[issue45876] Improve accuracy of stdev functions in statistics

[Mark Dickinson]

Mark Dickinson <dickinsm at gmail.com> added the comment:

There's also a potential double-rounding issue with ldexp, when the first argument is an int: ldexp(n, e) will first round n to a float, and then (again for results in the subnormal range) potentially also need to round the result.

>>> n = 2**53 + 1
>>> e = -1128
>>> math.ldexp(n, e)
0.0
>>> n / (1 << -e)
5e-324

I'm a bit (but only a bit) surprised and disappointed by the Windows issue; thanks, Tim. It seems to be okay on Mac (Intel, macOS 11.6.1):

>>> import math
>>> d = math.nextafter(0.0, 1.0)
>>> d
5e-324
>>> d3 = 7 * d
>>> d3
3.5e-323
>>> d3 / 4.0
1e-323
>>> math.ldexp(d3, -2)
1e-323

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<https://bugs.python.org/issue45876>
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