Re: LOGO-L> Number Sculpturing

[Yehuda Katz <yehuka@beitberl.beitberl.ac.il>]

Olga Tuzova wrote:
> 
> Hello everybody,
> 
> We have enjoyed Word Sculpturing proposed by Yehuda, and what about
> number sculpturing? Let's begin with the following pyramid.
> 
> This pyramid uses the procedure of multiplication which I took from
> the "Informatics", the newspaper I've mentioned. This procedure
> imitates the process of large number multiplication we follow using
> pen and paper. As the integers are not large here, it isn't
> necessary to use the procedure, but without it the program
> wouldn't be interesting at all. :-)
> I tried, but failed, to define the limits of it's implementation. The
> procedure allows to multiply the large integers, when the result
> is greater then the largest allowed integer, but in this process the
> intermediate sums shouldn't exceed it. I'm not sure, I'm making any
> sense. What I mean is --
> 
> let's multiply 234 and 567.
> The result may be obtained as
> 234  * 7 + (234 * 6) * 10 + (234 * 5 ) * 100
> So, every time we have to multiply 234 (the first integer) and
> 1-digital integer and then move the result left and add it to the
> previous intermediate sum. If we'll store the result as a word (why
> not, if it's useful? :-) ) then it may exceed the largest allowed
> integer. But intermediate results shouldn't exceed this largest
> integer. And I don't know how this problem may be solved before hand,
> that is, before we begin  multiplication  and get something like
> "remainder doesn't like 999 999 999 999 999 as an input".
> 
> And now here is a Number Pyramid:
> 
> to number.pyramid.ini
> ct
> number.pyramid 1 1
> end
> 
> to number.pyramid  :l :k
> if :l>9 [stop]
> (pr :k "*8+ :l "= proc.mult :k 8 :l ")
> number.pyramid  :l+1 10*:k+:l+1
> end
> 
> to proc.mult :x :y :s :res
> ifelse not :y=0 [make "s :s+:x*(remainder :y 10)
>                  op proc.mult :x int :y/10 int :s/10 ~
>                             word remainder :s 10 :res]~
>                 [if not :s=0 [make "res word :s :res] op :res ]
> end
> ------------------------------------
> Hope, you'll like it.
> 


Olga,

Beautiful AND interesting.

If you want your number pyramid to look more like a number pyramid,
you might try the following (there's really no need for PROC.MULT here):

=======================================
to main ; Pyramid by Olga T.
ts ct
pyramid 1 1
end

to pyramid  :l :k
if :l>9[stop]
pr(word form :k 9 0 "*8+ :l "= :k*8+:l)
pyramid :l+1 10*:k+:l+1
end
=======================================

Enjoy,

[[Yehuda]]

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