[issue39484] time_ns() and time() cannot be compared on windows

[Eryk Sun]

Eryk Sun <eryksun at gmail.com> added the comment:

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

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nosy: +eryksun

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<https://bugs.python.org/issue39484>
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