On entry: ifail must be set to , . If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value is recommended. If the output of error messages is undesirable, then the value is recommended. Otherwise, if you are not familiar with this argument, the recommended value is . When the value 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, . x is too large and positive. The function returns zero.
On entry, . x is too large and negative. The function returns zero.
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.
For negative arguments the function is oscillatory and hence absolute error is appropriate. In the positive region the function has essentially exponential behaviour and hence relative error is needed. The absolute error, , and the relative error , are related in principle to the relative error in the argument , by
In practice, approximate equality is the best that can be expected. When , or is of the order of the machine precision, the errors in the result will be somewhat larger.
For small , positive or negative, errors are strongly attenuated by the function and hence will effectively be bounded by the machine precision.
For moderate to large negative , the error is, like the function, oscillatory. However, the amplitude of the absolute error grows like . Therefore it becomes impossible to calculate the function with any accuracy if .
For large positive , the relative error amplification is considerable: . However, very large arguments are not possible due to the danger of overflow. Thus in practice the actual amplification that occurs is limited.
8Parallelism and Performance
s17akf 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.