Re: Table 4 proposal version 0.2...
Vincent & P1788
I apologise for having been away from this discussion for too long owing to teaching commitments and working on a paper.
On 5 Mar 2012, at 02:10, Vincent Lefevre wrote:
> Even though not all FP arithmetic are IEEE-754 conforming, the
> fact that P1788 already requires +inf and -inf means that NaN
> should be available in the FP implementation.
>
> BTW, I think that P1788 should allow non-FP formats (e.g.
> double-double and rational arithmetics). Requirements could
> be at least: the number of values is finite, the format is
> symmetric (-x is exact), and +inf, -inf and NaN are available.
I think this is an excellent suggestion. As we're seeing, the interface of intervals to floating point is necessary but contentious. Since, early on, we rejected tying P1788 exclusively to IEEE 754, we need some ground rules like this. Vincent's rules are *necessary* properties to my philosophy of how we create this interface, except for "-x is exact", which is sensible rather than necessary.
Vincent, will you propose a motion about it?
I suggest another couple of things:
- There be at most two flavours of zero, and that in
comparison relations they behave as in 754.
(E.g. -0 == +0 returns true.)
- Doing (+inf)-(-inf) shall return +inf.
Dan mentioned there is/was an arithmetic that doesn't
do this; we shall not make allowances for it.
How does double-double work? Must the two pieces have disjoint exponent ranges, so there is only one way to represent a nonzero number?
John Pryce