NAG Library Routine Document
S01BAF returns a value of the shifted logarithmic function, , via the function name.
|REAL (KIND=nag_wp) S01BAF
S01BAF computes values of
, retaining full relative precision even when
is small. The routine is based on the Chebyshev expansion
, and choosing
the expansion is valid in the domain
Outside this domain, is computed by the standard logarithmic function.
Lyusternik L A, Chervonenkis O A and Yanpolskii A R (1965) Handbook for Computing Elementary Functions p. 57 Pergamon Press
- 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, .
The result is returned as zero.
The returned result should be accurate almost to machine precision, with a limit of about significant figures due to the precision of internal constants. Note however that if lies very close to and is not exact (for example if is the result of some previous computation and has been rounded), then precision will be lost in the computation of , and hence , in S01BAF.
Empirical tests show that the time taken for a call of S01BAF usually lies between about and times the time for a call to the standard logarithm function.
The example program 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 (s01bafe.f90)
9.2 Program Data
Program Data (s01bafe.d)
9.3 Program Results
Program Results (s01bafe.r)