Re: [boost] Yet another bignum type

From: Maarten Kronenburg (M.Kronenburg_at_[hidden])
Date: 2006-11-29 17:39:31

"Herve Bronnimann"  wrote in message
>
> >> The unsigned integer inherits from the signed one. While this does
model
> >>arithmetics correctly (a natural number is an integer, after all), it is
the
> >>unsigned integer that has richer functionality. It's clumsy and not
> >>extensible to use inheritance in such a case.
> >
> >The normal and the unsigned integer have the same functionality, only the
> >implementation is slightly different.
>
> I've heard this often enough since the beginning of this discussion, and
imho it's a major source of confusion and problems in the design. Google
"Liskov Substitution Principle",  "ISA Relationship" or other similar
keywords, for more information.  The famous example is
Shape/Rectangle/Square (read
http://www.objectmentor.com/resources/articles/lsp.pdf for a good
discussion).
>
> So I have to say this loud and clear: a natural number <NOT> "is a" </NOT>
integer.  It is not, no more than a modular one is.  Try subtracting 1 to 0,
and you will not get the same behavior in either three types.  This violates
the LSP (Liskov Subst. Princ. mentioned above)

For determining whether an arithmetic result is positive or negative, you
have to compute it first, and for determining whether a modular integer
arithmetic result needs to be modulo reduced, you need to know the result
first, which may not be in the modulo range. For this practical reason the
unsigned and modular integer are built up from a normal integer. Software
design is (in this case) a little more practical than pure mathematics,
where an unsigned integer is always by definition positive and a modulo
integer is always by definition in the modulo range. The ideal mathematical
world can (in this case) not be achieved by real software, but only
approached.
Regards, Maarten.

>
> However, a const_unsigned_integer "IsA" const_integer, so long as you
can't modify the value.  Thus if you think of integer as a value semantic
type, all is well in your relationships, but the presence of operator--,
etc.  dictates that unsigned_integer and integer should be unrelated
classes.  There is a hierarchy, equivalent to the famous example of
Shape/Square/Rectangle, where (loosely speaking, and without syntactic
rigor):
>     class const_integer;
>     class const_unsigned_integer : public const_integer; // a natural
number is an integer, when talking about value semantics
>     class integer : public const_integer;
>     class unsigned_integer : public const_unsigned integer;
> But note that the fourth side of the rectangle (unsigned_integer: public
integer) is *not* provided.
>
> The same goes even more drastically with modular_integer where some
operations (operator<) don't make real sense.
>
> I think this was mentioned back in June, perhaps not in such details, but
I remember some people objecting to the inheritance back then.  I think you
should think about this seriously, Maarten, since imho it's a major flaw in
your design, not taking any position on allocators or other issues.  I don't
have a particular opinion about how to fix the proposal, but I just want
this forum to be at least aware of the issues.
> Regards,
> --
> Herve Bronnimann
>
>