Centralize control-parameter math functions in libpbd.

Functions formerly in ardour/util.h and some more functions.
The main motivation is libevoral which can use libpbd but not libardour.

The eventual goal is to consolidate various different interpolation,
scaling and deflection methods.

libs/pbd/pbd/control_math.h

@@ -0,0 +1,105 @@
+/*
+ * Copyright (C) 2017 Robin Gareus <robin@gareus.org>
+ * Copyright (C) 1999 Paul Davis
+ *
+ * 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.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+ */
+
+#ifndef __pbd_control_math_h__
+#define __pbd_control_math_h__
+
+#include <assert.h>
+#include <math.h>
+
+/* map gain-coeff [0..2] to position [0..1] */
+static inline double
+gain_to_position (double g)
+{
+	if (g == 0) {
+		return 0;
+	}
+	return pow ((6.0 * log (g) / log (2.0) + 192.0) / 198.0, 8.0);
+}
+
+/* map position [0..1] to gain-coeff [0..2] */
+static inline double
+position_to_gain (double pos)
+{
+	if (pos == 0.0) {
+		return 0.0;
+	}
+	return exp (((pow (pos, 1.0 / 8.0) * 198.0) - 192.0) / 6.0 * log (2.0));
+}
+
+/* map position [0..1] to parameter [lower..upper] on a logarithmic scale */
+static inline double
+position_to_logscale (double pos, double lower, double upper)
+{
+	assert (upper > lower && lower * upper > 0);
+	assert (pos >= 0.0 && pos <= 1.0);
+	return lower * pow (upper / lower, pos);
+}
+
+/* map parameter [lower..upper] to position [0..1] on a logarithmic scale*/
+static inline double
+logscale_to_position (double val, double lower, double upper)
+{
+	assert (upper > lower && lower * upper > 0);
+	assert (val >= lower && val <= upper);
+	return log (val / lower) / log (upper / lower);
+}
+
+static inline double
+logscale_to_position_with_steps (double val, double lower, double upper, uint32_t steps)
+{
+	assert (steps > 1);
+	double v = logscale_to_position (val, lower, upper) * (steps - 1.0);
+	return round (v) / (steps - 1.0);
+}
+
+static inline double
+position_to_logscale_with_steps (double pos, double lower, double upper, uint32_t steps)
+{
+	assert (steps > 1);
+	double p = round (pos * (steps - 1.0)) / (steps - 1.0);
+	return position_to_logscale (p, lower, upper);
+}
+
+
+static inline double
+interpolate_linear (double from, double to, double fraction)
+{
+	return from + (fraction * (to - from));
+}
+
+static inline double
+interpolate_logarithmic (double from, double to, double fraction, double lower, double upper)
+{
+	// this is expensive -- optimize
+	double l0 = logscale_to_position (from, lower, upper);
+	double l1 = logscale_to_position (to, lower, upper);
+	return position_to_logscale (l0 + fraction * (l1 - l0), lower, upper);
+}
+
+static inline double
+interpolate_gain (double from, double to, double fraction, double upper)
+{
+	// this is expensive -- optimize
+	double g0 = gain_to_position (from * 2. / upper);
+	double g1 = gain_to_position (to * 2. / upper);
+	return position_to_gain (g0 + fraction * (g1 - g0)) * upper / 2.;
+}
+
+#endif