The routine may be called by the names s14ahf or nagf_specfun_gamma_log_scaled_real.
s14ahf calculates an approximate value for , where . This is a variant of the function (see also s14abf), which avoids rounding problems for very large arguments by computing with the Stirling approximation factored out.
For , ;
and for , , where is a suitable Remez approximation.
For , the value is undefined; s14ahf returns zero and exits with .
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, . On soft failure, the function value returned is 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.
s14ahf has been designed to produce full relative accuracy for all input arguments. Empirical results obtained by comparing with multiprecision software confirm this.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s14ahf 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.