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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_machine_complex_safe (x02an)

## Purpose

nag_machine_complex_safe (x02an) returns the safe range of complex floating-point arithmetic.

## Syntax

[result] = x02an
[result] = nag_machine_complex_safe

## Description

nag_machine_complex_safe (x02an) is defined to be the smallest positive model number $z$ such that for any $x$ in the range [$z,1/z$] the following can be computed without undue loss of accuracy, overflow, underflow or other error:
• $-w$
• $1/w$
• $-1/w$
• $\sqrt{w}$
• $\mathrm{log}\left(w\right)$
• $\mathrm{exp}\left(\mathrm{log}\left(w\right)\right)$
• ${y}^{\left(\mathrm{log}\left(w\right)/\mathrm{log}\left(y\right)\right)}$ for any $y$
• $\left|w\right|$
where $w$ is any of $x$, $ix$, $x+ix$, $1/x$, $i/x$, $1/x+i/x$, and $i$ is the square root of $-1$

None.

## Parameters

None.

None.

### Output Parameters

1:     $\mathrm{result}$ – double scalar
The result of the function.

None.

None.

None.

## Example

See Example in nag_machine_precision (x02aj).
```function x02an_example

fprintf('x02an example results\n\n');

fprintf('the complex safe range parameter = %22.15e\n', ...
x02an);

```
```x02an example results

the complex safe range parameter = 2.225073858507202e-308
```