!-*-f90-*-
!
!  API: Mathematical Functions
!
!> \page "Comments on elementary mathematical functions"
!> Please go to api/math.finc for the API documentation.
!> Note that many of the elementary functions are also available as Fortran 
!> intrinsics. The file also contains constructors for function objects. 
  function fgsl_isnan(x) 
    real(fgsl_double), intent(in) :: x
    integer(fgsl_int) :: fgsl_isnan
    fgsl_isnan = gsl_isnan(x)
  end function fgsl_isnan
  function fgsl_isinf(x)
    real(fgsl_double), intent(in) :: x
    integer(fgsl_int) :: fgsl_isinf
    fgsl_isinf = gsl_isinf(x)
  end function fgsl_isinf
  function fgsl_finite(x)
    real(fgsl_double), intent(in) :: x
    integer(fgsl_int) :: fgsl_finite
    fgsl_finite = gsl_finite(x)
  end function fgsl_finite
  function fgsl_log1p(x) 
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_log1p
    fgsl_log1p = gsl_log1p(x)
  end function fgsl_log1p
  function fgsl_expm1(x) 
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_expm1
    fgsl_expm1 = gsl_expm1(x)
  end function fgsl_expm1
  function fgsl_acosh(x) 
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_acosh
    fgsl_acosh = gsl_acosh(x)
  end function fgsl_acosh
  function fgsl_asinh(x) 
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_asinh
    fgsl_asinh = gsl_asinh(x)
  end function fgsl_asinh
  function fgsl_atanh(x) 
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_atanh
    fgsl_atanh = gsl_atanh(x)
  end function fgsl_atanh
  function fgsl_ldexp(x,e) 
    real(fgsl_double), intent(in) :: x
    integer(fgsl_int), intent(in) :: e
    real(fgsl_double) :: fgsl_ldexp
    fgsl_ldexp = gsl_ldexp(x,e)
  end function fgsl_ldexp
  function fgsl_frexp(x,e) 
    real(fgsl_double), intent(in) :: x
    integer(fgsl_int), intent(out) :: e
    real(fgsl_double) :: fgsl_frexp
    fgsl_frexp = gsl_frexp(x,e)
  end function fgsl_frexp
  function fgsl_fcmp(x,y,eps)
    real(fgsl_double), intent(in) :: x, y, eps
    integer(fgsl_int) :: fgsl_fcmp
    fgsl_fcmp = gsl_fcmp(x,y,eps)
  end function fgsl_fcmp
!> Constructor for an FGSL function type
!> \param func - interface for a double precision valued function with
!> a parameter of arbitrary type
!> \param params - parameter of arbitrary type
!> \result FGSL function object.
  function fgsl_function_init(func, params)
    interface
       function func(x, params) bind(c)
         use, intrinsic :: iso_c_binding
         real(c_double), value :: x
         type(c_ptr), value :: params
         real(c_double) :: func
       end function func
    end interface
    type(c_ptr), intent(in) :: params
    type(fgsl_function) :: fgsl_function_init
!
    type(c_funptr) :: fp
    fp = c_funloc(func)
    fgsl_function_init%gsl_function = fgsl_function_cinit(fp, params)
  end function fgsl_function_init
!> Constructor for an FGSL function type including a derivative
!> \param f - interface for a double precision valued function with
!> a parameter of arbitrary type
!> \param df - interface for a function evaluating the derivative of f
!> \param fdf - interface for a subroutine evaluating f as well as its
!> derivative given an argument and a parameter.
!> \param params - parameter of arbitrary type
!> \result FGSL function with derivative object.
 function fgsl_function_fdf_init(f, df, fdf, params)
    interface
       function f(x, params) bind(c)
         use, intrinsic :: iso_c_binding
         real(c_double), value :: x
         type(c_ptr), value :: params
         real(c_double) :: f
       end function f
       function df(x, params) bind(c)
         use, intrinsic :: iso_c_binding
         real(c_double), value :: x
         type(c_ptr), value :: params
         real(c_double) :: df
       end function df
       subroutine fdf(x, params, f, df) bind(c)
         use, intrinsic :: iso_c_binding
         real(c_double), value :: x
         type(c_ptr), value :: params
         real(c_double), intent(out) :: f, df
       end subroutine fdf
    end interface
    type(c_ptr), intent(in) :: params
    type(fgsl_function_fdf) :: fgsl_function_fdf_init
!
    type(c_funptr) :: fp, dfp, fdfp
    fp = c_funloc(f)
    dfp = c_funloc(df)
    fdfp = c_funloc(fdf)
    fgsl_function_fdf_init%gsl_function_fdf = fgsl_function_fdf_cinit(fp, dfp, fdfp, params)
  end function fgsl_function_fdf_init
!> Free resources associated with a FGSL function object. 
  subroutine fgsl_function_free(sfunc)
    type(fgsl_function), intent(inout) :: sfunc
    call fgsl_function_cfree(sfunc%gsl_function)
  end subroutine fgsl_function_free
!> Free resources associated with a FGSL function with derivative object. 
  subroutine fgsl_function_fdf_free(sfunc)
    type(fgsl_function_fdf), intent(inout) :: sfunc
    call fgsl_function_fdf_cfree(sfunc%gsl_function_fdf)
  end subroutine fgsl_function_fdf_free
!> Evaluate a function value for a FGSL function object.
!> \param sfunc - function object.
!> \param x - argument value
!> \result Function value 
  function fgsl_fn_eval(sfunc, x)
    type(fgsl_function), intent(inout) :: sfunc
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_fn_eval
    fgsl_fn_eval = fgsl_fn_eval_aux(sfunc%gsl_function, x)
  end function fgsl_fn_eval
!> Evaluate a function value for a FGSL function with derivative object.
!> \param sfunc - function with derivative object.
!> \param x - argument value
!> \result Function value 
  function fgsl_fn_fdf_eval_f(sfunc, x)
    type(fgsl_function_fdf), intent(inout) :: sfunc
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_fn_fdf_eval_f
    fgsl_fn_fdf_eval_f = fgsl_fn_fdf_eval_f_aux(sfunc%gsl_function_fdf, x)
  end function fgsl_fn_fdf_eval_f
!> Evaluate a derivative value for a FGSL function with derivative object.
!> \param sfunc - function with derivative object.
!> \param x - argument value
!> \result Derivative value
  function fgsl_fn_fdf_eval_df(sfunc, x)
    type(fgsl_function_fdf), intent(inout) :: sfunc
    real(fgsl_double), intent(in) :: x
    real(fgsl_double) :: fgsl_fn_fdf_eval_df
    fgsl_fn_fdf_eval_df = fgsl_fn_fdf_eval_df_aux(sfunc%gsl_function_fdf, x)
  end function fgsl_fn_fdf_eval_df
!> Evaluate function as well as derivative value for a FGSL function with derivative object.
!> \param sfunc - function with derivative object.
!> \param x - argument value
!> \param y - function value
!> \param dy - derivative value  
 subroutine fgsl_fn_fdf_eval_f_df(sfunc, x, y, dy)
    type(fgsl_function_fdf), intent(inout) :: sfunc
    real(fgsl_double), intent(in) :: x
    real(fgsl_double), intent(out) :: y, dy
    call fgsl_fn_fdf_eval_f_df_aux(sfunc%gsl_function_fdf, x, y, dy)
  end subroutine fgsl_fn_fdf_eval_f_df