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libalgebra.h
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libalgebra.h
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// License for libalgebra.h
/*
* Copyright (c) 2019 Marcus D. R. Klarqvist
* Author(s): Marcus D. R. Klarqvist
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
// License for pospopcnt.h
/*
* Copyright (c) 2019
* Author(s): Marcus D. R. Klarqvist, Wojciech Muła, and Daniel Lemire
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
// License for libpopcnt.h
/*
* libpopcnt.h - C/C++ library for counting the number of 1 bits (bit
* population count) in an array as quickly as possible using
* specialized CPU instructions i.e. POPCNT, AVX2, AVX512, NEON.
*
* Copyright (c) 2016 - 2018, Kim Walisch
* Copyright (c) 2016 - 2018, Wojciech Muła
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
* ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef LIBALGEBRA_H_8723467365934
#define LIBALGEBRA_H_8723467365934
/* *************************************
* Includes
***************************************/
#include <stdint.h>
#include <assert.h>
#include <memory.h>
#include <string.h>
#include <math.h>
/* *************************************
* Safety
***************************************/
#if !(defined(__APPLE__)) && !(defined(__FreeBSD__))
#include <malloc.h> // this should never be needed but there are some reports that it is needed.
#endif
#if defined(__SIZEOF_LONG_LONG__) && __SIZEOF_LONG_LONG__ != 8
#error This code assumes 64-bit long longs (by use of the GCC intrinsics). Your system is not currently supported.
#endif
/****************************
* Memory management
*
* The subroutines aligned_malloc and aligned_free had to be renamed to
* STORM_aligned_malloc and STORM_aligned_free to prevent clashing with the
* same subroutines in Roaring. These subroutines are included here
* since there is no hard dependency on using Roaring bitmaps.
*
* These subroutines and definitions are taken from the CRoaring repo
* by Daniel Lemire et al. available under the Apache 2.0 License
* (same as libalgebra.h):
* https://github.com/RoaringBitmap/CRoaring/
****************************/
// portable version of posix_memalign
#ifndef _MSC_VER
#include <x86intrin.h>
#endif
#ifndef STORM_aligned_malloc
static
void* STORM_aligned_malloc(size_t alignment, size_t size) {
void *p;
#ifdef _MSC_VER
p = _aligned_malloc(size, alignment);
#elif defined(__MINGW32__) || defined(__MINGW64__)
p = __mingw_aligned_malloc(size, alignment);
#else
// somehow, if this is used before including "x86intrin.h", it creates an
// implicit defined warning.
if (posix_memalign(&p, alignment, size) != 0)
return NULL;
#endif
return p;
}
#endif
#ifndef STORM_aligned_free
static
void STORM_aligned_free(void* memblock) {
#ifdef _MSC_VER
_aligned_free(memblock);
#elif defined(__MINGW32__) || defined(__MINGW64__)
__mingw_aligned_free(memblock);
#else
free(memblock);
#endif
}
#endif
// portable alignment
#if defined (__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L) /* C11+ */
# include <stdalign.h>
# define STORM_ALIGN(n) alignas(n)
#elif defined(__GNUC__)
# define STORM_ALIGN(n) __attribute__ ((aligned(n)))
#elif defined(_MSC_VER)
# define STORM_ALIGN(n) __declspec(align(n))
#else
# define STORM_ALIGN(n) /* disabled */
#endif
/* *************************************
* Compiler Specific Options
***************************************/
// Taken from XXHASH
#ifdef _MSC_VER /* Visual Studio */
# pragma warning(disable : 4127) /* disable: C4127: conditional expression is constant */
# define STORM_FORCE_INLINE static __forceinline
# define STORM_NO_INLINE static __declspec(noinline)
#else
# if defined (__cplusplus) || defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L /* C99 */
# ifdef __GNUC__
# define STORM_FORCE_INLINE static inline __attribute__((always_inline))
# define STORM_NO_INLINE static __attribute__((noinline))
# else
# define STORM_FORCE_INLINE static inline
# define STORM_NO_INLINE static
# endif
# else
# define STORM_FORCE_INLINE static
# define STORM_NO_INLINE static
# endif /* __STDC_VERSION__ */
#endif
/****************************
* General checks
****************************/
#ifndef __has_builtin
#define STORM_HAS_BUILTIN(x) 0
#else
#define STORM_HAS_BUILTIN(x) __has_builtin(x)
#endif
#ifndef __has_attribute
#define STORM_HAS_ATTRIBUTE(x) 0
#else
#define STORM_HAS_ATTRIBUTE(x) __has_attribute(x)
#endif
// disable noise
#ifdef __GNUC__
#define STORM_WARN_UNUSED __attribute__((warn_unused_result))
#else
#define STORM_WARN_UNUSED
#endif
#if defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L /* >= C99 */
# define STORM_RESTRICT restrict
#else
/* note : it might be useful to define __restrict or STORM_RESTRICT for some C++ compilers */
# define STORM_RESTRICT /* disable */
#endif
#ifdef __GNUC__
#define GNUC_PREREQ(x, y) \
(__GNUC__ > x || (__GNUC__ == x && __GNUC_MINOR__ >= y))
#else
#define GNUC_PREREQ(x, y) 0
#endif
#ifdef __clang__
#define CLANG_PREREQ(x, y) \
(__clang_major__ > x || (__clang_major__ == x && __clang_minor__ >= y))
#else
#define CLANG_PREREQ(x, y) 0
#endif
#if (defined(__i386__) || \
defined(__x86_64__) || \
defined(_M_IX86) || \
defined(_M_X64))
#define X86_OR_X64
#endif
#if defined(X86_OR_X64) && \
(defined(__cplusplus) || \
defined(_MSC_VER) || \
(GNUC_PREREQ(4, 2) || \
STORM_HAS_BUILTIN(__sync_val_compare_and_swap)))
#define STORM_HAVE_CPUID
#endif
#if GNUC_PREREQ(4, 2) || \
STORM_HAS_BUILTIN(__builtin_popcount)
#define STORM_HAVE_BUILTIN_POPCOUNT
#endif
#if GNUC_PREREQ(4, 2) || \
CLANG_PREREQ(3, 0)
#define STORM_HAVE_ASM_POPCNT
#endif
#if defined(STORM_HAVE_CPUID) && \
(defined(STORM_HAVE_ASM_POPCNT) || \
defined(_MSC_VER))
#define STORM_HAVE_POPCNT
#endif
#if defined(STORM_HAVE_CPUID) && \
GNUC_PREREQ(4, 9)
#define STORM_HAVE_SSE42
#define STORM_HAVE_AVX2
#endif
#if defined(STORM_HAVE_CPUID) && \
GNUC_PREREQ(5, 0)
#define STORM_HAVE_AVX512
#endif
#if defined(STORM_HAVE_CPUID) && \
defined(_MSC_VER) && \
defined(__AVX2__)
#define STORM_HAVE_SSE42
#define STORM_HAVE_AVX2
#endif
#if defined(STORM_HAVE_CPUID) && \
defined(_MSC_VER) && \
defined(__AVX512__)
#define STORM_HAVE_AVX512
#endif
#if defined(STORM_HAVE_CPUID) && \
CLANG_PREREQ(3, 8) && \
STORM_HAS_ATTRIBUTE(target) && \
(!defined(_MSC_VER) || defined(__AVX2__)) && \
(!defined(__apple_build_version__) || __apple_build_version__ >= 8000000)
#define STORM_HAVE_SSE42
#define STORM_HAVE_AVX2
#define STORM_HAVE_AVX512
#endif
// Target attribute
#if !defined(_MSC_VER)
#define STORM_TARGET(x) __attribute__ ((target (x)))
#else
#define STORM_TARGET(x) 0
#endif
/****************************
* CPUID and SIMD
****************************/
#define STORM_SSE_ALIGNMENT 16
#define STORM_AVX2_ALIGNMENT 32
#define STORM_AVX512_ALIGNMENT 64
#ifdef __cplusplus
extern "C" {
#endif
#if defined(STORM_HAVE_CPUID)
#if defined(_MSC_VER)
#include <intrin.h>
#include <immintrin.h>
#endif
// CPUID flags. See https://en.wikipedia.org/wiki/CPUID for more info.
/* %ecx bit flags */
#define STORM_CPUID_runtime_bit_POPCNT (1 << 23) // POPCNT instruction
#define STORM_CPUID_runtime_bit_SSE41 (1 << 19) // CPUID.01H:ECX.SSE41[Bit 19]
#define STORM_CPUID_runtime_bit_SSE42 (1 << 20) // CPUID.01H:ECX.SSE41[Bit 20]
/* %ebx bit flags */
#define STORM_CPUID_runtime_bit_AVX2 (1 << 5) // CPUID.(EAX=07H, ECX=0H):EBX.AVX2[bit 5]
#define STORM_CPUID_runtime_bit_AVX512BW (1 << 30) // AVX-512 Byte and Word Instructions
/* xgetbv bit flags */
#define STORM_XSTATE_SSE (1 << 1)
#define STORM_XSTATE_YMM (1 << 2)
#define STORM_XSTATE_ZMM (7 << 5)
static
void STORM_run_cpuid(int eax, int ecx, int* abcd) {
#if defined(_MSC_VER)
__cpuidex(abcd, eax, ecx);
#else
int ebx = 0;
int edx = 0;
#if defined(__i386__) && \
defined(__PIC__)
/* in case of PIC under 32-bit EBX cannot be clobbered */
__asm__ ("movl %%ebx, %%edi;"
"cpuid;"
"xchgl %%ebx, %%edi;"
: "=D" (ebx),
"+a" (eax),
"+c" (ecx),
"=d" (edx));
#else
__asm__ ("cpuid;"
: "+b" (ebx),
"+a" (eax),
"+c" (ecx),
"=d" (edx));
#endif
abcd[0] = eax;
abcd[1] = ebx;
abcd[2] = ecx;
abcd[3] = edx;
#endif
}
#if defined(STORM_HAVE_AVX2) || \
defined(STORM_HAVE_AVX512)
static
int STORM_get_xcr0() {
int xcr0;
#if defined(_MSC_VER)
xcr0 = (int) _xgetbv(0);
#else
__asm__ ("xgetbv" : "=a" (xcr0) : "c" (0) : "%edx" );
#endif
return xcr0;
}
#endif
static
int STORM_get_cpuid() {
int flags = 0;
int abcd[4];
STORM_run_cpuid(1, 0, abcd);
// Check for POPCNT instruction
if ((abcd[2] & STORM_CPUID_runtime_bit_POPCNT) == STORM_CPUID_runtime_bit_POPCNT)
flags |= STORM_CPUID_runtime_bit_POPCNT;
// Check for SSE4.1 instruction set
if ((abcd[2] & STORM_CPUID_runtime_bit_SSE41) == STORM_CPUID_runtime_bit_SSE41)
flags |= STORM_CPUID_runtime_bit_SSE41;
// Check for SSE4.2 instruction set
if ((abcd[2] & STORM_CPUID_runtime_bit_SSE42) == STORM_CPUID_runtime_bit_SSE42)
flags |= STORM_CPUID_runtime_bit_SSE42;
#if defined(STORM_HAVE_AVX2) || \
defined(STORM_HAVE_AVX512)
int osxsave_mask = (1 << 27);
/* ensure OS supports extended processor state management */
if ((abcd[2] & osxsave_mask) != osxsave_mask)
return 0;
int ymm_mask = STORM_XSTATE_SSE | STORM_XSTATE_YMM;
int zmm_mask = STORM_XSTATE_SSE | STORM_XSTATE_YMM | STORM_XSTATE_ZMM;
int xcr0 = STORM_get_xcr0();
if ((xcr0 & ymm_mask) == ymm_mask) {
STORM_run_cpuid(7, 0, abcd);
if ((abcd[1] & STORM_CPUID_runtime_bit_AVX2) == STORM_CPUID_runtime_bit_AVX2)
flags |= STORM_CPUID_runtime_bit_AVX2;
if ((xcr0 & zmm_mask) == zmm_mask) {
if ((abcd[1] & STORM_CPUID_runtime_bit_AVX512BW) == STORM_CPUID_runtime_bit_AVX512BW)
flags |= STORM_CPUID_runtime_bit_AVX512BW;
}
}
#endif
return flags;
}
#endif // defined(STORM_HAVE_CPUID)
/// Taken from libpopcnt.h
#if defined(STORM_HAVE_ASM_POPCNT) && \
defined(__x86_64__)
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT(uint64_t x)
{
__asm__ ("popcnt %1, %0" : "=r" (x) : "0" (x));
return x;
}
#elif defined(STORM_HAVE_ASM_POPCNT) && \
defined(__i386__)
STORM_FORCE_INLINE
uint32_t STORM_popcnt32(uint32_t x)
{
__asm__ ("popcnt %1, %0" : "=r" (x) : "0" (x));
return x;
}
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT(uint64_t x)
{
return STORM_popcnt32((uint32_t) x) +
STORM_popcnt32((uint32_t)(x >> 32));
}
#elif defined(_MSC_VER) && \
defined(_M_X64)
#include <nmmintrin.h>
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT(uint64_t x) {
return _mm_popcnt_u64(x);
}
#elif defined(_MSC_VER) && \
defined(_M_IX86)
#include <nmmintrin.h>
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT(uint64_t x)
{
return _mm_popcnt_u32((uint32_t) x) +
_mm_popcnt_u32((uint32_t)(x >> 32));
}
/* non x86 CPUs */
#elif defined(STORM_HAVE_BUILTIN_POPCOUNT)
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT(uint64_t x) {
return __builtin_popcountll(x);
}
/* no hardware POPCNT,
* use pure integer algorithm */
#else
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT(uint64_t x) {
return STORM_popcount64(x);
}
#endif
static
uint64_t STORM_intersect_count_unrolled(const uint64_t* STORM_RESTRICT data1,
const uint64_t* STORM_RESTRICT data2,
size_t size)
{
const uint64_t limit = size - size % 4;
uint64_t cnt = 0;
uint64_t i = 0;
for (/**/; i < limit; i += 4) {
cnt += STORM_POPCOUNT(data1[i+0] & data2[i+0]);
cnt += STORM_POPCOUNT(data1[i+1] & data2[i+1]);
cnt += STORM_POPCOUNT(data1[i+2] & data2[i+2]);
cnt += STORM_POPCOUNT(data1[i+3] & data2[i+3]);
}
for (/**/; i < size; ++i)
cnt += STORM_POPCOUNT(data1[i] & data2[i]);
return cnt;
}
static
uint64_t STORM_union_count_unrolled(const uint64_t* STORM_RESTRICT data1,
const uint64_t* STORM_RESTRICT data2,
size_t size)
{
const uint64_t limit = size - size % 4;
uint64_t cnt = 0;
uint64_t i = 0;
for (/**/; i < limit; i += 4) {
cnt += STORM_POPCOUNT(data1[i+0] | data2[i+0]);
cnt += STORM_POPCOUNT(data1[i+1] | data2[i+1]);
cnt += STORM_POPCOUNT(data1[i+2] | data2[i+2]);
cnt += STORM_POPCOUNT(data1[i+3] | data2[i+3]);
}
for (/**/; i < size; ++i)
cnt += STORM_POPCOUNT(data1[i] | data2[i]);
return cnt;
}
static
uint64_t STORM_diff_count_unrolled(const uint64_t* STORM_RESTRICT data1,
const uint64_t* STORM_RESTRICT data2,
size_t size)
{
const uint64_t limit = size - size % 4;
uint64_t cnt = 0;
uint64_t i = 0;
for (/**/; i < limit; i += 4) {
cnt += STORM_POPCOUNT(data1[i+0] ^ data2[i+0]);
cnt += STORM_POPCOUNT(data1[i+1] ^ data2[i+1]);
cnt += STORM_POPCOUNT(data1[i+2] ^ data2[i+2]);
cnt += STORM_POPCOUNT(data1[i+3] ^ data2[i+3]);
}
for (/**/; i < size; ++i)
cnt += STORM_POPCOUNT(data1[i] ^ data2[i]);
return cnt;
}
static
int STORM_pospopcnt_u16_scalar_naive(const uint16_t* data, size_t len, uint32_t* out) {
for (int i = 0; i < len; ++i) {
for (int j = 0; j < 16; ++j) {
out[j] += ((data[i] & (1 << j)) >> j);
}
}
return 0;
}
#ifndef _MSC_VER
STORM_FORCE_INLINE
uint64_t STORM_pospopcnt_umul128(uint64_t a, uint64_t b, uint64_t* hi) {
unsigned __int128 x = (unsigned __int128)a * (unsigned __int128)b;
*hi = (uint64_t)(x >> 64);
return (uint64_t)x;
}
STORM_FORCE_INLINE
uint64_t STORM_pospopcnt_loadu_u64(const void* ptr) {
uint64_t data;
memcpy(&data, ptr, sizeof(data));
return data;
}
// By @aqrit (https://github.com/aqrit)
// @see: https://gist.github.com/aqrit/c729815b0165c139d0bac642ab7ee104
static
int STORM_pospopcnt_u16_scalar_umul128_unroll2(const uint16_t* in, size_t n, uint32_t* out) {
while (n >= 8) {
uint64_t counter_a = 0; // 4 packed 12-bit counters
uint64_t counter_b = 0;
uint64_t counter_c = 0;
uint64_t counter_d = 0;
// end before overflowing the counters
uint32_t len = ((n < 0x0FFF) ? n : 0x0FFF) & ~7;
n -= len;
for (const uint16_t* end = &in[len]; in != end; in += 8) {
const uint64_t mask_a = UINT64_C(0x1111111111111111);
const uint64_t mask_b = mask_a + mask_a;
const uint64_t mask_c = mask_b + mask_b;
const uint64_t mask_0001 = UINT64_C(0x0001000100010001);
const uint64_t mask_cnts = UINT64_C(0x000000F00F00F00F);
uint64_t v0 = STORM_pospopcnt_loadu_u64(&in[0]);
uint64_t v1 = STORM_pospopcnt_loadu_u64(&in[4]);
uint64_t a = (v0 & mask_a) + (v1 & mask_a);
uint64_t b = ((v0 & mask_b) + (v1 & mask_b)) >> 1;
uint64_t c = ((v0 & mask_c) + (v1 & mask_c)) >> 2;
uint64_t d = ((v0 >> 3) & mask_a) + ((v1 >> 3) & mask_a);
uint64_t hi;
a = STORM_pospopcnt_umul128(a, mask_0001, &hi);
a += hi; // broadcast 4-bit counts
b = STORM_pospopcnt_umul128(b, mask_0001, &hi);
b += hi;
c = STORM_pospopcnt_umul128(c, mask_0001, &hi);
c += hi;
d = STORM_pospopcnt_umul128(d, mask_0001, &hi);
d += hi;
counter_a += a & mask_cnts;
counter_b += b & mask_cnts;
counter_c += c & mask_cnts;
counter_d += d & mask_cnts;
}
out[0] += counter_a & 0x0FFF;
out[1] += counter_b & 0x0FFF;
out[2] += counter_c & 0x0FFF;
out[3] += counter_d & 0x0FFF;
out[4] += (counter_a >> 36);
out[5] += (counter_b >> 36);
out[6] += (counter_c >> 36);
out[7] += (counter_d >> 36);
out[8] += (counter_a >> 24) & 0x0FFF;
out[9] += (counter_b >> 24) & 0x0FFF;
out[10] += (counter_c >> 24) & 0x0FFF;
out[11] += (counter_d >> 24) & 0x0FFF;
out[12] += (counter_a >> 12) & 0x0FFF;
out[13] += (counter_b >> 12) & 0x0FFF;
out[14] += (counter_c >> 12) & 0x0FFF;
out[15] += (counter_d >> 12) & 0x0FFF;
}
// assert(n < 8)
if (n != 0) {
uint64_t tail_counter_a = 0;
uint64_t tail_counter_b = 0;
do { // zero-extend a bit to 8-bits (emulate pdep) then accumulate
const uint64_t mask_01 = UINT64_C(0x0101010101010101);
const uint64_t magic = UINT64_C(0x0000040010004001); // 1+(1<<14)+(1<<28)+(1<<42)
uint64_t x = *in++;
tail_counter_a += ((x & 0x5555) * magic) & mask_01; // 0101010101010101
tail_counter_b += (((x >> 1) & 0x5555) * magic) & mask_01;
} while (--n);
out[0] += tail_counter_a & 0xFF;
out[8] += (tail_counter_a >> 8) & 0xFF;
out[2] += (tail_counter_a >> 16) & 0xFF;
out[10] += (tail_counter_a >> 24) & 0xFF;
out[4] += (tail_counter_a >> 32) & 0xFF;
out[12] += (tail_counter_a >> 40) & 0xFF;
out[6] += (tail_counter_a >> 48) & 0xFF;
out[14] += (tail_counter_a >> 56) & 0xFF;
out[1] += tail_counter_b & 0xFF;
out[9] += (tail_counter_b >> 8) & 0xFF;
out[3] += (tail_counter_b >> 16) & 0xFF;
out[11] += (tail_counter_b >> 24) & 0xFF;
out[5] += (tail_counter_b >> 32) & 0xFF;
out[13] += (tail_counter_b >> 40) & 0xFF;
out[7] += (tail_counter_b >> 48) & 0xFF;
out[15] += (tail_counter_b >> 56) & 0xFF;
}
return 0;
}
#endif
/*
* This uses fewer arithmetic operations than any other known
* implementation on machines with fast multiplication.
* It uses 12 arithmetic operations, one of which is a multiply.
* http://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
*/
STORM_FORCE_INLINE
uint64_t STORM_popcount64(uint64_t x)
{
uint64_t m1 = UINT64_C(0x5555555555555555);
uint64_t m2 = UINT64_C(0x3333333333333333);
uint64_t m4 = UINT64_C(0x0F0F0F0F0F0F0F0F);
uint64_t h01 = UINT64_C(0x0101010101010101);
x -= (x >> 1) & m1;
x = (x & m2) + ((x >> 2) & m2);
x = (x + (x >> 4)) & m4;
return (x * h01) >> 56;
}
static
const uint8_t STORM_popcnt_lookup8bit[256] = {
/* 0 */ 0, /* 1 */ 1, /* 2 */ 1, /* 3 */ 2,
/* 4 */ 1, /* 5 */ 2, /* 6 */ 2, /* 7 */ 3,
/* 8 */ 1, /* 9 */ 2, /* a */ 2, /* b */ 3,
/* c */ 2, /* d */ 3, /* e */ 3, /* f */ 4,
/* 10 */ 1, /* 11 */ 2, /* 12 */ 2, /* 13 */ 3,
/* 14 */ 2, /* 15 */ 3, /* 16 */ 3, /* 17 */ 4,
/* 18 */ 2, /* 19 */ 3, /* 1a */ 3, /* 1b */ 4,
/* 1c */ 3, /* 1d */ 4, /* 1e */ 4, /* 1f */ 5,
/* 20 */ 1, /* 21 */ 2, /* 22 */ 2, /* 23 */ 3,
/* 24 */ 2, /* 25 */ 3, /* 26 */ 3, /* 27 */ 4,
/* 28 */ 2, /* 29 */ 3, /* 2a */ 3, /* 2b */ 4,
/* 2c */ 3, /* 2d */ 4, /* 2e */ 4, /* 2f */ 5,
/* 30 */ 2, /* 31 */ 3, /* 32 */ 3, /* 33 */ 4,
/* 34 */ 3, /* 35 */ 4, /* 36 */ 4, /* 37 */ 5,
/* 38 */ 3, /* 39 */ 4, /* 3a */ 4, /* 3b */ 5,
/* 3c */ 4, /* 3d */ 5, /* 3e */ 5, /* 3f */ 6,
/* 40 */ 1, /* 41 */ 2, /* 42 */ 2, /* 43 */ 3,
/* 44 */ 2, /* 45 */ 3, /* 46 */ 3, /* 47 */ 4,
/* 48 */ 2, /* 49 */ 3, /* 4a */ 3, /* 4b */ 4,
/* 4c */ 3, /* 4d */ 4, /* 4e */ 4, /* 4f */ 5,
/* 50 */ 2, /* 51 */ 3, /* 52 */ 3, /* 53 */ 4,
/* 54 */ 3, /* 55 */ 4, /* 56 */ 4, /* 57 */ 5,
/* 58 */ 3, /* 59 */ 4, /* 5a */ 4, /* 5b */ 5,
/* 5c */ 4, /* 5d */ 5, /* 5e */ 5, /* 5f */ 6,
/* 60 */ 2, /* 61 */ 3, /* 62 */ 3, /* 63 */ 4,
/* 64 */ 3, /* 65 */ 4, /* 66 */ 4, /* 67 */ 5,
/* 68 */ 3, /* 69 */ 4, /* 6a */ 4, /* 6b */ 5,
/* 6c */ 4, /* 6d */ 5, /* 6e */ 5, /* 6f */ 6,
/* 70 */ 3, /* 71 */ 4, /* 72 */ 4, /* 73 */ 5,
/* 74 */ 4, /* 75 */ 5, /* 76 */ 5, /* 77 */ 6,
/* 78 */ 4, /* 79 */ 5, /* 7a */ 5, /* 7b */ 6,
/* 7c */ 5, /* 7d */ 6, /* 7e */ 6, /* 7f */ 7,
/* 80 */ 1, /* 81 */ 2, /* 82 */ 2, /* 83 */ 3,
/* 84 */ 2, /* 85 */ 3, /* 86 */ 3, /* 87 */ 4,
/* 88 */ 2, /* 89 */ 3, /* 8a */ 3, /* 8b */ 4,
/* 8c */ 3, /* 8d */ 4, /* 8e */ 4, /* 8f */ 5,
/* 90 */ 2, /* 91 */ 3, /* 92 */ 3, /* 93 */ 4,
/* 94 */ 3, /* 95 */ 4, /* 96 */ 4, /* 97 */ 5,
/* 98 */ 3, /* 99 */ 4, /* 9a */ 4, /* 9b */ 5,
/* 9c */ 4, /* 9d */ 5, /* 9e */ 5, /* 9f */ 6,
/* a0 */ 2, /* a1 */ 3, /* a2 */ 3, /* a3 */ 4,
/* a4 */ 3, /* a5 */ 4, /* a6 */ 4, /* a7 */ 5,
/* a8 */ 3, /* a9 */ 4, /* aa */ 4, /* ab */ 5,
/* ac */ 4, /* ad */ 5, /* ae */ 5, /* af */ 6,
/* b0 */ 3, /* b1 */ 4, /* b2 */ 4, /* b3 */ 5,
/* b4 */ 4, /* b5 */ 5, /* b6 */ 5, /* b7 */ 6,
/* b8 */ 4, /* b9 */ 5, /* ba */ 5, /* bb */ 6,
/* bc */ 5, /* bd */ 6, /* be */ 6, /* bf */ 7,
/* c0 */ 2, /* c1 */ 3, /* c2 */ 3, /* c3 */ 4,
/* c4 */ 3, /* c5 */ 4, /* c6 */ 4, /* c7 */ 5,
/* c8 */ 3, /* c9 */ 4, /* ca */ 4, /* cb */ 5,
/* cc */ 4, /* cd */ 5, /* ce */ 5, /* cf */ 6,
/* d0 */ 3, /* d1 */ 4, /* d2 */ 4, /* d3 */ 5,
/* d4 */ 4, /* d5 */ 5, /* d6 */ 5, /* d7 */ 6,
/* d8 */ 4, /* d9 */ 5, /* da */ 5, /* db */ 6,
/* dc */ 5, /* dd */ 6, /* de */ 6, /* df */ 7,
/* e0 */ 3, /* e1 */ 4, /* e2 */ 4, /* e3 */ 5,
/* e4 */ 4, /* e5 */ 5, /* e6 */ 5, /* e7 */ 6,
/* e8 */ 4, /* e9 */ 5, /* ea */ 5, /* eb */ 6,
/* ec */ 5, /* ed */ 6, /* ee */ 6, /* ef */ 7,
/* f0 */ 4, /* f1 */ 5, /* f2 */ 5, /* f3 */ 6,
/* f4 */ 5, /* f5 */ 6, /* f6 */ 6, /* f7 */ 7,
/* f8 */ 5, /* f9 */ 6, /* fa */ 6, /* fb */ 7,
/* fc */ 6, /* fd */ 7, /* fe */ 7, /* ff */ 8
};
/****************************
* SSE4.1 functions
****************************/
#if defined(STORM_HAVE_SSE42)
#include <immintrin.h>
STORM_TARGET("sse4.2")
STORM_FORCE_INLINE
uint64_t STORM_POPCOUNT_SSE(const __m128i n) {
return(STORM_POPCOUNT(_mm_cvtsi128_si64(n)) +
STORM_POPCOUNT(_mm_cvtsi128_si64(_mm_unpackhi_epi64(n, n))));
}
STORM_TARGET("sse4.2")
STORM_FORCE_INLINE
void STORM_CSA128(__m128i* h, __m128i* l, __m128i a, __m128i b, __m128i c) {
__m128i u = _mm_xor_si128(a, b);
*h = _mm_or_si128(_mm_and_si128(a, b), _mm_and_si128(u, c));
*l = _mm_xor_si128(u, c);
}
/**
* Carry-save adder update step.
* @see https://en.wikipedia.org/wiki/Carry-save_adder#Technical_details
*
* Steps:
* 1) U = *L ⊕ B
* 2) *H = (*L ^ B) | (U ^ C)
* 3) *L = *L ⊕ B ⊕ C = U ⊕ C
*
* B and C are 16-bit staggered registers such that &C - &B = 1.
*
* Example usage:
* pospopcnt_csa_sse(&twosA, &v1, _mm_loadu_si128(data + i + 0), _mm_loadu_si128(data + i + 1));
*
* @param h
* @param l
* @param b
* @param c
*/
STORM_TARGET("sse4.2")
STORM_FORCE_INLINE
void STORM_pospopcnt_csa_sse(__m128i* STORM_RESTRICT h,
__m128i* STORM_RESTRICT l,
const __m128i b,
const __m128i c)
{
const __m128i u = _mm_xor_si128(*l, b);
*h = _mm_or_si128(*l & b, u & c); // shift carry (sc_i).
*l = _mm_xor_si128(u, c); // partial sum (ps).
}
// By @aqrit (https://github.com/aqrit)
// @see: https://gist.github.com/aqrit/cb52b2ac5b7d0dfe9319c09d27237bf3
STORM_TARGET("sse4.2")
static
int STORM_pospopcnt_u16_sse_sad(const uint16_t* data, size_t len, uint32_t* flag_counts) {
const __m128i zero = _mm_setzero_si128();
const __m128i mask_lo_byte = _mm_srli_epi16(_mm_cmpeq_epi8(zero, zero), 8);
const __m128i mask_lo_cnt = _mm_srli_epi16(mask_lo_byte, 2);
const __m128i mask_bits_a = _mm_set1_epi8(0x41); // 01000001
const __m128i mask_bits_b = _mm_add_epi8(mask_bits_a, mask_bits_a);
uint32_t buffer[16];
__m128i counterA = zero;
__m128i counterB = zero;
__m128i counterC = zero;
__m128i counterD = zero;
for (const uint16_t* end = &data[(len & ~31)]; data != end; data += 32) {
__m128i r0 = _mm_loadu_si128((__m128i*)&data[0]);
__m128i r1 = _mm_loadu_si128((__m128i*)&data[8]);
__m128i r2 = _mm_loadu_si128((__m128i*)&data[16]);
__m128i r3 = _mm_loadu_si128((__m128i*)&data[24]);
__m128i r4, r5, r6, r7;
// seperate LOBYTE and HIBYTE of each WORD
// (emulate PSHUFB F,D,B,9,7,5,3,1, E,C,A,8,6,4,2,0)
r4 = _mm_and_si128(mask_lo_byte, r0);
r5 = _mm_and_si128(mask_lo_byte, r1);
r6 = _mm_and_si128(mask_lo_byte, r2);
r7 = _mm_and_si128(mask_lo_byte, r3);
r0 = _mm_srli_epi16(r0, 8);
r1 = _mm_srli_epi16(r1, 8);
r2 = _mm_srli_epi16(r2, 8);
r3 = _mm_srli_epi16(r3, 8);
r0 = _mm_packus_epi16(r0, r4);
r1 = _mm_packus_epi16(r1, r5);
r2 = _mm_packus_epi16(r2, r6);
r3 = _mm_packus_epi16(r3, r7);
// isolate bits to count
r4 = _mm_and_si128(mask_bits_a, r0);
r5 = _mm_and_si128(mask_bits_a, r1);
r6 = _mm_and_si128(mask_bits_a, r2);
r7 = _mm_and_si128(mask_bits_a, r3);
// horizontal sum of qwords
r4 = _mm_sad_epu8(r4, zero);
r5 = _mm_sad_epu8(r5, zero);
r6 = _mm_sad_epu8(r6, zero);
r7 = _mm_sad_epu8(r7, zero);
// sum 6-bit counts
r4 = _mm_add_epi16(r4,r5);
r4 = _mm_add_epi16(r4,r6);
r4 = _mm_add_epi16(r4,r7);
// unpack 6-bit counts to 32-bits
r5 = _mm_and_si128(mask_lo_cnt, r4);
r4 = _mm_srli_epi16(r4, 6);
r4 = _mm_packs_epi32(r4, r5);
// accumulate
counterA = _mm_add_epi32(counterA, r4);
// do it again...
r4 = _mm_and_si128(mask_bits_b, r0);
r5 = _mm_and_si128(mask_bits_b, r1);
r6 = _mm_and_si128(mask_bits_b, r2);
r7 = _mm_and_si128(mask_bits_b, r3);
r4 = _mm_sad_epu8(r4, zero);
r5 = _mm_sad_epu8(r5, zero);
r6 = _mm_sad_epu8(r6, zero);
r7 = _mm_sad_epu8(r7, zero);
r4 = _mm_add_epi16(r4,r5);
r4 = _mm_add_epi16(r4,r6);
r4 = _mm_add_epi16(r4,r7);
r5 = _mm_avg_epu8(zero, r4); // shift right 1
r5 = _mm_and_si128(r5, mask_lo_cnt);
r4 = _mm_srli_epi16(r4, 7);
r4 = _mm_packs_epi32(r4, r5);
counterB = _mm_add_epi32(counterB, r4); // accumulate
// rotate right 4
r4 = _mm_slli_epi16(r0, 12);
r5 = _mm_slli_epi16(r1, 12);
r6 = _mm_slli_epi16(r2, 12);
r7 = _mm_slli_epi16(r3, 12);
r0 = _mm_srli_epi16(r0, 4);
r1 = _mm_srli_epi16(r1, 4);
r2 = _mm_srli_epi16(r2, 4);
r3 = _mm_srli_epi16(r3, 4);
r0 = _mm_or_si128(r0, r4);
r1 = _mm_or_si128(r1, r5);
r2 = _mm_or_si128(r2, r6);
r3 = _mm_or_si128(r3, r7);
// do it again...
r4 = _mm_and_si128(mask_bits_a, r0);
r5 = _mm_and_si128(mask_bits_a, r1);
r6 = _mm_and_si128(mask_bits_a, r2);
r7 = _mm_and_si128(mask_bits_a, r3);
r4 = _mm_sad_epu8(r4, zero);
r5 = _mm_sad_epu8(r5, zero);
r6 = _mm_sad_epu8(r6, zero);
r7 = _mm_sad_epu8(r7, zero);
r4 = _mm_add_epi16(r4,r5);
r4 = _mm_add_epi16(r4,r6);
r4 = _mm_add_epi16(r4,r7);
r5 = _mm_and_si128(mask_lo_cnt, r4);
r4 = _mm_srli_epi16(r4, 6);
r4 = _mm_packs_epi32(r4, r5);
counterC = _mm_add_epi32(counterC, r4); // accumulate
// do it again...
r0 = _mm_and_si128(r0, mask_bits_b);
r1 = _mm_and_si128(r1, mask_bits_b);
r2 = _mm_and_si128(r2, mask_bits_b);
r3 = _mm_and_si128(r3, mask_bits_b);
r0 = _mm_sad_epu8(r0, zero);
r1 = _mm_sad_epu8(r1, zero);
r2 = _mm_sad_epu8(r2, zero);
r3 = _mm_sad_epu8(r3, zero);
r0 = _mm_add_epi16(r0,r1);
r0 = _mm_add_epi16(r0,r2);
r0 = _mm_add_epi16(r0,r3);
r1 = _mm_avg_epu8(zero, r0);
r1 = _mm_and_si128(r1, mask_lo_cnt);
r0 = _mm_srli_epi16(r0, 7);
r0 = _mm_packs_epi32(r0, r1);
counterD = _mm_add_epi32(counterD, r0); // accumulate
}
// transpose then store counters
__m128i counter_1098 = _mm_unpackhi_epi32(counterA, counterB);
__m128i counter_76FE = _mm_unpacklo_epi32(counterA, counterB);
__m128i counter_32BA = _mm_unpacklo_epi32(counterC, counterD);
__m128i counter_54DC = _mm_unpackhi_epi32(counterC, counterD);
__m128i counter_7654 = _mm_unpackhi_epi64(counter_54DC, counter_76FE);
__m128i counter_FEDC = _mm_unpacklo_epi64(counter_54DC, counter_76FE);
__m128i counter_3210 = _mm_unpackhi_epi64(counter_1098, counter_32BA);
__m128i counter_BA98 = _mm_unpacklo_epi64(counter_1098, counter_32BA);
_mm_storeu_si128((__m128i*)&buffer[0], counter_3210);
_mm_storeu_si128((__m128i*)&buffer[4], counter_7654);
_mm_storeu_si128((__m128i*)&buffer[8], counter_BA98);
_mm_storeu_si128((__m128i*)&buffer[12], counter_FEDC);
for (int i = 0; i < 16; ++i) flag_counts[i] += buffer[i];
// scalar tail loop
int tail = len & 31;
if (tail != 0) {
uint64_t countsA = 0;
uint64_t countsB = 0;
do {
// zero-extend a bit to 8-bits then accumulate
// (emulate pdep)