Public Shared Function s01ba ( _ x As Double, _ <OutAttribute> ByRef ifail As Integer _ ) As Double
public: static double s01ba( double x, [OutAttribute] int% ifail )
- Type: System..::..DoubleOn entry: the argument of the function.Constraint: .
s01ba computes values of , retaining full relative precision even when is small. The method 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
Errors or warnings detected by the method:
- 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 s01ba.
Empirical tests show that the time taken for a call of s01ba 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.