pi_critical_correct.cc
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	#include <chrono>
	#include <cmath>
	#include <cstdio>

	#if defined(_OPENMP)
	#include <omp.h>
	#endif

	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, lsum, pi;

	#if defined(_OPENMP)
	int num_threads = omp_get_max_threads();
	#endif

	#if defined(_OPENMP)
	auto omp_t1 = omp_get_wtime();
	#endif
	auto t1 = clk::now();

	sum = 0.;
	#pragma omp parallel shared(sum) private(x, lsum)
	{
	/* calculate pi = integral [0..1] 4 / (1 + x*2) dx /
	dx = 1. / n;
	lsum = 0.0;
	#pragma omp for
	for (i = 1; i <= n; i++) {
	x = (1. * i - 0.5) * dx;
	lsum = lsum + f(x);
	}

	#pragma omp critical
	sum += lsum;
	}

	pi = dx * sum;

	#if defined(_OPENMP)
	auto omp_elapsed = omp_get_wtime() - omp_t1;
	#endif
	second elapsed = clk::now() - t1;

	std::printf("computed pi = %.16g\n", pi);
	#if defined(_OPENMP)
	std::printf("wall clock time (omp_get_wtime) = %.4gs on %d threads\n",
	omp_elapsed, num_threads);
	#endif
	std::printf("wall clock time (chrono) = %.4gs\n", elapsed.count());

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

	return 0;
	}