Binade

In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent. In other words, a binade is the interval ${\displaystyle [2^{e},2^{e+1})}$ or ${\displaystyle (-2^{e+1},-2^{e}]}$ for some integer value ${\displaystyle e}$, that is, the set of real numbers or floating-point numbers ${\displaystyle x}$ of the same sign such that ${\displaystyle 2^{e}\leq |x|<2^{e+1}}$.^[1][2][3]

Some authors use the convention of the closed interval ${\displaystyle [2^{e},2^{e+1}]}$ instead of a half-open interval,^[4] sometimes using both conventions in a single paper.^[5] Some authors additionally treat each of various special quantities such as NaN, infinities, and zeroes as its own binade,^[6] or similarly for the exceptional interval ${\displaystyle (0,2^{\mathrm {emin} })}$ of subnormal numbers.^[7]