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Example 6.10. Using named group of regular remote references.

REAL A1(M,N1+1), A2(M1+1,N2+1), A3(M2+1,N2+1)

CDVM$ DISTRIBUTE (BLOCK,BLOCK) :: A1, A2, A3

CDVM$ REMOTE_GROUP RS

DO 1 ITER = 1, MIT

. . .

C edge exchange along division line D

CDVM$ PREFETCH RS

. . .

CDVM$ PARALLEL ( I ) ON A1(I,N1+1), REMOTE_ACCESS (RS: A2(I,2))

DO 10 I = 1, M1

10 A1(I,N1+1) = A2(I,2)

CDVM$ PARALLEL ( I ) ON A1(I,N1+1), REMOTE_ACCESS (RS: A3(I-M1,2))

DO 20 I = M1+1, M

20 A1(I,N1+1) = A3(I-M1,2)

CDVM$ PARALLEL ( I ) ON A2(I,1), REMOTE_ACCESS (RS: A1(I,N1))

DO 30 I = 1, M1

30 A2(I,1) = A1(I,N1)

CDVM$ PARALLEL ( I ) ON A3(I,1), REMOTE_ACCESS (RS: A1(I+M1,N1))

DO 40 I = 1, M2

40 A3(I,1) = A1(I+M1,N1)

. . .

IF (NOBLN) THEN

C redistribution of arrays to balance loading

. . .

CDVM$ RESET RS

END IF

. . .

1 CONTINUE

6.3.4Asynchronous copying by REMOTE type references

If parallel loop contains only assignment statement without computations, the access by REMOTE type references can be performed more effectively using asynchronous copying of distributed arrays.

6.3.4.1Loop and copy-statements

Consider following loop

DO 10 I₁ = L₁,H₁,S₁

. . .

DO 10 I_n = L_n,H_n,S_n

10 A(f₁,…,f_k) = B (g₁,…,g_m)

where A, B - identifiers of different distributed arrays.

L_i, H_i, S_i – the loop invariants

f_i = a_i *I_i + b_i

g_j = c_j *I_j + d_j

a_i, b_i , c_j, d_j – integer expressions, the loop invariants (the expressions, which values are not updated during the loop execution).

Every loop variable I_l can be used at most in one expression f_i and at most in one expression g_j.

The loop can contain several statements satisfying the restrictions above. Such loop will be called copy-loop.

Copy-loop can be described by one or several copy-statements of the form

A(₁,…,_k) = B(₁,…,_m)

where

_i = l_i : h_i : s_i

_j = l_j : h_j : s_j

_i, _j are triplets of Fortran 90.

Copy-statement is similar to array section assignment statement in Fortran 90.

The rules of compact notation exist for triplets. Define these rules for triplet _i for example.

1. If the whole dimension of array take part in coping, then

_i = :

1. If s_i = 1, then

_i = l_i : h_i

1. If L_i = h_i, then

_i = l_i

For copy-loop 10 triplet expressions are defined in the following way

For i	For j
li = ai *Li + bi	lj = cj *Lj + dj
hi = ai *Hi + bi	hj = cj *Hj + dj
si = ai *Si	sj = cj *Sj

Consider the following copy-loop

REAL A(N1,N2,N3), B(N1,N3)

DO 10 I1 = 1, N1

DO 10 I2 = 2, N3-1

10 A(I1, 5, I2+1) = B(I1, I2-1)

Following copy-statement corresponds to this loop

A( :, 5, 3:N3 ) = B( :, 1:N3-2 )

6.3.4.2Asynchronous coping directives

Asynchronous coping allows to overlap data passing between processors with execution of other statements.

Asynchronous coping is specified by combination of start coping directive (ASYNCHRONOUS ID) and the directive of waiting for coping completion (ASYNCWAIT ID). The correspondence of directives is defined by the same identifier ID.

6.3.4.2.1ASYNCID directive

ASYNCID directive describes individual identifier for every pair of asynchronous copying directives.

The directive syntax:

6.3.4.2.2F90 directive

F90 directive is prefix for every copy-statement.

Syntax.

6.3.4.2.3ASYNCHRONOUS and END ASYNCHRONOUS directives

ASYNCHRONOUS and END ASYNCHRONOUS directives specify block construction.

Syntax.

All assignment statements in copy-loops should be described by F90 directives with corresponding copy-statement.

6.3.4.2.4ASYNCWAIT directive

Syntax.

The example from section 6.3.4.1 can be specified as asynchronous coping in the following way.

CDVM$ ASYNCID TR

REAL A(N1,N2,N3), B(N1,N3)

. . .

CDVM$ ASYNCHRONOUS TR

CDVM$ F90 A( :, 5, 3:N3 ) = B( :, 1:N3-2 )

DO 10 I1 = 1, N1

DO 10 I2 = 2, N3-1

10 A(I1,5,I2+1) = B(I1,I2-1)

CDVM$ END ASYNCHRONOUS

. . .

sequence of statements,

that are performed against a background of data passing

. . .

CDVM$ ASYNCWAIT TR

6.4REDUCTION type references

6.4.1Synchronous specification of REDUCTION type references

If there is no group name in REDUCTION specification of parallel loop, it is synchronous specification and executed in the following way.

1. Local reduction calculation. During the loop execution on each processor local value of reduction is calculated for the part of data, allocated at the processor.

2. Global reduction calculation. After the loop completion inter-processor reduction of local values is automatically calculated. Resulted value is assigned to the reduction variable on each processor.

6.4.2Asynchronous specification of REDUCTION type references

Asynchronous specification allows:

• to joint in one group the reduction variables, calculated in different loops;

• overlap global group reduction execution with other computations.

For asynchronous specification besides REDUCTION directive (with the group name) the following additional directives are required.

Typical sequence of asynchronous specifications of REDUCTION type is the following.

CDVM$ REDUCTION_GROUP RD

. . .

CDVM$ PARALLEL . . . , REDUCTION (RD : d₁)

C local reduction d₁

. . .

CDVM$ PARALLEL . . . , REDUCTION (RD : d_n)

C local reduction d_n

. . .

CDVM$ REDUCTION_START RD

C beginning of global reduction d_i  ... d_n

. . .

CDVM$ REDUCTION_WAIT RD

C end of global reduction d_i  ... d_n

Constraints:

• Before executing REDUCTION_START directive, the reduction variables of the group may be used in reduction statements of parallel loops only.

• REDUCTION_START and REDUCTION_WAIT directives must be executed after the completion of the loop (loops) where the local values of the reduction variables were calculated. The only statements allowed between these directives are those that don't use the reduction variable values.

• REDUCTION_WAIT directive deletes the reduction group.

Example 6.11. Asynchronous specification of REDUCTION type references.

CDVM$ DISTRIBUTE A (BLOCK)

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

CDVM$ REDUCTION_GROUP RD

. . .

S = 0.

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

CDVM$* REDUCTION (RD : SUM(S))

DO 10 I = 1, N

10 S = S + A(I)

X = 0.

CDVM$ PARALLEL ( I ) ON B( I ),

CDVM$* REDUCTION (RD : MAX(X))

DO 20 I = 1, N

20 X = MAX(X, ABS(B(I)))

CDVM$ REDUCTION_START RD

C beginning of global reduction SUM(S) and MAX(X)

CDVM$ PARALLEL ( I ) ON A( I )

DO 30 I = 1, N

30 A(I) = A(I) + B(I)

CDVM$ REDUCTION_WAIT RD

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