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mcsin.c
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mcsin.c
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/* mcsin.c - Monte Carlo Integral of sin(x) Version 1.0.0 */
/* Copyright (C) 2016 aquila62 at github.com */
/* 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: */
/* Free Software Foundation, Inc. */
/* 59 Temple Place - Suite 330 */
/* Boston, MA 02111-1307, USA. */
/***********************************************************/
/* mcsin estimates the integral of sin(x) through a Monte */
/* Carlo simulation. */
/* x = uniform random number 0-pi */
/* y = uniform random number 0-1 */
/* n = 1 million */
/* If y < sin(x) then tally a counter */
/* Pi * the ratio of the (counter / 1 million) */
/* is approximately 2.0 to 3 decimal places */
/* or approximately 2.000... */
/***********************************************************/
#include <stdio.h>
#include <time.h>
#include <sys/times.h>
#include <math.h>
#include <gsl/gsl_rng.h>
#include "etaus.h"
#ifndef M_PI
#define M_PI (3.14159265358979323846)
#endif
int main(void)
{
int i; /* loop counter */
int etauselap; /* elapsed time for etaus */
int mtelap; /* elapsed time for mt19937 */
int ranlxelap; /* elapsed time for ranlxd2 */
unsigned int dttk; /* combined date, time #ticks */
double tot; /* total points within a circle */
double bot; /* 1 million */
double ratio; /* estimated 2 / pi */
time_t now; /* current date and time */
clock_t clk; /* current number of ticks */
clock_t etausstart; /* start time for etaus */
clock_t etausfin; /* end time for etaus */
clock_t mtstart; /* start time for mt19937 */
clock_t mtfin; /* end time for mt19937 */
clock_t ranlxstart; /* start time for ranlxd2 */
clock_t ranlxfin; /* end time for ranlxd2 */
struct tms t; /* structure used by times() */
gsl_rng *r; /* GSL RNG structure */
etfmt *et; /* etaus structure */
et = (etfmt *) etausinit(); /* initialize the etaus structure */
bot = 1000000.0; /* set to 1 million */
/************************************************************/
tot = 0.0; /* initialize total */
i = (int) bot; /* set loop counter */
/* get clock ticks since boot */
etausstart = times(&t); /* start time for etaus */
while (i--) /* loop 1 million times */
{
double x; /* horizontal coordinate */
double y; /* vertical coordinate */
double wyy; /* y = sin(x) */
x = etausunif(et) * M_PI; /* uniform number 0-pi */
y = etausunif(et); /* uniform number 0-1 */
wyy = sin(x); /* the sine curve */
if (y < wyy) tot += 1.0; /* if y is under the curve, tally */
} /* for each point above or below a sine curve */
ratio = M_PI * (tot / bot); /* calculate est. 2.0 */
etausfin = times(&t); /* finish time for etaus */
printf("Monte Carlo Definite Integral of sin(x)\n");
printf(" From zero to Pi\n");
printf(" Expected error is 1/1000\n");
printf(" n = 1 million\n");
printf(" etaus %18.15f\n", ratio);
/************************************************************/
/* allocate the mt19937 random number generator */
r = (gsl_rng *) gsl_rng_alloc(gsl_rng_mt19937);
/* get clock ticks since boot */
clk = times(&t);
/* get date & time */
time(&now);
/* combine date, time, and ticks into a single UINT */
dttk = (unsigned int) (now ^ clk);
/* initialize the GSL Mersenne Twister */
/* random number generator to date,time,#ticks */
gsl_rng_set(r, dttk); /* initialize mt19937 seed */
tot = 0.0; /* initialize total */
i = (int) bot; /* set loop counter */
/* get clock ticks since boot */
mtstart = times(&t); /* start time for GSL mt19937 */
while (i--) /* loop 1 million times */
{
double x; /* horizontal coordinate */
double y; /* vertical coordinate */
double wyy; /* y = sin(x) */
/* use the mt19937 random number generator this time */
x = gsl_rng_uniform(r) * M_PI; /* uniform number 0-pi */
y = gsl_rng_uniform(r); /* uniform number 0-1 */
wyy = sin(x); /* the sine curve */
if (y < wyy) tot += 1.0; /* if under the curve, tally */
} /* for each point above or below a sine curve */
ratio = M_PI * tot / bot; /* calculate est. 2.0 */
mtfin = times(&t); /* finish time for GSL mt19937 */
printf("GSL mt19937 %18.15f\n", ratio);
gsl_rng_free(r);
/************************************************************/
/* allocate the ranlxd2 random number generator */
r = (gsl_rng *) gsl_rng_alloc(gsl_rng_ranlxd2);
/* get clock ticks since boot */
clk = times(&t);
/* get date & time */
time(&now);
/* combine date, time, and ticks into a single UINT */
dttk = (unsigned int) (now ^ clk);
/* initialize the GSL ranlxd2 random number generator */
/* to date,time,#ticks */
gsl_rng_set(r, dttk); /* initialize ranlxd2 seed */
tot = 0.0; /* initialize total */
i = (int) bot; /* set loop counter */
/* get clock ticks since boot */
ranlxstart = times(&t); /* start time for GSL ranlxd2 */
while (i--) /* loop 1 million times */
{
double x; /* horizontal coordinate */
double y; /* vertical coordinate */
double wyy; /* y = sin(x) */
/* use the ranlxd2 random number generator this time */
x = gsl_rng_uniform(r) * M_PI; /* uniform number 0-pi */
y = gsl_rng_uniform(r); /* uniform number 0-1 */
wyy = sin(x); /* the sine curve */
if (y < wyy) tot += 1.0; /* if under the curve, tally */
} /* for each point above or below a sine curve */
ratio = M_PI * (tot / bot); /* calculate est. 2.0 */
ranlxfin = times(&t); /* finish time for GSL ranlxd2 */
printf("GSL ranlxd2 %18.15f\n", ratio);
printf(" Actual %18.15f\n", 2.0);
etauselap = etausfin - etausstart;
mtelap = mtfin - mtstart;
ranlxelap = ranlxfin - ranlxstart;
printf(" etaus ticks %6d\n", etauselap);
printf("GSL mt19937 ticks %6d\n", mtelap);
printf("GSL ranlxd2 ticks %6d\n", ranlxelap);
gsl_rng_free(r);
free(et->state);
free(et);
return(0);
} /* main */