[FFmpeg-devel] [PATCH] swresample/resample: speed up build_filter for Blackman-Nuttall filter

[Ganesh Ajjanagadde]

This uses the trigonometric double and triple angle formulae to avoid
repeated (expensive) evaluation of libc's cos().

Sample benchmark (x86-64, Haswell, GNU/Linux)
old:
1104466600 decicycles in build_filter(loop 1000),     256 runs,      0 skips
1096765286 decicycles in build_filter(loop 1000),     512 runs,      0 skips
1070479590 decicycles in build_filter(loop 1000),    1024 runs,      0 skips

new:
588861423 decicycles in build_filter(loop 1000),     256 runs,      0 skips
591262754 decicycles in build_filter(loop 1000),     512 runs,      0 skips
577355145 decicycles in build_filter(loop 1000),    1024 runs,      0 skips

This results in small differences with the old expression:
difference (worst case on [0, 2*M_PI]), argmax 0.008:
max diff (relative): 0.000000000000157289807188
blackman_old(0.008): 0.000363951585488813192382
blackman_new(0.008): 0.000363951585488755946507

These are judged to be insignificant for the performance gain. PSNR to
reference file is unchanged up to second decimal point for instance.

Signed-off-by: Ganesh Ajjanagadde <gajjanagadde at gmail.com>
---
 libswresample/resample.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libswresample/resample.c b/libswresample/resample.c
index a2cbb48..5d32cc2 100644
--- a/libswresample/resample.c
+++ b/libswresample/resample.c
@@ -171,7 +171,7 @@ static int build_filter(ResampleContext *c, void *filter, double factor, int tap
                 break;}
             case SWR_FILTER_TYPE_BLACKMAN_NUTTALL:
                 w = 2.0*x / (factor*tap_count) + M_PI;
-                y *= 0.3635819 - 0.4891775 * cos(w) + 0.1365995 * cos(2*w) - 0.0106411 * cos(3*w);
+                y *= 0.3635819 - 0.4891775 * cos(w) + 0.1365995 * (2*cos(w)*cos(w)-1) - 0.0106411 * (4*cos(w)*cos(w)*cos(w) - 3*cos(w));
                 break;
             case SWR_FILTER_TYPE_KAISER:
                 w = 2.0*x / (factor*tap_count*M_PI);
-- 
2.6.2