Re: [Algorithms] fast pow() for limited inputs

[Jon W. <jw...@gm...>]

Depending on accuracy needs, a look-up table with interpolation (say,
cubic interpolation) can be just fine and dandy. Consider the
0-255/0-255 texture typically used to approximate pow() for specular
lighting back in the days; it would be 65 kB in size and thus fit in
L2 on a modern CPU (if you use bytes to represent that 0..1 range).

Another, even faster, and even worse, approximation is simply to make
a line from (1,1) that intersects y=0 somewhere between x=0 and x=1,
and move it farther to the right for higher exponents. It all depends
on what kind of precision you need this for.

Sincerely,

jw


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On Thu, Aug 19, 2010 at 11:17 AM, Fabian Giesen <ry...@gm...> wrote:
> On 19.08.2010 10:57, Robin Green wrote:
>> On Wed, Aug 18, 2010 at 11:35 PM, Fabian Giesen<ry...@gm...>  wrote:
>>>
>>>> I would also love to just see a sample implementation of pow(), log(),
>>>> and exp() somewhere, even that might be helpful.
>>>
>>> glibc math implementations are in sysdeps/ieee754 for generic IEEE-754
>>> compliant platforms, with optimized versions for all relevant
>>> architectures in sysdeps/<arch>. If you really want to know how it's
>>> implemented :)
>>
>>
>> What he said.
>>
>> Also, take a look at the CEPHES library for platform agnostic
>> reference implementations of the C math functions and some extras like
>> cotangent, cuberoot and integer powers:
>>
>>      http://www.netlib.org/cephes/
>>
>> And here's an X86 specific implementation of powf() that claims to be
>> faster (than what, it doesn't say):
>>
>>     http://www.xyzw.de/c190.html
>
> Now that's interesting :). I wrote most of that header file, around 2000
> or so. It's faster than what used to be the standard pow()
> implementation on x86 (as in the VC++ 6.0 runtime library), using fscale
> (that method is still used for sFExp below). This is all code for 64k
> intros so it was optimized for size originally, but pow was a bottleneck
> during texture generation, and Agner Fogs version was 20-30% faster if I
> recall correctly. (This was back when P3s were the norm though, no idea
> how it looks now). The main change is to replace the fscale (which used
> to be very slow on some processors) with a longer code sequence that's
> faster.
>
> The original code sequence used to be commented out before the "//
> faster pow" comment, but I guess that got removed at some point :).
>
> Since VS2002 or 2003, the C library contains a much better pow()
> implementation (using SSE on processors that support it) that should be
> faster than this code. It's also a lot bigger though.
>
> -Fabian
>
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