WITH text_io, integer_text_io;
  USE text_io, integer_text_io;

--------------------------------------------------------------------

PROCEDURE rats IS
-- Simple test of rational_number routines

  TYPE rational IS
  RECORD
    numerator : integer;
    denominator:integer;
  END RECORD;

  a,b,c: rational;

--------------------------------------------------------------------

  PROCEDURE putrat (caption: string; ratval: rational) IS
  -- Prints caption followed by rational value
  BEGIN

    put (caption);
    put (ratval.numerator); put ("/"); put (ratval.denominator);
    new_line;

  END;

  FUNCTION hcf (x, y: integer) RETURN integer IS
  -- Returns the Highest Common Factor of x and y
    p, q, r: integer;
  BEGIN
    p := x;  q := y;
    IF q = 0 THEN q := 1; END IF;
    LOOP  -- Euclidean Algorithm to find HCF
      r := p mod q;
      EXIT WHEN r = 0;
      p := q;  q := r;
    END LOOP;
    RETURN q;
  END;

  FUNCTION reduced (x: rational) RETURN rational IS
  -- Reduces a rational number to co-prime parts with +ve denominator
  -- The parts are thus as small as possible and also unique
    n, d, h: integer;
  BEGIN
    -- form a positive denominator
    IF x.denominator >= 0 THEN
      n := x.numerator;
      d := x.denominator;
    ELSE
      n := -x.numerator;
      d := -x.denominator;
    END IF;
    -- calculate HCF and divide into numerator and denominator
    h := hcf (n,d);
    RETURN (n/h, d/h);
  END;

  FUNCTION "/" (x, y: integer) RETURN rational IS
  -- Forms a rational number from two integers
  BEGIN
    RETURN reduced (rational'(x,y));
  END;

  FUNCTION "/" (x, y: rational) RETURN rational IS
  -- Divides one rational number by another
    n, d: rational;
  BEGIN
    -- the technique used here, which first forms rational numbers from 
    -- numerators and denominators respectively, with co-prime parts, 
    -- helps to remove unnecessary overflows.
    n := x.numerator / y.numerator;
    d := x.denominator / y.denominator;
    RETURN (n.numerator * d.numerator) / (n.denominator * d.denominator);
  END;

  FUNCTION "*" (x, y: rational) RETURN rational IS
  -- Multiplies two rational numbers
    x1, y1: rational;
  BEGIN
    -- forms rational numbers from numerator of each with denominator of
    -- the other; as this removes common factors helps reduce overflow
    x1 := x.numerator / y.denominator;
    y1 := y.numerator / x.denominator;
    RETURN rational' (x1.numerator * y1.numerator,  x1.denominator *  y1.denominator);
  END;

  FUNCTION "+" ( x, y: rational) RETURN rational IS
  -- Forms sum of two rational numbers
    nf, df, xn, xd, yn, yd: integer;
  BEGIN
    -- first extracts common factors from numerators and denominators to
    -- help reduce overflow
    nf := hcf (x.numerator, y.numerator);
    df := hcf (x.denominator, y.denominator);
    xn := x.numerator / nf;
    yn := y.numerator / nf;
    xd := x.denominator / df;
    yd := y.denominator / df;
    RETURN rational'(nf,df) * rational'(xn*yd + yn*xd, xd*yd);
  END;

  FUNCTION "-" (x: rational) RETURN rational IS
  -- Returns negative of a rational number
  BEGIN
    RETURN rational'(-x.numerator, x.denominator);
  END;

  FUNCTION "-" (x, y: rational) RETURN rational IS
  -- Returns difference of two rationals
  BEGIN
    RETURN x + (-y);
  END;


--------------------------------------------------------------------

BEGIN

  a := 7/5;    b := 2/3;
  put_line ("Rational-Numbers Test");
  putrat ("a = ",a);
  putrat ("b = ",b);
  putrat ("a+b = ",a+b);
  putrat ("a*b = ",a*b);
  putrat ("a/b = ",a/b);
  put_line ("End of Test.");

END;

-------------------------------------------------------------------