Runtime Repeated Recursion Unfolding: A Just-In-Time Online Program Optimization That Can Achieve Super-Linear Speedup
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We introduce a just-in-time runtime program transformation based on repeated recursion unfolding. Our online polyvariant program specialization generates several versions of a recursion differentiated by the minimal number of recursive steps covered. The base case of the recursion is ignored in our technique. Our method is presented here on the basis of linear direct recursive rules. When a recursive call is encountered at runtime, first an unfolder creates specializations of the associated recursive rule on-the-fly and then an interpreter applies these rules to the call. Our approach reduces the number of recursive rule applications to its logarithm at the expense of introducing a logarithmic number of unfolded rules. Each rule is applied at most once. We prove correctness of our technique and determine its worst-case time complexity. For recursions that solve tractable problems and which have enough unfoldings that can sufficiently simplified, we prove a super-linear speedup theorem, i.e. speedup by more than a constant factor. The simplification is problem-specific and has to be provided at compile-time. In the best case, the complexity of the given recursion is reduced to that of its first recursive step. We have implemented the necessary unfolder and meta-interpreter for runtime repeated recursion unfolding in Constraint Handling Rules (CHR) with just five rules. We illustrate the feasibility of our approach with complexity results and benchmarks for several classical algorithms. The runtime improvement quickly reaches several orders of magnitude.
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