1 files changed, 98 insertions, 27 deletions
diff --git a/libswresample/resample.c b/libswresample/resample.c
index 82f004c802..072e0d6a78 100644
--- a/libswresample/resample.c
+++ b/libswresample/resample.c
@@ -1,6 +1,7 @@
 /*
  * audio resampling
  * Copyright (c) 2004-2012 Michael Niedermayer <michaelni@gmx.at>
+ * bessel function: Copyright (c) 2006 Xiaogang Zhang
  *
  * This file is part of FFmpeg.
  *
@@ -28,38 +29,108 @@
 #include "libavutil/avassert.h"
 #include "resample.h"
 
+static inline double eval_poly(const double *coeff, int size, double x) {
+    double sum = coeff[size-1];
+    int i;
+    for (i = size-2; i >= 0; --i) {
+        sum *= x;
+        sum += coeff[i];
+    }
+    return sum;
+}
+
 /**
  * 0th order modified bessel function of the first kind.
+ * Algorithm taken from the Boost project, source:
+ * https://searchcode.com/codesearch/view/14918379/
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0 (see notice below).
+ * Boost Software License - Version 1.0 - August 17th, 2003
+Permission is hereby granted, free of charge, to any person or organization
+obtaining a copy of the software and accompanying documentation covered by
+this license (the "Software") to use, reproduce, display, distribute,
+execute, and transmit the Software, and to prepare derivative works of the
+Software, and to permit third-parties to whom the Software is furnished to
+do so, all subject to the following:
+
+The copyright notices in the Software and this entire statement, including
+the above license grant, this restriction and the following disclaimer,
+must be included in all copies of the Software, in whole or in part, and
+all derivative works of the Software, unless such copies or derivative
+works are solely in the form of machine-executable object code generated by
+a source language processor.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+DEALINGS IN THE SOFTWARE.
  */
-static double bessel(double x){
-    double lastv=0;
-    double t, v;
-    int i;
-    static const double inv[100]={
- 1.0/( 1* 1), 1.0/( 2* 2), 1.0/( 3* 3), 1.0/( 4* 4), 1.0/( 5* 5), 1.0/( 6* 6), 1.0/( 7* 7), 1.0/( 8* 8), 1.0/( 9* 9), 1.0/(10*10),
- 1.0/(11*11), 1.0/(12*12), 1.0/(13*13), 1.0/(14*14), 1.0/(15*15), 1.0/(16*16), 1.0/(17*17), 1.0/(18*18), 1.0/(19*19), 1.0/(20*20),
- 1.0/(21*21), 1.0/(22*22), 1.0/(23*23), 1.0/(24*24), 1.0/(25*25), 1.0/(26*26), 1.0/(27*27), 1.0/(28*28), 1.0/(29*29), 1.0/(30*30),
- 1.0/(31*31), 1.0/(32*32), 1.0/(33*33), 1.0/(34*34), 1.0/(35*35), 1.0/(36*36), 1.0/(37*37), 1.0/(38*38), 1.0/(39*39), 1.0/(40*40),
- 1.0/(41*41), 1.0/(42*42), 1.0/(43*43), 1.0/(44*44), 1.0/(45*45), 1.0/(46*46), 1.0/(47*47), 1.0/(48*48), 1.0/(49*49), 1.0/(50*50),
- 1.0/(51*51), 1.0/(52*52), 1.0/(53*53), 1.0/(54*54), 1.0/(55*55), 1.0/(56*56), 1.0/(57*57), 1.0/(58*58), 1.0/(59*59), 1.0/(60*60),
- 1.0/(61*61), 1.0/(62*62), 1.0/(63*63), 1.0/(64*64), 1.0/(65*65), 1.0/(66*66), 1.0/(67*67), 1.0/(68*68), 1.0/(69*69), 1.0/(70*70),
- 1.0/(71*71), 1.0/(72*72), 1.0/(73*73), 1.0/(74*74), 1.0/(75*75), 1.0/(76*76), 1.0/(77*77), 1.0/(78*78), 1.0/(79*79), 1.0/(80*80),
- 1.0/(81*81), 1.0/(82*82), 1.0/(83*83), 1.0/(84*84), 1.0/(85*85), 1.0/(86*86), 1.0/(87*87), 1.0/(88*88), 1.0/(89*89), 1.0/(90*90),
- 1.0/(91*91), 1.0/(92*92), 1.0/(93*93), 1.0/(94*94), 1.0/(95*95), 1.0/(96*96), 1.0/(97*97), 1.0/(98*98), 1.0/(99*99), 1.0/(10000)
-    };
 
-    x= x*x/4;
-    t = x;
-    v = 1 + x;
-    for(i=1; v != lastv; i+=2){
-        t *= x*inv[i];
-        v += t;
-        lastv=v;
-        t *= x*inv[i + 1];
-        v += t;
-        av_assert2(i<98);
+static double bessel(double x) {
+// Modified Bessel function of the first kind of order zero
+// minimax rational approximations on intervals, see
+// Blair and Edwards, Chalk River Report AECL-4928, 1974
+    static const double p1[] = {
+        -2.2335582639474375249e+15,
+        -5.5050369673018427753e+14,
+        -3.2940087627407749166e+13,
+        -8.4925101247114157499e+11,
+        -1.1912746104985237192e+10,
+        -1.0313066708737980747e+08,
+        -5.9545626019847898221e+05,
+        -2.4125195876041896775e+03,
+        -7.0935347449210549190e+00,
+        -1.5453977791786851041e-02,
+        -2.5172644670688975051e-05,
+        -3.0517226450451067446e-08,
+        -2.6843448573468483278e-11,
+        -1.5982226675653184646e-14,
+        -5.2487866627945699800e-18,
+    };
+    static const double q1[] = {
+        -2.2335582639474375245e+15,
+         7.8858692566751002988e+12,
+        -1.2207067397808979846e+10,
+         1.0377081058062166144e+07,
+        -4.8527560179962773045e+03,
+         1.0L,
+    };
+    static const double p2[] = {
+        -2.2210262233306573296e-04,
+         1.3067392038106924055e-02,
+        -4.4700805721174453923e-01,
+         5.5674518371240761397e+00,
+        -2.3517945679239481621e+01,
+         3.1611322818701131207e+01,
+        -9.6090021968656180000e+00,
+    };
+    static const double q2[] = {
+        -5.5194330231005480228e-04,
+         3.2547697594819615062e-02,
+        -1.1151759188741312645e+00,
+         1.3982595353892851542e+01,
+        -6.0228002066743340583e+01,
+         8.5539563258012929600e+01,
+        -3.1446690275135491500e+01,
+        1.0L,
+    };
+    double y, r, factor;
+    if (x == 0)
+        return 1.0;
+    x = fabs(x);
+    if (x <= 15) {
+        y = x * x;
+        return eval_poly(p1, FF_ARRAY_ELEMS(p1), y) / eval_poly(q1, FF_ARRAY_ELEMS(q1), y);
+    }
+    else {
+        y = 1 / x - 1.0 / 15;
+        r = eval_poly(p2, FF_ARRAY_ELEMS(p2), y) / eval_poly(q2, FF_ARRAY_ELEMS(q2), y);
+        factor = exp(x) / sqrt(x);
+        return factor * r;
     }
-    return v;
 }
 
 /**