Re: Power (^) function speed depending on argument types

[Denis Simon <denis.simon@unicaen.fr>]

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.