Optimization_1x4_4

Copy the contents of file MMult_1x4_3.c into a file named MMult_1x4_4.c and change the contents:

from

/* Create macros so that the matrices are stored in column-major order */

#define A(i,j) a[ (j)*lda + (i) ]
#define B(i,j) b[ (j)*ldb + (i) ]
#define C(i,j) c[ (j)*ldc + (i) ]

/* Routine for computing C = A * B + C */

void AddDot( int, double *, int, double *, double * );
void AddDot1x4( int, double *, int,  double *, int, double *, int )

void MY_MMult( int m, int n, int k, double *a, int lda, 
                                    double *b, int ldb,
                                    double *c, int ldc )
{
  int i, j;

  for ( j=0; j<n; j+=4 ){        /* Loop over the columns of C, unrolled by 4 */
    for ( i=0; i<m; i+=1 ){        /* Loop over the rows of C */
      /* Update C( i,j ), C( i,j+1 ), C( i,j+2 ), and C( i,j+3 ) in
	 one routine (four inner products) */

      AddDot1x4( k, &A( i,0 ), lda, &B( 0,j ), ldb, &C( i,j ), ldc );
    }
  }
}


void AddDot1x4( int k, double *a, int lda,  double *b, int ldb, double *c, int ldc )
{
  /* So, this routine computes four elements of C: 

           C( 0, 0 ), C( 0, 1 ), C( 0, 2 ), C( 0, 3 ).  

     Notice that this routine is called with c = C( i, j ) in the
     previous routine, so these are actually the elements 

           C( i, j ), C( i, j+1 ), C( i, j+2 ), C( i, j+3 ) 
	  
     in the original matrix C */ 

  AddDot( k, &A( 0, 0 ), lda, &B( 0, 0 ), &C( 0, 0 ) );
  AddDot( k, &A( 0, 0 ), lda, &B( 0, 1 ), &C( 0, 1 ) );
  AddDot( k, &A( 0, 0 ), lda, &B( 0, 2 ), &C( 0, 2 ) );
  AddDot( k, &A( 0, 0 ), lda, &B( 0, 3 ), &C( 0, 3 ) );
}


/* Create macro to let X( i ) equal the ith element of x */

#define X(i) x[ (i)*incx ]

void AddDot( int k, double *x, int incx,  double *y, double *gamma )
{
  /* compute gamma := x' * y + gamma with vectors x and y of length n.

     Here x starts at location x with increment (stride) incx and y starts at location y and has (implicit) stride of 1.
  */
 
  int p;

  for ( p=0; p<k; p++ ){
    *gamma += X( p ) * y[ p ];     
  }
}

to

/* Create macros so that the matrices are stored in column-major order */

#define A(i,j) a[ (j)*lda + (i) ]
#define B(i,j) b[ (j)*ldb + (i) ]
#define C(i,j) c[ (j)*ldc + (i) ]

/* Routine for computing C = A * B + C */

void AddDot1x4( int, double *, int,  double *, int, double *, int )

void MY_MMult( int m, int n, int k, double *a, int lda, 
                                    double *b, int ldb,
                                    double *c, int ldc )
{
  int i, j;

  for ( j=0; j<n; j+=4 ){        /* Loop over the columns of C, unrolled by 4 */
    for ( i=0; i<m; i+=1 ){        /* Loop over the rows of C */
      /* Update C( i,j ), C( i,j+1 ), C( i,j+2 ), and C( i,j+3 ) in
	 one routine (four inner products) */

      AddDot1x4( k, &A( i,0 ), lda, &B( 0,j ), ldb, &C( i,j ), ldc );
    }
  }
}


void AddDot1x4( int k, double *a, int lda,  double *b, int ldb, double *c, int ldc )
{
  /* So, this routine computes four elements of C: 

           C( 0, 0 ), C( 0, 1 ), C( 0, 2 ), C( 0, 3 ).  

     Notice that this routine is called with c = C( i, j ) in the
     previous routine, so these are actually the elements 

           C( i, j ), C( i, j+1 ), C( i, j+2 ), C( i, j+3 ) 
	  
     in the original matrix C.

     In this version, we "inline" AddDot */ 

  int p;

  //  AddDot( k, &A( 0, 0 ), lda, &B( 0, 0 ), &C( 0, 0 ) );
  for ( p=0; p<k; p++ ){
    C( 0, 0 ) += A( 0, p ) * B( p, 0 );     
  }

  //  AddDot( k, &A( 0, 0 ), lda, &B( 0, 1 ), &C( 0, 1 ) );
  for ( p=0; p<k; p++ ){
    C( 0, 1 ) += A( 0, p ) * B( p, 1 );     
  }

  //  AddDot( k, &A( 0, 0 ), lda, &B( 0, 2 ), &C( 0, 2 ) );
  for ( p=0; p<k; p++ ){
    C( 0, 2 ) += A( 0, p ) * B( p, 2 );     
  }

  //  AddDot( k, &A( 0, 0 ), lda, &B( 0, 3 ), &C( 0, 3 ) );
  for ( p=0; p<k; p++ ){
    C( 0, 3 ) += A( 0, p ) * B( p, 3 );     
  }
}

• Change the first lines in the makefile to

OLD  := MMult_1x4_3
NEW  := MMult_1x4_4     

• make run

octave:3> PlotAll        % this will create the plot

This time the performance graph will look something like

Still, no performance benefit.