Re: math function accuracy -- was Re: text2interval again /
On 2013-03-12 02:41:18 +0100, Siegfried M. Rump wrote:
> The trick described in
>
> M. Payne and R. Hanek: Radian Reduction for Trigonometric Function, SIGNUM Neweleter, 18:19-24, 1983
>
> can be used (apparently, I rediscovered and used it in
>
> S.M. Rump. Rigorous and portable standard functions. BIT Numerical Mathematics, 41(3):540–562, 2001.
>
> which you can download from my homepage). It uses the limited exponent
> range, and only a computation with few extra digits is necessary, even
> for huge arguments like sin(2^1000). The method is implemented in
> INTLAB with rigorous error bounds.
That's OK when the exponent range is limited enough, but not for
the exponent ranges used in multiple precision with MPFR (31-bit
exponent by default, possible 63-bit exponent on 64-bit machines),
for instance.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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