1: $x$ – Real (Kind=nag_wp) Input: On entry: the argument $x$ of the function.
2: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

None.

7 Accuracy

Let

δ

and

ε

be the relative errors in the argument and result respectively.

δ

is considerably greater than the machine precision (i.e., if

δ

is due to data errors etc.), then

ε

and

δ

are approximately related by:

ε ≃ | \frac{x (1 - 2 x F (x))}{F (x)} | δ .

The following graph shows the behaviour of the error amplification factor

| \frac{x (1 - 2 x F (x))}{F (x)} |

Figure 1

However, if

δ

is of the same order as machine precision, then rounding errors could make

ε

somewhat larger than the above relation indicates. In fact

ε

will be largely independent of

x

δ

, but will be of the order of a few times the machine precision.

Background information to multithreading can be found in the Multithreading documentation.

s15aff is not threaded in any implementation.

None.

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

s15af: FL CL CPP AD PY MB