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@INPROCEEDINGS{Wuttke:1040612,
      author       = {Wuttke, Joachim},
      title        = {{H}ow to compute a special function with near
                      machine-precision accuracy},
      reportid     = {FZJ-2025-01961},
      year         = {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.},
      month         = {Feb},
      date          = {2025-02-25},
      organization  = {5th conference for Research Software
                       Engineering in Germany, Karlsruhe
                       (Germany), 25 Feb 2025 - 27 Feb 2025},
      subtyp        = {Other},
      cin          = {JCNS-4 / JCNS-FRM-II / MLZ},
      cid          = {I:(DE-Juel1)JCNS-4-20201012 /
                      I:(DE-Juel1)JCNS-FRM-II-20110218 / I:(DE-588b)4597118-3},
      pnm          = {6G4 - Jülich Centre for Neutron Research (JCNS) (FZJ)
                      (POF4-6G4) / 632 - Materials – Quantum, Complex and
                      Functional Materials (POF4-632)},
      pid          = {G:(DE-HGF)POF4-6G4 / G:(DE-HGF)POF4-632},
      experiment   = {EXP:(DE-MLZ)SCG-20150203},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/1040612},
}