1: $x$ – Real (Kind=nag_wp) Input: On entry: the argument $x$ of the function.

Constraint: $x > - 1.0$ .
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

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The returned result should be accurate almost to machine precision, with a limit of about

20

significant figures due to the precision of internal constants. Note however, that if

x

lies very close to

- 1.0

and is not exact (for example if

x

is the result of some previous computation and has been rounded), then precision will be lost in the computation of

1 + x

, and hence

\ln (1 + x)

, in s01baf.

s01baf is not threaded in any implementation.

Empirical tests show that the time taken for a call of s01baf usually lies between about

1.25

and

2.5

times the time for a call to the standard logarithm function.

The example program reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

s01ba: FL CL CPP AD