On 2014-07-08 17:57, Steven D'Aprano wrote:
[snip]
In particular, reflexivity for NANs was dropped for a number of reasons,
some stronger than others:
- One of the weaker reasons for NAN non-reflexivity is that it preserved
the identity x == y <=> x - y == 0. Although that is the cornerstone
of real arithmetic, it's violated by IEEE-754 INFs, so violating it
for NANs is not a big deal either.
- Dropping reflexivity preserves the useful property that NANs compare
unequal to everything.
- Practicality beats purity: dropping reflexivity allowed programmers
to identify NANs without waiting years or decades for programming
languages to implement isnan() functions. E.g. before Python had
math.isnan(), I made my own:
def isnan(x):
return isinstance(x, float) and x != x
- Keeping reflexivity for NANs would have implied some pretty nasty
things, e.g. if log(-3) == log(-5), then -3 == -5.
The log of a negative number is a complex number.
Basically, and I realise that many people disagree with their decision
(notably Bertrand Meyer of Eiffel fame, and our own Mark Dickenson), the
IEEE-754 committee led by William Kahan decided that the problems caused
by having NANs compare unequal to themselves were much less than the
problems that would have been caused without it.
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