= Half-precision floating-point format
{title2=binary16}
{wiki}
= Half-precision floating-point number
{synonym}
A sixteen-<bit> <floating-point representation> with one sign <bit>, five <exponent> <bits> and ten stored fraction <bits>. For sign $s$, stored <exponent> $E$ and fraction <integer> $F$, normal finite values are
$$
(-1)^s(1+F2^{-10})2^{E-15},\qquad1\leq E\leq30,\quad0\leq F<1024.
$$
The implicit leading one gives eleven significant <binary digits>. With $E=0$, the value is $(-1)^sF2^{-24}$, including signed zero at $F=0$ and <subnormal numbers> otherwise. The stored <exponent> $E=31$ is reserved for infinities at $F=0$ and <NaN> otherwise. The positive normal range is $2^{-14}$ through $65504$; the least positive <subnormal number> is $2^{-24}$.
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