On Feb 20, 2004, at 12:43 PM, Dr Strange wrote:

> Guys, thanks for the feedback!  Hey this list is responsive, <relief>.
>
> >I can't tell from your original question ....
>
> Suppose we have the number
> 14229499582749302182940392839403938400058748399920384875773202816267485 
> 94937267261
> (82 characters long), and we want to divide this by 47, and get an  
> answer correct to 4 decimal places.....?

Well, sort of. If you do that division, you'll actually get a Fraction  
object, which is exact, and can be used in further calculations.  
Fractions can be converted to Floats, with the expected loss of  
precision. Offhand I don't see any methods for converting Fractions to  
base 10 strings, but I doubt it would be hard to write one.

> Ducasse mentions 1000 and 2000 length number strings could we actually  
> perform operations on these and get accurate results to four decimal  
> places with out rounding off? Could you give an example of how this  
> might be done in code (roughly)? Is it quite the acrobatic feat or  
> just normal Squeak math operations inline? Call me dense..... (I'm  
> sometimes a bit thick / slow - when first trying to viusalize  
> something.....) but I can't yet see how this would be done ....

Actually Stéphane gave the classic example of large number support in  
Squeak. He sent the message #factorial to the SmallInteger 1000, which  
resulted in a LargeInteger with 2568 digits. The following snippet of  
code does the same thing, then converts the result to a (decimal)  
string and returns the number characters:

1000 factorial asString size

A similar operation on 2000 gives you a LargeInteger of 5736 digits.

This sort of thing is possible in Squeak because there are no "math  
operations," just objects and messages. For example adding 3 and 4 to  
get 7 is really sending the #+ message to 3, with a parameter of 4.  
142294995827493021829403928394039384000587483999203848757732028162674859 
4937267261 and 47 have different internal representations, but they  
both respond to #+ and similar messages in appropriate ways.

So, to answer your question, the example you give is very simple with  
normal Squeak math messages. The code would be:

142294995827493021829403928394039384000587483999203848757732028162674859 
4937267261 / 47

You would get an exact answer, which would be usable for further  
calculations. You might have to do a bit of work to convert that answer  
into a string of numerals with a given accuracy.

> I'm working with number theory.... yeah I know, why would I choose VB,  
> Delphi... loooong story (nopun intended), my data set and current code  
> is immense so I can't port it all in a short period of time, yet....  
> But perhaps I can create a small applet in Squeak, compile a small  
> utility to exe and then shell out from my current app and get the num  
> string generated to text by the squeak applet and pull the value in,  
> cumbersome, but if it works in the mean time?

That would be doable. Personally I'd opt for a "math server" in Squeak,  
that you'd communicate with via XML-RPC or some such.

> You guys mentioned Smalltalk can generate to .DLL?  Could I design a  
> small utility in Squeak and then easily port the code to Smalltalk and  
> then generate the DLL callable to my current app?  If so that would be  
> GREAT!

Squeak is a specific implementation of Smalltalk, so porting to another  
implementation should be trivial. (That's not always the case, but the  
math stuff is pretty standard.)

Hope this helps,

Colin