[Algorithms] fast pow() for limited inputs

[Jeff R. <je...@8m...>]

So I need to speed up the CRT pow() function a bit, but I have some
restrictions on the input which hopefully should give me some room to
optimize:

I need to compute pow(x,y), where x is on [0,1], and y is guaranteed
positive and could have an upper bound in the neighborhood of 1000.

I need "reasonable" accuracy (could be a little looser than the standard
pow() implementation). I've searched online and found some bit twiddling
approaches that claim to be very fast, but they seem to be too inaccurate
for my purposes. I've tried implementing pow() as exp( log(x), y ), with my
own cheap Taylor series in place of the natural log function. It did produce
good output but wasn't very fast (slightly slower than the CRT pow()). It is
probably worth mentioning before anyone asks that yes I have confirmed pow()
as the bottleneck with a profiling tool ;-)

I would also love to just see a sample implementation of pow(), log(), and
exp() somewhere, even that might be helpful.

Thanks,

Jeff

-- 
Jeff Russell
Engineer, 8monkey Labs
www.8monkeylabs.com