[issue37787] Minimum denormal or ** bug

[Tim Peters]

Tim Peters <tim at python.org> added the comment:

Python delegates exponentiation with a Python float result to the platform C's double precision `pow()` function.  So this is just what the Windows C pow(2.0, -1075.0) returns.  All native floating point operations are subject various kinds of error, and this is one.

>>> import math
>>> math.pow(2.0, -1075.0)
5e-324
>>> math.pow(2.0, -1074.0) # same thing
5e-324

To avoid intermediate libm rounding errors, use ldexp instead:

>>> math.ldexp(1, -1074) # 2.0 ** -1074
5e-324
>>> math.ldexp(1, -1075) # 2.0 ** -1075
0.0

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nosy: +tim.peters

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Python tracker <report at bugs.python.org>
<https://bugs.python.org/issue37787>
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