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:                             

 *                                                                      

 * Redistribution  and  use in  source and binary forms, with or without

 * modification, are  permitted provided  that the following  conditions

 * are met:                                                             

 *                                                                      

 * 1. Redistributions  of  source  code  must retain the above copyright

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

 *                                                                      

 * 2. Redistributions in binary form must reproduce  the above copyright

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

 * documentation and/or other materials provided with the distribution. 

 *                                                                      

 * 3. All  advertising  materials  mentioning  features  or  use of this

 * software must display the following acknowledgement:                 

 * This  product  includes  software  developed  at  the  University  of

 * Tennessee, Knoxville, Innovative Computing Laboratory.             

 *                                                                      

 * 4. The name of the  University,  the name of the  Laboratory,  or the

 * names  of  its  contributors  may  not  be used to endorse or promote

 * products  derived   from   this  software  without  specific  written

 * permission.                                                          

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 * -- Disclaimer:                                                       

 *                                                                      

 * THIS  SOFTWARE  IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

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

 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR

 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE UNIVERSITY

 * OR  CONTRIBUTORS  BE  LIABLE FOR ANY  DIRECT,  INDIRECT,  INCIDENTAL,

 * SPECIAL,  EXEMPLARY,  OR  CONSEQUENTIAL DAMAGES  (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_pdtrsv

(

   HPL_T_grid *                     GRID,

   HPL_T_pmat *                     AMAT

)

#else

void HPL_pdtrsv

( GRID, AMAT )

   HPL_T_grid *                     GRID;

   HPL_T_pmat *                     AMAT;

#endif

{

/* 

 * Purpose

 * =======

 *

 * HPL_pdtrsv solves an upper triangular system of linear equations.

 *  

 * The rhs is the last column of the N by N+1 matrix A. The solve starts

 * in the process  column owning the  Nth  column of A, so the rhs b may

 * need to be moved one process column to the left at the beginning. The

 * routine therefore needs  a column  vector in every process column but

 * the one owning  b. The result is  replicated in all process rows, and

 * returned in XR, i.e. XR is of size nq = LOCq( N ) in all processes.

 *  

 * The algorithm uses decreasing one-ring broadcast in process rows  and

 * columns  implemented  in terms of  synchronous communication point to

 * point primitives.  The  lookahead of depth 1 is used to minimize  the

 * critical path. This entire operation is essentially ``latency'' bound

 * and an estimate of its running time is given by:

 *  

 *    (move rhs) lat + N / ( P bdwth ) +            

 *    (solve)    ((N / NB)-1) 2 (lat + NB / bdwth) +

 *               gam2 N^2 / ( P Q ),                

 *  

 * where  gam2   is an estimate of the   Level 2 BLAS rate of execution.

 * There are  N / NB  diagonal blocks. One must exchange  2  messages of

 * length NB to compute the next  NB  entries of the vector solution, as

 * well as performing a total of N^2 floating point operations.

 *

 * Arguments

 * =========

 *

 * GRID    (local input)                 HPL_T_grid *

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

 *         process grid information.

 *

 * AMAT    (local input/output)          HPL_T_pmat *

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

 *         local array information.

 *

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

 */ 

/*

 * .. Local Variables ..

 */

   MPI_Comm                   Ccomm, Rcomm;

   double                     * A=NULL, * Aprev=NULL, * Aptr, * XC=NULL,

                              * XR=NULL, * Xd=NULL, * Xdprev=NULL,

                              * W=NULL;

   int                        Alcol, Alrow, Anpprev, Anp, Anq, Bcol,

                              Cmsgid, GridIsNotPx1, GridIsNot1xQ, Rmsgid,

                              Wfr=0, colprev, kb, kbprev, lda, mycol,

                              myrow, n, n1, n1p, n1pprev=0, nb, npcol,

                              nprow, rowprev, tmp1, tmp2;

/* ..

 * .. Executable Statements ..

 */

#ifdef HPL_DETAILED_TIMING

   HPL_ptimer( HPL_TIMING_PTRSV );

#endif

   if( ( n = AMAT->n ) <= 0 ) return;

   nb = AMAT->nb; lda = AMAT->ld; A = AMAT->A; XR = AMAT->X;

   (void) HPL_grid_info( GRID, &nprow, &npcol, &myrow, &mycol );

   Rcomm = GRID->row_comm; Rmsgid = MSGID_BEGIN_PTRSV;

   Ccomm = GRID->col_comm; Cmsgid = MSGID_BEGIN_PTRSV + 1;

   GridIsNot1xQ = ( nprow > 1 ); GridIsNotPx1 = ( npcol > 1 );

/*

 * Move the rhs in the process column owning the last column of A.

 */

   Mnumroc( Anp, n, nb, nb, myrow, 0, nprow );

   Mnumroc( Anq, n, nb, nb, mycol, 0, npcol );

   tmp1  = ( n - 1 ) / nb;

   Alrow = tmp1 - ( tmp1 / nprow ) * nprow;

   Alcol = tmp1 - ( tmp1 / npcol ) * npcol;

   kb    = n    - tmp1 * nb;

   Aptr = (double *)(A); XC = Mptr( Aptr, 0, Anq, lda );

   Mindxg2p( n, nb, nb, Bcol, 0, npcol );

   if( ( Anp > 0 ) && ( Alcol != Bcol ) )

   {

      if( mycol == Bcol  )

      { (void) HPL_send( XC, Anp, Alcol, Rmsgid, Rcomm ); }

      else if( mycol == Alcol )

      { (void) HPL_recv( XC, Anp, Bcol,  Rmsgid, Rcomm ); }

   }

   Rmsgid = ( Rmsgid + 2 >

              MSGID_END_PTRSV ? MSGID_BEGIN_PTRSV : Rmsgid + 2 );

   if( mycol != Alcol )

   { for( tmp1=0; tmp1 < Anp; tmp1++ ) XC[tmp1] = HPL_rzero; }

/*

 * Set up lookahead

 */

   n1 = ( npcol - 1 ) * nb; n1 = Mmax( n1, nb );

   if( Anp > 0 )

   {

      W = (double*)malloc( (size_t)(Mmin( n1, Anp )) * sizeof( double ) );

      if( W == NULL )

      { HPL_pabort( __LINE__, "HPL_pdtrsv", "Memory allocation failed" ); }

      Wfr = 1;

   }

   Anpprev = Anp; Xdprev = XR; Aprev = Aptr = Mptr( Aptr, 0, Anq, lda );

   tmp1    = n - kb; tmp1 -= ( tmp2 = Mmin( tmp1, n1 ) );

   MnumrocI( n1pprev, tmp2, Mmax( 0, tmp1 ), nb, nb, myrow, 0, nprow );

   if( myrow == Alrow ) { Anpprev = ( Anp -= kb ); }

   if( mycol == Alcol )

   {

      Aprev = ( Aptr -= lda * kb ); Anq -= kb; Xdprev = ( Xd = XR + Anq );

      if( myrow == Alrow )

      {

         HPL_dtrsv( HplColumnMajor, HplUpper, HplNoTrans, HplNonUnit,

                    kb, Aptr+Anp, lda, XC+Anp, 1 );

         HPL_dcopy( kb, XC+Anp, 1, Xd, 1 );

      }

   }

   rowprev = Alrow; Alrow = MModSub1( Alrow, nprow );

   colprev = Alcol; Alcol = MModSub1( Alcol, npcol );

   kbprev  = kb; n -= kb;

   tmp1    = n - ( kb = nb ); tmp1 -= ( tmp2 = Mmin( tmp1, n1 ) );

   MnumrocI( n1p, tmp2, Mmax( 0, tmp1 ), nb, nb, myrow, 0, nprow );

/*

 * Start the operations

 */

   while( n > 0 )

   {

      if( mycol == Alcol ) { Aptr -= lda * kb; Anq -= kb; Xd = XR + Anq; }

      if( myrow == Alrow ) { Anp -= kb; }

/*

 * Broadcast  (decreasing-ring)  of  previous solution block in previous

 * process column,  compute  partial update of current block and send it

 * to current process column.

 */

      if( mycol == colprev )

      {

/*

 * Send previous solution block in process row above

 */

         if( myrow == rowprev )

         {

            if( GridIsNot1xQ )

               (void) HPL_send( Xdprev, kbprev, MModSub1( myrow, nprow ),

                                Cmsgid, Ccomm );

         }

         else

         {

            (void) HPL_recv( Xdprev, kbprev, MModAdd1( myrow, nprow ),

                             Cmsgid, Ccomm );

         } 

/*

 * Compute partial update of previous solution block and send it to cur-

 * rent column

 */

         if( n1pprev > 0 )

         {

            tmp1 = Anpprev - n1pprev;

            HPL_dgemv( HplColumnMajor, HplNoTrans, n1pprev, kbprev,

                       -HPL_rone, Aprev+tmp1, lda, Xdprev, 1, HPL_rone,

                       XC+tmp1, 1 );

            if( GridIsNotPx1 )

               (void) HPL_send( XC+tmp1, n1pprev, Alcol, Rmsgid, Rcomm );

         }

/*

 * Finish  the (decreasing-ring) broadcast of the solution block in pre-

 * vious process column

 */

         if( ( myrow != rowprev ) &&

             ( myrow != MModAdd1( rowprev, nprow ) ) )

            (void) HPL_send( Xdprev, kbprev, MModSub1( myrow, nprow ),

                             Cmsgid, Ccomm );

      }

      else if( mycol == Alcol )

      {

/*

 * Current  column  receives  and accumulates partial update of previous

 * solution block

 */

         if( n1pprev > 0 )

         {

            (void) HPL_recv( W, n1pprev, colprev, Rmsgid, Rcomm );

            HPL_daxpy( n1pprev, HPL_rone, W, 1, XC+Anpprev-n1pprev, 1 );

         }

      }

/*

 * Solve current diagonal block 

 */

      if( ( mycol == Alcol ) && ( myrow == Alrow ) )

      {

         HPL_dtrsv( HplColumnMajor, HplUpper, HplNoTrans, HplNonUnit,

                    kb, Aptr+Anp, lda, XC+Anp, 1 );

         HPL_dcopy( kb, XC+Anp, 1, XR+Anq, 1 );

      }

/*

*  Finish previous update

*/

      if( ( mycol == colprev ) && ( ( tmp1 = Anpprev - n1pprev ) > 0 ) )

         HPL_dgemv( HplColumnMajor, HplNoTrans, tmp1, kbprev, -HPL_rone,

                    Aprev, lda, Xdprev, 1, HPL_rone, XC, 1 );

/*

*  Save info of current step and update info for the next step

*/

      if( mycol == Alcol ) { Xdprev   = Xd; Aprev = Aptr; }

      if( myrow == Alrow ) { Anpprev -= kb; }

      rowprev = Alrow; colprev = Alcol;

      n1pprev = n1p;   kbprev  = kb; n -= kb;

      Alrow = MModSub1( Alrow, nprow ); Alcol = MModSub1( Alcol, npcol );

      tmp1  = n - ( kb = nb ); tmp1 -= ( tmp2 = Mmin( tmp1, n1 ) );

      MnumrocI( n1p, tmp2, Mmax( 0, tmp1 ), nb, nb, myrow, 0, nprow );

      Rmsgid = ( Rmsgid+2 > MSGID_END_PTRSV ? 

                 MSGID_BEGIN_PTRSV   : Rmsgid+2 );

      Cmsgid = ( Cmsgid+2 > MSGID_END_PTRSV ?

                 MSGID_BEGIN_PTRSV+1 : Cmsgid+2 );

   }

/*

 * Replicate last solution block

 */

   if( mycol == colprev )

      (void) HPL_broadcast( (void *)(XR), kbprev, HPL_DOUBLE, rowprev,

                            Ccomm );

   if( Wfr  ) free( W  );

#ifdef HPL_DETAILED_TIMING

   HPL_ptimer( HPL_TIMING_PTRSV );

#endif

/*

 * End of HPL_pdtrsv

 */

}