Unified Tables for Exponential and Logarithm Families

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....

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Bibliographic Details
Published in:ACM transactions on mathematical software 2010-09, Vol.37 (3)
Main Authors: Anand, Christopher Kumar, Sharma, Anuroop
Format: Article
Language:English
Subjects:
Architecture
Computer programs
Logarithms
Mathematical analysis
Performance enhancement
Software
Tables
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Summary: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.
ISSN:0098-3500
DOI:10.1145/1141885.1141890