Re: How to check a Float for NaN

[Adam Beneschan <adambeneschan@gmail.com>]

On Thursday, May 22, 2014 9:31:12 AM UTC-7, Dmitry A. Kazakov wrote:

> > No, I don't think so.  3.5.7(8) says "The set of values for a floating
> > point type is the (infinite) set of rational numbers."  This excludes NaN
> > and infinities, which are not rational numbers (nor any kind of number).
> 
> These are not values of Long_Float. I guess that values of Long_Float are
> "machine numbers" defined in the following sentence.

I'm not sure why the RM defined the "set of values" to be an infinite set; I'm sure that this made the rest of the semantics easier to specify in some way, but I don't know what that is.  The set of *machine numbers* for a type is a subset of this set of values.  I think that intermediate computations can involve numbers that aren't machine numbers (if they're performed using a type with greater precision, for example); I'm not sure.  In any case, though, it's clear that infinities and NaN aren't part of the "set of values", and thus they can't be part of the set of machine numbers which is a subset of the "set of values".


> Why doesn't it preclude NaN returned and accepted by arithmetic operations? 
> Either 3.5.7 lies or the operations do.

I think it *does* preclude NaN, unless I don't understand what you mean.  I guess you could say that the "operations lie", because if Machine_Overflows is False, an operation on two values of a floating-point type may have an invalid result.  Normally, that's not supposed to happen.  But we can consider Machine_Overflows=False to work somewhat similarly to a Suppress pragma in that undefined results may happen.  If B is a Boolean variable whose value is True, what does B := Boolean'Succ(B) do if Suppress(Range_Check) is in effect?  It will quite possibly set B to something that is not a valid Boolean value.  But I'm not sure that means the 'Succ operation is lying.  And I don't think that the arithmetic operations "lie" any more than 'Succ is in this example.

                                 -- Adam