SSE instructions to add all elements of an array

Question

I am new to SSE2 instructions. I have found an instruction _mm_add_epi8 which can add two array elements. But I want an SSE instruction which can add all elements of an array.

I was trying to develop this concept using this code:

#include <iostream>
#include <conio.h>
#include <emmintrin.h>

void sse(unsigned char* a,unsigned char* b); 

void main()
{
    /*unsigned char *arr;
    arr=(unsigned char *)malloc(50);*/

    unsigned char arr[]={'a','b','c','d','e','f','i','j','k','l','m','n','o','p','q','r','a','b','c','d','e','f','i','j','k','l','m','n','o','p','q','r'};
    unsigned char *next_arr=arr+16;
    for(int i=0;i<16;i++)
          printf("%d,%c   ",next_arr[i],next_arr[i]);
    sse(arr,next_arr);

    getch();
}

void sse(unsigned char* a,unsigned char* b)                                                                                                                                                                          
{                                                                                                                                                                                                                                                                                                                                                                                            
  __m128i* l = (__m128i*)a;                                                                                                                                                                                      
  __m128i* r = (__m128i*)b; 
  __m128i result;

      result= _mm_add_epi8(*l, *r);

      unsigned char *p;
         p=(unsigned char *)&result;

        for(int i=0;i<16;i++)
          printf("%d ",p[i]);

         printf("\n");
         l=(__m128i*)p;
         r=(__m128i*)(p+8);         
         result=_mm_add_epi8(*l, *r);
         p=(unsigned char *)&result;
         printf("%d ",p[0]);

         l=(__m128i*)p;
         r=(__m128i*)(p+4);
         result=_mm_add_epi8(*l, *r);
         p=(unsigned char *)&result;
         l=(__m128i*)p;
         r=(__m128i*)(p+2);
         result=_mm_add_epi8(*l, *r);
         p=(unsigned char *)&result;
         l=(__m128i*)p;
         r=(__m128i*)(p+1);
         result=_mm_add_epi8(*l, *r);
          p=(unsigned char *)&result;
            printf("result =%d ",p[0]);
}

So can anybody please tell me how it is possible to add all elements of an array using SSE2 instructions ?

Any help will be appreciated.

Answer 1

If you just want to sum all the elements of an array then you need to load the data, unpack it to a wider element size, and then sum the unpacked elements. Note that you can maintain multiple partial sums until after the loop and then just do one final sum of these partial sums. For example:

uint32_t sum_array(const uint8_t a[], int n)
{
    const __m128i vk0 = _mm_set1_epi8(0);       // constant vector of all 0s for use with _mm_unpacklo_epi8/_mm_unpackhi_epi8
    const __m128i vk1 = _mm_set1_epi16(1);      // constant vector of all 1s for use with _mm_madd_epi16
    __m128i vsum = _mm_set1_epi32(0);           // initialise vector of four partial 32 bit sums
    uint32_t sum;
    int i;

    for (i = 0; i < n; i += 16)
    {
        __m128i v = _mm_load_si128(&a[i]);      // load vector of 8 bit values
        __m128i vl = _mm_unpacklo_epi8(v, vk0); // unpack to two vectors of 16 bit values
        __m128i vh = _mm_unpackhi_epi8(v, vk0);
        vsum = _mm_add_epi32(vsum, _mm_madd_epi16(vl, vk1));
        vsum = _mm_add_epi32(vsum, _mm_madd_epi16(vh, vk1));
                                                // unpack and accumulate 16 bit values to
                                                // 32 bit partial sum vector

    }
    // horizontal add of four 32 bit partial sums and return result
    vsum = _mm_add_epi32(vsum, _mm_srli_si128(vsum, 8));
    vsum = _mm_add_epi32(vsum, _mm_srli_si128(vsum, 4));
    sum = _mm_cvtsi128_si32(vsum);
    return sum;
}

Note that there is one non-obvious trick in the above code - rather than further unpacking each 16 bit vector to a pair of 32 bit vectors (requiring 4 unpack instructions) and then using four 32 bit adds (another 4 instructions), we use _mm_madd_epi16 (PMADDWD) with a multiplicand of 1 and _mm_add_epi32 to effectively give us free unpacking, so we get the same result using 4 instructions instead of 8.

Note also that the input array, a[], needs to be 16 byte aligned, and n should be a multiple of 16.