Create ziggurat.c
This commit is contained in:
Simon D. Levy
683
c/ziggurat.c
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683
c/ziggurat.c
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/*
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ziggurat.c Ziggurat random-number generator
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Downloaded from
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http://people.sc.fsu.edu/~jburkardt/c_src/ziggurat/ziggurat.c
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on 20 July 2014.
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This code is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as
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published by the Free Software Foundation, either version 3 of the
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License, or (at your option) any later version.
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This code is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this code. If not, see <http:#www.gnu.org/licenses/>.
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*/
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# include <stdlib.h>
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# include <stdio.h>
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# include <math.h>
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# include <time.h>
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# include <stdint.h>
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# include "ziggurat.h"
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/******************************************************************************/
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uint32_t cong_seeded ( uint32_t *jcong )
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/******************************************************************************/
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/*
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Purpose:
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CONG_SEEDED evaluates the CONG congruential random number generator.
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Licensing:
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This code is distributed under the GNU LGPL license.
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Modified:
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16 October 2013
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Author:
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John Burkardt
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Reference:
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George Marsaglia, Wai Wan Tsang,
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The Ziggurat Method for Generating Random Variables,
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Journal of Statistical Software,
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Volume 5, Number 8, October 2000, seven pages.
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Parameters:
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Input/output, uint32_t *JCONG, the seed, which is updated
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on each call.
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Output, uint32_t CONG_SEEDED, the new value.
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*/
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{
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uint32_t value;
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*jcong = 69069 * ( *jcong ) + 1234567;
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value = *jcong;
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return value;
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}
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/******************************************************************************/
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double cpu_time ( )
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/******************************************************************************/
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/*
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Purpose:
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CPU_TIME returns the current reading on the CPU clock.
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Licensing:
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This code is distributed under the GNU LGPL license.
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Modified:
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08 December 2008
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Author:
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John Burkardt
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Parameters:
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Output, double CPU_TIME, the current reading of the CPU clock, in seconds.
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*/
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{
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double value;
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value = ( double ) clock ( ) / ( double ) CLOCKS_PER_SEC;
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return value;
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}
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/******************************************************************************/
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uint32_t kiss_seeded ( uint32_t *jcong, uint32_t *jsr, uint32_t *w, uint32_t *z )
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/******************************************************************************/
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/*
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Purpose:
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KISS_SEEDED evaluates the KISS random number generator.
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Licensing:
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This code is distributed under the GNU LGPL license.
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Modified:
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15 October 2013
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Author:
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John Burkardt
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Reference:
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George Marsaglia, Wai Wan Tsang,
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|
The Ziggurat Method for Generating Random Variables,
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|
Journal of Statistical Software,
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|
Volume 5, Number 8, October 2000, seven pages.
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|
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Parameters:
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Input/output, uint32_t *JCONG, uint32_t *JSR, uint32_t *W, uint32_t *Z,
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the seeds, which are updated on each call.
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Output, uint32_t KISS_SEEDED, the new value.
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*/
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{
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uint32_t value;
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value = ( mwc_seeded ( w, z ) ^ cong_seeded ( jcong ) ) + shr3_seeded ( jsr );
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return value;
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}
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/******************************************************************************/
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uint32_t mwc_seeded ( uint32_t *w, uint32_t *z )
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/******************************************************************************/
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/*
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Purpose:
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MWC_SEEDED evaluates the MWC multiply-with-carry random number generator.
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Licensing:
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|
This code is distributed under the GNU LGPL license.
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Modified:
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15 October 2013
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Author:
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John Burkardt
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|
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|
Reference:
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||||||
|
|
||||||
|
George Marsaglia, Wai Wan Tsang,
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||||||
|
The Ziggurat Method for Generating Random Variables,
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|
Journal of Statistical Software,
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|
Volume 5, Number 8, October 2000, seven pages.
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|
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|
Parameters:
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Input/output, uint32_t *W, uint32_t *Z, the seeds, which are updated
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on each call.
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Output, uint32_t MWC_SEEDED, the new value.
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*/
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{
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uint32_t value;
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*z = 36969 * ( *z & 65535 ) + ( *z >> 16 );
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*w = 18000 * ( *w & 65535 ) + ( *w >> 16 );
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value = ( *z << 16 ) + *w;
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return value;
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}
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/******************************************************************************/
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float r4_exp ( uint32_t *jsr, uint32_t ke[256], float fe[256], float we[256] )
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/******************************************************************************/
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/*
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Purpose:
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R4_EXP returns an exponentially distributed single precision real value.
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Discussion:
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The underlying algorithm is the ziggurat method.
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Before the first call to this function, the user must call R4_EXP_SETUP
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to determine the values of KE, FE and WE.
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Licensing:
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|
This code is distributed under the GNU LGPL license.
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|
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|
Modified:
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|
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15 October 2013
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Author:
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John Burkardt
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Reference:
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|
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||||||
|
George Marsaglia, Wai Wan Tsang,
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|
The Ziggurat Method for Generating Random Variables,
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|
Journal of Statistical Software,
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|
Volume 5, Number 8, October 2000, seven pages.
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||||||
|
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|
Parameters:
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|
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Input/output, uint32_t *JSR, the seed.
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Input, uint32_t KE[256], data computed by R4_EXP_SETUP.
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Input, float FE[256], WE[256], data computed by R4_EXP_SETUP.
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Output, float R4_EXP, an exponentially distributed random value.
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*/
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{
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uint32_t iz;
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uint32_t jz;
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float value;
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float x;
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jz = shr3_seeded ( jsr );
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iz = ( jz & 255 );
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if ( jz < ke[iz] )
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{
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value = ( float ) ( jz ) * we[iz];
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}
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else
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{
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for ( ; ; )
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{
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if ( iz == 0 )
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{
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value = 7.69711 - log ( r4_uni ( jsr ) );
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break;
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}
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x = ( float ) ( jz ) * we[iz];
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if ( fe[iz] + r4_uni ( jsr ) * ( fe[iz-1] - fe[iz] ) < exp ( - x ) )
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{
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value = x;
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break;
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}
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jz = shr3_seeded ( jsr );
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iz = ( jz & 255 );
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if ( jz < ke[iz] )
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{
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value = ( float ) ( jz ) * we[iz];
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break;
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}
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}
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}
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return value;
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}
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/******************************************************************************/
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void r4_exp_setup ( uint32_t ke[256], float fe[256], float we[256] )
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/******************************************************************************/
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/*
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Purpose:
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R4_EXP_SETUP sets data needed by R4_EXP.
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|
Licensing:
|
||||||
|
|
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|
This code is distributed under the GNU LGPL license.
|
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|
|
||||||
|
Modified:
|
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|
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|
14 October 2013
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|
Author:
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John Burkardt
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|
|
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|
Reference:
|
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|
|
||||||
|
George Marsaglia, Wai Wan Tsang,
|
||||||
|
The Ziggurat Method for Generating Random Variables,
|
||||||
|
Journal of Statistical Software,
|
||||||
|
Volume 5, Number 8, October 2000, seven pages.
|
||||||
|
|
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|
Parameters:
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|
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Output, uint32_t KE[256], data needed by R4_EXP.
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Output, float FE[256], WE[256], data needed by R4_EXP.
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*/
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{
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double de = 7.697117470131487;
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int i;
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const double m2 = 2147483648.0;
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double q;
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double te = 7.697117470131487;
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const double ve = 3.949659822581572E-03;
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q = ve / exp ( - de );
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ke[0] = ( uint32_t ) ( ( de / q ) * m2 );
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ke[1] = 0;
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we[0] = ( float ) ( q / m2 );
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we[255] = ( float ) ( de / m2 );
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fe[0] = 1.0;
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|
fe[255] = ( float ) ( exp ( - de ) );
|
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|
|
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|
for ( i = 254; 1 <= i; i-- )
|
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|
{
|
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|
de = - log ( ve / de + exp ( - de ) );
|
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|
ke[i+1] = ( uint32_t ) ( ( de / te ) * m2 );
|
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|
te = de;
|
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|
fe[i] = ( float ) ( exp ( - de ) );
|
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|
we[i] = ( float ) ( de / m2 );
|
||||||
|
}
|
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|
return;
|
||||||
|
}
|
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|
/******************************************************************************/
|
||||||
|
|
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|
float r4_nor ( uint32_t *jsr, uint32_t kn[128], float fn[128], float wn[128] )
|
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|
|
||||||
|
/******************************************************************************/
|
||||||
|
/*
|
||||||
|
Purpose:
|
||||||
|
|
||||||
|
R4_NOR returns a normally distributed single precision real value.
|
||||||
|
|
||||||
|
Discussion:
|
||||||
|
|
||||||
|
The value returned is generated from a distribution with mean 0 and
|
||||||
|
variance 1.
|
||||||
|
|
||||||
|
The underlying algorithm is the ziggurat method.
|
||||||
|
|
||||||
|
Before the first call to this function, the user must call R4_NOR_SETUP
|
||||||
|
to determine the values of KN, FN and WN.
|
||||||
|
|
||||||
|
Licensing:
|
||||||
|
|
||||||
|
This code is distributed under the GNU LGPL license.
|
||||||
|
|
||||||
|
Modified:
|
||||||
|
|
||||||
|
14 October 2013
|
||||||
|
|
||||||
|
Author:
|
||||||
|
|
||||||
|
John Burkardt
|
||||||
|
|
||||||
|
Reference:
|
||||||
|
|
||||||
|
George Marsaglia, Wai Wan Tsang,
|
||||||
|
The Ziggurat Method for Generating Random Variables,
|
||||||
|
Journal of Statistical Software,
|
||||||
|
Volume 5, Number 8, October 2000, seven pages.
|
||||||
|
|
||||||
|
Parameters:
|
||||||
|
|
||||||
|
Input/output, uint32_t *JSR, the seed.
|
||||||
|
|
||||||
|
Input, uint32_t KN[128], data computed by R4_NOR_SETUP.
|
||||||
|
|
||||||
|
Input, float FN[128], WN[128], data computed by R4_NOR_SETUP.
|
||||||
|
|
||||||
|
Output, float R4_NOR, a normally distributed random value.
|
||||||
|
*/
|
||||||
|
{
|
||||||
|
int hz;
|
||||||
|
uint32_t iz;
|
||||||
|
const float r = 3.442620;
|
||||||
|
float value;
|
||||||
|
float x;
|
||||||
|
float y;
|
||||||
|
|
||||||
|
hz = ( int ) shr3_seeded ( jsr );
|
||||||
|
iz = ( hz & 127 );
|
||||||
|
|
||||||
|
if ( fabs ( hz ) < kn[iz] )
|
||||||
|
{
|
||||||
|
value = ( float ) ( hz ) * wn[iz];
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
for ( ; ; )
|
||||||
|
{
|
||||||
|
if ( iz == 0 )
|
||||||
|
{
|
||||||
|
for ( ; ; )
|
||||||
|
{
|
||||||
|
x = - 0.2904764 * log ( r4_uni ( jsr ) );
|
||||||
|
y = - log ( r4_uni ( jsr ) );
|
||||||
|
if ( x * x <= y + y )
|
||||||
|
{
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if ( hz <= 0 )
|
||||||
|
{
|
||||||
|
value = - r - x;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
value = + r + x;
|
||||||
|
}
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
x = ( float ) ( hz ) * wn[iz];
|
||||||
|
|
||||||
|
if ( fn[iz] + r4_uni ( jsr ) * ( fn[iz-1] - fn[iz] )
|
||||||
|
< exp ( - 0.5 * x * x ) )
|
||||||
|
{
|
||||||
|
value = x;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
hz = ( int ) shr3_seeded ( jsr );
|
||||||
|
iz = ( hz & 127 );
|
||||||
|
|
||||||
|
if ( fabs ( hz ) < kn[iz] )
|
||||||
|
{
|
||||||
|
value = ( float ) ( hz ) * wn[iz];
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return value;
|
||||||
|
}
|
||||||
|
/******************************************************************************/
|
||||||
|
|
||||||
|
void r4_nor_setup ( uint32_t kn[128], float fn[128], float wn[128] )
|
||||||
|
|
||||||
|
/******************************************************************************/
|
||||||
|
/*
|
||||||
|
Purpose:
|
||||||
|
|
||||||
|
R4_NOR_SETUP sets data needed by R4_NOR.
|
||||||
|
|
||||||
|
Licensing:
|
||||||
|
|
||||||
|
This code is distributed under the GNU LGPL license.
|
||||||
|
|
||||||
|
Modified:
|
||||||
|
|
||||||
|
14 October 2013
|
||||||
|
|
||||||
|
Author:
|
||||||
|
|
||||||
|
John Burkardt
|
||||||
|
|
||||||
|
Reference:
|
||||||
|
|
||||||
|
George Marsaglia, Wai Wan Tsang,
|
||||||
|
The Ziggurat Method for Generating Random Variables,
|
||||||
|
Journal of Statistical Software,
|
||||||
|
Volume 5, Number 8, October 2000, seven pages.
|
||||||
|
|
||||||
|
Parameters:
|
||||||
|
|
||||||
|
Output, uint32_t KN[128], data needed by R4_NOR.
|
||||||
|
|
||||||
|
Output, float FN[128], WN[128], data needed by R4_NOR.
|
||||||
|
*/
|
||||||
|
{
|
||||||
|
double dn = 3.442619855899;
|
||||||
|
int i;
|
||||||
|
const double m1 = 2147483648.0;
|
||||||
|
double q;
|
||||||
|
double tn = 3.442619855899;
|
||||||
|
const double vn = 9.91256303526217E-03;
|
||||||
|
|
||||||
|
q = vn / exp ( - 0.5 * dn * dn );
|
||||||
|
|
||||||
|
kn[0] = ( uint32_t ) ( ( dn / q ) * m1 );
|
||||||
|
kn[1] = 0;
|
||||||
|
|
||||||
|
wn[0] = ( float ) ( q / m1 );
|
||||||
|
wn[127] = ( float ) ( dn / m1 );
|
||||||
|
|
||||||
|
fn[0] = 1.0;
|
||||||
|
fn[127] = ( float ) ( exp ( - 0.5 * dn * dn ) );
|
||||||
|
|
||||||
|
for ( i = 126; 1 <= i; i-- )
|
||||||
|
{
|
||||||
|
dn = sqrt ( - 2.0 * log ( vn / dn + exp ( - 0.5 * dn * dn ) ) );
|
||||||
|
kn[i+1] = ( uint32_t ) ( ( dn / tn ) * m1 );
|
||||||
|
tn = dn;
|
||||||
|
fn[i] = ( float ) ( exp ( - 0.5 * dn * dn ) );
|
||||||
|
wn[i] = ( float ) ( dn / m1 );
|
||||||
|
}
|
||||||
|
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
/******************************************************************************/
|
||||||
|
|
||||||
|
float r4_uni ( uint32_t *jsr )
|
||||||
|
|
||||||
|
/******************************************************************************/
|
||||||
|
/*
|
||||||
|
Purpose:
|
||||||
|
|
||||||
|
R4_UNI returns a uniformly distributed real value.
|
||||||
|
|
||||||
|
Licensing:
|
||||||
|
|
||||||
|
This code is distributed under the GNU LGPL license.
|
||||||
|
|
||||||
|
Modified:
|
||||||
|
|
||||||
|
04 October 2013
|
||||||
|
|
||||||
|
Author:
|
||||||
|
|
||||||
|
John Burkardt
|
||||||
|
|
||||||
|
Reference:
|
||||||
|
|
||||||
|
George Marsaglia, Wai Wan Tsang,
|
||||||
|
The Ziggurat Method for Generating Random Variables,
|
||||||
|
Journal of Statistical Software,
|
||||||
|
Volume 5, Number 8, October 2000, seven pages.
|
||||||
|
|
||||||
|
Parameters:
|
||||||
|
|
||||||
|
Input/output, uint32_t *JSR, the seed.
|
||||||
|
|
||||||
|
Output, float R4_UNI, a uniformly distributed random value in
|
||||||
|
the range [0,1].
|
||||||
|
*/
|
||||||
|
{
|
||||||
|
uint32_t jsr_input;
|
||||||
|
float value;
|
||||||
|
|
||||||
|
jsr_input = *jsr;
|
||||||
|
|
||||||
|
*jsr = ( *jsr ^ ( *jsr << 13 ) );
|
||||||
|
*jsr = ( *jsr ^ ( *jsr >> 17 ) );
|
||||||
|
*jsr = ( *jsr ^ ( *jsr << 5 ) );
|
||||||
|
|
||||||
|
value = fmod ( 0.5
|
||||||
|
+ ( float ) ( jsr_input + *jsr ) / 65536.0 / 65536.0, 1.0 );
|
||||||
|
|
||||||
|
return value;
|
||||||
|
}
|
||||||
|
/******************************************************************************/
|
||||||
|
|
||||||
|
uint32_t shr3_seeded ( uint32_t *jsr )
|
||||||
|
|
||||||
|
/******************************************************************************/
|
||||||
|
/*
|
||||||
|
Purpose:
|
||||||
|
|
||||||
|
SHR3_SEEDED evaluates the SHR3 generator for integers.
|
||||||
|
|
||||||
|
Discussion:
|
||||||
|
|
||||||
|
Thanks to Dirk Eddelbuettel for pointing out that this code needed to
|
||||||
|
use the uint32_t data type in order to execute properly in 64 bit mode,
|
||||||
|
03 October 2013.
|
||||||
|
|
||||||
|
Licensing:
|
||||||
|
|
||||||
|
This code is distributed under the GNU LGPL license.
|
||||||
|
|
||||||
|
Modified:
|
||||||
|
|
||||||
|
04 October 2013
|
||||||
|
|
||||||
|
Author:
|
||||||
|
|
||||||
|
John Burkardt
|
||||||
|
|
||||||
|
Reference:
|
||||||
|
|
||||||
|
George Marsaglia, Wai Wan Tsang,
|
||||||
|
The Ziggurat Method for Generating Random Variables,
|
||||||
|
Journal of Statistical Software,
|
||||||
|
Volume 5, Number 8, October 2000, seven pages.
|
||||||
|
|
||||||
|
Parameters:
|
||||||
|
|
||||||
|
Input/output, uint32_t *JSR, the seed, which is updated
|
||||||
|
on each call.
|
||||||
|
|
||||||
|
Output, uint32_t SHR3_SEEDED, the new value.
|
||||||
|
*/
|
||||||
|
{
|
||||||
|
uint32_t value;
|
||||||
|
|
||||||
|
value = *jsr;
|
||||||
|
|
||||||
|
*jsr = ( *jsr ^ ( *jsr << 13 ) );
|
||||||
|
*jsr = ( *jsr ^ ( *jsr >> 17 ) );
|
||||||
|
*jsr = ( *jsr ^ ( *jsr << 5 ) );
|
||||||
|
|
||||||
|
value = value + *jsr;
|
||||||
|
|
||||||
|
return value;
|
||||||
|
}
|
||||||
|
/******************************************************************************/
|
||||||
|
|
||||||
|
void timestamp ( )
|
||||||
|
|
||||||
|
/******************************************************************************/
|
||||||
|
/*
|
||||||
|
Purpose:
|
||||||
|
|
||||||
|
TIMESTAMP prints the current YMDHMS date as a time stamp.
|
||||||
|
|
||||||
|
Example:
|
||||||
|
|
||||||
|
31 May 2001 09:45:54 AM
|
||||||
|
|
||||||
|
Licensing:
|
||||||
|
|
||||||
|
This code is distributed under the GNU LGPL license.
|
||||||
|
|
||||||
|
Modified:
|
||||||
|
|
||||||
|
24 September 2003
|
||||||
|
|
||||||
|
Author:
|
||||||
|
|
||||||
|
John Burkardt
|
||||||
|
|
||||||
|
Parameters:
|
||||||
|
|
||||||
|
None
|
||||||
|
*/
|
||||||
|
{
|
||||||
|
# define TIME_SIZE 40
|
||||||
|
|
||||||
|
static char time_buffer[TIME_SIZE];
|
||||||
|
const struct tm *tm;
|
||||||
|
/* size_t len; UNUSED; COMMENTED-OUT BY SIMON D. LEVY 20 JUL 2014 */
|
||||||
|
time_t now;
|
||||||
|
|
||||||
|
now = time ( NULL );
|
||||||
|
tm = localtime ( &now );
|
||||||
|
|
||||||
|
/* len = */ strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );
|
||||||
|
|
||||||
|
printf ( "%s\n", time_buffer );
|
||||||
|
|
||||||
|
return;
|
||||||
|
# undef TIME_SIZE
|
||||||
|
}
|
||||||
Reference in New Issue
Block a user