1: $result$ – double scalar: The result of the function.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: On entry, $x \leq - 1.0$ .

The result is returned as zero.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

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 nag_specfun_log_shifted (s01ba).

Further Comments

Empirical tests show that the time taken for a call of nag_specfun_log_shifted (s01ba) usually lies between about

1.25

and

2.5

times the time for a call to the standard logarithm function.

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.

Open in the MATLAB editor: s01ba_example

function s01ba_example


fprintf('s01ba example results\n\n');

x = [2.5  1.25e-1 -9.06e-1  1.29e-3 -7.83e-6  1.00e-9];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s01ba(x(j));
end

disp('      x         log(1+x)');
fprintf('%12.4e%12.4e\n',[x; result]);

s01ba example results

      x         log(1+x)
  2.5000e+00  1.2528e+00
  1.2500e-01  1.1778e-01
 -9.0600e-01 -2.3645e+00
  1.2900e-03  1.2892e-03
 -7.8300e-06 -7.8300e-06
  1.0000e-09  1.0000e-09

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox