BigRational.java

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

/******************************************************************************
 *  Compilation:  javac BigRational.java
 *  Execution:    java BigRational
 *
 *  Immutable ADT for arbitrarily large Rational numbers.
 *
 *  Invariants
 *  ----------
 *   -  gcd(num, den) = 1, i.e., rational number is in reduced form
 *   -  den >= 1, i.e., the denominator is always a positive integer
 *   -  0/1 is the unique representation of zero
 *
 *  % java BigRational
 *  5/6
 *  1
 *  1/120000000
 *  1073741789/12
 *  1
 *  841/961
 *  -1/3
 *  0
 *  true
 *  Exception in thread "main" java.lang.ArithmeticException: Denominator is zero
 *
 ******************************************************************************/

import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.Objects;

public class BigRational implements Comparable<BigRational> {

    public final static BigRational ZERO = new BigRational(0);
    public final static BigRational ONE  = new BigRational(1);
    public final static BigRational TWO  = new BigRational(2);

    private BigInteger num;   // the numerator
    private BigInteger den;   // the denominator (always a positive integer)


    // create and initialize a new BigRational object
    public BigRational(int numerator, int denominator) {
        this(BigInteger.valueOf(numerator), BigInteger.valueOf(denominator));
    }

    // create and initialize a new BigRational object
    public BigRational(int numerator) {
        this(numerator, 1);
    }

    // create and initialize a new BigRational object from a string, e.g., "-343/1273"
    public BigRational(String s) {
        String[] tokens = s.split("/");
        if (tokens.length == 2)
            init(new BigInteger(tokens[0]), new BigInteger(tokens[1]));
        else if (tokens.length == 1)
            init(new BigInteger(tokens[0]), BigInteger.ONE);
        else
            throw new IllegalArgumentException("For input string: \"" + s + "\"");
    }

    // create and initialize a new BigRational object
    public BigRational(BigInteger numerator, BigInteger denominator) {
        init(numerator, denominator);
    }

    private void init(BigInteger numerator, BigInteger denominator) {

        // deal with x / 0
        if (denominator.equals(BigInteger.ZERO)) {
           throw new ArithmeticException("Denominator is zero");
        }

        // reduce fraction (if num = 0, will always yield den = 0)
        BigInteger g = numerator.gcd(denominator);
        num = numerator.divide(g);
        den = denominator.divide(g);

        // to ensure invariant that denominator is positive
        if (den.compareTo(BigInteger.ZERO) < 0) {
            den = den.negate();
            num = num.negate();
        }
    }

    // return string representation of (this)
    public String toString() {
        if (den.equals(BigInteger.ONE)) return num + "";
        else                            return num + "/" + den;
    }

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

    // is this BigRational negative, zero, or positive?
    public boolean isZero()     { return num.signum() == 0; }
    public boolean isPositive() { return num.signum() >  0; }
    public boolean isNegative() { return num.signum() <  0; }

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

    // hashCode consistent with equals() and compareTo()
    public int hashCode() {
        return Objects.hash(num, den);
    }


    // return a * b
    public BigRational times(BigRational b) {
        BigRational a = this;
        return new BigRational(a.num.multiply(b.num), a.den.multiply(b.den));
    }

    // return a + b
    public BigRational plus(BigRational b) {
        BigRational a = this;
        BigInteger numerator   = a.num.multiply(b.den).add(b.num.multiply(a.den));
        BigInteger denominator = a.den.multiply(b.den);
        return new BigRational(numerator, denominator);
    }

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

    // return |a|
    public BigRational abs() {
        if (isNegative()) return negate();
        else return this;
    }

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

    // return 1 / a
    public BigRational reciprocal() {
        return new BigRational(den, num);
    }

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

    // return double reprentation (within given precision)
    public double doubleValue() {
        int SCALE = 32;        // number of digits after the decimal place
        BigDecimal numerator   = new BigDecimal(num);
        BigDecimal denominator = new BigDecimal(den);
        BigDecimal quotient    = numerator.divide(denominator, SCALE, RoundingMode.HALF_EVEN);
        return quotient.doubleValue();
    }


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

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

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

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

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

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

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

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

        // 0
        x = new BigRational(0,  5);
        StdOut.println(x);
        StdOut.println(x.plus(x).compareTo(x) == 0);
        /// StdOut.println(x.reciprocal());   // divide-by-zero

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

    }

}