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/*
COMPILATION: gcc -fopenmp integral1d_OMP.c -lm
USAGE: ./a.out thread# trial#
This program computes integral of ( 1 / (1 + x*x) ) in x=[0,1] by using importance sampling Monte Carlo
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <omp.h>
// f() is the function to be integrated
double f(double x)
{
return (1.0 / (1.0 + x*x) ) ;
}
// random x values are generated according to probability distribution function w()
double w(double x)
{
return ((1.0/3.0) * (4 - 2 * x)) ;
}
// my_rand() function generates random numbers according to p.d.f w()
// this function uses inverse of the p.d.f w()
double my_rand()
{
double y = (double)rand() / (double)RAND_MAX ;
return (2.0 - sqrt(4.0 - 3.0*y) ) ;
}
int main(int argc, char* argv[])
{
int i;
double sum = 0;
double x;
int thread_count = atoi(argv[1]); // number of threads participating computation is read from the command lile arguments
int trials = atoi(argv[2]); // trials is total number of random points, it is read from the command line arguments
// multiple threads are started after this compiler directive, num_threads() function indicates number of threads to be started
// reduction(+:sum) function indicates end of the parallel region total_hits variables of each thread are gathered in master thread
// private(x) indicates variable x is private to each thread instead of being shared by threads
#pragma omp parallel num_threads(thread_count) reduction(+:sum) private(x)
{
// It is desired every thread to generate different random numbers so
// each thread are seeded with different number (thread id)
srand(omp_get_thread_num());
//this compiler directive divides the loop iterations between the spawned threads
#pragma omp for
for(i=0 ; i < trials ; i++ )
{
x = my_rand() ;
sum += ( f(x) / w(x) ) ;
}
}// all threads are joined after this block
double integral = sum / trials ;
printf("computed value of the integral= %f \n", integral);
printf("true value of the integral= %f \n", atan(1.0));
printf("error= %f \n", fabs( integral - atan(1.0)));
return 0;
}