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 $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. 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

None.

7 Accuracy

δ

and

ε

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

| ε | ≃ | \frac{x}{\sqrt{1 + x^{2}} arcsinh x} δ | .

That is, the relative error in the argument,

x

, is amplified by a factor at least

\frac{x}{\sqrt{1 + x^{2}} arcsinh x}

, in the result.

The equality should hold if

δ

is greater than the machine precision (

δ

due to data errors etc.) but if

δ

is simply due to round-off in the machine representation it is possible that an extra figure may be lost in internal calculation round-off.

The behaviour of the amplification factor is shown in the following graph:

Figure 1

It should be noted that this factor is always less than or equal to one. For large

x

we have the absolute error in the result,

E

, in principle, given by

E \sim δ .

This means that eventually accuracy is limited by machine precision.

s11abf 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.

s11ab: FL CL CPP AD