new header with an efficient implementation of integer division-rounding-to-nearest

libs/pbd/pbd/integer_division.h

@@ -0,0 +1,39 @@
+/*
+    Copyright (C) 2020 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., 675 Mass Ave, Cambridge, MA 02139, USA.
+*/
+
+#ifndef __libpbd_integer_division_h__
+#define __libpbd_integer_division_h__
+
+#define PBD_IDIV_ASR(x) ((x) < 0 ? -1 : 0)  // Compiles into a (N-1)-bit arithmetic shift right
+
+/* The value of PBD_IDIV_ROUNDING will have the same sign as the dividend (x) and half
+ * the magnitude of the divisor (y). Adding ROUNDING to the dividend thus
+ * increases its magnitude before the integer division truncates the resulting
+ * quotient.
+ */
+
+#define PBD_IDIV_ROUNDING(x,y) ( (y)/2 - (PBD_IDIV_ASR((x)^(y)) & (y)))
+
+template<typename T>
+T int_div_round (T x, T y)
+{
+	/* essentially ((x + (y/2)) / y) but handles signed/negative values correcvtly */
+	return (x + PBD_IDIV_ROUNDING(x,y)) / y ;
+}
+
+#endif /* __libpbd_integer_division_h___ */