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Re: [Help-gsl] acosh, getting consistent results from GSL and Guile

From: Brian Gough
Subject: Re: [Help-gsl] acosh, getting consistent results from GSL and Guile
Date: Mon, 14 Aug 2006 11:32:12 +0100
User-agent: Wanderlust/2.14.0 (Africa) Emacs/21.3 Mule/5.0 (SAKAKI)

At Sat, 12 Aug 2006 08:37:12 +0200,
Marco Maggi wrote:
>   for  some values of  the operand  I get  different results
> from  'acosh' when  using  GSL (1.8),  Guile  (1.8) and  GNU
> Octave (2.1.63).  Other functions give me different results,
> too. Below  is the output  of my tests.   I am not at  all a
> math expert.


There are different branch cut conventions used by different programs.
acosh or other inverse functions are mutiple-valued functions so the
result is not uniquely defined.  

GSL uses one of the two common conventions (W.Kahan's) because it has
better consistency with IEEE arithmetic.  It is also used by Common
Lisp -- see the GSL Reference manual for details and references.  The
others are using a different convention (Abramowitz & Stegun).  As
such, all the answers are correct.

best regards,

Brian Gough

Network Theory Ltd,
Publishing the GSL Manual -

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