## Question

Suppose we toss darts randomly at a square dartboard, whose bullseye is at the origin, and whose sides are 2 feet in length. Suppose also that there's a circle inscribed in the square dartboard. The radius of the circle is 1 foot, and itβs area is π square feet. If the points that are hit by the darts are uniformly distributed (and we always hit the square), then the number of darts that hit inside the circle should approximately satisfy the equation

number in circle π

---------------------------- = ---------- ,

total number of tosses 4

since the ratio of the area of the circle to the area of the square is π/4. We can use this formula to estimate the value of ir with a random number generator:

number_in_circle = 0;

for (toss =0; toss < number_of_tosses ; toss++) {

x = random double between β1 and 1;

y = random double between β1 and 1;

distance_squared = xβx + yβy;

if (distance_squared <= 1) number_in_circle++;

}

pi_estimate = 4βnumber_in_circle/((double) number_of_tosses);

This is called a "Monte Carlo" method, since it uses randomness (the dart tosses). Write an OpenMP program that uses a Monte Carlo method to estimate π. Read in the total number of tosses before forking any threads. Use a reduction clause to find the total number of darts hitting inside the circle. Print the result after joining all the threads. You may want to use long long ints for the number of hits in the circle and the number of tosses, since both may have to be very large to get a reasonable estimate of π .

## Solution Preview

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#include <stdio.h>#include <stdlib.h>

#include <omp.h>

#include <time.h>

int main(int argc, char* argv[]){

long long number_in_circle = 0;

long long thread_count = 5;

double pi_estimate;

long long total_number_of_tosh, number_tossed_per_thread;

srand ( (unsigned)time ( NULL ) );

total_number_of_tosh = strtol(argv[1], NULL, 10);

thread_count = total_number_of_tosh > thread_count ? thread_count : 1;

printf("Please wait for a while\n");

number_tossed_per_thread = total_number_of_tosh/thread_count + 1...

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