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tile.h
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tile.h
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/* 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) ]
*/
#define A(i,j) a[ (i)*lda + (j) ]
#define B(i,j) b[ (i)*ldb + (j) ]
#define C(i,j) c[ (i)*ldc + (j) ]
//#define packedC(i,j) packedC[ (i)*ldc + (j) ]
#define Bs(i,j) Bs[ (j)*ldb + (i) ]
typedef union
{
__m256d v;
double d[4];
} v4df_t;
void AddDot4x4( int, double *, int, double *, int, double *, int);
void AddDot4x8( int, double *, int, double *, int, double *, int);
void AddDot12x4( int, double *, int, double *, int, double *, int);
void PackB_and_AddDot12x4( int, double *, int, double *, int, double *, int, double *, int);
void PackMatrixA_4( int, double *, int, double *, int, int);
void PackMatrixA_12( int, double *, int, double *, int, int);
void PackMatrixB_12( int, double *, int, double * );
void PackMatrixB_4( int, double *, int, double * );
void InnerKernel12x4( int m, int n, int k, double *a, int lda,
double *b, int ldb,
double *c, int ldc, int first_time, double* packedA, double* packedB)
{
int i, j;
for ( j=0; j<m; j+=12 ){ /* Loop over the columns of C, unrolled by 4 */
if ( first_time )
{
if(j!=60)
PackMatrixA_12( k, &A( j, 0 ), lda, &packedA[ j*k ], j, m);
else
PackMatrixA_4( k, &A( j, 0 ), lda, &packedA[ j*k ], j, m);
}
for ( i=0; i<n; i+=4 ){ /* 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) */
if ( j == 0 )
{
// PackMatrixB( k, &B( 0, i ), ldb, &packedB[ i*k ]);
PackB_and_AddDot12x4( k, &packedA[ j*k ], 6, &B( 0, i ), ldb, &packedB[ i*k ], 8, &C( j,i ), ldc);
// AddDot6x8( k, &packedA[ j*k ], 6, &packedB[ i*k ], 8, &C( j,i ), ldc);
}
else if(j==60)
AddDot4x4( k, &packedA[ j*k ], 6, &packedB[ i*k ], 8, &C( j,i ), ldc);
else
AddDot12x4( k, &packedA[ j*k ], 6, &packedB[ i*k ], 8, &C( j,i ), ldc);
}
}
}
void PackMatrixB_12( int k, double *b, int ldb, double *b_to)
{
int j;
__m256d reg1;
#pragma unroll(4)
//#pragma noprefetch
for( j=0; j<k; j++){ /* loop over columns of A */
double
*b_ij_pntr = b + j * ldb;
reg1 = _mm256_load_pd(b_ij_pntr);
_mm256_store_pd(b_to, reg1);
b_to += 4;
reg1 = _mm256_load_pd(b_ij_pntr + 4);
_mm256_store_pd(b_to, reg1);
b_to += 4;
reg1 = _mm256_load_pd(b_ij_pntr + 8);
_mm256_store_pd(b_to, reg1);
b_to += 4;
}
}
void PackMatrixA_12( int k, double *a, int lda, double *a_to, int j, int m)
{
int i;
double
*a_i0_pntr = &A( 0, 0 ), *a_i1_pntr = &A( 1, 0 ),
*a_i2_pntr = &A( 2, 0 ), *a_i3_pntr = &A( 3, 0 ),
*a_i4_pntr = &A( 4, 0 ), *a_i5_pntr = &A( 5, 0 ),
*a_i6_pntr = &A( 6, 0 ), *a_i7_pntr = &A( 6, 0 ),
*a_i8_pntr = &A( 8, 0 ), *a_i9_pntr = &A( 9, 0 ),
*a_i10_pntr = &A( 10, 0 ), *a_i11_pntr = &A( 11, 0 );
v4df_t vreg;
#pragma unroll(4)
for( i=0; i<k; i++){ /* loop over rows of B */
*a_to++ = *a_i0_pntr++;
*a_to++ = *a_i1_pntr++;
*a_to++ = *a_i2_pntr++;
*a_to++ = *a_i3_pntr++;
*a_to++ = *a_i4_pntr++;
*a_to++ = *a_i5_pntr++;
*a_to++ = *a_i6_pntr++;
*a_to++ = *a_i7_pntr++;
*a_to++ = *a_i8_pntr++;
*a_to++ = *a_i9_pntr++;
*a_to++ = *a_i10_pntr++;
*a_to++ = *a_i11_pntr++;
}
}
void PackMatrixB_4( int k, double *b, int ldb, double *b_to)
{
int j;
__m256d reg1;
#pragma unroll(4)
//#pragma noprefetch
for( j=0; j<k; j++){ /* loop over columns of A */
double
*b_ij_pntr = b + j * ldb;
reg1 = _mm256_load_pd(b_ij_pntr);
_mm256_store_pd(b_to, reg1);
b_to += 4;
}
}
void PackMatrixA_4( int k, double *a, int lda, double *a_to, int j, int m)
{
int i;
double
*a_i0_pntr = &A( 0, 0 ), *a_i1_pntr = &A( 1, 0 ),
*a_i2_pntr = &A( 2, 0 ), *a_i3_pntr = &A( 3, 0 );
v4df_t vreg;
#pragma unroll(4)
for( i=0; i<k; i++){ /* loop over rows of B */
*a_to++ = *a_i0_pntr++;
*a_to++ = *a_i1_pntr++;
*a_to++ = *a_i2_pntr++;
*a_to++ = *a_i3_pntr++;
}
}
void AddDot4x4( int k, double *a, int lda, double *b, int ldb, double *c, int ldc)
{
int p;
v4df_t
zero_vreg,
c00_vreg, c04_vreg,
c10_vreg, c14_vreg,
c20_vreg, c24_vreg,
c30_vreg, c34_vreg,
b00_vreg,
a0_vreg;
zero_vreg.v = _mm256_set1_pd(0);
c00_vreg.v = zero_vreg.v;
c04_vreg.v = zero_vreg.v;
c10_vreg.v = zero_vreg.v;
c14_vreg.v = zero_vreg.v;
c20_vreg.v = zero_vreg.v;
c24_vreg.v = zero_vreg.v;
c30_vreg.v = zero_vreg.v;
c34_vreg.v = zero_vreg.v;
#pragma noprefetch
#pragma unroll(8)
for ( p=0; p<k; p++ ){
b00_vreg.v = _mm256_load_pd( (double *) b );
b += 4;
/* First row and second rows */
a0_vreg.v = _mm256_set1_pd( *(double *) a ); /* load and duplicate */
c00_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c00_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+1) ); /* load and duplicate */
c10_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c10_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+2) ); /* load and duplicate */
c20_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c20_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+3) ); /* load and duplicate */
c30_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c30_vreg.v);
a += 4;
/*
if(profiling)
{
print256(" in computing a ", a_0p_a_1p_a_2p_a_3p_vreg);
print256(" in computing b ", b_p0_vreg);
print256(" in computing c ", c_00_c_10_c_20_c_30_vreg);
}
*/
}
// _mm_prefetch((const char *)b+k*8, _MM_HINT_T1);
c00_vreg.v = _mm256_add_pd(c00_vreg.v, _mm256_load_pd(&C(0,0)));
c10_vreg.v = _mm256_add_pd(c10_vreg.v, _mm256_load_pd(&C(1,0)));
c20_vreg.v = _mm256_add_pd(c20_vreg.v, _mm256_load_pd(&C(2,0)));
c30_vreg.v = _mm256_add_pd(c30_vreg.v, _mm256_load_pd(&C(3,0)));
_mm256_store_pd(&C(0, 0), c00_vreg.v);
_mm256_store_pd(&C(1, 0), c10_vreg.v);
_mm256_store_pd(&C(2, 0), c20_vreg.v);
_mm256_store_pd(&C(3, 0), c30_vreg.v);
}
void PackB_and_AddDot12x4( int k, double *a, int lda, double *ob, int ldb, double *b, int ldb2, double *c, int ldc)
{
int j;
double* b_to = b;
int p;
v4df_t
zero_vreg,
c00_vreg, c60_vreg,
c10_vreg, c70_vreg,
c20_vreg, c80_vreg,
c30_vreg, c90_vreg,
c40_vreg, c100_vreg,
c50_vreg, c110_vreg,
b00_vreg,
a0_vreg;
zero_vreg.v = _mm256_set1_pd(0);
c00_vreg.v = zero_vreg.v;
c60_vreg.v = zero_vreg.v;
c10_vreg.v = zero_vreg.v;
c70_vreg.v = zero_vreg.v;
c20_vreg.v = zero_vreg.v;
c80_vreg.v = zero_vreg.v;
c30_vreg.v = zero_vreg.v;
c90_vreg.v = zero_vreg.v;
c40_vreg.v = zero_vreg.v;
c100_vreg.v = zero_vreg.v;
c50_vreg.v = zero_vreg.v;
c110_vreg.v = zero_vreg.v;
#pragma noprefetch
#pragma unroll(8)
for ( p=0; p<k; p++ ){
_mm_prefetch((const char *)(ob + (p+1)*ldb), _MM_HINT_T1);
_mm_prefetch((const char *)a+8, _MM_HINT_T1);
double *b_ij_pntr = ob + p * ldb;
b00_vreg.v = _mm256_load_pd(b_ij_pntr);
// b00_vreg.v = _mm256_load_pd( (double *) b );
// b04_vreg.v = _mm256_load_pd( (double *) (b+4) );
// b += 8;
/* First row and second rows */
a0_vreg.v = _mm256_set1_pd( *(double *) a ); /* load and duplicate */
c00_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c00_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+1) ); /* load and duplicate */
c10_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c10_vreg.v);
_mm256_store_pd(b_to, b00_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+2) ); /* load and duplicate */
c20_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c20_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+3) ); /* load and duplicate */
c30_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c30_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+4) ); /* load and duplicate */
c40_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c40_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+5) ); /* load and duplicate */
c50_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c50_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+6) ); /* load and duplicate */
c60_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c60_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+7) ); /* load and duplicate */
c70_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c70_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+8) ); /* load and duplicate */
c80_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c80_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+9) ); /* load and duplicate */
c90_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c90_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+10) ); /* load and duplicate */
c100_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c100_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+11) ); /* load and duplicate */
c110_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c110_vreg.v);
a += 12;
b_to += 4;
/*
if(profiling)
{
print256(" in computing a ", a_0p_a_1p_a_2p_a_3p_vreg);
print256(" in computing b ", b_p0_vreg);
print256(" in computing c ", c_00_c_10_c_20_c_30_vreg);
}
*/
}
// _mm_prefetch((const char *)b+k*8, _MM_HINT_T1);
c00_vreg.v = _mm256_add_pd(c00_vreg.v, _mm256_load_pd(&C(0,0)));
c60_vreg.v = _mm256_add_pd(c60_vreg.v, _mm256_load_pd(&C(6,0)));
c10_vreg.v = _mm256_add_pd(c10_vreg.v, _mm256_load_pd(&C(1,0)));
c70_vreg.v = _mm256_add_pd(c70_vreg.v, _mm256_load_pd(&C(7,0)));
c20_vreg.v = _mm256_add_pd(c20_vreg.v, _mm256_load_pd(&C(2,0)));
c80_vreg.v = _mm256_add_pd(c80_vreg.v, _mm256_load_pd(&C(8,0)));
c30_vreg.v = _mm256_add_pd(c30_vreg.v, _mm256_load_pd(&C(3,0)));
c90_vreg.v = _mm256_add_pd(c90_vreg.v, _mm256_load_pd(&C(9,0)));
c40_vreg.v = _mm256_add_pd(c40_vreg.v, _mm256_load_pd(&C(4,0)));
c100_vreg.v = _mm256_add_pd(c100_vreg.v, _mm256_load_pd(&C(10,0)));
c50_vreg.v = _mm256_add_pd(c50_vreg.v, _mm256_load_pd(&C(5,0)));
c110_vreg.v = _mm256_add_pd(c110_vreg.v, _mm256_load_pd(&C(11,0)));
_mm256_store_pd(&C(0, 0), c00_vreg.v);
_mm256_store_pd(&C(6, 0), c60_vreg.v);
_mm256_store_pd(&C(1, 0), c10_vreg.v);
_mm256_store_pd(&C(7, 0), c70_vreg.v);
_mm256_store_pd(&C(2, 0), c20_vreg.v);
_mm256_store_pd(&C(8, 0), c80_vreg.v);
_mm256_store_pd(&C(3, 0), c30_vreg.v);
_mm256_store_pd(&C(9, 0), c90_vreg.v);
_mm256_store_pd(&C(4, 0), c40_vreg.v);
_mm256_store_pd(&C(10, 0), c100_vreg.v);
_mm256_store_pd(&C(5, 0), c50_vreg.v);
_mm256_store_pd(&C(11, 0), c110_vreg.v);
}
void AddDot12x4( int k, double *a, int lda, double *b, int ldb, double *c, int ldc)
{
int j;
int p;
v4df_t
zero_vreg,
c00_vreg, c60_vreg,
c10_vreg, c70_vreg,
c20_vreg, c80_vreg,
c30_vreg, c90_vreg,
c40_vreg, c100_vreg,
c50_vreg, c110_vreg,
b00_vreg,
a0_vreg;
zero_vreg.v = _mm256_set1_pd(0);
c00_vreg.v = zero_vreg.v;
c60_vreg.v = zero_vreg.v;
c10_vreg.v = zero_vreg.v;
c70_vreg.v = zero_vreg.v;
c20_vreg.v = zero_vreg.v;
c80_vreg.v = zero_vreg.v;
c30_vreg.v = zero_vreg.v;
c90_vreg.v = zero_vreg.v;
c40_vreg.v = zero_vreg.v;
c100_vreg.v = zero_vreg.v;
c50_vreg.v = zero_vreg.v;
c110_vreg.v = zero_vreg.v;
#pragma noprefetch
#pragma unroll(8)
for ( p=0; p<k; p++ ){
b00_vreg.v = _mm256_load_pd( (double *) b );
b += 4;
/* First row and second rows */
a0_vreg.v = _mm256_set1_pd( *(double *) a ); /* load and duplicate */
c00_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c00_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+1) ); /* load and duplicate */
c10_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c10_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+2) ); /* load and duplicate */
c20_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c20_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+3) ); /* load and duplicate */
c30_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c30_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+4) ); /* load and duplicate */
c40_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c40_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+5) ); /* load and duplicate */
c50_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c50_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+6) ); /* load and duplicate */
c60_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c60_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+7) ); /* load and duplicate */
c70_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c70_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+8) ); /* load and duplicate */
c80_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c80_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+9) ); /* load and duplicate */
c90_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c90_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+10) ); /* load and duplicate */
c100_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c100_vreg.v);
a0_vreg.v = _mm256_set1_pd( *(double *) (a+11) ); /* load and duplicate */
c110_vreg.v = _mm256_fmadd_pd(b00_vreg.v, a0_vreg.v, c110_vreg.v);
a += 12;
/*
if(profiling)
{
print256(" in computing a ", a_0p_a_1p_a_2p_a_3p_vreg);
print256(" in computing b ", b_p0_vreg);
print256(" in computing c ", c_00_c_10_c_20_c_30_vreg);
}
*/
}
// _mm_prefetch((const char *)b+k*8, _MM_HINT_T1);
c00_vreg.v = _mm256_add_pd(c00_vreg.v, _mm256_load_pd(&C(0,0)));
c60_vreg.v = _mm256_add_pd(c60_vreg.v, _mm256_load_pd(&C(6,0)));
c10_vreg.v = _mm256_add_pd(c10_vreg.v, _mm256_load_pd(&C(1,0)));
c70_vreg.v = _mm256_add_pd(c70_vreg.v, _mm256_load_pd(&C(7,0)));
c20_vreg.v = _mm256_add_pd(c20_vreg.v, _mm256_load_pd(&C(2,0)));
c80_vreg.v = _mm256_add_pd(c80_vreg.v, _mm256_load_pd(&C(8,0)));
c30_vreg.v = _mm256_add_pd(c30_vreg.v, _mm256_load_pd(&C(3,0)));
c90_vreg.v = _mm256_add_pd(c90_vreg.v, _mm256_load_pd(&C(9,0)));
c40_vreg.v = _mm256_add_pd(c40_vreg.v, _mm256_load_pd(&C(4,0)));
c100_vreg.v = _mm256_add_pd(c100_vreg.v, _mm256_load_pd(&C(10,0)));
c50_vreg.v = _mm256_add_pd(c50_vreg.v, _mm256_load_pd(&C(5,0)));
c110_vreg.v = _mm256_add_pd(c110_vreg.v, _mm256_load_pd(&C(11,0)));
_mm256_store_pd(&C(0, 0), c00_vreg.v);
_mm256_store_pd(&C(6, 0), c60_vreg.v);
_mm256_store_pd(&C(1, 0), c10_vreg.v);
_mm256_store_pd(&C(7, 0), c70_vreg.v);
_mm256_store_pd(&C(2, 0), c20_vreg.v);
_mm256_store_pd(&C(8, 0), c80_vreg.v);
_mm256_store_pd(&C(3, 0), c30_vreg.v);
_mm256_store_pd(&C(9, 0), c90_vreg.v);
_mm256_store_pd(&C(4, 0), c40_vreg.v);
_mm256_store_pd(&C(10, 0), c100_vreg.v);
_mm256_store_pd(&C(5, 0), c50_vreg.v);
_mm256_store_pd(&C(11, 0), c110_vreg.v);
}