pi_reduce.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 <mpi.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, pi;

	MPI_Init(NULL, NULL);
	int prank, psize;
	MPI_Comm_rank(MPI_COMM_WORLD, &prank);
	MPI_Comm_size(MPI_COMM_WORLD, &psize);
	auto t1 = clk::now();

	auto ln = n/psize + (prank < n % psize ? 1 : 0);

	auto i_start = prank * ln + (prank < n % psize ? 0 : n % psize);
	auto i_end = i_start + ln;

	/* calculate pi = integral [0..1] 4 / (1 + x*2) dx /
	dx = 1. / n;
	double sum = 0.0;
	for (i = i_start; i < i_end; i++) {
	x = 1. * i * dx;
	sum = sum + f(x);
	}


	MPI_Allreduce(MPI_IN_PLACE, &sum, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);

	pi = dx * sum;


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

	if (prank == 0) {
	std::printf("computed pi = %.16g\n", pi);
	std::printf("wall clock time (chrono) = %.4gs\n", elapsed.count());
	std::printf("n mpi process = %.d\n", psize);


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

	MPI_Finalize();

	return 0;
	}