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Optimization_1x4_3
Jianyu Huang edited this page Aug 11, 2016
·
4 revisions
Copy the contents of file MMult2.c
into a file named MMult_1x4_3.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 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 the C( i,j ) with the inner product of the ith row of A
and the jth column of B */
AddDot( k, &A( i,0 ), lda, &B( 0,j ), &C( i,j ) );
/* Update the C( i,j+1 ) with the inner product of the ith row of A
and the (j+1)th column of B */
AddDot( k, &A( i,0 ), lda, &B( 0,j+1 ), &C( i,j+1 ) );
/* Update the C( i,j+2 ) with the inner product of the ith row of A
and the (j+2)th column of B */
AddDot( k, &A( i,0 ), lda, &B( 0,j+2 ), &C( i,j+2 ) );
/* Update the C( i,j+3 ) with the inner product of the ith row of A
and the (j+1)th column of B */
AddDot( k, &A( i,0 ), lda, &B( 0,j+3 ), &C( i,j+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 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 ];
}
}
Change the first lines in the makefile
to
OLD := MMult2
NEW := MMult_1x4_3 # Notice the two underscores!!
make run
octave:3> PlotAll % this will create the plot
This time the performance graph will look something like
Still, no performance benefit.