Genetic improvement of data for maths functions

Abstract

Genetic Improvement (GI) can be used to give better quality software and to create new functionality. We show that GI can evolve the PowerPC open source GNU C runtime library square root function into cube root, binary logarithm log2 and reciprocal square root. The GI cbrt is competitive in run-time performance and our inverted square root x-1/2 is far more accurate than the approximation used in the Quake video game. We use CMA-ES to adapt constants in a Newton-Raphson table, originally from glibc's sqrt, for other double precision mathematics functions. Such automatically customised math libraries might be used for mobile or low resource, IoT, mote, smart dust, bespoke cyber-physical systems. Evolutionary Computing (EC) can be used to not only adapt source code but also data, such as numerical constants, and could enable a new way to conduct software data maintenance. This is an exciting opportunity for the GECCO and optimisation communities.