Re: GCC optimizes integer overflow: bug or feature?

[Richard B. Kreckel]

Marcin Dalecki wrote:

> Numerical stability of incomplete floating point representations are 
> an entirely different
> problem category then some simple integer tricks. In the first case 
> the difficulties are inherent
> to the incomplete representation of the calculation domain. In the 
> second case it's just some
> peculiarities of the underlying machine as well as the fact that the 
> unsigned qualifier is not
> used nearly enough frequently in common code. Or in other words: Z/32 
> resp. 64 IS AN ALGEBRA but
> float isn't! Thus this argument by analogy simply isn't valid.


Sheesh! This argument is totally confused...

1) Z/Zn and, by isomorphism, unsigned types may be an algebra. But this 
entire discussion is about signed types, not unsigned types.
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?)
3) Making behavior partially undefined certainly does not help making it 
an algebra or any other well-defined mathematical structure.

Integral types are an incomplete representation of the calculation 
domain, which is the natural numbers. This corroborates the validity of 
the analogy with IEEE real arithmetic.

-richy.

--
Richard B. Kreckel
<http://www.ginac.de/~kreckel/>