[FFmpeg-devel] [PATCHv2] lavc/cbrt_tablegen: speed up tablegen

[Ganesh Ajjanagadde]

On Tue, Jan 5, 2016 at 7:44 AM, Daniel Serpell <dserpell at gmail.com> wrote:
> Hi!,
>
> El Mon, Jan 04, 2016 at 06:33:59PM -0800, Ganesh Ajjanagadde escribio:
>> This exploits an approach based on the sieve of Eratosthenes, a popular
>> method for generating prime numbers.
>>
>> Tables are identical to previous ones.
>>
>> Tested with FATE with/without --enable-hardcoded-tables.
>>
>> Sample benchmark (Haswell, GNU/Linux+gcc):
>> prev:
>> 7860100 decicycles in cbrt_tableinit,       1 runs,      0 skips
>> 7777490 decicycles in cbrt_tableinit,       2 runs,      0 skips
>> [...]
>> 7582339 decicycles in cbrt_tableinit,     256 runs,      0 skips
>> 7563556 decicycles in cbrt_tableinit,     512 runs,      0 skips
>>
>> new:
>> 2099480 decicycles in cbrt_tableinit,       1 runs,      0 skips
>> 2044470 decicycles in cbrt_tableinit,       2 runs,      0 skips
>> [...]
>> 1796544 decicycles in cbrt_tableinit,     256 runs,      0 skips
>> 1791631 decicycles in cbrt_tableinit,     512 runs,      0 skips
>>
>
> See attached code, function "test1", based on an approximation of:
>
>   (i+1)^(1/3) ~= i^(1/3) * ( 1 + 1/(3i) - 1/(9i) + 5/(81i) - .... )

I assume 1/(3i), 1/(9i^2), etc obtained via a Taylor series at x = 0.

>
> Generated values are the same as original floats (max error in double
> is < 4*10^-10), it is faster (and I think, simpler) than your version.

Had thought of these ideas, but did not examine as I was a little
concerned about accuracy. Thanks, will give it a spin. Or
alternatively, you can submit a patch since you put it into action.

Alternatively, one could directly expand the series for (i+1)^(4/3).
And it may be possible to tighten the number of terms needed by
expanding not about x = 0, but x = i to get i+1. Or fancier polynomial
approximations can be used. Have you tried these?

>
> Perhaps altering the constants it could be made faster still, but it is
> currently dominated by de division in the main loop.

Thanks for letting me know.

>
>     Daniel.
>
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