[FFmpeg-devel] [PATCH] avfilter/af_afade: improve accuracy and speed of gain computation

[Paul B Mahol]

On 11/25/15, Ganesh Ajjanagadde <gajjanagadde at gmail.com> wrote:
> Gain computation for various curves was being done in a needlessly
> inaccurate fashion. Of course these are all subjective curves, but when
> a curve is advertised to the user, it should be matched as closely as
> possible within the limitations of libm. In particular, the constants
> kept here were pretty inaccurate for double precision.
>
> Speed improvements are mainly due to the avoidance of pow, the most
> notorious of the libm functions in terms of performance. To be fair, it
> is the GNU libm that is among the worst, but it is not really GNU libm's
> fault
> since others simply yield a higher error as measured in ULP.
>
> "Magic" constants are also accordingly documented, since they take at
> least a minute of thought for a casual reader.
>
> Signed-off-by: Ganesh Ajjanagadde <gajjanagadde at gmail.com>
> ---
>  libavfilter/af_afade.c | 20 ++++++++++++--------
>  1 file changed, 12 insertions(+), 8 deletions(-)
>
> diff --git a/libavfilter/af_afade.c b/libavfilter/af_afade.c
> index ca9f2c4..c8b6ed8 100644
> --- a/libavfilter/af_afade.c
> +++ b/libavfilter/af_afade.c
> @@ -92,6 +92,7 @@ static int query_formats(AVFilterContext *ctx)
>
>  static double fade_gain(int curve, int64_t index, int range)
>  {
> +#define CUBE(a) ((a)*(a)*(a))
>      double gain;
>
>      gain = av_clipd(1.0 * index / range, 0, 1.0);
> @@ -101,22 +102,25 @@ static double fade_gain(int curve, int64_t index, int
> range)
>          gain = sin(gain * M_PI / 2.0);
>          break;
>      case IQSIN:
> -        gain = 0.636943 * asin(gain);
> +        /* 0.6... = 2 / M_PI */
> +        gain = 0.6366197723675814 * asin(gain);
>          break;
>      case ESIN:
> -        gain = 1.0 - cos(M_PI / 4.0 * (pow(2.0*gain - 1, 3) + 1));
> +        gain = 1.0 - cos(M_PI / 4.0 * (CUBE(2.0*gain - 1) + 1));
>          break;
>      case HSIN:
>          gain = (1.0 - cos(gain * M_PI)) / 2.0;
>          break;
>      case IHSIN:
> -        gain = 0.318471 * acos(1 - 2 * gain);
> +        /* 0.3... = 1 / M_PI */
> +        gain = 0.3183098861837907 * acos(1 - 2 * gain);
>          break;
>      case EXP:
> -        gain = pow(0.1, (1 - gain) * 5.0);
> +        /* -11.5... = 5*ln(0.1) */
> +        gain = exp(-11.512925464970227 * (1 - gain));
>          break;
>      case LOG:
> -        gain = av_clipd(0.0868589 * log(100000 * gain), 0, 1.0);
> +        gain = av_clipd(1 + 0.2 * log10(gain), 0, 1.0);
>          break;
>      case PAR:
>          gain = 1 - sqrt(1 - gain);
> @@ -128,7 +132,7 @@ static double fade_gain(int curve, int64_t index, int
> range)
>          gain *= gain;
>          break;
>      case CUB:
> -        gain = gain * gain * gain;
> +        gain = CUBE(gain);
>          break;
>      case SQU:
>          gain = sqrt(gain);
> @@ -137,10 +141,10 @@ static double fade_gain(int curve, int64_t index, int
> range)
>          gain = cbrt(gain);
>          break;
>      case DESE:
> -        gain = gain <= 0.5 ? pow(2 * gain, 1/3.) / 2: 1 - pow(2 * (1 -
> gain), 1/3.) / 2;
> +        gain = gain <= 0.5 ? cbrt(2 * gain) / 2: 1 - cbrt(2 * (1 - gain)) /
> 2;
>          break;
>      case DESI:
> -        gain = gain <= 0.5 ? pow(2 * gain, 3) / 2: 1 - pow(2 * (1 - gain),
> 3) / 2;
> +        gain = gain <= 0.5 ? CUBE(2 * gain) / 2: 1 - CUBE(2 * (1 - gain)) /
> 2;
>          break;
>      }
>
> --
> 2.6.2
>
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>

ok