[Cfp-interest 2852] Re: CFP review of TS-4 and TS-5 revisions

[Damian McGuckin]

David,

(... augmented operations)

On Thu, 24 Aug 2023, David Hough CFP wrote:

> Double-double represents numbers as a pair of doubles, the second much 
> smaller in magnitude than the first.  Ideally, in a pair (a.h,a.t), a.h 
> would contain the correctly rounded result of computed(a.h+a.t), and a.t 
> would contain the correctly rounded result of computed(a.h+a.t)-a.h. 
> Performance considerations often compromise this ideal.

Should it be mandated that a.h be correctly rounded where I assume that 
correctly rounded means round-to-nearest, ties to even.

Or, should the sign of a.h and a.t be mandated to match?

Obviously, given say two doubles, x and y, and (a.h,a.t) the result of 
some augmented operation OP then obviously

         (x OP y) correctly-rounded using the non-augmented OP

should match exactly

         (a.h OP a.t) correctly-rounded using the non-augmented OP

I think to have the same sign, you need to round OP as round-towards-zero. 
That probably makes it more complicated. There are advantages to having 
them match but that means that a.h is then not the correctedly rounded 
result (of say) the sum to the same precision as the original operands.

I tried to read Jason Riedy's and Jim Demmel's paper on this but I am sure 
that it has not all permeated my brain yet.

Thanks - Damian

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