'**********************************************
'*  This program allows making arithmetic     *
'*  operations in any base between 2 and 36.  *
'* ------------------------------------------ *
'* Ref.: "Mathematiques en Turbo-Pascal by    *
'*        M. Ducamp and A. Reverchon (2),     *
'*        Eyrolles, Paris, 1988" [BIBLI 05].  *
'* ------------------------------------------ *
'* Sample runs:                               *
'*                                            *
'* ARITHMETIC OPERATIONS IN ANY BASE          *
'* BETWEEN 2 AND 36                           *
'*                                            *
'* Enter base (2 to 36): 25                   *
'* Enter 1st number : AM3G                    *
'*                                            *
'* Enter next number: 28                      *
'* Operator (+-*/^) : +                       *
'* Result           : AM50                    *
'* Enter next number: J                       *
'* Operator (+-*/^) : *                       *
'* Result           : 86MD6                   *
'* Enter next number: 2B                      *
'* Operator (+-*/^) : /                       *
'* Result           : 39JM                    *
'*                                            *
'* ARITHMETIC OPERATIONS IN ANY BASE          *
'* BETWEEN 2 AND 36                           *
'*                                            *
'* Enter base (2 to 36): 2                    *
'* Enter 1st number : 11001010                *
'*                                            *
'* Enter next number: 1100                    *
'* Operator (+-*/^) : -                       *
'* Result           : 10111110                *
'* Enter next number: 1110                    *
'* Operator (+-*/^) : -                       *
'* Result           : 10110000                *
'* Enter next number: 10101                   *
'* Operator (+-*/^) : +                       *
'* Result           : 11000101                *
'* Enter next number: 10                      *
'* Operator (+-*/^) : /                       *
'* Result           : 1100010                 *
'* Enter next number: 11                      *
'* Operator (+-*/^) : *                       *
'* Result           : 100100110               *
'*                                            *
'* ARITHMETIC OPERATIONS IN ANY BASE          *
'* BETWEEN 2 AND 36                           *
'*                                            *
'* Enter base (2 to 36): 16                   *
'* Enter 1st number : FEAA                    *
'*                                            *
'* Enter next number: FF                      *
'* Operator (+-*/^) : +                       *
'* Result           : FFA9                    *
'* Enter next number: 1799                    *
'* Operator (+-*/^) : -                       *
'* Result           : E810                    *
'* Enter next number: 2                       *
'* Operator (+-*/^) : /                       *
'* Result           : 7408                    *
'*                                            *
'* Note: Enter null string to exit.           *
'*                                            *
'*                Basic Release By J-P Moreau *
'*                     (www.jpmoreau.fr)      *
'**********************************************
'Explanations:
'------------
'The letters A,B,...,Z  represent 10,11,...,36
'in the base > 10.

'The numbers are first converted from base b to
'base 10 by Function Decodebase, then  operation
'is made in base 10 and result is converted from
'base 10 to base b by Function Codebase.

'Note: assuming that a real number has a mantissa of
'      40 digits in base 2, the number of useful
'      digits udg in base b is given by formula:
	
'	   udg = integer(40*log(2)/log(b))

'          b=10: udg = 12
'	   b=16: udg = 10
'	   b=36: udg = 7

'---------------------------------------------------
defint i-n

XMAXREAL = 1E30
'ib:integer  (numerical base)

  cls
  print
  print " ARITHMETIC OPERATIONS IN ANY BASE BETWEEN 2 AND 36"
  print

10 input " Enter base (2 to 36): ", ib
   input " Enter 1st number : ", x$
   gosub 1000 : r1=r  'Decodebase(x$,ib,r1)
  if IERROR<>0 then goto 10

20 print
   input " Enter next number: ", x$
   if x$<>"" then
    gosub 1000 : r2=r 'Decodebase(x$,ib,r2)
    if IERROR=0 then
      input " Operator (+-*/^) : ", op$
      if op$="+" then r1=r1+r2
      if op$="-" then r1=ABS(r1-r2)
      if op$="*" then r1=r1*r2
      if op$="/" then r1=INT(r1/r2)
      if op$="^" then r1=INT(EXP(r2*LOG(r1)))
      r=r1 : gosub 2000  'Codebase(r,ib,y$)
      if IERROR=0 then
        print " Result           : "; y$
      else
        print " Error in coding result."
      end if
    else
      print " Number not valid or decoding error."
    end if
   end if
  if x$<>"" then goto 20
  print
END

'Convert a number x$ from base ib to base 10. The subroutine set
'IERROR to 1 if ib not in [2..36] or if string x$ contains invalid
'characters in base ib or if result r is too big, else IERROR=0.
'Subroutine Decodebase(x$,ib,r)
'xmult: REAL
'ch$:CHAR
1000  IERROR=1
  if ib<2 or ib>36 then
    print " base must be between 2 and 36 !"
    return
  end if
  r=0 : xmult=1
  long=len(x$)
  for i=1 to long
    ch$=mid$(x$,long+1-i,1)
    if ch$<"0" or ch$>"Z" or (ch$>"9" and ch$<"A") then return
    if ch$<="9" then
      j=asc(ch$)-asc("0")
    else
      j=asc(ch$)-asc("A")+10
    end if
    if j>=ib then return
    r=r+xmult*j
    if xmult>XMAXREAL/ib then return
    xmult=xmult*ib
  next i
  IERROR=0
Return


'Convert a number r from base 10 to base ib. The subroutine set
'IERROR to 1 if ib not in [2..36], else IERROR=0.
'Subroutine Codebase(r,ib,y$)
2000 IERROR=1
  if ib<2 or ib>36 then
    print " base must be between 2 and 36 !"
    return
  end if
  y$="": x=r
2010 if x<=0 then goto 2020
    n=INT(x-ib*INT(x/ib))
    if n<10 then
      y$=Chr$(Asc("0")+n)+y$
    else
      y$=Chr$(Asc("A")+n-10)+y$
    end if
    x=INT(x/ib)
  goto 2010
2020 IERROR=0
Return


'end of file basisop.bas