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Diffstat (limited to 'gsl-1.9/rng/slatec.c')
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diff --git a/gsl-1.9/rng/slatec.c b/gsl-1.9/rng/slatec.c new file mode 100644 index 0000000..57e9ffb --- /dev/null +++ b/gsl-1.9/rng/slatec.c @@ -0,0 +1,205 @@ +/* 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; |