"Tim Peters" <tim.peters at gmail.com> wrote: > > One low-effort approach is to use a general root-finding algorithm and > build ln(x) on top of exp() via (numerically) solving the equation > exp(ln(x)) == x for ln(x). ... Not a general one, please! At least use one that assumes the continuity of second derivatives :-) > However, the IBM spec requires < 1 ULP worst-case error, and that may > be unreasonably hard to meet with a root-finding approach. ... It's a doddle in a software implementation for civilised functions like log. All you do is to do the calculation in a sufficiently extended precision - and you can work that out in advance for very little extra effort. Then you round to the result - and, hey! Bob's your uncle! 0.501 ULPs is as easy as 1, if a bit slower. Now, doing that for the power function is a right royal pain in the neck, and you really DON'T want to even contemplate a generic gamma function, let alone one of the beta functions :-( But none of this is specific to a decimal base, of course. Regards, Nick Maclaren, University of Cambridge Computing Service, New Museums Site, Pembroke Street, Cambridge CB2 3QH, England. Email: nmm1 at cam.ac.uk Tel.: +44 1223 334761 Fax: +44 1223 334679
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