5538

Unified Tables for Exponential and Logarithm Families

Christopher Kumar Anand, Anuroop Sharma
McMaster University
ACM Transactions on Mathematical Software (TOMS), Volume 37 Issue 3, September 2010

@article{anand2010unified,

   title={Unified tables for exponential and logarithm families},

   author={Anand, C.K. and Sharma, A.},

   journal={ACM Transactions on Mathematical Software (TOMS)},

   volume={37},

   number={3},

   pages={1–23},

   year={2010},

   publisher={ACM}

}

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Accurate table methods allow for very accurate and efficient evaluation of elementary functions. We present new single-table approaches to logarithm and exponential evaluation, by which we mean that a single table of values works for both log(x) and log(1+x), and a single table for ex and ex-1. This approach eliminates special cases normally required to evaluate log(1+x) and ex-1 accurately near zero, which will significantly improve performance on architectures which use SIMD parallelism, or on which data-dependent branching is expensive. We have implemented it on the Cell/B.E. SPU (SIMD compute engine) and found the resulting functions to be up to twice as fast as the conventional implementations distributed in the IBM Mathematical Acceleration Subsystem (MASS). We include the literate code used to generate all the variants of exponential and log functions in the article, and discuss relevant language and hardware features.
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