, 169, 178, 179, 196, 213, 242, 255, 258], "ln": [10, 11, 61, 62, 64, 66, 126], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 97, 99, 126, 127, 128, 129, 167, 169, 179, 195, 210], "multi": [10, 11, 61, 62, 64, 66, 195, 213, 216, 217, 239, 268], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 93, 97, 99, 126, 128, 144, 153, 166, 167, 169, 178, 179, 266], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 97, 99, 126, 128, 153, 166, 167, 169, 178, 179, 266], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 93, 97, 99, 144, 166, 167, 169, 178, 179, 266], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 89, 90, 126, 128, 137, 139, 141, 153, 154, 169, 173, 175, 190, 191, 212, 213, 239, 262, 267], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 94, 95, 100, 105, 106, 107, 125, 149, 150, 161, 193, 194, 195, 203, 205, 210, 214, 217, 225, 236, 251], "line": [10, 11, 61, 62, 64, 66, 178, 179, 205, 213, 266, 267, 268, 269], "segment": [10, 11, 61, 62, 64, 66, 213], "infti": [10, 11, 61, 62, 64, 66, 86, 126, 128, 153, 169, 213], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 98, 102, 126, 128, 137, 139, 141, 143, 153, 154, 158, 161, 168, 169, 171, 172, 173, 175, 176, 177, 180, 181, 189, 190, 191, 195, 210, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 246, 259, 260, 266], "rang": [10, 61, 62, 64, 66, 77, 89, 90, 126, 128, 154, 169, 175, 196, 210, 216, 258, 266], "strip": [10, 61, 62, 64, 66, 126, 128], "unbound": [10, 61, 62, 64, 66, 126, 128], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 100, 102, 126, 128, 137, 139, 141, 154, 158, 161, 168, 169, 172, 173, 175, 176, 177, 178, 179, 181, 189, 190, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 258, 260, 262], "c99": [10, 11, 61, 62, 64, 66, 93, 126, 128, 144, 153, 169, 213, 263], "provision": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "statu": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 93, 103, 104, 126, 128, 153, 157, 163, 164, 165, 167, 169, 171, 179, 195, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 89, 90, 92, 93, 101, 102, 103, 104, 105, 126, 127, 128, 129, 135, 139, 144, 153, 154, 157, 163, 164, 165, 167, 169, 171, 173, 175, 176, 179, 184, 185, 186, 187, 188, 190, 196, 205, 208, 211, 214, 217, 218, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 246, 247, 248, 251, 258, 260, 262, 263, 266, 268], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 93, 104, 126, 127, 128, 129, 153, 157, 163, 164, 165, 169, 173, 190, 195, 196, 210, 214, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 247, 248, 251, 260, 266], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 97, 99, 100, 126, 128, 149, 150, 164, 167, 169, 179, 213, 253], "nonzero": [10, 11, 12, 62, 66, 87, 93, 97, 99, 104, 144, 167, 179, 195, 196, 210, 251], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 166, 167, 178, 179, 213], "aco": [11, 61, 195, 210, 212], "simpli": [11, 99, 128, 211, 222, 266, 268], "upper": [11, 77, 100, 183, 210, 238, 252], "half": [11, 15, 66, 125, 143, 169, 180, 196, 227], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 126, 128], "3\u03c0j": [11, 126, 128], "sum": [12, 21, 90, 110, 130, 154, 195, 210, 246, 258, 260, 262], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "union": [12, 13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 65, 67, 69, 70, 71, 72, 75, 77, 78, 85, 88, 93, 94, 96, 101, 102, 104, 106, 107, 108, 109, 110, 111, 118, 119, 123, 124, 125, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 153, 154, 157, 158, 160, 161, 171, 172, 173, 174, 175, 180, 190, 192, 193, 227, 231, 246, 248, 251, 260, 267], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 89, 90, 92, 96, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 161, 172, 174, 178, 179, 180, 185, 186, 187, 191, 192, 196, 213, 239, 242, 250, 252, 253, 255, 256, 262, 266, 267, 268, 269], "At": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 160, 174, 192], "least": [12, 40, 65, 67, 69, 70, 71, 72, 85, 88, 93, 96, 104, 108, 109, 110, 118, 119, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 147, 148, 153, 157, 160, 174, 185, 186, 187, 188, 192, 196, 211, 212, 251], "remain": [12, 93, 96, 104, 119, 121, 122, 144, 148, 157, 159, 164, 196, 214, 237], "neither": [12, 40, 93, 104, 135, 144, 180, 255, 267], "nor": [12, 93, 104, 144, 255, 267], "mathemat": [12, 19, 65, 84, 86, 87, 93, 99, 104, 126, 128, 144, 166, 167, 178, 179, 195, 213, 246, 260], "round": [12, 15, 76, 93, 103, 104, 144, 169, 184, 195, 210, 212], "nearest": [12, 93, 144, 162, 184, 212], "mode": [12, 93, 144, 212, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 252], "too": [12, 26, 93, 104, 144, 262, 266], "larg": [12, 93, 104, 144, 216, 222, 253, 266], "appropri": [12, 26, 93, 104, 144, 213, 218], "commut": 12, "associ": [12, 42, 144, 198, 205, 248, 251, 254, 262, 265, 267], "tabl": [12, 93, 144, 195], "c": [12, 93, 96, 125, 144, 147, 148, 158, 172, 173, 179, 190, 196, 210, 213, 216, 219, 238, 242, 243, 244, 252, 254, 255, 263, 265, 266, 268], "d": [12, 93, 96, 125, 144, 148, 205, 225, 236], "dj": [12, 93, 144], "independ": [12, 93, 139, 144, 162, 196, 208, 216, 239, 252, 254, 262, 263, 266], "abov": [12, 89, 90, 93, 96, 126, 128, 144, 148, 153, 154, 169, 175, 182, 183, 196, 205, 213, 214, 216, 217, 220, 241, 242, 258, 262, 265, 268], "similarli": [12, 57, 119, 139, 140, 238, 255], "henc": [12, 77, 79, 98, 147, 158, 185, 186, 187, 188, 196, 211, 213, 215, 216, 220, 221, 222, 266, 268], "z1": 12, "z2": 12, "2024": [12, 26, 28, 31, 32, 33, 37, 39, 43, 65, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 88, 89, 90, 92, 93, 96, 104, 108, 109, 110, 114, 123, 124, 130, 131, 133, 134, 138, 139, 142, 144, 146, 148, 153, 155, 156, 157, 160, 163, 174, 176, 177, 192, 225, 236, 254], "keepdim": [13, 14, 16, 17, 88, 137, 139, 141, 154, 173, 175, 190, 246, 260], "test": [13, 14, 91, 120, 121, 122, 139, 210, 212, 264, 266, 267, 268], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 97, 99, 126, 127, 128, 129, 145, 152, 164, 165, 170, 208, 266], "ax": [13, 14, 16, 17, 19, 55, 56, 88, 89, 90, 102, 137, 139, 141, 143, 151, 154, 161, 171, 173, 175, 176, 180, 181, 190, 191, 196, 210, 226, 227, 230, 231, 234, 237, 239, 246, 251, 254, 257, 260], "logic": [13, 14, 24, 26, 93, 96, 131, 132, 133, 134, 144, 148, 217, 220, 226, 230, 234, 237], "AND": [13, 67, 96, 131, 265], "entir": [13, 14, 86, 87, 88, 97, 99, 137, 139, 141, 154, 166, 167, 173, 175, 190], "valid": [13, 14, 26, 27, 92, 98, 117, 143, 163, 172, 180, 189, 196, 212, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 242, 252, 255, 267], "count": [13, 14, 78, 88, 89, 90, 92, 102, 176, 177, 185, 186, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 243], "last": [13, 14, 18, 19, 55, 78, 89, 90, 92, 102, 161, 168, 172, 176, 177, 180, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 246, 252, 255, 258], "invalid": [13, 14, 23, 92, 98, 218, 266], "wa": [13, 14, 19, 26, 88, 104, 137, 139, 141, 154, 173, 175, 190, 205, 217, 222, 266, 268], "OR": [14, 24, 70, 133, 148, 265], "start": [15, 125, 196, 210, 222, 266, 268], "stop": [15, 125, 196, 210, 267], "step": [15, 125, 196, 267], "evenli": [15, 125], "space": [15, 125, 225, 227, 236], "open": [15, 125, 143, 180, 196], "inclus": [15, 196, 266], "end": [15, 65, 86, 125, 164, 166, 178, 179, 203, 214, 253, 266, 267, 268], "exclus": [15, 196], "distanc": [15, 110], "adjac": 15, "output": [15, 60, 63, 75, 78, 89, 90, 94, 95, 98, 100, 102, 105, 106, 107, 114, 125, 140, 149, 150, 159, 161, 163, 171, 172, 176, 181, 193, 194, 208, 210, 213, 214, 217, 219, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 235, 236, 237, 254, 258, 266], "infer": [15, 60, 63, 95, 106, 107, 150, 159, 194, 196, 215, 262, 267], "cannot": [15, 26, 57, 105, 178, 179, 210, 213, 215, 266], "error": [15, 19, 23, 24, 25, 26, 29, 34, 35, 51, 55, 93, 105, 137, 141, 178, 179, 205, 212, 253, 266], "ceil": [15, 195], "indic": [16, 17, 18, 26, 60, 89, 90, 91, 105, 114, 119, 125, 143, 147, 161, 163, 164, 176, 177, 180, 182, 183, 185, 187, 196, 205, 210, 260, 266], "occur": [16, 17, 75, 110, 178, 179, 185, 186, 187, 188, 213, 267], "occurr": [16, 17, 185], "comparison": [16, 17, 18, 28, 31, 33, 37, 39, 43, 96, 108, 109, 123, 124, 137, 138, 141, 142, 148, 168, 195, 210, 213, 263, 267], "search": [16, 17, 163, 195], "flatten": [16, 17, 78, 158, 161, 185, 186, 187, 188, 260, 262], "descend": [18, 168, 255, 256], "stabl": [18, 168, 216], "sort": [18, 163, 195, 210, 242, 243, 255, 256], "ascend": [18, 163, 168, 210], "stabil": [18, 168], "maintain": [18, 168, 211, 266, 268], "rel": [18, 19, 55, 102, 138, 142, 161, 168, 210, 241, 248, 251, 258], "compar": [18, 168, 185, 186, 187, 188, 212, 217, 267, 269], "properti": [19, 53, 54, 55, 56, 57, 58, 118, 210, 213, 217, 222, 266], "transpos": [19, 40, 55, 135, 136, 180, 238, 242, 251, 255, 262], "instanc": [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 59, 91, 205, 208, 210, 217], "permut": [19, 55, 151], "revers": [19, 55, 65, 102], "origin": [19, 55, 65, 110, 143, 159, 161, 210, 214, 224, 226, 229, 230, 233, 234, 235, 237, 266, 267], "limit": [19, 101, 111, 119, 212, 262, 265], "matric": [19, 40, 55, 135, 136, 140, 182, 183, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 262], "deviat": [19, 139, 173, 212, 218, 266, 268], "et": [19, 196, 255, 256], "al": 19, "intent": [19, 65], "found": [19, 213, 216, 268, 269], "problemat": [19, 63, 211, 214], "conflict": [19, 26, 210], "definit": [19, 86, 87, 166, 167, 178, 179, 210, 238, 267], "batch": [19, 260, 262], "cetera": [19, 196, 255, 256], "permute_dim": [19, 195], "interfac": [19, 216, 262, 266, 268], "ab": [20, 110, 153, 195, 210, 246, 260], "augend": 21, "addend": 21, "self_i": [22, 28, 30, 31, 33, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52], "other_i": [22, 28, 30, 31, 33, 37, 38, 39, 41, 43, 45, 47, 48, 50, 51, 52], "bitwise_and": [22, 195, 210], "api_vers": [23, 266], "object": [23, 24, 25, 26, 29, 32, 34, 35, 53, 57, 59, 60, 91, 101, 105, 111, 113, 115, 116, 117, 195, 196, 205, 208, 210, 214, 216, 217, 220, 222, 261, 263, 267, 268], "2020": [23, 222, 263, 265, 266], "10": [23, 27, 127, 196, 266], "latest": [23, 216], "modul": [23, 208, 263, 267, 268, 269], "everi": [23, 106, 107, 252, 266], "top": [23, 208, 266, 268], "level": [23, 205, 211, 216, 217, 261, 262, 266, 267], "public": [23, 261, 267, 268], "well": [23, 211, 213, 216, 217, 252, 268, 269], "part": [23, 35, 182, 183, 205, 210, 216, 221, 263, 266, 268], "convert": [24, 25, 29, 34, 35, 60, 105, 205, 210, 211, 213, 216, 266, 268], "handl": [24, 26, 61, 64, 86, 89, 90, 105, 127, 129, 139, 153, 154, 156, 164, 166, 170, 175, 178, 210, 211, 213, 214, 217, 218, 258, 266], "lazi": [24, 25, 29, 34, 35, 208, 210, 219, 268], "languag": [24, 25, 29, 34, 35, 196, 218, 220, 262, 266, 268], "therefor": [24, 25, 29, 32, 34, 35, 208, 216, 217, 218, 220, 222, 263, 266, 268], "abl": [24, 25, 29, 34, 35, 105, 214, 216, 217, 266, 268], "kind": [24, 25, 26, 28, 29, 31, 33, 34, 35, 37, 39, 43, 47, 51, 77, 93, 96, 101, 105, 107, 108, 109, 111, 116, 118, 119, 123, 124, 148, 153, 160, 205, 210, 220, 262, 265], "here": [24, 25, 26, 29, 34, 35, 196, 205, 216, 221, 222, 268], "valueerror": [24, 25, 29, 34, 35, 60, 105, 159, 171, 268], "instead": [24, 25, 29, 34, 35, 63, 213, 216, 220, 267, 268], "2023": [24, 25, 26, 29, 34, 35, 59, 63, 77, 85, 90, 105, 110, 137, 138, 141, 142, 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method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "count_nonzero() (in module array_api)": [[88, "array_api.count_nonzero"]], "cumulative_prod() (in module array_api)": [[89, "array_api.cumulative_prod"]], "cumulative_sum() (in module array_api)": [[90, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[91, "array_api.data_types.__eq__"]], "diff() (in module array_api)": [[92, "array_api.diff"]], "divide() (in module array_api)": [[93, "array_api.divide"]], "empty() (in module array_api)": [[94, "array_api.empty"]], "empty_like() (in module array_api)": [[95, "array_api.empty_like"]], "equal() (in module array_api)": [[96, "array_api.equal"]], "exp() (in module array_api)": [[97, "array_api.exp"]], "expand_dims() (in module array_api)": [[98, "array_api.expand_dims"]], "expm1() (in module array_api)": [[99, "array_api.expm1"]], "eye() (in module array_api)": [[100, "array_api.eye"]], "finfo() (in module array_api)": [[101, "array_api.finfo"]], "flip() (in module array_api)": [[102, "array_api.flip"]], "floor() (in module array_api)": [[103, "array_api.floor"]], "floor_divide() (in module array_api)": [[104, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[105, "array_api.from_dlpack"]], "full() (in module array_api)": [[106, "array_api.full"]], "full_like() (in module array_api)": [[107, "array_api.full_like"]], "greater() (in module array_api)": [[108, "array_api.greater"]], "greater_equal() (in module array_api)": [[109, "array_api.greater_equal"]], "hypot() (in module array_api)": [[110, "array_api.hypot"]], "iinfo() (in module array_api)": [[111, "array_api.iinfo"]], "imag() (in module array_api)": [[112, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[113, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[114, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[115, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[116, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[117, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[118, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[119, "array_api.isdtype"]], "isfinite() (in module array_api)": [[120, "array_api.isfinite"]], "isinf() (in module array_api)": [[121, "array_api.isinf"]], "isnan() (in module array_api)": [[122, "array_api.isnan"]], "less() (in module array_api)": [[123, "array_api.less"]], "less_equal() (in module array_api)": [[124, "array_api.less_equal"]], "linspace() (in module array_api)": [[125, "array_api.linspace"]], "log() (in module array_api)": [[126, "array_api.log"]], "log10() (in module array_api)": [[127, "array_api.log10"]], "log1p() (in module array_api)": [[128, "array_api.log1p"]], "log2() (in module array_api)": [[129, "array_api.log2"]], "logaddexp() (in module array_api)": [[130, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[131, "array_api.logical_and"]], "logical_not() (in module array_api)": [[132, "array_api.logical_not"]], "logical_or() (in module array_api)": [[133, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[134, "array_api.logical_xor"]], "matmul() (in module array_api)": [[135, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[136, "array_api.matrix_transpose"]], "max() (in module array_api)": [[137, "array_api.max"]], "maximum() (in module array_api)": [[138, "array_api.maximum"]], "mean() (in module array_api)": [[139, "array_api.mean"]], "meshgrid() (in module array_api)": [[140, "array_api.meshgrid"]], "min() (in module array_api)": [[141, "array_api.min"]], "minimum() (in module array_api)": [[142, "array_api.minimum"]], "moveaxis() (in module array_api)": [[143, "array_api.moveaxis"]], "multiply() (in module array_api)": [[144, "array_api.multiply"]], "negative() (in module array_api)": [[145, "array_api.negative"]], "nextafter() (in module array_api)": [[146, "array_api.nextafter"]], "nonzero() (in module array_api)": [[147, "array_api.nonzero"]], "not_equal() (in module array_api)": [[148, "array_api.not_equal"]], "ones() (in module array_api)": [[149, "array_api.ones"]], "ones_like() (in module array_api)": [[150, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[151, "array_api.permute_dims"]], "positive() (in module array_api)": [[152, "array_api.positive"]], "pow() (in module array_api)": [[153, "array_api.pow"]], "prod() (in module array_api)": [[154, "array_api.prod"]], "real() (in module array_api)": [[155, "array_api.real"]], "reciprocal() (in module array_api)": [[156, "array_api.reciprocal"]], "remainder() (in module array_api)": [[157, "array_api.remainder"]], "repeat() (in module array_api)": [[158, "array_api.repeat"]], "reshape() (in module array_api)": [[159, "array_api.reshape"]], "result_type() (in module array_api)": [[160, "array_api.result_type"]], "roll() (in module array_api)": [[161, "array_api.roll"]], "round() (in module array_api)": [[162, "array_api.round"]], "searchsorted() (in module array_api)": [[163, "array_api.searchsorted"]], "sign() (in module array_api)": [[164, "array_api.sign"]], "signbit() (in module array_api)": [[165, "array_api.signbit"]], "sin() (in module array_api)": [[166, "array_api.sin"]], "sinh() (in module array_api)": [[167, "array_api.sinh"]], "sort() (in module array_api)": [[168, "array_api.sort"]], "sqrt() (in module array_api)": [[169, "array_api.sqrt"]], "square() (in module array_api)": [[170, "array_api.square"]], "squeeze() (in module array_api)": [[171, "array_api.squeeze"]], "stack() (in module array_api)": [[172, "array_api.stack"]], "std() (in module array_api)": [[173, "array_api.std"]], "subtract() (in module array_api)": [[174, "array_api.subtract"]], "sum() (in module array_api)": [[175, "array_api.sum"]], "take() (in module array_api)": [[176, "array_api.take"]], "take_along_axis() (in module array_api)": [[177, "array_api.take_along_axis"]], "tan() (in module array_api)": [[178, "array_api.tan"]], "tanh() (in module array_api)": [[179, "array_api.tanh"]], "tensordot() (in module array_api)": [[180, "array_api.tensordot"]], "tile() (in module array_api)": [[181, "array_api.tile"]], "tril() (in module array_api)": [[182, "array_api.tril"]], "triu() (in module array_api)": [[183, "array_api.triu"]], "trunc() (in module array_api)": [[184, "array_api.trunc"]], "unique_all() (in module array_api)": [[185, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[186, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[187, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[188, "array_api.unique_values"]], "unstack() (in module array_api)": [[189, "array_api.unstack"]], "var() (in module array_api)": [[190, "array_api.var"]], "vecdot() (in module array_api)": [[191, "array_api.vecdot"]], "where() (in module array_api)": [[192, "array_api.where"]], "zeros() (in module array_api)": [[193, "array_api.zeros"]], "zeros_like() (in module array_api)": [[194, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[224, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[225, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[226, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[227, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[228, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[229, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[230, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[231, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[232, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[233, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[234, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[235, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[236, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[237, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[238, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[239, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[240, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[241, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[242, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[243, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[244, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[245, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[246, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[247, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[248, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[249, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[250, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[251, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[252, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[253, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[254, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[255, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[256, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[257, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[258, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[259, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[260, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file
diff --git a/latest/changelog.html b/latest/changelog.html
index afbf59d4a..ae7120be4 100644
--- a/latest/changelog.html
+++ b/latest/changelog.html
@@ -701,18 +701,18 @@ <h5 id="id4">APIs<a class="headerlink" href="#id4" title="Link to this heading">
 <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this heading">¶</a></h4>
 <p>The following is a list of fixes and points of clarification with regard to the previous version of the specification:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__add__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__bool__</span></code>: fix typo in special case notes (<a class="reference external" href="https://github.com/data-apis/array-api/pull/785">gh-785</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__dlpack__</span></code>: resolve conflicting exception guidance (<a class="reference external" href="https://github.com/data-apis/array-api/pull/887">gh-887</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__eq__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__getitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__mul__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__ne__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__pow__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: clarify required indexing semantics (<a class="reference external" href="https://github.com/data-apis/array-api/pull/821">gh-821</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-https://github.com/data-apis/array-api/pull/905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__setitem__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">value</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__sub__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">__truediv__</span></code>: fix typing for <code class="docutils literal notranslate"><span class="pre">other</span></code> argument (<a class="reference external" href="https://github.com/data-apis/array-api/pull/905">gh-905</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify broadcast behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/888">gh-888</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code>: clarify required exception behavior (<a class="reference external" href="https://github.com/data-apis/array-api/pull/897">gh-897</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">clip</span></code>: clarify that the operation is only defined when elements in <code class="docutils literal notranslate"><span class="pre">min</span></code> and <code class="docutils literal notranslate"><span class="pre">max</span></code> are inside the bounds of the input array data type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/814">gh-814</a>)</p></li>
@@ -726,7 +726,7 @@ <h4 id="errata">Errata<a class="headerlink" href="#errata" title="Link to this h
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.irfftn</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">fft.hfft</span></code>: fix typo in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/806">gh-806</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">linalg.solve</span></code>: clarify broadcasting semantics and output shape (<a class="reference external" href="https://github.com/data-apis/array-api/pull/810">gh-810</a>)</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-https://github.com/data-apis/array-api/pull/904</a>)</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">nonzero</span></code>: fix return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/803">gh-803</a> and <a class="reference external" href="https://github.com/data-apis/array-api/pull/904">gh-904</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">searchsorted</span></code>: fix incorrect boundary conditions (<a class="reference external" href="https://github.com/data-apis/array-api/pull/898">gh-898</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">sign</span></code>: fix equation in function description (<a class="reference external" href="https://github.com/data-apis/array-api/pull/844">gh-844</a>)</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">tile</span></code>: fix missing return type (<a class="reference external" href="https://github.com/data-apis/array-api/pull/798">gh-798</a>)</p></li>
diff --git a/latest/searchindex.js b/latest/searchindex.js
index 60ad5943a..c359eb2ce 100644
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+++ b/latest/searchindex.js
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"The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 102, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 205, 208, 210, 211, 212, 214, 215, 216, 217, 220, 221, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 263, 265, 266, 267, 268, 269], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 79, 89, 90, 92, 93, 104, 118, 119, 120, 121, 122, 135, 140, 144, 145, 152, 153, 154, 155, 162, 164, 170, 174, 175, 180, 205, 212, 224, 226, 229, 230, 233, 234, 235, 237, 239, 250, 251, 253, 258, 262, 266, 268], "__invert__": [0, 195], "inv": [0, 210, 262], "invert": [0, 68, 244, 247, 254], "__inv__": 0, "__and__": [0, 195], "__or__": [0, 195], "__xor__": [0, 195], "xor": [0, 72, 134], "__lshift__": [0, 195], "lshift": 0, "__rshift__": [0, 195], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 49, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 89, 90, 92, 93, 103, 104, 106, 107, 111, 114, 118, 119, 125, 137, 139, 141, 145, 153, 154, 157, 158, 160, 162, 163, 173, 175, 176, 184, 190, 191, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247, 248, 258, 260, 266], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 90, 91, 105, 106, 107, 114, 118, 119, 125, 131, 132, 133, 134, 147, 192, 195, 205, 210], "__lt__": [0, 195, 210], "lt": 0, "__le__": [0, 195, 210], "le": 0, "__gt__": [0, 195, 210], "gt": [0, 252, 255], "__ge__": [0, 195, 210], "ge": 0, "__eq__": [0, 195, 210, 217], "eq": 0, "__ne__": [0, 195, 210], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 43, 49, 55, 58, 60, 77, 85, 86, 88, 91, 92, 93, 96, 97, 100, 101, 102, 104, 105, 108, 109, 110, 117, 118, 123, 124, 125, 131, 132, 133, 134, 135, 139, 144, 147, 148, 153, 158, 160, 161, 162, 166, 178, 179, 181, 185, 187, 191, 196, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 229, 230, 231, 233, 234, 235, 236, 237, 239, 242, 243, 248, 251, 252, 255, 261, 262, 263, 266, 267, 268, 269], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 77, 102, 105, 110, 116, 118, 119, 125, 131, 132, 133, 134, 135, 139, 173, 190, 191, 195, 196, 205, 208, 210, 211, 213, 214, 216, 217, 218, 220, 222, 227, 239, 244, 251, 252, 254, 262, 263, 266, 267, 268, 269], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 91, 93, 99, 104, 105, 128, 143, 144, 160, 173, 190, 196, 198, 208, 210, 212, 213, 214, 215, 216, 217, 218, 222, 239, 251, 261, 262, 265, 266, 268], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 91, 92, 96, 110, 120, 121, 148, 169, 195, 196, 205, 210, 213, 214, 216, 222, 255, 263, 265, 266, 269], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 77, 79, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 153, 154, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 175, 178, 179, 184, 185, 186, 187, 188, 196, 203, 208, 212, 213, 214, 215, 217, 220, 225, 234, 236, 253, 255, 256, 258, 266, 268, 269], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 92, 108, 109, 123, 124, 125, 137, 138, 141, 142, 157, 168, 191, 196, 210, 213, 214, 218, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 266], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 125, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 159, 168, 173, 174, 175, 177, 190, 191, 192, 196, 205, 210, 213, 214, 218, 239, 246, 248, 251, 254, 260, 266, 268], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 75, 91, 92, 93, 96, 104, 105, 108, 109, 110, 113, 118, 119, 123, 124, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 148, 158, 159, 160, 163, 168, 173, 179, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 242, 252, 253, 255, 261, 262, 266, 267, 268], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 89, 90, 93, 96, 97, 99, 100, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 160, 162, 164, 166, 167, 168, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 205, 216, 217, 219, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 89, 90, 104, 108, 109, 110, 119, 123, 124, 125, 137, 138, 141, 142, 158, 163, 168, 176, 178, 179, 196, 208, 211, 212, 213, 214, 215, 217, 262, 263, 266, 268], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 108, 109, 123, 124, 137, 138, 141, 142, 168], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 60, 62, 66, 77, 78, 79, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 167, 168, 169, 172, 176, 177, 179, 196, 203, 205, 210, 226, 227, 230, 231, 234, 237, 242, 243, 266], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 57, 60, 71, 77, 79, 89, 90, 92, 96, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 168, 176, 178, 179, 196, 203, 212, 213, 226, 227, 230, 231, 234, 237, 242, 243, 255, 262], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 93, 96, 97, 99, 108, 109, 114, 123, 124, 125, 126, 127, 128, 129, 144, 145, 148, 153, 160, 163, 166, 167, 168, 178, 179, 192, 203, 205, 212, 213, 216, 219, 220, 222, 242, 243, 252, 253, 254, 255, 262, 266, 268, 269], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 85, 88, 93, 96, 99, 104, 105, 107, 108, 109, 110, 113, 114, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 147, 148, 153, 154, 156, 157, 158, 159, 160, 163, 164, 168, 169, 170, 173, 174, 175, 177, 185, 186, 187, 188, 190, 191, 192, 195, 196, 205, 207, 208, 211, 213, 215, 216, 217, 222, 239, 246, 248, 251, 254, 260, 261, 266, 267, 268, 269], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 91, 92, 102, 104, 105, 108, 109, 123, 124, 137, 138, 141, 142, 147, 158, 163, 168, 178, 179, 180, 185, 186, 187, 188, 196, 203, 205, 210, 212, 214, 215, 216, 218, 233, 234, 242, 243, 246, 255, 256, 260, 262, 263, 266, 267], "discuss": [0, 96, 148, 210, 216, 217, 221, 266, 267, 268], "copi": [0, 1, 26, 59, 60, 63, 105, 159, 168, 210, 211, 216, 217, 219, 265, 266], "view": [0, 105, 219], "behavior": [0, 5, 26, 32, 47, 49, 59, 60, 63, 74, 77, 89, 90, 92, 93, 104, 106, 107, 110, 125, 144, 153, 157, 159, 160, 163, 176, 177, 185, 186, 187, 188, 195, 196, 198, 205, 208, 210, 212, 213, 219, 220, 221, 226, 227, 230, 231, 234, 237, 262, 263, 266, 267, 268, 269], "mutabl": [0, 219], "refer": [0, 1, 13, 14, 92, 99, 100, 128, 163, 173, 176, 177, 180, 181, 190, 191, 196, 213, 214, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 254], "what": [0, 163, 208, 216, 218, 222, 262, 266, 267, 268, 269], "call": [0, 7, 34, 92, 216, 217, 220, 253, 266, 267, 268], "http": [0, 210, 216, 263, 269], "doc": 0, "org": 0, "html": 0, "do": [0, 1, 26, 75, 93, 144, 157, 203, 208, 210, 211, 213, 214, 216, 217, 218, 262, 263, 265, 266, 268, 269], "mutat": [0, 176, 210], "choos": [0, 51, 57, 59, 92, 93, 104, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 158, 160, 173, 185, 186, 187, 188, 190, 195, 196, 203, 213, 214, 215, 217, 220, 266, 268], "when": [0, 5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 75, 77, 89, 90, 93, 99, 104, 105, 110, 116, 118, 125, 128, 137, 138, 139, 141, 142, 144, 153, 154, 158, 159, 163, 173, 175, 176, 179, 190, 192, 195, 196, 205, 210, 211, 213, 214, 215, 216, 218, 220, 221, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 244, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268], "doe": [0, 1, 15, 26, 105, 148, 176, 177, 196, 205, 208, 211, 212, 213, 214, 215, 217, 218, 220, 222, 262, 266, 268, 269], "correspond": [0, 1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 96, 105, 108, 109, 114, 115, 116, 123, 124, 148, 153, 159, 161, 163, 173, 177, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 226, 230, 234, 237, 239, 242, 246, 265, 266], "fall": 0, "back": [0, 268], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 77, 104, 110, 131, 132, 133, 134, 157, 162, 176, 196, 205, 210, 213, 214, 248, 251, 254, 260, 266], "binari": [0, 5, 67, 70, 72, 178, 179, 211], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 90, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 159, 160, 162, 163, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 192, 208, 224, 225, 226, 228, 229, 230, 233, 234, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263, 266, 268, 269], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 89, 90, 92, 94, 95, 98, 102, 106, 107, 114, 135, 136, 140, 149, 150, 159, 161, 163, 168, 172, 176, 177, 180, 181, 182, 183, 189, 191, 193, 194, 195, 210, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 266, 268], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 93, 96, 97, 99, 103, 104, 108, 109, 110, 112, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 173, 174, 175, 178, 179, 180, 184, 185, 190, 196, 203, 205, 210, 212, 213, 214, 220, 238, 239, 241, 246, 247, 253, 254, 260, 266, 267, 268, 269], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 92, 93, 96, 97, 99, 104, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 139, 142, 144, 145, 148, 153, 156, 157, 160, 166, 167, 169, 170, 172, 173, 174, 178, 179, 180, 190, 191, 192, 195, 210, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 142, 144, 145, 148, 153, 156, 157, 160, 164, 166, 167, 169, 170, 172, 174, 178, 179, 180, 191, 192, 195, 196, 210, 213, 216, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262, 266, 268], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 173, 174, 175, 177, 180, 190, 191, 192, 195, 196, 210, 239, 246, 248, 251, 254, 260, 266], "let": [0, 1, 9, 10, 11, 12, 62, 66, 85, 87, 89, 90, 92, 96, 97, 99, 105, 120, 121, 122, 125, 126, 128, 139, 148, 154, 158, 163, 164, 167, 169, 173, 175, 179, 181, 190, 191, 196, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 243, 244, 252, 254, 255, 258], "If": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 114, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 211, 213, 217, 223, 224, 225, 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169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 193, 195, 203, 210, 212, 213, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "creat": [3, 15, 60, 94, 95, 100, 105, 106, 107, 125, 149, 150, 193, 194, 202, 208, 217, 225, 236, 262, 266], "its": [5, 26, 40, 73, 93, 101, 135, 144, 159, 161, 212, 213, 216, 217, 261, 266, 267, 268], "main": [5, 100, 182, 183, 211, 216, 241, 258, 261, 268], "namespac": [5, 7, 23, 113, 198, 208, 210, 223, 261, 262, 263, 266, 269], "under": [5, 261, 265, 266], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 89, 90, 92, 94, 98, 101, 102, 106, 116, 118, 119, 125, 149, 154, 157, 158, 161, 171, 172, 175, 176, 177, 181, 182, 183, 185, 186, 187, 188, 191, 193, 196, 205, 210, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 232, 233, 234, 235, 237, 241, 258, 260, 262, 263, 266, 268, 269], "name": [5, 7, 23, 26, 104, 118, 185, 186, 187, 196, 213, 214, 242, 251, 252, 253, 255, 261, 266, 267], "descript": [5, 7, 210, 212, 246, 260], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 67, 70, 72, 75, 88, 89, 90, 91, 96, 105, 106, 107, 108, 109, 118, 119, 120, 121, 122, 123, 124, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 160, 165, 168, 173, 175, 190, 192, 205, 210, 220, 238, 246, 255, 260], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 101, 104, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 147, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 192, 196, 210, 214, 238, 246, 255, 260, 262], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 196, 238, 246, 255, 260], "int8": [5, 118, 119, 196, 205], "bit": [5, 68, 69, 71, 85, 89, 90, 101, 111, 154, 165, 175, 205, 210, 212, 258], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 89, 90, 93, 97, 99, 104, 118, 119, 126, 128, 137, 138, 141, 142, 144, 145, 153, 154, 157, 163, 165, 167, 169, 175, 179, 185, 186, 187, 188, 195, 203, 210, 213, 252, 253, 258], "exist": [5, 7, 26, 60, 78, 105, 208, 210, 213, 216, 217, 218, 244, 263, 266, 267], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 98, 125, 126, 128, 143, 172, 180, 182, 183, 189, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 263], "128": 5, "127": 5, "int16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "16": [5, 205], "32": [5, 205], "767": 5, "int32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "147": 5, "483": 5, "647": 5, "int64": [5, 89, 90, 118, 119, 154, 175, 205, 258], "64": [5, 205], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 118, 119, 196, 205], "unsign": [5, 89, 90, 118, 119, 154, 175, 195, 258], "255": 5, "uint16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "65": 5, "535": [5, 210], "uint32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "294": 5, "967": 5, "295": 5, "uint64": [5, 118, 119, 205], "18": 5, "446": [5, 210], "744": [5, 210], "073": 5, "709": [5, 210], "551": [5, 210], "615": 5, "float32": [5, 112, 118, 119, 155, 205, 253, 255, 256], "ieee": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "754": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "singl": [5, 7, 24, 25, 29, 34, 35, 116, 118, 185, 186, 195, 205, 210, 211, 213, 216, 217, 222, 262, 266, 267, 268], "2019": [5, 12, 93, 99, 110, 128, 144, 195, 212, 266, 268], "float64": [5, 9, 20, 118, 119, 205, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "doubl": [5, 180, 205, 210], "complex64": [5, 112, 118, 119, 155, 205, 210, 253, 255, 256], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 162, 167, 169, 179, 210, 213], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 155, 162, 167, 169, 178, 179, 185, 186, 187, 188, 210, 213, 227, 236], "complex128": [5, 9, 20, 118, 119, 205, 210, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "method": [5, 26, 34, 105, 195, 198, 208, 214, 216, 217, 220, 221, 222, 266, 267, 268], "attribut": [5, 23, 101, 111, 160, 195, 207, 210, 263, 266, 267, 268], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 75, 89, 90, 105, 110, 119, 154, 160, 169, 172, 175, 176, 177, 179, 185, 186, 188, 189, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 236, 239, 258, 261, 262, 266, 267, 268], "beyond": [5, 161, 205, 210, 266], "It": [5, 23, 26, 105, 208, 214, 216, 266, 268, 269], "also": [5, 7, 26, 32, 34, 105, 110, 164, 208, 213, 214, 215, 216, 222, 226, 230, 234, 237, 255, 261, 268], "subnorm": [5, 110, 212], "k": [5, 40, 100, 110, 135, 147, 182, 183, 196, 212, 238, 242, 243, 244, 252, 254, 255, 256, 258, 266], "denorm": [5, 110, 212], "gradual": [5, 110, 212, 266], "underflow": [5, 9, 93, 104, 110, 212, 253], "hardwar": [5, 53, 110, 158, 212, 216, 217, 242, 255, 262, 266], "univers": [5, 110, 211, 212, 217, 262, 266], "mani": [5, 110, 181, 212, 266, 268], "platform": [5, 26, 110, 212], "compil": [5, 110, 179, 208, 211, 212, 215, 266], "toggl": [5, 110, 212], "daz": [5, 110, 212], "flush": [5, 110, 212], "ftz": [5, 110, 212], "increas": [5, 110, 212, 267], "guard": [5, 110, 212], "against": [5, 40, 73, 110, 135, 179, 196, 212, 248, 251, 269], "time": [5, 7, 16, 17, 26, 92, 110, 158, 185, 186, 208, 210, 212, 215, 216, 221, 238, 242, 243, 244, 252, 254, 255, 262, 266, 268], "attack": [5, 110, 212], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 75, 88, 93, 99, 104, 110, 125, 126, 128, 137, 139, 140, 141, 144, 147, 154, 158, 160, 163, 169, 173, 175, 185, 186, 187, 188, 190, 196, 205, 212, 213, 214, 215, 217, 246, 252, 260, 262], "vari": [5, 110, 163, 179, 185, 186, 187, 188, 205, 212], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 75, 77, 78, 86, 87, 89, 90, 92, 97, 99, 102, 105, 110, 117, 118, 119, 125, 126, 128, 131, 132, 133, 134, 135, 139, 147, 153, 154, 157, 158, 159, 160, 164, 166, 167, 168, 169, 172, 173, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 195, 198, 208, 210, 211, 213, 214, 215, 216, 217, 220, 221, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 244, 248, 251, 252, 253, 254, 255, 256, 258, 261, 262, 263, 266, 267, 268], "access": [5, 26, 32, 105, 113, 196, 210, 216, 261, 263, 266], "variou": [5, 210], "introspect": 5, "isdtyp": [5, 195, 210], "integr": [5, 63, 77, 116, 118, 119], "keyword": [5, 7, 26, 60, 63, 89, 90, 117, 140, 154, 159, 175, 195, 210, 217, 221, 222, 225, 236, 258, 262, 263, 266, 267, 268], "affect": [5, 15, 49, 214, 217], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 89, 90, 92, 93, 97, 99, 126, 127, 128, 129, 130, 137, 139, 141, 144, 153, 154, 166, 167, 169, 173, 174, 175, 178, 179, 190, 210, 253], "implementor": [5, 261], "free": [5, 214, 217, 265], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 113, 222], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 89, 90, 93, 97, 98, 99, 104, 107, 135, 139, 140, 143, 144, 145, 147, 153, 154, 166, 167, 171, 173, 175, 176, 178, 179, 180, 181, 185, 186, 187, 188, 190, 196, 205, 208, 213, 216, 217, 220, 221, 239, 246, 254, 255, 258, 260, 262, 263, 266, 268, 269], "wai": [5, 26, 63, 105, 208, 211, 217, 218, 263, 266, 267, 268, 269], "f4": [5, 205], "recommend": [5, 7, 19, 23, 26, 125, 131, 132, 133, 134, 139, 157, 173, 190, 203, 210, 212, 214, 216, 217, 266], "guidanc": [5, 7, 26, 49, 210, 211, 218, 266], "govern": [5, 50, 174, 205, 262, 263], "interact": [5, 213], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 89, 90, 93, 96, 97, 99, 101, 104, 105, 110, 113, 119, 120, 121, 125, 126, 127, 128, 129, 130, 135, 137, 138, 141, 142, 144, 146, 154, 157, 164, 165, 166, 169, 175, 178, 179, 180, 192, 196, 212, 213, 214, 218, 222, 253, 258, 266, 267, 269], "exampl": [5, 12, 23, 26, 118, 119, 139, 172, 195, 196, 208, 213, 214, 215, 217, 220, 221, 222, 258, 262, 266, 268, 269], "whether": [5, 13, 14, 26, 59, 60, 63, 75, 79, 89, 90, 91, 105, 114, 119, 122, 125, 139, 155, 159, 165, 210, 217, 238, 242, 243, 252, 254, 261, 265, 266, 268], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 88, 105, 114, 116, 118, 137, 139, 141, 154, 158, 159, 163, 164, 173, 175, 190, 191, 192, 195, 196, 208, 217, 238, 240, 246, 253, 254, 260, 265], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 192, 195, 196, 210, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 267, 268, 269], "possibl": [5, 26, 60, 75, 104, 105, 137, 141, 159, 160, 178, 179, 208, 211, 212, 213, 214, 216, 217, 218, 220, 222, 262, 266, 267, 268, 269], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 88, 89, 135, 137, 139, 141, 144, 145, 154, 173, 175, 190, 196, 208, 211, 213, 216, 217, 221, 222, 243, 244, 262, 263, 266, 268], "In": [5, 12, 19, 26, 59, 89, 90, 93, 96, 104, 119, 121, 122, 139, 144, 148, 154, 157, 164, 175, 195, 196, 198, 205, 212, 213, 214, 216, 218, 233, 234, 252, 253, 255, 258, 262, 263, 267, 268, 269], "clearli": [5, 59, 119, 203, 213, 262, 263], "warn": [5, 158, 218], "about": [5, 7, 26, 101, 111, 214, 262, 266, 268, 269], "organ": [5, 210, 262, 267, 268], "within": [5, 15, 27, 196, 205, 208, 210, 213, 217, 224, 226, 229, 230, 233, 234, 235, 237, 266], "accord": [5, 12, 60, 71, 75, 89, 90, 93, 101, 104, 106, 125, 144, 153, 160, 163, 164, 173, 177, 190, 191, 192, 196, 210, 212, 213], "These": [5, 214, 242, 267], "intend": [5, 89, 90, 154, 175, 208, 258], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 93, 98, 100, 101, 104, 121, 126, 128, 143, 144, 147, 157, 161, 165, 167, 169, 179, 195, 196, 208, 210, 212, 222, 236, 238, 252, 267], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 208, 210, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262], "extern": [7, 268], "usabl": 7, "accept": [7, 26, 131, 132, 133, 134, 139, 157, 173, 190, 208, 263], "argument": [7, 10, 11, 12, 26, 40, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 85, 86, 89, 90, 93, 96, 104, 108, 109, 110, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 138, 142, 144, 148, 153, 154, 157, 159, 160, 163, 166, 169, 174, 175, 178, 179, 180, 192, 195, 205, 212, 216, 217, 224, 225, 226, 229, 230, 233, 234, 235, 236, 237, 258, 262, 266, 267, 268], "map": [7, 213, 214], "base": [7, 47, 57, 58, 97, 98, 126, 127, 128, 129, 153, 185, 186, 187, 188, 196, 210, 214, 220, 222, 262, 263, 266, 267, 268], "sole": [7, 196, 203, 262], "incompat": [7, 26, 74, 105, 208, 263, 266], "normal": [7, 78, 172, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237], "practic": [7, 19, 196, 262, 267], "avail": [7, 105, 117, 208, 216, 261, 263, 267], "still": [7, 26, 222, 262, 267, 268, 269], "consid": [7, 26, 63, 105, 131, 132, 133, 134, 185, 186, 187, 188, 213, 217, 236, 251, 262, 266, 268, 269], "compliant": [7, 26, 51, 93, 99, 105, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 173, 190, 212, 215, 217, 263, 266], "altern": [7, 214, 216, 269], "thei": [7, 26, 205, 211, 214, 216, 217, 221, 222, 261, 262, 263, 266, 268, 269], "were": [7, 104, 158, 163, 210, 266], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 195, 210, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 262, 267, 268], "lead": [7, 104, 213, 252, 255, 266], "readabl": [7, 205, 262, 267], "code": [7, 59, 205, 214, 215, 217, 220, 222, 262, 266, 267, 268], "easier": [7, 208, 214, 262], "evolv": [7, 208, 262], "over": [7, 13, 14, 26, 88, 125, 137, 139, 141, 154, 173, 175, 176, 180, 190, 191, 196, 212, 213, 214, 216, 217, 221, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 258, 260, 262, 266], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 77, 79, 85, 86, 87, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 138, 139, 140, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 160, 162, 164, 166, 167, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 196, 209, 210, 211, 217, 225, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "worri": 7, "xi": [7, 140], "annot": [7, 210, 222, 266], "individu": [7, 139, 196, 217, 220, 221, 222, 225, 236, 266, 267], "aim": [7, 211, 222, 261, 262, 263, 266, 267, 268, 269], "strongli": [7, 214, 268], "look": [7, 268], "like": [7, 196, 208, 211, 213, 220, 222, 263, 266, 267, 268], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 114, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 196, 210, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 266, 267, 269], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 210, 211, 214, 216, 220, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 265, 268], "int": [7, 12, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 74, 77, 78, 85, 88, 89, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 123, 124, 125, 130, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 151, 153, 154, 157, 158, 159, 160, 161, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 189, 190, 191, 192, 193, 196, 205, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 241, 246, 247, 257, 258, 259, 260, 267], "str": [7, 8, 23, 118, 119, 140, 267], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 91, 210, 268], "few": [7, 212, 220, 266, 268], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 115, 116, 118, 125, 137, 139, 140, 141, 147, 149, 150, 154, 158, 159, 161, 163, 168, 172, 173, 175, 177, 180, 182, 183, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 210, 212, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 246, 248, 251, 252, 255, 258, 260], "form": [7, 23, 26, 40, 79, 135, 136, 182, 183, 196, 214, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 263, 267], "question": [7, 211, 266], "commonli": [7, 173, 190, 196, 211, 213, 215, 261, 262, 266, 267], "written": [7, 208, 266, 268], "yyyi": [8, 23, 263], "mm": [8, 23, 263], "string": [8, 23, 118, 119, 210, 263, 266], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 195, 208, 211, 217, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 264, 266, 268], "absolut": [9, 20, 85, 164, 212, 214, 246, 247, 253, 262], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 97, 99, 103, 112, 120, 121, 122, 126, 127, 128, 129, 132, 137, 139, 141, 145, 152, 155, 156, 162, 164, 165, 166, 167, 169, 170, 173, 178, 179, 184, 190], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 110, 112, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 203, 208, 210, 213, 215, 217, 218, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 255, 256, 258, 260, 262, 266, 268], "magnitud": [9, 12, 20, 85, 93, 104, 110, 144, 210, 255, 256], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 93, 101, 104, 111, 144, 145, 146, 178, 179, 210, 216, 267], "known": [9, 164, 212, 215, 216], "norm": [9, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 260, 262], "modulu": [9, 157], "z": [9, 10, 11, 61, 62, 64, 66, 126, 213], "bj": [9, 12, 79, 93, 144], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 92, 93, 96, 98, 104, 108, 109, 110, 123, 124, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 144, 145, 147, 148, 152, 154, 158, 173, 175, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 215, 220, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 164, 166, 167, 178, 179, 213, 242, 243, 253, 255], "sqrt": [9, 10, 11, 61, 62, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 260], "take": [9, 126, 128, 153, 169, 195, 210, 217, 222, 266], "care": [9, 262], "undu": [9, 215], "overflow": [9, 12, 89, 90, 93, 104, 110, 125, 154, 175, 205, 253, 258, 262], "dure": [9, 40, 59, 110, 135, 173, 190, 205, 208, 251, 266, 267], "stage": [9, 110, 263], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 193, 196, 210, 212, 213, 214, 216, 220, 221, 225, 226, 227, 230, 231, 234, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 268], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 157, 162, 163, 164, 165, 166, 167, 169, 173, 178, 179, 184, 185, 186, 187, 188, 190, 195, 203, 210, 213, 266], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 126, 127, 128, 129, 130, 137, 141, 144, 148, 153, 157, 162, 165, 166, 167, 169, 178, 179, 184, 213, 253, 260], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 96, 97, 99, 120, 121, 122, 125, 126, 128, 139, 148, 162, 164, 167, 169, 179, 195, 210, 211, 266, 267, 268], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 93, 96, 97, 99, 104, 110, 114, 120, 121, 126, 128, 144, 148, 153, 157, 165, 167, 169, 179, 212], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 93, 96, 97, 99, 100, 101, 106, 107, 111, 112, 119, 120, 121, 122, 125, 126, 127, 128, 129, 135, 140, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 162, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 97, 99, 104, 126, 127, 128, 129, 153, 166, 167, 178, 179, 212, 248, 251], "princip": [10, 11, 61, 62, 64, 66, 126, 169, 213, 262], "invers": [10, 11, 61, 62, 64, 65, 66, 213, 224, 226, 229, 230, 231, 232, 233, 234, 235, 237, 244, 247, 251, 262], "cosin": [10, 11, 86, 87, 179], "express": [10, 61, 63, 64, 65, 86, 166, 178, 196, 205, 214, 262, 265], "radian": [10, 61, 64, 65, 86, 166, 178], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 93, 125, 127, 129, 164, 166, 167, 178, 179, 213, 253], "pi": [10, 11, 61, 62, 64, 66, 87, 126, 128, 167, 178, 179, 195], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 93, 97, 99, 125, 126, 128, 139, 144, 163, 164, 166, 167, 169, 178, 179, 196, 213, 242, 255, 258], "ln": [10, 11, 61, 62, 64, 66, 126], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 97, 99, 126, 127, 128, 129, 167, 169, 179, 195, 210], "multi": [10, 11, 61, 62, 64, 66, 195, 213, 216, 217, 239, 268], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 93, 97, 99, 126, 128, 144, 153, 166, 167, 169, 178, 179, 266], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 97, 99, 126, 128, 153, 166, 167, 169, 178, 179, 266], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 93, 97, 99, 144, 166, 167, 169, 178, 179, 266], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 89, 90, 126, 128, 137, 139, 141, 153, 154, 169, 173, 175, 190, 191, 212, 213, 239, 262, 267], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 94, 95, 100, 105, 106, 107, 125, 149, 150, 161, 193, 194, 195, 203, 205, 210, 214, 217, 225, 236, 251], "line": [10, 11, 61, 62, 64, 66, 178, 179, 205, 213, 266, 267, 268, 269], "segment": [10, 11, 61, 62, 64, 66, 213], "infti": [10, 11, 61, 62, 64, 66, 86, 126, 128, 153, 169, 213], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 98, 102, 126, 128, 137, 139, 141, 143, 153, 154, 158, 161, 168, 169, 171, 172, 173, 175, 176, 177, 180, 181, 189, 190, 191, 195, 210, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 246, 259, 260, 266], "rang": [10, 61, 62, 64, 66, 77, 89, 90, 126, 128, 154, 169, 175, 196, 210, 216, 258, 266], "strip": [10, 61, 62, 64, 66, 126, 128], "unbound": [10, 61, 62, 64, 66, 126, 128], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 100, 102, 126, 128, 137, 139, 141, 154, 158, 161, 168, 169, 172, 173, 175, 176, 177, 178, 179, 181, 189, 190, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 258, 260, 262], "c99": [10, 11, 61, 62, 64, 66, 93, 126, 128, 144, 153, 169, 213, 263], "provision": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "statu": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 93, 103, 104, 126, 128, 153, 157, 163, 164, 165, 167, 169, 171, 179, 195, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 89, 90, 92, 93, 101, 102, 103, 104, 105, 126, 127, 128, 129, 135, 139, 144, 153, 154, 157, 163, 164, 165, 167, 169, 171, 173, 175, 176, 179, 184, 185, 186, 187, 188, 190, 196, 205, 208, 211, 214, 217, 218, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 246, 247, 248, 251, 258, 260, 262, 263, 266, 268], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 93, 104, 126, 127, 128, 129, 153, 157, 163, 164, 165, 169, 173, 190, 195, 196, 210, 214, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 247, 248, 251, 260, 266], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 97, 99, 100, 126, 128, 149, 150, 164, 167, 169, 179, 213, 253], "nonzero": [10, 11, 12, 62, 66, 87, 93, 97, 99, 104, 144, 167, 179, 195, 196, 210, 251], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 166, 167, 178, 179, 213], "aco": [11, 61, 195, 210, 212], "simpli": [11, 99, 128, 211, 222, 266, 268], "upper": [11, 77, 100, 183, 210, 238, 252], "half": [11, 15, 66, 125, 143, 169, 180, 196, 227], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 126, 128], "3\u03c0j": [11, 126, 128], "sum": [12, 21, 90, 110, 130, 154, 195, 210, 246, 258, 260, 262], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "union": [12, 13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 65, 67, 69, 70, 71, 72, 75, 77, 78, 85, 88, 93, 94, 96, 101, 102, 104, 106, 107, 108, 109, 110, 111, 118, 119, 123, 124, 125, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 153, 154, 157, 158, 160, 161, 171, 172, 173, 174, 175, 180, 190, 192, 193, 227, 231, 246, 248, 251, 260, 267], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 89, 90, 92, 96, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 161, 172, 174, 178, 179, 180, 185, 186, 187, 191, 192, 196, 213, 239, 242, 250, 252, 253, 255, 256, 262, 266, 267, 268, 269], "At": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 160, 174, 192], "least": [12, 40, 65, 67, 69, 70, 71, 72, 85, 88, 93, 96, 104, 108, 109, 110, 118, 119, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 147, 148, 153, 157, 160, 174, 185, 186, 187, 188, 192, 196, 211, 212, 251], "remain": [12, 93, 96, 104, 119, 121, 122, 144, 148, 157, 159, 164, 196, 214, 237], "neither": [12, 40, 93, 104, 135, 144, 180, 255, 267], "nor": [12, 93, 104, 144, 255, 267], "mathemat": [12, 19, 65, 84, 86, 87, 93, 99, 104, 126, 128, 144, 166, 167, 178, 179, 195, 213, 246, 260], "round": [12, 15, 76, 93, 103, 104, 144, 169, 184, 195, 210, 212], "nearest": [12, 93, 144, 162, 184, 212], "mode": [12, 93, 144, 212, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 252], "too": [12, 26, 93, 104, 144, 262, 266], "larg": [12, 93, 104, 144, 216, 222, 253, 266], "appropri": [12, 26, 93, 104, 144, 213, 218], "commut": 12, "associ": [12, 42, 144, 198, 205, 248, 251, 254, 262, 265, 267], "tabl": [12, 93, 144, 195], "c": [12, 93, 96, 125, 144, 147, 148, 158, 172, 173, 179, 190, 196, 210, 213, 216, 219, 238, 242, 243, 244, 252, 254, 255, 263, 265, 266, 268], "d": [12, 93, 96, 125, 144, 148, 205, 225, 236], "dj": [12, 93, 144], "independ": [12, 93, 139, 144, 162, 196, 208, 216, 239, 252, 254, 262, 263, 266], "abov": [12, 89, 90, 93, 96, 126, 128, 144, 148, 153, 154, 169, 175, 182, 183, 196, 205, 213, 214, 216, 217, 220, 241, 242, 258, 262, 265, 268], "similarli": [12, 57, 119, 139, 140, 238, 255], "henc": [12, 77, 79, 98, 147, 158, 185, 186, 187, 188, 196, 211, 213, 215, 216, 220, 221, 222, 266, 268], "z1": 12, "z2": 12, "2024": [12, 26, 28, 31, 32, 33, 37, 39, 43, 65, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 88, 89, 90, 92, 93, 96, 104, 108, 109, 110, 114, 123, 124, 130, 131, 133, 134, 138, 139, 142, 144, 146, 148, 153, 155, 156, 157, 160, 163, 174, 176, 177, 192, 225, 236, 254], "keepdim": [13, 14, 16, 17, 88, 137, 139, 141, 154, 173, 175, 190, 246, 260], "test": [13, 14, 91, 120, 121, 122, 139, 210, 212, 264, 266, 267, 268], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 97, 99, 126, 127, 128, 129, 145, 152, 164, 165, 170, 208, 266], "ax": [13, 14, 16, 17, 19, 55, 56, 88, 89, 90, 102, 137, 139, 141, 143, 151, 154, 161, 171, 173, 175, 176, 180, 181, 190, 191, 196, 210, 226, 227, 230, 231, 234, 237, 239, 246, 251, 254, 257, 260], "logic": [13, 14, 24, 26, 93, 96, 131, 132, 133, 134, 144, 148, 217, 220, 226, 230, 234, 237], "AND": [13, 67, 96, 131, 265], "entir": [13, 14, 86, 87, 88, 97, 99, 137, 139, 141, 154, 166, 167, 173, 175, 190], "valid": [13, 14, 26, 27, 92, 98, 117, 143, 163, 172, 180, 189, 196, 212, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 242, 252, 255, 267], "count": [13, 14, 78, 88, 89, 90, 92, 102, 176, 177, 185, 186, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 243], "last": [13, 14, 18, 19, 55, 78, 89, 90, 92, 102, 161, 168, 172, 176, 177, 180, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 246, 252, 255, 258], "invalid": [13, 14, 23, 92, 98, 218, 266], "wa": [13, 14, 19, 26, 88, 104, 137, 139, 141, 154, 173, 175, 190, 205, 217, 222, 266, 268], "OR": [14, 24, 70, 133, 148, 265], "start": [15, 125, 196, 210, 222, 266, 268], "stop": [15, 125, 196, 210, 267], "step": [15, 125, 196, 267], "evenli": [15, 125], "space": [15, 125, 225, 227, 236], "open": [15, 125, 143, 180, 196], "inclus": [15, 196, 266], "end": [15, 65, 86, 125, 164, 166, 178, 179, 203, 214, 253, 266, 267, 268], "exclus": [15, 196], "distanc": [15, 110], "adjac": 15, "output": [15, 60, 63, 75, 78, 89, 90, 94, 95, 98, 100, 102, 105, 106, 107, 114, 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39, 43, 91, 96, 108, 109, 123, 124, 148, 269], "undefin": [28, 31, 33, 37, 39, 43, 96, 108, 109, 123, 124, 148, 205, 262], "outsid": [29, 77, 172, 189, 196, 205, 210, 216], "bound": [29, 77, 176, 177, 196, 205, 210, 222], "divis": [30, 41, 71, 93, 104, 157, 164, 213], "floor_divid": [30, 195, 210], "greater_equ": [31, 195, 210], "kei": [32, 49, 114, 116, 118, 266], "slice": [32, 49, 189, 195, 214], "ellipsi": [32, 49, 196], "semant": [32, 40, 49, 104, 135, 157, 176, 195, 196, 208, 210, 214, 216, 218, 220, 221, 254, 262, 266, 267, 268], "iter": [32, 196, 210], "directli": [32, 266, 268], "__iter__": 32, "sequenc": [32, 60, 78, 125, 172, 180, 189, 196, 210, 226, 227, 230, 231, 234, 237, 257], "clarifi": [32, 59, 74, 77, 137, 141, 176, 185, 186, 187, 192, 210, 254], "pep": [34, 40, 104, 135, 216, 263], "357": 34, "overflowerror": 35, "bitwise_invert": [36, 195], "less_equ": [37, 195, 210], "bitwise_left_shift": [38, 195, 210], "matrix": [40, 55, 135, 136, 140, 180, 182, 183, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266], "product": [40, 42, 58, 89, 135, 144, 154, 180, 191, 210, 239, 250, 262], "built": [40, 135, 196, 205, 266], "465": [40, 135], "m": [40, 55, 92, 135, 136, 140, 158, 163, 180, 181, 182, 183, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258], "remov": [40, 135, 171, 196, 213, 241, 258], "innermost": [40, 135, 136, 182, 183, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258], "conjug": [40, 79, 135, 180, 191, 210, 238, 242, 255, 262], "transposit": [40, 135, 180], "desir": [40, 63, 75, 135, 143, 180, 212, 213, 216, 222], "prior": [40, 92, 135, 180], "inner": [40, 135, 210, 242, 262], "stack": [40, 55, 135, 136, 182, 183, 195, 221, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 262], "l": [40, 135, 238, 258], "remaind": [41, 195, 196, 210], "multipli": [42, 89, 154, 170, 195, 210, 212, 242, 255], "not_equ": [43, 195, 210], "negat": [44, 79, 145], "bitwise_or": [45, 195, 210], "exponenti": [47, 97, 99, 130, 153, 213], "power": [47, 71, 97, 153, 213, 247, 268], "expon": [47, 153, 247], "versu": [47, 51, 63, 77, 93, 144, 153, 210], "bitwise_right_shift": [48, 195, 210], "current": [49, 59, 116, 118, 139, 176, 196, 203, 214, 217, 222, 266, 267, 268], "revisit": [49, 196, 217], "revis": [49, 196, 210, 213, 217], "mix": [49, 125, 139, 160, 173, 190, 192, 195, 210, 214, 217, 262, 266], "how": [49, 93, 144, 208, 212, 217, 221, 267, 268, 269], "minuend": 50, "subtrahend": 50, "subtract": [50, 195, 210, 212], "divid": [51, 104, 156, 164, 195, 196, 210, 212], "bitwise_xor": [52, 195, 210], "resid": [53, 59, 98, 143, 180, 196, 210, 216, 266], "fewer": 55, "unknown": [57, 58, 158], "graph": [57, 58, 75, 147, 158, 160, 185, 186, 187, 188, 196, 215, 220, 266], "static": [57, 215, 219], "know": [57, 147, 158, 185, 186, 187, 188, 208, 211, 212, 215, 266, 268], "content": [57, 215, 265], "warrant": 57, "custom": [57, 211, 218], "immut": 57, "retriev": [57, 196, 208, 223, 262, 268], "behav": [57, 213], "__dlpack__": [59, 105, 195, 210, 214, 216], "caveat": 59, "locat": [59, 210, 214], "explicit": [59, 60, 105, 176, 180, 217, 268], "enqueu": 59, "asynchron": 59, "explain": [59, 211], "obj": 60, "nestedsequ": 60, "supportsbufferprotocol": 60, "possibli": [60, 221, 266], "nest": [60, 221], "protocol": [60, 208, 216, 222, 266, 268], "turn": [60, 208, 261], "memoryview": 60, "preced": [60, 213, 216, 217], "mixtur": 60, "convers": [60, 125, 196, 210, 211, 214, 266], "obei": [60, 125], "permit": [60, 63, 125, 215, 265], "To": [60, 104, 196, 210, 212, 213, 222, 266, 267, 269], "array_api": [60, 266], "astyp": [60, 195, 210, 214], "exce": [60, 106, 107, 125], "sine": [61, 62, 166, 167, 179], "1j": [61, 64, 86, 87, 97, 99, 110, 166, 167, 178], "asinh": [61, 195, 210, 212], "asin": [62, 195, 210, 212], "irrespect": [63, 75, 213], "histor": [63, 179, 262], "discard": 63, "arbitrari": [63, 73, 114, 140, 160, 212], "achiev": [63, 196, 212], "outcom": 63, "clariti": 63, "newli": [63, 217], "alloc": [63, 182, 183, 215, 217], "tangent": [64, 65, 66, 178, 179], "atanh": [64, 195, 210, 212], "quotient": [65, 93, 104, 196], "domain": [65, 210, 212, 213, 266, 268], "notat": 65, "denot": [65, 191, 251], "pair": [65, 104, 239, 255], "codomain": 65, "quadrant": 65, "chosen": [65, 192, 216], "angl": [65, 87, 110, 167, 179], "rai": 65, "role": 65, "coordin": [65, 126, 140, 178, 179, 196, 221, 266], "tradit": 65, "atan": [66, 195, 210, 212], "bitwis": [67, 70, 72, 195], "flip": [68, 195], "shift": [69, 71, 161, 227, 231], "arithmet": [71, 93, 139, 144, 195, 205, 213, 266], "propag": [71, 105, 137, 139, 141, 173, 190, 212], "floor": [71, 104, 195], "anoth": [73, 75, 105, 196, 208, 210, 211, 213, 214, 216, 217, 220, 242, 255, 266, 268], "capabl": [74, 113, 195, 198, 210], "being": [74, 196, 216, 217, 262, 266, 269], "versionchang": 74, 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[210, "id3"], [210, "id6"]], "APIs": [[210, "apis"], [210, "id2"], [210, "id4"], [210, "id7"], [210, "id10"], [210, "id16"], [210, "id20"]], "Scalar Argument Support": [[210, "scalar-argument-support"]], "Extensions": [[210, "extensions"], [210, "id8"], [210, "id13"], [210, "id17"], [210, "id21"], [261, "extensions"]], "Additions": [[210, "additions"], [210, "id9"], [210, "id19"]], "Breaking Changes": [[210, "breaking-changes"], [210, "id12"]], "Errata": [[210, "errata"], [210, "id14"], [210, "id22"]], "v2023.12": [[210, "v2023-12"]], "v2022.12": [[210, "v2022-12"]], "Complex Number Support": [[210, "complex-number-support"], [210, "id18"]], "C API": [[211, "c-api"]], "Example situations for C/Cython usage": [[211, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[211, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[211, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[211, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[211, "device-support"], [217, "device-support"]], "Other longer-term approaches": [[211, "other-longer-term-approaches"]], "Further Python API standardization": [[211, "further-python-api-standardization"]], "HPy": [[211, "hpy"]], "Accuracy": [[212, "accuracy"]], "Arithmetic Operations": [[212, "arithmetic-operations"]], "Mathematical Functions": [[212, "mathematical-functions"]], "Linear Algebra": [[212, "linear-algebra"]], "Operations Involving Complex Numbers": [[212, "operations-involving-complex-numbers"]], "Complex Numbers": [[213, "complex-numbers"]], "The Complex Plane": [[213, "the-complex-plane"]], "Branch Cuts": [[213, "branch-cuts"]], "Complex Number Ordering": [[213, "complex-number-ordering"]], "Valued-based Promotion": [[213, "valued-based-promotion"]], "Copy-view behavior and mutability": [[214, "copy-view-behavior-and-mutability"]], "Mutating views": [[214, null]], "Copy keyword argument behavior": [[214, "copy-keyword-argument-behavior"]], "Data-dependent output shapes": [[215, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[216, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[216, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[216, "non-supported-use-cases"]], "Intended usage": [[217, "intended-usage"]], "Syntax for device assignment": [[217, "syntax-for-device-assignment"]], "Semantics": [[217, "semantics"]], "Out of scope for device support": [[217, "out-of-scope-for-device-support"]], "Exceptions": [[218, "exceptions"]], "Design topics & constraints": [[219, "design-topics-constraints"], [219, null]], "Lazy vs. eager execution": [[220, "lazy-vs-eager-execution"]], "Parallelism": [[221, "parallelism"]], "Static typing": [[222, "static-typing"]], "Fourier transform Functions": [[223, "fourier-transform-functions"]], "Extension name and usage": [[223, "extension-name-and-usage"], [262, "extension-name-and-usage"]], "fft": [[224, "fft"]], "fftfreq": [[225, "fftfreq"]], "fftn": [[226, "fftn"]], "fftshift": [[227, "fftshift"]], "hfft": [[228, "hfft"]], "ifft": [[229, "ifft"]], "ifftn": [[230, "ifftn"]], "ifftshift": [[231, "ifftshift"]], "ihfft": [[232, "ihfft"]], "irfft": [[233, "irfft"]], "irfftn": [[234, "irfftn"]], "rfft": [[235, "rfft"]], "rfftfreq": [[236, "rfftfreq"]], "rfftn": [[237, "rfftn"]], "cholesky": [[238, "cholesky"]], "cross": [[239, "cross"]], "det": [[240, "det"]], "diagonal": [[241, "diagonal"]], "eigh": [[242, "eigh"]], "eigvalsh": [[243, "eigvalsh"]], "inv": [[244, "inv"]], "matrix_norm": [[246, "matrix-norm"]], "matrix_power": [[247, "matrix-power"]], "matrix_rank": [[248, "matrix-rank"]], "outer": [[250, "outer"]], "pinv": [[251, "pinv"]], "qr": [[252, "qr"]], "slogdet": [[253, "slogdet"]], "solve": [[254, "solve"]], "svd": [[255, "svd"]], "svdvals": [[256, "svdvals"]], "trace": [[258, "trace"]], "vector_norm": [[260, "vector-norm"]], "Extension modules:": [[261, null]], "Linear Algebra Extension": [[262, "linear-algebra-extension"]], "Design Principles": [[262, "design-principles"]], "Future API standard evolution": [[263, "future-api-standard-evolution"]], "Scope extensions": [[263, "scope-extensions"]], "Versioning": [[263, "versioning"]], "Python array API standard": [[264, "python-array-api-standard"]], "Contents": [[264, "contents"]], "Context": [[264, null]], "API": [[264, null]], "Methodology and Usage": [[264, null]], "Other": [[264, null]], "License": [[265, "license"]], "Purpose and scope": [[266, "purpose-and-scope"]], "Introduction": [[266, "introduction"], [267, "introduction"]], "This API standard": [[266, "this-api-standard"]], "History": [[266, "history"]], "Scope (includes out-of-scope / non-goals)": [[266, "scope-includes-out-of-scope-non-goals"]], "In scope": [[266, "in-scope"]], "Out of scope": [[266, "out-of-scope"]], "Implications of in/out of scope": [[266, "implications-of-in-out-of-scope"]], "Stakeholders": [[266, "stakeholders"]], "How to read this document": [[266, "how-to-read-this-document"]], "How to adopt this API": [[266, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[266, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[266, "discoverability-of-conforming-implementations"]], "Optional feature": [[266, null]], "Conformance": [[266, "conformance"]], "Terms and Definitions": [[266, "terms-and-definitions"]], "Normative References": [[266, "normative-references"]], "Usage Data": [[267, "usage-data"]], "Design": [[267, "design"]], "Usage": [[267, "usage"]], "Use in Decision-Making": [[267, "use-in-decision-making"]], "Use cases": [[268, "use-cases"]], "Types of use cases": [[268, "types-of-use-cases"]], "Concrete use cases": [[268, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[268, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[268, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[268, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[268, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[269, "verification-test-suite"]], "Measuring conformance": [[269, "measuring-conformance"]], "Running the tests": [[269, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "count_nonzero() (in module array_api)": [[88, "array_api.count_nonzero"]], "cumulative_prod() (in module array_api)": [[89, "array_api.cumulative_prod"]], "cumulative_sum() (in module array_api)": [[90, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[91, "array_api.data_types.__eq__"]], "diff() (in module array_api)": [[92, "array_api.diff"]], "divide() (in module array_api)": [[93, "array_api.divide"]], "empty() (in module array_api)": [[94, "array_api.empty"]], "empty_like() (in module array_api)": [[95, "array_api.empty_like"]], "equal() (in module array_api)": [[96, "array_api.equal"]], "exp() (in module array_api)": [[97, "array_api.exp"]], "expand_dims() (in module array_api)": [[98, "array_api.expand_dims"]], "expm1() (in module array_api)": [[99, "array_api.expm1"]], "eye() (in module array_api)": [[100, "array_api.eye"]], "finfo() (in module array_api)": [[101, "array_api.finfo"]], "flip() (in module array_api)": [[102, "array_api.flip"]], "floor() (in module array_api)": [[103, "array_api.floor"]], "floor_divide() (in module array_api)": [[104, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[105, "array_api.from_dlpack"]], "full() (in module array_api)": [[106, "array_api.full"]], "full_like() (in module array_api)": [[107, "array_api.full_like"]], "greater() (in module array_api)": [[108, "array_api.greater"]], "greater_equal() (in module array_api)": [[109, "array_api.greater_equal"]], "hypot() (in module array_api)": [[110, "array_api.hypot"]], "iinfo() (in module array_api)": [[111, "array_api.iinfo"]], "imag() (in module array_api)": [[112, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[113, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[114, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[115, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[116, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[117, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[118, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[119, "array_api.isdtype"]], "isfinite() (in module array_api)": [[120, "array_api.isfinite"]], "isinf() (in module array_api)": [[121, "array_api.isinf"]], "isnan() (in module array_api)": [[122, "array_api.isnan"]], "less() (in module array_api)": [[123, "array_api.less"]], "less_equal() (in module array_api)": [[124, "array_api.less_equal"]], "linspace() (in module array_api)": [[125, "array_api.linspace"]], "log() (in module array_api)": [[126, "array_api.log"]], "log10() (in module array_api)": [[127, "array_api.log10"]], "log1p() (in module array_api)": [[128, "array_api.log1p"]], "log2() (in module array_api)": [[129, "array_api.log2"]], "logaddexp() (in module array_api)": [[130, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[131, "array_api.logical_and"]], "logical_not() (in module array_api)": [[132, "array_api.logical_not"]], "logical_or() (in module array_api)": [[133, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[134, "array_api.logical_xor"]], "matmul() (in module array_api)": [[135, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[136, "array_api.matrix_transpose"]], "max() (in module array_api)": [[137, "array_api.max"]], "maximum() (in module array_api)": [[138, "array_api.maximum"]], "mean() (in module array_api)": [[139, "array_api.mean"]], "meshgrid() (in module array_api)": [[140, "array_api.meshgrid"]], "min() (in module array_api)": [[141, "array_api.min"]], "minimum() (in module array_api)": [[142, "array_api.minimum"]], "moveaxis() (in module array_api)": [[143, "array_api.moveaxis"]], "multiply() (in module array_api)": [[144, "array_api.multiply"]], "negative() (in module array_api)": [[145, "array_api.negative"]], "nextafter() (in module array_api)": [[146, "array_api.nextafter"]], "nonzero() (in module array_api)": [[147, "array_api.nonzero"]], "not_equal() (in module array_api)": [[148, "array_api.not_equal"]], "ones() (in module array_api)": [[149, "array_api.ones"]], "ones_like() (in module array_api)": [[150, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[151, "array_api.permute_dims"]], "positive() (in module array_api)": [[152, "array_api.positive"]], "pow() (in module array_api)": [[153, "array_api.pow"]], "prod() (in module array_api)": [[154, "array_api.prod"]], "real() (in module array_api)": [[155, "array_api.real"]], "reciprocal() (in module array_api)": [[156, "array_api.reciprocal"]], "remainder() (in module array_api)": [[157, "array_api.remainder"]], "repeat() (in module array_api)": [[158, "array_api.repeat"]], "reshape() (in module array_api)": [[159, "array_api.reshape"]], "result_type() (in module array_api)": [[160, "array_api.result_type"]], "roll() (in module array_api)": [[161, "array_api.roll"]], "round() (in module array_api)": [[162, "array_api.round"]], "searchsorted() (in module array_api)": [[163, "array_api.searchsorted"]], "sign() (in module array_api)": [[164, "array_api.sign"]], "signbit() (in module array_api)": [[165, "array_api.signbit"]], "sin() (in module array_api)": [[166, "array_api.sin"]], "sinh() (in module array_api)": [[167, "array_api.sinh"]], "sort() (in module array_api)": [[168, "array_api.sort"]], "sqrt() (in module array_api)": [[169, "array_api.sqrt"]], "square() (in module array_api)": [[170, "array_api.square"]], "squeeze() (in module array_api)": [[171, "array_api.squeeze"]], "stack() (in module array_api)": [[172, "array_api.stack"]], "std() (in module array_api)": [[173, "array_api.std"]], "subtract() (in module array_api)": [[174, "array_api.subtract"]], "sum() (in module array_api)": [[175, "array_api.sum"]], "take() (in module array_api)": [[176, 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"The": [0, 1, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 55, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 102, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 196, 205, 208, 210, 211, 212, 214, 215, 216, 217, 220, 221, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 261, 262, 263, 265, 266, 267, 268, 269], "numer": [0, 5, 9, 12, 20, 21, 40, 42, 44, 46, 47, 50, 51, 79, 89, 90, 92, 93, 104, 118, 119, 120, 121, 122, 135, 140, 144, 145, 152, 153, 154, 155, 162, 164, 170, 174, 175, 180, 205, 212, 224, 226, 229, 230, 233, 234, 235, 237, 239, 250, 251, 253, 258, 262, 266, 268], "__invert__": [0, 195], "inv": [0, 210, 262], "invert": [0, 68, 244, 247, 254], "__inv__": 0, "__and__": [0, 195], "__or__": [0, 195], "__xor__": [0, 195], "xor": [0, 72, 134], "__lshift__": [0, 195], "lshift": 0, "__rshift__": [0, 195], "rshift": 0, "integ": [0, 5, 9, 13, 14, 15, 20, 22, 26, 29, 30, 34, 35, 36, 38, 41, 44, 45, 47, 48, 49, 51, 52, 60, 67, 68, 69, 70, 71, 72, 76, 77, 88, 89, 90, 92, 93, 103, 104, 106, 107, 111, 114, 118, 119, 125, 137, 139, 141, 145, 153, 154, 157, 158, 160, 162, 163, 173, 175, 176, 184, 190, 191, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247, 248, 258, 260, 266], "boolean": [0, 5, 22, 24, 25, 26, 29, 35, 36, 43, 45, 52, 57, 60, 63, 67, 68, 70, 72, 88, 89, 90, 91, 105, 106, 107, 114, 118, 119, 125, 131, 132, 133, 134, 147, 192, 195, 205, 210], "__lt__": [0, 195, 210], "lt": 0, "__le__": [0, 195, 210], "le": 0, "__gt__": [0, 195, 210], "gt": [0, 252, 255], "__ge__": [0, 195, 210], "ge": 0, "__eq__": [0, 195, 210, 217], "eq": 0, "__ne__": [0, 195, 210], "ne": 0, "ar": [0, 1, 5, 7, 15, 16, 17, 19, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 43, 49, 55, 58, 60, 77, 85, 86, 88, 91, 92, 93, 96, 97, 100, 101, 102, 104, 105, 108, 109, 110, 117, 118, 123, 124, 125, 131, 132, 133, 134, 135, 139, 144, 147, 148, 153, 158, 160, 161, 162, 166, 178, 179, 181, 185, 187, 191, 196, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 229, 230, 231, 233, 234, 235, 236, 237, 239, 242, 243, 248, 251, 252, 255, 261, 262, 263, 266, 267, 268, 269], "onli": [0, 1, 5, 7, 16, 17, 23, 26, 40, 57, 58, 63, 77, 102, 105, 110, 116, 118, 119, 125, 131, 132, 133, 134, 135, 139, 173, 190, 191, 195, 196, 205, 208, 210, 211, 213, 214, 216, 217, 218, 220, 222, 227, 239, 244, 251, 252, 254, 262, 263, 266, 267, 268, 269], "other": [0, 5, 21, 22, 23, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 50, 51, 52, 63, 91, 93, 99, 104, 105, 128, 143, 144, 160, 173, 190, 196, 198, 208, 210, 212, 213, 214, 215, 216, 217, 218, 222, 239, 251, 261, 262, 265, 266, 268], "ani": [0, 1, 9, 10, 11, 23, 24, 25, 26, 28, 29, 34, 35, 43, 59, 61, 62, 66, 91, 92, 96, 110, 120, 121, 148, 169, 195, 196, 205, 210, 213, 214, 216, 222, 255, 263, 265, 266, 269], "For": [0, 1, 5, 7, 9, 10, 11, 12, 16, 17, 18, 20, 24, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 57, 58, 61, 62, 64, 65, 66, 76, 77, 79, 85, 86, 87, 89, 90, 93, 96, 97, 99, 103, 104, 108, 109, 110, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 153, 154, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 175, 178, 179, 184, 185, 186, 187, 188, 196, 203, 208, 212, 213, 214, 215, 217, 220, 225, 234, 236, 253, 255, 256, 258, 266, 268, 269], "backward": [0, 13, 14, 16, 17, 18, 31, 33, 37, 39, 92, 108, 109, 123, 124, 125, 137, 138, 141, 142, 157, 168, 191, 196, 210, 213, 214, 218, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 266], "compat": [0, 1, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 125, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 159, 168, 173, 174, 175, 177, 190, 191, 192, 196, 205, 210, 213, 214, 218, 239, 246, 248, 251, 254, 260, 266, 268], "mai": [0, 5, 7, 15, 16, 17, 18, 23, 26, 28, 31, 33, 37, 39, 43, 51, 57, 58, 59, 60, 75, 91, 92, 93, 96, 104, 105, 108, 109, 110, 113, 118, 119, 123, 124, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 148, 158, 159, 160, 163, 168, 173, 179, 185, 186, 187, 188, 190, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 242, 252, 253, 255, 261, 262, 266, 267, 268], "complex": [0, 5, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 24, 25, 28, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 88, 89, 90, 93, 96, 97, 99, 100, 101, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 160, 162, 164, 166, 167, 168, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 205, 216, 217, 219, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "howev": [0, 5, 16, 17, 18, 31, 33, 37, 39, 57, 89, 90, 104, 108, 109, 110, 119, 123, 124, 125, 137, 138, 141, 142, 158, 163, 168, 176, 178, 179, 196, 208, 211, 212, 213, 214, 215, 217, 262, 263, 266, 268], "inequ": [0, 16, 17, 18, 31, 33, 37, 39, 108, 109, 123, 124, 137, 138, 141, 142, 168], "unspecifi": [0, 5, 10, 11, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 60, 62, 66, 77, 78, 79, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 167, 168, 169, 172, 176, 177, 179, 196, 203, 205, 210, 226, 227, 230, 231, 234, 237, 242, 243, 266], "thu": [0, 5, 16, 17, 18, 28, 30, 31, 32, 33, 37, 39, 41, 43, 47, 49, 57, 60, 71, 77, 79, 89, 90, 92, 96, 104, 106, 107, 108, 109, 123, 124, 125, 137, 138, 141, 142, 148, 153, 155, 157, 160, 163, 168, 176, 178, 179, 196, 203, 212, 213, 226, 227, 230, 231, 234, 237, 242, 243, 255, 262], "depend": [0, 5, 9, 10, 11, 16, 17, 18, 20, 26, 28, 29, 31, 33, 37, 39, 43, 44, 47, 51, 57, 58, 59, 61, 62, 63, 64, 65, 66, 77, 86, 87, 93, 96, 97, 99, 108, 109, 114, 123, 124, 125, 126, 127, 128, 129, 144, 145, 148, 153, 160, 163, 166, 167, 168, 178, 179, 192, 203, 205, 212, 213, 216, 219, 220, 222, 242, 243, 252, 253, 254, 255, 262, 266, 268, 269], "see": [0, 5, 10, 11, 12, 13, 14, 16, 17, 18, 21, 22, 26, 28, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 53, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 85, 88, 93, 96, 99, 104, 105, 107, 108, 109, 110, 113, 114, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 147, 148, 153, 154, 156, 157, 158, 159, 160, 163, 164, 168, 169, 170, 173, 174, 175, 177, 185, 186, 187, 188, 190, 191, 192, 195, 196, 205, 207, 208, 211, 213, 215, 216, 217, 222, 239, 246, 248, 251, 254, 260, 261, 266, 267, 268, 269], "order": [0, 5, 7, 16, 17, 18, 19, 26, 31, 33, 37, 39, 55, 60, 63, 65, 91, 92, 102, 104, 105, 108, 109, 123, 124, 137, 138, 141, 142, 147, 158, 163, 168, 178, 179, 180, 185, 186, 187, 188, 196, 203, 205, 210, 212, 214, 215, 216, 218, 233, 234, 242, 243, 246, 255, 256, 260, 262, 263, 266, 267], "discuss": [0, 96, 148, 210, 216, 217, 221, 266, 267, 268], "copi": [0, 1, 26, 59, 60, 63, 105, 159, 168, 210, 211, 216, 217, 219, 265, 266], "view": [0, 105, 219], "behavior": [0, 5, 26, 32, 47, 49, 59, 60, 63, 74, 77, 89, 90, 92, 93, 104, 106, 107, 110, 125, 144, 153, 157, 159, 160, 163, 176, 177, 185, 186, 187, 188, 195, 196, 198, 205, 208, 210, 212, 213, 219, 220, 221, 226, 227, 230, 231, 234, 237, 262, 263, 266, 267, 268, 269], "mutabl": [0, 219], "refer": [0, 1, 13, 14, 92, 99, 100, 128, 163, 173, 176, 177, 180, 181, 190, 191, 196, 213, 214, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 254], "what": [0, 163, 208, 216, 218, 222, 262, 266, 267, 268, 269], "call": [0, 7, 34, 92, 216, 217, 220, 253, 266, 267, 268], "http": [0, 216, 263, 269], "doc": 0, "org": 0, "html": 0, "do": [0, 1, 26, 75, 93, 144, 157, 203, 208, 210, 211, 213, 214, 216, 217, 218, 262, 263, 265, 266, 268, 269], "mutat": [0, 176, 210], "choos": [0, 51, 57, 59, 92, 93, 104, 125, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 147, 158, 160, 173, 185, 186, 187, 188, 190, 195, 196, 203, 213, 214, 215, 217, 220, 266, 268], "when": [0, 5, 7, 12, 16, 17, 26, 32, 47, 49, 59, 63, 75, 77, 89, 90, 93, 99, 104, 105, 110, 116, 118, 125, 128, 137, 138, 139, 141, 142, 144, 153, 154, 158, 159, 163, 173, 175, 176, 179, 190, 192, 195, 196, 205, 210, 211, 213, 214, 215, 216, 218, 220, 221, 222, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 244, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266, 267, 268], "doe": [0, 1, 15, 26, 105, 148, 176, 177, 196, 205, 208, 211, 212, 213, 214, 215, 217, 218, 220, 222, 262, 266, 268, 269], "correspond": [0, 1, 16, 17, 23, 28, 31, 33, 37, 39, 43, 47, 59, 65, 73, 77, 96, 105, 108, 109, 114, 115, 116, 123, 124, 148, 153, 159, 161, 163, 173, 177, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 226, 230, 234, 237, 239, 242, 246, 265, 266], "fall": 0, "back": [0, 268], "equival": [0, 20, 21, 22, 28, 30, 31, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 71, 77, 104, 110, 131, 132, 133, 134, 157, 162, 176, 196, 205, 210, 213, 214, 248, 251, 254, 260, 266], "binari": [0, 5, 67, 70, 72, 178, 179, 211], "chang": [0, 1, 9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 90, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 159, 160, 162, 163, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 192, 208, 224, 225, 226, 228, 229, 230, 233, 234, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263, 266, 268, 269], "shape": [0, 1, 18, 40, 55, 63, 73, 74, 78, 89, 90, 92, 94, 95, 98, 102, 106, 107, 114, 135, 136, 140, 149, 150, 159, 161, 163, 168, 172, 176, 177, 180, 181, 182, 183, 189, 191, 193, 194, 195, 210, 219, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 266, 268], "result": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 79, 85, 86, 87, 88, 93, 96, 97, 99, 103, 104, 108, 109, 110, 112, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 141, 142, 144, 145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 172, 173, 174, 175, 178, 179, 180, 184, 185, 190, 196, 203, 205, 210, 212, 213, 214, 220, 238, 239, 241, 246, 247, 253, 254, 260, 266, 267, 268, 269], "promot": [0, 1, 5, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 92, 93, 96, 97, 99, 104, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 139, 142, 144, 145, 148, 153, 156, 157, 160, 166, 167, 169, 170, 172, 173, 174, 178, 179, 180, 190, 191, 192, 195, 210, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262], "rule": [0, 5, 7, 10, 11, 12, 21, 22, 28, 30, 31, 33, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 78, 85, 86, 87, 89, 90, 92, 93, 96, 97, 99, 104, 106, 107, 108, 109, 110, 123, 124, 125, 126, 127, 128, 129, 130, 135, 138, 142, 144, 145, 148, 153, 156, 157, 160, 164, 166, 167, 169, 170, 172, 174, 178, 179, 180, 191, 192, 195, 196, 210, 213, 216, 238, 239, 244, 246, 247, 248, 250, 251, 252, 253, 254, 260, 262, 266, 268], "broadcast": [0, 12, 13, 14, 16, 17, 21, 22, 28, 30, 31, 33, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 65, 67, 69, 70, 71, 72, 73, 74, 77, 85, 88, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 137, 138, 139, 141, 142, 144, 146, 148, 153, 154, 157, 158, 173, 174, 175, 177, 180, 190, 191, 192, 195, 196, 210, 239, 246, 248, 251, 254, 260, 266], "let": [0, 1, 9, 10, 11, 12, 62, 66, 85, 87, 89, 90, 92, 96, 97, 99, 105, 120, 121, 122, 125, 126, 128, 139, 148, 154, 158, 163, 164, 167, 169, 173, 175, 179, 181, 190, 191, 196, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 242, 243, 244, 252, 254, 255, 258], "If": [0, 1, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 29, 34, 35, 40, 44, 47, 51, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 74, 76, 77, 78, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 110, 114, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 193, 194, 196, 211, 213, 217, 223, 224, 225, 226, 227, 228, 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88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 192, 193, 195, 203, 210, 212, 213, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 267], "point": [2, 5, 9, 10, 11, 12, 13, 14, 15, 20, 24, 25, 26, 29, 34, 35, 40, 41, 42, 44, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 76, 77, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 110, 112, 116, 118, 119, 120, 121, 122, 125, 126, 127, 128, 129, 130, 135, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 184, 185, 186, 187, 188, 190, 191, 193, 195, 203, 210, 212, 213, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 240, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266, 268], "creat": [3, 15, 60, 94, 95, 100, 105, 106, 107, 125, 149, 150, 193, 194, 202, 208, 217, 225, 236, 262, 266], "its": [5, 26, 40, 73, 93, 101, 135, 144, 159, 161, 212, 213, 216, 217, 261, 266, 267, 268], "main": [5, 100, 182, 183, 211, 216, 241, 258, 261, 268], "namespac": [5, 7, 23, 113, 198, 208, 210, 223, 261, 262, 263, 266, 269], "under": [5, 261, 265, 266], "specifi": [5, 13, 14, 15, 16, 17, 18, 26, 29, 59, 60, 63, 74, 78, 88, 89, 90, 92, 94, 98, 101, 102, 106, 116, 118, 119, 125, 149, 154, 157, 158, 161, 171, 172, 175, 176, 177, 181, 182, 183, 185, 186, 187, 188, 191, 193, 196, 205, 210, 212, 213, 214, 216, 217, 218, 222, 224, 226, 227, 228, 229, 230, 232, 233, 234, 235, 237, 241, 258, 260, 262, 263, 266, 268, 269], "name": [5, 7, 23, 26, 104, 118, 185, 186, 187, 196, 213, 214, 242, 251, 252, 253, 255, 261, 266, 267], "descript": [5, 7, 210, 212, 246, 260], "bool": [5, 13, 14, 16, 17, 18, 22, 24, 26, 28, 31, 33, 37, 39, 43, 45, 49, 52, 60, 63, 67, 70, 72, 75, 88, 89, 90, 91, 96, 105, 106, 107, 108, 109, 118, 119, 120, 121, 122, 123, 124, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 160, 165, 168, 173, 175, 190, 192, 205, 210, 220, 238, 246, 255, 260], "true": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 101, 104, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 147, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 192, 196, 210, 214, 238, 246, 255, 260, 262], "fals": [5, 13, 14, 16, 17, 18, 24, 25, 26, 29, 35, 60, 63, 75, 88, 89, 90, 96, 105, 114, 120, 121, 122, 125, 131, 132, 133, 134, 137, 139, 141, 148, 154, 159, 165, 168, 173, 175, 185, 186, 187, 188, 190, 196, 238, 246, 255, 260], "int8": [5, 118, 119, 196, 205], "bit": [5, 68, 69, 71, 85, 89, 90, 101, 111, 154, 165, 175, 205, 210, 212, 258], "sign": [5, 9, 10, 11, 12, 15, 20, 41, 44, 62, 65, 66, 71, 85, 87, 89, 90, 93, 97, 99, 104, 118, 119, 126, 128, 137, 138, 141, 142, 144, 145, 153, 154, 157, 163, 165, 167, 169, 175, 179, 185, 186, 187, 188, 195, 203, 210, 213, 252, 253, 258], "exist": [5, 7, 26, 60, 78, 105, 208, 210, 213, 216, 217, 218, 244, 263, 266, 267], "interv": [5, 10, 11, 13, 14, 15, 61, 62, 64, 66, 92, 98, 125, 126, 128, 143, 172, 180, 182, 183, 189, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 263], "128": 5, "127": 5, "int16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "16": [5, 205], "32": [5, 205], "767": 5, "int32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "147": 5, "483": 5, "647": 5, "int64": [5, 89, 90, 118, 119, 154, 175, 205, 258], "64": [5, 205], "9": [5, 27], "223": 5, "372": 5, "036": 5, "854": 5, "775": 5, "807": 5, "uint8": [5, 118, 119, 196, 205], "unsign": [5, 89, 90, 118, 119, 154, 175, 195, 258], "255": 5, "uint16": [5, 89, 90, 118, 119, 154, 175, 205, 258], "65": 5, "535": [5, 210], "uint32": [5, 89, 90, 118, 119, 154, 175, 205, 258], "294": 5, "967": 5, "295": 5, "uint64": [5, 118, 119, 205], "18": 5, "446": [5, 210], "744": [5, 210], "073": 5, "709": [5, 210], "551": [5, 210], "615": 5, "float32": [5, 112, 118, 119, 155, 205, 253, 255, 256], "ieee": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "754": [5, 12, 65, 80, 81, 82, 84, 93, 99, 101, 110, 128, 144, 157, 169, 178, 179, 195, 203, 210, 212, 213, 266], "singl": [5, 7, 24, 25, 29, 34, 35, 116, 118, 185, 186, 195, 205, 210, 211, 213, 216, 217, 222, 262, 266, 267, 268], "2019": [5, 12, 93, 99, 110, 128, 144, 195, 212, 266, 268], "float64": [5, 9, 20, 118, 119, 205, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "doubl": [5, 180, 205, 210], "complex64": [5, 112, 118, 119, 155, 205, 210, 253, 255, 256], "imaginari": [5, 10, 11, 12, 13, 14, 44, 61, 62, 63, 64, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 162, 167, 169, 179, 210, 213], "compon": [5, 10, 11, 12, 13, 14, 44, 62, 63, 66, 79, 87, 88, 93, 96, 97, 99, 101, 112, 126, 128, 139, 144, 145, 147, 148, 149, 150, 153, 155, 162, 167, 169, 178, 179, 185, 186, 187, 188, 210, 213, 227, 236], "complex128": [5, 9, 20, 118, 119, 205, 210, 228, 232, 233, 234, 235, 237, 242, 243, 246, 260], "method": [5, 26, 34, 105, 195, 198, 208, 214, 216, 217, 220, 221, 222, 266, 267, 268], "attribut": [5, 23, 101, 111, 160, 195, 207, 210, 263, 266, 267, 268], "requir": [5, 10, 11, 24, 25, 29, 34, 35, 59, 61, 62, 63, 64, 66, 75, 89, 90, 105, 110, 119, 154, 160, 169, 172, 175, 176, 177, 179, 185, 186, 188, 189, 195, 196, 203, 205, 208, 210, 211, 212, 213, 214, 215, 216, 217, 220, 222, 224, 225, 226, 228, 229, 230, 233, 234, 236, 239, 258, 261, 262, 266, 267, 268], "beyond": [5, 161, 205, 210, 266], "It": [5, 23, 26, 105, 208, 214, 216, 266, 268, 269], "also": [5, 7, 26, 32, 34, 105, 110, 164, 208, 213, 214, 215, 216, 222, 226, 230, 234, 237, 255, 261, 268], "subnorm": [5, 110, 212], "k": [5, 40, 100, 110, 135, 147, 182, 183, 196, 212, 238, 242, 243, 244, 252, 254, 255, 256, 258, 266], "denorm": [5, 110, 212], "gradual": [5, 110, 212, 266], "underflow": [5, 9, 93, 104, 110, 212, 253], "hardwar": [5, 53, 110, 158, 212, 216, 217, 242, 255, 262, 266], "univers": [5, 110, 211, 212, 217, 262, 266], "mani": [5, 110, 181, 212, 266, 268], "platform": [5, 26, 110, 212], "compil": [5, 110, 179, 208, 211, 212, 215, 266], "toggl": [5, 110, 212], "daz": [5, 110, 212], "flush": [5, 110, 212], "ftz": [5, 110, 212], "increas": [5, 110, 212, 267], "guard": [5, 110, 212], "against": [5, 40, 73, 110, 135, 179, 196, 212, 248, 251, 269], "time": [5, 7, 16, 17, 26, 92, 110, 158, 185, 186, 208, 210, 212, 215, 216, 221, 238, 242, 243, 244, 252, 254, 255, 262, 266, 268], "attack": [5, 110, 212], "accordingli": [5, 10, 11, 13, 14, 16, 17, 59, 61, 62, 64, 66, 75, 88, 93, 99, 104, 110, 125, 126, 128, 137, 139, 140, 141, 144, 147, 154, 158, 160, 163, 169, 173, 175, 185, 186, 187, 188, 190, 196, 205, 212, 213, 214, 215, 217, 246, 252, 260, 262], "vari": [5, 110, 163, 179, 185, 186, 187, 188, 205, 212], "function": [5, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 74, 75, 77, 78, 86, 87, 89, 90, 92, 97, 99, 102, 105, 110, 117, 118, 119, 125, 126, 128, 131, 132, 133, 134, 135, 139, 147, 153, 154, 157, 158, 159, 160, 164, 166, 167, 168, 169, 172, 173, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 190, 191, 195, 198, 208, 210, 211, 213, 214, 215, 216, 217, 220, 221, 222, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 244, 248, 251, 252, 253, 254, 255, 256, 258, 261, 262, 263, 266, 267, 268], "access": [5, 26, 32, 105, 113, 196, 210, 216, 261, 263, 266], "variou": [5, 210], "introspect": 5, "isdtyp": [5, 195, 210], "integr": [5, 63, 77, 116, 118, 119], "keyword": [5, 7, 26, 60, 63, 89, 90, 117, 140, 154, 159, 175, 195, 210, 217, 221, 222, 225, 236, 258, 262, 263, 266, 267, 268], "affect": [5, 15, 49, 214, 217], "calcul": [5, 9, 10, 11, 12, 20, 21, 42, 47, 50, 61, 62, 64, 65, 66, 86, 87, 89, 90, 92, 93, 97, 99, 126, 127, 128, 129, 130, 137, 139, 141, 144, 153, 154, 166, 167, 169, 173, 174, 175, 178, 179, 190, 210, 253], "implementor": [5, 261], "free": [5, 214, 217, 265], "accumul": 5, "reduct": [5, 13, 14], "long": [5, 113, 222], "ha": [5, 9, 13, 14, 20, 23, 29, 34, 35, 40, 44, 47, 55, 77, 86, 87, 88, 89, 90, 93, 97, 98, 99, 104, 107, 135, 139, 140, 143, 144, 145, 147, 153, 154, 166, 167, 171, 173, 175, 176, 178, 179, 180, 181, 185, 186, 187, 188, 190, 196, 205, 208, 213, 216, 217, 220, 221, 239, 246, 254, 255, 258, 260, 262, 263, 266, 268, 269], "wai": [5, 26, 63, 105, 208, 211, 217, 218, 263, 266, 267, 268, 269], "f4": [5, 205], "recommend": [5, 7, 19, 23, 26, 125, 131, 132, 133, 134, 139, 157, 173, 190, 203, 210, 212, 214, 216, 217, 266], "guidanc": [5, 7, 26, 49, 210, 211, 218, 266], "govern": [5, 50, 174, 205, 262, 263], "interact": [5, 213], "either": [5, 9, 10, 11, 12, 24, 26, 35, 40, 65, 77, 87, 89, 90, 93, 96, 97, 99, 101, 104, 105, 110, 113, 119, 120, 121, 125, 126, 127, 128, 129, 130, 135, 137, 138, 141, 142, 144, 146, 154, 157, 164, 165, 166, 169, 175, 178, 179, 180, 192, 196, 212, 213, 214, 218, 222, 253, 258, 266, 267, 269], "exampl": [5, 12, 23, 26, 118, 119, 139, 172, 195, 196, 208, 213, 214, 215, 217, 220, 221, 222, 258, 262, 266, 268, 269], "whether": [5, 13, 14, 26, 59, 60, 63, 75, 79, 89, 90, 91, 105, 114, 119, 122, 125, 139, 155, 159, 165, 210, 217, 238, 242, 243, 252, 254, 261, 265, 266, 268], "otherwis": [5, 13, 14, 15, 16, 17, 26, 59, 60, 63, 75, 88, 105, 114, 116, 118, 137, 139, 141, 154, 158, 159, 163, 164, 173, 175, 190, 191, 192, 195, 196, 208, 217, 238, 240, 246, 253, 254, 260, 265], "note": [5, 7, 9, 10, 11, 12, 13, 14, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 184, 185, 186, 187, 188, 189, 190, 191, 192, 195, 196, 210, 216, 220, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 267, 268, 269], "possibl": [5, 26, 60, 75, 104, 105, 137, 141, 159, 160, 178, 179, 208, 211, 212, 213, 214, 216, 217, 218, 220, 222, 262, 266, 267, 268, 269], "multipl": [5, 7, 13, 14, 16, 17, 40, 42, 44, 88, 89, 135, 137, 139, 141, 144, 145, 154, 173, 175, 190, 196, 208, 211, 213, 216, 217, 221, 222, 243, 244, 262, 263, 266, 268], "In": [5, 12, 19, 26, 59, 89, 90, 93, 96, 104, 119, 121, 122, 139, 144, 148, 154, 157, 164, 175, 195, 196, 198, 205, 212, 213, 214, 216, 218, 233, 234, 252, 253, 255, 258, 262, 263, 267, 268, 269], "clearli": [5, 59, 119, 203, 213, 262, 263], "warn": [5, 158, 218], "about": [5, 7, 26, 101, 111, 214, 262, 266, 268, 269], "organ": [5, 210, 262, 267, 268], "within": [5, 15, 27, 196, 205, 208, 210, 213, 217, 224, 226, 229, 230, 233, 234, 235, 237, 266], "accord": [5, 12, 60, 71, 75, 89, 90, 93, 101, 104, 106, 125, 144, 153, 160, 163, 164, 173, 177, 190, 191, 192, 196, 210, 212, 213], "These": [5, 214, 242, 267], "intend": [5, 89, 90, 154, 175, 208, 258], "posit": [7, 9, 10, 11, 13, 14, 20, 46, 62, 65, 66, 81, 93, 98, 100, 101, 104, 121, 126, 128, 143, 144, 147, 157, 161, 165, 167, 169, 179, 195, 196, 208, 210, 212, 222, 236, 238, 252, 267], "paramet": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 208, 210, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 262], "extern": [7, 268], "usabl": 7, "accept": [7, 26, 131, 132, 133, 134, 139, 157, 173, 190, 208, 263], "argument": [7, 10, 11, 12, 26, 40, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 85, 86, 89, 90, 93, 96, 104, 108, 109, 110, 117, 123, 124, 126, 128, 130, 131, 133, 134, 135, 138, 142, 144, 148, 153, 154, 157, 159, 160, 163, 166, 169, 174, 175, 178, 179, 180, 192, 195, 205, 212, 216, 217, 224, 225, 226, 229, 230, 233, 234, 235, 236, 237, 258, 262, 266, 267, 268], "map": [7, 213, 214], "base": [7, 47, 57, 58, 97, 98, 126, 127, 128, 129, 153, 185, 186, 187, 188, 196, 210, 214, 220, 222, 262, 263, 266, 267, 268], "sole": [7, 196, 203, 262], "incompat": [7, 26, 74, 105, 208, 263, 266], "normal": [7, 78, 172, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237], "practic": [7, 19, 196, 262, 267], "avail": [7, 105, 117, 208, 216, 261, 263, 267], "still": [7, 26, 222, 262, 267, 268, 269], "consid": [7, 26, 63, 105, 131, 132, 133, 134, 185, 186, 187, 188, 213, 217, 236, 251, 262, 266, 268, 269], "compliant": [7, 26, 51, 93, 99, 105, 125, 128, 131, 132, 133, 134, 137, 138, 139, 141, 142, 173, 190, 212, 215, 217, 263, 266], "altern": [7, 214, 216, 269], "thei": [7, 26, 205, 211, 214, 216, 217, 221, 222, 261, 262, 263, 266, 268, 269], "were": [7, 104, 158, 163, 210, 266], "option": [7, 13, 14, 15, 16, 17, 23, 26, 57, 58, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 195, 210, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 262, 267, 268], "lead": [7, 104, 213, 252, 255, 266], "readabl": [7, 205, 262, 267], "code": [7, 59, 205, 214, 215, 217, 220, 222, 262, 266, 267, 268], "easier": [7, 208, 214, 262], "evolv": [7, 208, 262], "over": [7, 13, 14, 26, 88, 125, 137, 139, 141, 154, 173, 175, 176, 180, 190, 191, 196, 212, 213, 214, 216, 217, 221, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 258, 260, 262, 266], "ad": [7, 9, 10, 11, 12, 13, 14, 20, 21, 24, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 77, 79, 85, 86, 87, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 114, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 138, 139, 140, 142, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 157, 160, 162, 164, 166, 167, 169, 170, 174, 175, 178, 179, 180, 185, 186, 187, 188, 191, 192, 196, 209, 210, 211, 217, 225, 236, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "worri": 7, "xi": [7, 140], "annot": [7, 210, 222, 266], "individu": [7, 139, 196, 217, 220, 221, 222, 225, 236, 266, 267], "aim": [7, 211, 222, 261, 262, 263, 266, 267, 268, 269], "strongli": [7, 214, 268], "look": [7, 268], "like": [7, 196, 208, 211, 213, 220, 222, 263, 266, 267, 268], "funcnam": 7, "key1": 7, "key2": 7, "none": [7, 13, 14, 15, 16, 17, 23, 26, 32, 49, 57, 58, 59, 60, 63, 77, 78, 83, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 114, 116, 118, 125, 137, 139, 141, 149, 150, 154, 158, 159, 161, 163, 173, 175, 176, 190, 193, 194, 196, 210, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 246, 248, 251, 258, 260, 266, 267, 269], "out": [7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 210, 211, 214, 216, 220, 221, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 265, 268], "int": [7, 12, 13, 14, 15, 16, 17, 18, 21, 22, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 74, 77, 78, 85, 88, 89, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 123, 124, 125, 130, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 151, 153, 154, 157, 158, 159, 160, 161, 168, 171, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 189, 190, 191, 192, 193, 196, 205, 220, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 239, 241, 246, 247, 257, 258, 259, 260, 267], "str": [7, 8, 23, 118, 119, 140, 267], "modulo": 7, "self": [7, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 91, 210, 268], "few": [7, 212, 220, 266, 268], "enhanc": 7, "default": [7, 13, 14, 15, 16, 17, 18, 23, 26, 59, 60, 63, 77, 78, 88, 89, 90, 92, 94, 95, 100, 102, 105, 106, 107, 115, 116, 118, 125, 137, 139, 140, 141, 147, 149, 150, 154, 158, 159, 161, 163, 168, 172, 173, 175, 177, 180, 182, 183, 185, 186, 187, 189, 190, 191, 193, 194, 195, 196, 210, 212, 217, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 246, 248, 251, 252, 255, 258, 260], "form": [7, 23, 26, 40, 79, 135, 136, 182, 183, 196, 214, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 263, 267], "question": [7, 211, 266], "commonli": [7, 173, 190, 196, 211, 213, 215, 261, 262, 266, 267], "written": [7, 208, 266, 268], "yyyi": [8, 23, 263], "mm": [8, 23, 263], "string": [8, 23, 118, 119, 210, 263, 266], "version": [8, 9, 10, 11, 12, 13, 14, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 195, 208, 211, 217, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 264, 266, 268], "absolut": [9, 20, 85, 164, 212, 214, 246, 247, 253, 262], "x_i": [9, 10, 11, 61, 62, 64, 66, 68, 76, 77, 79, 86, 87, 97, 99, 103, 112, 120, 121, 122, 126, 127, 128, 129, 132, 137, 139, 141, 145, 152, 155, 156, 162, 164, 165, 166, 167, 169, 170, 173, 178, 179, 184, 190], "input": [9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 26, 30, 41, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 110, 112, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 203, 208, 210, 213, 215, 217, 218, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 255, 256, 258, 260, 262, 266, 268], "magnitud": [9, 12, 20, 85, 93, 104, 110, 144, 210, 255, 256], "represent": [9, 12, 20, 29, 44, 67, 70, 72, 80, 81, 82, 84, 93, 101, 104, 111, 144, 145, 146, 178, 179, 210, 216, 267], "known": [9, 164, 212, 215, 216], "norm": [9, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 260, 262], "modulu": [9, 157], "z": [9, 10, 11, 61, 62, 64, 66, 126, 213], "bj": [9, 12, 79, 93, 144], "comput": [9, 12, 28, 31, 33, 37, 39, 40, 43, 57, 58, 67, 70, 72, 79, 88, 89, 90, 91, 92, 93, 96, 98, 104, 108, 109, 110, 123, 124, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 144, 145, 147, 148, 152, 154, 158, 173, 175, 180, 185, 186, 187, 188, 190, 191, 196, 210, 212, 215, 220, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 242, 243, 244, 246, 248, 251, 252, 253, 254, 255, 256, 258, 260, 262, 266], "operatornam": [9, 10, 11, 61, 62, 64, 66, 86, 87, 164, 166, 167, 178, 179, 213, 242, 243, 253, 255], "sqrt": [9, 10, 11, 61, 62, 195, 210, 212, 213, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 260], "take": [9, 126, 128, 153, 169, 195, 210, 217, 222, 266], "care": [9, 262], "undu": [9, 215], "overflow": [9, 12, 89, 90, 93, 104, 110, 125, 154, 175, 205, 253, 258, 262], "dure": [9, 40, 59, 110, 135, 173, 190, 205, 208, 251, 266, 267], "stage": [9, 110, 263], "contain": [9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 26, 28, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 99, 103, 104, 105, 108, 109, 110, 112, 113, 114, 116, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 190, 191, 193, 196, 210, 212, 213, 214, 216, 220, 221, 225, 226, 227, 230, 231, 234, 236, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 266, 268], "nan": [9, 10, 11, 12, 13, 14, 24, 25, 35, 61, 62, 63, 64, 65, 66, 76, 77, 85, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 122, 126, 127, 128, 129, 130, 137, 138, 139, 141, 142, 144, 146, 148, 153, 157, 162, 163, 164, 165, 166, 167, 169, 173, 178, 179, 184, 185, 186, 187, 188, 190, 195, 203, 210, 213, 266], "infin": [9, 10, 11, 12, 13, 14, 24, 25, 35, 62, 63, 64, 65, 66, 76, 81, 86, 87, 93, 96, 97, 99, 103, 104, 110, 120, 121, 126, 127, 128, 129, 130, 137, 141, 144, 148, 153, 157, 162, 165, 166, 167, 169, 178, 179, 184, 213, 253, 260], "imag": [9, 10, 11, 12, 24, 62, 63, 66, 87, 96, 97, 99, 120, 121, 122, 125, 126, 128, 139, 148, 162, 164, 167, 169, 179, 195, 210, 211, 266, 267, 268], "finit": [9, 10, 11, 12, 25, 35, 42, 62, 65, 66, 87, 93, 96, 97, 99, 104, 110, 114, 120, 121, 126, 128, 144, 148, 153, 157, 165, 167, 169, 179, 212], "2022": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 35, 40, 42, 43, 44, 46, 47, 50, 51, 60, 61, 62, 63, 64, 66, 79, 86, 87, 93, 96, 97, 99, 100, 101, 106, 107, 111, 112, 119, 120, 121, 122, 125, 126, 127, 128, 129, 135, 140, 144, 145, 147, 148, 149, 150, 152, 153, 154, 155, 162, 164, 166, 167, 169, 170, 174, 175, 176, 178, 179, 180, 185, 186, 187, 188, 191, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260], "12": [9, 10, 11, 12, 13, 14, 20, 21, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 37, 39, 40, 42, 43, 44, 46, 47, 50, 51, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 86, 87, 88, 89, 90, 92, 93, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 158, 160, 162, 163, 164, 165, 166, 167, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 185, 186, 187, 188, 189, 191, 192, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258, 260, 263], "approxim": [10, 11, 47, 61, 62, 64, 65, 66, 86, 87, 97, 99, 104, 126, 127, 128, 129, 153, 166, 167, 178, 179, 212, 248, 251], "princip": [10, 11, 61, 62, 64, 66, 126, 169, 213, 262], "invers": [10, 11, 61, 62, 64, 65, 66, 213, 224, 226, 229, 230, 231, 232, 233, 234, 235, 237, 244, 247, 251, 262], "cosin": [10, 11, 86, 87, 179], "express": [10, 61, 63, 64, 65, 86, 166, 178, 196, 205, 214, 262, 265], "radian": [10, 61, 64, 65, 86, 166, 178], "arc": [10, 61, 64], "frac": [10, 11, 61, 62, 64, 66, 86, 87, 93, 125, 127, 129, 164, 166, 167, 178, 179, 213, 253], "pi": [10, 11, 61, 62, 64, 66, 87, 126, 128, 167, 178, 179, 195], "j": [10, 11, 12, 25, 61, 62, 64, 66, 87, 93, 97, 99, 125, 126, 128, 139, 144, 163, 164, 166, 167, 169, 178, 179, 196, 213, 242, 255, 258], "ln": [10, 11, 61, 62, 64, 66, 126], "zj": [10, 61, 62, 64, 66], "conj": [10, 11, 61, 62, 64, 66, 87, 97, 99, 126, 127, 128, 129, 167, 169, 179, 195, 210], "multi": [10, 11, 61, 62, 64, 66, 195, 213, 216, 217, 239, 268], "branch": [10, 11, 61, 62, 64, 65, 66, 86, 87, 93, 97, 99, 126, 128, 144, 153, 166, 167, 169, 178, 179, 266], "cut": [10, 11, 61, 62, 64, 66, 86, 87, 97, 99, 126, 128, 153, 166, 167, 169, 178, 179, 266], "plane": [10, 11, 61, 62, 64, 66, 86, 87, 93, 97, 99, 144, 166, 167, 169, 178, 179, 266], "By": [10, 11, 13, 14, 61, 62, 64, 65, 66, 88, 89, 90, 126, 128, 137, 139, 141, 153, 154, 169, 173, 175, 190, 191, 212, 213, 239, 262, 267], "place": [10, 11, 15, 60, 61, 62, 63, 64, 66, 94, 95, 100, 105, 106, 107, 125, 149, 150, 161, 193, 194, 195, 203, 205, 210, 214, 217, 225, 236, 251], "line": [10, 11, 61, 62, 64, 66, 178, 179, 205, 213, 266, 267, 268, 269], "segment": [10, 11, 61, 62, 64, 66, 213], "infti": [10, 11, 61, 62, 64, 66, 86, 126, 128, 153, 169, 213], "axi": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 98, 102, 126, 128, 137, 139, 141, 143, 153, 154, 158, 161, 168, 169, 171, 172, 173, 175, 176, 177, 180, 181, 189, 190, 191, 195, 210, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 239, 246, 259, 260, 266], "rang": [10, 61, 62, 64, 66, 77, 89, 90, 126, 128, 154, 169, 175, 196, 210, 216, 258, 266], "strip": [10, 61, 62, 64, 66, 126, 128], "unbound": [10, 61, 62, 64, 66, 126, 128], "along": [10, 11, 13, 14, 16, 17, 18, 61, 62, 64, 66, 78, 88, 89, 90, 92, 100, 102, 126, 128, 137, 139, 141, 154, 158, 161, 168, 169, 172, 173, 175, 176, 177, 178, 179, 181, 189, 190, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 258, 260, 262], "c99": [10, 11, 61, 62, 64, 66, 93, 126, 128, 144, 153, 169, 213, 263], "provision": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "statu": [10, 11, 61, 62, 64, 66, 126, 128, 153, 169, 213], "greater": [10, 11, 33, 38, 48, 61, 62, 65, 66, 69, 71, 77, 85, 93, 103, 104, 126, 128, 153, 157, 163, 164, 165, 167, 169, 171, 179, 195, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 247], "than": [10, 11, 19, 26, 32, 38, 40, 47, 48, 49, 55, 61, 62, 63, 65, 66, 69, 71, 76, 77, 85, 89, 90, 92, 93, 101, 102, 103, 104, 105, 126, 127, 128, 129, 135, 139, 144, 153, 154, 157, 163, 164, 165, 167, 169, 171, 173, 175, 176, 179, 184, 185, 186, 187, 188, 190, 196, 205, 208, 211, 214, 217, 218, 221, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 246, 247, 248, 251, 258, 260, 262, 263, 266, 268], "less": [10, 11, 39, 47, 61, 65, 66, 76, 85, 93, 104, 126, 127, 128, 129, 153, 157, 163, 164, 165, 169, 173, 190, 195, 196, 210, 214, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 246, 247, 248, 251, 260, 266], "\u03c0": [10, 64, 65, 84], "0j": [10, 11, 12, 25, 62, 63, 66, 87, 97, 99, 100, 126, 128, 149, 150, 164, 167, 169, 179, 213, 253], "nonzero": [10, 11, 12, 62, 66, 87, 93, 97, 99, 104, 144, 167, 179, 195, 196, 210, 251], "3\u03c0": [10, 65], "hyperbol": [11, 62, 66, 86, 87, 166, 167, 178, 179, 213], "aco": [11, 61, 195, 210, 212], "simpli": [11, 99, 128, 211, 222, 266, 268], "upper": [11, 77, 100, 183, 210, 238, 252], "half": [11, 15, 66, 125, 143, 169, 180, 196, 227], "area": [11, 62, 66], "sector": [11, 62, 66], "\u03c0j": [11, 62, 66, 126, 128], "3\u03c0j": [11, 126, 128], "sum": [12, 21, 90, 110, 130, 154, 195, 210, 246, 258, 260, 262], "x1_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "x2_i": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 174, 192, 210], "union": [12, 13, 14, 15, 21, 22, 26, 28, 30, 31, 32, 33, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 59, 60, 65, 67, 69, 70, 71, 72, 75, 77, 78, 85, 88, 93, 94, 96, 101, 102, 104, 106, 107, 108, 109, 110, 111, 118, 119, 123, 124, 125, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 144, 146, 148, 149, 153, 154, 157, 158, 160, 161, 171, 172, 173, 174, 175, 180, 190, 192, 193, 227, 231, 246, 248, 251, 260, 267], "first": [12, 16, 17, 19, 65, 67, 69, 70, 71, 72, 89, 90, 92, 96, 108, 109, 110, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 148, 153, 161, 172, 174, 178, 179, 180, 185, 186, 187, 191, 192, 196, 213, 239, 242, 250, 252, 253, 255, 256, 262, 266, 267, 268, 269], "At": [12, 65, 67, 69, 70, 71, 72, 85, 93, 96, 104, 108, 109, 110, 123, 124, 130, 131, 133, 134, 138, 142, 144, 146, 148, 153, 157, 160, 174, 192], "least": [12, 40, 65, 67, 69, 70, 71, 72, 85, 88, 93, 96, 104, 108, 109, 110, 118, 119, 123, 124, 130, 131, 133, 134, 135, 138, 142, 144, 146, 147, 148, 153, 157, 160, 174, 185, 186, 187, 188, 192, 196, 211, 212, 251], "remain": [12, 93, 96, 104, 119, 121, 122, 144, 148, 157, 159, 164, 196, 214, 237], "neither": [12, 40, 93, 104, 135, 144, 180, 255, 267], "nor": [12, 93, 104, 144, 255, 267], "mathemat": [12, 19, 65, 84, 86, 87, 93, 99, 104, 126, 128, 144, 166, 167, 178, 179, 195, 213, 246, 260], "round": [12, 15, 76, 93, 103, 104, 144, 169, 184, 195, 210, 212], "nearest": [12, 93, 144, 162, 184, 212], "mode": [12, 93, 144, 212, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 252], "too": [12, 26, 93, 104, 144, 262, 266], "larg": [12, 93, 104, 144, 216, 222, 253, 266], "appropri": [12, 26, 93, 104, 144, 213, 218], "commut": 12, "associ": [12, 42, 144, 198, 205, 248, 251, 254, 262, 265, 267], "tabl": [12, 93, 144, 195], "c": [12, 93, 96, 125, 144, 147, 148, 158, 172, 173, 179, 190, 196, 210, 213, 216, 219, 238, 242, 243, 244, 252, 254, 255, 263, 265, 266, 268], "d": [12, 93, 96, 125, 144, 148, 205, 225, 236], "dj": [12, 93, 144], "independ": [12, 93, 139, 144, 162, 196, 208, 216, 239, 252, 254, 262, 263, 266], "abov": [12, 89, 90, 93, 96, 126, 128, 144, 148, 153, 154, 169, 175, 182, 183, 196, 205, 213, 214, 216, 217, 220, 241, 242, 258, 262, 265, 268], "similarli": [12, 57, 119, 139, 140, 238, 255], "henc": [12, 77, 79, 98, 147, 158, 185, 186, 187, 188, 196, 211, 213, 215, 216, 220, 221, 222, 266, 268], "z1": 12, "z2": 12, "2024": [12, 26, 28, 31, 32, 33, 37, 39, 43, 65, 67, 69, 70, 71, 72, 74, 75, 77, 79, 85, 88, 89, 90, 92, 93, 96, 104, 108, 109, 110, 114, 123, 124, 130, 131, 133, 134, 138, 139, 142, 144, 146, 148, 153, 155, 156, 157, 160, 163, 174, 176, 177, 192, 225, 236, 254], "keepdim": [13, 14, 16, 17, 88, 137, 139, 141, 154, 173, 175, 190, 246, 260], "test": [13, 14, 91, 120, 121, 122, 139, 210, 212, 264, 266, 267, 268], "evalu": [13, 14, 22, 30, 36, 38, 41, 44, 45, 46, 48, 51, 52, 97, 99, 126, 127, 128, 129, 145, 152, 164, 165, 170, 208, 266], "ax": [13, 14, 16, 17, 19, 55, 56, 88, 89, 90, 102, 137, 139, 141, 143, 151, 154, 161, 171, 173, 175, 176, 180, 181, 190, 191, 196, 210, 226, 227, 230, 231, 234, 237, 239, 246, 251, 254, 257, 260], "logic": [13, 14, 24, 26, 93, 96, 131, 132, 133, 134, 144, 148, 217, 220, 226, 230, 234, 237], "AND": [13, 67, 96, 131, 265], "entir": [13, 14, 86, 87, 88, 97, 99, 137, 139, 141, 154, 166, 167, 173, 175, 190], "valid": [13, 14, 26, 27, 92, 98, 117, 143, 163, 172, 180, 189, 196, 212, 220, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 242, 252, 255, 267], "count": [13, 14, 78, 88, 89, 90, 92, 102, 176, 177, 185, 186, 191, 196, 210, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 243], "last": [13, 14, 18, 19, 55, 78, 89, 90, 92, 102, 161, 168, 172, 176, 177, 180, 191, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 239, 241, 246, 252, 255, 258], "invalid": [13, 14, 23, 92, 98, 218, 266], "wa": [13, 14, 19, 26, 88, 104, 137, 139, 141, 154, 173, 175, 190, 205, 217, 222, 266, 268], "OR": [14, 24, 70, 133, 148, 265], "start": [15, 125, 196, 210, 222, 266, 268], "stop": [15, 125, 196, 210, 267], "step": [15, 125, 196, 267], "evenli": [15, 125], "space": [15, 125, 225, 227, 236], "open": [15, 125, 143, 180, 196], "inclus": [15, 196, 266], "end": [15, 65, 86, 125, 164, 166, 178, 179, 203, 214, 253, 266, 267, 268], "exclus": [15, 196], "distanc": [15, 110], "adjac": 15, "output": [15, 60, 63, 75, 78, 89, 90, 94, 95, 98, 100, 102, 105, 106, 107, 114, 125, 140, 149, 150, 159, 161, 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109, 123, 124, 148, 269], "undefin": [28, 31, 33, 37, 39, 43, 96, 108, 109, 123, 124, 148, 205, 262], "outsid": [29, 77, 172, 189, 196, 205, 210, 216], "bound": [29, 77, 176, 177, 196, 205, 210, 222], "divis": [30, 41, 71, 93, 104, 157, 164, 213], "floor_divid": [30, 195, 210], "greater_equ": [31, 195, 210], "kei": [32, 49, 114, 116, 118, 266], "slice": [32, 49, 189, 195, 214], "ellipsi": [32, 49, 196], "semant": [32, 40, 49, 104, 135, 157, 176, 195, 196, 208, 210, 214, 216, 218, 220, 221, 254, 262, 266, 267, 268], "iter": [32, 196, 210], "directli": [32, 266, 268], "__iter__": 32, "sequenc": [32, 60, 78, 125, 172, 180, 189, 196, 210, 226, 227, 230, 231, 234, 237, 257], "clarifi": [32, 59, 74, 77, 137, 141, 176, 185, 186, 187, 192, 210, 254], "pep": [34, 40, 104, 135, 216, 263], "357": 34, "overflowerror": 35, "bitwise_invert": [36, 195], "less_equ": [37, 195, 210], "bitwise_left_shift": [38, 195, 210], "matrix": [40, 55, 135, 136, 140, 180, 182, 183, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 262, 266], "product": [40, 42, 58, 89, 135, 144, 154, 180, 191, 210, 239, 250, 262], "built": [40, 135, 196, 205, 266], "465": [40, 135], "m": [40, 55, 92, 135, 136, 140, 158, 163, 180, 181, 182, 183, 196, 224, 226, 228, 229, 230, 232, 233, 234, 235, 237, 238, 240, 241, 242, 243, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 258], "remov": [40, 135, 171, 196, 213, 241, 258], "innermost": [40, 135, 136, 182, 183, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258], "conjug": [40, 79, 135, 180, 191, 210, 238, 242, 255, 262], "transposit": [40, 135, 180], "desir": [40, 63, 75, 135, 143, 180, 212, 213, 216, 222], "prior": [40, 92, 135, 180], "inner": [40, 135, 210, 242, 262], "stack": [40, 55, 135, 136, 182, 183, 195, 221, 238, 240, 241, 242, 243, 244, 246, 247, 248, 251, 252, 253, 254, 255, 256, 258, 262], "l": [40, 135, 238, 258], "remaind": [41, 195, 196, 210], "multipli": [42, 89, 154, 170, 195, 210, 212, 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216, 221, 252, 263, 266, 268], "full": [75, 101, 160, 195, 210, 214, 252, 254, 255, 268], "account": [75, 126, 128, 153, 160, 169, 210, 266], "context": [75, 116, 118, 160, 196, 210, 213, 217, 267], "smallest": [76, 101, 111, 246], "closest": [76, 103, 104, 162], "alreadi": [76, 103, 144, 162, 184, 216, 218, 263, 268], "min": [77, 101, 111, 182, 183, 191, 195, 210, 239, 246, 252, 255, 256, 260], "clamp": [77, 210], "conceptu": [77, 176], "min_i": 77, "max_i": 77, "insid": [77, 210, 222, 261], "join": [78, 172, 205], "befor": [78, 89, 90, 154, 163, 175, 185, 186, 187, 188, 191, 196, 210, 213, 239, 258, 266], "concaten": 78, "leav": [78, 143, 172, 196, 203, 210, 212, 214, 251], "famili": [78, 172], "intxx": [78, 172, 205], "floatxx": [78, 172, 205], "share": [79, 155, 160, 208, 266], "718281828459045": 80, "euler": 80, "constant": [80, 84, 195, 196, 210], "71828182845904523536028747135266249775724709369995": 80, "Not": 82, "alia": [83, 118, 196, 210, 245, 249, 257, 259], 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[210, "id3"], [210, "id6"]], "APIs": [[210, "apis"], [210, "id2"], [210, "id4"], [210, "id7"], [210, "id10"], [210, "id16"], [210, "id20"]], "Scalar Argument Support": [[210, "scalar-argument-support"]], "Extensions": [[210, "extensions"], [210, "id8"], [210, "id13"], [210, "id17"], [210, "id21"], [261, "extensions"]], "Additions": [[210, "additions"], [210, "id9"], [210, "id19"]], "Breaking Changes": [[210, "breaking-changes"], [210, "id12"]], "Errata": [[210, "errata"], [210, "id14"], [210, "id22"]], "v2023.12": [[210, "v2023-12"]], "v2022.12": [[210, "v2022-12"]], "Complex Number Support": [[210, "complex-number-support"], [210, "id18"]], "C API": [[211, "c-api"]], "Example situations for C/Cython usage": [[211, "example-situations-for-c-cython-usage"]], "Situation 1: a Python package that is mostly pure Python, with a limited number of Cython extensions": [[211, "situation-1-a-python-package-that-is-mostly-pure-python-with-a-limited-number-of-cython-extensions"]], "Situation 2: a Python package that contains a lot of Cython code": [[211, "situation-2-a-python-package-that-contains-a-lot-of-cython-code"]], "Situation 3: a Python package that uses the NumPy or Python C API directly": [[211, "situation-3-a-python-package-that-uses-the-numpy-or-python-c-api-directly"]], "Device support": [[211, "device-support"], [217, "device-support"]], "Other longer-term approaches": [[211, "other-longer-term-approaches"]], "Further Python API standardization": [[211, "further-python-api-standardization"]], "HPy": [[211, "hpy"]], "Accuracy": [[212, "accuracy"]], "Arithmetic Operations": [[212, "arithmetic-operations"]], "Mathematical Functions": [[212, "mathematical-functions"]], "Linear Algebra": [[212, "linear-algebra"]], "Operations Involving Complex Numbers": [[212, "operations-involving-complex-numbers"]], "Complex Numbers": [[213, "complex-numbers"]], "The Complex Plane": [[213, "the-complex-plane"]], "Branch Cuts": [[213, "branch-cuts"]], "Complex Number Ordering": [[213, "complex-number-ordering"]], "Valued-based Promotion": [[213, "valued-based-promotion"]], "Copy-view behavior and mutability": [[214, "copy-view-behavior-and-mutability"]], "Mutating views": [[214, null]], "Copy keyword argument behavior": [[214, "copy-keyword-argument-behavior"]], "Data-dependent output shapes": [[215, "data-dependent-output-shapes"]], "Data interchange mechanisms": [[216, "data-interchange-mechanisms"]], "DLPack: An in-memory tensor structure": [[216, "dlpack-an-in-memory-tensor-structure"]], "Non-supported use cases": [[216, "non-supported-use-cases"]], "Intended usage": [[217, "intended-usage"]], "Syntax for device assignment": [[217, "syntax-for-device-assignment"]], "Semantics": [[217, "semantics"]], "Out of scope for device support": [[217, "out-of-scope-for-device-support"]], "Exceptions": [[218, "exceptions"]], "Design topics & constraints": [[219, "design-topics-constraints"], [219, null]], "Lazy vs. eager execution": [[220, "lazy-vs-eager-execution"]], "Parallelism": [[221, "parallelism"]], "Static typing": [[222, "static-typing"]], "Fourier transform Functions": [[223, "fourier-transform-functions"]], "Extension name and usage": [[223, "extension-name-and-usage"], [262, "extension-name-and-usage"]], "fft": [[224, "fft"]], "fftfreq": [[225, "fftfreq"]], "fftn": [[226, "fftn"]], "fftshift": [[227, "fftshift"]], "hfft": [[228, "hfft"]], "ifft": [[229, "ifft"]], "ifftn": [[230, "ifftn"]], "ifftshift": [[231, "ifftshift"]], "ihfft": [[232, "ihfft"]], "irfft": [[233, "irfft"]], "irfftn": [[234, "irfftn"]], "rfft": [[235, "rfft"]], "rfftfreq": [[236, "rfftfreq"]], "rfftn": [[237, "rfftn"]], "cholesky": [[238, "cholesky"]], "cross": [[239, "cross"]], "det": [[240, "det"]], "diagonal": [[241, "diagonal"]], "eigh": [[242, "eigh"]], "eigvalsh": [[243, "eigvalsh"]], "inv": [[244, "inv"]], "matrix_norm": [[246, "matrix-norm"]], "matrix_power": [[247, "matrix-power"]], "matrix_rank": [[248, "matrix-rank"]], "outer": [[250, "outer"]], "pinv": [[251, "pinv"]], "qr": [[252, "qr"]], "slogdet": [[253, "slogdet"]], "solve": [[254, "solve"]], "svd": [[255, "svd"]], "svdvals": [[256, "svdvals"]], "trace": [[258, "trace"]], "vector_norm": [[260, "vector-norm"]], "Extension modules:": [[261, null]], "Linear Algebra Extension": [[262, "linear-algebra-extension"]], "Design Principles": [[262, "design-principles"]], "Future API standard evolution": [[263, "future-api-standard-evolution"]], "Scope extensions": [[263, "scope-extensions"]], "Versioning": [[263, "versioning"]], "Python array API standard": [[264, "python-array-api-standard"]], "Contents": [[264, "contents"]], "Context": [[264, null]], "API": [[264, null]], "Methodology and Usage": [[264, null]], "Other": [[264, null]], "License": [[265, "license"]], "Purpose and scope": [[266, "purpose-and-scope"]], "Introduction": [[266, "introduction"], [267, "introduction"]], "This API standard": [[266, "this-api-standard"]], "History": [[266, "history"]], "Scope (includes out-of-scope / non-goals)": [[266, "scope-includes-out-of-scope-non-goals"]], "In scope": [[266, "in-scope"]], "Out of scope": [[266, "out-of-scope"]], "Implications of in/out of scope": [[266, "implications-of-in-out-of-scope"]], "Stakeholders": [[266, "stakeholders"]], "How to read this document": [[266, "how-to-read-this-document"]], "How to adopt this API": [[266, "how-to-adopt-this-api"]], "Checking an array object for Compliance": [[266, "checking-an-array-object-for-compliance"]], "Discoverability of conforming implementations": [[266, "discoverability-of-conforming-implementations"]], "Optional feature": [[266, null]], "Conformance": [[266, "conformance"]], "Terms and Definitions": [[266, "terms-and-definitions"]], "Normative References": [[266, "normative-references"]], "Usage Data": [[267, "usage-data"]], "Design": [[267, "design"]], "Usage": [[267, "usage"]], "Use in Decision-Making": [[267, "use-in-decision-making"]], "Use cases": [[268, "use-cases"]], "Types of use cases": [[268, "types-of-use-cases"]], "Concrete use cases": [[268, "concrete-use-cases"]], "Use case 1: add hardware accelerator and distributed support to SciPy": [[268, "use-case-1-add-hardware-accelerator-and-distributed-support-to-scipy"]], "Use case 2: simplify einops by removing the backend system": [[268, "use-case-2-simplify-einops-by-removing-the-backend-system"]], "Use case 3: adding a Python API to xtensor": [[268, "use-case-3-adding-a-python-api-to-xtensor"]], "Use case 4: make JIT compilation of array computations easier and more robust": [[268, "use-case-4-make-jit-compilation-of-array-computations-easier-and-more-robust"]], "Verification - test suite": [[269, "verification-test-suite"]], "Measuring conformance": [[269, "measuring-conformance"]], "Running the tests": [[269, "running-the-tests"]]}, "indexentries": {"__array_api_version__ (in module array_api)": [[8, "array_api.__array_api_version__"]], "abs() (in module array_api)": [[9, "array_api.abs"]], "acos() (in module array_api)": [[10, "array_api.acos"]], "acosh() (in module array_api)": [[11, "array_api.acosh"]], "add() (in module array_api)": [[12, "array_api.add"]], "all() (in module array_api)": [[13, "array_api.all"]], "any() (in module array_api)": [[14, "array_api.any"]], "arange() (in module array_api)": [[15, "array_api.arange"]], "argmax() (in module array_api)": [[16, "array_api.argmax"]], "argmin() (in module array_api)": [[17, "array_api.argmin"]], "argsort() (in module array_api)": [[18, "array_api.argsort"]], "t (array property)": [[19, "array_api.array.T"]], "__abs__() (array method)": [[20, "array_api.array.__abs__"]], "__add__() (array method)": [[21, "array_api.array.__add__"]], "__and__() (array method)": [[22, "array_api.array.__and__"]], "__array_namespace__() (array method)": [[23, "array_api.array.__array_namespace__"]], "__bool__() (array method)": [[24, "array_api.array.__bool__"]], "__complex__() (array method)": [[25, "array_api.array.__complex__"]], "__dlpack__() (array method)": [[26, "array_api.array.__dlpack__"]], "__dlpack_device__() (array method)": [[27, "array_api.array.__dlpack_device__"]], "__eq__() (array method)": [[28, "array_api.array.__eq__"]], "__float__() (array method)": [[29, "array_api.array.__float__"]], "__floordiv__() (array method)": [[30, "array_api.array.__floordiv__"]], "__ge__() (array method)": [[31, "array_api.array.__ge__"]], "__getitem__() (array method)": [[32, "array_api.array.__getitem__"]], "__gt__() (array method)": [[33, "array_api.array.__gt__"]], "__index__() (array method)": [[34, "array_api.array.__index__"]], "__int__() (array method)": [[35, "array_api.array.__int__"]], "__invert__() (array method)": [[36, "array_api.array.__invert__"]], "__le__() (array method)": [[37, "array_api.array.__le__"]], "__lshift__() (array method)": [[38, "array_api.array.__lshift__"]], "__lt__() (array method)": [[39, "array_api.array.__lt__"]], "__matmul__() (array method)": [[40, "array_api.array.__matmul__"]], "__mod__() (array method)": [[41, "array_api.array.__mod__"]], "__mul__() (array method)": [[42, "array_api.array.__mul__"]], "__ne__() (array method)": [[43, "array_api.array.__ne__"]], "__neg__() (array method)": [[44, "array_api.array.__neg__"]], "__or__() (array method)": [[45, "array_api.array.__or__"]], "__pos__() (array method)": [[46, "array_api.array.__pos__"]], "__pow__() (array method)": [[47, "array_api.array.__pow__"]], "__rshift__() (array method)": [[48, "array_api.array.__rshift__"]], "__setitem__() (array method)": [[49, "array_api.array.__setitem__"]], "__sub__() (array method)": [[50, "array_api.array.__sub__"]], "__truediv__() (array method)": [[51, "array_api.array.__truediv__"]], "__xor__() (array method)": [[52, "array_api.array.__xor__"]], "device (array property)": [[53, "array_api.array.device"]], "dtype (array property)": [[54, "array_api.array.dtype"]], "mt (array property)": [[55, "array_api.array.mT"]], "ndim (array property)": [[56, "array_api.array.ndim"]], "shape (array property)": [[57, "array_api.array.shape"]], "size (array property)": [[58, "array_api.array.size"]], "to_device() (array method)": [[59, "array_api.array.to_device"]], "asarray() (in module array_api)": [[60, "array_api.asarray"]], "asin() (in module array_api)": [[61, "array_api.asin"]], "asinh() (in module array_api)": [[62, "array_api.asinh"]], "astype() (in module array_api)": [[63, "array_api.astype"]], "atan() (in module array_api)": [[64, "array_api.atan"]], "atan2() (in module array_api)": [[65, "array_api.atan2"]], "atanh() (in module array_api)": [[66, "array_api.atanh"]], "bitwise_and() (in module array_api)": [[67, "array_api.bitwise_and"]], "bitwise_invert() (in module array_api)": [[68, "array_api.bitwise_invert"]], "bitwise_left_shift() (in module array_api)": [[69, "array_api.bitwise_left_shift"]], "bitwise_or() (in module array_api)": [[70, "array_api.bitwise_or"]], "bitwise_right_shift() (in module array_api)": [[71, "array_api.bitwise_right_shift"]], "bitwise_xor() (in module array_api)": [[72, "array_api.bitwise_xor"]], "broadcast_arrays() (in module array_api)": [[73, "array_api.broadcast_arrays"]], "broadcast_to() (in module array_api)": [[74, "array_api.broadcast_to"]], "can_cast() (in module array_api)": [[75, "array_api.can_cast"]], "ceil() (in module array_api)": [[76, "array_api.ceil"]], "clip() (in module array_api)": [[77, "array_api.clip"]], "concat() (in module array_api)": [[78, "array_api.concat"]], "conj() (in module array_api)": [[79, "array_api.conj"]], "e (in module array_api.constants)": [[80, "array_api.constants.e"]], "inf (in module array_api.constants)": [[81, "array_api.constants.inf"]], "nan (in module array_api.constants)": [[82, "array_api.constants.nan"]], "newaxis (in module array_api.constants)": [[83, "array_api.constants.newaxis"]], "pi (in module array_api.constants)": [[84, "array_api.constants.pi"]], "copysign() (in module array_api)": [[85, "array_api.copysign"]], "cos() (in module array_api)": [[86, "array_api.cos"]], "cosh() (in module array_api)": [[87, "array_api.cosh"]], "count_nonzero() (in module array_api)": [[88, "array_api.count_nonzero"]], "cumulative_prod() (in module array_api)": [[89, "array_api.cumulative_prod"]], "cumulative_sum() (in module array_api)": [[90, "array_api.cumulative_sum"]], "__eq__() (in module array_api.data_types)": [[91, "array_api.data_types.__eq__"]], "diff() (in module array_api)": [[92, "array_api.diff"]], "divide() (in module array_api)": [[93, "array_api.divide"]], "empty() (in module array_api)": [[94, "array_api.empty"]], "empty_like() (in module array_api)": [[95, "array_api.empty_like"]], "equal() (in module array_api)": [[96, "array_api.equal"]], "exp() (in module array_api)": [[97, "array_api.exp"]], "expand_dims() (in module array_api)": [[98, "array_api.expand_dims"]], "expm1() (in module array_api)": [[99, "array_api.expm1"]], "eye() (in module array_api)": [[100, "array_api.eye"]], "finfo() (in module array_api)": [[101, "array_api.finfo"]], "flip() (in module array_api)": [[102, "array_api.flip"]], "floor() (in module array_api)": [[103, "array_api.floor"]], "floor_divide() (in module array_api)": [[104, "array_api.floor_divide"]], "from_dlpack() (in module array_api)": [[105, "array_api.from_dlpack"]], "full() (in module array_api)": [[106, "array_api.full"]], "full_like() (in module array_api)": [[107, "array_api.full_like"]], "greater() (in module array_api)": [[108, "array_api.greater"]], "greater_equal() (in module array_api)": [[109, "array_api.greater_equal"]], "hypot() (in module array_api)": [[110, "array_api.hypot"]], "iinfo() (in module array_api)": [[111, "array_api.iinfo"]], "imag() (in module array_api)": [[112, "array_api.imag"]], "__array_namespace_info__() (in module array_api.info)": [[113, "array_api.info.__array_namespace_info__"]], "capabilities() (in module array_api.info)": [[114, "array_api.info.capabilities"]], "default_device() (in module array_api.info)": [[115, "array_api.info.default_device"]], "default_dtypes() (in module array_api.info)": [[116, "array_api.info.default_dtypes"]], "devices() (in module array_api.info)": [[117, "array_api.info.devices"]], "dtypes() (in module array_api.info)": [[118, "array_api.info.dtypes"]], "isdtype() (in module array_api)": [[119, "array_api.isdtype"]], "isfinite() (in module array_api)": [[120, "array_api.isfinite"]], "isinf() (in module array_api)": [[121, "array_api.isinf"]], "isnan() (in module array_api)": [[122, "array_api.isnan"]], "less() (in module array_api)": [[123, "array_api.less"]], "less_equal() (in module array_api)": [[124, "array_api.less_equal"]], "linspace() (in module array_api)": [[125, "array_api.linspace"]], "log() (in module array_api)": [[126, "array_api.log"]], "log10() (in module array_api)": [[127, "array_api.log10"]], "log1p() (in module array_api)": [[128, "array_api.log1p"]], "log2() (in module array_api)": [[129, "array_api.log2"]], "logaddexp() (in module array_api)": [[130, "array_api.logaddexp"]], "logical_and() (in module array_api)": [[131, "array_api.logical_and"]], "logical_not() (in module array_api)": [[132, "array_api.logical_not"]], "logical_or() (in module array_api)": [[133, "array_api.logical_or"]], "logical_xor() (in module array_api)": [[134, "array_api.logical_xor"]], "matmul() (in module array_api)": [[135, "array_api.matmul"]], "matrix_transpose() (in module array_api)": [[136, "array_api.matrix_transpose"]], "max() (in module array_api)": [[137, "array_api.max"]], "maximum() (in module array_api)": [[138, "array_api.maximum"]], "mean() (in module array_api)": [[139, "array_api.mean"]], "meshgrid() (in module array_api)": [[140, "array_api.meshgrid"]], "min() (in module array_api)": [[141, "array_api.min"]], "minimum() (in module array_api)": [[142, "array_api.minimum"]], "moveaxis() (in module array_api)": [[143, "array_api.moveaxis"]], "multiply() (in module array_api)": [[144, "array_api.multiply"]], "negative() (in module array_api)": [[145, "array_api.negative"]], "nextafter() (in module array_api)": [[146, "array_api.nextafter"]], "nonzero() (in module array_api)": [[147, "array_api.nonzero"]], "not_equal() (in module array_api)": [[148, "array_api.not_equal"]], "ones() (in module array_api)": [[149, "array_api.ones"]], "ones_like() (in module array_api)": [[150, "array_api.ones_like"]], "permute_dims() (in module array_api)": [[151, "array_api.permute_dims"]], "positive() (in module array_api)": [[152, "array_api.positive"]], "pow() (in module array_api)": [[153, "array_api.pow"]], "prod() (in module array_api)": [[154, "array_api.prod"]], "real() (in module array_api)": [[155, "array_api.real"]], "reciprocal() (in module array_api)": [[156, "array_api.reciprocal"]], "remainder() (in module array_api)": [[157, "array_api.remainder"]], "repeat() (in module array_api)": [[158, "array_api.repeat"]], "reshape() (in module array_api)": [[159, "array_api.reshape"]], "result_type() (in module array_api)": [[160, "array_api.result_type"]], "roll() (in module array_api)": [[161, "array_api.roll"]], "round() (in module array_api)": [[162, "array_api.round"]], "searchsorted() (in module array_api)": [[163, "array_api.searchsorted"]], "sign() (in module array_api)": [[164, "array_api.sign"]], "signbit() (in module array_api)": [[165, "array_api.signbit"]], "sin() (in module array_api)": [[166, "array_api.sin"]], "sinh() (in module array_api)": [[167, "array_api.sinh"]], "sort() (in module array_api)": [[168, "array_api.sort"]], "sqrt() (in module array_api)": [[169, "array_api.sqrt"]], "square() (in module array_api)": [[170, "array_api.square"]], "squeeze() (in module array_api)": [[171, "array_api.squeeze"]], "stack() (in module array_api)": [[172, "array_api.stack"]], "std() (in module array_api)": [[173, "array_api.std"]], "subtract() (in module array_api)": [[174, "array_api.subtract"]], "sum() (in module array_api)": [[175, "array_api.sum"]], "take() (in module array_api)": [[176, "array_api.take"]], "take_along_axis() (in module array_api)": [[177, "array_api.take_along_axis"]], "tan() (in module array_api)": [[178, "array_api.tan"]], "tanh() (in module array_api)": [[179, "array_api.tanh"]], "tensordot() (in module array_api)": [[180, "array_api.tensordot"]], "tile() (in module array_api)": [[181, "array_api.tile"]], "tril() (in module array_api)": [[182, "array_api.tril"]], "triu() (in module array_api)": [[183, "array_api.triu"]], "trunc() (in module array_api)": [[184, "array_api.trunc"]], "unique_all() (in module array_api)": [[185, "array_api.unique_all"]], "unique_counts() (in module array_api)": [[186, "array_api.unique_counts"]], "unique_inverse() (in module array_api)": [[187, "array_api.unique_inverse"]], "unique_values() (in module array_api)": [[188, "array_api.unique_values"]], "unstack() (in module array_api)": [[189, "array_api.unstack"]], "var() (in module array_api)": [[190, "array_api.var"]], "vecdot() (in module array_api)": [[191, "array_api.vecdot"]], "where() (in module array_api)": [[192, "array_api.where"]], "zeros() (in module array_api)": [[193, "array_api.zeros"]], "zeros_like() (in module array_api)": [[194, "array_api.zeros_like"]], "fft() (in module array_api.fft)": [[224, "array_api.fft.fft"]], "fftfreq() (in module array_api.fft)": [[225, "array_api.fft.fftfreq"]], "fftn() (in module array_api.fft)": [[226, "array_api.fft.fftn"]], "fftshift() (in module array_api.fft)": [[227, "array_api.fft.fftshift"]], "hfft() (in module array_api.fft)": [[228, "array_api.fft.hfft"]], "ifft() (in module array_api.fft)": [[229, "array_api.fft.ifft"]], "ifftn() (in module array_api.fft)": [[230, "array_api.fft.ifftn"]], "ifftshift() (in module array_api.fft)": [[231, "array_api.fft.ifftshift"]], "ihfft() (in module array_api.fft)": [[232, "array_api.fft.ihfft"]], "irfft() (in module array_api.fft)": [[233, "array_api.fft.irfft"]], "irfftn() (in module array_api.fft)": [[234, "array_api.fft.irfftn"]], "rfft() (in module array_api.fft)": [[235, "array_api.fft.rfft"]], "rfftfreq() (in module array_api.fft)": [[236, "array_api.fft.rfftfreq"]], "rfftn() (in module array_api.fft)": [[237, "array_api.fft.rfftn"]], "cholesky() (in module array_api.linalg)": [[238, "array_api.linalg.cholesky"]], "cross() (in module array_api.linalg)": [[239, "array_api.linalg.cross"]], "det() (in module array_api.linalg)": [[240, "array_api.linalg.det"]], "diagonal() (in module array_api.linalg)": [[241, "array_api.linalg.diagonal"]], "eigh() (in module array_api.linalg)": [[242, "array_api.linalg.eigh"]], "eigvalsh() (in module array_api.linalg)": [[243, "array_api.linalg.eigvalsh"]], "inv() (in module array_api.linalg)": [[244, "array_api.linalg.inv"]], "matmul() (in module array_api.linalg)": [[245, "array_api.linalg.matmul"]], "matrix_norm() (in module array_api.linalg)": [[246, "array_api.linalg.matrix_norm"]], "matrix_power() (in module array_api.linalg)": [[247, "array_api.linalg.matrix_power"]], "matrix_rank() (in module array_api.linalg)": [[248, "array_api.linalg.matrix_rank"]], "matrix_transpose() (in module array_api.linalg)": [[249, "array_api.linalg.matrix_transpose"]], "outer() (in module array_api.linalg)": [[250, "array_api.linalg.outer"]], "pinv() (in module array_api.linalg)": [[251, "array_api.linalg.pinv"]], "qr() (in module array_api.linalg)": [[252, "array_api.linalg.qr"]], "slogdet() (in module array_api.linalg)": [[253, "array_api.linalg.slogdet"]], "solve() (in module array_api.linalg)": [[254, "array_api.linalg.solve"]], "svd() (in module array_api.linalg)": [[255, "array_api.linalg.svd"]], "svdvals() (in module array_api.linalg)": [[256, "array_api.linalg.svdvals"]], "tensordot() (in module array_api.linalg)": [[257, "array_api.linalg.tensordot"]], "trace() (in module array_api.linalg)": [[258, "array_api.linalg.trace"]], "vecdot() (in module array_api.linalg)": [[259, "array_api.linalg.vecdot"]], "vector_norm() (in module array_api.linalg)": [[260, "array_api.linalg.vector_norm"]]}})
\ No newline at end of file