! This Fortran 90 module provides a template for automatic
! differentiation.

MODULE AUTOMATIC_DIFFERENTIATION
      INTEGER, PARAMETER, PRIVATE :: KD = KIND(1D0)

      TYPE AUTODIFF
         REAL(KIND=KD) :: VALUE, DERIV
      END TYPE AUTODIFF

 !Interface to the basic operations

      INTERFACE OPERATOR(+)
         MODULE PROCEDURE ADD
      END INTERFACE

      INTERFACE OPERATOR(**)
         MODULE PROCEDURE IPOWER
      END INTERFACE


CONTAINS

 ! Basic operation functions

    FUNCTION ADD(A,B) RESULT(SUM)
       TYPE(AUTODIFF) :: SUM
       TYPE(AUTODIFF), INTENT(IN) :: A, B
       SUM%VALUE = A%VALUE + B%VALUE
       SUM%DERIV = A%DERIV + B%DERIV
    END FUNCTION ADD

    FUNCTION IPOWER(A,N) RESULT(A_TO_N)
       TYPE(AUTODIFF) :: A_TO_N
       TYPE(AUTODIFF), INTENT(IN) :: A
       INTEGER, INTENT(IN) :: N
       A_TO_N%VALUE = A%VALUE **N
       A_TO_N%DERIV = N* A%VALUE **(N-1) * A%DERIV
    END FUNCTION IPOWER

END MODULE AUTOMATIC_DIFFERENTIATION