'**********************************************
'* This program allows user performing combi- *
'* natory analysis, such as Factorial N,      *
'* Combination C(n,p) and Permutation A(n,p). *
'* ------------------------------------------ *
'* Ref.: "Mathematiques en Turbo-Pascal By    *
'*        M. Ducamp and A. Reverchon (2),     *
'*        Eyrolles, Paris, 1988" [BIBLI 05].  *
'* ------------------------------------------ *
'* Sample runs:                               *
'*                                            *
'* COMBINATORY ANALYSIS                       *
'*                                            *
'*   1:  Factorial n!                         *
'*   2:  Combination C n,p                    *
'*   3:  Permutation A n,p                    *
'*   0:  Quit                                 *
'*                                            *
'*   Your choice (0 to 3): 1                  *
'*                                            *
'*   N = 100                                  *
'*   N! = 9.3248476268  10^ 157               *
'*                                            *
'*   Your choice (0 to 3): 2                  *
'*                                            *
'*   N = 7                                    *
'*   P = 3                                    *
'*   Cnp =           35                       *
'*                                            *
'*   Your choice (0 to 3): 3                  *
'*                                            *
'*   N = 10                                   *
'*   P = 6                                    *
'*   Anp =       151200                       *
'*                                            *
'*           BASIC Release 1.1 By J-P Moreau  *
'*                 (www.jpmoreau.fr)          *
'* ------------------------------------------ *
'* Release 1.1: bug corrected in subroutine   *
'*              1100.                         *
'**********************************************
MAXREAL=1E30
PI=3.1415926535

choice%=1

10  cls
    print
    print " COMBINATORY ANALYSIS"
    print
    print "  1:  Factorial n!"
    print "  2:  Combination C n,p"
    print "  3:  Permutation A n,p\n"
    print "  0:  Quit"
    print
    input "  Your choice (0 to 3): ", choice%
    print
    if choice%<0 then choice%=0
    if choice%>3 then choice%=3
    if choice%=0 then goto 100   'quit
    if choice%=1 then            'Factorial n
       input "  N = ", n%
       gosub 1000 : s=Factorial
       print "  N! = ";
       if s>0 then
         print using "############"; s
       else
         print using "##.############";r1;
         print "   10^"; : print using "####"; r2
       end if
    end if			
    if Choice%=2 then            'Combination n,p
       input "  N = ", n%
       input "  P = ", p%
       gosub 1100 : s=Cnp
       print "  Cnp = ";
       if s>0 then
         print using "############"; s
       else
         print "  Quantity impossible to evaluate"
       end if
    end if	
    if Choice%=3 then            'Permutation n,p
       input "  N = ", n%
       input "  P = ", p%
       gosub 1200 : s=Anp
       print "  Anp = ";
       if s>0 then
         print using "############"; s
       else
         print "  Quantity impossible to evaluate"
       end if
    end if
    print
    input " Hit a key to continue...",r$
if choice%<>0 then goto 10
100 end


'Factorial n!
1000 fa=1
  if n%<25 then
    for i%=1 to n%
      fa=fa*i%
    next
    Factorial=fa
  else
    fa=(log(2*PI*n%)/2 + n%*log(n%)-n%)/log(10)
    r2= int(fa)
    r1= exp((fa-int(fa))*log(10))
    Factorial=0
  end if
return

'Combination Cn,p
1100 if p%>n% then
    Cnp=0 : return
  end if
  r=1
  if p%>n%-p% then
    u%=n%-p%
  else
    u%=p%
  end if
  for i%=0 to u%-1
    x= (n%-i%)/(u%-i%)
    if r>MAXREAL/x then return
    r=r*x
  next
  Cnp=r
return

'Permutation An,p
1200 if p%>n% then
    Anp=0
    return
  end if
  r=1
  for i%=n%-p%+1 to n%
    if r>MAXREAL/i% then
      Anp=0
      return
    end if
    r=r*i%
  next
  Anp=r
return

' end of file combi.bas