[Cfp-interest 2216] Re: quantum

[Vincent Lefevre]

On 2021-10-06 21:25:53 -0700, David Hough CFP wrote:
> A problem with "ulp" is deciding what the ulp of an exact power of the
> base should be

Yes, the different definitions of ulp.

> - and thus ulp depends on the format;

but ditto with the quantum (which also depends on the representation).

> a real number doesn't have an "ulp".

It is practical, only for proofs (such as error analysis) I suppose,
to define the ulp (associated with a format) on a real number.

For instance, |RN(x) - x| ≤ (1/2) ulp(x).

>     Then there's the question about what it means for
> logarithmic formats.

This is off-topic, and there would be the same issue for the quantum.

> But for conventional floating-point formats, the "ulp"  mostly arises
> in terms of error bounds stated as ulps of the computed result.

It is generally better to state error bounds as ulps of the exact
result.

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