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Re: acosh, getting consistent results from GSL and Guile

From: Neil Jerram
Subject: Re: acosh, getting consistent results from GSL and Guile
Date: Fri, 18 Aug 2006 14:55:27 +0100
User-agent: Gnus/5.1007 (Gnus v5.10.7) Emacs/21.4 (gnu/linux)

"Marco Maggi" <address@hidden> writes:

> Ciao,
>   on the GNU Scientific Library mailing list I asked the
> following:
>>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. [...]
>>Browsing Wikipedia for acosh  formulas it seems to me
>>that GSL is using an equivalent of:
>>    (log (- x (sqrt (- (* x x) 1))))
>>while the others are using an equivalent of:
>>    (log (+ x (sqrt (- (* x x) 1))))
>>I'm interested in having equal results from GSL
>>and Guile, [...]
> and got the following reply:
>>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.
> So, do you suggest me to override the GSL function to
> make it equal to the Guile one, or vice versa?

It depends on the context of the problem you are trying to solve.
It's some time since I was doing this kind of maths, but if I remember
correctly, the fact that there are multiple possible values usually
maps on to something meaningful in your problem domain.


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