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 the result, respectively, then in principle
The equality should hold if is greater than the machine precision ( is due to data errors etc.), but if is due simply to round-off in the machine it is possible that rounding etc. in internal calculations may lose one extra figure.
The behaviour of the amplification factor is shown in the graph below.
In the region of this factor tends to zero and the accuracy will be limited by the machine precision. For close to one, , the above analysis is not applicable owing to the fact that both the argument and the result are bounded , .
In the region of we have , that is the result will have approximately half as many correct significant figures as the argument.
In the region , we have that the absolute error in the result, , is given by , that is the result will have approximately half as many decimal places correct as there are correct figures in the argument.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s09abf 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.