Question

This post is closely related to another one I posted some days ago. This time, I wrote a simple code that just adds a pair of arrays of elements, multiplies the result by the values in another array and stores it in a forth array, all variables floating point double precision typed.

I made two versions of that code: one with SSE instructions, using calls to and another one without them I then compiled them with gcc and -O0 optimization level. I write them below:

// SSE VERSION

#define N 10000
#define NTIMES 100000
#include <time.h>
#include <stdio.h>
#include <xmmintrin.h>
#include <pmmintrin.h>

double a[N] __attribute__((aligned(16)));
double b[N] __attribute__((aligned(16)));
double c[N] __attribute__((aligned(16)));
double r[N] __attribute__((aligned(16)));

int main(void){
  int i, times;
  for( times = 0; times < NTIMES; times++ ){
     for( i = 0; i <N; i+= 2){ 
        __m128d mm_a = _mm_load_pd( &a[i] );  
        _mm_prefetch( &a[i+4], _MM_HINT_T0 );
        __m128d mm_b = _mm_load_pd( &b[i] );  
        _mm_prefetch( &b[i+4] , _MM_HINT_T0 );
        __m128d mm_c = _mm_load_pd( &c[i] );
        _mm_prefetch( &c[i+4] , _MM_HINT_T0 );
        __m128d mm_r;
        mm_r = _mm_add_pd( mm_a, mm_b );
        mm_a = _mm_mul_pd( mm_r , mm_c );
        _mm_store_pd( &r[i], mm_a );
      }   
   }
 }

//NO SSE VERSION
//same definitions as before
int main(void){
  int i, times;
   for( times = 0; times < NTIMES; times++ ){
     for( i = 0; i < N; i++ ){
      r[i] = (a[i]+b[i])*c[i];
    }   
  }
}

When compiling them with -O0, gcc makes use of XMM/MMX registers and SSE intstructions, if not specifically given the -mno-sse (and others) options. I inspected the assembly code generated for the second code and I noticed that it makes use of movsd, addsd and mulsd instructions. So it makes use of SSE instructions but only of those that use the lowest part of the registers, if I am not wrong. The assembly code generated for the first C code made use, as expected, of the addp and mulpd instructions, though a pretty larger assembly code was generated.

Anyway, the first code should get better profit, as far as I know, of SIMD paradigm, since every iteration two result values are computed. Still that, the second code performs something such as a 25 per cent faster than the first one. I also made a test with single precision values and get similar results. What’s the reason for that?

Answer 1

Vectorization in GCC is enabled at -O3. That’s why at -O0, you see only the ordinary scalar SSE2 instructions (movsd, addsd, etc). Using GCC 4.6.1 and your second example:

#define N 10000
#define NTIMES 100000

double a[N] __attribute__ ((aligned (16)));
double b[N] __attribute__ ((aligned (16)));
double c[N] __attribute__ ((aligned (16)));
double r[N] __attribute__ ((aligned (16)));

int
main (void)
{
  int i, times;
  for (times = 0; times < NTIMES; times++)
    {
      for (i = 0; i < N; ++i)
        r[i] = (a[i] + b[i]) * c[i];
    }

  return 0;
}

and compiling with gcc -S -O3 -msse2 sse.c produces for the inner loop the following instructions, which is pretty good:

.L3:
    movapd  a(%eax), %xmm0
    addpd   b(%eax), %xmm0
    mulpd   c(%eax), %xmm0
    movapd  %xmm0, r(%eax)
    addl    $16, %eax
    cmpl    $80000, %eax
    jne .L3

As you can see, with the vectorization enabled GCC emits code to perform two loop iterations in parallel. It can be improved, though – this code uses the lower 128 bits of the SSE registers, but it can use the full the 256-bit YMM registers, by enabling the AVX encoding of SSE instructions (if available on the machine). So, compiling the same program with gcc -S -O3 -msse2 -mavx sse.c gives for the inner loop:

.L3:
    vmovapd a(%eax), %ymm0
    vaddpd  b(%eax), %ymm0, %ymm0
    vmulpd  c(%eax), %ymm0, %ymm0
    vmovapd %ymm0, r(%eax)
    addl    $32, %eax
    cmpl    $80000, %eax
    jne .L3

Note that v in front of each instruction and that instructions use the 256-bit YMM registers, four iterations of the original loop are executed in parallel.