is too large, the result underflows. contains zero. The threshold value is the same as for in s19acf
, as defined in the the Users' Note for your implementation.
, the function is undefined. contains .
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.
Let be the absolute error in the result, be the relative error in the result and be the relative error in the argument. If is somewhat larger than the machine precision, then we have:
For very small , the relative error amplification factor is approximately given by , which implies a strong attenuation of relative error. However, in general cannot be less than the machine precision.
For small , errors are damped by the function and hence are limited by the machine precision.
For medium and large , the error behaviour, like the function itself, is oscillatory, and hence only the absolute accuracy for the function can be maintained. For this range of , the amplitude of the absolute error decays like which implies a strong attenuation of error. Eventually, , which asymptotically behaves like , becomes so small that it cannot be calculated without causing underflow, and the routine returns zero. Note that for large the errors are dominated by those of the standard function exp.
8Parallelism and Performance
s19aqf is not threaded in any implementation.
Underflow may occur for a few values of close to the zeros of , below the limit which causes a failure with .
This example reads values of x from a file, evaluates the function at each value of and prints the results.