The routine may be called by the names s01baf or nagf_specfun_log_shifted.
s01baf computes values of , retaining full relative precision even when is small. The routine is based on the Chebyshev expansion
Setting , 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: – Real (Kind=nag_wp)Input
On entry: the argument of the function.
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).
Errors or warnings detected by the routine:
On entry, .
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 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.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s01baf is not threaded in any implementation.
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.