[FFmpeg-devel] [PATCH 3/3] lavu/internal: tighten errors for avpriv_exp10

[Ganesh Ajjanagadde]

On Fri, Dec 25, 2015 at 9:11 AM, Ganesh Ajjanagadde
<gajjanagadde at gmail.com> wrote:
> This tightens the errors by doing a first order Taylor approximation of
> one obvious source of error. This results in negligible runtime
> slowdown, but improves worst case relative error by ~ 30%, worst case
> ulp count from  673 to 391. Another illustration is:
> arg   : -303.137207600000010643270798027515
> exp10 : 7.2910890073523505e-304, 2 ulp
> exp10l: 7.2910890073523489e-304, 0 ulp
> simple: 7.2910890073526541e-304, 377 ulp
> corr  : 7.2910890073524274e-304, 97 ulp
> real  : 7.2910890073523489e-304, 0 ulp
> next  : 7.2910890073533033e-304, 1178 ulp
> prev  : 7.2910890073513954e-304, 1178 ulp
>
> where next, prev denote:
> exp10l(nextafter(x, INFINITY))
> exp10l(nextafter(x, -INFINITY)),
> and simple the exp2(M_LOG2_10 * x), corr this approach.
>
> Signed-off-by: Ganesh Ajjanagadde <gajjanagadde at gmail.com>
> ---
>  libavutil/internal.h | 4 +++-
>  1 file changed, 3 insertions(+), 1 deletion(-)
>
> diff --git a/libavutil/internal.h b/libavutil/internal.h
> index ae11601..b6d72b7 100644
> --- a/libavutil/internal.h
> +++ b/libavutil/internal.h
> @@ -304,7 +304,9 @@ static av_always_inline av_const int64_t ff_rint64_clip(double a, int64_t amin,
>   */
>  static av_always_inline double avpriv_exp10(double x)
>  {
> -    return exp2(M_LOG2_10 * x);
> +    /* log(2)*(log2(10) - (double)log2_10) */
> +    static const double log2_10_eps = 1.02495895001049072e-16;
> +    return exp2(M_LOG2_10 * x) * (1 + log2_10_eps * x);
>  }
>
>  static av_always_inline float avpriv_exp10f(float x)
> --
> 2.6.4
>

Michael: I don't recall you opposing this, but I also recall that you
don't believe this is useful. It will make me feel a bit better about
ff_exp10 if this goes in, so at what level (percentage) of runtime
slowdown are you willing to accept this?