machine epsilon

The gap between 1.0 and the next float above it - about 1.2 * 10^-7 for float and 2.2 * 10^-16 for double.

Machine epsilon is ulp(1) = 2^(1 - p), returned by std::numeric_limits::epsilon() (2^-23 for float, 2^-52 for double); the relative rounding error of one correctly rounded operation is at most half of it.

Examples

For double, machine epsilon is 2⁻⁵², about 2.22 × 10⁻¹⁶.