7.3.2 Global Forward Substitution

A global forward substitution pass finds relations between variables that do not necessarily depend on the loop index variables, such as n and np1 , as shown in the following example:

np1 = n + 1;
   for ( i=0; i<m; i++ ) {
   a[i][n] = a[i-1][np1];
   }

Becomes:

    for ( i = 0; i<m; i++ ) {
     a[i][n] = a[i-1][n+1];
    }

Here, the relation between n and np1 is known and the assumed data dependence can be broken.