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

[Ronald S. Bultje]

Hi,

On Sat, Dec 26, 2015 at 6:37 AM, Michael Niedermayer <michael at niedermayer.cc
> wrote:

> On Fri, Dec 25, 2015 at 08:10:16PM -0800, Ganesh Ajjanagadde wrote:
> > 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?
>
> i dont know if the speed difference of exp10 really matters for any
> speed relevant code (probably not) and i dont know if the accuracy
> increase really matters for any code either
> so its weighting 2 "dont knows" against each other
> i cant really say what is better


I share this concern. I'd prefer to keep it simple, so prefer without this
patch.

Ronald