c - 用于乘以特定数组元素的等效 SIMD 指令

Question

我刚刚了解了如何获得 2 个数组的点积(如以下代码所示):

int A[8] = {1,2,3,4,5,1,2,3};
int B[8] = {2,3,4,5,6,2,3,4};

float result = 0;

for (int i = 0; i < 8; i ++) {
    result += A[i] * B[i];
}

等同于(在 SIMD 中):

int A[8] = {1,2,3,4,5,1,2,3};
int B[8] = {2,3,4,5,6,2,3,4};

float result = 0;

__m128 r1 = {0,0,0,0};
__m128 r2 = {0,0,0,0};
__m128 r3 = {0,0,0,0};

for (int i = 0; i < 8; i += 4) {
  float C[4] = {A[i], A[i+1], A[i+2], A[i+3]};
  float D[4] = {B[i], B[i+1], B[i+2], B[i+3]};
  __m128 a = _mm_loadu_ps(C);
  __m128 b = _mm_loadu_ps(D);

  r1 = _mm_mul_ps(a,b);
  r2 = _mm_hadd_ps(r1, r1);
  r3 = _mm_add_ss(_mm_hadd_ps(r2, r2), r3);
  _mm_store_ss(&result, r3);
}

我现在很好奇，如果我想乘以数组中不连续的元素，如何在 SIMD 中获得等效代码。例如，如果我想执行以下操作，SIMD 中的等效项是什么？

int A[8] = {1,2,3,4,5,1,2,3};
int B[8] = {2,3,4,5,6,2,3,4};

float result = 0;
for (int i = 0; i < 8; i++) {
    for (int j = 0; j < 8; j++) {
        result += A[foo(i)] * B[foo(j)]
    }
}

foo 只是一些函数，它返回一个 int 作为输入参数的某个函数。

Answer 1

如果我必须做这个任务，我会做如下:

int A[8] = {1,2,3,4,5,1,2,3};
int B[8] = {2,3,4,5,6,2,3,4};

float PA[8], PB[8];
for (int i = 0; i < 8; i++) 
{
    PA[i] = A[foo(i)]; 
    PB[i] = B[foo(i)]; 
}

__m128 sums = _mm_set1_ps(0);
for (int i = 0; i < 8; i++) 
{
    __m128 a = _mm_set1_ps(PA[i]);
    for (int j = 0; j < 8; j += 4) 
    {
        __m128 b = _mm_loadu_ps(PB + j);
        sums = _mm_add_ps(sums, _mm_mul_ps(a, b));
    }
}
float results[4];
_mm_storeu_ps(results, sums);
float result = results[0] + results[1] + results[2] + results[3];