|
Machine epsilon gives an upper bound on the relative error due to rounding in floating point arithmetic. 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 or unit roundoff, and it has the symbols Greek epsilon or bold Roman u, respectively. ==Values for standard hardware floating point arithmetics== The following values of machine epsilon apply to standard floating point formats: |- |align="center"|binary16||align="right"|half precision||align="center"|short||align="center"|2||align="center"|11 (one bit is implicit)||align="center"|2−11 ≈ 4.88e-04||align="center"|2−10 ≈ 9.77e-04 |- |align="center"|binary32||align="right"|single precision||align="center"|float||align="center"|2||align="center"|24 (one bit is implicit)||align="center"|2−24 ≈ 5.96e-08||align="center"|2−23 ≈ 1.19e-07 |- |align="center"|binary64||align="right"|double precision||align="center"|double||align="center"|2||align="center"|53 (one bit is implicit)||align="center"|2−53 ≈ 1.11e-16||align="center"|2−52 ≈ 2.22e-16 |- |align="center"| ||align="right"|extended precision||align="center"|_float80〔(Floating Types - Using the GNU Compiler Collection (GCC) )〕||align="center"|2||align="center"|64||align="center"|2−64 ≈ 5.42e-20||align="center"|2−63 ≈ 1.08e-19 |- |align="center"|binary128||align="right"|quad(ruple) precision||align="center"|_float128〔||align="center"|2||align="center"|113 (one bit is implicit)||align="center"|2−113 ≈ 9.63e-35||align="center"|2−112 ≈ 1.93e-34 |- |align="center"|decimal32||align="right"|single precision decimal||align="center"|_Decimal32〔(Decimal Float - Using the GNU Compiler Collection (GCC) )〕||align="center"|10||align="center"|7||align="center"|5 × 10−7||align="center"|10−6 |- |align="center"|decimal64||align="right"|double precision decimal||align="center"|_Decimal64〔||align="center"|10||align="center"|16||align="center"|5 × 10−16||align="center"|10−15 |- |align="center"|decimal128||align="right"|quad(ruple) precision decimal||align="center"|_Decimal128〔||align="center"|10||align="center"|34||align="center"|5 × 10−34||align="center"|10−33 |} according to Prof. Demmel, LAPACK, Scilab according to Prof. Higham; ISO C standard; C, C++ and Python language constants; Mathematica, MATLAB and Octave; various textbooks - see below for the latter definition 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「machine epsilon」の詳細全文を読む スポンサード リンク
|