/*---------------------------------------------------------------------------
*
* Compute matrix product using recursive tiling.
*
* Input
* int argc - length of argv[] array
* char* argv[] - pointer to command line parameter array
* int verbosity - program verification: verbosity > 0 gives more output
* char* order - string indicating loop order, e.g., "ijk" or "jki"
*
* Output
* double - elapsed time for product computation
*/
double multiply_by_recursive_blocks( int argc, char* argv[], int verbosity,
char* order )
{
int rows, cols, mids, block_size;
double **a, **b, **c;
double t1, t2;
double sec;
double gflop_count;
/*
* process command line arguments
*/
rows = atoi( argv[0] );
mids = atoi( argv[1] );
cols = atoi( argv[2] );
block_size = atoi( argv[3] );
gflop_count = 2.0 * rows * mids * cols / 1.0e9;
if ( verbosity > 0 )
{
printf( "Recursive blocks(%3s): rows = %d, mids = %d, columns = %d\n",
order, rows, mids, cols );
printf( "block size = %d\n", block_size );
}
/*
* allocate and initialize matrices
*/
a = (double**) allocateMatrix( rows, mids );
b = (double**) allocateMatrix( mids, cols );
c = (double**) allocateMatrix( rows, cols );
initialize_matrices( a, b, c, rows, cols, mids, verbosity );
/*
* compute product
*/
t1 = wtime();
mm_rec( c, a, b, 0, 0, 0, 0, 0, 0, rows, mids, cols, cols, block_size );
t2 = wtime();
sec = t2 - t1;
if ( verbosity > 1 )
printf( "checksum = %f\n", checksum( c, rows, cols ) );
printf( "blocks(%3s): %6.3f secs %6.3f gflops ",
order, sec, gflop_count / sec );
printf( "( %5d x %5d x %5d ) ( %6d )\n", rows, mids, cols, block_size );
/*
* clean up
*/
deallocateMatrix( a );
deallocateMatrix( b );
deallocateMatrix( c );
return t2 - t1;
}
int main(int argc, char** argv) {
#pragma omp parallel
{
#pragma omp for
for (int i=0; i<N; i++) {
for (int j=0; j<M; j++) {
A[i][j] = i*j;
}
}
// B is the identity matrix
#pragma omp for
for (int i=0; i<M; i++) {
for (int j=0; j<K; j++) {
B[i][j] = (i==j)?1:0;
}
}
// process recursively
mm_rec();
}
// verify result
int success = 1;
for (int i=0; i<N; i++) {
for (int j=0; j<MIN(M,K); j++) {
if (A[i][j] != C[i][j]) {
success = 0;
}
}
for (int j=MIN(M,K); j<MAX(M,K); j++) {
if (C[i][j] != 0) {
success = 0;
}
}
}
// print verification result
printf("Verification: %s\n", (success)?"OK":"ERR");
}
/*---------------------------------------------------------------------------
*
* Computes block-oriented matrix-matrix product recursively.
*
* Input:
* double** c - matrix product C = A * B
* double** a - first factor of product
* double** b - second factor of product
* int crow, ccol - starting row and column of block of C
* int arow, acol - starting row and column of block of A
* int brow, bcol - starting row and column of block of B
* int l, m, n - dims of blocks: A is l x m, B is m x n, C is l x n
* int N - full row length (column dimension) of matrix B
* int threshold - B blocks larger than this are partitioned
*
* Output:
* double** c - matrix product C = A * B
*
* Algorithm based on one presented on page 276 of "Parallel Programming in
* C with MPI and OpenMP", Michael J. Quinn, McGraw-Hill, 2004.
*
* **** NOTE ****: There is a typo in Quinn's code in the recursive call
* to mm_rec(). The 5th parameter should be "ccol + nhalf[j]" and not
* use "mhalf" as shown in the text. The error only shows up when the
* dimensions of the matrices are not uniform.
*/
void mm_rec( double** c, double** a, double** b,
int crow, int ccol, int arow, int acol, int brow, int bcol,
int l, int m, int n, int N, int threshold )
{
int lhalf[3], mhalf[3], nhalf[3];
int i, j, k;
if ( m * n > threshold )
{
lhalf[0] = 0; lhalf[1] = l/2; lhalf[2] = l - lhalf[1];
mhalf[0] = 0; mhalf[1] = m/2; mhalf[2] = m - mhalf[1];
nhalf[0] = 0; nhalf[1] = n/2; nhalf[2] = n - nhalf[1];
for ( i = 0; i < 2; i++ )
{
for ( j = 0; j < 2; j++ )
{
for ( k = 0; k < 2; k++ )
{
mm_rec( c, a, b,
crow + lhalf[i], ccol + nhalf[j],
arow + lhalf[i], acol + mhalf[k],
brow + mhalf[k], bcol + nhalf[j],
lhalf[i + 1], mhalf[k + 1], nhalf[j + 1],
N, threshold );
}
}
}
}
else
{
do_product( a, b, c,
arow, arow + l - 1,
bcol, bcol + n - 1,
acol, acol + m - 1 );
}
}