program serial_pi
  integer n, i
  integer, parameter:: dp = kind(1.0d0)
  real(dp), parameter :: PI25DT = 3.141592653589793238462643_dp
  real(dp) pi, h, sum, x
  logical done

  done = .false.
  do while ( .not.done)
     write(*,'("Enter the number of intervals: (0 quits) ")')
     read(*,*) n

     if (n == 0) exit
      
     h   = 1.0_dp/n
     sum = 0.0_dp
     do i = 1, n
	x = h * (i - 0.5_dp)
	sum = sum + 4.0_dp/(1.0_dp + x*x)
     enddo
     pi = h * sum
     
     write(*,'(" pi is approximately ",f16.13," Error is ",f16.13)') &
          pi, abs(pi - PI25DT)

  end do
  
  stop
end program serial_pi