[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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