Re: GCC optimizes integer overflow: bug or feature?

[Marcin Dalecki]

On 2006-12-20, at 22:48, Richard B. Kreckel wrote:

> 2) Signed types are not an algebra, they are not even a ring, at  
> least when their elements are interpreted in the canonical way as  
> integer numbers. (Heck, what are they?)

You are apparently using a different definition of an algebra or ring  
than the common one.

> Integral types are an incomplete representation of the calculation  
> domain, which is the natural numbers.

This is an arbitrary assumption. In fact most people simply are well  
aware of the fact that computer
don't to infinite arithmetics. You are apparently confusing natural  
numbers, which don't include negatives,
with integers. However it's a quite common mistake to forget how  
"bad" floats "model" real numbers.

> This corroborates the validity of the analogy with IEEE real  
> arithmetic.

And wrong assumptions lead to wrong conclusions.

Marcin Dalecki