Journal Article

FZJ-2026-02134

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Algorithm 1062: Code Generation for Piecewise Chebyshev Approximation

Wuttke, J. (Corresponding author)FZJ* ; Kleinsorge, A.

2026
ACM New York, NY

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Please use a persistent id in citations: doi:10.1145/3805698  doi:10.34734/FZJ-2026-02134

Abstract: A Lipschitz continuous function f that has a high-precision, albeit slow reference implementation can beevaluated more rapidly by piecewise polynomials, obtained by Chebyshev approximation. The partition intosubdomains should be made such that the computation of subdomain index and reduced function argument isfast and introduces no rounding errors. A rigorous analysis of truncation and rounding errors shows thatthe maximum relative error can be chosen arbitrarily close to 2ε, except around zeroes of f . Alignment ofcoefficients minimizes cache loading times. Code generation and target algorithms are implemented in theopen source project ppapp, maintained at https://jugit.fz-juelich.de/mlz/ppapp, with a snapshot archived inthe Collected Algorithms of the ACM. It has been successfully applied to three real-valued functions in theopen source complex error function library libcerf.

Keyword(s): Information and Communication (1st) ; Instrument and Method Development (1st) ; Instrument and Method Development (2nd) ; 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. No specific instrument

Appears in the scientific report 2026

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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