1: $x$ – Real (Kind=nag_wp) Input: On entry: the argument $x$ of the function.
2: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

There are no failure exits from this routine. The argument ifail is included for consistency with other routines in this chapter.

7 Accuracy

Because of its close relationship with

erfc

the accuracy of this routine is very similar to that in s15adf. If

ε

and

δ

are the relative errors in result and argument, respectively, then in principle they are related by

|ε| ≃ |\frac{x e^{- x^{2} / 2}}{\sqrt{2 π} Q (x)} δ| .

For

x

negative or small positive this factor is always less than

1

and accuracy is mainly limited by machine precision. For large positive

x

we find

ε \sim x^{2} δ

and hence to a certain extent relative accuracy is unavoidably lost. However, the absolute error in the result,

E

, is given by

|E| ≃ |\frac{x e^{- x^{2} / 2}}{\sqrt{2 π}} δ|

and since this factor is always less than one absolute accuracy can be guaranteed for all

x

s15acf is not threaded in any implementation.

None.

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

Interfaces: FL CL AD

s15ac: FL CL AD