Re: About missing inverse hyperbolic function

[Bastien ROUCARIES]

Le mercredi 2 janvier 2008, Bruno Haible a écrit :
> Hello,
>
> Bastien Roucaries wrote:
> > I need for my program to use asinh acosh and atanh. For now I used to
> > define
> >
> > it if missing using
> > #define asinh(x) log(x+sqrt(x*x+1))
> > #define acosh(x) log(x+sqrt(x-1.0)*sqrt(x+1.0))
> > #define atanh(x)  (0.5*log(x+1)-0.5*log(1-x))
> >
> > How can I create a gnulib module in order to do that?
>
> First, look in the gnulib documentation which portability problems are
> already known and which of them are already handled by gnulib. In this
> case, you see that the problem is that mingw does not provide the
> functions, and that gnulib provides no workaround so far.

I have done that. 
> Second, decide which include file should declare the functions. POSIX says
> <math.h> in this case; in gnulib the source code of this file is in
> lib/math.in.h. Try to write the declarations here. Add the proper autoconf
> tests; see e.g. how it was done for the 'trunc' function or some other
> functions.

I have added the proper autoconf test

> Third, write an implementation of these functions that is portable enough;
> each function it its own file.

I need isfinite how can I do that? It is a dependancy I suppose but I do not 
know how to declare it... Could you explain how can I do?

> The formula you gave for asinh(x) is ok for x >= 0; for x < 0 it is
> unusable since it will lead to numerical instability (i.e. rounding errors
> that are far too big).
>
> The formula you gave for acosh(x) may be ok, but is it necessary to call
> sqrt twice?
>
> The formula you gave for atanh(x): similarly, it is necessary to call log
> twice? Furthermore, for x near 0, say abs(x) < 2^-53, your formula will
> return 0, which has a relative error of 100%; it's possible to do better.

I will use glibc function.

> Fourth, write a test suite for each function. The test suite should cover
> particular values as well as special cases like +/- infinity and NaN.

Ok will do

> Then you can submit the patch here.

Ok will
> Bruno



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"ROUCARIES Bastien"
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