On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, .
The routine has been called with an argument greater than or equal to in magnitude, for which is not defined.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
If and are the relative errors in the argument and result, respectively, then in principle
That is, the relative error in the argument, , is amplified by at least a factor in the result. The equality should hold if is greater than the machine precision ( due to data errors etc.) but if is simply due to round-off in the machine representation then 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:
The factor is not significantly greater than one except for arguments close to . However, in the region where is close to one, , the above analysis is inapplicable since is bounded by definition, . In this region where arctanh is tending to infinity we have
which implies an obvious, unavoidable serious loss of accuracy near , e.g., if and agree to significant figures, the result for would be correct to at most about one figure.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s11aaf is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.