On Tuesday 13 January 2009 19:26:07 Carl Witty wrote:
> On Jan 13, 2:38 am, ja...@njkfrudils.plus.com wrote:
> > > > The other issue here is that there are multiple algorithms here and
> > > > it is quite likely that very small examples will use the basic xgcd
> > > > which may well guarantee minimality. Only if you have say hundreds of
> > > > thousands of bits will the algorithm used not return minimally
> > > > guaranteed results. I'm sure when the time comes we can give some
> > > > explicit million digit integers for which minimality is not
> > > > guaranteed.
> >
> > The non-minimal examples could be dependant on tuning parameters that
> > select between different algorithms, making this sort testing impratical.
>
> That's painful.
>
> One of the great selling points for MPFR is that it always gives the
> exact same answers on all platforms; it would be sad if MPIR doesn't
> provide the same guarantees.
>
> How much speed difference are we talking about? IMHO, I would accept
> a few percent slowdown for huge GCDs on some platforms to get
> portable, identical results cross-platform in Sage. (Of course, it's
> not my decision to make.)
>
> Carl
>
If a function says it returns and anwser that satisfys certain conditions ,
then that it what you should rely on. If your relying on unspecified behavour
then it's on your own head :)
Of course in common cases then the user expects certains properties to hold ,
and if their not then confusion results.
Consider this from the current gmp manual
-- Function: void mpz_gcdext (mpz_t G, mpz_t S, mpz_t T, mpz_t A,
mpz_t B)
Set G to the greatest common divisor of A and B, and in addition
set S and T to coefficients satisfying A*S + B*T = G. G is always
positive, even if one or both of A and B are negative.
If T is `NULL' then that value is not computed.
The function is free to return ANY solution (S,T) to the above , If your
relying on certains bounds for S and T to be satisfied then you would have
wrap this function in a layer to reduce the general case to the specific.
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