#include <float.h>
#include <math.h>
#include <stddef.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/times.h>
#include <unistd.h>
void
initGeMatrix(size_t m, size_t n,
double *A,
ptrdiff_t incRowA, ptrdiff_t incColA)
{
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
A[i*incRowA+j*incColA] = i*n + j + 1;
}
}
}
void
printGeMatrix(size_t m, size_t n,
const double *A,
ptrdiff_t incRowA, ptrdiff_t incColA)
{
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
printf("%11.4lf ", A[i*incRowA+j*incColA]);
}
printf("\n");
}
printf("\n");
}
void
dgemm_ref(size_t m, size_t n, size_t k,
double alpha,
const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
const double *B, ptrdiff_t incRowB, ptrdiff_t incColB,
double beta,
double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
size_t i, j, l;
if (beta!=1) {
if (beta!=0) {
for (i=0; i<m; ++i) {
for (j=0; j<n; ++j) {
C[i*incRowC+j*incColC] *= beta;
}
}
} else {
for (i=0; i<m; ++i) {
for (j=0; j<n; ++j) {
C[i*incRowC+j*incColC] = 0;
}
}
}
}
if (alpha!=0) {
for (i=0; i<m; ++i) {
for (j=0; j<n; ++j) {
for (l=0; l<k; ++l) {
C[i*incRowC+j*incColC] += alpha*A[i*incRowA+l*incColA]
*B[l*incRowB+j*incColB];
}
}
}
}
}
#ifndef DGEMM_MR
#define DGEMM_MR 4
#endif
#ifndef DGEMM_NR
#define DGEMM_NR 4
#endif
#ifndef DGEMM_MC
#define DGEMM_MC 256
#endif
#ifndef DGEMM_NC
#define DGEMM_NC 256
#endif
#ifndef DGEMM_KC
#define DGEMM_KC 512
#endif
void
dgepack_A(size_t m, size_t k,
const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
double *p)
{
size_t mb = (m+DGEMM_MR-1)/DGEMM_MR;
for (size_t l=0; l<k; ++l) {
for (size_t i1=0; i1<mb; ++i1) {
for (size_t i0=0; i0<DGEMM_MR; ++i0) {
size_t i = i1*DGEMM_MR + i0;
size_t nu = i1*DGEMM_MR*k + l*DGEMM_MR + i0;
p[nu] = (i<m) ? A[i*incRowA + l*incColA]
: 0;
}
}
}
}
void
dgepack_B(size_t k, size_t n,
const double *B, ptrdiff_t incRowB, ptrdiff_t incColB,
double *p)
{
size_t nb = (n+DGEMM_NR-1)/DGEMM_NR;
for (size_t j1=0; j1<nb; ++j1) {
for (size_t j0=0; j0<DGEMM_NR; ++j0) {
for (size_t l=0; l<k; ++l) {
size_t j = j1*DGEMM_NR + j0;
size_t nu = j1*DGEMM_NR*k + l*DGEMM_NR + j0;
p[nu] = (j<n) ? B[l*incRowB + j*incColB]
: 0;
}
}
}
}
void
dgemm_micro(size_t k, double alpha,
const double *A, const double *B,
double beta,
double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
double AB[DGEMM_MR*DGEMM_NR];
for (size_t i=0; i<DGEMM_MR*DGEMM_NR; ++i) {
AB[i] = 0;
}
for (size_t l=0; l<k; ++l) {
for (size_t i=0; i<DGEMM_MR; ++i) {
for (size_t j=0; j<DGEMM_NR; ++j) {
AB[i+j*DGEMM_MR] += A[i+l*DGEMM_MR]*B[l*DGEMM_NR+j];
}
}
}
if (beta!=1) {
if (beta!=0) {
for (size_t i=0; i<DGEMM_MR; ++i) {
for (size_t j=0; j<DGEMM_NR; ++j) {
C[i*incRowC+j*incColC] *= beta;
}
}
} else {
for (size_t i=0; i<DGEMM_MR; ++i) {
for (size_t j=0; j<DGEMM_NR; ++j) {
C[i*incRowC+j*incColC] = 0;
}
}
}
}
for (size_t i=0; i<DGEMM_MR; ++i) {
for (size_t j=0; j<DGEMM_NR; ++j) {
C[i*incRowC+j*incColC] += alpha*AB[i+j*DGEMM_MR];
}
}
}
void
dgescal(size_t m, size_t n,
double alpha,
double *X, size_t incRowX, size_t incColX)
{
if (alpha==1) {
return;
}
if (alpha!=0) {
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
X[i*incRowX+j*incColX] *= alpha;
}
}
} else {
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
X[i*incRowX+j*incColX] = 0;
}
}
}
}
void
dgeaxpy(size_t m, size_t n,
double alpha,
const double *X, size_t incRowX, size_t incColX,
double *Y, size_t incRowY, size_t incColY)
{
if (alpha==0) {
return;
}
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
Y[i*incRowY+j*incColY] += alpha*X[i*incRowX+j*incColX];
}
}
}
void
dgemm_macro(size_t m, size_t n, size_t k, double alpha,
const double *A, const double *B,
double beta,
double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
double AB[DGEMM_MR*DGEMM_NR];
size_t mb = (m+DGEMM_MR-1) / DGEMM_MR;
size_t nb = (n+DGEMM_NR-1) / DGEMM_NR;
size_t mr = m % DGEMM_MR;
size_t nr = n % DGEMM_NR;
for (size_t i=0; i<mb; ++i) {
size_t m_ = (i<mb-1 || mr==0) ? DGEMM_MR
: mr;
for (size_t j=0; j<nb; ++j) {
size_t n_ = (j<nb-1 || nr==0) ? DGEMM_NR
: nr;
if (m_==DGEMM_MR && n_==DGEMM_NR) {
dgemm_micro(k, alpha,
&A[i*DGEMM_MR*k], &B[j*k*DGEMM_NR],
beta,
&C[i*DGEMM_MR*incRowC+j*DGEMM_NR*incColC],
incRowC, incColC);
} else {
dgemm_micro(k, alpha,
&A[i*DGEMM_MR*k], &B[j*k*DGEMM_NR],
0,
AB, 1, DGEMM_MR);
dgescal(DGEMM_MR, DGEMM_NR,
beta,
&C[i*DGEMM_MR*incRowC+j*DGEMM_NR*incColC],
incRowC, incColC);
dgeaxpy(DGEMM_MR, DGEMM_NR,
1,
AB, 1, DGEMM_MR,
&C[i*DGEMM_MR*incRowC+j*DGEMM_NR*incColC],
incRowC, incColC);
}
}
}
}
void
dgemm_frame(size_t m, size_t n, size_t k, double alpha,
const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
const double *B, ptrdiff_t incRowB, ptrdiff_t incColB,
double beta,
double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
if (k==0 || alpha==0) {
dgescal(m, n, beta, C, incRowC, incColC);
return;
}
size_t mb = (m+DGEMM_MC-1) / DGEMM_MC;
size_t nb = (n+DGEMM_NC-1) / DGEMM_NC;
size_t kb = (k+DGEMM_KC-1) / DGEMM_KC;
size_t mr = m % DGEMM_MC;
size_t nr = n % DGEMM_NC;
size_t kr = k % DGEMM_KC;
double *Ap = malloc(DGEMM_MC*DGEMM_KC*sizeof(*Ap));
double *Bp = malloc(DGEMM_KC*DGEMM_NC*sizeof(*Bp));
for (size_t j=0; j<nb; ++j) {
size_t n_ = (j<nb-1 || nr==0) ? DGEMM_NC
: nr;
for (size_t l=0; l<kb; ++l) {
size_t k_ = (l<kb-1 || kr==0) ? DGEMM_KC
: kr;
double beta_ = (l==0) ? beta
: 1;
dgepack_B(k_, n_,
&B[l*DGEMM_KC*incRowB+j*DGEMM_NC*incColB],
incRowB, incColB,
Bp);
for (size_t i=0; i<mb; ++i) {
size_t m_ = (i<mb-1 || mr==0) ? DGEMM_MC
: mr;
dgepack_A(m_, k_,
&A[i*DGEMM_MC*incRowA+l*DGEMM_KC*incColA],
incRowA, incColA,
Ap);
dgemm_macro(m_, n_, k_,
alpha,
Ap, Bp,
beta_,
&C[i*DGEMM_MC*incRowC+j*DGEMM_NC*incColC],
incRowC, incColC);
}
}
}
free(Bp);
free(Ap);
}
double
walltime()
{
struct tms ts;
static double ClockTick=0.0;
if (ClockTick==0.0) {
ClockTick = 1.0 / ((double) sysconf(_SC_CLK_TCK));
}
return ((double) times(&ts)) * ClockTick;
}
void
randGeMatrix(size_t m, size_t n, double *A, ptrdiff_t incRowA, ptrdiff_t incColA)
{
for (size_t j=0; j<n; ++j) {
for (size_t i=0; i<m; ++i) {
A[i*incRowA+j*incColA] = ((double)rand()-RAND_MAX/2)*200/RAND_MAX;
}
}
}
#define MIN(X,Y) ((X)<(Y) ? (X) : (Y))
#define MAX(X,Y) ((X)>(Y) ? (X) : (Y))
double
dgenrm1(size_t m, size_t n, const double *A, ptrdiff_t incRowA, ptrdiff_t incColA)
{
double result = 0;
for (size_t j=0; j<n; ++j) {
double sum = 0;
for (size_t i=0; i<m; ++i) {
sum += fabs(A[i*incRowA+j*incColA]);
}
if (sum>result) {
result = sum;
}
}
return result;
}
double
err_dgemm(size_t m, size_t n, size_t k,
double alpha,
const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
const double *B, ptrdiff_t incRowB, ptrdiff_t incColB,
double beta,
const double *C0, ptrdiff_t incRowC0, ptrdiff_t incColC0,
double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
double normA = dgenrm1(m, k, A, incRowA, incColA);
double normB = dgenrm1(k, n, B, incRowB, incColB);
double normC = dgenrm1(m, n, C, incRowC0, incColC0);
double normD;
size_t mn = (m>n) ? m : n;
size_t mnk = (mn>k) ? mn : k;
normA = MAX(normA, fabs(alpha)*normA);
normC = MAX(normC, fabs(beta)*normC);
dgeaxpy(m, n, -1.0, C0, incRowC0, incColC0, C, incRowC, incColC);
normD = dgenrm1(m, n, C, incRowC, incColC);
return normD/(mnk*normA*normB*normC);
}
void
dcopy(size_t n,
const double *x, ptrdiff_t incX,
double *y, ptrdiff_t incY)
{
for (size_t i=0; i<n; ++i) {
y[i*incY] = x[i*incX];
}
}
void
dgecopy(size_t m, size_t n,
const double *X, ptrdiff_t incRowX, ptrdiff_t incColX,
double *Y, ptrdiff_t incRowY, ptrdiff_t incColY)
{
if (incRowX<incColX) {
for (size_t j=0; j<n; ++j) {
dcopy(m, &X[j*incColX], incRowX, &Y[j*incColY], incRowY);
}
} else {
for (size_t i=0; i<m; ++i) {
dcopy(n, &X[i*incRowX], incColX, &Y[i*incRowY], incColY);
}
}
}
#ifndef MIN_N
#define MIN_N 100
#endif
#ifndef MAX_N
#define MAX_N 4000
#endif
#ifndef INC_N
#define INC_N 100
#endif
#ifndef MIN_M
#define MIN_M 100
#endif
#ifndef MAX_M
#define MAX_M 4000
#endif
#ifndef INC_M
#define INC_M 100
#endif
#ifndef MIN_K
#define MIN_K 100
#endif
#ifndef MAX_K
#define MAX_K 4000
#endif
#ifndef INC_K
#define INC_K 100
#endif
#ifndef ALPHA
#define ALPHA 1
#endif
#ifndef BETA
#define BETA 1
#endif
#ifndef ROWMAJOR_A
#define ROWMAJOR_A 0
#endif
#ifndef ROWMAJOR_B
#define ROWMAJOR_B 0
#endif
#ifndef ROWMAJOR_C
#define ROWMAJOR_C 0
#endif
double A_[MAX_M*MAX_K];
double B_[MAX_K*MAX_N];
double C_[MAX_M*MAX_N];
double C0[MAX_M*MAX_N];
double C1[MAX_M*MAX_N];
int
main()
{
randGeMatrix(MAX_M, MAX_K, A_, 1, MAX_M);
randGeMatrix(MAX_K, MAX_N, B_, 1, MAX_K);
randGeMatrix(MAX_N, MAX_M, C_, 1, MAX_M);
printf("#%9s %9s %9s", "m", "n", "k");
printf(" %12s %12s %17s", "t", "MFLOPS", "Residual Error");
printf("\n");
for (size_t m=MIN_M, n=MIN_N, k=MIN_K; n<=MAX_N && m<=MAX_M && k<=MAX_K;
m+=INC_M, n+=INC_N, k+=INC_K)
{
double t, dt, err;
size_t runs = 1;
double ops = 2.0*m/1000*n/1000*k;
ptrdiff_t incRowA = (ROWMAJOR_A==1) ? k : 1;
ptrdiff_t incColA = (ROWMAJOR_A==1) ? 1 : m;
ptrdiff_t incRowB = (ROWMAJOR_B==1) ? n : 1;
ptrdiff_t incColB = (ROWMAJOR_B==1) ? 1 : k;
ptrdiff_t incRowC = (ROWMAJOR_C==1) ? n : 1;
ptrdiff_t incColC = (ROWMAJOR_C==1) ? 1 : m;
printf(" %9zu %9zu %9td", m, n, k);
dgecopy(m, n, C_, 1, MAX_M, C0, incRowC, incColC);
dgemm_ref(m, n, k,
ALPHA,
A_, incRowA, incRowA,
B_, incRowB, incColB,
BETA,
C0, incRowC, incColC);
t = 0;
runs = 0;
do {
dgecopy(m, n, C_, 1, MAX_M, C1, incRowC, incColC);
dt = walltime();
dgemm_frame(m, n, k,
ALPHA,
A_, incRowA, incRowA,
B_, incRowB, incColB,
BETA,
C1, incRowC, incColC);
dt = walltime() - dt;
t += dt;
++runs;
} while (t<0.3);
t /= runs;
err = err_dgemm(m, n, k,
ALPHA,
A_, incRowA, incColA,
B_, incRowB, incColB,
BETA,
C0, incRowC, incColC,
C1, incRowC, incColC);
printf(" %12.2e %12.2lf %12.2e %4s", t, ops/t,
err, (err<DBL_EPSILON) ? "PASS" : "FAIL");
printf("\n");
}
return 0;
}