Charles Greathouse on Sun, 14 Mar 2010 22:06:09 +0100

 Re: floor function not doing what it should

```sqrtint(x^3) should be used rather than floor(sqrt(x^(3/2))) if you
actually be faster.

This does raise the question (which has been discussed before, though
perhaps on pari-dev?) about the usefulness of a generalized sqrtint
(raise x to the a/b power with exact integer rounding).

Ah, here it is:
http://pari.math.u-bordeaux.fr/archives/pari-users-0802/msg00005.html
ff.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Sun, Mar 14, 2010 at 5:54 AM, Bill Allombert
<Bill.Allombert@math.u-bordeaux1.fr> wrote:
> On Sun, Mar 14, 2010 at 06:54:54AM +0100, ewan.Delanoy@math.unicaen.fr wrote:
>>
>>    Dear PARI-GP users,
>>
>>   my problem can be summed up in a one-line command :
>
> Hello Ewan,
>
>> parisize = 4000000, primelimit = 500000
>> ? floor(6400^(3/2))
>> %1 = 511999
>
> floor is not at fault:
> ? 6400^(3/2)
> %1 = 512000.0000000000000000000000
> ? \p100
>   realprecision = 105 significant digits (100 digits displayed)
> ? %1
> %2 = 511999.99999999999999999999999
> ? 6400^(3/2)==(512000*(1-2^-95))
> %3 = 1
>
> So actually %1 is slightly less than 512000.
>
> 6400^(3/2) is computed using the formula exp(3/2*log(6400))
> which incurrs some rounding errors.
> Using the formula sqrt(6400)^3 give a better result:
> ? sqrt(6400)^3
> %2 = 512000.00000000000000000000000000000000
> or even
> ? sqrtint(6400)^3
> %3 = 512000
>
> To convert real to i\$ntegers, I would suggest you to use round:
>
> ? round(6400^(3/2))
> %4 = 512000
>
> Cheers,
> Bill.
>

```