Choosing Mathematical Function Implementations for Speed and Accuracy
summary
A tool named optuner selects among 45 cosine and 49 sine implementations (about 4.8 million configurations) by building a linear error model from Taylor expansions, a simple additive cost model, and encoding a multiobjective ILP solved with Z3 to extract the Pareto frontier. Evaluation uses 36 FPBench-derived kernels (avg run 5 minutes, worst 30) and a ray tracer case where glibc costs 27 ns per photon, a table lookup 12.7 ns, and the chosen configuration runs 10.85 ns while producing bit-for-bit equal images to glibc.
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chapters (8)
- 0:00Start
- 3:33POV-Ray hand rolled code
- 6:13OpTuner Input
- 6:53Modeling Error and Speed
- 9:37Error Taylor Series
- 10:06Linear Cost Model
- 13:37Benchmark Results
- 14:33What about ray tracing?
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