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2 CONTINUE

3 OPEN (3, FILE='JACOBI.DAT', FORM='FORMATTED')

WRITE (3,*) B

CLOSE (3)

END

Example 3. Jacobi algorithm (asynchronous version)

PROGRAM JACOB1

PARAMETER (K=8, ITMAX=20)

REAL A(K,K), B(K,K), EPS, MAXEPS

CDVM$ DISTRIBUTE A ( BLOCK, BLOCK)

CDVM$ ALIGN B( I, J ) WITH A( I, J )

C arrays A and B with block distribution

CDVM$ REDUCTION_GROUP REPS

PRINT *, '********** TEST_JACOBI_ASYNCHR **********'

CDVM SHADOW_GROUP SA ( A )

C creation of shadow edge group

MAXEPS = 0.5E - 7

CDVM$ PARALLEL (J,I) ON A(I, J)

C nest of two parallel loops, iteration (i,j) will be executed on

C processor, which is owner of element A(i,j)

DO 1 J = 1, K

DO 1 I = 1, K

A(I, J) = 0.

IF(I.EQ.1 .OR. J.EQ.1 .OR. I.EQ.K .OR. J.EQ.K) THEN

B(I, J) = 0.

ELSE

B(I, J) = 1. + I + J

ENDIF

1 CONTINUE

DO 2 IT = 1, ITMAX

EPS = 0.

C group of reduction operations is created

C and initial values of reduction variables are stored

CDVM$ PARALLEL (J, I) ON A(I, J), SHADOW_START SA,

CDVM$*REDUCTION_GROUP ( REPS : MAX( EPS ))

C the loops iteration order is changed:

C at first boundary elements of A are calculated and sent,

C then internal elements of array A are calculated

DO 21 J = 2, K-1

DO 21 I = 2, K-1

EPS = MAX ( EPS, ABS( B( I, J) - A( I, J)))

A(I, J) = B(I, J)

21 CONTINUE

CDVM$ REDUCTION_START REPS

C start of reduction operation to accumulate the partial results

C calculated in copies of variable EPS on every processor

CDVM$ PARALLEL (J, I) ON B(I, J), SHADOW_WAIT SA

C the loops iteration order is changed:

C at first internal elements of B are calculated, then shadow edge elements

C of array A from neighboring processors are received,

C then boundary elements of array B are calculated

DO 22 J = 2, K-1

DO 22 I = 2, K-1

B(I, J) = (A( I-1, J ) + A( I, J-1 ) + A( I+1, J) + A( I, J+1 )) / 4

22 CONTINUE

CDVM$ REDUCTION_WAIT REPS

C waiting completion of reduction operation

PRINT *, 'IT = ', IT, ' EPS = ', EPS

IF ( EPS . LT . MAXEPS ) GO TO 3

2 CONTINUE

3 OPEN (3, FILE='JACOBI.DAT', FORM='FORMATTED')

WRITE (3,*) B

CLOSE (3)

END

Example 4. Successive over-relaxation

PROGRAM SOR

PARAMETER ( N = 100 )

REAL A( N, N ), EPS, MAXEPS, W

INTEGER ITMAX

CDVM$ DISTRIBUTE A ( BLOCK, BLOCK )

ITMAX=20

MAXEPS = 0.5E - 5

W = 0.5

*DVM$ PARALLEL ( I, J ) ON A( I, J )

DO 1 I = 1, N

DO 1 J = 1, N

IF ( I .EQ.J) THEN

A( I, J ) = N + 2

ELSE

A( I, J ) = -1.0

ENDIF

1 CONTINUE

DO 2 IT = 1, ITMAX

EPS = 0.

*DVM$ PARALLEL ( I, J) ON A( I, J), NEW (S),

*DVM$* REDUCTION ( MAX( EPS )), ACROSS (A(1:1,1:1))

C S variable – private variable

С (its usage is localized in one iteration range)

C EPS variable is used for maximum calculation

DO 21 I = 2, N-1

DO 21 J = 2, N-1

S = A( I, J )

A( I, J ) = (W / 4) * (A( I-1, J ) + A( I+1, J ) + A( I, J-1 ) +

* A( I, J+1 )) + ( 1-W ) * A( I, J)

EPS = MAX ( EPS, ABS( S - A( I, J )))

21 CONTINUE

PRINT *, 'IT = ', IT, ' EPS = ', EPS

IF (EPS .LT. MAXEPS ) GO TO 4

2 CONTINUE

4 PRINT *, A

END

Example 5. Red-black successive over-relaxation

PROGRAM REDBLACK

PARAMETER ( N = 100 )

REAL A( N, N ), EPS, MAXEPS, W

INTEGER ITMAX

*DVM$ DISTRIBUTE A ( BLOCK, BLOCK )

ITMAX=20

MAXEPS = 0.5E - 5

W = 0.5

*DVM$ PARALLEL ( I, J ) ON A( I, J )

DO 1 I = 1, N

DO 1 J = 1, N

IF ( I .EQ.J) THEN

A( I, J ) = N + 2

ELSE

A( I, J ) = -1.0

ENDIF

1 CONTINUE

DO 2 IT = 1, ITMAX

EPS = 0.

C loop for red and black variables

DO 3 IRB = 1,2

*DVM$ PARALLEL ( I, J) ON A( I, J), NEW (S),

*DVM$* REDUCTION ( MAX( EPS )), SHADOW_RENEW (A)

C variable S - private variable in loop iterations

C variable EPS is used for calculation of maximum value

C Exception : iteration space is not rectangular

DO 21 I = 2, N-1

DO 21 J = 2 + MOD ( I+ IRB, 2 ), N-1, 2

S = A( I, J )

A( I, J ) = (W / 4) * (A( I-1, J ) + A( I+1, J ) + A( I, J-1 ) +

* A( I, J+1 )) + ( 1-W ) * A( I, J)

EPS = MAX ( EPS, ABS( S - A( I, J )))

21 CONTINUE

3 CONTINUE

PRINT *, 'IT = ', IT, ' EPS = ', EPS

IF (EPS .LT. MAXEPS ) GO TO 4

2 CONTINUE

4 PRINT *, A

END

Example 6. Static tasks (parallel sections)

PROGRAM TASKS

rectangular grid is subdivided on two areas

C

C

PARAMETER (K=100, N1 = 50, ITMAX=10, N2 = K – N1 )

CDVM$ PROCESSORS P(NUMBER_OF_PROCESSORS( ))

REAL A1(N1+1,K), A2(N2+1,K), B1(N1+1,K), B2(N2+1,K)

INTEGER LP(2), HP(2)

CDVM$ TASK MB( 2 )

CDVM$ ALIGN B1( I, J ) WITH A1( I, J )

CDVM$ ALIGN B2( I, J ) WITH A2( I, J )

CDVM$ DISTRIBUTE :: A1, A2

CDVM$ REMOTE_GROUP BOUND

CALL DPT(LP, HP, 2)

C Task (area) distribution over processors

C Array distribution over tasks

CDVM$ MAP MB( 1 ) ONTO P( LP(1) : HP(1) )

CDVM$ REDISTRIBUTE A1( *, BLOCK ) ONTO MB( 1 )

CDVM$ MAP MB( 2 ) ONTO P( LP(2) : HP(2) )

CDVM$ REDISTRIBUTE A2( *, BLOCK ) ONTO MB( 2 )

C Initialization

CDVM$ PARALLEL ( J, I ) ON A1(I, J)

DO 10 J = 1, K

DO 10 I = 1, N1

IF(I.EQ.1 .OR. J.EQ.1 .OR. J.EQ.K) THEN

A1(I, J) = 0.

B1(I, J) = 0.

ELSE

B1(I, J) = 1. + I + J

A1(I, J) = B1(I, J)

ENDIF

10 CONTINUE

CDVM$ PARALLEL ( J, I ) ON A2(I, J)

DO 20 J = 1, K

DO 20 I = 2, N2+1

IF(I.EQ.N2+1 .OR. J.EQ.1 .OR. J.EQ.K) THEN

A2(I, J) = 0.

B2(I, J) = 0.

ELSE

B2(I, J) = 1. + ( I + N1 – 1 ) + J

A2(I, J) = B2(I, J)

ENDIF

20 CONTINUE

DO 2 IT = 1, ITMAX

CDVM$ PREFETCH BOUND

C exchange of edges

CDVM$ PARALLEL ( J ) ON A1(N1+1, J),

CDVM$*REMOTE_ACCESS (BOUND : B2( 2, J ) )

DO 30 J = 1, K

30 A1(N1+1, J) = B2(2, J)

CDVM$ PARALLEL ( J ) ON A2( 1, J),

CDVM$*REMOTE_ACCESS (BOUND : B1( N1, J ) )

DO 40 J = 1, K

40 A2(1, J) = B1(N1, J)

CDVM$ TASK_REGION MB

CDVM$ ON MB( 1 )

CDVM$ PARALLEL ( J, I ) ON B1(I, J),

CDVM$*SHADOW_RENEW ( A1 )

DO 50 J = 2, K-1

DO 50 I = 2, N1

50 B1(I, J) = (A1( I-1, J ) + A1( I, J-1 ) + A1( I+1, J) + A1( I, J+1 )) / 4

CDVM$ PARALLEL ( J, I ) ON A1(I, J)

DO 60 J = 2, K-1

DO 60 I = 2, N1

60 A1(I, J) = B1( I, J )

CDVM$ END ON

CDVM$ ON MB( 2 )

CDVM$ PARALLEL ( J, I ) ON B2(I, J),

CDVM$*SHADOW_RENEW ( A2 )

DO 70 J = 2, K-1

DO 70 I = 2, N2

70 B2(I, J) = (A2( I-1, J ) + A2( I, J-1 ) + A2( I+1, J) + A2( I, J+1 )) / 4

CDVM$ PARALLEL ( J, I ) ON A2(I, J)

DO 80 J = 2, K-1

DO 80 I = 2, N2

80 A2(I, J) = B2( I, J )

CDVM$ END ON

CDVM$ END TASK_REGION

2 CONTINUE

PRINT *, 'A1 '

PRINT *, A1

PRINT *, 'A2 '

PRINT *, A2

END

SUBROUTINE DPT( LP, HP, NT )

C processor distribution for NT tasks (NT = 2)

INTEGER LP(2), HP(2)

NUMBER_OF_PROCESSORS( ) = 1

NP = NUMBER_OF_PROCESSORS( )

NTP = NP/NT

IF(NP.EQ.1) THEN

LP(1) = 1

HP(1) = 1

LP(2) = 1

HP(2) = 1

ELSE

LP(1) = 1

HP(1) = NTP

LP(2) = NTP+1

HP(2) = NP

END IF

END

Example 7. Dynamic tasks (task loop)

PROGRAM MULTIBLOCK

С Model of multi-area task.

C Area amount, size of each area, external and internal edges

C are defined during program execution.

C Test of following DVM-constructions: dynamic arrays,

C dynamic tasks, asynchronous REMOTE_ACCESS for dynamic

C arrays (formal parameters)

*DVM$ PROCESSORS MBC100( NUMBER_OF_PROCESSORS( ) )

PARAMETER (M = 8, N =8, NTST = 1)

C MXSIZE – dynamic memory size

C MXBL – maximal number of areas

PARAMETER ( MXS=10000 )

PARAMETER ( MXBL=2 )

C HEAP – dynamic memory

REAL HEAP(MXS)

C PA,PB – arrays of pointers for dynamic arrays

C PA(I),PB(I) – function value on previous and current step in I-th area

*DVM$ REAL, POINTER ( :, : ) :: PA, PB, P1, P2

*DVM$ DYNAMIC PA, PB, P1, P2

INTEGER PA(MXBL), PB(MXBL), P1, P2

C SIZE( 1:2, I) – sizes of dimensions of I-th area

INTEGER SIZE( 2, MXBL ) , ALLOCATE

C TINB( :,I ) – table of internal edges of I-th area

C TINB( 1,I ) - - edge amount (from 1 till 4)

C TINB( 2,I ) = J - number of adjacent area

C TINB( 3,I ) TBOUND( 4,I ), - edges of one-dimensional section

C TINB( 5,I ) - dimension number in I-th area (1 or 2)

C TINB( 6,I ) - dimension coordinate in I-th area

C TINB( 7,I ) - dimension number in J-th area (1 or 2)

C TINB( 8,I ) - dimension coordinate in J-th area

INTEGER TINB( 29, MXBL )

C TEXB( :,I ) – table of external edges of I-th area

C TEXB( 1,I ) - (от 1 до 4) edges amount (from 1 to 4)

C TEXB( 2,I ) TBOUND( 3,I ), - coordinates of one-dimensional section of array

C for 1-th edge

C TEXB( 4,I ) - dimension number (1 or 2)

C TEXB( 5,I ) - coordinate of given dimension

INTEGER TEXB(17,MXBL)

C NBL - a number of blocks

C NTST – a number of steps

INTEGER NBL, NTST

C IDM – pointer to free dynamic memory

INTEGER IDM

COMMON IDM,MXSIZE

C по каждой области postponed distribution of arrays on each area

*DVM$ DISTRIBUTE :: PA, P1

*DVM$ ALIGN :: PB, P2

C task array

*DVM$ TASK TSA ( MXBL )

C name of group exchange of internal edges

*DVM$ REMOTE_GROUP GRINB

C LP( I ), HP( I ) – edges of processor array section of I-th area

INTEGER LP(MXBL), HP(MXBL)

C TGLOB( :, I ) – table of global coordinates in Jacobi algorithm grid

C for I-th area

C TGLOB( 1, I ) – 1-th dimension coordinate

C TGLOB( 2, I ) – 2-th dimension coordinate

INTEGER TGLOB(2,MXBL)

MXSIZE = MXS

C subdividing M*N area on sub-areas

CALL DISDOM(NBL,TGLOB,TEXB,TINB,SIZE,M,N,MXBL)

C Dividing processor array on areas

CALL MPROC(LP,HP,SIZE,NBL)

C Distribution of tasks (areas) over processors.

C Array distribution over tasks

IDM = 1

DO 10 IB = 1, NBL

*DVM$ MAP TSA( IB ) ONTO MBC100( LP(IB) : HP(IB) )

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