[Bug math/14469] Inaccurate j0f function
joseph at codesourcery dot com
sourceware-bugzilla@sourceware.org
Mon Feb 3 14:57:00 GMT 2020
https://sourceware.org/bugzilla/show_bug.cgi?id=14469
--- Comment #6 from joseph at codesourcery dot com <joseph at codesourcery dot com> ---
To fix the large errors properly, all of the j0 / j1 / y0 / y1 functions
probably need to be reimplemented along the lines described in
<http://www.cl.cam.ac.uk/~jrh13/papers/bessel.ps.gz> - expansions around
each zero of the functions for small arguments, expansions based on phase
and magnitude or similar functions for larger arguments (plus range
reduction for phase) where the phase is either rigorously / exhaustively
shown to be accurate enough (for float) or is heuristically accurate
enough (for other floating-point formats, if exhaustive checks around the
zeroes, until the phase approximation gets simple enough to use results on
rational approximation of pi, are infeasible).
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