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
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
|
/* mpfr_grandom (rop1, rop2, state, rnd_mode) -- Generate up to two
pseudorandom real numbers according to a standard normal Gaussian
distribution and round it to the precision of rop1, rop2 according
to the given rounding mode.
Copyright 2011-2019 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
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
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
/* #define MPFR_NEED_LONGLONG_H */
#include "mpfr-impl.h"
int
mpfr_grandom (mpfr_ptr rop1, mpfr_ptr rop2, gmp_randstate_t rstate,
mpfr_rnd_t rnd)
{
int inex1, inex2, s1, s2;
mpz_t x, y, xp, yp, t, a, b, s;
mpfr_t sfr, l, r1, r2;
mpfr_prec_t tprec, tprec0;
inex2 = inex1 = 0;
if (rop2 == NULL) /* only one output requested. */
{
tprec0 = MPFR_PREC (rop1);
}
else
{
tprec0 = MAX (MPFR_PREC (rop1), MPFR_PREC (rop2));
}
tprec0 += 11;
/* We use "Marsaglia polar method" here (cf.
George Marsaglia, Normal (Gaussian) random variables for supercomputers
The Journal of Supercomputing, Volume 5, Number 1, 49–55
DOI: 10.1007/BF00155857).
First we draw uniform x and y in [0,1] using mpz_urandomb (in
fixed precision), and scale them to [-1, 1].
*/
mpz_init (xp);
mpz_init (yp);
mpz_init (x);
mpz_init (y);
mpz_init (t);
mpz_init (s);
mpz_init (a);
mpz_init (b);
mpfr_init2 (sfr, MPFR_PREC_MIN);
mpfr_init2 (l, MPFR_PREC_MIN);
mpfr_init2 (r1, MPFR_PREC_MIN);
if (rop2 != NULL)
mpfr_init2 (r2, MPFR_PREC_MIN);
mpz_set_ui (xp, 0);
mpz_set_ui (yp, 0);
for (;;)
{
tprec = tprec0;
do
{
mpz_urandomb (xp, rstate, tprec);
mpz_urandomb (yp, rstate, tprec);
mpz_mul (a, xp, xp);
mpz_mul (b, yp, yp);
mpz_add (s, a, b);
}
while (mpz_sizeinbase (s, 2) > tprec * 2); /* x^2 + y^2 <= 2^{2tprec} */
for (;;)
{
/* FIXME: compute s as s += 2x + 2y + 2 */
mpz_add_ui (a, xp, 1);
mpz_add_ui (b, yp, 1);
mpz_mul (a, a, a);
mpz_mul (b, b, b);
mpz_add (s, a, b);
if ((mpz_sizeinbase (s, 2) <= 2 * tprec) ||
((mpz_sizeinbase (s, 2) == 2 * tprec + 1) &&
(mpz_scan1 (s, 0) == 2 * tprec)))
goto yeepee;
/* Extend by 32 bits */
mpz_mul_2exp (xp, xp, 32);
mpz_mul_2exp (yp, yp, 32);
mpz_urandomb (x, rstate, 32);
mpz_urandomb (y, rstate, 32);
mpz_add (xp, xp, x);
mpz_add (yp, yp, y);
tprec += 32;
mpz_mul (a, xp, xp);
mpz_mul (b, yp, yp);
mpz_add (s, a, b);
if (mpz_sizeinbase (s, 2) > tprec * 2)
break;
}
}
yeepee:
/* FIXME: compute s with s -= 2x + 2y + 2 */
mpz_mul (a, xp, xp);
mpz_mul (b, yp, yp);
mpz_add (s, a, b);
/* Compute the signs of the output */
mpz_urandomb (x, rstate, 2);
s1 = mpz_tstbit (x, 0);
s2 = mpz_tstbit (x, 1);
for (;;)
{
/* s = xp^2 + yp^2 (loop invariant) */
mpfr_set_prec (sfr, 2 * tprec);
mpfr_set_prec (l, tprec);
mpfr_set_z (sfr, s, MPFR_RNDN); /* exact */
mpfr_mul_2si (sfr, sfr, -2 * tprec, MPFR_RNDN); /* exact */
mpfr_log (l, sfr, MPFR_RNDN);
mpfr_neg (l, l, MPFR_RNDN);
mpfr_mul_2si (l, l, 1, MPFR_RNDN);
mpfr_div (l, l, sfr, MPFR_RNDN);
mpfr_sqrt (l, l, MPFR_RNDN);
mpfr_set_prec (r1, tprec);
mpfr_mul_z (r1, l, xp, MPFR_RNDN);
mpfr_div_2ui (r1, r1, tprec, MPFR_RNDN); /* exact */
if (s1)
mpfr_neg (r1, r1, MPFR_RNDN);
if (MPFR_CAN_ROUND (r1, tprec - 2, MPFR_PREC (rop1), rnd))
{
if (rop2 != NULL)
{
mpfr_set_prec (r2, tprec);
mpfr_mul_z (r2, l, yp, MPFR_RNDN);
mpfr_div_2ui (r2, r2, tprec, MPFR_RNDN); /* exact */
if (s2)
mpfr_neg (r2, r2, MPFR_RNDN);
if (MPFR_CAN_ROUND (r2, tprec - 2, MPFR_PREC (rop2), rnd))
break;
}
else
break;
}
/* Extend by 32 bits */
mpz_mul_2exp (xp, xp, 32);
mpz_mul_2exp (yp, yp, 32);
mpz_urandomb (x, rstate, 32);
mpz_urandomb (y, rstate, 32);
mpz_add (xp, xp, x);
mpz_add (yp, yp, y);
tprec += 32;
mpz_mul (a, xp, xp);
mpz_mul (b, yp, yp);
mpz_add (s, a, b);
}
inex1 = mpfr_set (rop1, r1, rnd);
if (rop2 != NULL)
{
inex2 = mpfr_set (rop2, r2, rnd);
inex2 = mpfr_check_range (rop2, inex2, rnd);
}
inex1 = mpfr_check_range (rop1, inex1, rnd);
if (rop2 != NULL)
mpfr_clear (r2);
mpfr_clear (r1);
mpfr_clear (l);
mpfr_clear (sfr);
mpz_clear (b);
mpz_clear (a);
mpz_clear (s);
mpz_clear (t);
mpz_clear (y);
mpz_clear (x);
mpz_clear (yp);
mpz_clear (xp);
return INEX (inex1, inex2);
}
|
