Ublas :

Subject: Re: [ublas] Matrix multiplication performance
From: Michael Lehn (michael.lehn_at_[hidden])
Date: 2016-01-30 11:48:26

Here the same in slightly more general form

template <typename Index>
typename std::enable_if<std::is_convertible<Index, std::int64_t>::value
&& BlockSize<double>::MR==4
&& BlockSize<double>::NR==12
&& BlockSize<double>::align==32,
void>::type
ugemm(Index kc, double alpha,
const double *A, const double *B,
double beta,
double *C, Index incRowC, Index incColC)
{
static const Index MR = BlockSize<double>::MR;
static const Index NR = BlockSize<double>::NR/4;
typedef double vx __attribute__((vector_size (4*sizeof(double))));

A = (const double*) __builtin_assume_aligned (A, 32);
B = (const double*) __builtin_assume_aligned (B, 32);

vx P[MR*NR] = {};

for (Index l=0; l<kc; ++l) {
const vx *b = (const vx *)B;

for (Index i=0; i<MR; ++i) {
for (Index j=0; j<NR; ++j) {
P[i*NR+j] += A[i]*b[j];
}
}
A += MR;
B += NR*4;
}

if (alpha!=double(1)) {
for (Index i=0; i<MR; ++i) {
for (Index j=0; j<NR; ++j) {
P[i*NR+j] *= alpha;
}
}
}

for (Index i=0; i<MR; ++i) {
for (Index j=0; j<NR; ++j) {
const double *p = (const double *) &P[i*NR+j];
for (Index j1=0; j1<4; ++j1) {
C[i*incRowC+(j*4+j1)*incColC] *= beta;
C[i*incRowC+(j*4+j1)*incColC] += p[j1];
}
}
}
}

On 30 Jan 2016, at 13:49, Michael Lehn <michael.lehn_at_[hidden]> wrote:

> Ok, and this version for MR=4, NR=12 even beats the asm kernel on Haswell:
>
> //-- Micro Kernel --------------------------------------------------------------
> template <typename Index>
> typename std::enable_if<std::is_convertible<Index, std::int64_t>::value
> && BlockSize<double>::MR==4
> && BlockSize<double>::NR==12
> && BlockSize<double>::align==32,
> void>::type
> ugemm(Index kc, double alpha,
> const double *A, const double *B,
> double beta,
> double *C, Index incRowC, Index incColC)
> {
> static const Index MR = BlockSize<double>::MR;
> static const Index NR = BlockSize<double>::NR;
> typedef double vx __attribute__((vector_size (4*sizeof(double))));
>
> A = (const double*) __builtin_assume_aligned (A, 32);
> B = (const double*) __builtin_assume_aligned (B, 32);
>
> vx P0_03 = {}; vx P0_47 = {}; vx P0_811 = {};
> vx P1_03 = {}; vx P1_47 = {}; vx P1_811 = {};
> vx P2_03 = {}; vx P2_47 = {}; vx P2_811 = {};
> vx P3_03 = {}; vx P3_47 = {}; vx P3_811 = {};
>
> for (Index l=0; l<kc; ++l) {
> const vx *b = (const vx *)B;
>
> P0_03 += A[0]*b[0]; P0_47 += A[0]*b[1]; P0_811 += A[0]*b[2];
> P1_03 += A[1]*b[0]; P1_47 += A[1]*b[1]; P1_811 += A[1]*b[2];
> P2_03 += A[2]*b[0]; P2_47 += A[2]*b[1]; P2_811 += A[2]*b[2];
> P3_03 += A[3]*b[0]; P3_47 += A[3]*b[1]; P3_811 += A[3]*b[2];
> A += MR;
> B += NR;
> }
>
> P0_03 *= alpha; P0_47 *= alpha; P0_811 *= alpha;
> P1_03 *= alpha; P1_47 *= alpha; P1_811 *= alpha;
> P2_03 *= alpha; P2_47 *= alpha; P2_811 *= alpha;
> P3_03 *= alpha; P3_47 *= alpha; P3_811 *= alpha;
>
> if (beta!=double(1)) {
> for (Index i=0; i<MR; ++i) {
> for (Index j=0; j<NR; ++j) {
> C[i*incRowC+j*incColC] *= beta;
> }
> }
> }
>
> const double *p = (const double *) &P0_03;
> C[0*incRowC+0*incColC] += p[0];
> C[0*incRowC+1*incColC] += p[1];
> C[0*incRowC+2*incColC] += p[2];
> C[0*incRowC+3*incColC] += p[3];
>
> p = (const double *) &P0_47;
> C[0*incRowC+4*incColC] += p[0];
> C[0*incRowC+5*incColC] += p[1];
> C[0*incRowC+6*incColC] += p[2];
> C[0*incRowC+7*incColC] += p[3];
>
> p = (const double *) &P0_811;
> C[0*incRowC+8*incColC] += p[0];
> C[0*incRowC+9*incColC] += p[1];
> C[0*incRowC+10*incColC] += p[2];
> C[0*incRowC+11*incColC] += p[3];
>
> p = (const double *) &P1_03;
> C[1*incRowC+0*incColC] += p[0];
> C[1*incRowC+1*incColC] += p[1];
> C[1*incRowC+2*incColC] += p[2];
> C[1*incRowC+3*incColC] += p[3];
>
> p = (const double *) &P1_47;
> C[1*incRowC+4*incColC] += p[0];
> C[1*incRowC+5*incColC] += p[1];
> C[1*incRowC+6*incColC] += p[2];
> C[1*incRowC+7*incColC] += p[3];
>
> p = (const double *) &P1_811;
> C[1*incRowC+8*incColC] += p[0];
> C[1*incRowC+9*incColC] += p[1];
> C[1*incRowC+10*incColC] += p[2];
> C[1*incRowC+11*incColC] += p[3];
>
> p = (const double *) &P2_03;
> C[2*incRowC+0*incColC] += p[0];
> C[2*incRowC+1*incColC] += p[1];
> C[2*incRowC+2*incColC] += p[2];
> C[2*incRowC+3*incColC] += p[3];
>
> p = (const double *) &P2_47;
> C[2*incRowC+4*incColC] += p[0];
> C[2*incRowC+5*incColC] += p[1];
> C[2*incRowC+6*incColC] += p[2];
> C[2*incRowC+7*incColC] += p[3];
>
> p = (const double *) &P2_811;
> C[2*incRowC+8*incColC] += p[0];
> C[2*incRowC+9*incColC] += p[1];
> C[2*incRowC+10*incColC] += p[2];
> C[2*incRowC+11*incColC] += p[3];
>
> p = (const double *) &P3_03;
> C[3*incRowC+0*incColC] += p[0];
> C[3*incRowC+1*incColC] += p[1];
> C[3*incRowC+2*incColC] += p[2];
> C[3*incRowC+3*incColC] += p[3];
>
> p = (const double *) &P3_47;
> C[3*incRowC+4*incColC] += p[0];
> C[3*incRowC+5*incColC] += p[1];
> C[3*incRowC+6*incColC] += p[2];
> C[3*incRowC+7*incColC] += p[3];
>
> p = (const double *) &P3_811;
> C[3*incRowC+8*incColC] += p[0];
> C[3*incRowC+9*incColC] += p[1];
> C[3*incRowC+10*incColC] += p[2];
> C[3*incRowC+11*incColC] += p[3];
>
> }