problem2.cpp

#include <iostream>
#include <omp.h>

//use synchronization for accumulation

int main()
{
	double t = omp_get_wtime();
	int N = 100000000;
	double dx = 1.0 / N;
	double I = 0;
	const double pi = 3.14159265358979323846;
	int nthreads = 1; //to store the number of threads I actually get
	omp_set_num_threads(12);
#pragma omp parallel
	{

		int id = omp_get_thread_num();
		int nthrds = omp_get_num_threads(); //this could be LESS THAN 15! I don't set num_threads; I request for a certain num of threads
		double sum = 0;
		if (id == 0) nthreads = nthrds; // I need to know this AFTER threads have joined for sum. And can't risk multiple threads writing together
		for (int i = id; i < N; i += nthrds)
		{
			double x = (i + 0.5) / N;
			sum += 4 / (1 + x * x);// *dx --  just do it l8r;
		}
		sum *= dx;

#pragma omp critical //run by only one thread at a time, could also say #pragma omp atomic if i'm only enclosing simple operations
		{
			I += sum;
		}
	}

	
	std::cout << "nthreads: " << nthreads << std::endl;
	printf("calculated: %1.18f\nactual____: %1.18f\ndifference: %1.18f\n", I, pi, I - pi);
	printf("Time elapsed: %f", omp_get_wtime() - t);
}

//NOTE: I didn't note my power settings so comparing w/ & w/o sync. sections isn't meaningful. Observe speedup v/s nthreads


//WITH SYNCHRONIZATION
/*
nthreads: 1
calculated: 3.141592653590426387
actual____: 3.141592653589793116
difference: 0.000000000000633271
Time elapsed: 3.112252

nthreads: 4
calculated: 3.141592653590216777
actual____: 3.141592653589793116
difference: 0.000000000000423661
Time elapsed: 0.932348

nthreads: 12
calculated: 3.141592653589739381
actual____: 3.141592653589793116
difference: -0.000000000000053735
Time elapsed: 0.430023
*/


//WITHOUT SYNCHRONIZATION
/*
nthreads: 1
calculated: 3.141592653590426387
actual____: 3.141592653589793116
difference: 0.000000000000633271
Time elapsed: 1.326220

nthreads: 2
calculated: 3.141592653590022266
actual____: 3.141592653589793116
difference: 0.000000000000229150
Time elapsed: 0.674603

nthreads: 4
calculated: 3.141592653590216777
actual____: 3.141592653589793116
difference: 0.000000000000423661
Time elapsed: 0.339127

nthreads: 12
calculated: 3.141592653589739825
actual____: 3.141592653589793116
difference: -0.000000000000053291
Time elapsed: 0.182399

nthreads: 24
calculated: 3.141592653589754036
actual____: 3.141592653589793116
difference: -0.000000000000039080
Time elapsed: 0.208672

*/