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

None.

## Parameters

None.

None.

None.

### Output Parameters

1:     result – double scalar
The result of the function.

None.

None.

None.

## Example

```function nag_machine_complex_safe_example
[result] = nag_machine_complex_safe
```
```

result =

2.2251e-308

```
```function x02an_example
[result] = x02an
```
```

result =

2.2251e-308

```