/* rng/slatec.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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;