Re: math function accuracy -- was Re: text2interval again /
Am 11.03.2013, 21:42 Uhr, schrieb Richard Fateman <fateman@xxxxxxxxxxxxxxxxx>:
The current problem is for sin(x) where x is a float_with_huge-exponent.
This may cause problems because any value for sin(x) first
requires a value for pi good to a huge number of places..
so as to reduce x modulo pi/2 or pi/4 to < 1 ULP.
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.
Best wishes,
Siegfried M. Rump
--
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
Schwarzenbergstr. 95
21071 Hamburg
Germany
phone +49 40 42878 3027
fax +49 40 42878 2489
http://www.ti3.tuhh.de
and
Visiting Professor at Waseda University
Faculty of Science and Engineering
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Tokyo 169-8555
Japan
phone/fax in Japan +81 3 5286 3330