Values For Standard Hardware Floating Point Arithmetics
The following values of machine epsilon are encountered in practice.
| IEEE 754 - 2008 | Common name | C++ data type | Base | Precision | Machine epsilon | C++ or Python formula | Value |
|---|---|---|---|---|---|---|---|
| binary16 | half precision | not available | 2 | 11 (one bit is implicit) | 2 -11 | pow (2, -11) | 4.88e-04 |
| binary32 | single precision | float | 2 | 24 (one bit is implicit) | 2 -23 | pow (2, -23) | 1.192e-07 |
| binary64 | double precision | double | 2 | 53 (one bit is implicit) | 2 -52 | pow (2, -52) | 2.22e-16 |
| binary80 | extended precision | _float80 | 2 | 64 | 2 -64 | pow (2, -64) | 5.42e-20 |
| binary128 | quad(ruple) precision | _float128 | 2 | 113 (one bit is implicit) | 2 -113 | pow (2, -113) | 9.63e-35 |
| decimal32 | single precision decimal | _Decimal32 | 10 | 7 | 0.5 × 10 -6 | pow (10, -6) / 2 | 5e-7 |
| decimal64 | double precision decimal | _Decimal64 | 10 | 16 | 0.5 × 10 -15 | pow (10, -15) / 2 | 5e-16 |
| decimal128 | quad(ruple) precision decimal | _Decimal128 | 10 | 34 | 0.5 × 10 -33 | pow (10, -33) / 2 | 5e-34 |
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