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RE: Q on NaN

From: Drew Adams
Subject: RE: Q on NaN
Date: Fri, 24 Jun 2005 14:49:04 -0700

    > I didn't say above that (/0.0 0.0) should give `arith-error'.

    Well, you seemed to: you complained that it did so in previous

No, I said "fair enough" to that change in behavior. I did not suggest it
was a bug. My question was about numberp's behavior:

    > I suggested that perhaps `numberp' should return nil for
    > a NaN argument, since "NaN"
    > means "not a number" and "numberp" means "a number".
    > NaN is a floating-point value, but is it a number?

    Any floating-point value is a ``number'' as far as `numberp' is
    concerned.  The fact that NaN is a short for not-a-number does not
    mean that Lisp should treat it like that.

I can see that from the behavior, but then perhaps it should be mentioned
explicitly in the doc. Since the names suggest something different, perhaps
a note of clarification should be added.

    >     As for a way to test for a NaN, try this:
    >            (= (/ 0.0 0.0) (/ 0.0 0.0))
    >     It should evaluate to nil, since a NaN is defined to fail _any_
    >     arithmetic comparison, even a comparison to itself.
    > That doesn't tell me how to test if `foobar' is a NaN.

    Exactly the same: (= foobar foobar).  (Did you try that?)

Right. Got it; thanks. A couple of people replied with the same solution.

I am using (equal 0.0e+Nan), which also seems to work (and if equivalent,
would perhaps be clearer, since it mentions NaN: anything equal to NaN is
NaN). Does anyone know that these are not equivalent:

 (equal 0.0e+NaN) <=?=> (and (numberp x) (/= x x))

That is, are there any objects equal to 0.0e+NaN that are not NaN?

It might also be useful to mention such an idiom - either expression - in
the doc, or else to provide a predicate.

    > See my previous email: I knew I could test
    > `(equal foo 0.0e+Nan)', but I thought I would
    > need to test against all of the possible NaN values.

    No need: the arithmetic equality trick takes care of all of the
    possible values.

Right. All NaNs are `equal', but they are not `=', even to themselves.

    Note that you should use `=', not `equal' (nor `eql', btw).

Yes, for testing a numberp to see if it is not NaN. However, I am testing an
arbitrary object. For that, (and (numberp x) (/= x x)) works and (equal x
0.0e+Nan) works. For the latter test, it must be `equal' or `eql', not `='
or `eq'.

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