Re: Sine code for ANSI C

From: CBFalconer (cbfalconer_at_yahoo.com)
Date: 05/16/04 

Date: Sun, 16 May 2004 21:21:22 GMT

Joe Wright wrote:
>
... snip ...
>
> 2. Large Angles. The circle is 360 degrees or '2 pi radians'.
> Why is something like..
>
> double r = 52147.3, s;
> s = sin(fmod(r,2*PI));
>
> ..not the solution for large angle argument reduction?

That depends highly on how you compute the fmod. Say you compute
r/(2*PI), truncate it to an integer, multiply by (2*PI), and
subtract that from r. Now you have the difference of two
comparable magnitudes, with attendant loss of significant bits.

Compare with methods of computing sigma f(n) for n = 1 ....
infinity. If you start with n=1 (using the normally available
floating point system) you will end up with something quite
divergent from the true answer, regardless of whether the series
actually converges or not. A reasonably accurate computation
requires starting with the smallest terms. 

-- 
"I'm a war president.  I make decisions here in the Oval Office
 in foreign policy matters with war on my mind." -         Bush.
"Churchill and Bush can both be considered wartime leaders, just
 as Secretariat and Mr Ed were both horses." -     James Rhodes.

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