Pseudo prime tests (Was: Re: _mp_alloc vs ALLOC)

[bodrato at mail.dm.unipi.it]

Ciao,

Il Mar, 5 Giugno 2012 11:34 pm, Torbjorn Granlund ha scritto:
> 1. mpz_pprime_p, for doing some trial dividing and unspecified
>    probabilistic primality tests to specified probability.

I'd like to keep the "Return 2 if n is definitely prime" feature of the
current _probab_prime_ function.

> 2. mpz_notdiv_pprime_p, like mpz_pprime_p but without trial dividing.

Do we really need a new function for this? An additional parameter should
be enough.

> 3. mpz_millerrabin, replacing the current internal function with the
>    same name (but with different parameters).

This can be useful if we decide to export it, but it (slightly) slows down
the repeated use, because nm1, one, nredc, q and k must be recomputed at
each call.
Moreover, the comment to this function says: "FIXME: Stay in REDC,
requires reimplementation of mpz_powm". In this case we should require an
already redcified base argument. A loop like the one in _pprime_p will
then use the random numbers generated by _urandomm as redcified...
Or we can write a mpn_redc_millerrabin, and use it for all the mpz
functions above.

> The new code makes use of redc functions at the mpz level, which I wrote
> several years ago.  (Such functions could also at some point be made
> part of the public GMP interface.)

But I fear mpz_millerrabin doesn't use them the best way: nm1 is redcfied
too early, then it's compared to the non redcfied result of _powm,
possibly giving a wrong "composite" answer on prime numbers! Moreover we
don't need to use the redcfy function on both 1 and (n-1). I attach a
working copy.

About the redcfy interface: _modredc can be used both after a
multiplication, or after a (sequence of) subtraction/addition?

Regards,
Marco

-- 
http://bodrato.it/software/strassen.html
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