program reduce

! modified from Mattson, Sanders and McGill's book
! Patterns for Parallel Programming
integer :: i, num_steps
double precision :: x, pi, step, sum

sum =0.0d0
nsteps = 1000000000
step = 1.0d0 / dble(nsteps)

!$OMP PARALLEL DO PRIVATE(X) REDUCTION(+:SUM)
do i = 1, nsteps
  x = (dble(i) + 0.5d0) * step
  sum = sum + 4.0d0 /(1.0d0 + x*x)
enddo
!$OMP END PARALLEL DO

pi = step * sum
print *, "estimate of Pi with is ",pi


end program reduce