Re: forprime

[Charles Greathouse <charles.greathouse@case.edu>]

Yes, the snippet I posted did not include the tail processing, which would be

for(n=precprime(lim)+1,lim, /* code here */)

> How much dedicated code ? I intended to add a few more loop constructs to GP:
>
>   - forstepprime()    [ loop over primes in an arithmetic progression ]
>   - forprimepowers()  [ loop over prime powers ]

I agree that loop constructs are useful. I would use both of these.

I would use forcomposite as well, though it's less important since
it's easier to simulate.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Sep 17, 2012 at 4:21 PM, Karim Belabas
<Karim.Belabas@math.u-bordeaux1.fr> wrote:
> * Bill Allombert [2012-09-17 18:50]:
>> On Sun, Sep 16, 2012 at 09:12:14AM +0200, Karim Belabas wrote:
>> > > On Sat, Sep 15, 2012 at 3:36 AM,  <michel.marcus@free.fr> wrote:
>> > > > forprime loops over prime numbers.
>> > > >
>> > > > is there a  function that would loop over composite numbers ?
>> > * Charles Greathouse [2012-09-15 09:41]:
>> > > I typically write
>> > >
>> > > p=3; forprime(q=5, lim, for(n=p+1, q-1, /* your code here */); p=q)
>> >
>> > It's not easy to do this properly in GP and the result is not that readable
>> > [ N.B. the above loops through composites only up to precprime(lim) ]
>> >
>> > I just committed a function forcomposite() to 'master', following the (new)
>> > forprime() model:
> [...]
>> What is the usecase for such function ? I never needed it myself.
>>
>> At worse you can do
>> for(a=1,1000,if(!isprime(a),print(a)))
>
> Rather slower than the original code snippet, but more correct.
>
> (20:07) gp > lim=10^8;
> (20:07) gp > s=0;forcomposite(q=3,lim,s++); s
> time = 12,846 ms.
> %2 = 94238544
>
> (20:07) gp > s=0; p=3; forprime(q=5, lim, for(n=p+1, q-1, s++); p=q)
> time = 13,801 ms.  \\ result not printed we know it's a little wrong
>
> (20:07) gp > s=0;for(q=3,lim,if (!isprime(q),s++)); s
> time = 54,684 ms.
> %1 = 94238544
>
>> I feel concerned because I will have to write dedicated code for GP2C to
>> handle it...
>
> How much dedicated code ? I intended to add a few more loop constructs to GP:
>
>   - forstepprime()    [ loop over primes in an arithmetic progression ]
>   - forprimepowers()  [ loop over prime powers ]
>
> How costly would these be ? (The first one is already in master, only not
> exported to GP yet.)
>
> Those are (much) more useful than forcomposite(), although I thought it didn't
> hurt to have the latter. Since it's non-trivial to write properly...
>
> Cheers,
>
>     K.B.
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
> 351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
> `
>