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/* (C) Copyright 2004, 2005, 2006, 2007, 2008, 2009 Stijn van Dongen
*
* (C) Ziggurat method Copyright 2005 Jochen Voss.
*
* This file is part of tingea. You can redistribute and/or modify tingea
* under the terms of the GNU General Public License; either version 3 of the
* License or (at your option) any later version. You should have received a
* copy of the GPL along with tingea, in the file COPYING.
*/
#include <sys/types.h>
#include <unistd.h>
#include <stdio.h>
#include <time.h>
#include "rand.h"
#include "math.h"
#include "types.h"
unsigned long mcxSeed
( unsigned long i
)
{ pid_t p = getpid()
; pid_t pp = getppid()
; time_t t = time(NULL)
; unsigned long s = (p ^ p << 4 ^ p << 16 ^ p << 28)
^ (pp ^ pp << 8 ^ pp << 24)
^ (t ^ t << 12 ^ t << 20)
^ (i ^ i << 3 ^ i << 23 ^ i << 26)
/* I have no solid evidence backing up the usefulness of the xors.
* They won't increase entropy anyway of course.
* Anyway, the xors do seem useful in order to spread input
* bits out over the output space, as seen from some hashing
* experiments.
*/
; return s
; }
/* Box-Muller transform */
double mcxNormalBoxMuller
( void
)
{ double a = 1.0 - (random() * 1.0) / (RAND_MAX + 1.0)
; double b = 1.0 - (random() * 1.0) / (RAND_MAX + 1.0)
; return sqrt( -2.0 * log(a)) * cos(2*3.14159265358979323846*b)
; }
double mcxNormal
( void
)
{ return mcxNormalZiggurat()
; }
double mcxNormalCut
( double radius
, double stddev
)
{ dim d
; if (radius < 0)
radius = -radius
; for (d=0;d<256;d++)
{ double r = stddev * mcxNormal()
; if (r >= -radius && r <= radius)
return r
; }
return 0.0
; }
double mcxNormalSample
( double radius
, double stddev
)
{ int n_try = 0
; double r = 2 * radius * (((1.0 * random()) / RAND_MAX) - 0.5)
; while (n_try++ < 1000)
{ double n = exp( - (r * r) / (2 * stddev * stddev)) / (2.5066282746 * stddev)
; double p = (1.0 * random()) / RAND_MAX
; if (n >= p)
break
; r = 2 * radius * (((1.0 * random()) / RAND_MAX) - 0.5)
; }
return r
; }
/* Ziggurat method
*
* Copyright (C) 2005 Jochen Voss.
*
* For details see the following article.
*
* George Marsaglia, Wai Wan Tsang
* The Ziggurat Method for Generating Random Variables
* Journal of Statistical Software, vol. 5 (2000), no. 8
* http://www.jstatsoft.org/v05/i08/
*/
/* position of right-most step */
#define PARAM_R 3.44428647676
/* tabulated values for the heigt of the Ziggurat levels */
static const double ytab[128] =
{ 1.000000000000 , 0.963598623011 , 0.936280813353 , 0.913041104253
, 0.892278506696 , 0.873239356919 , 0.855496407634 , 0.838778928349
, 0.822902083699 , 0.807732738234 , 0.793171045519 , 0.779139726505
, 0.765577436082 , 0.752434456248 , 0.739669787677 , 0.727249120285
, 0.715143377413 , 0.703327646455 , 0.691780377035 , 0.680482768910
, 0.669418297233 , 0.658572339120 , 0.647931876189 , 0.637485254896
, 0.627221991450 , 0.617132611532 , 0.607208517467 , 0.597441877296
, 0.587825531465 , 0.578352913803 , 0.569017984198 , 0.559815170911
, 0.550739320877 , 0.541785656682 , 0.532949739145 , 0.524227434628
, 0.515614886373 , 0.507108489253 , 0.498704867478 , 0.490400854812
, 0.482193476986 , 0.474079936010 , 0.466057596125 , 0.458123971214
, 0.450276713467 , 0.442513603171 , 0.434832539473 , 0.427231532022
, 0.419708693379 , 0.412262232120 , 0.404890446548 , 0.397591718955
, 0.390364510382 , 0.383207355816 , 0.376118859788 , 0.369097692334
, 0.362142585282 , 0.355252328834 , 0.348425768415 , 0.341661801776
, 0.334959376311 , 0.328317486588 , 0.321735172063 , 0.315211514970
, 0.308745638367 , 0.302336704338 , 0.295983912320 , 0.289686497571
, 0.283443729739 , 0.277254911560 , 0.271119377649 , 0.265036493387
, 0.259005653912 , 0.253026283183 , 0.247097833139 , 0.241219782932
, 0.235391638239 , 0.229612930649 , 0.223883217122 , 0.218202079518
, 0.212569124201 , 0.206983981709 , 0.201446306496 , 0.195955776745
, 0.190512094256 , 0.185114984406 , 0.179764196185 , 0.174459502324
, 0.169200699492 , 0.163987608600 , 0.158820075195 , 0.153697969964
, 0.148621189348 , 0.143589656295 , 0.138603321143 , 0.133662162669
, 0.128766189309 , 0.123915440582 , 0.119109988745 , 0.114349940703
, 0.109635440230 , 0.104966670533 , 0.100343857232 , 0.0957672718266
, 0.0912372357329 , 0.0867541250127 , 0.082318375932 , 0.0779304915295
, 0.0735910494266 , 0.0693007111742 , 0.065060233529 , 0.0608704821745
, 0.0567324485840 , 0.0526472709800 , 0.0486162607163 , 0.0446409359769
, 0.0407230655415 , 0.0368647267386 , 0.0330683839378 , 0.0293369977411
, 0.0256741818288 , 0.0220844372634 , 0.0185735200577 , 0.0151490552854
, 0.0118216532614 , 0.00860719483079, 0.00553245272614, 0.00265435214565
} ;
/* tabulated values for 2^24 times x[i]/x[i+1],
* used to accept for U*x[i+1]<=x[i]
* without any floating point operations
*/
static const unsigned long ktab[128] =
{ 0 , 12590644 , 14272653 , 14988939
, 15384584 , 15635009 , 15807561 , 15933577
, 16029594 , 16105155 , 16166147 , 16216399
, 16258508 , 16294295 , 16325078 , 16351831
, 16375291 , 16396026 , 16414479 , 16431002
, 16445880 , 16459343 , 16471578 , 16482744
, 16492970 , 16502368 , 16511031 , 16519039
, 16526459 , 16533352 , 16539769 , 16545755
, 16551348 , 16556584 , 16561493 , 16566101
, 16570433 , 16574511 , 16578353 , 16581977
, 16585398 , 16588629 , 16591685 , 16594575
, 16597311 , 16599901 , 16602354 , 16604679
, 16606881 , 16608968 , 16610945 , 16612818
, 16614592 , 16616272 , 16617861 , 16619363
, 16620782 , 16622121 , 16623383 , 16624570
, 16625685 , 16626730 , 16627708 , 16628619
, 16629465 , 16630248 , 16630969 , 16631628
, 16632228 , 16632768 , 16633248 , 16633671
, 16634034 , 16634340 , 16634586 , 16634774
, 16634903 , 16634972 , 16634980 , 16634926
, 16634810 , 16634628 , 16634381 , 16634066
, 16633680 , 16633222 , 16632688 , 16632075
, 16631380 , 16630598 , 16629726 , 16628757
, 16627686 , 16626507 , 16625212 , 16623794
, 16622243 , 16620548 , 16618698 , 16616679
, 16614476 , 16612071 , 16609444 , 16606571
, 16603425 , 16599973 , 16596178 , 16591995
, 16587369 , 16582237 , 16576520 , 16570120
, 16562917 , 16554758 , 16545450 , 16534739
, 16522287 , 16507638 , 16490152 , 16468907
, 16442518 , 16408804 , 16364095 , 16301683
, 16207738 , 16047994 , 15704248 , 15472926
} ;
/* tabulated values of 2^{-24}*x[i] */
static const double wtab[128] =
{ 1.62318314817e-08 , 2.16291505214e-08 , 2.54246305087e-08, 2.84579525938e-08
, 3.10340022482e-08 , 3.33011726243e-08 , 3.53439060345e-08, 3.72152672658e-08
, 3.89509895720e-08 , 4.05763964764e-08 , 4.21101548915e-08, 4.35664624904e-08
, 4.49563968336e-08 , 4.62887864029e-08 , 4.75707945735e-08, 4.88083237257e-08
, 5.00063025384e-08 , 5.11688950428e-08 , 5.22996558616e-08, 5.34016475624e-08
, 5.44775307871e-08 , 5.55296344581e-08 , 5.65600111659e-08, 5.75704813695e-08
, 5.85626690412e-08 , 5.95380306862e-08 , 6.04978791776e-08, 6.14434034901e-08
, 6.23756851626e-08 , 6.32957121259e-08 , 6.42043903937e-08, 6.51025540077e-08
, 6.59909735447e-08 , 6.68703634341e-08 , 6.77413882848e-08, 6.86046683810e-08
, 6.94607844804e-08 , 7.03102820203e-08 , 7.11536748229e-08, 7.19914483720e-08
, 7.28240627230e-08 , 7.36519550992e-08 , 7.44755422158e-08, 7.52952223703e-08
, 7.61113773308e-08 , 7.69243740467e-08 , 7.77345662086e-08, 7.85422956743e-08
, 7.93478937793e-08 , 8.01516825471e-08 , 8.09539758128e-08, 8.17550802699e-08
, 8.25552964535e-08 , 8.33549196661e-08 , 8.41542408569e-08, 8.49535474601e-08
, 8.57531242006e-08 , 8.65532538723e-08 , 8.73542180955e-08, 8.81562980590e-08
, 8.89597752521e-08 , 8.97649321908e-08 , 9.05720531451e-08, 9.13814248700e-08
, 9.21933373471e-08 , 9.30080845407e-08 , 9.38259651738e-08, 9.46472835298e-08
, 9.54723502847e-08 , 9.63014833769e-08 , 9.71350089201e-08, 9.79732621669e-08
, 9.88165885297e-08 , 9.96653446693e-08 , 1.00519899658e-07, 1.01380636230e-07
, 1.02247952126e-07 , 1.03122261554e-07 , 1.04003996769e-07, 1.04893609795e-07
, 1.05791574313e-07 , 1.06698387725e-07 , 1.07614573423e-07, 1.08540683296e-07
, 1.09477300508e-07 , 1.10425042570e-07 , 1.11384564771e-07, 1.12356564007e-07
, 1.13341783071e-07 , 1.14341015475e-07 , 1.15355110887e-07, 1.16384981291e-07
, 1.17431607977e-07 , 1.18496049514e-07 , 1.19579450872e-07, 1.20683053909e-07
, 1.21808209468e-07 , 1.22956391410e-07 , 1.24129212952e-07, 1.25328445797e-07
, 1.26556042658e-07 , 1.27814163916e-07 , 1.29105209375e-07, 1.30431856341e-07
, 1.31797105598e-07 , 1.33204337360e-07 , 1.34657379914e-07, 1.36160594606e-07
, 1.37718982103e-07 , 1.39338316679e-07 , 1.41025317971e-07, 1.42787873535e-07
, 1.44635331499e-07 , 1.46578891730e-07 , 1.48632138436e-07, 1.50811780719e-07
, 1.53138707402e-07 , 1.55639532047e-07 , 1.58348931426e-07, 1.61313325908e-07
, 1.64596952856e-07 , 1.68292495203e-07 , 1.72541128694e-07, 1.77574279496e-07
, 1.83813550477e-07 , 1.92166040885e-07 , 2.05295471952e-07, 2.22600839893e-07
} ;
double mcxNormalZiggurat
( void
)
{ unsigned long U, sign, i, j
; double x = 0.0, y
; while (1)
{ U = random()
; i = U & 0x0000007F /* 7 bit to choose the step */
; sign = U & 0x00000080 /* 1 bit for the sign */
; j = random() & 0x00FFFFFF /* 24 bit for the x-value */
; x = j*wtab[i]
; if (j < ktab[i])
break
; if (i<127)
{ double y0, y1
; y0 = ytab[i]
; y1 = ytab[i+1]
; y = y1+(y0-y1) * mcxUniform0
; }
else
{ x = PARAM_R - log(mcxUniform1)/PARAM_R
; y = exp(-PARAM_R*(x-0.5*PARAM_R)) * mcxUniform0
; }
if (y < exp(-0.5*x*x))
break
; }
return sign ? x : -x
; }
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