!-*-f90-*-
!
! Interfaces: Numerical Integration
!
    function gsl_integration_qng(f, a, b, epsabs, epsrel, result, abserr, neval) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, b, epsabs, epsrel
      real(c_double), intent(out) :: result, abserr
      integer(c_size_t), intent(inout) :: neval
      integer(c_int) :: gsl_integration_qng
    end function gsl_integration_qng
    function gsl_integration_workspace_alloc (n) bind(c)
      import
      integer(c_size_t), value :: n
      type(c_ptr) :: gsl_integration_workspace_alloc
    end function gsl_integration_workspace_alloc
    subroutine gsl_integration_workspace_free (w) bind(c)
      import
      type(c_ptr), value :: w
    end subroutine gsl_integration_workspace_free
    function gsl_integration_qag(f, a, b, epsabs, epsrel, limit, key, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, b, epsabs, epsrel
      integer(c_size_t), value :: limit
      integer(c_int), value :: key
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qag
    end function gsl_integration_qag
    function gsl_integration_qags(f, a, b, epsabs, epsrel, limit, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, b, epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qags
    end function gsl_integration_qags
    function gsl_integration_qagp(f, pts, npts, epsabs, epsrel, limit, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      type(c_ptr), value :: pts
      integer(c_size_t), value :: npts
      real(c_double), value :: epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qagp
    end function gsl_integration_qagp
    function gsl_integration_qagi(f, epsabs, epsrel, limit, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qagi
    end function gsl_integration_qagi
    function gsl_integration_qagiu(f, a, epsabs, epsrel, limit, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qagiu
    end function gsl_integration_qagiu
    function gsl_integration_qagil(f, b, epsabs, epsrel, limit, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: b, epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qagil
    end function gsl_integration_qagil
    function gsl_integration_qawc(f, a, b, c, epsabs, epsrel, limit, &
         workspace, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, b, c, epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qawc
    end function gsl_integration_qawc
    function gsl_integration_qaws_table_alloc (alpha, beta, mu, nu) bind(c)
      import
      real(c_double), value :: alpha, beta
      integer(c_int), value :: mu, nu
      type(c_ptr) :: gsl_integration_qaws_table_alloc
    end function gsl_integration_qaws_table_alloc
    function gsl_integration_qaws_table_set(t, alpha, beta, mu, nu) bind(c)
      import
      type(c_ptr), value :: t
      real(c_double), value :: alpha, beta
      integer(c_int), value :: mu, nu
      integer(c_int) :: gsl_integration_qaws_table_set
    end function gsl_integration_qaws_table_set
    subroutine gsl_integration_qaws_table_free (w) bind(c)
      import
      type(c_ptr), value :: w
    end subroutine gsl_integration_qaws_table_free
    function gsl_integration_qaws(f, a, b, t, epsabs, epsrel, limit, workspace, &
         result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, b, epsabs, epsrel
      type(c_ptr), value :: t
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qaws
    end function gsl_integration_qaws
    function gsl_integration_qawo_table_alloc(omega, l, sine, n) bind(c)
      import
      real(c_double), value :: omega, l
      integer(c_int), value :: sine
      integer(c_size_t), value :: n
      type(c_ptr) :: gsl_integration_qawo_table_alloc
    end function gsl_integration_qawo_table_alloc
    function gsl_integration_qawo_table_set(t, omega, l, sine) bind(c)
      import
      type(c_ptr), value :: t
      real(c_double), value :: omega, l
      integer(c_int), value :: sine
      integer(c_int) :: gsl_integration_qawo_table_set
    end function gsl_integration_qawo_table_set
    function gsl_integration_qawo_table_set_length(t, l) bind(c)
      import
      type(c_ptr), value :: t
      real(c_double), value :: l
      integer(c_int) :: gsl_integration_qawo_table_set_length
    end function gsl_integration_qawo_table_set_length
    subroutine gsl_integration_qawo_table_free (w) bind(c)
      import
      type(c_ptr), value :: w
    end subroutine gsl_integration_qawo_table_free
    function gsl_integration_qawo(f, a, epsabs, epsrel, limit, workspace, &
         wf, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a,  epsabs, epsrel
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace, wf
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qawo
    end function gsl_integration_qawo
    function gsl_integration_qawf(f, a, epsabs, limit, workspace, cyc_workspace, &
         wf, result, abserr) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a,  epsabs
      integer(c_size_t), value :: limit
      type(c_ptr), value :: workspace, cyc_workspace, wf
      real(c_double), intent(out) :: result, abserr
      integer(c_int) :: gsl_integration_qawf
    end function gsl_integration_qawf
    function gsl_integration_cquad_workspace_alloc (n) bind(c)
      import
      integer(c_size_t), value :: n
      type(c_ptr) :: gsl_integration_cquad_workspace_alloc
    end function gsl_integration_cquad_workspace_alloc
    subroutine gsl_integration_cquad_workspace_free (w) bind(c)
      import
      type(c_ptr), value :: w
    end subroutine gsl_integration_cquad_workspace_free
    function gsl_integration_cquad(f, a, b, epsabs, epsrel, &
         workspace, result, abserr, nevals) bind(c)
      import
      type(c_ptr), value :: f
      real(c_double), value :: a, b, epsabs, epsrel
      type(c_ptr), value :: workspace
      real(c_double), intent(out) :: result, abserr
      integer(c_size_t) :: nevals
      integer(c_int) :: gsl_integration_cquad
    end function gsl_integration_cquad
    function gsl_integration_romberg_alloc(n) bind(c)
      import :: c_ptr, c_size_t
      type(c_ptr) :: gsl_integration_romberg_alloc
      integer(c_size_t), value :: n
    end function gsl_integration_romberg_alloc
    subroutine gsl_integration_romberg_free(w) bind(c)
      import :: c_ptr
      type(c_ptr), value :: w 
    end subroutine gsl_integration_romberg_free
    function gsl_integration_romberg(f, a, b, epsabs, epsrel, result, neval, w) &
         bind(c)
      import :: c_ptr, c_double, c_size_t, c_int
      integer(c_int) :: gsl_integration_romberg
      type(c_ptr), value :: f
      real(c_double), value :: a, b, epsabs, epsrel
      real(c_double) :: result
      integer(c_size_t) :: neval
      type(c_ptr), value :: w
    end function gsl_integration_romberg
    function gsl_integration_glfixed_table_alloc(n) bind(c)
      import :: c_size_t, c_ptr
      integer(c_size_t), value :: n
      type(c_ptr) :: gsl_integration_glfixed_table_alloc
    end function gsl_integration_glfixed_table_alloc
    subroutine gsl_integration_glfixed_table_free(t) bind(c)
      import :: c_ptr
      type(c_ptr), value :: t
    end subroutine gsl_integration_glfixed_table_free
    function gsl_integration_glfixed(f, a, b, t) bind(c)
      import :: c_double, c_ptr
      real(c_double) :: gsl_integration_glfixed
      type(c_ptr), value :: f
      real(c_double), value :: a, b
      type(c_ptr), value :: t
    end function gsl_integration_glfixed
    function gsl_integration_glfixed_point(a, b, i, xi, wi, t) bind(c)
      import :: c_double, c_ptr, c_size_t, c_int
      integer(c_int) :: gsl_integration_glfixed_point
      real(c_double), value :: a, b
      integer(c_size_t), value :: i
      real(c_double) :: xi, wi
      type(c_ptr), value :: t
    end function gsl_integration_glfixed_point
    subroutine gsl_integration_fixed_free(w) bind(c)
      import :: c_ptr
      type(c_ptr), value :: w
    end subroutine gsl_integration_fixed_free
    function gsl_integration_fixed_n(w) bind(c)
      import :: c_size_t, c_ptr
      integer(c_size_t) :: gsl_integration_fixed_n
      type(c_ptr), value :: w
    end function gsl_integration_fixed_n
    function gsl_integration_fixed_nodes(w) bind(c)
      import :: c_ptr
      type(c_ptr) :: gsl_integration_fixed_nodes
      type(c_ptr), value :: w
    end function gsl_integration_fixed_nodes
    function gsl_integration_fixed_weights(w) bind(c)
      import :: c_ptr
      type(c_ptr) :: gsl_integration_fixed_weights
      type(c_ptr), value :: w
    end function gsl_integration_fixed_weights
    function gsl_integration_fixed(func, result, w) bind(c)
      import :: c_ptr, c_int
      integer(c_int) :: gsl_integration_fixed
      type(c_ptr), value :: func, w, result
    end function gsl_integration_fixed
!
    function gsl_aux_sizeof_integration_workspace() bind(c)
      import :: c_size_t
      integer(c_size_t) :: gsl_aux_sizeof_integration_workspace
    end function gsl_aux_sizeof_integration_workspace
    function gsl_aux_sizeof_integration_qaws_table() bind(c)
      import :: c_size_t
      integer(c_size_t) :: gsl_aux_sizeof_integration_qaws_table
    end function gsl_aux_sizeof_integration_qaws_table
    function gsl_aux_sizeof_integration_qawo_table() bind(c)
      import :: c_size_t
      integer(c_size_t) :: gsl_aux_sizeof_integration_qawo_table
    end function gsl_aux_sizeof_integration_qawo_table
    function gsl_aux_integration_fixed_alloc(t, n, a, b, alpha, beta) bind(c)
      import :: c_ptr, c_size_t, c_double, c_int
      type(c_ptr) :: gsl_aux_integration_fixed_alloc
      integer(c_int), value :: t
      integer(c_size_t), value :: n
      real(c_double), value :: a, b, alpha, beta
    end function gsl_aux_integration_fixed_alloc