4.2.5 FORALL Statement and Construct

The FORALL statement and construct is a generalization of the Fortran 95/90 masked array assignment (WHERE statement and construct). It allows more general array shapes to be assigned, especially in construct form.

FORALL is a feature of Fortran 95. It takes the following form:

FORALL (triplet-spec [, triplet-spec]...[, mask-expr]) assign-stmt

The FORALL construct takes the following form:

[name:] FORALL (triplet-spec [, triplet-spec]...[, mask-expr])

Is a triplet specification with the following form:

subscript-name = subscript-1 : subscript-2 [:stride]

The subscript-name must be a scalar of type integer. It is valid only within the scope of the FORALL; its value is undefined on completion of the FORALL.

The subscripts and stride cannot contain a reference to any subscript-name in triplet-spec.

The stride cannot be zero. If it is omitted, the default value is 1.

Evaluation of an expression in a triplet specification must not affect the result of evaluating any other expression in another triplet specification.

Is a logical array expression (called the mask expression). If it is omitted, the value .TRUE. is assumed. The mask expression can reference the subscript name in triplet-spec.

Is an assignment statement or a pointer assignment statement. The variable being assigned to must be an array element or array section and must reference all subscript names included in all triplet-specs.

Is the name of the FORALL construct.

Is one of the following:

Rules and Behavior

If a construct name is specified in the FORALL statement, the same name must appear in the corresponding END FORALL statement.

A FORALL statement is executed by first evaluating all bounds and stride expressions in the triplet specifications, giving a set of values for each subscript name. The FORALL assignment statement is executed for all combinations of subscript name values for which the mask expression is true.

The FORALL assignment statement is executed as if all expressions (on both sides of the assignment) are completely evaluated before any part of the left side is changed. Valid values are assigned to corresponding elements of the array being assigned to. No element of an array can be assigned a value more than once.

A FORALL construct is executed as if it were multiple FORALL statements, with the same triplet specifications and mask expressions. Each statement in the FORALL body is executed completely before execution begins on the next FORALL body statement.

Any procedure referenced in the mask expression or FORALL assignment statement must be pure.

Pure functions can be used in the mask expression or called directly in a FORALL statement. Pure subroutines cannot be called directly in a FORALL statement, but can be called from other pure procedures.


Consider the following:

FORALL(I = 1:N, J = 1:N, A(I, J) .NE. 0.0) B(I, J) = 1.0 / A(I, J)

This statement takes the reciprocal of each nonzero element of array A(1:N, 1:N) and assigns it to the corresponding element of array B. Elements of A that are zero do not have their reciprocal taken, and no assignments are made to corresponding elements of B.

Every array assignment statement and WHERE statement can be written as a FORALL statement, but some FORALL statements cannot be written using just array syntax. For example, the preceding FORALL statement is equivalent to the following:

WHERE(A /= 0.0) B = 1.0 / A

It is also equivalent to:

FORALL (I = 1:N, J = 1:N)
  WHERE(A(I, J) .NE. 0.0) B(I, J) = 1.0/A(I, J)

However, the following FORALL example cannot be written using just array syntax:

FORALL(I = 1:N, J = 1:N) H(I, J) = 1.0/REAL(I + J - 1)

This statement sets array element H(I, J) to the value 1.0 /REAL(I + J - 1) for values of I and J between 1 and N.

Consider the following:



This FORALL statement causes elements 1 through 8 of array PATTERN to point to elements 3, 4, 1, 2, 7, 8, 5, and 6, respectively, of OBJECT. IEOR can be referenced here because it is pure.

The following example shows a FORALL construct:

FORALL(I = 3:N + 1, J = 3:N + 1)
  C(I, J) = C(I, J + 2) + C(I, J - 2) + C(I + 2, J) + C(I - 2, J)
  D(I, J) = C(I, J)

The assignment to array D uses the values of C computed in the first statement in the construct, not the values before the construct began execution.

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