Invent random_normal() to provide normally-distributed random numbers.

There is already a version of this in contrib/tablefunc, but it
seems sufficiently widely useful to justify having it in core.

Paul Ramsey

Discussion: https://postgr.es/m/CACowWR0DqHAvOKUCNxTrASFkWsDLqKMd6WiXvVvaWg4pV1BMnQ@mail.gmail.com

src/common/pg_prng.c

@@ -19,11 +19,17 @@
 
 #include "c.h"
 
-#include <math.h>				/* for ldexp() */
+#include <math.h>
 
 #include "common/pg_prng.h"
 #include "port/pg_bitutils.h"
 
+/* X/Open (XSI) requires <math.h> to provide M_PI, but core POSIX does not */
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+
 /* process-wide state vector */
 pg_prng_state pg_global_prng_state;
 
@@ -235,6 +241,35 @@ pg_prng_double(pg_prng_state *state)
 	return ldexp((double) (v >> (64 - 52)), -52);
 }
 
+/*
+ * Select a random double from the normal distribution with
+ * mean = 0.0 and stddev = 1.0.
+ *
+ * To get a result from a different normal distribution use
+ *   STDDEV * pg_prng_double_normal() + MEAN
+ *
+ * Uses https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
+ */
+double
+pg_prng_double_normal(pg_prng_state *state)
+{
+	double		u1,
+				u2,
+				z0;
+
+	/*
+	 * pg_prng_double generates [0, 1), but for the basic version of the
+	 * Box-Muller transform the two uniformly distributed random numbers are
+	 * expected to be in (0, 1]; in particular we'd better not compute log(0).
+	 */
+	u1 = 1.0 - pg_prng_double(state);
+	u2 = 1.0 - pg_prng_double(state);
+
+	/* Apply Box-Muller transform to get one normal-valued output */
+	z0 = sqrt(-2.0 * log(u1)) * sin(2.0 * M_PI * u2);
+	return z0;
+}
+
 /*
  * Select a random boolean value.
  */