Re: Accuracy of cancellative addition and subtraction
Marco, P1788
On 2014 Jun 17, at 15:56, Marco Nehmeier wrote:
> may I am wrong and I am not seeing the problem. But I think that the following code
> is sufficient to compute cancellative subtraction for inf-sup intervals with bounds of
> a floating point type supporting correctly rounded subtraction (like IEEE 754 bin64)
> with a tightest accuracy.
I haven't checked it out in detail, but using error-free transformations certainly seems to be a valid method. So I will assume you have solved the problem!
You wrote:
> I suggest to change
>
> "12.10.2. Accuracy requirements. Following the categories of functions in Table 9.1, the accuracy of the basic operations, the integer functions and the absmax functions shall be tightest."
adding
> as well as the cancellative addition and subtraction in §10.5.6
I'm not convinced.
- You have shown "tightest" is easily achieved for infsup (actually 754-conforming) types. But for general types it may be harder.
- 12.12.5 states accuracy requirements, basically saying they shall be "tightest" for 754-conforming types, and "valid" otherwise.
I think instead of your proposed change, para 1 of 12.10.2 should just refer to 12.12.5. Or do you think the accuracy stated in 12.12.5 needs changing?
> (*) I guess that cancelMinus([-1,a],[-b,1) in §12.12.5 is a Typo and it should be cancelMinus([-1,a],[-b,1])
Yes, thanks. Done.
John Pryce