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493 lines
14 KiB
Java
493 lines
14 KiB
Java
/*
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* @(#)Rational.java
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*
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* Copyright (c) 2009-2011 Werner Randelshofer, Goldau, Switzerland.
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* All rights reserved.
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*
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* You may not use, copy or modify this file, except in compliance with the
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* license agreement you entered into with Werner Randelshofer.
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* For details see accompanying license terms.
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*/
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package org.monte.media.math;
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import static java.lang.Math.*;
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import java.math.BigInteger;
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import static org.monte.media.math.IntMath.*;
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/**
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* Represents a TIFF RATIONAL number. <p> Two LONGs 32-bit (4-byte) unsigned
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* integer: the first represents the numerator of a fraction; the second, the
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* denominator. </p> <p> Invariants: </p> <ul> <li>denominator>=0, the
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* denominator is always a positive integer</li> <li>0/1 is the unique
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* representation of 0.</li> <li>1/0,-1/0 are the unique representations of
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* infinity.</li> </ul>
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*
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* @author Werner Randelshofer
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* @version $Id: Rational.java 299 2013-01-03 07:40:18Z werner $
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*/
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public class Rational extends Number {
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public static final Rational ONE = new Rational(1, 1,false);
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public static final Rational ZERO = new Rational(0, 1,false);
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public static final long serialVersionUID = 1L;
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private final long num;
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private final long den;
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public Rational(long numerator) {
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this(numerator, 1);
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}
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public Rational(long numerator, long denominator) {
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this(numerator, denominator, true);
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}
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private Rational(long numerator, long denominator, boolean reduceFraction) {
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if (numerator == 0) {
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// Invariant: 0/1 is unique representation of 0
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denominator = 1;
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}
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if (denominator == 0) {
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// Invariant: 1/0, -1/0 are unique representations of infinity
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numerator = (numerator > 0) ? 1 : -1;
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} else if (denominator < 0) {
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// Invariant: denominator is always positive
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denominator = -denominator;
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numerator = -numerator;
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}
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if (reduceFraction) {
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long g = gcd(numerator, denominator);
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num = numerator / g;
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den = denominator / g;
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} else {
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num = numerator;
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den = denominator;
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}
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}
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private Rational(BigInteger numerator, BigInteger denominator, boolean reduceFraction) {
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if (numerator.equals(BigInteger.ZERO)) {
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// Invariant: 0/1 is unique representation of 0
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denominator = BigInteger.ONE;
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}
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if (denominator.equals(BigInteger.ZERO)) {
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// Invariant: 1/0, -1/0 are unique representations of infinity
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numerator = (numerator.compareTo(BigInteger.ZERO) > 0) ? BigInteger.ONE : BigInteger.ONE.negate();
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} else if (denominator.compareTo(BigInteger.ZERO) < 0) {
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// Invariant: denominator is always positive
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denominator = denominator.negate();
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numerator = numerator.negate();
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}
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BigInteger numB, denB;
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if (reduceFraction) {
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BigInteger g = gcd(numerator, denominator);
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numB = numerator.divide(g);
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denB = denominator.divide(g);
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} else {
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numB = numerator;
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denB = denominator;
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}
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int bitLength = Math.max(numB.bitLength(), denB.bitLength());
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if (bitLength > 63) {
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numB = numB.shiftRight(bitLength - 63);
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denB = denB.shiftRight(bitLength - 63);
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if (numB.equals(BigInteger.ZERO)) {
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// Invariant: 0/1 is unique representation of 0
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denB = BigInteger.ONE;
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}
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if (denB.equals(BigInteger.ZERO)) {
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// Invariant: 1/0, -1/0 are unique representations of infinity
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numB = (numB.compareTo(BigInteger.ZERO) > 0) ? BigInteger.ONE : BigInteger.ONE.negate();
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}
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}
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num = numB.longValue();
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den = denB.longValue();
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}
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public Rational(Rational r) {
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this(r.num, r.den);
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}
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public long getNumerator() {
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return num;
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}
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public long getDenominator() {
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return den;
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}
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public Rational add(Rational that) {
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return add(that, true);
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}
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private Rational add(Rational that, boolean reduceFraction) {
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if (this.den == that.den) {
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// => same denominator: add numerators
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return new Rational(this.num + that.num, this.den, reduceFraction);
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}
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// FIXME - handle overflow
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long s = scm(this.den, that.den);
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Rational result = new Rational(
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this.num * (s / this.den) + that.num * (s / that.den),
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s, reduceFraction);
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return result;
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}
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/**
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* Warning. Rational is supposed to be immutable. *
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*
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* private Rational addAssign(Rational that) { if (this.den == that.den) {
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* // => same denominator: add numerators this.num += that.num; return this;
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* }
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*
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* // FIXME - handle overflow long s = scm(this.den, that.den); this.num =
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* this.num * (s / this.den) + that.num * (s / that.den); this.den = s;
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*
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*
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* return reduceAssign(); }
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*/
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public Rational subtract(Rational that) {
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return add(that.negate());
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}
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public Rational negate() {
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return valueOf(-num, den);
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}
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public Rational inverse() {
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return valueOf(den, num, false);
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}
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/**
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* Returns the closest rational with the specified denominator which is
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* smaller or equal than this number.
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*/
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public Rational floor(long d) {
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if (d == den) {
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return valueOf(num, den);
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}
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long s = scm(this.den, d);
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if (s == d) {
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return valueOf(num * s / den, d);
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} else if (s == den) {
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return valueOf(num * d / den, d);
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} else {
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return valueOf(num * d / den, d);
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}
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}
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/**
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* Returns the closest rational with the specified denominator which is
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* greater or equal than this number.
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*/
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public Rational ceil(long d) {
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if (d == den) {
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return valueOf(num, den);
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}
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long s = scm(this.den, d);
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if (s == d) {
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return valueOf((num * s + den - 1) / den, d);
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} else if (s == den) {
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return valueOf((num * d + den - 1) / den, d);
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} else {
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return valueOf((num * d + den - 1) / den, d);
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}
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}
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public Rational multiply(Rational that) {
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if (abs(this.num) < Integer.MAX_VALUE
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&& abs(this.den) < Integer.MAX_VALUE
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&& abs(that.num) < Integer.MAX_VALUE
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&& abs(that.den) < Integer.MAX_VALUE) {
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return valueOf(this.num * that.num,
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this.den * that.den);
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} else {
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return new Rational(
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BigInteger.valueOf(this.num).multiply(BigInteger.valueOf(that.num)),
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BigInteger.valueOf(this.den).multiply(BigInteger.valueOf(that.den)),
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true);
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}
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}
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public Rational multiply(long integer) {
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if (integer==0) {
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return ZERO;
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} else if (this.den % integer == 0) {
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return valueOf(
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this.num,
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this.den / integer);
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} else if (abs(this.num) < Integer.MAX_VALUE
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&& abs(integer) < Integer.MAX_VALUE) {
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return valueOf(
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this.num * integer,
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this.den);
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} else {
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return new Rational(
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BigInteger.valueOf(this.num).multiply(BigInteger.valueOf(integer)),
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BigInteger.valueOf(this.den), true);
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}
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}
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public Rational divide(Rational that) {
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if (abs(this.num) < Integer.MAX_VALUE
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&& abs(this.den) < Integer.MAX_VALUE
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&& abs(that.num) < Integer.MAX_VALUE
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&& abs(that.den) < Integer.MAX_VALUE) {
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return valueOf(this.num * that.den,
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this.den * that.num);
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} else {
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return valueOf(
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BigInteger.valueOf(this.num).multiply(BigInteger.valueOf(that.den)),
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BigInteger.valueOf(this.den).multiply(BigInteger.valueOf(that.num)),
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true);
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}
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}
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@Override
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public String toString() {
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//long gcd = IntMath.gcd(num, den);
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if (num == 0) {
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return "0";
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} else if (den == 1) {
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return Long.toString(num);
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} else {
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return num + "/" + den;
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/*
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} else {
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return Float.toString((float) num / den);
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*/
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}
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}
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public String toDescriptiveString() {
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long gcd = IntMath.gcd(num, den);
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if (gcd == 0 || num == 0) {
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return num + "/" + den + " = " + 0;
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} else if (gcd == den) {
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return num + "/" + den + " = " + Long.toString(num / den);
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} else {
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return num + "/" + den + " ≈ " + ((float) num / den);
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}
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}
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@Override
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public int intValue() {
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return (int) (num / den);
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}
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@Override
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public long longValue() {
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return num / den;
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}
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@Override
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public float floatValue() {
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return (float) num / (float) den;
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}
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@Override
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public double doubleValue() {
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return (double) num / (double) den;
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}
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@Override
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public boolean equals(Object obj) {
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if (obj == null) {
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return false;
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}
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if (getClass() != obj.getClass()) {
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return false;
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}
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final Rational that = (Rational) obj;
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return compareTo(that) == 0;
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}
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/**
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* return { -1, 0, +1 } if a < b, a = b, or a > b.
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*/
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public int compareTo(Rational that) {
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// The following code avoids BigInteger allocation if the denominators
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// are equal
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if (this.den == that.den) {
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if (this.num < that.num) {
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return -1;
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} else if (this.num > that.num) {
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return 1;
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} else {
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return 0;
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}
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}
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// Work with longs if overflow can not occur
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if (abs(this.num) < Integer.MAX_VALUE
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&& abs(this.den) < Integer.MAX_VALUE
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&& abs(that.num) < Integer.MAX_VALUE
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&& abs(that.den) < Integer.MAX_VALUE) {
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long lhs = this.num * that.den;
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long rhs = this.den * that.num;
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if (lhs < rhs) {
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return -1;
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} else if (lhs > rhs) {
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return 1;
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} else {
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return 0;
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}
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}
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// Use big integers to avoid overflows
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BigInteger lhs;
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BigInteger rhs;
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lhs = BigInteger.valueOf(this.num).multiply(BigInteger.valueOf(that.den));
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rhs = BigInteger.valueOf(this.den).multiply(BigInteger.valueOf(that.num));
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return lhs.compareTo(rhs);
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}
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@Override
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public int hashCode() {
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return (int) ((num ^ (num >>> 32))
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^ (den ^ (den >>> 32)));
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}
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public static Rational max(Rational a, Rational b) {
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return (a.compareTo(b) >= 0) ? a : b;
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}
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public static Rational min(Rational a, Rational b) {
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return (a.compareTo(b) <= 0) ? a : b;
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}
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public boolean isZero() {
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return num == 0;
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}
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public boolean isLessOrEqualZero() {
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return num <= 0;
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}
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public static Rational valueOf(double d) {
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if (d == 0) {
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return valueOf(0, 1);
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}
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if (abs(d) > Integer.MAX_VALUE) {
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throw new IllegalArgumentException("Value " + d + " is too big.");
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}
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if (Double.isInfinite(d)) {
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return valueOf((long) signum(d), 0);
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}
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if (Double.isNaN(d)) {
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return valueOf(0, 1); // no way to express a NaN :-(
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}
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return toRational(d, Integer.MAX_VALUE, 100);
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}
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public static Rational valueOf(long num, long den) {
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return valueOf(num, den, true);
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}
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private static Rational valueOf(long num, long den, boolean reduceFraction) {
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if (num == den) {
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return ONE;
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}
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if (num == 0) {
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return ZERO;
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}
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return new Rational(num, den, reduceFraction);
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}
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public static Rational valueOf(BigInteger num, BigInteger den) {
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return valueOf(num, den, true);
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}
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private static Rational valueOf(BigInteger num, BigInteger den, boolean reduceFraction) {
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if (num.equals(den)) {
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return ONE;
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}
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if (num.equals(BigInteger.ZERO)) {
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return ZERO;
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}
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return new Rational(num, den, reduceFraction);
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}
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/**
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* Iteratively computes rational from double. <p>Reference:<br> <a
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* href="http://www2.fz-juelich.de/video/cpp/html/exercises/exercise/Rational_cpp.html">
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* http://www2.fz-juelich.de/video/cpp/html/exercises/exercise/Rational_cpp.html</a>
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* </p>
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*/
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private static Rational toRational(double x, double limit, int iterations) {
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double intpart = Math.floor(x);
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double fractpart = x - intpart;
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double d = 1.0 / fractpart;
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long left = (long) intpart;
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if (d > limit || iterations == 0) {
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return valueOf(left, 1, false);
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} else {
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return valueOf(left, 1, false).add(toRational(d, limit * 0.1, iterations - 1).inverse(), false);
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}
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}
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public Rational round(long d) {
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if (d == den) {
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return valueOf(num, den);
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}
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Rational fl = floor(d);
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Rational diffFl = subtract(fl);
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if (diffFl.isZero()) {
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return fl;
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}
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Rational cl = ceil(d);
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Rational diffCl = subtract(cl);
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if (diffCl.isZero()) {
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return cl;
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}
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if (diffFl.isNegative()) {
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diffFl = diffFl.negate();
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}
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if (diffCl.isNegative()) {
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diffCl = diffCl.negate();
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}
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return diffFl.compareTo(diffCl) <= 0 ? fl : cl;
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}
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private boolean isNegative() {
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return num < 0;
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}
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/**
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* Parses a string.
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*
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* A rational can be represented in the following ways: <li>As a long
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* number</li> <li>As a double number</li> <li>As an integer/integer
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* rational number</li>
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*
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* @throws NumberFormatException if str can not be parsed.
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*/
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public static Rational valueOf(String str) {
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int p = str.indexOf('/');
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if (p != -1) {
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return valueOf(Long.valueOf(str.substring(0, p)), Long.valueOf(str.substring(p + 1)));
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}
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try {
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return valueOf(Long.valueOf(str));
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} catch (NumberFormatException e) {
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return valueOf(Double.valueOf(str));
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}
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}
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}
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