A simplified framework for reduction in strength

Reduction in strength is a traditional transformation for speeding up loop execution on sequential processors. The inverse transformation, induction variable substitution, can also speed up loops by decreasing register requirements, although it is typically a normalizing step in the detection of array dependences by parallelizing compilers. The author presents a simple framework for performing these transformations. In contrast to previous approaches to strength reduction, no unnecessary temporary variables or dead code fragments are introduced, only relevant intermediate language fragments are examined, iteration test replacement is not handled as a special case, and the execution time of the target code is never increased. The method is particularly easy to visualize, making it a useful teaching tool as well