Re: haversine in specfunc

[Brian Gough <bjg at network-theory dot co dot uk>]

Richard Mathar writes:
 > Since the evaluation of 1-cos(x) close to x=0, 2*pi etc
 > suffers from numerical instability in the standard implementations,
 > it would be convenient to have a haversine implementation,
 > where the haversine is defined according to section 4.3.147 of
 > the Abramowitz/Stegun book.

Hello,

Thanks for the suggestions.  For this case I think a double angle
formula will do the job: 1-cos(x) = 2 sin^2(x/2)

 > I also think that the error estimate for cos(x) for x around zero
 > is a factor of 2 too large, by comparison with the standard
 > Taylor series that is used.

Generally there is an extra factor of 2 for safety in the error terms.
I'll add a note about that to the design document.

-- 
Brian Gough