Mark Dickinson <[email protected]> added the comment:
Ah, now I've looked at the script. There's an issue with using
`random.random()` to create "small" values for testing, since its result is
always an integer multiple of 2**-53. That means in particular that if x =
random.random(), then 1 - x is always *exactly* representable (and 1 + x is
also exactly representable approximately half of the time), so there's no loss
of accuracy in the intermediate step of computing log(1 + x) if x =
-random.random().
Here's what I get if I run your script exactly as it stands (Python 3.7.3,
macOS 10.14.5)
mirzakhani:Desktop mdickinson$ python test.py
Counter({'equal': 51839, 'offset_log': 41988, 'regular_log': 6173})
Counter({'equal': 93727, 'regular_log': 6273})
But if I replace each `random.random()` call with `1e-3 * random.random()`, in
order to test small values of `x`, here's what I get:
mirzakhani:Desktop mdickinson$ python test.py
Counter({'offset_log': 99945, 'equal': 55})
Counter({'offset_log': 99893, 'equal': 107})
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<https://bugs.python.org/issue37454>
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