Superlinear Speedup by Program Transformation ( Extended Abstract ) Neil

There seems to be, at least in practice, a fundamental conflict within program transformations. One way: hand transformations can yield dramatic speedups, but seem to require human insight. They are thus are only suited to small programs and have not been successfully automated. On the other hand, there exist a number of well-known automatic program transformations; but these have been proven to give at most linear speedups. This work in progress addresses this apparent conflict, and concerns the principles and practice of superlinear program speedup. A disclaimer: we work in a simple sequential program context: no caches, parallelism, etc. Many interesting program transformations (by Burstall-Darlington, Bird, Pettorossi, and many others) have been published that give superlinear program speedups on some program examples. However, these techniques all seem to require a " Eureka step " where the transformer understands some essential property relevant to the problem being solved (e.g., associativity, commutativity, occurrence of repeated subproblems, etc.). Such transformations have proven to be very difficult to automate. On the other hand a number of fully automatic transformers exist , including: classical compiler optimisations, deforestation, partial evaluation and positive supercompilation. However these can be seen (and have been formally proven, e.g., by Jones for partial evaluation, and by Sørensen for positive supercompilation) only to yield linear time improvements. For example, a limit in automatic string pattern matching was for several years to achieve the speedup of the Knuth-Morris-Pratt algorithm. The KMP speedup is still linear though, although its