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Optimization_1x4_5
Jianyu Huang edited this page Aug 11, 2016
·
6 revisions
Copy the contents of file MMult_1x4_4.c
into a file named MMult_1x4_5.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 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 );
}
}
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 merge the four loops, computing four inner
products simultaneously. */
int p;
// 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 ) );
for ( p=0; p<k; p++ ){
C( 0, 0 ) += A( 0, p ) * B( p, 0 );
C( 0, 1 ) += A( 0, p ) * B( p, 1 );
C( 0, 2 ) += A( 0, p ) * B( p, 2 );
C( 0, 3 ) += A( 0, p ) * B( p, 3 );
}
}
Change the first lines in the makefile
to
OLD := MMult_1x4_4
NEW := MMult_1x4_5
make run
octave:3> PlotAll % this will create the plot
This time the performance graph will look something like
Now we start seeing a performance benefit. The reason is that the four loops have been fused and therefore the four inner products are now being performed simultaneously. This has the following benefits:
-
The index
p
needs only be updated once every eight floating point operations. -
Element
A( 0, p )
needs only be brought in from memory once instead of four times. (This only becomes a benefit when the matrices no longer fit in the L2 cache.)