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Karim Belabas on Mon, 11 Sep 2023 14:01:20 +0200
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Re: Power (^) function speed depending on argument types
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- To: Denis Simon <denis.simon@unicaen.fr>
- Subject: Re: Power (^) function speed depending on argument types
- From: Karim Belabas <Karim.Belabas@u-bordeaux.fr>
- Date: Mon, 11 Sep 2023 13:56:10 +0200
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- Cc: pari-users <pari-users@pari.math.u-bordeaux.fr>
- Delivery-date: Mon, 11 Sep 2023 14:01:20 +0200
- In-reply-to: <2093030652.9384973.1694430327575.JavaMail.zimbra@unicaen.fr>
- Mail-followup-to: Denis Simon <denis.simon@unicaen.fr>, pari-users <pari-users@pari.math.u-bordeaux.fr>
- References: <CAEn4z=7cVuuh-mxX9juiexKpty=9_-prUnF9-q2NYO5yxdbY7A@mail.gmail.com> <ZP4u14Spwnw6uhu0@seventeen> <2093030652.9384973.1694430327575.JavaMail.zimbra@unicaen.fr>
Hi Denis,
actually, the only command that increases the precision there is
the addition s + i; we add to the t_REAL s the t_INT i which has
- infinite accuracy (obviously)
- larger exponent than s after the first few loops
So the result s + i has a larger precision than s (in fact, the
bitprecision increases by 64 which is the minimal amount), raising that
to the power 1/5 keeps that precision. But the next loop with the new s
increases it again.
In practice, the precision increases by 64 bits every loop.
Cheers,
K.B.
* Denis Simon [2023-09-11 13:05]:
> Hi,
>
> what we learn with this example, is that the function
> (x) -> x^(1/5)
> can increase the precision of x when x is a t_REAL.
>
> Is it true for all x t_REAL ?
> For which values is this still true, instead of 1/5 ?
>
> Denis SIMON.
>
> ----- Mail original -----
> > De: "Bill Allombert" <Bill.Allombert@math.u-bordeaux.fr>
> > À: "pari-users" <pari-users@pari.math.u-bordeaux.fr>
> > Envoyé: Dimanche 10 Septembre 2023 23:02:15
> > Objet: Re: Power (^) function speed depending on argument types
>
> > On Sun, Sep 10, 2023 at 11:40:22PM +0300, Дмитрий Рыбас wrote:
> >> Hi All,
> >>
> >> I observe the following
> >>
> >> ? s=0.0;n=2000;for(i=1,n,s=(s+i)^(1/5));
> >> *cpu time = 4,148 ms,* real time = 4,148 ms.
> >> ? s=0.0;n=2000;for(i=1,n,s=(s+i+0.0)^(1/5));
> >> *cpu time = 51 ms,* real time = 51 ms.
> >> ? s=0.0;n=2000;for(i=1,n,s=(s+i)^(0.2));
> >> *cpu time = 70 ms,* real time = 73 ms.
> >> ? s=0.0;n=2000;for(i=1.0,n,s=(s+i)^(1/5));
> >> *cpu time = 50 ms,* real time = 49 ms.
> >> ?
> >>
> >> Please advise why the difference in computation time is so drastic?
> >
> > You are not computing s with the same accuracy!
> >
> > ? s=0.0;n=2000;for(i=1,n,s=(s+i)^(1/5));precision(s)
> > %10 = 38281
> > ? s=0.0;n=2000;for(i=1,n,s=(s+i+0.0)^(1/5));precision(s)
> > %11 = 57
> >
> > Cheers,
> > Bill.
--
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/