NAG Library Routine Document

s11acf (arccosh)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input

On entry: the argument $x$ of the function.

Constraint: $\mathbf{x}\ge 1.0$.

2:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ 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 $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

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

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\ge 1.0$.
The routine has been called with an argument less than $1.0$, for which $\mathrm{arccosh}x$ is not defined.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

If $\delta$ and $\epsilon$ are the relative errors in the argument and result respectively, then in principle

$$\left|\epsilon \right|\simeq \left|\frac{x}{\sqrt{x^2-1}\mathrm{arccosh}x}\times \delta \right|\text{.}$$

That is the relative error in the argument is amplified by a factor at least $\frac{x}{\sqrt{x^2-1}\mathrm{arccosh}x}$ in the result. The equality should apply if $\delta$ is greater than the machine precision ($\delta$ due to data errors etc.) but if $\delta$ is simply a result of round-off in the machine representation it is possible that an extra figure may be lost in internal calculation and round-off. The behaviour of the amplification factor is shown in the following graph:

Figure 1

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (s11acfe.f90)

10.2

Program Data

Program Data (s11acfe.d)

10.3

Program Results

Program Results (s11acfe.r)