summaryrefslogtreecommitdiff
path: root/Build/source/libs/mpfr/mpfr-src/src/erandom.c
diff options
context:
space:
mode:
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/erandom.c')
-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/erandom.c105
1 files changed, 105 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/erandom.c b/Build/source/libs/mpfr/mpfr-src/src/erandom.c
new file mode 100644
index 00000000000..b423bf4ec07
--- /dev/null
+++ b/Build/source/libs/mpfr/mpfr-src/src/erandom.c
@@ -0,0 +1,105 @@
+/* mpfr_erandom (rop, state, rnd_mode) -- Generate an exponential deviate with
+ mean 1 and round it to the precision of rop according to the given rounding
+ mode.
+
+Copyright 2013-2017 Free Software Foundation, Inc.
+Contributed by Charles Karney <charles@karney.com>, SRI International.
+
+This file is part of the GNU MPFR Library.
+
+The GNU MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MPFR Library 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 Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
+http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
+51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
+
+/*
+ * Sampling from the exponential distribution with unit mean using the method
+ * given in John von Neumann, Various techniques used in connection with random
+ * digits, in A. S. Householder, G. E. Forsythe, and H. H. Germond, editors,
+ * "Monte Carlo Method", number 12 in Applied Mathematics Series, pp. 36-38
+ * (NBS, Washington, DC, 1951), Proceedings of a symposium held June 29-July 1,
+ * 1949, in Los Angeles.
+ *
+ * A modification to this algorithm is given in:
+ * Charles F. F. Karney,
+ * "Sampling exactly from the normal distribution",
+ * ACM Trans. Math. Software 42(1), 3:1-14 (Jan. 2016).
+ * https://dx.doi.org/10.1145/2710016
+ * http://arxiv.org/abs/1303.6257
+ * Although this improves the bit efficiency, in practice, it results in
+ * a slightly slower algorithm for MPFR. So here the original von Neumann
+ * algorithm is used.
+ *
+ * There are a few "weasel words" regarding the accuracy of this
+ * implementation. The algorithm produces exactly rounded exponential deviates
+ * provided that gmp's random number engine delivers truly random bits. If it
+ * did, the algorithm would be perfect; however, this implementation would have
+ * problems, e.g., in that the integer part of the exponential deviate is
+ * represented by an unsigned long, whereas in reality the integer part in
+ * unbounded. In this implementation, asserts catch overflow in the integer
+ * part and similar (very, very) unlikely events. In reality, of course, gmp's
+ * random number engine has a finite internal state (19937 bits in the case of
+ * the MT19937 method). This means that these unlikely events in fact won't
+ * occur. If the asserts are triggered, then this is an indication that the
+ * random number engine is defective. (Even if a hardware random number
+ * generator were used, the most likely explanation for the triggering of the
+ * asserts would be that the hardware generator was broken.)
+ */
+
+#include "random_deviate.h"
+
+/* true with prob exp(-x) */
+static int
+E (mpfr_random_deviate_t x, gmp_randstate_t r,
+ mpfr_random_deviate_t p, mpfr_random_deviate_t q)
+{
+ /* p and q are temporaries */
+ mpfr_random_deviate_reset (p);
+ if (!mpfr_random_deviate_less (p, x, r))
+ return 1;
+ for (;;)
+ {
+ mpfr_random_deviate_reset (q);
+ if (!mpfr_random_deviate_less (q, p, r))
+ return 0;
+ mpfr_random_deviate_reset (p);
+ if (!mpfr_random_deviate_less (p, q, r))
+ return 1;
+ }
+}
+
+/* return an exponential random deviate with mean 1 as a MPFR */
+int
+mpfr_erandom (mpfr_t z, gmp_randstate_t r, mpfr_rnd_t rnd)
+{
+ mpfr_random_deviate_t x, p, q;
+ int inex;
+ unsigned long k = 0;
+
+ mpfr_random_deviate_init (x);
+ mpfr_random_deviate_init (p);
+ mpfr_random_deviate_init (q);
+ while (!E(x, r, p, q))
+ {
+ ++k;
+ /* Catch k wrapping around to 0; for a 32-bit unsigned long, the
+ * probability of this is exp(-2^32)). */
+ MPFR_ASSERTN (k != 0UL);
+ mpfr_random_deviate_reset (x);
+ }
+ mpfr_random_deviate_clear (q);
+ mpfr_random_deviate_clear (p);
+ inex = mpfr_random_deviate_value (0, k, x, z, r, rnd);
+ mpfr_random_deviate_clear (x);
+ return inex;
+}