Optimiser une boucle à l'aide d'instructions simd

**moomba** · 08/11/2012, 11h09

Bonjour,

Je cherche à optimiser une boucle classique, à savoir la résolution 2D de l’équation de la chaleur. Le calcul est très simple : on calcul U1 à partir de U0, puis U0 à partir de U1, et on recommence niter fois pour que le calcul converge. Il suffit de respecter le critère de stabilité pour que le calcul fonctionne.

Il s'agit d'une boucle utilisant des tableaux à deux dimensions et faisant appel à des instructions simples.

Je cherche à améliorer les performances en utilisant les instructions SIMD des processeurs, notamment les AVX des nouveaux Intels qui permettent de gérer 4 double à la fois. Il y a aussi l'instruction d'AMD permettant de faire une multiplication et une addition en 1 cycle.

Voici mon programme de test actuel, je cherche à pousser le compilateur à faire le travail lui même, mais ca en me dérange pas de mettre les mains dans le cambouis. Le raisonnement est très simple : je décompose de plus en plus les boucles pour étudier le comportement :

Code :

Sélectionner tout - Visualiser dans une fenêtre à part

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#include <stdio.h>
#include <time.h>
/*#include<emmintrin.h>*/
 
#define n1 102
#define n2 102
#define niter 20000
 
double U0[n1][n2];
double U1[n1][n2];
double U2[n1][n2]; /* tampon */
 
/* simd */
 
/*__m128d vU0[n1][n2];
__m128d vU1[n1][n2];
__m128d vU2[n1][n2]; *//* tampon */
 
 
int i,j,t;
double Dx,Dy,Lx,Ly,InvDxDx,InvDyDy,Dt,alpha,totaltime,Stab,DtAlpha,DxDx,DyDy;
clock_t time0,time1;
FILE *f1;
 
int main()
{
 
/* ---- GENERAL ---- */
 
   alpha = 0.4;
   totaltime = 1.0;
   Dt = totaltime/((niter-1)*1.0);
   Lx = 1.0;
   Ly = 1.0;
   Dx = Lx/((n1-1)*1.0);
   Dy = Ly/((n2-1)*1.0);
   InvDxDx = 1.0/(Dx*Dx);
   InvDyDy = 1.0/(Dy*Dy);
   DxDx = Dx*Dx;
   DyDy = Dy*Dy;
   Stab = alpha*Dt*(InvDxDx+InvDyDy);
   DtAlpha = Dt*alpha;
 
/* Stability if result <= 0.5 */
   printf("Stability factor : %f \n",Stab);
 
 
/* +----------------+ */
/* |     LOOP 0     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         U0[i][j] = 0.0;
         U1[i][j] = 0.0;
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      U0[i][0] = 1.0;
      U1[i][0] = 1.0;
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          U1[i][j] = U0[i][j] + DtAlpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy);
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          U0[i][j] = U1[i][j] + DtAlpha*( (U1[i+1][j]-2.0*U1[i][j]+U1[i-1][j])*InvDxDx + (U1[i][j+1]-2.0*U1[i][j]+U1[i][j-1])*InvDyDy);
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 0, total time : %f \n", (double) time1-time0);
 
 
 f1 = fopen ("out0.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j++)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, U0[i][j]);
    }
 }
 
 
 
 
/* +----------------+ */
/* |     LOOP 1     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         U0[i][j] = 0.0;
         U1[i][j] = 0.0;
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      U0[i][0] = 1.0;
      U1[i][0] = 1.0;
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          /* U1[i][j] = U0[i][j] + Dt*alpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy); */
 
          U1[i][j] = -2.0*U0[i][j];
 
          U1[i][j] = U1[i][j] + U0[i+1][j];
 
          U1[i][j] = U1[i][j] + U0[i-1][j];
 
          U1[i][j] = U1[i][j] * InvDxDx;
 
          U2[i][j] = -2.0*U0[i][j];
 
          U2[i][j] = U2[i][j] + U0[i][j+1];
 
          U2[i][j] = U2[i][j] + U0[i][j-1];
 
          U2[i][j] = U2[i][j] * InvDyDy;
 
          U1[i][j] = U1[i][j] + U2[i][j];
 
          U1[i][j] = U1[i][j] * DtAlpha;
 
          U1[i][j] = U1[i][j] + U0[i][j];
 
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
 
          U0[i][j] = -2.0*U1[i][j];
 
          U0[i][j] = U0[i][j] + U1[i+1][j];
 
          U0[i][j] = U0[i][j] + U1[i-1][j];
 
          U0[i][j] = U0[i][j] * InvDxDx;
 
          U2[i][j] = -2.0*U1[i][j];
 
          U2[i][j] = U2[i][j] + U1[i][j+1];
 
          U2[i][j] = U2[i][j] + U1[i][j-1];
 
          U2[i][j] = U2[i][j] * InvDyDy;
 
          U0[i][j] = U0[i][j] + U2[i][j];
 
          U0[i][j] = U0[i][j] * DtAlpha;
 
          U0[i][j] = U0[i][j] + U1[i][j];
 
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 1, total time : %f \n", (double) time1-time0);
 
 
 
/* End */
 
 f1 = fopen ("out1.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j++)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, U0[i][j]);
    }
 }
 
 
 
 
/* +----------------+ */
/* |     LOOP 2     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         U0[i][j] = 0.0;
         U1[i][j] = 0.0;
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      U0[i][0] = 1.0;
      U1[i][0] = 1.0;
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j=j+2)
       {
          /* U1[i][j] = U0[i][j] + Dt*alpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy); */
 
          U1[i][j] = -2.0*U0[i][j];
          U1[i][j+1] = -2.0*U0[i][j+1];
 
          U1[i][j] = U1[i][j] + U0[i+1][j];
          U1[i][j+1] = U1[i][j+1] + U0[i+1][j+1];
 
          U1[i][j] = U1[i][j] + U0[i-1][j];
          U1[i][j+1] = U1[i][j+1] + U0[i-1][j+1];
 
          U1[i][j] = U1[i][j] * InvDxDx;
          U1[i][j+1] = U1[i][j+1] * InvDxDx;
 
          U2[i][j] = -2.0*U0[i][j];
          U2[i][j+1] = -2.0*U0[i][j+1];
 
          U2[i][j] = U2[i][j] + U0[i][j+1];
          U2[i][j+1] = U2[i][j+1] + U0[i][j+2];
 
          U2[i][j] = U2[i][j] + U0[i][j-1];
          U2[i][j+1] = U2[i][j+1] + U0[i][j];
 
          U2[i][j] = U2[i][j] * InvDyDy;
          U2[i][j+1] = U2[i][j+1] * InvDyDy;
 
          U1[i][j] = U1[i][j] + U2[i][j];
          U1[i][j+1] = U1[i][j+1] + U2[i][j+1];
 
          U1[i][j] = U1[i][j] * DtAlpha;
          U1[i][j+1] = U1[i][j+1] * DtAlpha;
 
          U1[i][j] = U1[i][j] + U0[i][j];
          U1[i][j+1] = U1[i][j+1] + U0[i][j+1];
 
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j=j+2)
       {
 
          U0[i][j] = -2.0*U1[i][j];
          U0[i][j+1] = -2.0*U1[i][j+1];
 
          U0[i][j] = U0[i][j] + U1[i+1][j];
          U0[i][j+1] = U0[i][j+1] + U1[i+1][j+1];
 
          U0[i][j] = U0[i][j] + U1[i-1][j];
          U0[i][j+1] = U0[i][j+1] + U1[i-1][j+1];
 
          U0[i][j] = U0[i][j] * InvDxDx;
          U0[i][j+1] = U0[i][j+1] * InvDxDx;
 
          U2[i][j] = -2.0*U1[i][j];
          U2[i][j+1] = -2.0*U1[i][j+1];
 
          U2[i][j] = U2[i][j] + U1[i][j+1];
          U2[i][j+1] = U2[i][j+1] + U1[i][j+2];
 
          U2[i][j] = U2[i][j] + U1[i][j-1];
          U2[i][j+1] = U2[i][j+1] + U1[i][j];
 
          U2[i][j] = U2[i][j] * InvDyDy;
          U2[i][j+1] = U2[i][j+1] * InvDyDy;
 
          U0[i][j] = U0[i][j] + U2[i][j];
          U0[i][j+1] = U0[i][j+1] + U2[i][j+1];
 
          U0[i][j] = U0[i][j] * DtAlpha;
          U0[i][j+1] = U0[i][j+1] * DtAlpha;
 
          U0[i][j] = U0[i][j] + U1[i][j];
          U0[i][j+1] = U0[i][j+1] + U1[i][j+1];
 
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 2, total time : %f \n", (double) time1-time0);
 
 
 
/* End */
 
 f1 = fopen ("out2.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j++)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, U0[i][j]);
    }
 }
 
 
}

Les résultats sont pour le moment les mêmes avec gcc et icc : la première boucle est sensiblement moins rapide que la seconde, et la dernière est à la ramasse (presque deux fois plus lent). Je cherchai à le pousser à utiliser les SIMD par paquets de deux. (4 sur les Snady/Ivy Bridge)

Avez vous des idées sur la façon d'optimiser tout ça, et de pousser le compilateur à utiliser les SIMD pour accélérer le tout ?

Moomba

**moomba** · 08/11/2012, 12h04

Code mis à jours. Les instructions sont codés en dur, mais c'est encore plus lent...

Code :

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#include <stdio.h>
#include <time.h>
#include<emmintrin.h>
 
#define n1 102
#define n2 102
#define niter 20000
 
double U0[n1][n2];
double U1[n1][n2];
double U2[n1][n2]; /* tampon */
 
double *cU0[n1][n2];
 
/* simd */
 
__m128d vU0[n1][n2];
__m128d vU1[n1][n2];
__m128d vU2[n1][n2]; /* tampon */
 
int i,j,t;
double Dx,Dy,Lx,Ly,InvDxDx,InvDyDy,Dt,alpha,totaltime,Stab,DtAlpha,DxDx,DyDy;
clock_t time0,time1;
FILE *f1;
 
int main()
{
 
/* ---- GENERAL ---- */
 
   alpha = 0.4;
   totaltime = 1.0;
   Dt = totaltime/((niter-1)*1.0);
   Lx = 1.0;
   Ly = 1.0;
   Dx = Lx/((n1-1)*1.0);
   Dy = Ly/((n2-1)*1.0);
   InvDxDx = 1.0/(Dx*Dx);
   InvDyDy = 1.0/(Dy*Dy);
   DxDx = Dx*Dx;
   DyDy = Dy*Dy;
   Stab = alpha*Dt*(InvDxDx+InvDyDy);
   DtAlpha = Dt*alpha;
 
/* Stability if result <= 0.5 */
   printf("Stability factor : %f \n",Stab);
 
 
/* +----------------+ */
/* |     LOOP 0     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         U0[i][j] = 0.0;
         U1[i][j] = 0.0;
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      U0[i][0] = 1.0;
      U1[i][0] = 1.0;
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          U1[i][j] = U0[i][j] + DtAlpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy);
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          U0[i][j] = U1[i][j] + DtAlpha*( (U1[i+1][j]-2.0*U1[i][j]+U1[i-1][j])*InvDxDx + (U1[i][j+1]-2.0*U1[i][j]+U1[i][j-1])*InvDyDy);
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 0, total time : %f \n", (double) time1-time0);
 
 
 f1 = fopen ("out0.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j++)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, U0[i][j]);
    }
 }
 
 
 
 
/* +----------------+ */
/* |     LOOP 1     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         U0[i][j] = 0.0;
         U1[i][j] = 0.0;
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      U0[i][0] = 1.0;
      U1[i][0] = 1.0;
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          /* U1[i][j] = U0[i][j] + Dt*alpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy); */
 
          U1[i][j] = -2.0*U0[i][j];
 
          U1[i][j] = U1[i][j] + U0[i+1][j];
 
          U1[i][j] = U1[i][j] + U0[i-1][j];
 
          U1[i][j] = U1[i][j] * InvDxDx;
 
          U2[i][j] = -2.0*U0[i][j];
 
          U2[i][j] = U2[i][j] + U0[i][j+1];
 
          U2[i][j] = U2[i][j] + U0[i][j-1];
 
          U2[i][j] = U2[i][j] * InvDyDy;
 
          U1[i][j] = U1[i][j] + U2[i][j];
 
          U1[i][j] = U1[i][j] * DtAlpha;
 
          U1[i][j] = U1[i][j] + U0[i][j];
 
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
 
          U0[i][j] = -2.0*U1[i][j];
 
          U0[i][j] = U0[i][j] + U1[i+1][j];
 
          U0[i][j] = U0[i][j] + U1[i-1][j];
 
          U0[i][j] = U0[i][j] * InvDxDx;
 
          U2[i][j] = -2.0*U1[i][j];
 
          U2[i][j] = U2[i][j] + U1[i][j+1];
 
          U2[i][j] = U2[i][j] + U1[i][j-1];
 
          U2[i][j] = U2[i][j] * InvDyDy;
 
          U0[i][j] = U0[i][j] + U2[i][j];
 
          U0[i][j] = U0[i][j] * DtAlpha;
 
          U0[i][j] = U0[i][j] + U1[i][j];
 
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 1, total time : %f \n", (double) time1-time0);
 
 
 
/* End */
 
 f1 = fopen ("out1.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j++)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, U0[i][j]);
    }
 }
 
 
 
 
/* +----------------+ */
/* |     LOOP 2     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         U0[i][j] = 0.0;
         U1[i][j] = 0.0;
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      U0[i][0] = 1.0;
      U1[i][0] = 1.0;
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j=j+2)
       {
          /* U1[i][j] = U0[i][j] + Dt*alpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy); */
 
          U1[i][j] = -2.0*U0[i][j];
          U1[i][j+1] = -2.0*U0[i][j+1];
 
          U1[i][j] = U1[i][j] + U0[i+1][j];
          U1[i][j+1] = U1[i][j+1] + U0[i+1][j+1];
 
          U1[i][j] = U1[i][j] + U0[i-1][j];
          U1[i][j+1] = U1[i][j+1] + U0[i-1][j+1];
 
          U1[i][j] = U1[i][j] * InvDxDx;
          U1[i][j+1] = U1[i][j+1] * InvDxDx;
 
          U2[i][j] = -2.0*U0[i][j];
          U2[i][j+1] = -2.0*U0[i][j+1];
 
          U2[i][j] = U2[i][j] + U0[i][j+1];
          U2[i][j+1] = U2[i][j+1] + U0[i][j+2];
 
          U2[i][j] = U2[i][j] + U0[i][j-1];
          U2[i][j+1] = U2[i][j+1] + U0[i][j];
 
          U2[i][j] = U2[i][j] * InvDyDy;
          U2[i][j+1] = U2[i][j+1] * InvDyDy;
 
          U1[i][j] = U1[i][j] + U2[i][j];
          U1[i][j+1] = U1[i][j+1] + U2[i][j+1];
 
          U1[i][j] = U1[i][j] * DtAlpha;
          U1[i][j+1] = U1[i][j+1] * DtAlpha;
 
          U1[i][j] = U1[i][j] + U0[i][j];
          U1[i][j+1] = U1[i][j+1] + U0[i][j+1];
 
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j=j+2)
       {
 
          U0[i][j] = -2.0*U1[i][j];
          U0[i][j+1] = -2.0*U1[i][j+1];
 
          U0[i][j] = U0[i][j] + U1[i+1][j];
          U0[i][j+1] = U0[i][j+1] + U1[i+1][j+1];
 
          U0[i][j] = U0[i][j] + U1[i-1][j];
          U0[i][j+1] = U0[i][j+1] + U1[i-1][j+1];
 
          U0[i][j] = U0[i][j] * InvDxDx;
          U0[i][j+1] = U0[i][j+1] * InvDxDx;
 
          U2[i][j] = -2.0*U1[i][j];
          U2[i][j+1] = -2.0*U1[i][j+1];
 
          U2[i][j] = U2[i][j] + U1[i][j+1];
          U2[i][j+1] = U2[i][j+1] + U1[i][j+2];
 
          U2[i][j] = U2[i][j] + U1[i][j-1];
          U2[i][j+1] = U2[i][j+1] + U1[i][j];
 
          U2[i][j] = U2[i][j] * InvDyDy;
          U2[i][j+1] = U2[i][j+1] * InvDyDy;
 
          U0[i][j] = U0[i][j] + U2[i][j];
          U0[i][j+1] = U0[i][j+1] + U2[i][j+1];
 
          U0[i][j] = U0[i][j] * DtAlpha;
          U0[i][j+1] = U0[i][j+1] * DtAlpha;
 
          U0[i][j] = U0[i][j] + U1[i][j];
          U0[i][j+1] = U0[i][j+1] + U1[i][j+1];
 
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 2, total time : %f \n", (double) time1-time0);
 
 
 
/* End */
 
 f1 = fopen ("out2.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j++)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, U0[i][j]);
    }
 }
 
 
 
 
 
 
 
/* +----------------+ */
/* |     LOOP 3     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         vU0[i][j] = _mm_set1_pd(0.0);
         vU1[i][j] = _mm_set1_pd(0.0);
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      vU0[i][0] = _mm_set1_pd(1.0);
      vU1[i][0] = _mm_set1_pd(1.0);
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j+=2)
       {
          /* U1[i][j] = U0[i][j] + Dt*alpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy); */
 
          /*va = _mm_load_pd(cU0[i][j]);
          vb = __m128d -2.0;
          vU1[i][j] = _mm_mul_pd (vb, va);*/
 
 
          __m128d va = _mm_set1_pd(-2.0);			/* U1[i][j] = -2.0*U0[i][j]; */
          vU1[i][j] = _mm_mul_pd(va,vU0[i][j]);
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU0[i+1][j]);	/* U1[i][j] = U1[i][j] + U0[i+1][j]; */
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU0[i-1][j]);	/* U1[i][j] = U1[i][j] + U0[i-1][j]; */
 
          __m128d vb = _mm_set1_pd(InvDxDx);			/* U1[i][j] = U1[i][j] * InvDxDx; */
          vU1[i][j] = _mm_mul_pd(vb,vU1[i][j]);
 
          vU2[i][j] = _mm_mul_pd(va,vU0[i][j]);			/* U2[i][j] = -2.0*U0[i][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU0[i+1][j]);	/* U2[i][j] = U2[i][j] + U0[i+1][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU0[i-1][j]);	/* U2[i][j] = U2[i][j] + U0[i-1][j]; */
 
          __m128d vc = _mm_set1_pd(InvDyDy);			/* U2[i][j] = U2[i][j] * InvDyDy; */
          vU2[i][j] = _mm_mul_pd(vc,vU2[i][j]);
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU2[i][j]);		/* U1[i][j] = U1[i][j] + U2[i][j]; */
 
          __m128d vd = _mm_set1_pd(DtAlpha);			/* U1[i][j] = U1[i][j] * DtAlpha; */
          vU1[i][j] = _mm_mul_pd(vd,vU1[i][j]);
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU0[i][j]);		/* U1[i][j] = U1[i][j] + U0[i][j]; */
 
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
          __m128d va = _mm_set1_pd(-2.0);			/* U0[i][j] = -2.0*U1[i][j]; */
          vU0[i][j] = _mm_mul_pd(va,vU1[i][j]);
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU1[i+1][j]);	/* U0[i][j] = U0[i][j] + U1[i+1][j]; */
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU1[i-1][j]);	/* U0[i][j] = U0[i][j] + U1[i-1][j]; */
 
          __m128d vb = _mm_set1_pd(InvDxDx);			/* U0[i][j] = U0[i][j] * InvDxDx; */
          vU0[i][j] = _mm_mul_pd(vb,vU0[i][j]);
 
          vU2[i][j] = _mm_mul_pd(va,vU1[i][j]);			/* U2[i][j] = -2.0*U1[i][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU1[i+1][j]);	/* U2[i][j] = U2[i][j] + U1[i+1][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU1[i-1][j]);	/* U2[i][j] = U2[i][j] + U1[i-1][j]; */
 
          __m128d vc = _mm_set1_pd(InvDyDy);			/* U2[i][j] = U2[i][j] * InvDyDy; */
          vU2[i][j] = _mm_mul_pd(vc,vU2[i][j]);
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU2[i][j]);		/* U0[i][j] = U0[i][j] + U2[i][j]; */
 
          __m128d vd = _mm_set1_pd(DtAlpha);			/* U0[i][j] = U0[i][j] * DtAlpha; */
          vU0[i][j] = _mm_mul_pd(vd,vU0[i][j]);
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU1[i][j]);		/* U0[i][j] = U0[i][j] + U1[i][j]; */
 
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 3, total time : %f \n", (double) time1-time0);
 
 
 
/* End */
 
 f1 = fopen ("out3.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j+=2)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, vU0[i][j]);
    }
 }
 
 
 
 
/* +----------------+ */
/* |     LOOP 4     | */
/* +----------------+ */
 
/* Init */
   for( i = 0; i < n1; i++)
   {
      for( j = 0; j < n2; j++)
      {
         vU0[i][j] = _mm_set1_pd(0.0);
         vU1[i][j] = _mm_set1_pd(0.0);
      }
   }
 
   for( i = 0; i < n1; i++)
   {
      vU0[i][0] = _mm_set1_pd(1.0);
      vU1[i][0] = _mm_set1_pd(1.0);
   }
 
   printf("Init OK \n");
 
/* Core */
 
 time0=clock();
 
          __m128d va = _mm_set1_pd(-2.0);			/* U1[i][j] = -2.0*U0[i][j]; */
          __m128d vb = _mm_set1_pd(InvDxDx);			/* U1[i][j] = U1[i][j] * InvDxDx; */
          __m128d vc = _mm_set1_pd(InvDyDy);			/* U2[i][j] = U2[i][j] * InvDyDy; */
          __m128d vd = _mm_set1_pd(DtAlpha);			/* U1[i][j] = U1[i][j] * DtAlpha; */
 
 for( t = 0; t < niter; t++)
 {
 
    /* even */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j+=2)
       {
          /* U1[i][j] = U0[i][j] + Dt*alpha*( (U0[i+1][j]-2.0*U0[i][j]+U0[i-1][j])*InvDxDx + (U0[i][j+1]-2.0*U0[i][j]+U0[i][j-1])*InvDyDy); */
 
          /*va = _mm_load_pd(cU0[i][j]);
          vb = __m128d -2.0;
          vU1[i][j] = _mm_mul_pd (vb, va);*/
 
 
 
          vU1[i][j] = _mm_mul_pd(va,vU0[i][j]);
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU0[i+1][j]);	/* U1[i][j] = U1[i][j] + U0[i+1][j]; */
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU0[i-1][j]);	/* U1[i][j] = U1[i][j] + U0[i-1][j]; */
 
 
          vU1[i][j] = _mm_mul_pd(vb,vU1[i][j]);
 
          vU2[i][j] = _mm_mul_pd(va,vU0[i][j]);			/* U2[i][j] = -2.0*U0[i][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU0[i+1][j]);	/* U2[i][j] = U2[i][j] + U0[i+1][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU0[i-1][j]);	/* U2[i][j] = U2[i][j] + U0[i-1][j]; */
 
 
          vU2[i][j] = _mm_mul_pd(vc,vU2[i][j]);
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU2[i][j]);		/* U1[i][j] = U1[i][j] + U2[i][j]; */
 
 
          vU1[i][j] = _mm_mul_pd(vd,vU1[i][j]);
 
          vU1[i][j] = _mm_add_pd(vU1[i][j],vU0[i][j]);		/* U1[i][j] = U1[i][j] + U0[i][j]; */
 
       }
    }
 
    /* odd */
    for( i = 1; i < n1-1; i++)
    {
       for( j = 1; j < n2-1; j++)
       {
 
          vU0[i][j] = _mm_mul_pd(va,vU1[i][j]);
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU1[i+1][j]);	/* U0[i][j] = U0[i][j] + U1[i+1][j]; */
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU1[i-1][j]);	/* U0[i][j] = U0[i][j] + U1[i-1][j]; */
 
 
          vU0[i][j] = _mm_mul_pd(vb,vU0[i][j]);
 
          vU2[i][j] = _mm_mul_pd(va,vU1[i][j]);			/* U2[i][j] = -2.0*U1[i][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU1[i+1][j]);	/* U2[i][j] = U2[i][j] + U1[i+1][j]; */
 
          vU2[i][j] = _mm_add_pd(vU2[i][j],vU1[i-1][j]);	/* U2[i][j] = U2[i][j] + U1[i-1][j]; */
 
 
          vU2[i][j] = _mm_mul_pd(vc,vU2[i][j]);
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU2[i][j]);		/* U0[i][j] = U0[i][j] + U2[i][j]; */
 
 
          vU0[i][j] = _mm_mul_pd(vd,vU0[i][j]);
 
          vU0[i][j] = _mm_add_pd(vU0[i][j],vU1[i][j]);		/* U0[i][j] = U0[i][j] + U1[i][j]; */
 
       }
    }
 
   }
 
 time1=clock();
 
 printf("Loop 4, total time : %f \n", (double) time1-time0);
 
 
 
/* End */
 
 f1 = fopen ("out4.dat", "wt");
 for( i = 1; i < n1-1; i++)
 {
    for( j = 1; j < n2-1; j+=2)
    {
       fprintf (f1, "%d\t%d\t%f\n", i, j, vU0[i][j]);
    }
 }
 
}

**mith06** · 08/11/2012, 16h44

Salut,

Je doute qui tu puisse faire comprendre au compilo qu'il faut utiliser une instruction SIMD. je pense qu'il faut obligatoirement passer par de l'assembleur, mais je n'en mettrais pas ma main a couper...

Tu peux essayer de jouer avec les option de compilation
Avec gcc de tenterais le coup avec -O3 -march=corei7

SI ca ne marche pas , cela me confortera dans l'idée que les architectures CISC ca sert à rien, sinon à consommer + => polluer +.

Bon courage.

**moomba** · 08/11/2012, 17h22

Les deux dernières boucles utilisent des instructions spécifiques aux SIMD, mais effectivement gcc ne semble pas en tirer partie.

Cependant, concernant les CISC je peut t'assurer qu'elles fonctionnent : j'ai réussi en Fortran 95 à faire comprendre au compilateur Ifort 12.x d'utiliser les SSE dans une boucle particulière (qui consomme presque 95% du temps de calcul du code qui est de plusieurs semaines tout de même sur 1024 processeurs). Le gain est de 1.73x environ pour du double précision, donc quand on arrive à les lancer ça sert, et pas qu'un peu. J'attends des résultats encore meilleurs avec l'AVX.

Mais il faut les activer, tout le problème est là

**mith06** · 09/11/2012, 14h08

As tu essayer avec l'option de compilation -mavx?

**moomba** · 10/11/2012, 19h31

Bonne idée. Mais mon processeur ne supporte pas l'avx, c'est un xeon équivalent au i7 920, donc sur le socket 1366. et le super calculateur est sur westmer, donc pas d'avx non plus.

Je me demande si ce n'est pas due au fait que nos processeurs ont deux fpu, et que donc le sse en double précision ne sert à rien...

Optimiser une boucle à l'aide d'instructions simd

C

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