[Proj] Geo Transfoms and calculations

[OvV_HN]

Is GSL that accurate?
It could be that I'm missing something, but GNU GSL does the asinh, acosh 
and atanh functions with the aid of a log1p function which is not 
significantly accurate for small x, although the comments say "cancels 
errors with IEEE arithmetic". Just compare this with the Cephes log1p 
function, published by Steve Moshier; see the file cmath:unity.c. The Cephes 
log1p has a "Theoretical peak relative error = 2.32e-20". Could be sometimes 
worse than a complete error cancellation, but does the error always cancel?
What I´m trying to say is: don't bet all your horses blindly on GNU GSL.

Oscar van Vlijmen



----- Original Message ----- 
From: "Eric Miller" <EMiller at dfg.ca.gov>
To: <proj at lists.maptools.org>
Sent: Tuesday, December 30, 2008 6:39 PM
Subject: Re: [Proj] Geo Transfoms and calculations


You need only a minor modification to Gerald's libproj4 to compile on
windows.  Because Microsoft is lame, their math library does not include
atanh (or asinh or acosh).

Previously, I overcame this by building in a naive implementation of
atanh as:

double atanh( double x )
{
return log((1 + x)/(1 - x))/2;
}

Since Gerald has since embraced the GSL, maybe we can get him to use
the GSL versions of those functions and let the GNU folks handle
platform compatibility.