From Recursion to Iteration: What are the Optimizations?

Abstract

Transforming recursion into iteration eliminates the use of stack frames during program execution. It has been studied extensively. This paper describes a general and powerful method, based on incrementalization, for transforming general recursion into iteration: identify an input increment, derive an incremental version under the input increment, and form an iterative computation using the incremental version. Exploiting incrementalization yields iterative computation in a uniform way and also allows additional optimizations to be explored cleanly and applied systematically, in most cases yielding iterative programs that use constant additional space, reducing additional space usage asymptotically. We summarize major optimizations, complexity improvements, and performance measurements. Our analyses and measurements show that some previously considered ``optimizations'' can actually result in slower programs.