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Re: [Gcl-devel] [Maxima] Stable Maxima version on Gentoo

From: Camm Maguire
Subject: Re: [Gcl-devel] [Maxima] Stable Maxima version on Gentoo
Date: Fri, 05 Oct 2012 12:48:49 -0400
User-agent: Gnus/5.13 (Gnus v5.13) Emacs/23.2 (gnu/linux)


"Stewart W. Wilson" <address@hidden> writes:

> The fix does not seem to be exactly trivial.  Please see the attached
> paper by Steele and White from 1990.

Thanks so much for this reference!

Unfortunately, using up to forty 32bit words in bignum arithmetic to
print out floats looks prohibitively expensive, although the algorithm
does appear to work nicely, at least when coded in lisp.  

GCL uses strtod for conversion, and I've whipped up a quick
implementation which recursively truncates digits until this routine
delivers a different result.  See below.

It does appear to me however that there is nothing which will
comprehensively "do the right thing", in as much as the error between
the internal and the printed representations might always accumulate to
result in an incorrect rounding on output.  This is conceptually
different from your original query regarding simply the printed format
of floats, but I mention it as you gave an example using a sum of two
long-floats.  See the short float analog and question below.

Take care,




>(* 0.5 most-positive-long-float)


>(+ 1.234 2.567)









>>> I want to use GCL instead of paying for Allegro.
>>> But GCL often prints numbers with too many places.
>>> Example
>>>>(+ 1.234 2.567)
>>> 3.8010000000000002

Am I correct in the guess that Allegro cannot give 3.801s0 for
(+ 1.234s0 2.567s0), but rather (+ 1.234s0 2.567s0)?

Camm Maguire                                        address@hidden
"The earth is but one country, and mankind its citizens."  --  Baha'u'llah

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