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Re: Fast exponent and logarithm, given initial estimate
Posted:
Oct 19, 2004 10:22 PM
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> In case the exponentials are of some limited range (say -0.5 to 0.5 or
> -10 to 10 for example), and if some lookup tables are allowed, one
> could use static lookup tables of the exponent function that cover the
> individual decimals of the exponentials. Example: to calculate exp(7.345)
> one needs exp(7), exp(0.3), exp(0.04) and exp(0.005) (all of these
> are obviously to be multiplied to get the result), and these could be
> provided in lookup tables that store
> [exp(0)],exp(1),exp(2),..exp(10)
> exp(0.1),exp(0.2),..exp(0.9)
> exp(0.01),exp(0.02),..exp(0.09)
The problem with lookup tables is that SIMD code tends to fare badly
with extensive memory loads. Indeed given the current state of CPU
development, most CPU's now are much faster than memory, so
calculation is often faster than loading from memory. Of course if the
lookup tables are small and would fit into L1 or L2 cache, they could
be used.
This is meant to be a general purpose exponentiation routine as well.
Cheers
Glen low, Pixelglow Software
www.pixelglow.com
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