STINNER Victor added the comment:
"History, perhaps? In any case, the sign of a NaN isn't useful information in
the same way that the sign of an infinity is. The IEEE 754 standard explicitly
refuses to attach any meaning to the sign bit of a NaN. And if we were aiming
for a full and faithful representation of NaNs, we'd want to output the
payload, too (which is just about as meaningless / meaningful as the sign bit)."
So I understand that adding a math.neg_nan would be useless. As adding one
constant per possible "NaN" value :-) If I recall correctly the IEEE 754
standard, there is not single NaN value, but a range of NaN.
"Two kinds of NaN: a quiet NaN (qNaN) and a signaling NaN (sNaN). A NaN may
carry a payload that is intended for diagnostic information indicating the
source of the NaN. The sign of a NaN has no meaning, but it may be predictable
in some circumstances." says Wikipedia.
Well, the current definition of math.nan makes sense, it's the same value than
float("nan").
Note: On python-ideas, I asked if math.nan and math.inf should be singleton (as
it was requested for float("0.0") in issue #4024). The answer is no.
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<http://bugs.python.org/issue23185>
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