# NAG Library Routine Document

## 1Purpose

x02anf returns the safe range of complex floating-point arithmetic.

## 2Specification

Fortran Interface
 Function x02anf ( )
 Real (Kind=nag_wp) :: x02anf
#include nagmk26.h
 double x02anf_ ()

## 3Description

x02anf 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.

None.

None.

None.

## 8Parallelism and Performance

x02anf is not threaded in any implementation.