Maximilian Hasler on Sat, 29 Dec 2012 22:16:45 +0100

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 Re: Square of an unsigned integer without products.

```It would be nice if you could be a little less cryptic to save time
(needed to understand), to all those which receive this message.

I hope no computer uses
"
sum(i=1,2  (some other sum independent of i)  )
"
to compute twice that other sum, by doing all the calculation two
times ; while multiplication by 2 is achieved with nearly zero
computational complexity by binary left shift.

Why do you want to avoid "multiplication", do you think it is more
expensive than a triple nested sum ? This is certainly not the case.
(cf. e.g. http://en.wikipedia.org/wiki/Sch%C3%B6nhage%E2%80%93Strassen_algorithm)

As a side note (since you post this on a PARI list, which is maybe not
really the best place for such a question),
the " my(i,j,k); " statement leads to a useless duplicate of the
summation variables.
(They are automatically declared as local variable by the for(..) statement.)

Best regards,

Maximilian

On Sat, Dec 29, 2012 at 3:05 PM, Remy José Cano Ramírez
<aallggoorriitthhmmuuss@gmail.com> wrote:
> Greetings,
>
> About the following:
>
> ----------------------------------------------------------------------------------------
>
> /*
>    Please review and comment if at certain low level the computers today
> already
>    make such calculations with the method shown below.
> */
>
> uisqr(x)={my(i,j,k); x+sum(i=1,2,sum(j=1,(x-1),sum(k=(j+1),x,1)))};
>
> ----------------------------------------------------------------------------------------
>
> (Also available at: http://pastebin.com/qb7FHEzA)
>
> Regards,
>
> Remy

```