XLNSCUDA: a CUDA package for Logarithmic Number System eXperimentation
This repository provides xlns16d.cu and xlns32d.cu along with a few programs that illustrate their use. They are translated from similar routines in the xlnscpp repository. The appropriate C++ file (xlns16.cpp or xlns32.cpp) must be included before including the associated file from this repository. All these routines are based on similar math foundation (Gaussian logs, sb and db) as the Python xlns repository, but unlike the Python they use different internal storage format.
Unlike the Python xlns, here internal representation is not twos complement; it is offset by a constant (xlns16_logsignmask or xlns32_logsignmask). With the 16-bit format of xlns16d.cu, this is roughly similar to bfloat16 (1 sign bit, 8 int(log2) bits, 7 frac(log2) bits). With the 32-bit format of xlns32d.cu, this is roughly similar to float (1 sign bit, 8 int(log2) bits, 23 frac(log2) bits). There is an exact representation of 0.0, but no subnormals or NaNs.
Just as with xlns16.cpp and xlns32.cpp, there are two ways to use this library: function calls (like xlns16d_add or xlns32d_add) that operate on integer representations (typedef as xlns_16 or xlns_32, the same as used in xlns16.cpp and xlns32.cpp) that represent the LNS value; or C++ overloaded operators that operate on an LNS class (either xlns16d_float or xlns32d_float--note different than the C++ version). The functions are a bit faster but overloading is easier.
This CUDA package does not support (ignores) the xlns16_table from the C++ version because it is not practical to share the large tables involved with the many threads in typical CUDA usage. It is allowed to have the host use xlns16_table (for conversions) while the device uses another method of addition. Here only xlns32_ideal is supported; however, non-ideal implementations of addition (both varients of LPVIP, with and without xlns16_alt and xlns16_altopt) are supported in xlns16d.cu.