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

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 x02am_example

fprintf('x02am example results\n\n');

fprintf('the real safe range parameter = %22.15e\n', ...
x02am);

x02am example results

the real safe range parameter = 2.225073858507202e-308

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