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, they are in principle related by

|ε| ≃ |\frac{x e^{- \frac{1}{2} x^{2}}}{\sqrt{2 π} P (x)} δ|

so that the relative error in the argument,

x

, is amplified by a factor,

\frac{x e^{- \frac{1}{2} x^{2}}}{\sqrt{2 π} P (x)}

, in the result.

For

x

small and for

x

positive this factor is always less than

1

and accuracy is mainly limited by machine precision.

For large negative

x

the factor behaves like

\sim x^{2}

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^{- \frac{1}{2} x^{2}}}{\sqrt{2 π}} δ|

so absolute accuracy can be guaranteed for all

x

8 Parallelism and Performance

s15abf is not threaded in any implementation.

9 Further Comments

None.

10 Example

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

NAG FL Interface Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction

s15ab: FL CL AD

NAG FL Interfaces15abf (cdf_​normal)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
s15abf (cdf_normal)