pi_p2p_sendrecv_ring.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_p2p_sendrecv_ring

	use mpi

	implicit none

	integer, parameter :: n = 10000000
	double precision :: omp_t1, omp_t2
	double precision :: dx, x, sm, pif
	double precision, external :: f
	integer :: i

	integer :: ierror, prank, psize
	integer :: nlocal, istart, iend

	integer :: next, prev
	double precision :: send, recv


	call MPI_init(ierror)
	call MPI_Comm_size(MPI_COMM_WORLD, psize, ierror)
	call MPI_Comm_rank(MPI_COMM_WORLD, prank, ierror)

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

	nlocal = n / psize
	istart = 1 + nlocal * prank
	iend = nlocal * (prank + 1);

	dx = 1. / n
	sm = 0.0;

	do i = istart, iend
	x = (1. * i - 0.5) * dx
	sm = sm + f(x)
	enddo

	next = mod((prank + 1),psize)
	prev = mod((prank - 1 + psize), psize)

	send = sm

	do i = 2, psize
	call MPI_Sendrecv(send, 1, MPI_DOUBLE, next, 13, recv, 1, MPI_DOUBLE, prev, 13, MPI_COMM_WORLD, MPI_STATUS_IGNORE, ierror);
	sm = sm + recv
	send = recv
	enddo

	pif = dx * sm

	omp_t2 = MPI_Wtime()

	if (prank.eq.0) then
	print *, 'computed pi =',pif
	print *, 'Running time = ', (omp_t2-omp_t1)
	endif

	call MPI_Finalize(ierror)

	end program pi_p2p_sendrecv_ring


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