Conference Presentation (Other)

FZJ-2025-01961

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png How to compute a special function with near machine-precision accuracy

Wuttke, J.FZJ*

2025

Abstract: Based on my experience as developer and maintainer of some numerical open-source libraries (libcerf, libkww, libformfactor), I will explain key concepts for writing code that computes a special function or integral with high accuracy and high speed.- Choose different numerical algorithms for different argument regions.- Don't be afraid of divergent series or ill-conditioned recursions. - Confine Chebyshev fits to small subregions. - Use code instrumentation and bisection to ensure continuity where the algorithm changes. - Beware of literature that is only concerned with truncation. Near machine precision, cancellation is the bigger problem. Visualization may reveal the difference. - Never rely on non-standard facilities. "Long double" makes no sense if it is not longer than "double"? Tell Apple. - Generate test references and hard-coded coefficients with high-precision scripts (e.g. mpmath based). - Be graceful with relative accuracy measures near zeros and for real or imaginary parts of complex numbers.- Don't trust any performance measure you haven't tweaked yourself. Take caching into account.

Keyword(s): Information and Communication (1st) ; Others (2nd)

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Contributing Institute(s):

1. JCNS-4 (JCNS-4)
2. JCNS-FRM-II (JCNS-FRM-II)
3. Heinz Maier-Leibnitz Zentrum (MLZ)

Research Program(s):

1. 6G4 - Jülich Centre for Neutron Research (JCNS) (FZJ) (POF4-6G4) (POF4-6G4)
2. 632 - Materials – Quantum, Complex and Functional Materials (POF4-632) (POF4-632)

Experiment(s):

1. SCG: Scientific Computing Group

Appears in the scientific report 2025

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