英特尔AVX:点积的256位版本，用于双精度浮点变量 [英] Intel AVX: 256-bits version of dot product for double precision floating point variables

问题描述

Intel高级矢量扩展(AVX)在256位版本(YMM寄存器)中不提供用于双精度浮点变量的点积. 为什么?"这个问题已在另一个论坛中得到了非常简短的处理(此处 )和堆栈溢出(

The Intel Advanced Vector Extensions (AVX) offers no dot product in the 256-bit version (YMM register) for double precision floating point variables. The "Why?" question have been very briefly treated in another forum (here) and on Stack Overflow (here). But the question I am facing is how to replace this missing instruction with other AVX instructions in an efficient way?

存在用于单精度浮点变量的256位版本的点积(此处引用):

The dot product in 256-bit version exists for single precision floating point variables (reference here):

 __m256 _mm256_dp_ps(__m256 m1, __m256 m2, const int mask);

这个想法是为这种丢失的指令找到有效的等效物:

The idea is to find an efficient equivalent for this missing instruction:

 __m256d _mm256_dp_pd(__m256d m1, __m256d m2, const int mask);

更具体地说，我要从__m128(四个浮点数)转换为__m256d(四个双精度点)的代码使用以下指令:

To be more specific, the code I would like to transform from __m128 (four floats) to __m256d (4 doubles) use the following instructions:

   __m128 val0 = ...; // Four float values
   __m128 val1 = ...; //
   __m128 val2 = ...; //
   __m128 val3 = ...; //
   __m128 val4 = ...; //

   __m128 res = _mm_or_ps( _mm_dp_ps(val1,  val0,   0xF1),
                _mm_or_ps( _mm_dp_ps(val2,  val0,   0xF2),
                _mm_or_ps( _mm_dp_ps(val3,  val0,   0xF4),
                           _mm_dp_ps(val4,  val0,   0xF8) )));

此代码的结果是四个浮点数的_m128向量，其中包含val1和val0，val2和val0，val3和val0，val4和val0.

The result of this code is a _m128 vector of four floats containing the results of the dot products between val1 and val0, val2 and val0, val3 and val0, val4 and val0.

也许这可以给建议一些提示?

Maybe this can give hints for the suggestions?

推荐答案

我将使用4 * double乘法，然后使用hadd(不幸的是，其上半部和下半部仅添加2 * 2浮点数)，提取上半部分(随机播放应该等效，也许更快)，然后将其添加到下半部分.

I would use a 4*double multiplication, then a hadd (which unfortunately adds only 2*2 floats in the upper and lower half), extract the upper half (a shuffle should work equally, maybe faster) and add it to the lower half.

结果在dotproduct的低64位.

__m256d xy = _mm256_mul_pd( x, y );
__m256d temp = _mm256_hadd_pd( xy, xy );
__m128d hi128 = _mm256_extractf128_pd( temp, 1 );
__m128d dotproduct = _mm_add_pd( (__m128d)temp, hi128 );

在想到了Norbert P.之后，我将此版本扩展为一次可制作4个点产品.

After an idea of Norbert P. I extended this version to do 4 dot products at one time.

__m256d xy0 = _mm256_mul_pd( x[0], y[0] );
__m256d xy1 = _mm256_mul_pd( x[1], y[1] );
__m256d xy2 = _mm256_mul_pd( x[2], y[2] );
__m256d xy3 = _mm256_mul_pd( x[3], y[3] );

// low to high: xy00+xy01 xy10+xy11 xy02+xy03 xy12+xy13
__m256d temp01 = _mm256_hadd_pd( xy0, xy1 );   

// low to high: xy20+xy21 xy30+xy31 xy22+xy23 xy32+xy33
__m256d temp23 = _mm256_hadd_pd( xy2, xy3 );

// low to high: xy02+xy03 xy12+xy13 xy20+xy21 xy30+xy31
__m256d swapped = _mm256_permute2f128_pd( temp01, temp23, 0x21 );

// low to high: xy00+xy01 xy10+xy11 xy22+xy23 xy32+xy33
__m256d blended = _mm256_blend_pd(temp01, temp23, 0b1100);

__m256d dotproduct = _mm256_add_pd( swapped, blended );

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