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Author eryksun eryksun, larry, lemburg, mark.dickinson, rhettinger, serhiy.storchaka, stutzbach, vstinner, vxgmichel 2020-02-10.04:50:42 -1.0 Yes <1581310242.46.0.248495071154.issue39484@roundup.psfhosted.org>
Content
```A binary float has the form (-1)**sign * (1 + frac) * 2**exp, where sign is 0 or 1, frac is a rational value in the range [0, 1), and exp is a signed integer (but stored in non-negative, biased form). The smallest value of frac is epsilon, and the smallest increment for a given power of two is thus epsilon * 2**exp. To get exp for a given value, we have log2(abs(value)) == log2((1 + frac) * 2**exp) == log2(1 + frac) + log2(2**exp) == log2(1 + frac) + exp. Thus exp == log2(abs(value)) - log2(1 + frac). We know log2(1 + frac) is in the range [0, 1), so exp is the floor of the log2 result. For a binary64, epsilon is 2**-52, but we can leave it up to the floating point implementation by using sys.float_info:

>>> exp = math.floor(math.log2(time.time()))
>>> sys.float_info.epsilon * 2**exp
2.384185791015625e-07

Anyway, it's better to leave it to the experts:

>>> t = time.time()
>>> math.nextafter(t, math.inf) - t
2.384185791015625e-07```
History
Date User Action Args
2020-02-10 04:50:42eryksunsetrecipients: + eryksun, lemburg, rhettinger, mark.dickinson, vstinner, larry, stutzbach, serhiy.storchaka, vxgmichel
2020-02-10 04:50:42eryksunsetmessageid: <1581310242.46.0.248495071154.issue39484@roundup.psfhosted.org>