From: nobody@nowhere.invalid   
      
   On Sat, 06 Jul 2024 22:20:45 Krishna Myneni wrote:   
   > I've been working on extending the kForth-64 User's Manual and, in   
   > particular, illustrating double length arithmetic, which, being one of   
   > the strengths of Forth, often does not get enough exposure. Here's an   
   > exercise which you can do using only standard Forth words.   
   >   
   > 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.   
      
   --   
   M.O.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)