# Rational.java

Below is the syntax highlighted version of Rational.java from §9.2 Floating Point.

```/******************************************************************************
*  Compilation:  javac Rational.java
*  Execution:    java Rational
*
*  Immutable ADT for Rational numbers.
*
*  Invariants
*  -----------
*   - gcd(num, den) = 1, i.e, the rational number is in reduced form
*   - den >= 1, the denominator is always a positive integer
*   - 0/1 is the unique representation of 0
*
*  We employ some tricks to stave of overflow, but if you
*  need arbitrary precision rationals, use BigRational.java.
*
******************************************************************************/

public class Rational implements Comparable<Rational> {
private static Rational zero = new Rational(0, 1);

private int num;   // the numerator
private int den;   // the denominator

// create and initialize a new Rational object
public Rational(int numerator, int denominator) {

if (denominator == 0) {
throw new ArithmeticException("denominator is zero");
}

// reduce fraction
int g = gcd(numerator, denominator);
num = numerator   / g;
den = denominator / g;

// needed only for negative numbers
if (den < 0) { den = -den; num = -num; }
}

// return the numerator and denominator of (this)
public int numerator()   { return num; }
public int denominator() { return den; }

// return double precision representation of (this)
public double toDouble() {
return (double) num / den;
}

// return string representation of (this)
public String toString() {
if (den == 1) return num + "";
else          return num + "/" + den;
}

// return { -1, 0, +1 } if a < b, a = b, or a > b
public int compareTo(Rational b) {
Rational a = this;
int lhs = a.num * b.den;
int rhs = a.den * b.num;
if (lhs < rhs) return -1;
if (lhs > rhs) return +1;
return 0;
}

// is this Rational object equal to y?
public boolean equals(Object y) {
if (y == null) return false;
if (y.getClass() != this.getClass()) return false;
Rational b = (Rational) y;
return compareTo(b) == 0;
}

// hashCode consistent with equals() and compareTo()
// (better to hash the numerator and denominator and combine)
public int hashCode() {
return this.toString().hashCode();
}

// create and return a new rational (r.num + s.num) / (r.den + s.den)
public static Rational mediant(Rational r, Rational s) {
return new Rational(r.num + s.num, r.den + s.den);
}

// return gcd(|m|, |n|)
private static int gcd(int m, int n) {
if (m < 0) m = -m;
if (n < 0) n = -n;
if (0 == n) return m;
else return gcd(n, m % n);
}

// return lcm(|m|, |n|)
private static int lcm(int m, int n) {
if (m < 0) m = -m;
if (n < 0) n = -n;
return m * (n / gcd(m, n));    // parentheses important to avoid overflow
}

// return a * b, staving off overflow as much as possible by cross-cancellation
public Rational times(Rational b) {
Rational a = this;

// reduce p1/q2 and p2/q1, then multiply, where a = p1/q1 and b = p2/q2
Rational c = new Rational(a.num, b.den);
Rational d = new Rational(b.num, a.den);
return new Rational(c.num * d.num, c.den * d.den);
}

// return a + b, staving off overflow
public Rational plus(Rational b) {
Rational a = this;

// special cases
if (a.compareTo(zero) == 0) return b;
if (b.compareTo(zero) == 0) return a;

// Find gcd of numerators and denominators
int f = gcd(a.num, b.num);
int g = gcd(a.den, b.den);

// add cross-product terms for numerator
Rational s = new Rational((a.num / f) * (b.den / g) + (b.num / f) * (a.den / g),
lcm(a.den, b.den));

// multiply back in
s.num *= f;
return s;
}

// return -a
public Rational negate() {
return new Rational(-num, den);
}

// return |a|
public Rational abs() {
if (num >= 0) return this;
else return negate();
}

// return a - b
public Rational minus(Rational b) {
Rational a = this;
return a.plus(b.negate());
}

public Rational reciprocal() { return new Rational(den, num);  }

// return a / b
public Rational divides(Rational b) {
Rational a = this;
return a.times(b.reciprocal());
}

// test client
public static void main(String[] args) {
Rational x, y, z;

// 1/2 + 1/3 = 5/6
x = new Rational(1, 2);
y = new Rational(1, 3);
z = x.plus(y);
StdOut.println(z);

// 8/9 + 1/9 = 1
x = new Rational(8, 9);
y = new Rational(1, 9);
z = x.plus(y);
StdOut.println(z);

// 1/200000000 + 1/300000000 = 1/120000000
x = new Rational(1, 200000000);
y = new Rational(1, 300000000);
z = x.plus(y);
StdOut.println(z);

// 1073741789/20 + 1073741789/30 = 1073741789/12
x = new Rational(1073741789, 20);
y = new Rational(1073741789, 30);
z = x.plus(y);
StdOut.println(z);

//  4/17 * 17/4 = 1
x = new Rational(4, 17);
y = new Rational(17, 4);
z = x.times(y);
StdOut.println(z);

// 3037141/3247033 * 3037547/3246599 = 841/961
x = new Rational(3037141, 3247033);
y = new Rational(3037547, 3246599);
z = x.times(y);
StdOut.println(z);

// 1/6 - -4/-8 = -1/3
x = new Rational( 1,  6);
y = new Rational(-4, -8);
z = x.minus(y);
StdOut.println(z);
}

}
```