Move bessel_i0() from swresample/resample to avutil/mathematics

0th order modified bessel function of the first kind are used in multiple
places, lets avoid having 3+ different implementations
I picked this one as its accurate and quite fast, it can be replaced if
a better one is found

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

doc/APIchanges

@@ -2,6 +2,9 @@ The last version increases of all libraries were on 2023-02-09
 
 API changes, most recent first:
 
+2023-05-29 - xxxxxxxxxx - lavu 58.12.100 - mathematics.h
+  Add av_bessel_i0()
+
 2023-05-xx - xxxxxxxxxx - lavc 60.15.100 - avcodec.h
   Add AVHWAccel.update_thread_context, AVHWAccel.free_frame_priv,
   AVHWAccel.flush.

libavutil/mathematics.c

@@ -213,3 +213,107 @@ int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t i
         return av_sat_add64(av_rescale_q(old + 1, inc_tb, ts_tb), ts - old_ts);
     }
 }
+
+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.
+ */
+
+double av_bessel_i0(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,
+         1.0,
+    };
+    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,
+        1.0,
+    };
+    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;
+    }
+}

libavutil/mathematics.h

@@ -288,6 +288,10 @@ int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int
  */
 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
 
+/**
+ * 0th order modified bessel function of the first kind.
+ */
+double av_bessel_i0(double x);
 
 /**
  * @}

libavutil/version.h

@@ -79,7 +79,7 @@
  */
 
 #define LIBAVUTIL_VERSION_MAJOR  58
-#define LIBAVUTIL_VERSION_MINOR  11
+#define LIBAVUTIL_VERSION_MINOR  12
 #define LIBAVUTIL_VERSION_MICRO 100
 
 #define LIBAVUTIL_VERSION_INT   AV_VERSION_INT(LIBAVUTIL_VERSION_MAJOR, \

libswresample/resample.c

@@ -30,110 +30,6 @@
 #include "libavutil/cpu.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) {
-// 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,
-         1.0,
-    };
-    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,
-        1.0,
-    };
-    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;
-    }
-}
-
 /**
  * builds a polyphase filterbank.
  * @param factor resampling factor
@@ -189,7 +85,7 @@ static int build_filter(ResampleContext *c, void *filter, double factor, int tap
                 break;
             case SWR_FILTER_TYPE_KAISER:
                 w = 2.0*x / (factor*tap_count*M_PI);
-                y *= bessel(kaiser_beta*sqrt(FFMAX(1-w*w, 0)));
+                y *= av_bessel_i0(kaiser_beta*sqrt(FFMAX(1-w*w, 0)));
                 break;
             default:
                 av_assert0(0);