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 |
Read more about this topic: Machine Epsilon
Famous quotes containing the words values, standard, hardware, floating and/or point:
“We must be physicists in order ... to be creative since so far codes of values and ideals have been constructed in ignorance of physics or even in contradiction to physics.”
—Friedrich Nietzsche (1844–1900)
“If the Revolution has the right to destroy bridges and art monuments whenever necessary, it will stop still less from laying its hand on any tendency in art which, no matter how great its achievement in form, threatens to disintegrate the revolutionary environment or to arouse the internal forces of the Revolution, that is, the proletariat, the peasantry and the intelligentsia, to a hostile opposition to one another. Our standard is, clearly, political, imperative and intolerant.”
—Leon Trotsky (1879–1940)
“A friend of mine spoke of books that are dedicated like this: “To my wife, by whose helpful criticism ...” and so on. He said the dedication should really read: “To my wife. If it had not been for her continual criticism and persistent nagging doubt as to my ability, this book would have appeared in Harper’s instead of The Hardware Age.””
—Brenda Ueland (1891–1985)
“Gradually the village murmur subsided, and we seemed to be embarked on the placid current of our dreams, floating from past to future as silently as one awakes to fresh morning or evening thoughts.”
—Henry David Thoreau (1817–1862)
“The theater, which is in no thing, but makes use of everything—gestures, sounds, words, screams, light, darkness—rediscovers itself at precisely the point where the mind requires a language to express its manifestations.... To break through language in order to touch life is to create or recreate the theatre.”
—Antonin Artaud (1896–1948)