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From: Krishna Myneni <krishna.myneni@ccreweb.org>
Newsgroups: comp.lang.forth
Subject: Re: exercise in double number arithmetic
Date: Sun, 14 Jul 2024 20:15:10 -0500
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On 7/14/24 16:43, Marc Olschok wrote:
> On Sat, 06 Jul 2024 22:20:45 Krishna Myneni wrote:
....
>> How many different ways can you choose 42 distinct objects, 21 at a
>> time? This is "n choose k" or the binomial coefficent.
> 
> Yes, M*/ comes in handy for  C(n,0) = 1 , C(n+1,k+1) = C(n,k)*n/k
> 
> 42 21 binom d.
> gives  538257874440
> 
> where
> 
> : binom  ( n1 n2 -- nd ) \ n k --> C(n,k)
>    dup 0=
>    IF     2drop 1 s>d
>    ELSE   2dup 1- swap 1- swap binom 2swap m*/
>    THEN ;
> 
> Gforth SEE nicely replaced the original 'recurse' with 'binom' for
> better readability.
> 

THank you for the recursive version. It's nice to have both looping and 
recursive examples.

There's a reason why RECURSE (or equivalent) is preferable to having the 
name of the word in the output of SEE in Forth. This is because it is 
possible to have an earlier definition with the same name and to call it 
from within the definition e.g.

: binom ... ;

: binom ... binom ... ;

In the later definition of BINOM Forth requires the call to BINOM be the 
earlier definition if it exists in the search order. If it does not 
exist in the search order, then I believe the standard would require an 
error to occur.

Code such as shown in your output of SEE cannot be compiled when no 
earlier definition of BINOM exists. For this reason, it is not helpful 
for SEE to replace RECURSE with the word name.

The SEE in kForth shows the following:

see binom
5631665B9710    DUP
5631665B9711    0=
5631665B9712    JZ $1D
5631665B971B    2DROP
5631665B971C    #1
5631665B9725    S>D
5631665B9726    JMP $1A
5631665B972F    2DUP
5631665B9730    1-
5631665B9731    SWAP
5631665B9732    1-
5631665B9733    SWAP
5631665B9734    $5631665B9710
5631665B973D    EXECUTE-BC
5631665B973E    2SWAP
5631665B973F    M*/
5631665B9740    RET
  ok

A slightly smarter SEE would replace the address and the EXECUTE-BC 
virtual machine instruction with RECURSE.

--
Krishna