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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_machine_real_safe (x02am)

## Purpose

nag_machine_real_safe (x02am) returns the safe range of floating point arithmetic.

## Syntax

[result] = x02am
[result] = nag_machine_real_safe

## Description

nag_machine_real_safe (x02am) 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:
• x$-x$
• 1 / x$1/x$
• 1 / x$-1/x$
• sqrt(x)$\sqrt{x}$
• log(x)$\mathrm{log}\left(x\right)$
• exp(log(x))$\mathrm{exp}\left(\mathrm{log}\left(x\right)\right)$
• y(log(x) / log(y)) ${y}^{\left(\mathrm{log}\left(x\right)/\mathrm{log}\left(y\right)\right)}$ for any y$y$

None.

## Parameters

None.

None.

None.

### Output Parameters

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

None.

None.

None.

## Example

```function nag_machine_real_safe_example
[result] = nag_machine_real_safe
```
```

result =

2.2251e-308

```
```function x02am_example
[result] = x02am
```
```

result =

2.2251e-308

```