NAG CL Interface
s01bac (log_​shifted)

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1 Purpose

s01bac returns a value of the shifted logarithmic function, ln(1+x).

2 Specification

#include <nag.h>
double  s01bac (double x, NagError *fail)
The function may be called by the names: s01bac, nag_specfun_log_shifted or nag_shifted_log.

3 Description

s01bac computes values of ln(1+x), retaining full relative precision even when |x| is small. The function is based on the Chebyshev expansion
ln1+p2+2px¯ 1+p2-2px¯ =4k=0p2k+1 2k+1 T2k+1(x¯).  
Setting x¯= x(1+p2) 2p(x+2) , and choosing p= q-1 q+1 , q=24 the expansion is valid in the domain x[ 12-1,2-1] .
Outside this domain, ln(1+x) is computed by the standard logarithmic function.

4 References

Lyusternik L A, Chervonenkis O A and Yanpolskii A R (1965) Handbook for Computing Elementary Functions p. 57 Pergamon Press

5 Arguments

1: x double Input
On entry: the argument x of the function.
Constraint: x>-1.0.
2: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
On entry, x=value.
Constraint: x>-1.0.

7 Accuracy

The returned result should be accurate almost to machine precision, with a limit of about 20 significant figures due to the precision of internal constants. Note however, that if x lies very close to -1.0 and is not exact (for example if x is the result of some previous computation and has been rounded), then precision will be lost in the computation of 1+x, and hence ln(1+x), in s01bac.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s01bac is not threaded in any implementation.

9 Further Comments

Empirical tests show that the time taken for a call of s01bac usually lies between about 1.25 and 2.5 times the time for a call to the standard logarithm function.

10 Example

The example program reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

10.1 Program Text

Program Text (s01bace.c)

10.2 Program Data

Program Data (s01bace.d)

10.3 Program Results

Program Results (s01bace.r)