Ceil double problem

[Dik T. Winter]

>
> Recall that footnotes are not normative, however.

Yes, I know, it is just a clarification of what the standard itself
already does state.

> In any case, I think the intention of that foot note is to remind us
> that floating point arithmetic is merely "as-if" it followed that
> model.
>
> In any case, I don't think that the standard meant to allow
> non-integer bases, or it wouldn't have made the point in disallowing
> them.

The standard does not disallow them, as long as the arithmetic can be
modelled with an integer base. You may note that the radix given
is not necessarily the actual radix of the base arithmetic, nor is
it necessary that the base arithmetic is floating-point. The only
requirement is that it can be modelled as if it follows such a model,
and indeed, nearly every arithmetic can be modelled as such.

> Given that fact, and the fact that representing 4.0 only
> requires at most 2 significand digits (only base 3 requires more than
> 1) and an exponent value of at most 2 (only for base 2: 3 and 4
> require 1, all others can use 0), I don't see how you can make
> even a theoretical case for a conforming floating-point implementation
> that can fail to represent it.

That is all irrelevant as the standard allows all operations to be
as inexact as you wish, the only requirement is about the round-trip
conversion.