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/>
