Back Maschinengenauigkeit German Épsilon de la máquina Spanish اپسیلون ماشین FA Epsilon d'une machine French Epsilon di macchina Italian 計算機イプシロン Japanese 계산기 엡실론 Korean Epsilon maszynowy Polish Épsilon de máquina Portuguese Машинный ноль Russian
Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject of computational science. The quantity is also called macheps and it has the symbols Greek epsilon .
There are two prevailing definitions, denoted here as rounding machine epsilon or the formal definition and interval machine epsilon or mainstream definition.
In the mainstream definition, machine epsilon is independent of rounding method, and is defined simply as the difference between 1 and the next larger floating point number.
In the formal definition, machine epsilon is dependent on the type of rounding used and is also called unit roundoff, which has the symbol bold Roman u.
The two terms can generally be considered to differ by simply a factor of two, with the formal definition yielding an epsilon half the size of the mainstream definition, as summarized in the tables in the next section.