8.2.3 Global Forward Substitution

A global forward substitution pass finds relations between variables that do not necessarily depend on the loop index variables, such as the following one:

NP1 = N + 1
DO 10 I = 1,M
A(I,N) = A(I-1,NP1)
10    CONTINUE

Becomes:

NP1 = N + 1
DO 2 I=1,M
A(I,N) = A(I-1,N+1)
2   CONTINUE

Here, the relation between N and NP1 is known and the assumed data dependence relation is broken.