# NAG C Library Function Document

## 1Purpose

nag_complex_safe_small_number (X02ANC) returns the safe range of complex floating-point arithmetic.

## 2Specification

 #include #include
 double nag_complex_safe_small_number

## 3Description

nag_complex_safe_small_number (X02ANC) is a constant defined in the C Header file.
nag_complex_safe_small_number (X02ANC) 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.

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## 8Parallelism and Performance

nag_complex_safe_small_number (X02ANC) is not threaded in any implementation.