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, .
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, a 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 ( is a result of data errors etc.) but if is produced simply by round-off error in the machine it is possible that rounding in internal calculations may lose an extra figure in the result.
This factor stays close to one except near where its behaviour is shown in the following graph.
For close to unity, , the above analysis is no longer applicable owing to the fact that both argument and result are subject to finite bounds, ( and ). In this region ; that is the result will have approximately half as many correct significant figures as the argument.
For the result will be correct to full machine precision.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s09aaf 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.