is too large for an accurate result to be returned. contains zero. The threshold value is the same as for in s19abf
, as defined in the Users' Note for your implementation.
5: – IntegerInput/Output
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, at least one value of x was invalid.
Check ivalid for more information.
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.
Since the function is oscillatory, the absolute error rather than the relative error is important. Let be the absolute error in the function, and be the relative error in the argument. If is somewhat larger than the machine precision, then we have:
(provided is within machine bounds).
For small the error amplification is insignificant and thus the absolute error is effectively bounded by the machine precision.
For medium and large , the error behaviour is oscillatory and its amplitude grows like . Therefore, it is impossible to calculate the functions with any accuracy when . Note that this value of is much smaller than the minimum value of for which the function overflows.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s19apf is not threaded in any implementation.
This example reads values of x from a file, evaluates the function at each value of and prints the results.