Sve*_*ger 6 c x86 simd intrinsics avx
我正在修改AVX-2指令,我正在寻找一种快速计算__m256i单词中前导零数(具有256位)的方法.
到目前为止,我已经找到了以下方法:
// Computes the number of leading zero bits.
// Here, avx_word is of type _m256i.
if (!_mm256_testz_si256(avx_word, avx_word)) {
uint64_t word = _mm256_extract_epi64(avx_word, 0);
if (word > 0)
return (__builtin_clzll(word));
word = _mm256_extract_epi64(avx_word, 1);
if (word > 0)
return (__builtin_clzll(word) + 64);
word = _mm256_extract_epi64(avx_word, 2);
if (word > 0)
return (__builtin_clzll(word) + 128);
word = _mm256_extract_epi64(avx_word, 3);
return (__builtin_clzll(word) + 192);
} else
return 256; // word is entirely zero
但是,我发现在256位寄存器中找出确切的非零字是相当笨拙的.
有人知道是否有更优雅(或更快)的方法吗？
正如附加信息:我实际上想要计算由逻辑AND创建的任意长向量的第一个设置位的索引,并且我将标准64位操作的性能与SSE和AVX-2代码进行比较.这是我的整个测试代码:
#include <stdio.h>
#include <stdlib.h>
#include <immintrin.h>
#include <stdint.h>
#include <assert.h>
#include <time.h>
#include <sys/time.h>
#include <stdalign.h>
#define ALL 0xFFFFFFFF
#define NONE 0x0
#define BV_SHIFTBITS ((size_t) 6)
#define BV_MOD_WORD ((size_t) 63)
#define BV_ONE ((uint64_t) 1)
#define BV_ZERO ((uint64_t) 0)
#define BV_WORDSIZE ((uint64_t) 64)
uint64_t*
Vector_new(
size_t num_bits) {
assert ((num_bits % 256) == 0);
size_t num_words = num_bits >> BV_SHIFTBITS;
size_t mod = num_bits & BV_MOD_WORD;
if (mod > 0)
assert (0);
uint64_t* words;
posix_memalign((void**) &(words), 32, sizeof(uint64_t) * num_words);
for (size_t i = 0; i < num_words; ++i)
words[i] = 0;
return words;
}
void
Vector_set(
uint64_t* vector,
size_t pos) {
const size_t word_index = pos >> BV_SHIFTBITS;
const size_t offset = pos & BV_MOD_WORD;
vector[word_index] |= (BV_ONE << (BV_MOD_WORD - offset));
}
size_t
Vector_and_first_bit(
uint64_t** vectors,
const size_t num_vectors,
const size_t num_words) {
for (size_t i = 0; i < num_words; ++i) {
uint64_t word = vectors[0][i];
for (size_t j = 1; j < num_vectors; ++j)
word &= vectors[j][i];
if (word > 0)
return (1 + i * BV_WORDSIZE + __builtin_clzll(word));
}
return 0;
}
size_t
Vector_and_first_bit_256(
uint64_t** vectors,
const size_t num_vectors,
const size_t num_avx_words) {
for (size_t i = 0; i < num_avx_words; ++i) {
const size_t addr_offset = i << 2;
__m256i avx_word = _mm256_load_si256(
(__m256i const*) (vectors[0] + addr_offset));
// AND the AVX words
for (size_t j = 1; j < num_vectors; ++j) {
avx_word = _mm256_and_si256(
avx_word,
_mm256_load_si256((__m256i const*) (vectors[j] + addr_offset))
);
}
// test whether resulting AVX word is not zero
if (!_mm256_testz_si256(avx_word, avx_word)) {
uint64_t word = _mm256_extract_epi64(avx_word, 0);
const size_t shift = i << 8;
if (word > 0)
return (1 + shift + __builtin_clzll(word));
word = _mm256_extract_epi64(avx_word, 1);
if (word > 0)
return (1 + shift + __builtin_clzll(word) + 64);
word = _mm256_extract_epi64(avx_word, 2);
if (word > 0)
return (1 + shift + __builtin_clzll(word) + 128);
word = _mm256_extract_epi64(avx_word, 3);
return (1 + shift + __builtin_clzll(word) + 192);
}
}
return 0;
}
size_t
Vector_and_first_bit_128(
uint64_t** vectors,
const size_t num_vectors,
const size_t num_avx_words) {
for (size_t i = 0; i < num_avx_words; ++i) {
const size_t addr_offset = i << 1;
__m128i avx_word = _mm_load_si128(
(__m128i const*) (vectors[0] + addr_offset));
// AND the AVX words
for (size_t j = 1; j < num_vectors; ++j) {
avx_word = _mm_and_si128(
avx_word,
_mm_load_si128((__m128i const*) (vectors[j] + addr_offset))
);
}
// test whether resulting AVX word is not zero
if (!_mm_test_all_zeros(avx_word, avx_word)) {
uint64_t word = _mm_extract_epi64(avx_word, 0);
if (word > 0)
return (1 + (i << 7) + __builtin_clzll(word));
word = _mm_extract_epi64(avx_word, 1);
return (1 + (i << 7) + __builtin_clzll(word) + 64);
}
}
return 0;
}
uint64_t*
make_random_vector(
const size_t num_bits,
const size_t propability) {
uint64_t* vector = Vector_new(num_bits);
for (size_t i = 0; i < num_bits; ++i) {
const int x = rand() % 10;
if (x >= (int) propability)
Vector_set(vector, i);
}
return vector;
}
size_t
millis(
const struct timeval* end,
const struct timeval* start) {
struct timeval e = *end;
struct timeval s = *start;
return (1000 * (e.tv_sec - s.tv_sec) + (e.tv_usec - s.tv_usec) / 1000);
}
int
main(
int argc,
char** argv) {
if (argc != 6)
printf("fuck %s\n", argv[0]);
srand(time(NULL));
const size_t num_vectors = atoi(argv[1]);
const size_t size = atoi(argv[2]);
const size_t num_iterations = atoi(argv[3]);
const size_t num_dimensions = atoi(argv[4]);
const size_t propability = atoi(argv[5]);
const size_t num_words = size / 64;
const size_t num_sse_words = num_words / 2;
const size_t num_avx_words = num_words / 4;
assert(num_vectors > 0);
assert(size > 0);
assert(num_iterations > 0);
assert(num_dimensions > 0);
struct timeval t1;
gettimeofday(&t1, NULL);
uint64_t*** vectors = (uint64_t***) malloc(sizeof(uint64_t**) * num_vectors);
for (size_t j = 0; j < num_vectors; ++j) {
vectors[j] = (uint64_t**) malloc(sizeof(uint64_t*) * num_dimensions);
for (size_t i = 0; i < num_dimensions; ++i)
vectors[j][i] = make_random_vector(size, propability);
}
struct timeval t2;
gettimeofday(&t2, NULL);
printf("Creation: %zu ms\n", millis(&t2, &t1));
size_t* results_64 = (size_t*) malloc(sizeof(size_t) * num_vectors);
size_t* results_128 = (size_t*) malloc(sizeof(size_t) * num_vectors);
size_t* results_256 = (size_t*) malloc(sizeof(size_t) * num_vectors);
gettimeofday(&t1, NULL);
for (size_t j = 0; j < num_iterations; ++j)
for (size_t i = 0; i < num_vectors; ++i)
results_64[i] = Vector_and_first_bit(vectors[i], num_dimensions,
num_words);
gettimeofday(&t2, NULL);
const size_t millis_64 = millis(&t2, &t1);
printf("64 : %zu ms\n", millis_64);
gettimeofday(&t1, NULL);
for (size_t j = 0; j < num_iterations; ++j)
for (size_t i = 0; i < num_vectors; ++i)
results_128[i] = Vector_and_first_bit_128(vectors[i],
num_dimensions, num_sse_words);
gettimeofday(&t2, NULL);
const size_t millis_128 = millis(&t2, &t1);
const double factor_128 = (double) millis_64 / (double) millis_128;
printf("128 : %zu ms (factor: %.2f)\n", millis_128, factor_128);
gettimeofday(&t1, NULL);
for (size_t j = 0; j < num_iterations; ++j)
for (size_t i = 0; i < num_vectors; ++i)
results_256[i] = Vector_and_first_bit_256(vectors[i],
num_dimensions, num_avx_words);
gettimeofday(&t2, NULL);
const size_t millis_256 = millis(&t2, &t1);
const double factor_256 = (double) millis_64 / (double) millis_256;
printf("256 : %zu ms (factor: %.2f)\n", millis_256, factor_256);
for (size_t i = 0; i < num_vectors; ++i) {
if (results_64[i] != results_256[i])
printf("ERROR: %zu (64) != %zu (256) with i = %zu\n", results_64[i],
results_256[i], i);
if (results_64[i] != results_128[i])
printf("ERROR: %zu (64) != %zu (128) with i = %zu\n", results_64[i],
results_128[i], i);
}
free(results_64);
free(results_128);
free(results_256);
for (size_t j = 0; j < num_vectors; ++j) {
for (size_t i = 0; i < num_dimensions; ++i)
free(vectors[j][i]);
free(vectors[j]);
}
free(vectors);
return 0;
}
编译:
gcc -o main main.c -O3 -Wall -Wextra -pedantic-errors -Werror -march=native -std=c99 -fno-tree-vectorize
执行:
./main 1000 8192 50000 5 9
参数意味着:1000个测试用例,长度为8192位的向量,50000,测试重复(最后两个参数是小调整).
在我的机器上进行上述调用的示例输出:
Creation: 363 ms
64 : 15000 ms
128 : 10070 ms (factor: 1.49)
256 : 6784 ms (factor: 2.21)
如果您的输入值均匀分布,则几乎所有时间最高设置位都将位于向量的前64位(1 ^ 2 ^ 64).在这种情况下的分支将非常好地预测. @ Nejc的回答对那个案子有好处.
但是lzcnt解决方案的一部分的许多问题具有均匀分布的输出(或类似),因此无分支版本具有优势.不是严格一致的,而是最高设置位通常不是最高64位的任何地方.
Wim在比较位图上使用lzcnt来寻找合适的元素是一种非常好的方法.
但是,使用存储/重新加载的向量的运行时变量索引可能比shuffle更好.存储转发延迟很低(Skylake可能需要5到7个周期),并且延迟与索引生成并行(比较/ movemask/lzcnt).在movd/vpermd/movd已知索引之后,跨越通道的shuffle策略需要5个周期,以将正确的元素放入整数寄存器中.(见http://agner.org/optimize/)
我认为这个版本应该是Haswell/Skylake(和Ryzen)的更好的延迟,以及更好的吞吐量.(vpermd在Ryzen上非常慢,所以它应该非常好)负载的地址计算应该具有与存储转发类似的延迟,所以它是一个折腾,其中一个实际上是关键路径.
将堆栈对齐32以避免32字节存储上的高速缓存行拆分需要额外的指令,因此如果它可以内联到多次使用它的函数中,或者对于其他一些已经需要那么多的对齐,这是最好的__m256i.
#include <stdint.h>
#include <immintrin.h>
#ifndef _MSC_VER
#include <stdalign.h> //MSVC is missing this?
#else
#include <intrin.h>
#pragma intrinsic(_BitScanReverse) // https://msdn.microsoft.com/en-us/library/fbxyd7zd.aspx suggests this
#endif
// undefined result for mask=0, like BSR
uint32_t bsr_nonzero(uint32_t mask)
{
// on Intel, bsr has a minor advantage for the first step
// for AMD, BSR is slow so you should use 31-LZCNT.
//return 31 - _lzcnt_u32(mask);
// Intel's docs say there should be a _bit_scan_reverse(x), maybe try that with ICC
#ifdef _MSC_VER
unsigned long tmp;
_BitScanReverse(&tmp, mask);
return tmp;
#else
return 31 - __builtin_clz(mask);
#endif
}
而有趣的部分:
int mm256_lzcnt_si256(__m256i vec)
{
__m256i nonzero_elem = _mm256_cmpeq_epi8(vec, _mm256_setzero_si256());
unsigned mask = ~_mm256_movemask_epi8(nonzero_elem);
if (mask == 0)
return 256; // if this is rare, branching is probably good.
alignas(32) // gcc chooses to align elems anyway, with its clunky code
uint8_t elems[32];
_mm256_storeu_si256((__m256i*)elems, vec);
// unsigned lz_msk = _lzcnt_u32(mask);
// unsigned idx = 31 - lz_msk; // can use bsr to get the 31-x, because mask is known to be non-zero.
// This takes the 31-x latency off the critical path, in parallel with final lzcnt
unsigned idx = bsr_nonzero(mask);
unsigned lz_msk = 31 - idx;
unsigned highest_nonzero_byte = elems[idx];
return lz_msk * 8 + _lzcnt_u32(highest_nonzero_byte) - 24;
// lzcnt(byte)-24, because we don't want to count the leading 24 bits of padding.
}
在Godbolt用gcc7.3 -O3 -march=haswell,我们得到ASM这样算ymm1入esi.
vpxor xmm0, xmm0, xmm0
mov esi, 256
vpcmpeqd ymm0, ymm1, ymm0
vpmovmskb eax, ymm0
xor eax, -1 # ~mask and set flags, unlike NOT
je .L35
bsr eax, eax
vmovdqa YMMWORD PTR [rbp-48], ymm1 # note no dependency on anything earlier; OoO exec can run it early
mov ecx, 31
mov edx, eax # this is redundant, gcc should just use rax later. But it's zero-latency on HSW/SKL and Ryzen.
sub ecx, eax
movzx edx, BYTE PTR [rbp-48+rdx] # has to wait for the index in edx
lzcnt edx, edx
lea esi, [rdx-24+rcx*8] # lzcnt(byte) + lzcnt(vectormask) * 8
.L35:
为了找到最高的非零元素(the 31 - lzcnt(~movemask)),我们使用bsr直接获取位(以及字节)索引,并从关键路径中减去.只要我们将掩码分支为零,这是安全的.(无分支版本需要初始化寄存器以避免越界索引).
在AMD CPU上,bsr显着慢于lzcnt.在Intel CPU上,除了输出依赖性细节的微小变化外,它们的性能相同.
bsr如果输入为零,则目标寄存器不会被修改,但GCC没有提供利用它的方法.(英特尔仅将其记录为未定义的输出,但AMD记录了Intel/AMD CPU在目标寄存器中产生旧值的实际行为).
bsr如果输入为零,则设置ZF ,而不是像大多数指令那样基于输出.(这和输出依赖性可能是它在AMD上运行缓慢的原因.)BSR标志上的分支并不比ZF上的分支特别好xor eax,-1,因为它反转了掩码,这就是gcc所做的.无论如何,英特尔确实记录了一个_BitScanReverse(&idx, mask)返回a 的内在函数bool,但是gcc不支持它(甚至没有x86intrin.h).GNU C内置函数不会返回一个布尔值来让你使用标志结果,但是bsr如果检查输入C变量是否为非零,gcc可能会使用标志输出来生成智能asm .
使用dword(uint32_t)数组,vmovmskps让第二个lzcnt使用内存源操作数,而不是需要movzx零扩展单个字节.但是lzcnt在Skylake之前对Intel CPU的依赖性是错误的,因此编译器可能倾向于单独加载并且lzcnt same,same无论如何都要用作解决方法.(我没有检查.)
Wim的版本需要,lz_msk-24因为高位24位始终为零,具有8位掩码.但是32位掩码填充了32位寄存器.
这个版本具有8位元素和32位掩码是相反的:我们需要lzcnt选择的字节,不包括寄存器中的24个前导零位.所以我们-24移动到不同的位置,而不是索引数组的关键路径的一部分.
gcc选择将其作为单个3分量LEA(reg + reg*scale - const)的一部分来实现,这对于吞吐量非常有用,但在最终之后将其置于关键路径上lzcnt.(它不是免费的,因为3组件LEA与reg + reg*scale英特尔CPU 相比具有额外的延迟.请参阅Agner Fog的说明表).
乘以8可以作为a的一部分lea,但乘以32将需要移位(或折叠成两个单独的LEA).
英特尔的优化手册说(表2-24)甚至Sandybridge也可以从256位存储转发到单字节负载而没有问题,所以我认为它在AVX2 CPU上运行良好,就像转发到32位负载一样4商店的字节对齐的块.