你如何在 SSE2 上做带符号的 32 位扩展乘法？

Question

在查看扩展乘法的 WebAssembly SIMD 提议时提出了这个问题。

为了支持较旧的硬件，我们需要支持 SSE2，并且 32 位整数的唯一向量乘法运算是 pmuludq. (Signed pmuldq 仅在 SSE4.1 中添加)

（非加宽相对容易；随机输入 2x pmuludq 并取 4 个结果的低半部分来模拟 SSE4.1 pmulld）。

Answer 1

在##asm 上大声呼喊@GeDaMo 帮助提出这个解决方案。

Godbolt

C/C++:

#include <xmmintrin.h>
#include <stdint.h>
#include <tmmintrin.h>
#include <smmintrin.h>
#include <cstdio>

typedef int32_t int32x4_t __attribute__((vector_size(16))) __attribute__((aligned(16)));
typedef int64_t int64x2_t __attribute__((vector_size(16))) __attribute__((aligned(16)));

int64x2_t multiply32_low_s(int32x4_t a, int32x4_t b) {
    auto aSigns = a >> 31;
    auto bSigns = b >> 31;
    auto aInt = a ^ aSigns;
    aInt -= aSigns;
    auto bInt = b ^ bSigns;
    bInt -= bSigns;
    const auto shuffleMask = _MM_SHUFFLE(1,1,0,0);
    auto absProd = _mm_mul_epu32(_mm_shuffle_epi32((__m128i)aInt, shuffleMask), _mm_shuffle_epi32((__m128i)bInt, shuffleMask));
    auto aSignsInt = _mm_shuffle_epi32((__m128i)aSigns, shuffleMask);
    auto bSignsInt = _mm_shuffle_epi32((__m128i)bSigns,shuffleMask);
    auto prodSigns = aSignsInt ^ bSignsInt;
    absProd ^= prodSigns;
    absProd -= prodSigns;
    return (int64x2_t)absProd;
}

int64x2_t multiply32_high_s(int32x4_t a, int32x4_t b) {
    auto aSigns = a >> 31;
    auto bSigns = b >> 31;
    auto aInt = a ^ aSigns;
    aInt -= aSigns;
    auto bInt = b ^ bSigns;
    bInt -= bSigns;
    const auto shuffleMask = _MM_SHUFFLE(3,3,2,2);
    auto absProd = _mm_mul_epu32(_mm_shuffle_epi32((__m128i)aInt, shuffleMask), _mm_shuffle_epi32((__m128i)bInt, shuffleMask));
    auto aSignsInt = _mm_shuffle_epi32((__m128i)aSigns, shuffleMask);
    auto bSignsInt = _mm_shuffle_epi32((__m128i)bSigns,shuffleMask);
    auto prodSigns = aSignsInt ^ bSignsInt;
    absProd ^= prodSigns;
    absProd -= prodSigns;
    return (int64x2_t)absProd;
}


int main(int argc, char* argv[]) {
    int32x4_t a{-5,500,-5000,50000};
    int32x4_t b{10,-100,-5000,500000000};
    auto c = multiply32_low_s(a,b);
    auto d = multiply32_high_s(a,b);
    printf("%ld %ld\n", c[0],c[1]);
    printf("%ld %ld\n", d[0],d[1]);
}

大会

multiply32_low_s(int __vector(4), int __vector(4)):
 movdqa xmm3,xmm0
 movdqa xmm2,xmm1
 psrad  xmm3,0x1f
 psrad  xmm2,0x1f
 pxor   xmm0,xmm3
 pxor   xmm1,xmm2
 psubd  xmm1,xmm2
 psubd  xmm0,xmm3
 pshufd xmm2,xmm2,0x50
 pshufd xmm1,xmm1,0x50
 pshufd xmm0,xmm0,0x50
 pshufd xmm3,xmm3,0x50
 pmuludq xmm0,xmm1
 pxor   xmm2,xmm3
 pxor   xmm0,xmm2
 psubq  xmm0,xmm2
 ret    
 nop    WORD PTR [rax+rax*1+0x0]
multiply32_high_s(int __vector(4), int __vector(4)):
 movdqa xmm3,xmm0
 movdqa xmm2,xmm1
 psrad  xmm3,0x1f
 psrad  xmm2,0x1f
 pxor   xmm0,xmm3
 pxor   xmm1,xmm2
 psubd  xmm1,xmm2
 psubd  xmm0,xmm3
 pshufd xmm2,xmm2,0xfa
 pshufd xmm1,xmm1,0xfa
 pshufd xmm0,xmm0,0xfa
 pshufd xmm3,xmm3,0xfa
 pmuludq xmm0,xmm1
 pxor   xmm2,xmm3
 pxor   xmm0,xmm2
 psubq  xmm0,xmm2
 ret    
 nop    WORD PTR [rax+rax*1+0x0]

Answer 2

mulhs(a, b) = mulhu(a, b) - (a < 0 ? b : 0) - (b < 0 ? a : 0)

使用它，两个签名的 double-width 产品可以像这样计算，

__m128i mul_epi32(__m128i a, __m128i b) {
    a = _mm_shuffle_epi32(a, _MM_SHUFFLE(3, 1, 1, 0));
    b = _mm_shuffle_epi32(b, _MM_SHUFFLE(3, 1, 1, 0));
    __m128i unsignedProduct = _mm_mul_epu32(a, b);
    __m128i threshold = _mm_set_epi32(INT_MIN, 0, INT_MIN, 0);
    __m128i signA = _mm_cmplt_epi32(a, threshold);
    __m128i signB = _mm_cmplt_epi32(b, threshold);
    __m128i x = _mm_shuffle_epi32(_mm_and_si128(signA, b), _MM_SHUFFLE(2, 3, 0, 1));
    __m128i y = _mm_shuffle_epi32(_mm_and_si128(signB, a), _MM_SHUFFLE(2, 3, 0, 1));
    return _mm_sub_epi32(_mm_sub_epi32(unsignedProduct, x), y);
}

与其他提案相比，这节省了一些操作，但它非常接近，现在它包含一个负载，如果此代码是冷的，这可能会很糟糕。

你如何在 SSE2 上做带符号的 32 位扩展乘法？

How do you do signed 32bit widening multiplication on SSE2?

assembly

sse

simd

webassembly

sse2

在##asm 上大声呼喊@GeDaMo 帮助提出这个解决方案。

Godbolt

C/C++:

大会