Mercurial > hg > octave-nkf
annotate liboctave/numeric/randmtzig.c @ 19139:d5db1019ad4a
load-save.cc: Return string rather printing to octave_stdout
| author | Andreas Weber <andy.weber.aw@gmail.com> |
|---|---|
| date | Mon, 21 Jul 2014 18:27:10 +0200 |
| parents | 9ac2357f19bc |
| children | 4197fc428c7d |
| rev | line source |
|---|---|
| 7019 | 1 /* |
| 2 | |
|
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3 Copyright (C) 2006-2013 John W. Eaton |
| 7019 | 4 |
| 5 This file is part of Octave. | |
| 6 | |
| 7 Octave is free software; you can redistribute it and/or modify it | |
| 8 under the terms of the GNU General Public License as published by the | |
| 9 Free Software Foundation; either version 3 of the License, or (at your | |
| 10 option) any later version. | |
| 11 | |
| 12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 15 for more details. | |
| 16 | |
| 17 You should have received a copy of the GNU General Public License | |
| 18 along with Octave; see the file COPYING. If not, see | |
| 19 <http://www.gnu.org/licenses/>. | |
| 20 | |
| 21 */ | |
| 22 | |
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23 /* |
| 5742 | 24 A C-program for MT19937, with initialization improved 2002/2/10. |
| 25 Coded by Takuji Nishimura and Makoto Matsumoto. | |
| 26 This is a faster version by taking Shawn Cokus's optimization, | |
| 27 Matthe Bellew's simplification, Isaku Wada's real version. | |
| 28 David Bateman added normal and exponential distributions following | |
| 29 Marsaglia and Tang's Ziggurat algorithm. | |
| 30 | |
| 31 Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, | |
| 32 Copyright (C) 2004, David Bateman | |
| 33 All rights reserved. | |
| 34 | |
| 35 Redistribution and use in source and binary forms, with or without | |
| 36 modification, are permitted provided that the following conditions | |
| 37 are met: | |
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38 |
| 5742 | 39 1. Redistributions of source code must retain the above copyright |
| 40 notice, this list of conditions and the following disclaimer. | |
| 41 | |
| 42 2. Redistributions in binary form must reproduce the above copyright | |
| 43 notice, this list of conditions and the following disclaimer in the | |
| 44 documentation and/or other materials provided with the distribution. | |
| 45 | |
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46 3. The names of its contributors may not be used to endorse or promote |
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47 products derived from this software without specific prior written |
| 5742 | 48 permission. |
| 49 | |
| 50 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | |
| 51 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | |
| 52 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | |
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53 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER |
| 5742 | 54 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| 55 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, | |
| 56 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR | |
| 57 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF | |
| 58 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING | |
| 59 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS | |
| 60 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
| 61 | |
| 62 | |
| 63 Any feedback is very welcome. | |
| 64 http://www.math.keio.ac.jp/matumoto/emt.html | |
| 65 email: matumoto@math.keio.ac.jp | |
| 66 | |
| 67 * 2004-01-19 Paul Kienzle | |
| 68 * * comment out main | |
| 69 * add init_by_entropy, get_state, set_state | |
| 70 * * converted to allow compiling by C++ compiler | |
| 71 * | |
| 72 * 2004-01-25 David Bateman | |
| 73 * * Add Marsaglia and Tsang Ziggurat code | |
| 74 * | |
| 75 * 2004-07-13 Paul Kienzle | |
| 76 * * make into an independent library with some docs. | |
| 77 * * introduce new main and test code. | |
| 78 * | |
| 79 * 2004-07-28 Paul Kienzle & David Bateman | |
| 80 * * add -DALLBITS flag for 32 vs. 53 bits of randomness in mantissa | |
| 81 * * make the naming scheme more uniform | |
| 82 * * add -DHAVE_X86 for faster support of 53 bit mantissa on x86 arch. | |
| 83 * | |
| 84 * 2005-02-23 Paul Kienzle | |
| 85 * * fix -DHAVE_X86_32 flag and add -DUSE_X86_32=0|1 for explicit control | |
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86 * |
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87 * 2006-04-01 David Bateman |
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88 * * convert for use in octave, declaring static functions only used |
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89 * here and adding oct_ to functions visible externally |
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90 * * inverse sense of ALLBITS |
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91 * |
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92 * 2012-05-18 David Bateman |
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93 * * Remove randu64 and ALLBIT option |
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94 * * Add the single precision generators |
| 5742 | 95 */ |
| 96 | |
| 97 /* | |
| 98 === Build instructions === | |
| 99 | |
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100 Compile with -DHAVE_GETTIMEOFDAY if the gettimeofday function is |
| 5742 | 101 available. This is not necessary if your architecture has |
| 102 /dev/urandom defined. | |
| 103 | |
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104 Uses implicit -Di386 or explicit -DHAVE_X86_32 to determine if CPU=x86. |
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105 You can force X86 behaviour with -DUSE_X86_32=1, or suppress it with |
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106 -DUSE_X86_32=0. You should also consider -march=i686 or similar for |
| 5742 | 107 extra performance. Check whether -DUSE_X86_32=0 is faster on 64-bit |
| 108 x86 architectures. | |
| 109 | |
| 110 If you want to replace the Mersenne Twister with another | |
| 111 generator then redefine randi32 appropriately. | |
| 112 | |
| 113 === Usage instructions === | |
| 114 Before using any of the generators, initialize the state with one of | |
| 115 oct_init_by_int, oct_init_by_array or oct_init_by_entropy. | |
| 116 | |
| 117 All generators share the same state vector. | |
| 118 | |
| 119 === Mersenne Twister === | |
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120 void oct_init_by_int (uint32_t s) 32-bit initial state |
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121 void oct_init_by_array (uint32_t k[],int m) m*32-bit initial state |
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122 void oct_init_by_entropy (void) random initial state |
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123 void oct_get_state (uint32_t save[MT_N+1]) saves state in array |
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124 void oct_set_state (uint32_t save[MT_N+1]) restores state from array |
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125 static uint32_t randmt (void) returns 32-bit unsigned int |
| 5742 | 126 |
| 127 === inline generators === | |
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128 static uint32_t randi32 (void) returns 32-bit unsigned int |
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129 static uint64_t randi53 (void) returns 53-bit unsigned int |
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130 static uint64_t randi54 (void) returns 54-bit unsigned int |
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131 static float randu32 (void) returns 32-bit uniform in (0,1) |
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132 static double randu53 (void) returns 53-bit uniform in (0,1) |
| 5742 | 133 |
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134 double oct_randu (void) returns M-bit uniform in (0,1) |
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135 double oct_randn (void) returns M-bit standard normal |
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136 double oct_rande (void) returns N-bit standard exponential |
| 5742 | 137 |
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138 float oct_float_randu (void) returns M-bit uniform in (0,1) |
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139 float oct_float_randn (void) returns M-bit standard normal |
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140 float oct_float_rande (void) returns N-bit standard exponential |
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141 |
| 5742 | 142 === Array generators === |
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143 void oct_fill_randi32 (octave_idx_type, uint32_t []) |
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144 void oct_fill_randi64 (octave_idx_type, uint64_t []) |
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145 |
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146 void oct_fill_randu (octave_idx_type, double []) |
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147 void oct_fill_randn (octave_idx_type, double []) |
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148 void oct_fill_rande (octave_idx_type, double []) |
| 5742 | 149 |
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150 void oct_fill_float_randu (octave_idx_type, float []) |
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151 void oct_fill_float_randn (octave_idx_type, float []) |
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152 void oct_fill_float_rande (octave_idx_type, float []) |
| 5742 | 153 */ |
| 154 | |
| 155 #if defined (HAVE_CONFIG_H) | |
| 156 #include <config.h> | |
| 157 #endif | |
| 158 | |
| 159 #include <stdio.h> | |
| 160 #include <time.h> | |
| 161 | |
| 162 #ifdef HAVE_GETTIMEOFDAY | |
| 163 #include <sys/time.h> | |
| 164 #endif | |
| 165 | |
| 7231 | 166 #include "lo-math.h" |
| 5742 | 167 #include "randmtzig.h" |
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168 |
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169 /* FIXME may want to suppress X86 if sizeof(long) > 4 */ |
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170 #if !defined (USE_X86_32) |
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171 # if defined (i386) || defined (HAVE_X86_32) |
| 5742 | 172 # define USE_X86_32 1 |
| 173 # else | |
| 174 # define USE_X86_32 0 | |
| 175 # endif | |
| 176 #endif | |
| 177 | |
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178 /* ===== Mersenne Twister 32-bit generator ===== */ |
| 5742 | 179 |
| 180 #define MT_M 397 | |
| 181 #define MATRIX_A 0x9908b0dfUL /* constant vector a */ | |
| 182 #define UMASK 0x80000000UL /* most significant w-r bits */ | |
| 183 #define LMASK 0x7fffffffUL /* least significant r bits */ | |
| 184 #define MIXBITS(u,v) ( ((u) & UMASK) | ((v) & LMASK) ) | |
| 185 #define TWIST(u,v) ((MIXBITS(u,v) >> 1) ^ ((v)&1UL ? MATRIX_A : 0UL)) | |
| 186 | |
| 187 static uint32_t *next; | |
| 188 static uint32_t state[MT_N]; /* the array for the state vector */ | |
| 189 static int left = 1; | |
| 190 static int initf = 0; | |
| 191 static int initt = 1; | |
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192 static int inittf = 1; |
| 5742 | 193 |
| 194 /* initializes state[MT_N] with a seed */ | |
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195 void |
| 5742 | 196 oct_init_by_int (uint32_t s) |
| 197 { | |
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198 int j; |
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199 state[0] = s & 0xffffffffUL; |
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200 for (j = 1; j < MT_N; j++) |
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201 { |
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202 state[j] = (1812433253UL * (state[j-1] ^ (state[j-1] >> 30)) + j); |
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203 /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */ |
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204 /* In the previous versions, MSBs of the seed affect */ |
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205 /* only MSBs of the array state[]. */ |
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206 /* 2002/01/09 modified by Makoto Matsumoto */ |
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207 state[j] &= 0xffffffffUL; /* for >32 bit machines */ |
| 5742 | 208 } |
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209 left = 1; |
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210 initf = 1; |
| 5742 | 211 } |
| 212 | |
| 213 /* initialize by an array with array-length */ | |
| 214 /* init_key is the array for initializing keys */ | |
| 215 /* key_length is its length */ | |
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216 void |
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217 oct_init_by_array (uint32_t *init_key, int key_length) |
| 5742 | 218 { |
| 219 int i, j, k; | |
| 220 oct_init_by_int (19650218UL); | |
| 221 i = 1; | |
| 222 j = 0; | |
| 223 k = (MT_N > key_length ? MT_N : key_length); | |
| 224 for (; k; k--) | |
| 225 { | |
| 226 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1664525UL)) | |
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227 + init_key[j] + j; /* non linear */ |
| 5742 | 228 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
| 229 i++; | |
| 230 j++; | |
| 231 if (i >= MT_N) | |
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232 { |
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233 state[0] = state[MT_N-1]; |
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234 i = 1; |
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235 } |
| 5742 | 236 if (j >= key_length) |
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237 j = 0; |
| 5742 | 238 } |
| 239 for (k = MT_N - 1; k; k--) | |
| 240 { | |
| 241 state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL)) | |
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242 - i; /* non linear */ |
| 5742 | 243 state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
| 244 i++; | |
| 245 if (i >= MT_N) | |
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246 { |
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247 state[0] = state[MT_N-1]; |
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248 i = 1; |
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249 } |
| 5742 | 250 } |
| 251 | |
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252 state[0] = 0x80000000UL; /* MSB is 1; assuring nonzero initial array */ |
| 5742 | 253 left = 1; |
| 254 initf = 1; | |
| 255 } | |
| 256 | |
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257 void |
| 5742 | 258 oct_init_by_entropy (void) |
| 259 { | |
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260 uint32_t entropy[MT_N]; |
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261 int n = 0; |
| 5742 | 262 |
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263 /* Look for entropy in /dev/urandom */ |
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264 FILE* urandom = fopen ("/dev/urandom", "rb"); |
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265 if (urandom) |
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266 { |
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267 while (n < MT_N) |
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268 { |
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269 unsigned char word[4]; |
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270 if (fread (word, 4, 1, urandom) != 1) |
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271 break; |
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272 entropy[n++] = word[0]+(word[1]<<8)+(word[2]<<16)+((uint32_t)word[3]<<24); |
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273 } |
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274 fclose (urandom); |
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275 } |
| 5742 | 276 |
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277 /* If there isn't enough entropy, gather some from various sources */ |
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278 if (n < MT_N) |
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279 entropy[n++] = time (NULL); /* Current time in seconds */ |
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280 if (n < MT_N) |
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281 entropy[n++] = clock (); /* CPU time used (usec) */ |
| 5742 | 282 #ifdef HAVE_GETTIMEOFDAY |
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283 if (n < MT_N) |
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284 { |
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285 struct timeval tv; |
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286 if (gettimeofday (&tv, NULL) != -1) |
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287 entropy[n++] = tv.tv_usec; /* Fractional part of current time */ |
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288 } |
| 5742 | 289 #endif |
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290 /* Send all the entropy into the initial state vector */ |
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291 oct_init_by_array (entropy,n); |
| 5742 | 292 } |
| 293 | |
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294 void |
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295 oct_set_state (uint32_t *save) |
| 5742 | 296 { |
| 297 int i; | |
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298 for (i = 0; i < MT_N; i++) |
| 5742 | 299 state[i] = save[i]; |
| 300 left = save[MT_N]; | |
| 301 next = state + (MT_N - left + 1); | |
| 302 } | |
| 303 | |
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304 void |
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305 oct_get_state (uint32_t *save) |
| 5742 | 306 { |
| 307 int i; | |
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308 for (i = 0; i < MT_N; i++) |
| 5742 | 309 save[i] = state[i]; |
| 310 save[MT_N] = left; | |
| 311 } | |
| 312 | |
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313 static void |
| 5742 | 314 next_state (void) |
| 315 { | |
| 316 uint32_t *p = state; | |
| 317 int j; | |
| 318 | |
| 319 /* if init_by_int() has not been called, */ | |
| 320 /* a default initial seed is used */ | |
| 321 /* if (initf==0) init_by_int(5489UL); */ | |
| 322 /* Or better yet, a random seed! */ | |
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323 if (initf == 0) |
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324 oct_init_by_entropy (); |
| 5742 | 325 |
| 326 left = MT_N; | |
| 327 next = state; | |
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328 |
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329 for (j = MT_N - MT_M + 1; --j; p++) |
| 5742 | 330 *p = p[MT_M] ^ TWIST(p[0], p[1]); |
| 331 | |
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332 for (j = MT_M; --j; p++) |
| 5742 | 333 *p = p[MT_M-MT_N] ^ TWIST(p[0], p[1]); |
| 334 | |
| 335 *p = p[MT_M-MT_N] ^ TWIST(p[0], state[0]); | |
| 336 } | |
| 337 | |
| 338 /* generates a random number on [0,0xffffffff]-interval */ | |
| 5766 | 339 static uint32_t |
| 5742 | 340 randmt (void) |
| 341 { | |
| 342 register uint32_t y; | |
| 343 | |
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344 if (--left == 0) |
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345 next_state (); |
| 5742 | 346 y = *next++; |
| 347 | |
| 348 /* Tempering */ | |
| 349 y ^= (y >> 11); | |
| 350 y ^= (y << 7) & 0x9d2c5680UL; | |
| 351 y ^= (y << 15) & 0xefc60000UL; | |
| 352 return (y ^ (y >> 18)); | |
| 353 } | |
| 354 | |
| 355 /* ===== Uniform generators ===== */ | |
| 356 | |
| 357 /* Select which 32 bit generator to use */ | |
| 358 #define randi32 randmt | |
| 359 | |
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360 static uint64_t |
| 5742 | 361 randi53 (void) |
| 362 { | |
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363 const uint32_t lo = randi32 (); |
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364 const uint32_t hi = randi32 ()&0x1FFFFF; |
| 5742 | 365 #if HAVE_X86_32 |
| 366 uint64_t u; | |
| 367 uint32_t *p = (uint32_t *)&u; | |
| 368 p[0] = lo; | |
| 369 p[1] = hi; | |
| 370 return u; | |
| 371 #else | |
| 372 return (((uint64_t)hi<<32)|lo); | |
| 373 #endif | |
| 374 } | |
| 375 | |
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376 static uint64_t |
| 5742 | 377 randi54 (void) |
| 378 { | |
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379 const uint32_t lo = randi32 (); |
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380 const uint32_t hi = randi32 ()&0x3FFFFF; |
| 5742 | 381 #if HAVE_X86_32 |
| 382 uint64_t u; | |
| 383 uint32_t *p = (uint32_t *)&u; | |
| 384 p[0] = lo; | |
| 385 p[1] = hi; | |
| 386 return u; | |
| 387 #else | |
| 388 return (((uint64_t)hi<<32)|lo); | |
| 389 #endif | |
| 390 } | |
| 391 | |
| 392 /* generates a random number on (0,1)-real-interval */ | |
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393 static float |
| 5742 | 394 randu32 (void) |
| 395 { | |
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396 return ((float)randi32 () + 0.5) * (1.0/4294967296.0); |
| 5742 | 397 /* divided by 2^32 */ |
| 398 } | |
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399 |
| 5742 | 400 /* generates a random number on (0,1) with 53-bit resolution */ |
| 5766 | 401 static double |
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402 randu53 (void) |
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403 { |
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404 const uint32_t a = randi32 ()>>5; |
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405 const uint32_t b = randi32 ()>>6; |
| 6959 | 406 return (a*67108864.0+b+0.4) * (1.0/9007199254740992.0); |
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407 } |
| 5742 | 408 |
| 409 /* Determine mantissa for uniform doubles */ | |
| 410 double | |
| 411 oct_randu (void) | |
| 412 { | |
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413 return randu53 (); |
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414 } |
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415 |
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416 /* Determine mantissa for uniform floats */ |
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417 float |
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418 oct_float_randu (void) |
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419 { |
| 6959 | 420 return randu32 (); |
| 5742 | 421 } |
| 422 | |
| 423 /* ===== Ziggurat normal and exponential generators ===== */ | |
| 424 | |
| 425 #define ZIGGURAT_TABLE_SIZE 256 | |
| 426 | |
| 427 #define ZIGGURAT_NOR_R 3.6541528853610088 | |
| 428 #define ZIGGURAT_NOR_INV_R 0.27366123732975828 | |
| 429 #define NOR_SECTION_AREA 0.00492867323399 | |
| 430 | |
| 431 #define ZIGGURAT_EXP_R 7.69711747013104972 | |
| 432 #define ZIGGURAT_EXP_INV_R 0.129918765548341586 | |
| 433 #define EXP_SECTION_AREA 0.0039496598225815571993 | |
| 434 | |
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435 #define ZIGINT uint64_t |
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436 #define EMANTISSA 9007199254740992.0 /* 53 bit mantissa */ |
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437 #define ERANDI randi53() /* 53 bits for mantissa */ |
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438 #define NMANTISSA EMANTISSA |
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439 #define NRANDI randi54() /* 53 bits for mantissa + 1 bit sign */ |
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440 #define RANDU randu53() |
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441 |
| 5742 | 442 static ZIGINT ki[ZIGGURAT_TABLE_SIZE]; |
| 443 static double wi[ZIGGURAT_TABLE_SIZE], fi[ZIGGURAT_TABLE_SIZE]; | |
| 444 static ZIGINT ke[ZIGGURAT_TABLE_SIZE]; | |
| 445 static double we[ZIGGURAT_TABLE_SIZE], fe[ZIGGURAT_TABLE_SIZE]; | |
| 446 | |
| 447 /* | |
| 448 This code is based on the paper Marsaglia and Tsang, "The ziggurat method | |
| 449 for generating random variables", Journ. Statistical Software. Code was | |
| 450 presented in this paper for a Ziggurat of 127 levels and using a 32 bit | |
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451 integer random number generator. This version of the code, uses the |
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452 Mersenne Twister as the integer generator and uses 256 levels in the |
| 5742 | 453 Ziggurat. This has several advantages. |
| 454 | |
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455 1) As Marsaglia and Tsang themselves states, the more levels the few |
| 5742 | 456 times the expensive tail algorithm must be called |
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457 2) The cycle time of the generator is determined by the integer |
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458 generator, thus the use of a Mersenne Twister for the core random |
| 5742 | 459 generator makes this cycle extremely long. |
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460 3) The license on the original code was unclear, thus rewriting the code |
| 5742 | 461 from the article means we are free of copyright issues. |
| 462 4) Compile flag for full 53-bit random mantissa. | |
| 463 | |
| 464 It should be stated that the authors made my life easier, by the fact that | |
| 465 the algorithm developed in the text of the article is for a 256 level | |
| 466 ziggurat, even if the code itself isn't... | |
| 467 | |
| 468 One modification to the algorithm developed in the article, is that it is | |
| 469 assumed that 0 <= x < Inf, and "unsigned long"s are used, thus resulting in | |
| 470 terms like 2^32 in the code. As the normal distribution is defined between | |
| 471 -Inf < x < Inf, we effectively only have 31 bit integers plus a sign. Thus | |
| 472 in Marsaglia and Tsang, terms like 2^32 become 2^31. We use NMANTISSA for | |
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473 this term. The exponential distribution is one sided so we use the |
| 5742 | 474 full 32 bits. We use EMANTISSA for this term. |
| 475 | |
| 476 It appears that I'm slightly slower than the code in the article, this | |
| 477 is partially due to a better generator of random integers than they | |
| 478 use. But might also be that the case of rapid return was optimized by | |
| 479 inlining the relevant code with a #define. As the basic Mersenne | |
| 480 Twister is only 25% faster than this code I suspect that the main | |
| 481 reason is just the use of the Mersenne Twister and not the inlining, | |
| 482 so I'm not going to try and optimize further. | |
| 483 */ | |
| 484 | |
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485 static void |
| 5742 | 486 create_ziggurat_tables (void) |
| 487 { | |
| 488 int i; | |
| 489 double x, x1; | |
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490 |
| 5742 | 491 /* Ziggurat tables for the normal distribution */ |
| 492 x1 = ZIGGURAT_NOR_R; | |
| 493 wi[255] = x1 / NMANTISSA; | |
| 494 fi[255] = exp (-0.5 * x1 * x1); | |
| 495 | |
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496 /* Index zero is special for tail strip, where Marsaglia and Tsang |
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497 * defines this as |
| 5742 | 498 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1, |
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499 * where v is the area of each strip of the ziggurat. |
| 5742 | 500 */ |
| 501 ki[0] = (ZIGINT) (x1 * fi[255] / NOR_SECTION_AREA * NMANTISSA); | |
| 502 wi[0] = NOR_SECTION_AREA / fi[255] / NMANTISSA; | |
| 503 fi[0] = 1.; | |
| 504 | |
| 505 for (i = 254; i > 0; i--) | |
| 506 { | |
| 507 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus | |
| 508 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y)) | |
| 509 */ | |
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510 x = sqrt (-2. * log (NOR_SECTION_AREA / x1 + fi[i+1])); |
| 5742 | 511 ki[i+1] = (ZIGINT)(x / x1 * NMANTISSA); |
| 512 wi[i] = x / NMANTISSA; | |
| 513 fi[i] = exp (-0.5 * x * x); | |
| 514 x1 = x; | |
| 515 } | |
| 516 | |
| 517 ki[1] = 0; | |
| 518 | |
| 519 /* Zigurrat tables for the exponential distribution */ | |
| 520 x1 = ZIGGURAT_EXP_R; | |
| 521 we[255] = x1 / EMANTISSA; | |
| 522 fe[255] = exp (-x1); | |
| 523 | |
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524 /* Index zero is special for tail strip, where Marsaglia and Tsang |
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525 * defines this as |
| 5742 | 526 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1, |
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527 * where v is the area of each strip of the ziggurat. |
| 5742 | 528 */ |
| 529 ke[0] = (ZIGINT) (x1 * fe[255] / EXP_SECTION_AREA * EMANTISSA); | |
| 530 we[0] = EXP_SECTION_AREA / fe[255] / EMANTISSA; | |
| 531 fe[0] = 1.; | |
| 532 | |
| 533 for (i = 254; i > 0; i--) | |
| 534 { | |
| 535 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus | |
| 536 * need inverse operator of y = exp(-x) -> x = -ln(y) | |
| 537 */ | |
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538 x = - log (EXP_SECTION_AREA / x1 + fe[i+1]); |
| 5742 | 539 ke[i+1] = (ZIGINT)(x / x1 * EMANTISSA); |
| 540 we[i] = x / EMANTISSA; | |
| 541 fe[i] = exp (-x); | |
| 542 x1 = x; | |
| 543 } | |
| 544 ke[1] = 0; | |
| 545 | |
| 546 initt = 0; | |
| 547 } | |
| 548 | |
| 549 /* | |
| 550 * Here is the guts of the algorithm. As Marsaglia and Tsang state the | |
| 551 * algorithm in their paper | |
| 552 * | |
| 553 * 1) Calculate a random signed integer j and let i be the index | |
| 554 * provided by the rightmost 8-bits of j | |
| 555 * 2) Set x = j * w_i. If j < k_i return x | |
| 556 * 3) If i = 0, then return x from the tail | |
| 557 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x | |
| 558 * 5) goto step 1 | |
| 559 * | |
| 560 * Where f is the functional form of the distribution, which for a normal | |
| 561 * distribution is exp(-0.5*x*x) | |
| 562 */ | |
| 563 | |
| 564 double | |
| 565 oct_randn (void) | |
| 566 { | |
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567 if (initt) |
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568 create_ziggurat_tables (); |
| 5742 | 569 |
| 570 while (1) | |
| 571 { | |
| 572 /* The following code is specialized for 32-bit mantissa. | |
| 573 * Compared to the arbitrary mantissa code, there is a performance | |
| 574 * gain for 32-bits: PPC: 2%, MIPS: 8%, x86: 40% | |
| 575 * There is a bigger performance gain compared to using a full | |
| 576 * 53-bit mantissa: PPC: 60%, MIPS: 65%, x86: 240% | |
| 577 * Of course, different compilers and operating systems may | |
| 578 * have something to do with this. | |
| 579 */ | |
| 580 # if HAVE_X86_32 | |
| 581 /* 53-bit mantissa, 1-bit sign, x86 32-bit architecture */ | |
| 582 double x; | |
| 583 int si,idx; | |
| 584 register uint32_t lo, hi; | |
| 585 int64_t rabs; | |
| 586 uint32_t *p = (uint32_t *)&rabs; | |
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587 lo = randi32 (); |
| 5742 | 588 idx = lo&0xFF; |
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589 hi = randi32 (); |
| 5742 | 590 si = hi&UMASK; |
| 591 p[0] = lo; | |
| 592 p[1] = hi&0x1FFFFF; | |
| 593 x = ( si ? -rabs : rabs ) * wi[idx]; | |
| 594 # else /* !HAVE_X86_32 */ | |
| 595 /* arbitrary mantissa (selected by NRANDI, with 1 bit for sign) */ | |
| 596 const uint64_t r = NRANDI; | |
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597 const int64_t rabs = r>>1; |
| 5742 | 598 const int idx = (int)(rabs&0xFF); |
| 599 const double x = ( r&1 ? -rabs : rabs) * wi[idx]; | |
| 600 # endif /* !HAVE_X86_32 */ | |
| 601 if (rabs < (int64_t)ki[idx]) | |
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602 return x; /* 99.3% of the time we return here 1st try */ |
| 5742 | 603 else if (idx == 0) |
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604 { |
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605 /* As stated in Marsaglia and Tsang |
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606 * |
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607 * For the normal tail, the method of Marsaglia[5] provides: |
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608 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, |
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609 * then return r+x. Except that r+x is always in the positive |
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610 * tail!!!! Any thing random might be used to determine the |
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611 * sign, but as we already have r we might as well use it |
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612 * |
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613 * [PAK] but not the bottom 8 bits, since they are all 0 here! |
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614 */ |
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615 double xx, yy; |
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616 do |
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617 { |
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618 xx = - ZIGGURAT_NOR_INV_R * log (RANDU); |
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619 yy = - log (RANDU); |
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620 } |
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621 while ( yy+yy <= xx*xx); |
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622 return (rabs&0x100 ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); |
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623 } |
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624 else if ((fi[idx-1] - fi[idx]) * RANDU + fi[idx] < exp (-0.5*x*x)) |
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625 return x; |
| 5742 | 626 } |
| 627 } | |
| 628 | |
| 629 double | |
| 630 oct_rande (void) | |
| 631 { | |
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632 if (initt) |
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633 create_ziggurat_tables (); |
| 5742 | 634 |
| 635 while (1) | |
| 636 { | |
| 637 ZIGINT ri = ERANDI; | |
| 638 const int idx = (int)(ri & 0xFF); | |
| 639 const double x = ri * we[idx]; | |
| 640 if (ri < ke[idx]) | |
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641 return x; /* 98.9% of the time we return here 1st try */ |
| 5742 | 642 else if (idx == 0) |
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643 { |
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644 /* As stated in Marsaglia and Tsang |
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645 * |
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646 * For the exponential tail, the method of Marsaglia[5] provides: |
| 5742 | 647 * x = r - ln(U); |
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648 */ |
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649 return ZIGGURAT_EXP_R - log (RANDU); |
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650 } |
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651 else if ((fe[idx-1] - fe[idx]) * RANDU + fe[idx] < exp (-x)) |
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652 return x; |
| 5742 | 653 } |
| 654 } | |
| 655 | |
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656 #undef ZIGINT |
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657 #undef EMANTISSA |
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658 #undef ERANDI |
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659 #undef NMANTISSA |
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660 #undef NRANDI |
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661 #undef RANDU |
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662 |
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663 #define ZIGINT uint32_t |
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664 #define EMANTISSA 4294967296.0 /* 32 bit mantissa */ |
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665 #define ERANDI randi32() /* 32 bits for mantissa */ |
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666 #define NMANTISSA 2147483648.0 /* 31 bit mantissa */ |
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667 #define NRANDI randi32() /* 31 bits for mantissa + 1 bit sign */ |
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668 #define RANDU randu32() |
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669 |
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670 static ZIGINT fki[ZIGGURAT_TABLE_SIZE]; |
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671 static float fwi[ZIGGURAT_TABLE_SIZE], ffi[ZIGGURAT_TABLE_SIZE]; |
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672 static ZIGINT fke[ZIGGURAT_TABLE_SIZE]; |
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673 static float fwe[ZIGGURAT_TABLE_SIZE], ffe[ZIGGURAT_TABLE_SIZE]; |
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674 |
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675 |
|
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676 static void |
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677 create_ziggurat_float_tables (void) |
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678 { |
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679 int i; |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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680 float x, x1; |
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681 |
|
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682 /* Ziggurat tables for the normal distribution */ |
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683 x1 = ZIGGURAT_NOR_R; |
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684 fwi[255] = x1 / NMANTISSA; |
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685 ffi[255] = exp (-0.5 * x1 * x1); |
|
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686 |
|
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687 /* Index zero is special for tail strip, where Marsaglia and Tsang |
|
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688 * defines this as |
|
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689 * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1, |
|
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690 * where v is the area of each strip of the ziggurat. |
|
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691 */ |
|
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692 fki[0] = (ZIGINT) (x1 * ffi[255] / NOR_SECTION_AREA * NMANTISSA); |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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693 fwi[0] = NOR_SECTION_AREA / ffi[255] / NMANTISSA; |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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694 ffi[0] = 1.; |
|
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695 |
|
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|
696 for (i = 254; i > 0; i--) |
|
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|
697 { |
|
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698 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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699 * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y)) |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
700 */ |
|
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701 x = sqrt (-2. * log (NOR_SECTION_AREA / x1 + ffi[i+1])); |
|
14655
43db83eff9db
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changeset
|
702 fki[i+1] = (ZIGINT)(x / x1 * NMANTISSA); |
|
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|
703 fwi[i] = x / NMANTISSA; |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
704 ffi[i] = exp (-0.5 * x * x); |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
705 x1 = x; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
706 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
707 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
708 fki[1] = 0; |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
709 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
710 /* Zigurrat tables for the exponential distribution */ |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
711 x1 = ZIGGURAT_EXP_R; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
712 fwe[255] = x1 / EMANTISSA; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
713 ffe[255] = exp (-x1); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
714 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
715 /* Index zero is special for tail strip, where Marsaglia and Tsang |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
716 * defines this as |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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changeset
|
717 * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1, |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
718 * where v is the area of each strip of the ziggurat. |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
719 */ |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
720 fke[0] = (ZIGINT) (x1 * ffe[255] / EXP_SECTION_AREA * EMANTISSA); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
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changeset
|
721 fwe[0] = EXP_SECTION_AREA / ffe[255] / EMANTISSA; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
722 ffe[0] = 1.; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
723 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
724 for (i = 254; i > 0; i--) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
725 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
726 /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
727 * need inverse operator of y = exp(-x) -> x = -ln(y) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
728 */ |
|
15018
3d8ace26c5b4
maint: Use Octave coding conventions for cuddled parentheses in liboctave/.
Rik <rik@octave.org>
parents:
14846
diff
changeset
|
729 x = - log (EXP_SECTION_AREA / x1 + ffe[i+1]); |
|
14655
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
730 fke[i+1] = (ZIGINT)(x / x1 * EMANTISSA); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
731 fwe[i] = x / EMANTISSA; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
732 ffe[i] = exp (-x); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
733 x1 = x; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
734 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
735 fke[1] = 0; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
736 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
737 inittf = 0; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
738 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
739 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
740 /* |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
741 * Here is the guts of the algorithm. As Marsaglia and Tsang state the |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
742 * algorithm in their paper |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
743 * |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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changeset
|
744 * 1) Calculate a random signed integer j and let i be the index |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
745 * provided by the rightmost 8-bits of j |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
746 * 2) Set x = j * w_i. If j < k_i return x |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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14138
diff
changeset
|
747 * 3) If i = 0, then return x from the tail |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
748 * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
749 * 5) goto step 1 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
750 * |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
751 * Where f is the functional form of the distribution, which for a normal |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
752 * distribution is exp(-0.5*x*x) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
753 */ |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
754 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
755 float |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
756 oct_float_randn (void) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
757 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
758 if (inittf) |
|
14846
460a3c6d8bf1
maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents:
14655
diff
changeset
|
759 create_ziggurat_float_tables (); |
|
14655
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
760 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
761 while (1) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
762 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
diff
changeset
|
763 /* 32-bit mantissa */ |
|
14846
460a3c6d8bf1
maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
Rik <octave@nomad.inbox5.com>
parents:
14655
diff
changeset
|
764 const uint32_t r = randi32 (); |
|
14655
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
765 const uint32_t rabs = r&LMASK; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
766 const int idx = (int)(r&0xFF); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
767 const float x = ((int32_t)r) * fwi[idx]; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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changeset
|
768 if (rabs < fki[idx]) |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
769 return x; /* 99.3% of the time we return here 1st try */ |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
770 else if (idx == 0) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
771 { |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
772 /* As stated in Marsaglia and Tsang |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
773 * |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
774 * For the normal tail, the method of Marsaglia[5] provides: |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
775 * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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changeset
|
776 * then return r+x. Except that r+x is always in the positive |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
777 * tail!!!! Any thing random might be used to determine the |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
14138
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changeset
|
778 * sign, but as we already have r we might as well use it |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
779 * |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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780 * [PAK] but not the bottom 8 bits, since they are all 0 here! |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
781 */ |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
782 float xx, yy; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
783 do |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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parents:
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diff
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|
784 { |
|
43db83eff9db
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David Bateman <dbateman@free.fr>
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changeset
|
785 xx = - ZIGGURAT_NOR_INV_R * log (RANDU); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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changeset
|
786 yy = - log (RANDU); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
787 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
788 while ( yy+yy <= xx*xx); |
|
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David Bateman <dbateman@free.fr>
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|
789 return (rabs&0x100 ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
790 } |
|
15018
3d8ace26c5b4
maint: Use Octave coding conventions for cuddled parentheses in liboctave/.
Rik <rik@octave.org>
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diff
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|
791 else if ((ffi[idx-1] - ffi[idx]) * RANDU + ffi[idx] < exp (-0.5*x*x)) |
|
14655
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David Bateman <dbateman@free.fr>
parents:
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|
792 return x; |
|
43db83eff9db
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changeset
|
793 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
794 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
795 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
796 float |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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parents:
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|
797 oct_float_rande (void) |
|
43db83eff9db
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|
798 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
799 if (inittf) |
|
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460a3c6d8bf1
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Rik <octave@nomad.inbox5.com>
parents:
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|
800 create_ziggurat_float_tables (); |
|
14655
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
801 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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parents:
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diff
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|
802 while (1) |
|
43db83eff9db
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David Bateman <dbateman@free.fr>
parents:
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diff
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|
803 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
804 ZIGINT ri = ERANDI; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
805 const int idx = (int)(ri & 0xFF); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
806 const float x = ri * fwe[idx]; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
807 if (ri < fke[idx]) |
|
15970
ca6202597201
Use C-style comments in C code.
Mike Miller <mtmiller@ieee.org>
parents:
15408
diff
changeset
|
808 return x; /* 98.9% of the time we return here 1st try */ |
|
14655
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
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|
809 else if (idx == 0) |
|
43db83eff9db
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changeset
|
810 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
811 /* As stated in Marsaglia and Tsang |
|
43db83eff9db
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David Bateman <dbateman@free.fr>
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|
812 * |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
813 * For the exponential tail, the method of Marsaglia[5] provides: |
|
43db83eff9db
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David Bateman <dbateman@free.fr>
parents:
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|
814 * x = r - ln(U); |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
815 */ |
|
15018
3d8ace26c5b4
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Rik <rik@octave.org>
parents:
14846
diff
changeset
|
816 return ZIGGURAT_EXP_R - log (RANDU); |
|
14655
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David Bateman <dbateman@free.fr>
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diff
changeset
|
817 } |
|
15018
3d8ace26c5b4
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Rik <rik@octave.org>
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diff
changeset
|
818 else if ((ffe[idx-1] - ffe[idx]) * RANDU + ffe[idx] < exp (-x)) |
|
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Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
819 return x; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
820 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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|
821 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
822 |
| 5742 | 823 /* Array generators */ |
|
11586
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John W. Eaton <jwe@octave.org>
parents:
11523
diff
changeset
|
824 void |
| 5742 | 825 oct_fill_randu (octave_idx_type n, double *p) |
| 826 { | |
| 827 octave_idx_type i; | |
|
11586
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diff
changeset
|
828 for (i = 0; i < n; i++) |
|
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Rik <octave@nomad.inbox5.com>
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|
829 p[i] = oct_randu (); |
| 5742 | 830 } |
| 831 | |
|
11586
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parents:
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|
832 void |
| 5742 | 833 oct_fill_randn (octave_idx_type n, double *p) |
| 834 { | |
| 835 octave_idx_type i; | |
|
11586
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changeset
|
836 for (i = 0; i < n; i++) |
|
14846
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Rik <octave@nomad.inbox5.com>
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|
837 p[i] = oct_randn (); |
| 5742 | 838 } |
| 839 | |
|
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parents:
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changeset
|
840 void |
| 5742 | 841 oct_fill_rande (octave_idx_type n, double *p) |
| 842 { | |
| 843 octave_idx_type i; | |
|
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parents:
11523
diff
changeset
|
844 for (i = 0; i < n; i++) |
|
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Rik <octave@nomad.inbox5.com>
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diff
changeset
|
845 p[i] = oct_rande (); |
| 5742 | 846 } |
|
14655
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David Bateman <dbateman@free.fr>
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|
847 |
|
43db83eff9db
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David Bateman <dbateman@free.fr>
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|
848 void |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
849 oct_fill_float_randu (octave_idx_type n, float *p) |
|
43db83eff9db
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|
850 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
851 octave_idx_type i; |
|
43db83eff9db
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David Bateman <dbateman@free.fr>
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changeset
|
852 for (i = 0; i < n; i++) |
|
14846
460a3c6d8bf1
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Rik <octave@nomad.inbox5.com>
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14655
diff
changeset
|
853 p[i] = oct_float_randu (); |
|
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David Bateman <dbateman@free.fr>
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changeset
|
854 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
855 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
856 void |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
857 oct_fill_float_randn (octave_idx_type n, float *p) |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
parents:
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diff
changeset
|
858 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
859 octave_idx_type i; |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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diff
changeset
|
860 for (i = 0; i < n; i++) |
|
14846
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Rik <octave@nomad.inbox5.com>
parents:
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diff
changeset
|
861 p[i] = oct_float_randn (); |
|
14655
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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diff
changeset
|
862 } |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
863 |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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|
864 void |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
865 oct_fill_float_rande (octave_idx_type n, float *p) |
|
43db83eff9db
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changeset
|
866 { |
|
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
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changeset
|
867 octave_idx_type i; |
|
43db83eff9db
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changeset
|
868 for (i = 0; i < n; i++) |
|
14846
460a3c6d8bf1
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Rik <octave@nomad.inbox5.com>
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diff
changeset
|
869 p[i] = oct_float_rande (); |
|
14655
43db83eff9db
Implement single precision rand, randn, rande, randg and randp generators (bug #34351, #36293)
David Bateman <dbateman@free.fr>
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changeset
|
870 } |