'FRACTIONS.BAS      LBB     04-03-2017
'==============

' returns the result of a division  (a / b)   as a fraction , rather then as a decimal number
' this means:  < 2/3 >  rather then  < 0.66666... >
' both terms of a fraction are divided by the GCD (Greatest Common Divisor)
' results display:      < x = a / b >  as a decimal,     and  < x$ >  as a   "fraction to text"
' only 2 procedures: < SUB FRACTION  a, b > , which calls  < FUNCTION GCD (a, b) >
' xf$ is a fractionnary number like '1 1/4'

' examples, 11 couples of numbers loaded and divided by the main code
DATA 11
DATA 5, 0, 0, 0, 0, 6, 3, 6, -8, 6, 12, -8, -10, -24, 0.375, -0.500, 0.16, 0.08, -1.2, 0.8, 5, 4

[Main]

READ n
FOR i = 1 TO n
    CLS
    READ a,  b
    PRINT "a = "a, "b = "; b, "x = a / b"
    !PRINT''
    CALL FRACTION  a, b
    !PRINT''
    INPUT "Type <ENTER / RETURN > to continue..."; enter$
NEXT i

!* QUIT

[Procedures]

SUB FRACTION a, b

' *** special cases a/0 or 0/0 or 0/b

IF (a <> 0) AND (b = 0) THEN PRINT, "division by zero, no result": EXIT SUB
IF (a = 0) AND (b = 0) THEN PRINT, "dividing zero by zero , undetermination, no result": EXIT SUB
IF (a = 0) AND (b <> 0)  THEN x = 0: x$ = "0"

' *** common case, no zero's

x = a / b 

    IF x = INT(x) THEN x$ = STR$(x)      ' if   x = a/b   is an integer
    IF x <> INT(x) THEN                         ' if   x = a/b  has decimals
            a = ABS(a): b = ABS(b)              ' positive numbers only
            k = GCD (a, b)
            a = a/k
            b = b/k
            x$ = STR$(a)  + "/" + STR$(b)
            IF x < 0 THEN x$ = "-" + x$        ' restoring minus sign if needed
            'added here for displaying a fractionnal result
            xf$ = ""
            IF a > b THEN
            a = a - b
            k = GCD (a, b)
            a = a/k
            b = b/k
            xf$ = STR$(INT(x)) + " " + STR$(a) + "/" + STR$(b)
            END IF
    END IF   
    
' *** display results
    
           PRINT,, "x  = "; x
           PRINT
           PRINT,, "x$ = "; x$
           PRINT
           IF xf$ <> "" THEN PRINT,, "xf$ = "; xf$
               
END SUB

FUNCTION GCD (M, N)

' GCD    Greatest Common Divisor
' M and N receive the absolute values of  'a'  and  'b', even if decimals

	IF M = 0 OR N = 0 THEN EXIT FUNCTION
	! IF M < N THEN SWAP M, N

' case decimals, make them integer and hope everything works
' N is the lower of N, M

     factor = 1
     
     WHILE N < 1
        M = M*10
        N = N*10
        factor = factor * 10
     WEND

' now classical Euclides' algorithm

	DO
	R = M MOD N
		IF R = 0 THEN EXIT DO
		M = N
		N = R
	LOOP

      IF N < 1 THEN N = 1
      GCD = N / factor                   ' if no decimals, factor = 1 
      
END FUNCTION