| /* 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; |
