[FFmpeg-devel] [PATCHv2] avutil/mathematics: speed up av_gcd by using Stein's binary GCD algorithm

[wm4]

On Sat, 10 Oct 2015 21:58:47 -0400
Ganesh Ajjanagadde <gajjanagadde at gmail.com> wrote:

> This uses Stein's binary GCD algorithm:
> https://en.wikipedia.org/wiki/Binary_GCD_algorithm
> to get a roughly 4x speedup over Euclidean GCD on standard architectures
> with a compiler intrinsic for ctzll, and a roughly 2x speedup otherwise.
> At the moment, the compiler intrinsic is used on GCC and Clang due to
> its easy availability.
> 
> Quick note regarding overflow: yes, subtractions on int64_t can, but the
> llabs takes care of that. The llabs is also guaranteed to be safe, with
> no annoying INT64_MIN business since INT64_MIN being a power of 2, is
> shifted down before being sent to llabs.
> 
> The binary GCD needs ff_ctzll, an extension of ff_ctz for long long (int64_t). On
> GCC, this is provided by a built-in. On Microsoft, there is a
> BitScanForward64 analog of BitScanForward that should work; but I can't confirm.
> Apparently it is not available on 32 bit builds; so this may or may not
> work correctly. On Intel, per the documentation there is only an
> intrinsic for _bit_scan_forward and people have posted on forums
> regarding _bit_scan_forward64, but often their documentation is
> woeful. Again, I don't have it, so I can't test.
> 
> As such, to be safe, for now only the GCC/Clang intrinsic is added, the rest
> use a compiled version based on the De-Bruijn method of Leiserson et al:
> http://supertech.csail.mit.edu/papers/debruijn.pdf.
> 
> Tested with FATE, sample benchmark (x86-64, GCC 5.2.0, Haswell)
> with a START_TIMER and STOP_TIMER in libavutil/rationsl.c, followed by a
> make fate.
> 
> aac-am00_88.err:
> builtin:
> 714 decicycles in av_gcd,    4095 runs,      1 skips
> 
> de-bruijn:
> 1440 decicycles in av_gcd,    4096 runs,      0 skips
> 
> previous:
> 2889 decicycles in av_gcd,    4096 runs,      0 skips
> 
> Signed-off-by: Ganesh Ajjanagadde <gajjanagadde at gmail.com>
> ---
>  libavutil/intmath.h     | 19 +++++++++++++++++++
>  libavutil/mathematics.c | 26 +++++++++++++++++++++-----
>  2 files changed, 40 insertions(+), 5 deletions(-)
> 
> diff --git a/libavutil/intmath.h b/libavutil/intmath.h
> index 08d54a6..b412385 100644
> --- a/libavutil/intmath.h
> +++ b/libavutil/intmath.h
> @@ -114,6 +114,9 @@ static av_always_inline av_const int ff_log2_16bit_c(unsigned int v)
>  #ifndef ff_ctz
>  #define ff_ctz(v) __builtin_ctz(v)
>  #endif
> +#ifndef ff_ctzll
> +#define ff_ctzll(v) __builtin_ctzll(v)
> +#endif
>  #endif
>  #endif
>  
> @@ -158,6 +161,22 @@ static av_always_inline av_const int ff_ctz_c( int v )
>  #endif
>  #endif
>  
> +#ifndef ff_ctzll
> +#define ff_ctzll ff_ctzll_c
> +/* We use the De-Bruijn method outlined in:
> + * http://supertech.csail.mit.edu/papers/debruijn.pdf. */
> +static av_always_inline av_const int ff_ctzll_c(long long v)
> +{
> +    static const int debruijn_ctz64[64] = {
> +        0, 1, 2, 53, 3, 7, 54, 27, 4, 38, 41, 8, 34, 55, 48, 28,
> +        62, 5, 39, 46, 44, 42, 22, 9, 24, 35, 59, 56, 49, 18, 29, 11,
> +        63, 52, 6, 26, 37, 40, 33, 47, 61, 45, 43, 21, 23, 58, 17, 10,
> +        51, 25, 36, 32, 60, 20, 57, 16, 50, 31, 19, 15, 30, 14, 13, 12
> +    };
> +    return debruijn_ctz64[(uint64_t)((v & -v) * 0x022FDD63CC95386D) >> 58];
> +}
> +#endif
> +

Is this duplicated from somewhere?