Table-driven implementation of the logarithm function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
An accurate elementary mathematical library for the IEEE floating point standard
ACM Transactions on Mathematical Software (TOMS)
Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Table-driven implementation of the exponential function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Computing Elementary Functions: A New Approach for Achieving High Accuracy and Good Performance
Proceedings of the Symposium on Accurate Scientific Computations
CASCON '99 Proceedings of the 1999 conference of the Centre for Advanced Studies on Collaborative research
New Algorithms for Improved Transcendental Functions on IA-64
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Computing machine-efficient polynomial approximations
ACM Transactions on Mathematical Software (TOMS)
Elementary Functions: Algorithms and Implementation
Elementary Functions: Algorithms and Implementation
An Optimized Cell BE Special Function Library Generated by Coconut
IEEE Transactions on Computers
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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.