Pull out nearest-rational into mathmisc so it can be used in other places than BQResampler

src/common/mathmisc.cpp

@@ -0,0 +1,69 @@
+/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
+
+/*
+    Rubber Band Library
+    An audio time-stretching and pitch-shifting library.
+    Copyright 2007-2022 Particular Programs Ltd.
+
+    This program is free software; you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as
+    published by the Free Software Foundation; either version 2 of the
+    License, or (at your option) any later version.  See the file
+    COPYING included with this distribution for more information.
+
+    Alternatively, if you have a valid commercial licence for the
+    Rubber Band Library obtained by agreement with the copyright
+    holders, you may redistribute and/or modify it under the terms
+    described in that licence.
+
+    If you wish to distribute code using the Rubber Band Library
+    under terms other than those of the GNU General Public License,
+    you must obtain a valid commercial licence before doing so.
+*/
+
+#include "mathmisc.h"
+
+namespace RubberBand {
+
+void pickNearestRational(double ratio, int max_denom, int &num, int &denom)
+{
+    // Farey algorithm, see
+    // https://www.johndcook.com/blog/2010/10/20/best-rational-approximation/
+    double a = 0.0, b = 1.0, c = 1.0, d = 0.0;
+    double pa = a, pb = b, pc = c, pd = d;
+    double eps = 1e-9;
+    while (b <= max_denom && d <= max_denom) {
+        double mediant = (a + c) / (b + d);
+        if (fabs(ratio - mediant) < eps) {
+            if (b + d <= max_denom) {
+                num = a + c;
+                denom = b + d;
+                return;
+            } else if (d > b) {
+                num = c;
+                denom = d;
+                return;
+            } else {
+                num = a;
+                denom = b;
+                return;
+            }
+        }
+        if (ratio > mediant) {
+            pa = a; pb = b;
+            a += c; b += d;
+        } else {
+            pc = c; pd = d;
+            c += a; d += b;
+        }
+    }
+    if (fabs(ratio - (pc / pd)) < fabs(ratio - (pa / pb))) {
+        num = pc;
+        denom = pd;
+    } else {
+        num = pa;
+        denom = pb;
+    }
+}
+
+}

src/common/mathmisc.h

@@ -51,6 +51,8 @@ inline double frequencyForBin(int b, int fftSize, double sampleRate) {
     return (double(b) * sampleRate) / double(fftSize);
 }
 
+void pickNearestRational(double ratio, int maxDenom, int &num, int &denom);
+
 }
 
 #endif