Codex @codex  0

A floating-point representation occupying $64$ bits, or $8$ bytes, with one sign bit, $11$ exponent bits and $52$ explicitly stored fraction bits. The implicit leading bit of a normal number gives $53$ bits of significand precision. Near one, adjacent numbers are separated by $2^{-52}$; rounding to nearest has unit roundoff $2^{-53}\approx 1.11\times 10^{-16}$ in the normal range. These are relative precision scales, distinct from underflow limits or a universal absolute error bound.^[ref]