On 05/22/2014 10:16 PM, Vladimir Makarov wrote:
It also permits to
rematerialize not only on loop borders (although it is the most
important points).
That would certainly be interesting for the following hot subroutine in
our weather forecasting model (attached). Note the loop from (line 157):
+IF (KINT.EQ.3) THEN
C CUBIC INTERPOLATION
to (line 242):
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY+1,ILEV+1) ) )
ENDDO
ENDDO
Kind regards,
--
Toon Moene - e-mail: t...@moene.org - phone: +31 346 214290
Saturnushof 14, 3738 XG Maartensdijk, The Netherlands
At home: http://moene.org/~toon/; weather: http://moene.org/~hirlam/
Progress of GNU Fortran: http://gcc.gnu.org/wiki/GFortran#news
# 1 "/scratch/hirlam/hl_home/MPI/lib/src/grdy/verint.F"
# 1 "<built-in>"
# 1 "<command-line>"
# 1 "/scratch/hirlam/hl_home/MPI/lib/src/grdy/verint.F"
c Library:grdy $RCSfile$, $Revision: 7536 $
c checked in by $Author: ovignes $ at $Date: 2009-12-18 14:23:36 +0100 (Fri, 18 Dec 2009) $
c $State$, $Locker$
c $Log$
c Revision 1.3 1999/04/22 09:30:45 DagBjoerge
c MPP code
c
c Revision 1.2 1999/03/09 10:23:13 GerardCats
c Add SGI paralllellisation directives DOACROSS
c
c Revision 1.1 1996/09/06 13:12:18 GCats
c Created from grdy.apl, 1 version 2.6.1, by Gerard Cats
c
SUBROUTINE VERINT (
I KLON , KLAT , KLEV , KINT , KHALO
I , KLON1 , KLON2 , KLAT1 , KLAT2
I , KP , KQ , KR
R , PARG , PRES
R , PALFH , PBETH
R , PALFA , PBETA , PGAMA )
C
C*******************************************************************
C
C VERINT - THREE DIMENSIONAL INTERPOLATION
C
C PURPOSE:
C
C THREE DIMENSIONAL INTERPOLATION
C
C INPUT PARAMETERS:
C
C KLON NUMBER OF GRIDPOINTS IN X-DIRECTION
C KLAT NUMBER OF GRIDPOINTS IN Y-DIRECTION
C KLEV NUMBER OF VERTICAL LEVELS
C KINT TYPE OF INTERPOLATION
C = 1 - LINEAR
C = 2 - QUADRATIC
C = 3 - CUBIC
C = 4 - MIXED CUBIC/LINEAR
C KLON1 FIRST GRIDPOINT IN X-DIRECTION
C KLON2 LAST GRIDPOINT IN X-DIRECTION
C KLAT1 FIRST GRIDPOINT IN Y-DIRECTION
C KLAT2 LAST GRIDPOINT IN Y-DIRECTION
C KP ARRAY OF INDEXES FOR HORIZONTAL DISPLACEMENTS
C KQ ARRAY OF INDEXES FOR HORIZONTAL DISPLACEMENTS
C KR ARRAY OF INDEXES FOR VERTICAL DISPLACEMENTS
C PARG ARRAY OF ARGUMENTS
C PALFH ALFA HAT
C PBETH BETA HAT
C PALFA ARRAY OF WEIGHTS IN X-DIRECTION
C PBETA ARRAY OF WEIGHTS IN Y-DIRECTION
C PGAMA ARRAY OF WEIGHTS IN VERTICAL DIRECTION
C
C OUTPUT PARAMETERS:
C
C PRES INTERPOLATED FIELD
C
C HISTORY:
C
C J.E. HAUGEN 1 1992
C
C*******************************************************************
C
IMPLICIT NONE
C
INTEGER KLON , KLAT , KLEV , KINT , KHALO,
I KLON1 , KLON2 , KLAT1 , KLAT2
C
INTEGER KP(KLON,KLAT), KQ(KLON,KLAT), KR(KLON,KLAT)
REAL PARG(2-KHALO:KLON+KHALO-1,2-KHALO:KLAT+KHALO-1,KLEV) ,
R PRES(KLON,KLAT) ,
R PALFH(KLON,KLAT) , PBETH(KLON,KLAT) ,
R PALFA(KLON,KLAT,4) , PBETA(KLON,KLAT,4),
R PGAMA(KLON,KLAT,4)
C
INTEGER JX, JY, IDX, IDY, ILEV
REAL Z1MAH, Z1MBH
C
IF (KINT.EQ.1) THEN
C LINEAR INTERPOLATION
C
DO JY = KLAT1,KLAT2
DO JX = KLON1,KLON2
IDX = KP(JX,JY)
IDY = KQ(JX,JY)
ILEV = KR(JX,JY)
C
PRES(JX,JY) = PGAMA(JX,JY,1)*(
C
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY-1,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY-1,ILEV-1) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY ,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY ,ILEV-1) ) )
C +
+ + PGAMA(JX,JY,2)*(
C +
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY-1,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY-1,ILEV ) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY ,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY ,ILEV ) ) )
ENDDO
ENDDO
C
ELSE
+IF (KINT.EQ.2) THEN
C QUADRATIC INTERPOLATION
C
DO JY = KLAT1,KLAT2
DO JX = KLON1,KLON2
IDX = KP(JX,JY)
IDY = KQ(JX,JY)
ILEV = KR(JX,JY)
C
PRES(JX,JY) = PGAMA(JX,JY,1)*(
C
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY-1,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY-1,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY-1,ILEV-1) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY ,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY ,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY ,ILEV-1) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY+1,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY+1,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY+1,ILEV-1) ) )
C +
+ + PGAMA(JX,JY,2)*(
C +
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY-1,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY-1,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY-1,ILEV ) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY ,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY ,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY ,ILEV ) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY+1,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY+1,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY+1,ILEV ) ) )
C +
+ + PGAMA(JX,JY,3)*(
C +
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY-1,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY-1,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY-1,ILEV+1) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY ,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY ,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY ,ILEV+1) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-1,IDY+1,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX ,IDY+1,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX+1,IDY+1,ILEV+1) ) )
ENDDO
ENDDO
C
ELSE
+IF (KINT.EQ.3) THEN
C CUBIC INTERPOLATION
C
DO JY = KLAT1,KLAT2
DO JX = KLON1,KLON2
IDX = KP(JX,JY)
IDY = KQ(JX,JY)
ILEV = KR(JX,JY)
C
PRES(JX,JY) = PGAMA(JX,JY,1)*(
C
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-2,ILEV-2)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-2,ILEV-2)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-2,ILEV-2)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-2,ILEV-2) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-1,ILEV-2)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-1,ILEV-2)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-1,ILEV-2)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-1,ILEV-2) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY ,ILEV-2)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY ,ILEV-2)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY ,ILEV-2)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY ,ILEV-2) )
+ + PBETA(JX,JY,4)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY+1,ILEV-2)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY+1,ILEV-2)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY+1,ILEV-2)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY+1,ILEV-2) ) )
C +
+ + PGAMA(JX,JY,2)*(
C +
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-2,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-2,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-2,ILEV-1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-2,ILEV-1) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-1,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-1,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-1,ILEV-1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-1,ILEV-1) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY ,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY ,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY ,ILEV-1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY ,ILEV-1) )
+ + PBETA(JX,JY,4)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY+1,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY+1,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY+1,ILEV-1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY+1,ILEV-1) ) )
C +
+ + PGAMA(JX,JY,3)*(
C +
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-2,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-2,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-2,ILEV )
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-2,ILEV ) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-1,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-1,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-1,ILEV )
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-1,ILEV ) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY ,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY ,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY ,ILEV )
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY ,ILEV ) )
+ + PBETA(JX,JY,4)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY+1,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY+1,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY+1,ILEV )
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY+1,ILEV ) ) )
C +
+ + PGAMA(JX,JY,4)*(
C +
+ PBETA(JX,JY,1)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-2,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-2,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-2,ILEV+1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-2,ILEV+1) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-1,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-1,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-1,ILEV+1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-1,ILEV+1) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY ,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY ,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY ,ILEV+1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY ,ILEV+1) )
+ + PBETA(JX,JY,4)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY+1,ILEV+1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY+1,ILEV+1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY+1,ILEV+1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY+1,ILEV+1) ) )
ENDDO
ENDDO
C
ELSE
+IF (KINT.EQ.4) THEN
C MIXED CUBIC/LINEAR INTERPOLATION
C
DO JY = KLAT1,KLAT2
DO JX = KLON1,KLON2
IDX = KP(JX,JY)
IDY = KQ(JX,JY)
ILEV = KR(JX,JY)
C
Z1MAH = 1.0 - PALFH(JX,JY)
Z1MBH = 1.0 - PBETH(JX,JY)
C
PRES(JX,JY) = PGAMA(JX,JY,1)*(
C
+ PBETH(JX,JY) *( PALFH(JX,JY) *PARG(IDX-1,IDY-1,ILEV-2)
+ + Z1MAH *PARG(IDX ,IDY-1,ILEV-2) )
+ + Z1MBH *( PALFH(JX,JY) *PARG(IDX-1,IDY ,ILEV-2)
+ + Z1MAH *PARG(IDX ,IDY ,ILEV-2) ) )
C +
+ + PGAMA(JX,JY,4)*(
C +
+ PBETH(JX,JY) *( PALFH(JX,JY) *PARG(IDX-1,IDY-1,ILEV+1)
+ + Z1MAH *PARG(IDX ,IDY-1,ILEV+1) )
+ + Z1MBH *( PALFH(JX,JY) *PARG(IDX-1,IDY ,ILEV+1)
+ + Z1MAH *PARG(IDX ,IDY ,ILEV+1) ) )
C +
+ + PGAMA(JX,JY,2)*(
C +
+ PBETA(JX,JY,1)*( PALFH(JX,JY) *PARG(IDX-1,IDY-2,ILEV-1)
+ + Z1MAH *PARG(IDX ,IDY-2,ILEV-1) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-1,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-1,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-1,ILEV-1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-1,ILEV-1) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY ,ILEV-1)
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY ,ILEV-1)
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY ,ILEV-1)
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY ,ILEV-1) )
+ + PBETA(JX,JY,4)*( PALFH(JX,JY) *PARG(IDX-1,IDY+1,ILEV-1)
+ + Z1MAH *PARG(IDX ,IDY+1,ILEV-1) ) )
C +
+ + PGAMA(JX,JY,3)*(
C +
+ PBETA(JX,JY,1)*( PALFH(JX,JY) *PARG(IDX-1,IDY-2,ILEV )
+ + Z1MAH *PARG(IDX ,IDY-2,ILEV ) )
+ + PBETA(JX,JY,2)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY-1,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY-1,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY-1,ILEV )
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY-1,ILEV ) )
+ + PBETA(JX,JY,3)*( PALFA(JX,JY,1)*PARG(IDX-2,IDY ,ILEV )
+ + PALFA(JX,JY,2)*PARG(IDX-1,IDY ,ILEV )
+ + PALFA(JX,JY,3)*PARG(IDX ,IDY ,ILEV )
+ + PALFA(JX,JY,4)*PARG(IDX+1,IDY ,ILEV ) )
+ + PBETA(JX,JY,4)*( PALFH(JX,JY) *PARG(IDX-1,IDY+1,ILEV )
+ + Z1MAH *PARG(IDX ,IDY+1,ILEV ) ) )
ENDDO
ENDDO
C
ENDIF
C
RETURN
END
