Mercurial > octave
annotate liboctave/numeric/randmtzig.cc @ 29163:8f67ad8b3103
maint: Updating naming conventions for exceptions and use const where possible.
* GLCanvas.cc, interpreter-qobject.cc, file-editor-tab.cc,
octave-qscintilla.cc, octave-qobject.cc, Cell.cc, __eigs__.cc,
__magick_read__.cc, __qp__.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
file-io.cc, graphics.cc, graphics.in.h, input.cc, interpreter.cc,
ls-mat-ascii.cc, lsode.cc, oct-handle.h, oct-map.cc, quad.cc, rand.cc,
sparse.cc, sub2ind.cc, toplev.cc, utils.cc, __init_gnuplot__.cc, __ode15__.cc,
cdef-object.cc, ov-base-diag.cc, ov-base-mat.cc, ov-base-sparse.cc,
ov-base.cc, ov-fcn-handle.cc, ov-java.cc, ov-perm.cc, ov-range.cc,
ov-re-diag.cc, ov-str-mat.cc, ov.cc, pt-assign.cc, pt-eval.cc, pt-idx.cc,
pt-jit.cc, pt.cc, Array-util.cc, randmtzig.cc:
Update naming conventions for exceptions to use initial letter of exception
type. For example, "execution_exception" is named "ee", "index_exception" is
"ie". Catch "const" exceptions where possible.
* gzip.cc: Add block to catch and throw interrupt_exceptions before having
a catch block "(...)" for everything else.
author | Rik <rik@octave.org> |
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date | Tue, 08 Dec 2020 13:25:03 -0800 |
parents | a61b651914d6 |
children | 5c14f81e0937 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2006-2020 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
7019 | 25 |
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26 /* |
5742 | 27 A C-program for MT19937, with initialization improved 2002/2/10. |
28 Coded by Takuji Nishimura and Makoto Matsumoto. | |
29 This is a faster version by taking Shawn Cokus's optimization, | |
30 Matthe Bellew's simplification, Isaku Wada's real version. | |
31 David Bateman added normal and exponential distributions following | |
32 Marsaglia and Tang's Ziggurat algorithm. | |
33 | |
34 Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, | |
35 Copyright (C) 2004, David Bateman | |
36 All rights reserved. | |
37 | |
38 Redistribution and use in source and binary forms, with or without | |
39 modification, are permitted provided that the following conditions | |
40 are met: | |
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41 |
5742 | 42 1. Redistributions of source code must retain the above copyright |
43 notice, this list of conditions and the following disclaimer. | |
44 | |
45 2. Redistributions in binary form must reproduce the above copyright | |
46 notice, this list of conditions and the following disclaimer in the | |
47 documentation and/or other materials provided with the distribution. | |
48 | |
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49 3. The names of its contributors may not be used to endorse or promote |
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50 products derived from this software without specific prior written |
5742 | 51 permission. |
52 | |
53 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
54 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
55 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
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56 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER |
5742 | 57 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
58 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, | |
59 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
60 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF | |
61 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING | |
62 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS | |
63 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
64 | |
65 | |
66 Any feedback is very welcome. | |
67 http://www.math.keio.ac.jp/matumoto/emt.html | |
68 email: matumoto@math.keio.ac.jp | |
69 | |
70 * 2004-01-19 Paul Kienzle | |
71 * * comment out main | |
72 * add init_by_entropy, get_state, set_state | |
73 * * converted to allow compiling by C++ compiler | |
74 * | |
75 * 2004-01-25 David Bateman | |
76 * * Add Marsaglia and Tsang Ziggurat code | |
77 * | |
78 * 2004-07-13 Paul Kienzle | |
79 * * make into an independent library with some docs. | |
80 * * introduce new main and test code. | |
81 * | |
82 * 2004-07-28 Paul Kienzle & David Bateman | |
83 * * add -DALLBITS flag for 32 vs. 53 bits of randomness in mantissa | |
84 * * make the naming scheme more uniform | |
85 * * add -DHAVE_X86 for faster support of 53 bit mantissa on x86 arch. | |
86 * | |
87 * 2005-02-23 Paul Kienzle | |
88 * * fix -DHAVE_X86_32 flag and add -DUSE_X86_32=0|1 for explicit control | |
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89 * |
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90 * 2006-04-01 David Bateman |
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91 * * convert for use in octave, declaring static functions only used |
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92 * here and adding oct_ to functions visible externally |
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93 * * inverse sense of ALLBITS |
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94 * |
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95 * 2012-05-18 David Bateman |
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96 * * Remove randu64 and ALLBIT option |
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97 * * Add the single precision generators |
5742 | 98 */ |
99 | |
100 /* | |
101 === Build instructions === | |
102 | |
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103 Compile with -DHAVE_GETTIMEOFDAY if the gettimeofday function is |
5742 | 104 available. This is not necessary if your architecture has |
105 /dev/urandom defined. | |
106 | |
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107 Uses implicit -Di386 or explicit -DHAVE_X86_32 to determine if CPU=x86. |
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108 You can force X86 behavior with -DUSE_X86_32=1, or suppress it with |
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109 -DUSE_X86_32=0. You should also consider -march=i686 or similar for |
5742 | 110 extra performance. Check whether -DUSE_X86_32=0 is faster on 64-bit |
111 x86 architectures. | |
112 | |
113 If you want to replace the Mersenne Twister with another | |
114 generator then redefine randi32 appropriately. | |
115 | |
116 === Usage instructions === | |
117 Before using any of the generators, initialize the state with one of | |
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118 the init_mersenne_twister functions. |
5742 | 119 |
120 All generators share the same state vector. | |
121 | |
122 === Mersenne Twister === | |
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123 random initial state: |
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124 void init_mersenne_twister (void) |
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125 |
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126 // 32-bit initial state: |
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127 void init_mersenne_twister (uint32_t s) |
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128 |
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129 // m*32-bit initial state: |
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130 void init_mersenne_twister (uint32_t k[],int m) |
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131 |
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132 // saves state in array: |
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133 void get_mersenne_twister_state (uint32_t save[MT_N+1]) |
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134 |
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135 // restores state from array |
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136 void set_mersenne_twister_state (uint32_t save[MT_N+1]) |
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137 |
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138 static uint32_t randmt (void) returns 32-bit unsigned int |
5742 | 139 |
140 === inline generators === | |
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141 static uint32_t randi32 (void) returns 32-bit unsigned int |
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142 static uint64_t randi53 (void) returns 53-bit unsigned int |
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143 static uint64_t randi54 (void) returns 54-bit unsigned int |
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144 static float randu24 (void) returns 24-bit uniform in (0,1) |
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145 static double randu53 (void) returns 53-bit uniform in (0,1) |
5742 | 146 |
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147 double rand_uniform (void) returns M-bit uniform in (0,1) |
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148 double rand_normal (void) returns M-bit standard normal |
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149 double rand_exponential (void) returns N-bit standard exponential |
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150 |
5742 | 151 === Array generators === |
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152 void rand_uniform (octave_idx_type, double []) |
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153 void rand_normal (octave_idx_type, double []) |
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154 void rand_exponential (octave_idx_type, double []) |
5742 | 155 */ |
156 | |
157 #if defined (HAVE_CONFIG_H) | |
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158 # include "config.h" |
5742 | 159 #endif |
160 | |
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161 #include <cmath> |
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162 #include <cstdio> |
5742 | 163 |
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164 #include <algorithm> |
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165 #include <random> |
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166 |
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167 #include "oct-syscalls.h" |
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168 #include "oct-time.h" |
5742 | 169 #include "randmtzig.h" |
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170 |
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171 /* FIXME: may want to suppress X86 if sizeof(long) > 4 */ |
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172 #if ! defined (USE_X86_32) |
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173 # if defined (i386) || defined (HAVE_X86_32) |
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174 # define USE_X86_32 1 |
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175 # else |
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176 # define USE_X86_32 0 |
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177 # endif |
5742 | 178 #endif |
179 | |
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180 namespace octave |
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181 { |
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182 /* ===== Mersenne Twister 32-bit generator ===== */ |
5742 | 183 |
184 #define MT_M 397 | |
185 #define MATRIX_A 0x9908b0dfUL /* constant vector a */ | |
186 #define UMASK 0x80000000UL /* most significant w-r bits */ | |
187 #define LMASK 0x7fffffffUL /* least significant r bits */ | |
188 #define MIXBITS(u,v) ( ((u) & UMASK) | ((v) & LMASK) ) | |
189 #define TWIST(u,v) ((MIXBITS(u,v) >> 1) ^ ((v)&1UL ? MATRIX_A : 0UL)) | |
190 | |
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191 static uint32_t *next; |
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192 static uint32_t state[MT_N]; /* the array for the state vector */ |
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193 static int left = 1; |
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194 static int initf = 0; |
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195 static int initt = 1; |
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196 static int inittf = 1; |
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198 /* initializes state[MT_N] with a seed */ |
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199 void init_mersenne_twister (const uint32_t s) |
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200 { |
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201 int j; |
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202 state[0] = s & 0xffffffffUL; |
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203 for (j = 1; j < MT_N; j++) |
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204 { |
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205 state[j] = (1812433253UL * (state[j-1] ^ (state[j-1] >> 30)) + j); |
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206 /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */ |
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207 /* In the previous versions, MSBs of the seed affect */ |
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208 /* only MSBs of the array state[]. */ |
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209 /* 2002/01/09 modified by Makoto Matsumoto */ |
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210 state[j] &= 0xffffffffUL; /* for >32 bit machines */ |
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211 } |
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212 left = 1; |
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213 initf = 1; |
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214 } |
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216 /* initialize by an array with array-length */ |
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217 /* init_key is the array for initializing keys */ |
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218 /* key_length is its length */ |
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219 void init_mersenne_twister (const uint32_t *init_key, const int key_length) |
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220 { |
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221 int i, j, k; |
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222 init_mersenne_twister (19650218UL); |
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223 i = 1; |
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224 j = 0; |
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225 k = (MT_N > key_length ? MT_N : key_length); |
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226 for (; k; k--) |
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227 { |
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228 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1664525UL)) |
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229 + init_key[j] + j; /* non linear */ |
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230 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
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231 i++; |
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232 j++; |
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233 if (i >= MT_N) |
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234 { |
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235 state[0] = state[MT_N-1]; |
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236 i = 1; |
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237 } |
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238 if (j >= key_length) |
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239 j = 0; |
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240 } |
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241 for (k = MT_N - 1; k; k--) |
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242 { |
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243 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL)) |
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244 - i; /* non linear */ |
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245 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
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246 i++; |
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247 if (i >= MT_N) |
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248 { |
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249 state[0] = state[MT_N-1]; |
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250 i = 1; |
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251 } |
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252 } |
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254 state[0] = 0x80000000UL; /* MSB is 1; assuring nonzero initial array */ |
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255 left = 1; |
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256 initf = 1; |
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257 } |
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259 void init_mersenne_twister (void) |
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260 { |
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261 uint32_t entropy[MT_N]; |
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262 int n = 0; |
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264 // Gather some entropy from various sources |
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265 |
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266 sys::time now; |
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267 |
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268 // Current time in seconds |
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269 if (n < MT_N) |
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270 entropy[n++] = now.unix_time (); |
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271 |
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272 // CPU time used (usec) |
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273 if (n < MT_N) |
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274 entropy[n++] = clock (); |
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275 |
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276 // Fractional part of current time |
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277 if (n < MT_N) |
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278 entropy[n++] = now.usec (); |
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279 |
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280 // Include the PID to make sure that several processes reaching here at the |
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281 // same time use different random numbers. |
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282 if (n < MT_N) |
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283 entropy[n++] = sys::getpid (); |
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284 |
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285 if (n < MT_N) |
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286 { |
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287 try |
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288 { |
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289 // The standard doesn't *guarantee* that random_device provides |
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290 // non-deterministic random numbers. So add entropy from this |
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291 // source last to make sure we gathered at least some entropy from |
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292 // the earlier sources. |
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293 std::random_device rd; |
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294 std::uniform_int_distribution<uint32_t> dist; |
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295 // Add 1024 bit of "true" entropy |
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296 int n_max = std::min (n + 32, MT_N); |
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297 while (n < n_max) |
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298 entropy[n++] = dist (rd); |
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299 } |
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300 catch (const std::exception&) |
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301 { |
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302 // Just ignore any exception and skip that source of entropy. |
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303 } |
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304 } |
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305 |
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306 // Send all the entropy into the initial state vector |
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307 init_mersenne_twister (entropy, n); |
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308 } |
5742 | 309 |
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310 void set_mersenne_twister_state (const uint32_t *save) |
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311 { |
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312 std::copy_n (save, MT_N, state); |
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313 left = save[MT_N]; |
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314 next = state + (MT_N - left + 1); |
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315 } |
5742 | 316 |
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317 void get_mersenne_twister_state (uint32_t *save) |
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318 { |
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319 std::copy_n (state, MT_N, save); |
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320 save[MT_N] = left; |
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321 } |
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323 static void next_state (void) |
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324 { |
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325 uint32_t *p = state; |
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326 int j; |
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328 /* if init_by_int() has not been called, */ |
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329 /* a default initial seed is used */ |
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330 /* if (initf==0) init_by_int(5489UL); */ |
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331 /* Or better yet, a random seed! */ |
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332 if (initf == 0) |
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333 init_mersenne_twister (); |
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335 left = MT_N; |
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336 next = state; |
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337 |
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338 for (j = MT_N - MT_M + 1; --j; p++) |
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339 *p = p[MT_M] ^ TWIST(p[0], p[1]); |
5742 | 340 |
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341 for (j = MT_M; --j; p++) |
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342 *p = p[MT_M-MT_N] ^ TWIST(p[0], p[1]); |
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344 *p = p[MT_M-MT_N] ^ TWIST(p[0], state[0]); |
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345 } |
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346 |
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347 /* generates a random number on [0,0xffffffff]-interval */ |
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348 static uint32_t randmt (void) |
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349 { |
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350 uint32_t y; |
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352 if (--left == 0) |
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353 next_state (); |
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354 y = *next++; |
5742 | 355 |
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356 /* Tempering */ |
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357 y ^= (y >> 11); |
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358 y ^= (y << 7) & 0x9d2c5680UL; |
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359 y ^= (y << 15) & 0xefc60000UL; |
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360 return (y ^ (y >> 18)); |
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361 } |
5742 | 362 |
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363 /* ===== Uniform generators ===== */ |
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365 /* Select which 32 bit generator to use */ |
5742 | 366 #define randi32 randmt |
367 | |
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368 static uint64_t randi53 (void) |
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369 { |
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370 const uint32_t lo = randi32 (); |
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371 const uint32_t hi = randi32 () & 0x1FFFFF; |
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372 #if defined (HAVE_X86_32) |
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373 uint64_t u; |
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374 uint32_t *p = (uint32_t *)&u; |
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375 p[0] = lo; |
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376 p[1] = hi; |
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377 return u; |
5742 | 378 #else |
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379 return ((static_cast<uint64_t> (hi) << 32) | lo); |
5742 | 380 #endif |
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381 } |
5742 | 382 |
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383 static uint64_t randi54 (void) |
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384 { |
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385 const uint32_t lo = randi32 (); |
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386 const uint32_t hi = randi32 () & 0x3FFFFF; |
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387 #if defined (HAVE_X86_32) |
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388 uint64_t u; |
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389 uint32_t *p = static_cast<uint32_t *> (&u); |
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390 p[0] = lo; |
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391 p[1] = hi; |
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392 return u; |
5742 | 393 #else |
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394 return ((static_cast<uint64_t> (hi) << 32) | lo); |
5742 | 395 #endif |
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396 } |
5742 | 397 |
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398 /* generates a random number on (0,1)-real-interval */ |
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399 static float randu24 (void) |
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400 { |
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401 uint32_t i; |
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402 |
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403 do |
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404 { |
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405 i = randi32 () & static_cast<uint32_t> (0xFFFFFF); |
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406 } |
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407 while (i == 0); |
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408 |
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409 return i * (1.0f / 16777216.0f); |
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410 } |
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411 |
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412 /* generates a random number on (0,1) with 53-bit resolution */ |
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413 static double randu53 (void) |
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414 { |
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415 int32_t a, b; |
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416 |
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417 do |
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418 { |
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419 a = randi32 () >> 5; |
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420 b = randi32 () >> 6; |
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421 } |
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422 while (a == 0 && b == 0); |
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423 |
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424 return (a*67108864.0 + b) * (1.0/9007199254740992.0); |
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425 } |
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426 |
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427 /* Determine mantissa for uniform doubles */ |
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428 template <> |
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429 double |
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430 rand_uniform<double> (void) |
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431 { |
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432 return randu53 (); |
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433 } |
5742 | 434 |
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435 /* Determine mantissa for uniform floats */ |
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436 template <> |
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437 float |
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438 rand_uniform<float> (void) |
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439 { |
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440 return randu24 (); |
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441 } |
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442 |
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443 /* ===== Ziggurat normal and exponential generators ===== */ |
5742 | 444 |
445 #define ZIGGURAT_TABLE_SIZE 256 | |
446 | |
447 #define ZIGGURAT_NOR_R 3.6541528853610088 | |
448 #define ZIGGURAT_NOR_INV_R 0.27366123732975828 | |
449 #define NOR_SECTION_AREA 0.00492867323399 | |
450 | |
451 #define ZIGGURAT_EXP_R 7.69711747013104972 | |
452 #define ZIGGURAT_EXP_INV_R 0.129918765548341586 | |
453 #define EXP_SECTION_AREA 0.0039496598225815571993 | |
454 | |
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455 #define ZIGINT uint64_t |
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456 #define EMANTISSA 9007199254740992.0 /* 53 bit mantissa */ |
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457 #define ERANDI randi53() /* 53 bits for mantissa */ |
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458 #define NMANTISSA EMANTISSA |
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459 #define NRANDI randi54() /* 53 bits for mantissa + 1 bit sign */ |
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460 #define RANDU randu53() |
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461 |
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462 static ZIGINT ki[ZIGGURAT_TABLE_SIZE]; |
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463 static double wi[ZIGGURAT_TABLE_SIZE], fi[ZIGGURAT_TABLE_SIZE]; |
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464 static ZIGINT ke[ZIGGURAT_TABLE_SIZE]; |
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465 static double we[ZIGGURAT_TABLE_SIZE], fe[ZIGGURAT_TABLE_SIZE]; |
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466 |
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467 /* |
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468 This code is based on the paper Marsaglia and Tsang, "The ziggurat method |
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469 for generating random variables", Journ. Statistical Software. Code was |
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470 presented in this paper for a Ziggurat of 127 levels and using a 32 bit |
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471 integer random number generator. This version of the code, uses the |
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472 Mersenne Twister as the integer generator and uses 256 levels in the |
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473 Ziggurat. This has several advantages. |
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475 1) As Marsaglia and Tsang themselves states, the more levels the few |
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476 times the expensive tail algorithm must be called |
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477 2) The cycle time of the generator is determined by the integer |
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478 generator, thus the use of a Mersenne Twister for the core random |
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479 generator makes this cycle extremely long. |
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480 3) The license on the original code was unclear, thus rewriting the code |
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481 from the article means we are free of copyright issues. |
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482 4) Compile flag for full 53-bit random mantissa. |
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484 It should be stated that the authors made my life easier, by the fact that |
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485 the algorithm developed in the text of the article is for a 256 level |
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486 ziggurat, even if the code itself isn't... |
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488 One modification to the algorithm developed in the article, is that it is |
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489 assumed that 0 <= x < Inf, and "unsigned long"s are used, thus resulting in |
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490 terms like 2^32 in the code. As the normal distribution is defined between |
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491 -Inf < x < Inf, we effectively only have 31 bit integers plus a sign. Thus |
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492 in Marsaglia and Tsang, terms like 2^32 become 2^31. We use NMANTISSA for |
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493 this term. The exponential distribution is one sided so we use the |
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494 full 32 bits. We use EMANTISSA for this term. |
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496 It appears that I'm slightly slower than the code in the article, this |
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497 is partially due to a better generator of random integers than they |
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498 use. But might also be that the case of rapid return was optimized by |
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499 inlining the relevant code with a #define. As the basic Mersenne |
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500 Twister is only 25% faster than this code I suspect that the main |
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501 reason is just the use of the Mersenne Twister and not the inlining, |
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502 so I'm not going to try and optimize further. |
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503 */ |
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505 void create_ziggurat_tables (void) |
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506 { |
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507 int i; |
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508 double x, x1; |
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509 |
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510 /* Ziggurat tables for the normal distribution */ |
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511 x1 = ZIGGURAT_NOR_R; |
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512 wi[255] = x1 / NMANTISSA; |
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513 fi[255] = exp (-0.5 * x1 * x1); |
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514 |
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515 /* Index zero is special for tail strip, where Marsaglia and Tsang |
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516 * defines this as |
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517 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1, |
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518 * where v is the area of each strip of the ziggurat. |
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519 */ |
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520 ki[0] = static_cast<ZIGINT> (x1 * fi[255] / NOR_SECTION_AREA * NMANTISSA); |
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521 wi[0] = NOR_SECTION_AREA / fi[255] / NMANTISSA; |
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522 fi[0] = 1.; |
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524 for (i = 254; i > 0; i--) |
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525 { |
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526 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus |
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527 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y)) |
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528 */ |
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529 x = std::sqrt (-2. * std::log (NOR_SECTION_AREA / x1 + fi[i+1])); |
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530 ki[i+1] = static_cast<ZIGINT> (x / x1 * NMANTISSA); |
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531 wi[i] = x / NMANTISSA; |
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532 fi[i] = exp (-0.5 * x * x); |
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533 x1 = x; |
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534 } |
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536 ki[1] = 0; |
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538 /* Zigurrat tables for the exponential distribution */ |
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539 x1 = ZIGGURAT_EXP_R; |
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540 we[255] = x1 / EMANTISSA; |
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541 fe[255] = exp (-x1); |
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543 /* Index zero is special for tail strip, where Marsaglia and Tsang |
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544 * defines this as |
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545 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1, |
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546 * where v is the area of each strip of the ziggurat. |
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547 */ |
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548 ke[0] = static_cast<ZIGINT> (x1 * fe[255] / EXP_SECTION_AREA * EMANTISSA); |
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549 we[0] = EXP_SECTION_AREA / fe[255] / EMANTISSA; |
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550 fe[0] = 1.; |
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552 for (i = 254; i > 0; i--) |
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553 { |
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554 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus |
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555 * need inverse operator of y = exp(-x) -> x = -ln(y) |
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556 */ |
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557 x = - std::log (EXP_SECTION_AREA / x1 + fe[i+1]); |
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558 ke[i+1] = static_cast<ZIGINT> (x / x1 * EMANTISSA); |
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559 we[i] = x / EMANTISSA; |
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560 fe[i] = exp (-x); |
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561 x1 = x; |
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562 } |
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563 ke[1] = 0; |
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565 initt = 0; |
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566 } |
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568 /* |
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569 * Here is the guts of the algorithm. As Marsaglia and Tsang state the |
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570 * algorithm in their paper |
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571 * |
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572 * 1) Calculate a random signed integer j and let i be the index |
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573 * provided by the rightmost 8-bits of j |
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574 * 2) Set x = j * w_i. If j < k_i return x |
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575 * 3) If i = 0, then return x from the tail |
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576 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x |
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577 * 5) goto step 1 |
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578 * |
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579 * Where f is the functional form of the distribution, which for a normal |
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580 * distribution is exp(-0.5*x*x) |
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581 */ |
5742 | 582 |
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583 |
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584 template <> double rand_normal<double> (void) |
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585 { |
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586 if (initt) |
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587 create_ziggurat_tables (); |
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589 while (1) |
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590 { |
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591 /* The following code is specialized for 32-bit mantissa. |
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592 * Compared to the arbitrary mantissa code, there is a performance |
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593 * gain for 32-bits: PPC: 2%, MIPS: 8%, x86: 40% |
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594 * There is a bigger performance gain compared to using a full |
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595 * 53-bit mantissa: PPC: 60%, MIPS: 65%, x86: 240% |
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596 * Of course, different compilers and operating systems may |
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597 * have something to do with this. |
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598 */ |
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599 # if defined (HAVE_X86_32) |
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600 /* 53-bit mantissa, 1-bit sign, x86 32-bit architecture */ |
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601 double x; |
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602 int si,idx; |
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603 uint32_t lo, hi; |
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604 int64_t rabs; |
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605 uint32_t *p = (uint32_t *)&rabs; |
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606 lo = randi32 (); |
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607 idx = lo & 0xFF; |
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608 hi = randi32 (); |
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609 si = hi & UMASK; |
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610 p[0] = lo; |
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611 p[1] = hi & 0x1FFFFF; |
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612 x = ( si ? -rabs : rabs ) * wi[idx]; |
22188 | 613 # else |
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614 /* arbitrary mantissa (selected by NRANDI, with 1 bit for sign) */ |
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615 const uint64_t r = NRANDI; |
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616 const int64_t rabs = r >> 1; |
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617 const int idx = static_cast<int> (rabs & 0xFF); |
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618 const double x = ( (r & 1) ? -rabs : rabs) * wi[idx]; |
22188 | 619 # endif |
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620 if (rabs < static_cast<int64_t> (ki[idx])) |
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621 return x; /* 99.3% of the time we return here 1st try */ |
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622 else if (idx == 0) |
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623 { |
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624 /* As stated in Marsaglia and Tsang |
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625 * |
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626 * For the normal tail, the method of Marsaglia[5] provides: |
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627 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, |
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628 * then return r+x. Except that r+x is always in the positive |
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629 * tail!!!! Any thing random might be used to determine the |
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630 * sign, but as we already have r we might as well use it |
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631 * |
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632 * [PAK] but not the bottom 8 bits, since they are all 0 here! |
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633 */ |
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634 double xx, yy; |
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635 do |
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636 { |
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637 xx = - ZIGGURAT_NOR_INV_R * std::log (RANDU); |
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638 yy = - std::log (RANDU); |
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639 } |
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640 while ( yy+yy <= xx*xx); |
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641 return ((rabs & 0x100) ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); |
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642 } |
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643 else if ((fi[idx-1] - fi[idx]) * RANDU + fi[idx] < exp (-0.5*x*x)) |
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644 return x; |
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645 } |
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646 } |
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647 |
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648 template <> double rand_exponential<double> (void) |
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649 { |
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650 if (initt) |
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651 create_ziggurat_tables (); |
5742 | 652 |
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653 while (1) |
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654 { |
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655 ZIGINT ri = ERANDI; |
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656 const int idx = static_cast<int> (ri & 0xFF); |
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657 const double x = ri * we[idx]; |
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658 if (ri < ke[idx]) |
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659 return x; /* 98.9% of the time we return here 1st try */ |
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660 else if (idx == 0) |
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661 { |
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662 /* As stated in Marsaglia and Tsang |
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663 * |
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664 * For the exponential tail, the method of Marsaglia[5] provides: |
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665 * x = r - ln(U); |
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666 */ |
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667 return ZIGGURAT_EXP_R - std::log (RANDU); |
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668 } |
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669 else if ((fe[idx-1] - fe[idx]) * RANDU + fe[idx] < exp (-x)) |
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670 return x; |
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671 } |
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672 } |
5742 | 673 |
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674 template <> void rand_uniform<double> (octave_idx_type n, double *p) |
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675 { |
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676 std::generate_n (p, n, [](void) { return rand_uniform<double> (); }); |
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677 } |
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678 |
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679 template <> void rand_normal (octave_idx_type n, double *p) |
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680 { |
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681 std::generate_n (p, n, [](void) { return rand_normal<double> (); }); |
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682 } |
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683 |
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684 template <> void rand_exponential (octave_idx_type n, double *p) |
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685 { |
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686 std::generate_n (p, n, [](void) { return rand_exponential<double> (); }); |
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687 } |
5742 | 688 |
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689 #undef ZIGINT |
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690 #undef EMANTISSA |
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691 #undef ERANDI |
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692 #undef NMANTISSA |
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693 #undef NRANDI |
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694 #undef RANDU |
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695 |
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696 #define ZIGINT uint32_t |
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697 #define EMANTISSA 4294967296.0 /* 32 bit mantissa */ |
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698 #define ERANDI randi32() /* 32 bits for mantissa */ |
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699 #define NMANTISSA 2147483648.0 /* 31 bit mantissa */ |
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700 #define NRANDI randi32() /* 31 bits for mantissa + 1 bit sign */ |
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701 #define RANDU randu24() |
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702 |
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703 static ZIGINT fki[ZIGGURAT_TABLE_SIZE]; |
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704 static float fwi[ZIGGURAT_TABLE_SIZE], ffi[ZIGGURAT_TABLE_SIZE]; |
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705 static ZIGINT fke[ZIGGURAT_TABLE_SIZE]; |
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706 static float fwe[ZIGGURAT_TABLE_SIZE], ffe[ZIGGURAT_TABLE_SIZE]; |
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707 |
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708 static void create_ziggurat_float_tables (void) |
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709 { |
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710 int i; |
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711 float x, x1; |
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712 |
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713 /* Ziggurat tables for the normal distribution */ |
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714 x1 = ZIGGURAT_NOR_R; |
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715 fwi[255] = x1 / NMANTISSA; |
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716 ffi[255] = exp (-0.5 * x1 * x1); |
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717 |
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718 /* Index zero is special for tail strip, where Marsaglia and Tsang |
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719 * defines this as |
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720 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1, |
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721 * where v is the area of each strip of the ziggurat. |
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722 */ |
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723 fki[0] = static_cast<ZIGINT> (x1 * ffi[255] / NOR_SECTION_AREA * NMANTISSA); |
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724 fwi[0] = NOR_SECTION_AREA / ffi[255] / NMANTISSA; |
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725 ffi[0] = 1.; |
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726 |
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727 for (i = 254; i > 0; i--) |
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728 { |
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729 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus |
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730 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y)) |
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731 */ |
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732 x = std::sqrt (-2. * std::log (NOR_SECTION_AREA / x1 + ffi[i+1])); |
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733 fki[i+1] = static_cast<ZIGINT> (x / x1 * NMANTISSA); |
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734 fwi[i] = x / NMANTISSA; |
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735 ffi[i] = exp (-0.5 * x * x); |
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736 x1 = x; |
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737 } |
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738 |
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739 fki[1] = 0; |
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740 |
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741 /* Zigurrat tables for the exponential distribution */ |
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742 x1 = ZIGGURAT_EXP_R; |
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743 fwe[255] = x1 / EMANTISSA; |
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744 ffe[255] = exp (-x1); |
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745 |
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746 /* Index zero is special for tail strip, where Marsaglia and Tsang |
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747 * defines this as |
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748 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1, |
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749 * where v is the area of each strip of the ziggurat. |
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750 */ |
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751 fke[0] = static_cast<ZIGINT> (x1 * ffe[255] / EXP_SECTION_AREA * EMANTISSA); |
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752 fwe[0] = EXP_SECTION_AREA / ffe[255] / EMANTISSA; |
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753 ffe[0] = 1.; |
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754 |
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755 for (i = 254; i > 0; i--) |
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756 { |
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757 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus |
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758 * need inverse operator of y = exp(-x) -> x = -ln(y) |
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759 */ |
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760 x = - std::log (EXP_SECTION_AREA / x1 + ffe[i+1]); |
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761 fke[i+1] = static_cast<ZIGINT> (x / x1 * EMANTISSA); |
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762 fwe[i] = x / EMANTISSA; |
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763 ffe[i] = exp (-x); |
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764 x1 = x; |
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765 } |
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766 fke[1] = 0; |
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767 |
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768 inittf = 0; |
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769 } |
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770 |
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771 /* |
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772 * Here is the guts of the algorithm. As Marsaglia and Tsang state the |
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773 * algorithm in their paper |
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774 * |
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775 * 1) Calculate a random signed integer j and let i be the index |
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776 * provided by the rightmost 8-bits of j |
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777 * 2) Set x = j * w_i. If j < k_i return x |
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778 * 3) If i = 0, then return x from the tail |
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779 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x |
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780 * 5) goto step 1 |
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781 * |
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782 * Where f is the functional form of the distribution, which for a normal |
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783 * distribution is exp(-0.5*x*x) |
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784 */ |
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785 |
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786 template <> float rand_normal<float> (void) |
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787 { |
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788 if (inittf) |
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789 create_ziggurat_float_tables (); |
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790 |
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791 while (1) |
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792 { |
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793 /* 32-bit mantissa */ |
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794 const uint32_t r = randi32 (); |
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795 const uint32_t rabs = r & LMASK; |
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796 const int idx = static_cast<int> (r & 0xFF); |
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797 const float x = static_cast<int32_t> (r) * fwi[idx]; |
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798 if (rabs < fki[idx]) |
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799 return x; /* 99.3% of the time we return here 1st try */ |
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800 else if (idx == 0) |
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801 { |
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802 /* As stated in Marsaglia and Tsang |
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803 * |
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804 * For the normal tail, the method of Marsaglia[5] provides: |
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805 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, |
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806 * then return r+x. Except that r+x is always in the positive |
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807 * tail!!!! Any thing random might be used to determine the |
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808 * sign, but as we already have r we might as well use it |
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809 * |
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810 * [PAK] but not the bottom 8 bits, since they are all 0 here! |
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811 */ |
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812 float xx, yy; |
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813 do |
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814 { |
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815 xx = - ZIGGURAT_NOR_INV_R * std::log (RANDU); |
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816 yy = - std::log (RANDU); |
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817 } |
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818 while ( yy+yy <= xx*xx); |
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819 return ((rabs & 0x100) ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); |
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820 } |
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821 else if ((ffi[idx-1] - ffi[idx]) * RANDU + ffi[idx] < exp (-0.5*x*x)) |
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822 return x; |
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823 } |
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824 } |
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825 |
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826 template <> float rand_exponential<float> (void) |
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827 { |
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828 if (inittf) |
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829 create_ziggurat_float_tables (); |
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830 |
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831 while (1) |
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832 { |
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833 ZIGINT ri = ERANDI; |
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834 const int idx = static_cast<int> (ri & 0xFF); |
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835 const float x = ri * fwe[idx]; |
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836 if (ri < fke[idx]) |
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837 return x; /* 98.9% of the time we return here 1st try */ |
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838 else if (idx == 0) |
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839 { |
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840 /* As stated in Marsaglia and Tsang |
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841 * |
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842 * For the exponential tail, the method of Marsaglia[5] provides: |
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843 * x = r - ln(U); |
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844 */ |
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845 return ZIGGURAT_EXP_R - std::log (RANDU); |
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846 } |
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847 else if ((ffe[idx-1] - ffe[idx]) * RANDU + ffe[idx] < exp (-x)) |
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848 return x; |
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849 } |
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850 } |
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851 |
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852 template <> void rand_uniform (octave_idx_type n, float *p) |
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853 { |
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854 std::generate_n (p, n, [](void) { return rand_uniform<float> (); }); |
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855 } |
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856 |
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857 template <> void rand_normal (octave_idx_type n, float *p) |
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858 { |
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859 std::generate_n (p, n, [](void) { return rand_normal<float> (); }); |
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860 } |
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861 |
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862 template <> void rand_exponential (octave_idx_type n, float *p) |
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863 { |
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864 std::generate_n (p, n, [](void) { return rand_exponential<float> (); }); |
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865 } |
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866 } |
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867 |