From: krishna.myneni@ccreweb.org   
      
   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   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)