RE: [boost] Re: Floating Point comparisons

From: Paul A. Bristow (boost_at_[hidden])
Date: 2001-12-14 05:02:19

I have tried to read up reference 3 on the Boost Test Library: Floating
Point Comparison.

Knuth, D E, Vol III,

in the hope that the jacket puff by Jonanthan Laventhol

"It's always a pleasure when a problem is hard enough that you have to get
the Knuths of the shelf.  I find that merely opening one has a very useful
terrorising effect on computers."

would work,

but did not find anything in the index that looked relevant - only the Quote

"If you don't find it in the index look very carefully through the entire
catalogue" - Consumers Guide, Sears, Roebuck & Co (1897)"

Can you or Gennadiy give a more detailed reference please!

Paul

> -----Original Message-----
> From: Fernando Cacciola [mailto:fcacciola_at_[hidden]]
> Sent: Wednesday, December 12, 2001 11:37 PM
> To: boost_at_[hidden]
> Subject: RE: [boost] Re: Floating Point comparisons
>
>
>
> ----- 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,
>
>
>
>
>
> Info: http://www.boost.org  Send unsubscribe requests to:
> <mailto:boost-unsubscribe_at_[hidden]>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>
>