Machine epsilon

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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 ε {\displaystyle \varepsilon } . 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 {\displaystyle \mathbf {u}...

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