/* rng/slatec.c * * Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough * * 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, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /** * ====================================================================== * NIST Guide to Available Math Software. * Source for module RAND from package CMLIB. * Retrieved from TIBER on Fri Oct 11 11:43:42 1996. * ====================================================================== FUNCTION RAND(R) C***BEGIN PROLOGUE RAND C***DATE WRITTEN 770401 (YYMMDD) C***REVISION DATE 820801 (YYMMDD) C***CATEGORY NO. L6A21 C***KEYWORDS RANDOM NUMBER,SPECIAL FUNCTION,UNIFORM C***AUTHOR FULLERTON, W., (LANL) C***PURPOSE Generates a uniformly distributed random number. C***DESCRIPTION C C This pseudo-random number generator is portable among a wide C variety of computers. RAND(R) undoubtedly is not as good as many C readily available installation dependent versions, and so this C routine is not recommended for widespread usage. Its redeeming C feature is that the exact same random numbers (to within final round- C off error) can be generated from machine to machine. Thus, programs C that make use of random numbers can be easily transported to and C checked in a new environment. C The random numbers are generated by the linear congruential C method described, e.g., by Knuth in Seminumerical Methods (p.9), C Addison-Wesley, 1969. Given the I-th number of a pseudo-random C sequence, the I+1 -st number is generated from C X(I+1) = (A*X(I) + C) MOD M, C where here M = 2**22 = 4194304, C = 1731 and several suitable values C of the multiplier A are discussed below. Both the multiplier A and C random number X are represented in double precision as two 11-bit C words. The constants are chosen so that the period is the maximum C possible, 4194304. C In order that the same numbers be generated from machine to C machine, it is necessary that 23-bit integers be reducible modulo C 2**11 exactly, that 23-bit integers be added exactly, and that 11-bit C integers be multiplied exactly. Furthermore, if the restart option C is used (where R is between 0 and 1), then the product R*2**22 = C R*4194304 must be correct to the nearest integer. C The first four random numbers should be .0004127026, C .6750836372, .1614754200, and .9086198807. The tenth random number C is .5527787209, and the hundredth is .3600893021 . The thousandth C number should be .2176990509 . C In order to generate several effectively independent sequences C with the same generator, it is necessary to know the random number C for several widely spaced calls. The I-th random number times 2**22, C where I=K*P/8 and P is the period of the sequence (P = 2**22), is C still of the form L*P/8. In particular we find the I-th random C number multiplied by 2**22 is given by C I = 0 1*P/8 2*P/8 3*P/8 4*P/8 5*P/8 6*P/8 7*P/8 8*P/8 C RAND= 0 5*P/8 2*P/8 7*P/8 4*P/8 1*P/8 6*P/8 3*P/8 0 C Thus the 4*P/8 = 2097152 random number is 2097152/2**22. C Several multipliers have been subjected to the spectral test C (see Knuth, p. 82). Four suitable multipliers roughly in order of C goodness according to the spectral test are C 3146757 = 1536*2048 + 1029 = 2**21 + 2**20 + 2**10 + 5 C 2098181 = 1024*2048 + 1029 = 2**21 + 2**10 + 5 C 3146245 = 1536*2048 + 517 = 2**21 + 2**20 + 2**9 + 5 C 2776669 = 1355*2048 + 1629 = 5**9 + 7**7 + 1 C C In the table below LOG10(NU(I)) gives roughly the number of C random decimal digits in the random numbers considered I at a time. C C is the primary measure of goodness. In both cases bigger is better. C C LOG10 NU(I) C(I) C A I=2 I=3 I=4 I=5 I=2 I=3 I=4 I=5 C C 3146757 3.3 2.0 1.6 1.3 3.1 1.3 4.6 2.6 C 2098181 3.3 2.0 1.6 1.2 3.2 1.3 4.6 1.7 C 3146245 3.3 2.2 1.5 1.1 3.2 4.2 1.1 0.4 C 2776669 3.3 2.1 1.6 1.3 2.5 2.0 1.9 2.6 C Best C Possible 3.3 2.3 1.7 1.4 3.6 5.9 9.7 14.9 C C Input Argument -- C R If R=0., the next random number of the sequence is generated. C If R .LT. 0., the last generated number will be returned for C possible use in a restart procedure. C If R .GT. 0., the sequence of random numbers will start with C the seed R mod 1. This seed is also returned as the value of C RAND provided the arithmetic is done exactly. C C Output Value -- C RAND a pseudo-random number between 0. and 1. C***REFERENCES (NONE) C***ROUTINES CALLED (NONE) C***END PROLOGUE RAND DATA IA1, IA0, IA1MA0 /1536, 1029, 507/ DATA IC /1731/ DATA IX1, IX0 /0, 0/ C***FIRST EXECUTABLE STATEMENT RAND IF (R.LT.0.) GO TO 10 IF (R.GT.0.) GO TO 20 C C A*X = 2**22*IA1*IX1 + 2**11*(IA1*IX1 + (IA1-IA0)*(IX0-IX1) C + IA0*IX0) + IA0*IX0 C IY0 = IA0*IX0 IY1 = IA1*IX1 + IA1MA0*(IX0-IX1) + IY0 IY0 = IY0 + IC IX0 = MOD (IY0, 2048) IY1 = IY1 + (IY0-IX0)/2048 IX1 = MOD (IY1, 2048) C 10 RAND = IX1*2048 + IX0 RAND = RAND / 4194304. RETURN C 20 IX1 = AMOD(R,1.)*4194304. + 0.5 IX0 = MOD (IX1, 2048) IX1 = (IX1-IX0)/2048 GO TO 10 C END **/ #include <config.h> #include <stdlib.h> #include <gsl/gsl_rng.h> static inline unsigned long int slatec_get (void *vstate); static double slatec_get_double (void *vstate); static void slatec_set (void *state, unsigned long int s); typedef struct { long int x0, x1; } slatec_state_t; static const long P = 4194304; static const long a1 = 1536; static const long a0 = 1029; static const long a1ma0 = 507; static const long c = 1731; static inline unsigned long int slatec_get (void *vstate) { long y0, y1; slatec_state_t *state = (slatec_state_t *) vstate; y0 = a0 * state->x0; y1 = a1 * state->x1 + a1ma0 * (state->x0 - state->x1) + y0; y0 = y0 + c; state->x0 = y0 % 2048; y1 = y1 + (y0 - state->x0) / 2048; state->x1 = y1 % 2048; return state->x1 * 2048 + state->x0; } static double slatec_get_double (void *vstate) { return slatec_get (vstate) / 4194304.0 ; } static void slatec_set (void *vstate, unsigned long int s) { slatec_state_t *state = (slatec_state_t *) vstate; /* Only eight seeds are permitted. This is pretty limiting, but at least we are guaranteed that the eight sequences are different */ s = s % 8; s *= P / 8; state->x0 = s % 2048; state->x1 = (s - state->x0) / 2048; } static const gsl_rng_type slatec_type = {"slatec", /* name */ 4194303, /* RAND_MAX */ 0, /* RAND_MIN */ sizeof (slatec_state_t), &slatec_set, &slatec_get, &slatec_get_double}; const gsl_rng_type *gsl_rng_slatec = &slatec_type;

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