From: nobody@nowhere.invalid   
      
   On Mon, 15 Jul 2024 03:15:10 Krishna Myneni wrote:   
   >[...]   
   > THank you for the recursive version. It's nice to have both looping and   
   > recursive examples.   
      
   On second thought it might be nicer to make it tail-recursive.   
   This way one can see the comparison with the equivalent loop.   
   Of course one needs to accumulate the intermediate products in   
   ascending order to preserve integrality.   
      
   \ d , k , n-k , n  --> d*(n+1)/(k+1) , k+1 , n-k+1 , n   
   : mstep ( d n1 n2 n3 -- d n1 n2 n3 )   
      >r 1+ swap 1+ 2dup >r >r m*/ r> r> swap r> ;   
      
   \ d , 0 , n-k , n --> d*C(n,k) , k , n , n   
   : binom2_rec ( d n1 n2 -- d n1 n2 ) recursive   
      2dup < if mstep binom2_rec then ;   
      
   \ d , 0 , n-k , n --> d*C(n,k) , k , n , n   
   : binom2_loop ( d n1 n2 -- d n1 n2 )   
      2dup swap - 0 ?do mstep loop ;   
      
   : binom2 binom2_rec ;   
      
   \ n , k --> C(n,k)   
   : binom ( n1 n2 -- n )   
      >r >r 1 s>d 0 r> dup r> - swap binom2 2drop drop ;   
      
   >   
   > 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.   
      
   I remember this feature from long ago (I think it was mentioned in   
   'Starting Forth'), but it seems that since the edit/compile/run cycle   
   became so fast I had never used it.   
      
   --   
   M.O.   
      
   --- SoupGate-Win32 v1.05   
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