machine epsilon

The size of the smallest gap a floating-point format can represent right around the number 1 -- a direct measure of the format's own precision.

Machine epsilon, $\varepsilon_{\text{mach}}$ , is the distance between 1 and the next representable floating-point number greater than 1; for a format with $m$ mantissa bits, $\varepsilon_{\text{mach}}=2^{-m}$ .

Examples

IEEE double precision has 52 mantissa bits, so $\varepsilon_{\text{mach}}=2^{-52}\approx2.22\times10^{-16}$ .