MacLeod A J (1996) MISCFUN, a software package to compute uncommon special functions ACM Trans. Math. Software (TOMS)22(3) 288–301
1: – Real (Kind=nag_wp)Input
On entry: the argument of the function.
where is the machine precision as returned by x02ajf.
2: – 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).
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.
The Chebyshev coefficients used by this routine are internally represented to digits of precision. Calling the number of digits of precision in the floating-point arithmetic being used , then clearly the maximum number of correct digits in the results obtained is limited by .
Apart from this, rounding errors in internal arithmetic may result in a slight loss of accuracy, but it is reasonable to assume that the result is accurate to within a small multiple of the machine precision.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s17gaf is not threaded in any implementation.
For , is asymptotically close to the Bessel function which is approximately zero to machine precision.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.