/* * Mathlib : A C Library of Special Functions * Copyright (C) 1998 Ross Ihaka * Copyright (C) 2000-2022 The R Core Team * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, a copy is available at * https://www.R-project.org/Licenses/ * * SYNOPSIS * * #include * double norm_rand(void); * * DESCRIPTION * * Random variates from the STANDARD normal distribution N(0,1). * * Is called from rnorm(..), but also rt(), rf(), rgamma(), ... */ #include #include "nmath.h" #define repeat for(;;) #ifdef MATHLIB_STANDALONE static #else attribute_hidden #endif double BM_norm_keep = 0.0; N01type N01_kind = INVERSION; #ifndef MATHLIB_STANDALONE typedef void * (*DL_FUNC)(void); extern DL_FUNC User_norm_fun; /* declared and set in ../main/RNG.c */ #endif /* * REFERENCE * * Ahrens, J.H. and Dieter, U. * Extensions of Forsythe's method for random sampling from * the normal distribution. * Math. Comput. 27, 927-937. * * The definitions of the constants a[k], d[k], t[k] and * h[k] are according to the abovementioned article */ double norm_rand(void) { const static double a[32] = { 0.0000000, 0.03917609, 0.07841241, 0.1177699, 0.1573107, 0.19709910, 0.23720210, 0.2776904, 0.3186394, 0.36012990, 0.40225010, 0.4450965, 0.4887764, 0.53340970, 0.57913220, 0.6260990, 0.6744898, 0.72451440, 0.77642180, 0.8305109, 0.8871466, 0.94678180, 1.00999000, 1.0775160, 1.1503490, 1.22985900, 1.31801100, 1.4177970, 1.5341210, 1.67594000, 1.86273200, 2.1538750 }; const static double d[31] = { 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.2636843, 0.2425085, 0.2255674, 0.2116342, 0.1999243, 0.1899108, 0.1812252, 0.1736014, 0.1668419, 0.1607967, 0.1553497, 0.1504094, 0.1459026, 0.1417700, 0.1379632, 0.1344418, 0.1311722, 0.1281260, 0.1252791, 0.1226109, 0.1201036, 0.1177417, 0.1155119, 0.1134023, 0.1114027, 0.1095039 }; const static double t[31] = { 7.673828e-4, 0.002306870, 0.003860618, 0.005438454, 0.007050699, 0.008708396, 0.010423570, 0.012209530, 0.014081250, 0.016055790, 0.018152900, 0.020395730, 0.022811770, 0.025434070, 0.028302960, 0.031468220, 0.034992330, 0.038954830, 0.043458780, 0.048640350, 0.054683340, 0.061842220, 0.070479830, 0.081131950, 0.094624440, 0.112300100, 0.136498000, 0.171688600, 0.227624100, 0.330498000, 0.584703100 }; const static double h[31] = { 0.03920617, 0.03932705, 0.03950999, 0.03975703, 0.04007093, 0.04045533, 0.04091481, 0.04145507, 0.04208311, 0.04280748, 0.04363863, 0.04458932, 0.04567523, 0.04691571, 0.04833487, 0.04996298, 0.05183859, 0.05401138, 0.05654656, 0.05953130, 0.06308489, 0.06737503, 0.07264544, 0.07926471, 0.08781922, 0.09930398, 0.11555990, 0.14043440, 0.18361420, 0.27900160, 0.70104740 }; /*----------- Constants and definitions for Kinderman - Ramage --- */ /* * REFERENCE * * Kinderman A. J. and Ramage J. G. (1976). * Computer generation of normal random variables. * JASA 71, 893-896. */ #define C1 0.398942280401433 #define C2 0.180025191068563 #define g(x) (C1*exp(-x*x/2.0)-C2*(A-x)) const static double A = 2.216035867166471; double s, u1, w, y, u2, u3, aa, tt, theta, R; int i; switch(N01_kind) { case AHRENS_DIETER: /* see Reference above */ u1 = unif_rand(); s = 0.0; if (u1 > 0.5) s = 1.0; u1 = u1 + u1 - s; u1 *= 32.0; i = (int) u1; if (i == 32) i = 31; if (i != 0) { u2 = u1 - i; aa = a[i - 1]; while (u2 <= t[i - 1]) { u1 = unif_rand(); w = u1 * (a[i] - aa); tt = (w * 0.5 + aa) * w; repeat { if (u2 > tt) goto deliver; u1 = unif_rand(); if (u2 < u1) break; tt = u1; u2 = unif_rand(); } u2 = unif_rand(); } w = (u2 - t[i - 1]) * h[i - 1]; } else { i = 6; aa = a[31]; repeat { u1 = u1 + u1; if (u1 >= 1.0) break; aa = aa + d[i - 1]; i = i + 1; } u1 = u1 - 1.0; repeat { w = u1 * d[i - 1]; tt = (w * 0.5 + aa) * w; repeat { u2 = unif_rand(); if (u2 > tt) goto jump; u1 = unif_rand(); if (u2 < u1) break; tt = u1; } u1 = unif_rand(); } jump:; } deliver: y = aa + w; return (s == 1.0) ? -y : y; /*-----------------------------------------------------------*/ case BUGGY_KINDERMAN_RAMAGE: /* see Reference above */ /* note: this has problems, but is retained for * reproducibility of older codes, with the same * numeric code */ u1 = unif_rand(); if(u1 < 0.884070402298758) { u2 = unif_rand(); return A*(1.13113163544180*u1+u2-1); } if(u1 >= 0.973310954173898) { /* tail: */ repeat { u2 = unif_rand(); u3 = unif_rand(); tt = (A*A-2*log(u3)); if( u2*u2<(A*A)/tt ) return (u1 < 0.986655477086949) ? sqrt(tt) : -sqrt(tt); } } if(u1 >= 0.958720824790463) { /* region3: */ repeat { u2 = unif_rand(); u3 = unif_rand(); tt = A - 0.630834801921960* fmin2(u2,u3); if(fmax2(u2,u3) <= 0.755591531667601) return (u2= 0.911312780288703) { /* region2: */ repeat { u2 = unif_rand(); u3 = unif_rand(); tt = 0.479727404222441+1.105473661022070*fmin2(u2,u3); if( fmax2(u2,u3)<=0.872834976671790 ) return (u2= 0.973310954173898) { /* tail: */ repeat { u2 = unif_rand(); u3 = unif_rand(); tt = (A*A-2*log(u3)); if( u2*u2<(A*A)/tt ) return (u1 < 0.986655477086949) ? sqrt(tt) : -sqrt(tt); } } if(u1 >= 0.958720824790463) { /* region3: */ repeat { u2 = unif_rand(); u3 = unif_rand(); tt = A - 0.630834801921960* fmin2(u2,u3); if(fmax2(u2,u3) <= 0.755591531667601) return (u2= 0.911312780288703) { /* region2: */ repeat { u2 = unif_rand(); u3 = unif_rand(); tt = 0.479727404222441+1.105473661022070*fmin2(u2,u3); if( fmax2(u2,u3)<=0.872834976671790 ) return (u2