pi_reduction.f90
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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
	! ==========================================================================

	program pi_reduction

	implicit none

	integer :: myrank, num_threads
	integer, parameter :: n = 10000000
	double precision :: omp_t1, omp_t2
	double precision :: dx, x, sm, lsum, pif
	double precision, external :: second,f
	!$ double precision, external :: omp_get_wtime
	integer :: i

	! calculate pi = integral [0..1] 4 / (1 + x*2) dx /
	omp_t1 = second()
	!$ omp_t1 = omp_get_wtime()

	dx = 1. / n
	sm = 0.0;
	!$OMP parallel do private(i) reduction(+:sm)
	do i = 1, n
	x = (1. * i - 0.5) * dx
	sm = sm + f(x)
	enddo
	!$OMP end parallel do

	pif = dx * sm

	omp_t2 = second()
	!$ omp_t2 = omp_get_wtime()

	print *, 'computed pi =',pif
	print *, 'Running time = ', (omp_t2-omp_t1)

	end program pi_reduction


	double precision function f(a)
	implicit none
	double precision, intent(in) :: a
	f = 4. / (1. + (a**2))
	end function f