# Boost :

Subject: Re: [boost] New Boost.XInt Library, request preliminary review
From: Jeffrey Hellrung (jhellrung_at_[hidden])
Date: 2010-04-02 14:32:14

Scott McMurray wrote:
[...]
> I think is_nan(Inf) should be false, but is_finite(Inf) should also be false.

Well is_finite(NaN) should be false as well; is_infinity would be a more
appropriate predicate.

>> it's not something that can be calculated with, generally.
>>
>> [...]
>>
>> If I don't add an infinity value, I could. I'm leaning toward adding one
>> (with sign), but it will act exactly like a NaN except for comparisons.
>>
>
> Actually, you *can* calculate with infinity. That's the reason for
> having it separate from NaN, and why it needs a sign. Any operation
> with NaN gives a NaN, but at least the following for Infs don't give
> NaNs (for any x, y where is_finite(x) && !is_nan(y)):
>
> -(Inf) => -Inf
> -(-Inf) => Inf
> x + Inf => Inf
> x - Inf => -Inf
> x % Inf => x
> Inf + Inf => Inf
> -Inf - Inf => -Inf
> x < Inf => true
> x > -Inf => true
> y <= Inf => true
> y >= -Inf => true
> x / Inf => 0
> x / -Inf => 0
> if (y != 0) y * Inf => sign(y)Inf
> if (y != 0) y * -Inf => sign(-y)Inf
>
> But the indeterminate forms do, of course, give NaNs:
>
> Inf - Inf => NaN
> -Inf + Inf => NaN
> 0 * Inf => NaN
> 0 * -Inf => NaN
> Inf / Inf => NaN
> Inf / -Inf => NaN
> Inf % y => NaN
>
> Hopefully that'll make you lean further :P

Don't forget (assuming a single unsigned 0):

x / 0 => NaN

and I think you'd want Inf to compare equal with itself (unlike NaN,
which does not compare equal with itself...and doesn't compare unequal
with itself, either :/ ).

This is of secondary consideration to the core set of algorithms that
should just throw whenever something bad happens (e.g., division by 0),
though.

Another topic: Chad, how natural is it, implementation-wise, to have a
signed zero? I'm guessing you have a sign bit, leading naturally to
either providing both a +0 or a -0, or ensuring after each operation
that -0 is normalized to +0. What are the arguments against a signed
zero? Is it possible to simply be agnostic to the sign bit when the
mantissa is 0?

- Jeff