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1: 3.1 Arithmetics and Error Measures

… ► … ►

3.1.3 $$N_{\min }\equiv 2^{E_{\min }}\le |x|\le 2^{E_{\max }+1}\left(1-2^{-p}\right)\equiv N_{\max }.$$

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Defines:

$N_{\min }$: underflow (locally) and $N_{\max }$: overflow (locally)

Symbols:

$\equiv$: equals by definition, $p$: number of significant bits, $E_{\min }$: minimum exponent and $E_{\max }$: maximum exponent

Permalink:

http://dlmf.nist.gov/3.1.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §3.1(i), §3.1 and Ch.3

►Underflow (overflow) after computing $x\ne 0$ occurs when $|x|$ is smaller (larger) than $N_{\min }$ ($N_{\max }$). … ►To eliminate overflow or underflow in finite-precision arithmetic numbers are represented by using generalized logarithms ${\ln }_{\mathrm{\ell }}(x)$ given by …

2: 3.10 Continued Fractions

… ►However, this may be unstable; also overflow and underflow may occur when evaluating $A_n$ and $B_n$ (making it necessary to re-scale from time to time). …