[computer-go] LISP question (littlle bit off topic)

[Chrilly]

Paper 1 in the list below states:
Numbers were originally implemented in Lisp I as a list of atoms.
and the Lisp 1.5 manual states: Arithmetic in Lisp 1.5 is new....

Could you give an example how the number 3 was implemented in Lisp-1 and how 
2+1?

So far I have found only this remarks but not programming examples. It would 
be much more instructive for my article if I could quote these examples.

Chrilly

----- Original Message ----- 
From: "Ron Goldman" <rgoldman at cs.stanford.edu>
To: "computer-go" <computer-go at computer-go.org>
Cc: "Chrilly" <c.donninger at wavenet.at>
Sent: Sunday, April 08, 2007 2:23 AM
Subject: Re: [computer-go] LISP question (littlle bit off topic)


> Crilly,
>
> I used to program in LISP and had never heard of this, so I did some 
> checking. I think this is a misconception from the fact that numbers  were 
> considered atoms and hence stored on the list of atoms. Instead  of just 
> being a numeric value they consisted of an association list  (e.g. a list 
> of atoms) containing a tag to indicate the value was a  number and another 
> word with the value. The LISP I Programmers Manual  [1] gives an example:
>
>     -1 => (MINUS . (ASSOC NUMB FLO (1.0)))
>
> (In fact LISP I (1960) only supported floating-point numbers, LISP  1.5 
> (1961) supported both integers & floats. [2])
>
> As a result of storing values in an association list arithmetic  routines 
> had to do several memory references to obtain the numeric  value.
>
> In a paper on the "History of Lisp" John McCarthy [3] discussed this 
> writing that "Numbers were originally implemented in LISP I as lists  of 
> atoms, and this proved too slow for all but the simplest  computations. A 
> reasonably efficient implementation of numbers as  atoms in S-expressions 
> as made in LISP 1.5, but in all the early  LISPs, numerical computations 
> were still 10 to 100 times slower than  in FORTRAN."
>
> Later versions of LISP [4] used better tagging schemes for numbers  and 
> were able to produce compiled code that was as fast (or faster)  then C or 
> FORTRAN.
>
> Finally LISP early on had bignums to compute using arbitrary- precision 
> integers (similar to Java's BigInteger). Useful if you  needed to compute 
> factorial of 1000 exactly.
>
> -- Ron --
>
> 1. http://community.computerhistory.org/scc/projects/LISP/book/LISP% 
> 20I%20Programmers%20Manual.pdf
>
> 2. ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-024.pdf
>
> 3. http://www-formal.stanford.edu/jmc/history/lisp.ps
>
> 4. http://doi.acm.org/10.1145/1086803.1086804
>
> On Apr 7, 2007, at 12:54 PM, Chrilly wrote:
>> Up to my knowledge the first Lisp Versions had no number system.  The 
>> number n was represented as the list of numbers from 1 to n  (which is 
>> also the mathematical/axiomatic definition of the natural  numbers).
>> But its not very practical. Can anyone provide me with a link how  this 
>> was done. I am speaking some computer languages, but Lisp is  not among 
>> them.
>> I want to present the code in an article for the Austrian AI- Journal (as 
>> an example that mathematical elegance and practically  usefull are 2 
>> different things).
>>
>> Chrilly
>