Lightning Talk: A Compiler Optimization and the 2-Adic Numbers
summary
Shows a concrete algorithm that computes reciprocals via a Newton half-iteration that contains no division, implements two concrete code paths (double for 1/3 and unsigned integers for -3) and measures that each iteration doubles the number of correct bits. Demonstrates that the integer version exhibits 2-adic convergence — a variable becomes divisible by larger powers of two — explains why compilers replace division with a precomputed “magic” multiplier in pointer arithmetic, and shows both implementations work but converge in different number systems.
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