pi_slow_critical.cc
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	/*
	This exercise is taken from the class Parallel Programming Workshop (MPI,
	OpenMP and Advanced Topics) at HLRS given by Rolf Rabenseifner
	*/
	#include <chrono>
	#include <cstdio>
	#include <cmath>
	#include <omp.h>

	using clk = std::chrono::high_resolution_clock;
	using second = std::chrono::duration<double>;
	using time_point = std::chrono::time_point<clk>;

	inline int digit(double x, int n) {
	return std::trunc(x * std::pow(10., n)) - std::trunc(x * std::pow(10., n - 1)) *10.;
	}

	inline double f(double a) { return (4. / (1. + a * a)); }

	const int n = 10000000;

	int main(int /* argc / , char * /* argv */) {
	int i;
	double dx, x, sum, pi;

	auto nthreads = omp_get_max_threads();

	auto t1 = clk::now();

	/* calculate pi = integral [0..1] 4 / (1 + x*2) dx /
	dx = 1. / n;
	sum = 0.0;
	#pragma omp parallel for shared(sum) private(x)
	for (i = 0; i < n; i++) {
	x = 1. * i * dx;
	#pragma omp critical
	sum = sum + f(x);
	}
	pi = dx * sum;


	second elapsed = clk::now() - t1;

	std::printf("computed pi = %.16g\n", pi);
	std::printf("wall clock time (chrono) = %.4gs\n", elapsed.count());
	std::printf("using n threads = %.d\n", nthreads);

	for(int d = 1; d <= 15; ++d) {
	std::printf("%d", digit(pi, d));
	}

	return 0;
	}