1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
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 2013-2018 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;
}
|
