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

g01ea_a1w_f is the adjoint version of the primal routine g01eaf.

## 2Specification

Fortran Interface
 Subroutine g01ea_a1w_f ( ad_handle, tail, x, p, ifail)
 Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x Type (nagad_a1w_w_rtype), Intent (Out) :: p Character (1), Intent (In) :: tail Type (c_ptr), Intent (In) :: ad_handle
 void g01ea_a1w_f_ ( void *&ad_handle, const char *tail, const nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &p, Integer &ifail, const Charlen length_tail)
The routine may be called by the names g01ea_a1w_f or nagf_stat_prob_normal_a1w.

## 3Description

g01ea_a1w_f is the adjoint version of the primal routine g01eaf.
g01eaf returns a one or two tail probability for the standard Normal distribution. For further information see Section 3 in the documentation for g01eaf.

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, g01ea_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.
Note that the primal routine is a function whereas g01ea_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, p.
1: ad_handle – Type (c_ptr) Input
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: tail – character Input
3: Input
4: Output
On exit: a one or two tail probability for the standard Normal distribution.
5: ifail – Integer Input/Output

## 6Error Indicators and Warnings

g01ea_a1w_f preserves all error codes from g01eaf 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

g01ea_a1w_f is not threaded in any implementation.