NAG Library Routine Document

X02ANF

X02ANF returns the safe range of complex floating point arithmetic.

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:

• $-w$
• $1/w$
• $-1/w$
• $\sqrt{w}$
• $\log \left(w\right)$
• $\exp \left(\log \left(w\right)\right)$
• $y^{\left(\log \left(w\right)/\log \left(y\right)\right)}$ 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 $-1$.

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See Section 9 in X02AJF.