NAG Library Function Document
nag_shifted_log (s01bac) returns a value of the shifted logarithmic function, .
||nag_shifted_log (double x,
nag_shifted_log (s01bac) computes values of
, retaining full relative precision even when
is small. The function 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
x – doubleInput
On entry: the argument of the function.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, .
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 nag_shifted_log (s01bac).
Empirical tests show that the time taken for a call of nag_shifted_log (s01bac) 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 (s01bace.c)
9.2 Program Data
Program Data (s01bace.d)
9.3 Program Results
Program Results (s01bace.r)