primorial(negative)

[Marc Glisse]

(apparently I forgot to click on "send")

On Thu, 12 Nov 2015, paul zimmermann wrote:

>> Suggestions for the interface?

I don't have any particular suggestion. I have only needed this once, and 
it would help if other people who have needed something similar could 
explain what it was. If nobody needs it, we can forget it. And even 
otherwise, I am not sure it belongs in GMP. Just asking.

In our case, we have code to compute (persistent) homology in several 
fields Z/pZ at the same time, and the idea was to get a bunch of primes 
(the most natural notion of bunch was those in some interval [p,q]). 
Getting the primes takes a negligible amount of time compared to the rest.

> mpz_prime_t p;
>
> mpz_prime_init_ui (p, 17); /* initializes p to 17 */
>
> mpz_prime_next (p);     /* p <- next_prime(p) */
>
> mpz_prime_clear (p);
>
> We could access the current prime by:
>
> mpz_prime_get_z (z, p);

mpz_prime_next vs mpz_nextprime is going to get confusing :-(
Maybe mpz_primes_* (plural) or some other longer name would help convey 
the intent?
In my original use-case, I want all primes between p and q (though I am 
mostly interested in p=2). Does not knowing an upper bound complicate the 
implementation?
The idea was to use a simple sieve. If we don't start from 2, the doc 
needs to be clear that you will pay for the sieve even if you are only 
asking for a single prime.
If we are interested in small primes, using mpz_t could be wasteful. Maybe 
mpz_prime_get_ui (p), and it would return 0 instead of the prime if it 
doesn't fit? Enumerating all the primes that fit a 32-bit unsigned long 
should be doable, so maybe having unsigned long as the only possible type 
would be too restrictive?

-- 
Marc Glisse