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Date: Wed, 29 Aug 2007 10:06:38 -0700
From: Brian Dessent <brian AT dessent DOT net>
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Subject: Re: 1.5.24: sin() bug
References: <20070829153331 DOT GA95558 AT tetsuo DOT karasik DOT eu DOT org>
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Dmitry Karasik wrote:

> #include <math.h>
> #include <stdio.h>
> int main( int argc, char ** argv)
> {
>         double g = (double) 3.1415926535897900074;
>         printf("sin(%.10g)=%.10g\n", g, sin(g));
> }
> 
> output is :
> 
> sin(3.141592654)=3.231089149e-15
> 
> whereas all other sin() implementation I could find ( freebsd, linux, msvc)
> report this:
> 
> sin(3.141592654)=3.231085104e-015
> 
> the difference is in 7th digit, and is significant for double precision.

This appears to be due to an approximation in __kernel_sin in which if
|x| < 2**-27 the approximation sin(x) ~ x is used.

<http://sourceware.org/cgi-bin/cvsweb.cgi/~checkout~/src/newlib/libm/math/k_sin.c?content-type=text/plain&cvsroot=src>.

This code seems to be completely untouched since the original import
into CVS in 2000, so I'm guessing it's a very old implementation.  I'm
not sure how we'd go about fixing this other than to look for a more
sophisticated implementation and contribute it to newlib.

In any case this is more of a newlib issue than a Cygwin issue as we are
just a consumer of this code, so followups should go to the newlib list.

Brian

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