Loop Quantization: an Analysis and Algorithm

Loop unwinding is a well-known technique for reducing loop overhead, exposing parallelism, and increasing the efficiency of pipelining. Traditional loop unwinding is limited to the innermost loop of a set of nested loops and the amount of unwinding is either fixed or must be specified by the user. In this paper we present a general technique, loop quantization, for unwinding multiple nested loops, explain its advantages over other transformations, and illustrate its practical effectiveness. An abstraction of nested loops is presented which leads to results about the complexity of computing quantizations and an algorithm.