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Optimization_1x4_7
Jianyu Huang edited this page Aug 11, 2016
·
4 revisions
Copy the contents of file MMult_1x4_6.c
into a file named MMult_1x4_7.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 accumulate in registers and put A( 0, p ) in a register */
int p;
register double
/* hold contributions to
C( 0, 0 ), C( 0, 1 ), C( 0, 2 ), C( 0, 3 ) */
c_00_reg, c_01_reg, c_02_reg, c_03_reg,
/* holds A( 0, p ) */
a_0p_reg;
c_00_reg = 0.0;
c_01_reg = 0.0;
c_02_reg = 0.0;
c_03_reg = 0.0;
for ( p=0; p<k; p++ ){
a_0p_reg = A( 0, p );
c_00_reg += a_0p_reg * B( p, 0 );
c_01_reg += a_0p_reg * B( p, 1 );
c_02_reg += a_0p_reg * B( p, 2 );
c_03_reg += a_0p_reg * B( p, 3 );
}
C( 0, 0 ) += c_00_reg;
C( 0, 1 ) += c_01_reg;
C( 0, 2 ) += c_02_reg;
C( 0, 3 ) += c_03_reg;
}
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 use pointer to track where in four columns of B we are */
int p;
register double
/* hold contributions to
C( 0, 0 ), C( 0, 1 ), C( 0, 2 ), C( 0, 3 ) */
c_00_reg, c_01_reg, c_02_reg, c_03_reg,
/* holds A( 0, p ) */
a_0p_reg;
double
/* Point to the current elements in the four columns of B */
*bp0_pntr, *bp1_pntr, *bp2_pntr, *bp3_pntr;
bp0_pntr = &B( 0, 0 );
bp1_pntr = &B( 0, 1 );
bp2_pntr = &B( 0, 2 );
bp3_pntr = &B( 0, 3 );
c_00_reg = 0.0;
c_01_reg = 0.0;
c_02_reg = 0.0;
c_03_reg = 0.0;
for ( p=0; p<k; p++ ){
a_0p_reg = A( 0, p );
c_00_reg += a_0p_reg * *bp0_pntr++;
c_01_reg += a_0p_reg * *bp1_pntr++;
c_02_reg += a_0p_reg * *bp2_pntr++;
c_03_reg += a_0p_reg * *bp3_pntr++;
}
C( 0, 0 ) += c_00_reg;
C( 0, 1 ) += c_01_reg;
C( 0, 2 ) += c_02_reg;
C( 0, 3 ) += c_03_reg;
}
Change the first lines in the makefile
to
OLD := MMult_1x4_6
NEW := MMult_1x4_7
make run
octave:3> PlotAll % this will create the plot
This time the performance graph will look something like
We now use four pointers, bp0_pntr
, bp1_pntr
, bp2_pntr
, and bp3_pntr
, to access the elements B( p, 0 )
, B( p, 1 )
, B( p, 2 )
, B( p, 3 )
. This reduces indexing overhead.