Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

## 1Purpose

c05au_a1w_f is the adjoint version of the primal routine c05auf.

## 2Specification

Fortran Interface
 Subroutine c05au_a1w_f ( ad_handle, x, h, eps, eta, f, a, b, iuser, ruser, ifail)
 Integer, Intent (Inout) :: iuser(*), ifail External :: f Type (nagad_a1w_w_rtype), Intent (In) :: h, eps, eta Type (nagad_a1w_w_rtype), Intent (Inout) :: x, ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: a, b Type (c_ptr), Intent (In) :: ad_handle
The routine may be called by the names c05au_a1w_f or nagf_roots_contfn_brent_interval_a1w.

## 3Description

c05au_a1w_f is the adjoint version of the primal routine c05auf.
c05auf locates a simple zero of a continuous function from a given starting value. It uses a binary search to locate an interval containing a zero of the function, then Brent's method, which is a combination of nonlinear interpolation, linear extrapolation and bisection, to locate the zero precisely. For further information see Section 3 in the documentation for c05auf.

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, c05au_a1w_f includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine. A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
1: ad_handle – Type (c_ptr) Input
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: Input/Output
3: Input
4: Input
5: Input
6: f – Subroutine External Procedure
Note that f is a subroutine in this interface, returning the function value via the additional output parameter retval.
The specification of f is:
Fortran Interface
 Subroutine f ( ad_handle, x, retval, iuser, ruser)
 Integer, Intent (Inout) :: iuser(*) Type (nagad_a1w_w_rtype), Intent (In) :: x Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: retval Type (c_ptr), Intent (In) :: ad_handle
C++ Interface
1: ad_handle – Type (c_ptr) Input
On entry: a handle to the AD configuration data object.
2: Input
On exit: the value of $f$ at the specified point.
4: iuser – Integer array User Workspace
5: User Workspace
7: Output
8: Output
9: iuser($*$) – Integer array User Workspace
10: ruser($*$) – Type (nagad_a1w_w_rtype) array User Workspace
11: ifail – Integer Input/Output

## 6Error Indicators and Warnings

c05au_a1w_f preserves all error codes from c05auf and in addition can return:
$\mathbf{ifail}=-89$
See Section 4.5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 4.5.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

c05au_a1w_f is not threaded in any implementation.