%0 Conference Paper
%A Wuttke, Joachim
%T How to compute a special function with near machine-precision accuracy
%M FZJ-2025-01961
%D 2025
%X 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.
%B 5th conference for Research Software Engineering in Germany
%C 25 Feb 2025 - 27 Feb 2025, Karlsruhe (Germany)
Y2 25 Feb 2025 - 27 Feb 2025
M2 Karlsruhe, Germany
%F PUB:(DE-HGF)6
%9 Conference Presentation
%U https://juser.fz-juelich.de/record/1040612