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Operator strength reduction is a technique that improves compiler-generated code by reformulating certain costly computations in terms of less expensive ones. A common case arises in array addressing expressions used in loops. The compiler can replace the sequence of multiplies generated by a direct translation of the address expression with an equivalent sequence of additions. When combined with linear function test replacement, strength reduction can speed up the execution of loops containing array references. The improvement comes from two sources: a reduction in the number of operations needed to implement the loop and the use of less costly operations. This paper presents a new algorithm for operator strength reduction, called OSR. OSR improves upon an earlier algorithm of Allen, Cocke, and Kennedy [Allen et al. 1981]. OSR operates on the static single assignment (SSA) form of a procedure [Cytron et al. 1991]. By taking advantage of the properties of SSA form, we have derived an algorithm that is simple to understand, quick to implement, and, in practice, fast to run. Its asymptotic complexity is, in the worst case, the same as the Allen, Cocke, and Kennedy algorithm (ACK). OSR achieves optimization results that are equivalent to those obtained with the ACK algorithm. OSR has been implemented in several research and production compilers. Categories and Subject Descriptors: D.3.4 [Programming Languages]: Processors--Compilers, Optimization General Terms: Algorithms, Languages Additional Key Words and Phrases: loops, strength reduction, static single assignment form