Centre Blaise Pascal » HPL sur GPU

/* 

 * -- High Performance Computing Linpack Benchmark (HPL)                

 *    HPL - 2.0 - September 10, 2008                          

 *    Antoine P. Petitet                                                

 *    University of Tennessee, Knoxville                                

 *    Innovative Computing Laboratory                                 

 *    (C) Copyright 2000-2008 All Rights Reserved                       

 *                                                                      

 * -- Copyright notice and Licensing terms:                             

 *                                                                      

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 * modification, are  permitted provided  that the following  conditions

 * are met:                                                             

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 * notice, this list of conditions and the following disclaimer.        

 *                                                                      

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 *                                                                      

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 * software must display the following acknowledgement:                 

 * This  product  includes  software  developed  at  the  University  of

 * Tennessee, Knoxville, Innovative Computing Laboratory.             

 *                                                                      

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 * permission.                                                          

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 * THIS  SOFTWARE  IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,  INCLUDING,  BUT NOT

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 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 

 * ---------------------------------------------------------------------

 */ 

/*

 * Include files

 */

#include "hpl.h"

#ifdef STDC_HEADERS

void HPL_pdrpancrN

(

   HPL_T_panel *                    PANEL,

   const int                        M,

   const int                        N,

   const int                        ICOFF,

   double *                         WORK

)

#else

void HPL_pdrpancrN

( PANEL, M, N, ICOFF, WORK )

   HPL_T_panel *                    PANEL;

   const int                        M;

   const int                        N;

   const int                        ICOFF;

   double *                         WORK;

#endif

{

/* 

 * Purpose

 * =======

 *

 * HPL_pdrpancrN HPL_pdrpancrN recursively  factorizes  a panel of columns  using  the

 * recursive  Crout  variant of the usual one-dimensional algorithm. The

 * lower triangular  N0-by-N0  upper block  of  the  panel  is stored in

 * no-transpose form (i.e. just like the input matrix itself).

 *  

 * Bi-directional  exchange  is  used  to  perform  the  swap::broadcast

 * operations  at once  for one column in the panel.  This  results in a

 * lower number of slightly larger  messages than usual.  On P processes

 * and assuming bi-directional links,  the running time of this function

 * can be approximated by (when N is equal to N0):                      

 *  

 *    N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) +

 *    N0^2 * ( M - N0/3 ) * gam2-3

 *  

 * where M is the local number of rows of  the panel, lat and bdwth  are

 * the latency and bandwidth of the network for  double  precision  real

 * words, and  gam2-3  is  an estimate of the  Level 2 and Level 3  BLAS

 * rate of execution. The  recursive  algorithm  allows indeed to almost

 * achieve  Level 3 BLAS  performance  in the panel factorization.  On a

 * large  number of modern machines,  this  operation is however latency

 * bound,  meaning  that its cost can  be estimated  by only the latency

 * portion N0 * log_2(P) * lat.  Mono-directional links will double this

 * communication cost.

 *

 * Arguments

 * =========

 *

 * PANEL   (local input/output)          HPL_T_panel *

 *         On entry,  PANEL  points to the data structure containing the

 *         panel information.

 *

 * M       (local input)                 const int

 *         On entry,  M specifies the local number of rows of sub(A).

 *

 * N       (local input)                 const int

 *         On entry,  N specifies the local number of columns of sub(A).

 *

 * ICOFF   (global input)                const int

 *         On entry, ICOFF specifies the row and column offset of sub(A)

 *         in A.

 *

 * WORK    (local workspace)             double *

 *         On entry, WORK  is a workarray of size at least 2*(4+2*N0).

 *

 * ---------------------------------------------------------------------

 */ 

/*

 * .. Local Variables ..

 */

   double                     * A, * Aptr, * L1, * L1ptr;

#ifdef HPL_CALL_VSIPL

   vsip_mview_d               * Av0, * Lv0, * Av1, * Av2, * Lv1;

#endif

   int                        curr, ii, ioff, jb, jj, lda, m, n, n0, nb,

                              nbdiv, nbmin;

/* ..

 * .. Executable Statements ..

 */

   if( N <= ( nbmin = PANEL->algo->nbmin ) )

   { PANEL->algo->pffun( PANEL, M, N, ICOFF, WORK ); return; }

/*

 * Find  new recursive blocking factor.  To avoid an infinite loop,  one

 * must guarantee: 1 <= jb < N, knowing that  N  is greater than  NBMIN.

 * First, we compute nblocks:  the number of blocks of size  NBMIN in N,

 * including the last one that may be smaller.  nblocks  is thus  larger

 * than or equal to one, since N >= NBMIN.

 * The ratio ( nblocks + NDIV - 1 ) / NDIV  is thus larger than or equal

 * to one as  well.  For  NDIV >= 2,  we  are guaranteed  that the quan-

 * tity ( ( nblocks + NDIV  - 1 ) / NDIV ) * NBMIN  is less  than N  and

 * greater than or equal to NBMIN.

 */

   nbdiv = PANEL->algo->nbdiv; ii = jj = 0; m = M; n = N;

   nb = jb = ( (((N+nbmin-1) / nbmin) + nbdiv  - 1) / nbdiv ) * nbmin;

   A     = PANEL->A;   lda = PANEL->lda;

   L1    = PANEL->L1;  n0  = PANEL->jb;

   L1ptr = Mptr( L1, ICOFF, ICOFF, n0 );

   curr  = (int)( PANEL->grid->myrow == PANEL->prow );

   if( curr != 0 ) Aptr = Mptr( A, ICOFF, ICOFF, lda );

   else            Aptr = Mptr( A,     0, ICOFF, lda );

/*

 * The triangular solve is replicated in every  process row.  The  panel

 * factorization is  such that  the first rows of  A  are accumulated in

 * every process row during the (panel) swapping phase.  We  ensure this

 * way a minimum amount  of communication during the entire panel facto-

 * rization.

 */

   do

   {

      n -= jb; ioff = ICOFF + jj;

/*

 * Local update - Factor current panel - Replicated update and solve

 */

#ifdef HPL_CALL_VSIPL

/*

 * Admit the blocks

 */

      (void) vsip_blockadmit_d( PANEL->Ablock,  VSIP_TRUE );

      (void) vsip_blockadmit_d( PANEL->L1block, VSIP_TRUE );

/*

 * Create the matrix views

 */

      Av0 = vsip_mbind_d( PANEL->Ablock,  0, 1, lda, lda, PANEL->pmat->nq );

      Lv0 = vsip_mbind_d( PANEL->L1block, 0, 1,  n0,  n0, n0              );

/*

 * Create the matrix subviews

 */

      if( curr != 0 )

      {

         Av1 = vsip_msubview_d( Av0, PANEL->ii+ICOFF+ii, PANEL->jj+ICOFF,

                                m,  jj );

         Av2 = vsip_msubview_d( Av0, PANEL->ii+ICOFF+ii, PANEL->jj+ioff,

                                m, jb );

      }

      else

      {

         Av1 = vsip_msubview_d( Av0, PANEL->ii+ii, PANEL->jj+ICOFF, m, jj );

         Av2 = vsip_msubview_d( Av0, PANEL->ii+ii, PANEL->jj+ioff,  m, jb );

      }

      Lv1 = vsip_msubview_d( Lv0, ICOFF, ioff, jj, jb );

      vsip_gemp_d( -HPL_rone, Av1, VSIP_MAT_NTRANS, Lv1, VSIP_MAT_NTRANS,

                   HPL_rone, Av2 );

/*

 * Destroy the matrix subviews

 */

      (void) vsip_mdestroy_d( Lv1 );

      (void) vsip_mdestroy_d( Av2 );

      (void) vsip_mdestroy_d( Av1 );

/*

 * Release the blocks

 */

      (void) vsip_blockrelease_d( vsip_mgetblock_d( Lv0 ), VSIP_TRUE );

      (void) vsip_blockrelease_d( vsip_mgetblock_d( Av0 ), VSIP_TRUE );

/*

 * Destroy the matrix views

 */

      (void) vsip_mdestroy_d( Lv0 );

      (void) vsip_mdestroy_d( Av0 );

#else

      HPL_dgemm( HplColumnMajor, HplNoTrans, HplNoTrans, m, jb, jj,

                 -HPL_rone, Mptr( Aptr, ii, 0, lda ), lda, Mptr( L1ptr,

                 0, jj, n0 ), n0, HPL_rone, Mptr( Aptr, ii, jj, lda ),

                 lda );

#endif

      HPL_pdrpancrN( PANEL, m, jb, ioff, WORK );

      if( n > 0 )

      {

#ifdef HPL_CALL_VSIPL

/*

 * Admit the blocks

 */

         (void) vsip_blockadmit_d( PANEL->L1block, VSIP_TRUE );

/*

 * Create the matrix views

 */

         Lv0 = vsip_mbind_d( PANEL->L1block, 0, 1,  n0,  n0, n0 );

/*

 * Create the matrix subviews

 */

         Av1 = vsip_msubview_d( Lv0, ioff,  ICOFF,   jb, jj );

         Av2 = vsip_msubview_d( Lv0, ioff,  ioff+jb, jb,  n );

         Lv1 = vsip_msubview_d( Lv0, ICOFF, ioff+jb, jj,  n );

         vsip_gemp_d( -HPL_rone, Av1, VSIP_MAT_NTRANS, Lv1, VSIP_MAT_NTRANS,

                      HPL_rone, Av2 );

/*

 * Destroy the matrix subviews

 */

         (void) vsip_mdestroy_d( Lv1 );

         (void) vsip_mdestroy_d( Av2 );

         (void) vsip_mdestroy_d( Av1 );

/*

 * Release the blocks

 */

         (void) vsip_blockrelease_d( vsip_mgetblock_d( Lv0 ), VSIP_TRUE );

/*

 * Destroy the matrix views

 */

         (void) vsip_mdestroy_d( Lv0 );

#else

         HPL_dgemm( HplColumnMajor, HplNoTrans, HplNoTrans, jb, n,

                    jj, -HPL_rone, Mptr( L1ptr, jj, 0, n0 ), n0,

                    Mptr( L1ptr, 0, jj+jb, n0 ), n0, HPL_rone, 

                    Mptr( L1ptr, jj, jj+jb, n0 ), n0 );

#endif

         HPL_dtrsm( HplColumnMajor, HplLeft, HplLower, HplNoTrans,

                    HplUnit, jb, n, HPL_rone, Mptr( L1ptr, jj, jj,

                    n0 ), n0, Mptr( L1ptr, jj, jj+jb, n0 ), n0 );

      }

/*

 * Copy back upper part of A in current process row - Go the next block

 */

      if( curr != 0 )

      {

         HPL_dlacpy( ioff, jb, Mptr( L1, 0, ioff, n0 ), n0,

                     Mptr( A, 0, ioff, lda ), lda );

         ii += jb; m -= jb;

      }

      jj += jb; jb = Mmin( n, nb );

   } while( n > 0 );

/*

 * End of HPL_pdrpancrN

 */

}