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• swresample/resample : improve bessel function accuracy and speed

  2 novembre 2015, par Ganesh Ajjanagadde

  swresample/resample : improve bessel function accuracy and speed
  This improves accuracy for the bessel function at large arguments, and this in turn
  
  should improve the quality of the Kaiser window. It also improves the
  
  performance of the bessel function and hence build_filter by 20%.
  
  Details are given below.
  Algorithm : taken from the Boost project, who have done a detailed
  
  investigation of the accuracy of their method, as compared with e.g the
  
  GNU Scientific Library (GSL) :
  
  http://www.boost.org/doc/libs/1_52_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html.
  
  Boost source code (also cited and licensed in the code) :
  
  https://searchcode.com/codesearch/view/14918379/.
  Accuracy : sample values may be obtained as follows. i0 denotes the old bessel code,
  
  i0_boost the approach here, and i0_real an arbitrary precision result (truncated) from Wolfram Alpha :
  
  type "bessel i0(6.0)" to reproduce. These are evaluation points that occur for
  
  the default kaiser_beta = 9.
  Some illustrations :
  
  bessel(8.0)
  
  i0      (8.000000) = 427.564115721804739678191254
  
  i0_boost(8.000000) = 427.564115721804796521610115
  
  i0_real (8.000000) = 427.564115721804785177396791
  bessel(6.0)
  
  i0      (6.000000) = 67.234406976477956163762428
  
  i0_boost(6.000000) = 67.234406976477970374617144
  
  i0_real (6.000000) = 67.234406976477975326188025
  Reason for accuracy : Main accuracy benefits come at larger bessel arguments, where the
  
  Taylor-Maclaurin method is not that good : 23+ iterations
  
  (at large arguments, since the series is about 0) can cause
  
  significant floating point error accumulation.
  Benchmarks : Obtained on x86-64, Haswell, GNU/Linux via a loop calling
  
  build_filter 1000 times :
  
  test : fate-swr-resample-dblp-44100-2626
  new :
  
  995894468 decicycles in build_filter(loop 1000),     256 runs,      0 skips
  
  1029719302 decicycles in build_filter(loop 1000),     512 runs,      0 skips
  
  984101131 decicycles in build_filter(loop 1000),    1024 runs,      0 skips
  old :
  
  1250020763 decicycles in build_filter(loop 1000),     256 runs,      0 skips
  
  1246353282 decicycles in build_filter(loop 1000),     512 runs,      0 skips
  
  1220017565 decicycles in build_filter(loop 1000),    1024 runs,      0 skips
  A further 5% may be squeezed by enabling -ftree-vectorize. However,
  
  this is a separate issue from this patch.
  Reviewed-by : Michael Niedermayer <michael@niedermayer.cc>
  
  Signed-off-by : Ganesh Ajjanagadde <gajjanagadde@gmail.com>
  

  • [DH] libswresample/resample.c

• swresample/resample : speed up build_filter for Blackman-Nuttall filter

  5 novembre 2015, par Ganesh Ajjanagadde

  swresample/resample : speed up build_filter for Blackman-Nuttall filter
  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)
  
  test : fate-swr-resample-dblp-44100-2626
  
  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.
  Reviewed-by : Michael Niedermayer <michael@niedermayer.cc>
  
  Signed-off-by : Ganesh Ajjanagadde <gajjanagadde@gmail.com>
  

  • [DH] libswresample/resample.c

• Animation speed adjustment using ffmpeg in Python

  5 novembre 2015, par neither-nor

  I’m been for years using stock ffmpeg script to sequentially snitch together temporal plots in Python. However, I cannot figure out the trivial issue of how to, for instance, slow down the animation speed so that the resultant video file has a longer duration.

  Example :

  import matplotlib.pyplot as plt
  
  import os, sys
  
  
  
  for t in range(100):
  
      plt.cla()
  
      plt.text(0.5, 0.5, 'time %02d'%(t+1))
  
      plt.draw()
  
  
  
      fname = '_tmp%02d.png'%(t+1)
  
      plt.savefig(fname)
  
  
  
  os.system("ffmpeg -i _tmp%02d.png -pix_fmt yuv420p -r 20 -b:v 20M flipbook.mp4")
  
  os.system("rm _tmp*.png")    

  The resulting "flip book" takes 4s and the time stamp increases steadily. However, I tried to make the animation last twice as long by testing the following :

  1. Change 20 after -r to 1 : this still lasts 4s but now the time stamp "leaps" nonlinearly

  2. Change 20M to 1M : no discernible effect

  I can’t find much information about this line of code, either the usage of each flag or how to modify aspects of it (e.g.,speed).