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From: "Adam Beneschan" <adam@irvine.com>
Newsgroups: comp.lang.ada
Subject: Re: Unsigned Integer Restraint Errors
Date: 13 Mar 2007 10:31:57 -0700
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On Mar 13, 10:23 am, "Dmitry A. Kazakov" <mail...@dmitry-kazakov.de>
wrote:

>
> BTW, the arithmetic complexity can be further "reduced" by removing
> multiplication and computing k**2 using binomial decomposition
> (k+1)*(k+1)=k*k+2*k+1. So it could be:
>
> quadratic := 1; -- k*k, k=1
> linear := 2; -- 2*k+1, k=1
>
> loop
>    linear := linear + 2; -- 2*k+1
>    quadratic := quadratic + linear; -- k*k
>    exit when k>=n;
>    ...
> end loop;

Yep, that's certainly the way I'd do it on some of the *really* bare-
bones computers I occasionally had to work with---like the 6502 (used
in the Apple II).  Some of those chips, including the 6502, didn't
come with integer multiplication or division.

                                 -- Adam