MODULE quadratures

  IMPLICIT none
  
  integer(kind=8) :: subintervals = 100
  
  INTERFACE
     FUNCTION integrate(ibeg, iend, myfun, p) result(val)
       IMPLICIT none
       ! beginning of integration interval
       real(kind=8), intent(in) :: ibeg
       ! ending of integration interval
       real(kind=8), intent(in) :: iend
       ! function to be integrated
       procedure(funint) :: myfun
       ! polynomial order
       integer(kind=4), intent(in) :: p
       ! result of integration
       real(kind=8) :: val
     END FUNCTION integrate
  END INTERFACE
  
  INTERFACE
     FUNCTION funint(x) result(y)
       IMPLICIT none
       real(kind=8), intent(in) :: x
       real(kind=8) :: y
     END FUNCTION funint
  END INTERFACE
  
CONTAINS
  
  FUNCTION newton_cotes(ibeg, iend, fun, p) result(val)
    IMPLICIT none
    real(kind=8), intent(in) :: ibeg
    real(kind=8), intent(in) :: iend
    procedure(funint) :: fun
    integer(kind=4), intent(in) :: p
    real(kind=8) :: val

    SELECT CASE (p)
    CASE (:-1)
       STOP "negative interpolationg polynomial order passed"
    CASE (0)
       val = 0 ! rectangle(ibeg, iend, fun)
    CASE (1)
       val = 0 ! trapeze(ibeg, iend, fun)
    CASE (2)
       val = 0 ! simpson_1_third(ibeg, iend, fun)
    CASE default
       STOP "Newton-Cotes quadratures only implemented for order < 3"
    END SELECT
  END FUNCTION newton_cotes

  
END MODULE quadratures