INDEPENDENT appears in the executable area of a program unit -- it must prefix a DO loop or FORALL statement or construct. In both case the directive asserts that no `iteration' affects any other iteration either directly or indirectly.
For DO-loops INDEPENDENT means the iterations or assignments can be performed in any order (or equivalently, in parallel):
!HPF$ INDEPENDENT DO i = 1,n x(i) = i**2 END DO
Applying an INDEPENDENT directive to FORALL means that there does not have to be a synchronisation point between calculating the RHS expression and beginning to assign to the LHS. In other words, the whole RHS does not have to be evaluated before assignment to the LHS can begin. This should speed up execution.
!HPF$ INDEPENDENT FORALL (i = 1:n) x(i) = i**2