/* --------------------------------------------------------------------- * * -- PBLAS routine (version 2.0) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * April 1, 1998 * * --------------------------------------------------------------------- */ /* * Include files */ #include "pblas.h" #include "PBpblas.h" #include "PBtools.h" #include "PBblacs.h" #include "PBblas.h" #ifdef __STDC__ void pdgemm_( F_CHAR_T TRANSA, F_CHAR_T TRANSB, int * M, int * N, int * K, double * ALPHA, double * A, int * IA, int * JA, int * DESCA, double * B, int * IB, int * JB, int * DESCB, double * BETA, double * C, int * IC, int * JC, int * DESCC ) #else void pdgemm_( TRANSA, TRANSB, M, N, K, ALPHA, A, IA, JA, DESCA, B, IB, JB, DESCB, BETA, C, IC, JC, DESCC ) /* * .. Scalar Arguments .. */ F_CHAR_T TRANSA, TRANSB; int * IA, * IB, * IC, * JA, * JB, * JC, * K, * M, * N; double * ALPHA, * BETA; /* * .. Array Arguments .. */ int * DESCA, * DESCB, * DESCC; double * A, * B, * C; #endif { /* * Purpose * ======= * * PDGEMM performs one of the matrix-matrix operations * * sub( C ) := alpha*op( sub( A ) )*op( sub( B ) ) + beta*sub( C ), * * where * * sub( C ) denotes C(IC:IC+M-1,JC:JC+N-1), and, op( X ) is one of * op( X ) = X or op( X ) = X'. * * Thus, op( sub( A ) ) denotes A(IA:IA+M-1,JA:JA+K-1) if TRANSA = 'N', * A(IA:IA+K-1,JA:JA+M-1)' if TRANSA = 'T', * A(IA:IA+K-1,JA:JA+M-1)' if TRANSA = 'C', * * and, op( sub( B ) ) denotes B(IB:IB+K-1,JB:JB+N-1) if TRANSB = 'N', * B(IB:IB+N-1,JB:JB+K-1)' if TRANSB = 'T', * B(IB:IB+N-1,JB:JB+K-1)' if TRANSB = 'C', * * Alpha and beta are scalars. A, B and C are matrices; op( sub( A ) ) * is an m by k submatrix, op( sub( B ) ) is an k by n submatrix and * sub( C ) is an m by n submatrix. * * Notes * ===== * * A description vector is associated with each 2D block-cyclicly dis- * tributed matrix. This vector stores the information required to * establish the mapping between a matrix entry and its corresponding * process and memory location. * * In the following comments, the character _ should be read as * "of the distributed matrix". Let A be a generic term for any 2D * block cyclicly distributed matrix. Its description vector is DESC_A: * * NOTATION STORED IN EXPLANATION * ---------------- --------------- ------------------------------------ * DTYPE_A (global) DESCA[ DTYPE_ ] The descriptor type. * CTXT_A (global) DESCA[ CTXT_ ] The BLACS context handle, indicating * the NPROW x NPCOL BLACS process grid * A is distributed over. The context * itself is global, but the handle * (the integer value) may vary. * M_A (global) DESCA[ M_ ] The number of rows in the distribu- * ted matrix A, M_A >= 0. * N_A (global) DESCA[ N_ ] The number of columns in the distri- * buted matrix A, N_A >= 0. * IMB_A (global) DESCA[ IMB_ ] The number of rows of the upper left * block of the matrix A, IMB_A > 0. * INB_A (global) DESCA[ INB_ ] The number of columns of the upper * left block of the matrix A, * INB_A > 0. * MB_A (global) DESCA[ MB_ ] The blocking factor used to distri- * bute the last M_A-IMB_A rows of A, * MB_A > 0. * NB_A (global) DESCA[ NB_ ] The blocking factor used to distri- * bute the last N_A-INB_A columns of * A, NB_A > 0. * RSRC_A (global) DESCA[ RSRC_ ] The process row over which the first * row of the matrix A is distributed, * NPROW > RSRC_A >= 0. * CSRC_A (global) DESCA[ CSRC_ ] The process column over which the * first column of A is distributed. * NPCOL > CSRC_A >= 0. * LLD_A (local) DESCA[ LLD_ ] The leading dimension of the local * array storing the local blocks of * the distributed matrix A, * IF( Lc( 1, N_A ) > 0 ) * LLD_A >= MAX( 1, Lr( 1, M_A ) ) * ELSE * LLD_A >= 1. * * Let K be the number of rows of a matrix A starting at the global in- * dex IA,i.e, A( IA:IA+K-1, : ). Lr( IA, K ) denotes the number of rows * that the process of row coordinate MYROW ( 0 <= MYROW < NPROW ) would * receive if these K rows were distributed over NPROW processes. If K * is the number of columns of a matrix A starting at the global index * JA, i.e, A( :, JA:JA+K-1, : ), Lc( JA, K ) denotes the number of co- * lumns that the process MYCOL ( 0 <= MYCOL < NPCOL ) would receive if * these K columns were distributed over NPCOL processes. * * The values of Lr() and Lc() may be determined via a call to the func- * tion PB_Cnumroc: * Lr( IA, K ) = PB_Cnumroc( K, IA, IMB_A, MB_A, MYROW, RSRC_A, NPROW ) * Lc( JA, K ) = PB_Cnumroc( K, JA, INB_A, NB_A, MYCOL, CSRC_A, NPCOL ) * * Arguments * ========= * * TRANSA (global input) CHARACTER*1 * On entry, TRANSA specifies the form of op( sub( A ) ) to be * used in the matrix multiplication as follows: * * TRANSA = 'N' or 'n' op( sub( A ) ) = sub( A ), * * TRANSA = 'T' or 't' op( sub( A ) ) = sub( A )', * * TRANSA = 'C' or 'c' op( sub( A ) ) = sub( A )'. * * TRANSB (global input) CHARACTER*1 * On entry, TRANSB specifies the form of op( sub( B ) ) to be * used in the matrix multiplication as follows: * * TRANSB = 'N' or 'n' op( sub( B ) ) = sub( B ), * * TRANSB = 'T' or 't' op( sub( B ) ) = sub( B )', * * TRANSB = 'C' or 'c' op( sub( B ) ) = sub( B )'. * * M (global input) INTEGER * On entry, M specifies the number of rows of the submatrix * op( sub( A ) ) and of the submatrix sub( C ). M must be at * least zero. * * N (global input) INTEGER * On entry, N specifies the number of columns of the submatrix * op( sub( B ) ) and the number of columns of the submatrix * sub( C ). N must be at least zero. * * K (global input) INTEGER * On entry, K specifies the number of columns of the submatrix * op( sub( A ) ) and the number of rows of the submatrix * op( sub( B ) ). K must be at least zero. * * ALPHA (global input) DOUBLE PRECISION * On entry, ALPHA specifies the scalar alpha. When ALPHA is * supplied as zero then the local entries of the arrays A and * B corresponding to the entries of the submatrices sub( A ) * and sub( B ) respectively need not be set on input. * * A (local input) DOUBLE PRECISION array * On entry, A is an array of dimension (LLD_A, Ka), where Ka is * at least Lc( 1, JA+K-1 ) when TRANSA = 'N' or 'n', and is at * least Lc( 1, JA+M-1 ) otherwise. Before entry, this array * contains the local entries of the matrix A. * * IA (global input) INTEGER * On entry, IA specifies A's global row index, which points to * the beginning of the submatrix sub( A ). * * JA (global input) INTEGER * On entry, JA specifies A's global column index, which points * to the beginning of the submatrix sub( A ). * * DESCA (global and local input) INTEGER array * On entry, DESCA is an integer array of dimension DLEN_. This * is the array descriptor for the matrix A. * * B (local input) DOUBLE PRECISION array * On entry, B is an array of dimension (LLD_B, Kb), where Kb is * at least Lc( 1, JB+N-1 ) when TRANSB = 'N' or 'n', and is at * least Lc( 1, JB+K-1 ) otherwise. Before entry, this array * contains the local entries of the matrix B. * * IB (global input) INTEGER * On entry, IB specifies B's global row index, which points to * the beginning of the submatrix sub( B ). * * JB (global input) INTEGER * On entry, JB specifies B's global column index, which points * to the beginning of the submatrix sub( B ). * * DESCB (global and local input) INTEGER array * On entry, DESCB is an integer array of dimension DLEN_. This * is the array descriptor for the matrix B. * * BETA (global input) DOUBLE PRECISION * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then the local entries of the array C * corresponding to the entries of the submatrix sub( C ) need * not be set on input. * * C (local input/local output) DOUBLE PRECISION array * On entry, C is an array of dimension (LLD_C, Kc), where Kc is * at least Lc( 1, JC+N-1 ). Before entry, this array contains * the local entries of the matrix C. * On exit, the entries of this array corresponding to the local * entries of the submatrix sub( C ) are overwritten by the * local entries of the m by n updated submatrix. * * IC (global input) INTEGER * On entry, IC specifies C's global row index, which points to * the beginning of the submatrix sub( C ). * * JC (global input) INTEGER * On entry, JC specifies C's global column index, which points * to the beginning of the submatrix sub( C ). * * DESCC (global and local input) INTEGER array * On entry, DESCC is an integer array of dimension DLEN_. This * is the array descriptor for the matrix C. * * -- Written on April 1, 1998 by * Antoine Petitet, University of Tennessee, Knoxville 37996, USA. * * --------------------------------------------------------------------- */ /* * .. Local Scalars .. */ char DirAB, DirBC, OpC, OpR, TrA, TrB, ctop, ctopsave, rtop, rtopsave; int Ai, Aj, Bi, Bj, ChooseAB, ChooseBC, Ci, Cj, ForceTop, ctxt, info, mycol, myrow, nb, nota, notb, npcol, nprow; double ABest, ACest, BCest, tmp1, tmp2, tmp3, tmp4; PBTYP_T * type; /* * .. Local Arrays .. */ int Ad[DLEN_], Bd[DLEN_], Cd[DLEN_]; /* .. * .. Executable Statements .. * */ nota = ( ( TrA = Mupcase( F2C_CHAR( TRANSA )[0] ) ) == CNOTRAN ); notb = ( ( TrB = Mupcase( F2C_CHAR( TRANSB )[0] ) ) == CNOTRAN ); PB_CargFtoC( *IA, *JA, DESCA, &Ai, &Aj, Ad ); PB_CargFtoC( *IB, *JB, DESCB, &Bi, &Bj, Bd ); PB_CargFtoC( *IC, *JC, DESCC, &Ci, &Cj, Cd ); #ifndef NO_ARGCHK /* * Test the input parameters */ Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); if( !( info = ( ( nprow == -1 ) ? -( 1001 + CTXT_ ) : 0 ) ) ) { if( ( !nota ) && ( TrA != CTRAN ) && ( TrA != CCOTRAN ) ) { PB_Cwarn( ctxt, __LINE__, "PDGEMM", "Illegal TRANSA = %c\n", TrA ); info = -1; } else if( ( !notb ) && ( TrB != CTRAN ) && ( TrB != CCOTRAN ) ) { PB_Cwarn( ctxt, __LINE__, "PDGEMM", "Illegal TRANSB = %c\n", TrB ); info = -2; } if( nota ) PB_Cchkmat( ctxt, "PDGEMM", "A", *M, 3, *K, 5, Ai, Aj, Ad, 10, &info ); else PB_Cchkmat( ctxt, "PDGEMM", "A", *K, 5, *M, 3, Ai, Aj, Ad, 10, &info ); if( notb ) PB_Cchkmat( ctxt, "PDGEMM", "B", *K, 5, *N, 4, Bi, Bj, Bd, 14, &info ); else PB_Cchkmat( ctxt, "PDGEMM", "B", *N, 4, *K, 5, Bi, Bj, Bd, 14, &info ); PB_Cchkmat( ctxt, "PDGEMM", "C", *M, 3, *N, 4, Ci, Cj, Cd, 19, &info ); } if( info ) { PB_Cabort( ctxt, "PDGEMM", info ); return; } #endif /* * Quick return if possible */ if( ( *M == 0 ) || ( *N == 0 ) || ( ( ALPHA[REAL_PART] == ZERO || *K == 0 ) && ( BETA [REAL_PART] == ONE ) ) ) return; /* * Get type structure */ type = PB_Cdtypeset(); /* * If alpha or K is zero, sub( C ) := beta * sub( C ). */ if( ( ALPHA[REAL_PART] == ZERO ) || ( *K == 0 ) ) { if( BETA[REAL_PART] == ZERO ) { PB_Cplapad( type, ALL, NOCONJG, *M, *N, type->zero, type->zero, ((char * ) C), Ci, Cj, Cd ); } else if( !( BETA[REAL_PART] == ONE ) ) { PB_Cplascal( type, ALL, NOCONJG, *M, *N, ((char *) BETA), ((char * ) C), Ci, Cj, Cd ); } return; } /* * Start the operations */ #ifdef NO_ARGCHK Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); #endif /* * Algorithm selection is based on approximation of the communication volume * for distributed and aligned operands. * * ABest: both operands sub( A ) and sub( B ) are communicated (M, N >> K) * ACest: both operands sub( A ) and sub( C ) are communicated (K, N >> M) * BCest: both operands sub( B ) and sub( C ) are communicated (M, K >> N) */ ABest = (double)(*K); ACest = (double)(*M); BCest = (double)(*N); if( notb ) { if( nota ) { tmp1 = DNROC( *M, Cd[MB_], nprow ); tmp2 = DNROC( *N, Cd[NB_], npcol ); ABest *= ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 ) + ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 ); tmp1 = DNROC( *K, Bd[MB_], nprow ); tmp2 = DNROC( *N, Bd[NB_], npcol ); tmp3 = DNROC( *K, Ad[NB_], npcol ); ACest *= ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) + CBRATIO * ( nprow == 1 ? ZERO : tmp2 ); tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp2 = DNROC( *K, Ad[NB_], npcol ); tmp4 = DNROC( *K, Bd[MB_], nprow ); BCest *= CBRATIO * ( npcol == 1 ? ZERO : tmp1 ) + ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ); } else { tmp1 = DNROC( *M, Cd[MB_], nprow ); tmp2 = DNROC( *N, Cd[NB_], npcol ); tmp3 = DNROC( *M, Ad[NB_], npcol ); ABest *= ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) + ( nprow == 1 ? ZERO : tmp2 ); tmp1 = DNROC( *K, Bd[MB_], nprow ); tmp2 = DNROC( *N, Bd[NB_], npcol ); ACest *= ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 ) + CBRATIO * ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 ); tmp1 = DNROC( *K, Ad[MB_], nprow ); tmp2 = DNROC( *M, Bd[NB_], npcol ); tmp4 = DNROC( *M, Cd[MB_], nprow ); BCest *= ( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 ) + CBRATIO * ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ); } } else { if( nota ) { tmp1 = DNROC( *M, Cd[MB_], nprow ); tmp2 = DNROC( *N, Cd[NB_], npcol ); tmp4 = DNROC( *N, Bd[MB_], nprow ); ABest *= ( npcol == 1 ? ZERO : tmp1 ) + ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ); tmp1 = DNROC( *N, Bd[MB_], nprow ); tmp2 = DNROC( *K, Bd[NB_], npcol ); tmp3 = DNROC( *N, Cd[NB_], npcol ); ACest *= CBRATIO * ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) + ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 ); tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp2 = DNROC( *K, Ad[NB_], npcol ); BCest *= CBRATIO * ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 ) + ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 ); } else { tmp1 = DNROC( *M, Cd[MB_], nprow ); tmp2 = DNROC( *N, Cd[NB_], npcol ); tmp3 = DNROC( *M, Ad[NB_], npcol ); tmp4 = DNROC( *N, Bd[MB_], nprow ); ABest *= ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) + ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ); tmp1 = DNROC( *N, Bd[MB_], nprow ); tmp2 = DNROC( *K, Bd[NB_], npcol ); tmp3 = DNROC( *N, Cd[NB_], npcol ); tmp4 = DNROC( *K, Ad[MB_], nprow ); ACest *= CBRATIO * ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) + ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ); tmp1 = DNROC( *K, Ad[MB_], nprow ); tmp2 = DNROC( *M, Ad[NB_], npcol ); tmp3 = DNROC( *K, Bd[NB_], npcol ); tmp4 = DNROC( *M, Cd[MB_], nprow ); BCest *= ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) + CBRATIO * ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ); } } ChooseAB = ( ( ABest <= ( 1.3 * BCest ) ) && ( ABest <= ( 1.3 * ACest ) ) ); ChooseBC = ( ( BCest <= ACest ) && ( ( 1.3 * BCest ) <= ABest ) ); /* * BLACS topologies are enforced iff M, N and K are strictly greater than the * logical block size returned by pilaenv_. Otherwise, it is assumed that the * routine calling this routine has already selected an adequate topology. */ nb = pilaenv_( &ctxt, C2F_CHAR( &type->type ) ); ForceTop = ( ( *M > nb ) && ( *N > nb ) && ( *K > nb ) ); if( ChooseAB ) { OpR = CBCAST; OpC = CBCAST; } else if( ChooseBC ) { if( nota ) { OpR = CCOMBINE; OpC = CBCAST; } else { OpR = CBCAST; OpC = CCOMBINE; } } else { if( notb ) { OpR = CBCAST; OpC = CCOMBINE; } else { OpR = CCOMBINE; OpC = CBCAST; } } rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); if( ForceTop ) { rtopsave = rtop; ctopsave = ctop; /* * No clear winner for the ring topologies, so that if a ring topology is * already selected, keep it. */ if( ( rtop != CTOP_DRING ) && ( rtop != CTOP_IRING ) && ( rtop != CTOP_SRING ) ) rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_IRING ); if( ( ctop != CTOP_DRING ) && ( ctop != CTOP_IRING ) && ( ctop != CTOP_SRING ) ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_IRING ); /* * Remove the next 4 lines when the BLACS combine operations support ring * topologies */ if( OpR == CCOMBINE ) rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_DEFAULT ); if( OpC == CCOMBINE ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_DEFAULT ); } DirAB = ( rtop == CTOP_DRING ? CBACKWARD : CFORWARD ); DirBC = ( ctop == CTOP_DRING ? CBACKWARD : CFORWARD ); if( ChooseAB ) { PB_CpgemmAB( type, &DirAB, &DirBC, ( nota ? NOTRAN : TRAN ), ( notb ? NOTRAN : TRAN ), *M, *N, *K, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad, ((char *)B), Bi, Bj, Bd, ((char *)BETA), ((char *)C), Ci, Cj, Cd ); } else if( ChooseBC ) { PB_CpgemmBC( type, &DirAB, &DirBC, ( nota ? NOTRAN : TRAN ), ( notb ? NOTRAN : TRAN ), *M, *N, *K, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad, ((char *)B), Bi, Bj, Bd, ((char *)BETA), ((char *)C), Ci, Cj, Cd ); } else { PB_CpgemmAC( type, &DirAB, &DirBC, ( nota ? NOTRAN : TRAN ), ( notb ? NOTRAN : TRAN ), *M, *N, *K, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad, ((char *)B), Bi, Bj, Bd, ((char *)BETA), ((char *)C), Ci, Cj, Cd ); } /* * Restore the BLACS topologies when necessary. */ if( ForceTop ) { rtopsave = *PB_Ctop( &ctxt, &OpR, ROW, &rtopsave ); ctopsave = *PB_Ctop( &ctxt, &OpC, COLUMN, &ctopsave ); } /* * End of PDGEMM */ }