NAG Library Routine Document
S14AHF returns the value of , the scaled logarithm of the gamma function , via the function name.
|REAL (KIND=nag_wp) S14AHF
S14AHF calculates an approximate value for
. 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 .
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
- 1: X – REAL (KIND=nag_wp)Input
On entry: the argument of the function.
- 2: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction 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 parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, 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.
S14AHF has been designed to produce full relative accuracy for all input arguments. Empirical results obtained by comparing with multiprecision software confirm this.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s14ahfe.f90)
9.2 Program Data
Program Data (s14ahfe.d)
9.3 Program Results
Program Results (s14ahfe.r)