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DISTRIBUTE and REDISTRIBUTE Directives

The DISTRIBUTE directive specifies a mapping of data objects to abstract processors in a processor arrangement. For example, REAL SALAMI(10000) !HPF DISTRIBUTE WEISSWURST(BLOCK(256)) This specifies that groups of exactly 256 elements should be mapped to successive abstract processors. (There must be at least abstract processors if the directive is to be satisfied. The fortieth processor will contain a partial block of only 16 elements, namely WEISSWURST(9985:10000).)

HPF also provides a cyclic distribution format: REAL DECK_OF_CARDS(52) !HPF DISTRIBUTE CHESS_BOARD(BLOCK, BLOCK) !HPF DISTRIBUTE dist-attribute-stuff :: distributee-list is covered by syntax rule for a combined-directive.

Examples: !HPF DISTRIBUTE (BLOCK,*,BLOCK) ONTO SQUARE:: D2,D3,D4 The meanings of the alternatives for dist-format are given below.

Define the ceiling division function CD(J,K) = (J+K-1)/K (using Fortran integer arithmetic with truncation toward zero.)

Define the ceiling remainder function CR(J,K) = J-K*CD(J,K).

The dimensions of a processor arrangement appearing as a dist-target are said to correspond in left-to-right order with those dimensions of a distributee for which the corresponding dist-format is not *. In the example above, processor arrangement SQUARE must be two-dimensional; its first dimension corresponds to the first dimensions of D2, D3, and D4 and its second dimension corresponds to the third dimensions of D2, D3, and D4.

Let be the size of a distributee in a certain dimension and let be the size of the processor arrangement in the corresponding dimension. For simplicity, assume all dimensions have a lower bound of 1. Then BLOCK() means that a distributee position whose index along that dimension is is mapped to an abstract processor whose index along the corresponding dimension of the processor arrangement is CD(,) (note that must be true), and is position number +CR(,) among positions mapped to that abstract processor. The first distributee position in abstract processor along that axis is position number 1+*(-1).

BLOCK by definition means the same as BLOCK(CD(,)).

CYCLIC() means that a distributee position whose index along that dimension is is mapped to an abstract processor whose index along the corresponding dimension of the processor arrangement is 1+MODULO(CD(,)-1,). The first distributee position in abstract processor along that axis is position number 1+*(-1).

CYCLIC by definition means the same as CYCLIC(1).

CYCLIC() and BLOCK() imply the same distribution when , but BLOCK() additionally asserts that the distribution will not wrap around in a cyclic manner, which a compiler cannot determine at compile time if is not constant. Note that CYCLIC and BLOCK (without argument expressions) do not imply the same distribution unless , a degenerate case in which the block size is 1 and the distribution does not wrap around.

Suppose that we have 16 abstract processors and an array of length 100: !HPF DISTRIBUTE CENTURY(BLOCK) ONTO SEDECIM results in this mapping of array elements onto abstract processors:

Distributing the array BLOCK(8): !HPF DISTRIBUTE CENTURY(CYCLIC) ONTO SEDECIM results in this mapping of array elements onto abstract processors:

Distributing the array CYCLIC(3): !HPF DISTRIBUTE distributee ( dist-format-list ) ONTO dist-target is equivalent to _=13_}

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