From: do-not-use@swldwa.uk   
      
   On 15/07/2024 02:15, Krishna Myneni wrote:   
   > 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.   
   >   
      
   That's why the simplest way to achieve recursion by name is:   
      
   synonym binom recurse   
   : binom ... binom ... ;   
   but Gforth's RECURSIVE is better   
      
   --   
   Gerry   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)