For where the value of is given in the Users' Note for your implementation,
where and ,
For , to within the accuracy possible (see Section 7).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
1: – Real (Kind=nag_wp)Input
On entry: the argument of the function.
2: – IntegerInput/Output
On entry: ifail must be set to , . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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).
Error 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:
The routine has been called with an argument less than or equal to zero for which the function is not defined. The result returned is zero.
An unexpected error has been triggered by this routine. Please
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.
If and are the absolute and relative errors in the result and is the relative error in the argument then in principle these are related by
That is accuracy will be limited by machine precision near the origin and near the zeros of , but near the zeros of only absolute accuracy can be maintained.
The behaviour of this amplification is shown in Figure 1.
For large values of , therefore and since is limited by the finite precision of the machine it becomes impossible to return results which have any relative accuracy. That is, when we have that and hence is not significantly different from zero.
Hence is chosen such that for values of , in principle would have values less than the machine precision and so is essentially zero.
Parallelism and Performance
s13acf 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.