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Date: Tue, 31 May 2005 13:02:00 -0000
From: Andrew Haley <aph@redhat.com>
To: Scott Robert Ladd <scott.ladd@coyotegulch.com>
Cc: gcc@gcc.gnu.org
Subject: Re: Sine and Cosine Accuracy
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Scott Robert Ladd writes:
 > chris jefferson wrote:
 > > I would like to say yes, I disagree that this should be true. By your
 > > argument, why isn't sin(pow(2.0,90.0)+1) == sin(6.153104..)? Also, how
 > > the heck do you intend to actually calculate that value? You can't just
 > > keep subtracting multiples of 2*pi from pow(2.0, 90.0) else nothing will
 > > happen, and if you choose to subtract some large multiple of 2*pi, your
 > > answer wouldn't end up accurate to anywhere near that many decimal
 > > places. Floating point numbers approximate real numbers, and at the size
 > > you are considering, the approximation contains values for which sin(x)
 > > takes all values in the range [-1,1].
 > 
 > Nonsense.
 > 
 > Show me an example where the following function should *not* print the
 > same values for a and b:
 > 
 > void same_sines(double x)
 > {
 >     double a = sin(x);
 >     double b = sin(fmod(x, 2.0 * PI));
 >     printf("%20.15f,%20.15f\n",a,b);
 > }

Please!  Every correct implementation of libm will not print the same
result for these two values, because it is necessary to do the range
reduction in extended precision.

Andrew.