IRTH Faraidh - rational.js

// Rational number arithmetic
function Rational(i, j) {
  this.num = i * 1;
  this.denom = j * 1;
}

function zero() {
  return new Rational(0, 1);
}

function one() {
  return new Rational(1, 1);
}

function divides(i, j) {
  return ((i % j) == 0);
}

/**
 * Greatest common denominator of two integers x,y
 */
function gcd(x, y) {
  var i = x.denom;
  var j = y.denom;
  if (divides(i, j)) return i;
  else if (divides(j, i)) return j;
  else return i * j;
}

function isNegative(x) {
  return (x.num < 0);
}

function negate(x) {
  x.num = -(x.num);
  return x;
}

function isZero(x) {
  return (x.num == 0);
}

/**
 * Simplifies a fraction by reducing its numerator and denominator
 * to their simplest
 */
function simplify(x) {
  var isNeg = isNegative(x);
  var t = (isNeg ? -(x.num) : x.num);
  var b = x.denom;
  var smaller = Math.min(t, b);
  if (divides(t, b)) {
    t /= b;
    b = 1;
  } else if (divides(b, t)) {
    b /= t;
    t = 1;
  } else {
    for (var i = 2; i <= smaller; i++) {
      while (divides(t, i) && divides(b, i)) {
        t /= i;
        b /= i;
      }
      smaller = Math.min(t, b);
    }
  }
  var z = new Rational(1, 1);
  z.num = (isNeg ? -t : t);
  z.denom = b;
  return z;
}

function multiply(x, y) {
  var r = new Rational(1, 1);
  r.num = x.num * y.num;
  r.denom = x.denom * y.denom;
  return simplify(r);
}

function divide(x, y) {
  var r = new Rational(1, 1);
  r.num = x.num * y.denom;
  r.denom = x.denom * y.num;
  return simplify(r);
}

function add(x, y) {
  var i = gcd(x, y);
  var r = new Rational(1, 1);
  r.num = x.num * i / x.denom + y.num * i / y.denom;
  r.denom = i;
  return simplify(r);
}

function subtract(x, y) {
  var i = gcd(x, y);
  var r = new Rational(1, 1);
  r.num = x.num * i / x.denom - y.num * i / y.denom;
  r.denom = i;
  return simplify(r);
}

function max(x, y) {
  var z = subtract(x, y);
  if (isNegative(z)) return y;
  else return x;
}

function min(x, y) {
  var z = subtract(y, x);
  if (isNegative(z)) return y;
  else return x;
}

function isLtOne(x) {
  var z = simplify(x);
  return ((z.num - z.denom) < 0);
}

function isGtOne(x) {
  var z = simplify(x);
  return ((z.num - z.denom) > 0);
}

function isOne(x) {
  var z = simplify(x);
  return ((z.num - z.denom) == 0);
}

function isLt(x, y) {
  var z = subtract(x, y);
  if (isNegative(z)) return true;
  else return false;
}

function isGt(x, y) {
  var z = subtract(y, x);
  if (isNegative(z)) return true;
  else return false;
}

function equals(x, y) {
  var z = subtract(x, y);
  if (isZero(z)) return true;
  else return false;
}

function toRational(s) {
  if (!s) return zero();
  if ("" == s) return zero();
  if ("TIDAK ADA" == s.toUpperCase()) return zero();
  var i = s.indexOf("/");
  if (i < 0) {
    alert("Tidak dapat merubah " + s + " ke bilangan rasional");
    return null;
  }
  var z = one();
  z.num = s.substring(0, i);
  z.denom = s.substring(i + 1);
  if (z.denom < 0) {
    z.num = -(z.num);
    z.denom = -(z.denom);
  }
  return z;
}

function toString(x) {
  if (isZero(x)) return "TIDAK ADA";
  else if (isOne(x)) return "SEMUANYA";
  else if ((x.num == -1) && (x.denom == 1)) return "UNTUK DIBAGI LAGI";
  else return x.num + "/" + x.denom;
}