RE: [boost] Re: Floating Point comparisons

From: Fernando Cacciola (fcacciola_at_[hidden])
Date: 2001-12-12 18:36:31

----- Original Message -----
From: Paul A. Bristow <boost_at_[hidden]>
To: <boost_at_[hidden]>
Sent: Wednesday, December 12, 2001 8:26 PM
Subject: RE: [boost] Re: Floating Point comparisons

> You might also find helpful
>
> 3. D. Priest, On properties of floating point arithmetics: numerical
> stability
> and the cost of accurate computations. Ph.D. Diss, Berkeley 1992.
> and more references in http: www.cs.wisc.edu/~shoup/ntl/quad_float.txt.
>
> 15. ftp://ftp.ccs.neu.edu/pub/people/will/howtoread.ps
> William D Clinger,  In Proceedings of the 1990 ACM Conference on
Principles
> of Programming Languages, pages 92-101.
> How to read Floating-point accurately.
> Abstract: Consider the problem of converting decimal scientific notation
for
> a number into the best binary floating-point approximation to that number,
> for some fixed precision. This problem cannot be solved using arithmetic
of
> any fixed precision. Hence the IEEE Standard for Binary Floating-Point
> Arithmetic does not require the result of such a conversion to be the best
> approximation.
> This paper presents an efficient algorithm that always finds the best
> approximation. The algorithm uses a few extra bits of precision to compute
> an IEEE-conforming approximation while testing an intermediate result to
> determine whether the approximation could be other than the best. If the
> approximation might not be the best, then the best approximation is
> determined by a few simple operations on multiple-precision integers,
where
> the precision is determined by the input. When using 64 bits of precision
to
> compute IEEE double precision results, the algorithm avoids
higher-precision
> arithmetic over 99% of the time.
>
> 17. Cephes Mathematical Library, Stephen L. B. Moshier,
> www.netlib.org/cephes/ and
> http://people.ne.mediaone.net/moshier/index.html - in C. A perl interface
> and a DOS calculator also available.
> Methods and Programs for Mathematical Functions, Stephen L. B. Moshier, J
> Wiley, (1989) ISBN 0 7458-0289-3 & 0-470-21609 3 & 0 7458 0805 0.
>
>
> Paul
>
> Dr Paul A Bristow, hetp Chromatography
> Prizet Farmhouse
> Kendal, Cumbria
> LA8 8AB      UK
> [phone]
> Mobile [phone]
> mailto:pbristow_at_[hidden]
>
>
Thanks,

BTW: I just found Prof. William Kahan's home page (he's considered the
father of IEEE754):

http://http.cs.berkeley.edu/~wkahan/

Fernando,