# Rational.java

Below is the syntax highlighted version of Rational.java from §1.2 Data Abstraction.

```/******************************************************************************
*  Compilation:  javac Rational.java
*  Execution:    java Rational
*  Dependencies: StdOut.java
*
*  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 off overflow, but if you
*  need arbitrary precision rationals, use BigRational.java.
*
*  % java Rational
*  5/6
*  1
*  1/120000000
*  1073741789/12
*  1
*  841/961
*  -1/3
*
*  Todo
*  =====================
*   - better style to make instance variables final since
*     data type is immutable
*
******************************************************************************/

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

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

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

// deal with x/0
if (denominator == 0) {
throw new ArithmeticException("denominator is zero");
}

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

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

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

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

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

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

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

// hashCode consistent with equals() and compareTo()
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 long gcd(long m, long 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 long lcm(long m, long n) {
if (m < 0) m = -m;
if (n < 0) n = -n;
return m * (n / gcd(m, n));    // parentheses important to avoid overflow
}

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

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

// return this + that, staving off overflow
public Rational plus(Rational that) {

// special cases
if (this.compareTo(zero) == 0) return that;
if (that.compareTo(zero) == 0) return this;

// Find gcd of numerators and denominators
long f = gcd(this.num, that.num);
long g = gcd(this.den, that.den);

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

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

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

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

// return this - that
public Rational minus(Rational that) {
return this.plus(that.negate());
}

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

// return this / that
public Rational dividedBy(Rational that) {
return this.times(that.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);
}

}
```