912 lines
32 KiB
Java
912 lines
32 KiB
Java
/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package ch.usi.inf.sdm.sdm04.math;
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import java.math.BigInteger;
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import java.util.Objects;
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/**
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* {@link Fraction} is a {@link Number} implementation that
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* stores fractions accurately.
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*
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* <p>This class is immutable, and interoperable with most methods that accept
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* a {@link Number}.</p>
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*
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* <p>Note that this class is intended for common use cases, it is <i>int</i>
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* based and thus suffers from various overflow issues. For a BigInteger based
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* equivalent, please see the Commons Math BigFraction class.</p>
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*
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* @since 2.0
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*/
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public final class Fraction extends Number implements Comparable<Fraction> {
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/**
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* Required for serialization support. Lang version 2.0.
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*
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* @see java.io.Serializable
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*/
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private static final long serialVersionUID = 65382027393090L;
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/**
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* {@link Fraction} representation of 0.
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*/
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public static final Fraction ZERO = new Fraction(0, 1);
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/**
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* {@link Fraction} representation of 1.
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*/
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public static final Fraction ONE = new Fraction(1, 1);
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/**
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* {@link Fraction} representation of 1/2.
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*/
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public static final Fraction ONE_HALF = new Fraction(1, 2);
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/**
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* {@link Fraction} representation of 1/3.
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*/
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public static final Fraction ONE_THIRD = new Fraction(1, 3);
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/**
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* {@link Fraction} representation of 2/3.
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*/
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public static final Fraction TWO_THIRDS = new Fraction(2, 3);
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/**
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* {@link Fraction} representation of 1/4.
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*/
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public static final Fraction ONE_QUARTER = new Fraction(1, 4);
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/**
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* {@link Fraction} representation of 2/4.
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*/
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public static final Fraction TWO_QUARTERS = new Fraction(2, 4);
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/**
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* {@link Fraction} representation of 3/4.
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*/
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public static final Fraction THREE_QUARTERS = new Fraction(3, 4);
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/**
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* {@link Fraction} representation of 1/5.
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*/
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public static final Fraction ONE_FIFTH = new Fraction(1, 5);
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/**
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* {@link Fraction} representation of 2/5.
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*/
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public static final Fraction TWO_FIFTHS = new Fraction(2, 5);
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/**
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* {@link Fraction} representation of 3/5.
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*/
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public static final Fraction THREE_FIFTHS = new Fraction(3, 5);
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/**
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* {@link Fraction} representation of 4/5.
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*/
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public static final Fraction FOUR_FIFTHS = new Fraction(4, 5);
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/**
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* The numerator number part of the fraction (the three in three sevenths).
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*/
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private final int numerator;
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/**
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* The denominator number part of the fraction (the seven in three sevenths).
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*/
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private final int denominator;
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/**
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* Cached output hashCode (class is immutable).
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*/
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private transient int hashCode;
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/**
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* Cached output toString (class is immutable).
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*/
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private transient String toString;
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/**
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* Cached output toProperString (class is immutable).
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*/
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private transient String toProperString;
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/**
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* Constructs a {@link Fraction} instance with the 2 parts
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* of a fraction Y/Z.
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*
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* @param numerator the numerator, for example the three in 'three sevenths'
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* @param denominator the denominator, for example the seven in 'three sevenths'
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*/
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private Fraction(final int numerator, final int denominator) {
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this.numerator = numerator;
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this.denominator = denominator;
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}
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/**
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* Creates a {@link Fraction} instance with the 2 parts
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* of a fraction Y/Z.
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*
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* <p>Any negative signs are resolved to be on the numerator.</p>
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*
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* @param numerator the numerator, for example the three in 'three sevenths'
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* @param denominator the denominator, for example the seven in 'three sevenths'
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* @return a new fraction instance
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* @throws ArithmeticException if the denominator is {@code zero}
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* or the denominator is {@code negative} and the numerator is {@code Integer#MIN_VALUE}
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*/
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public static Fraction getFraction(int numerator, int denominator) {
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if (denominator == 0) {
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throw new ArithmeticException("The denominator must not be zero");
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}
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if (denominator < 0) {
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if (numerator == Integer.MIN_VALUE || denominator == Integer.MIN_VALUE) {
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throw new ArithmeticException("overflow: can't negate");
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}
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numerator = -numerator;
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denominator = -denominator;
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}
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return new Fraction(numerator, denominator);
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}
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/**
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* Creates a {@link Fraction} instance with the 3 parts
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* of a fraction X Y/Z.
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*
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* <p>The negative sign must be passed in on the whole number part.</p>
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*
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* @param whole the whole number, for example the one in 'one and three sevenths'
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* @param numerator the numerator, for example the three in 'one and three sevenths'
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* @param denominator the denominator, for example the seven in 'one and three sevenths'
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* @return a new fraction instance
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* @throws ArithmeticException if the denominator is {@code zero}
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* @throws ArithmeticException if the denominator is negative
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* @throws ArithmeticException if the numerator is negative
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* @throws ArithmeticException if the resulting numerator exceeds
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* {@code Integer.MAX_VALUE}
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*/
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public static Fraction getFraction(final int whole, final int numerator, final int denominator) {
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if (denominator == 0) {
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throw new ArithmeticException("The denominator must not be zero");
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}
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if (denominator < 0) {
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throw new ArithmeticException("The denominator must not be negative");
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}
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if (numerator < 0) {
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throw new ArithmeticException("The numerator must not be negative");
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}
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final long numeratorValue;
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if (whole < 0) {
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numeratorValue = whole * (long) denominator - numerator;
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} else {
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numeratorValue = whole * (long) denominator + numerator;
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}
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if (numeratorValue < Integer.MIN_VALUE || numeratorValue > Integer.MAX_VALUE) {
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throw new ArithmeticException("Numerator too large to represent as an Integer.");
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}
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return new Fraction((int) numeratorValue, denominator);
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}
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/**
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* Creates a reduced {@link Fraction} instance with the 2 parts
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* of a fraction Y/Z.
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*
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* <p>For example, if the input parameters represent 2/4, then the created
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* fraction will be 1/2.</p>
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*
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* <p>Any negative signs are resolved to be on the numerator.</p>
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*
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* @param numerator the numerator, for example the three in 'three sevenths'
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* @param denominator the denominator, for example the seven in 'three sevenths'
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* @return a new fraction instance, with the numerator and denominator reduced
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* @throws ArithmeticException if the denominator is {@code zero}
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*/
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public static Fraction getReducedFraction(int numerator, int denominator) {
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if (denominator == 0) {
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throw new ArithmeticException("The denominator must not be zero");
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}
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if (numerator == 0) {
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return ZERO; // normalize zero.
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}
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// allow 2^k/-2^31 as a valid fraction (where k>0)
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if (denominator == Integer.MIN_VALUE && (numerator & 1) == 0) {
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numerator /= 2;
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denominator /= 2;
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}
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if (denominator < 0) {
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if (numerator == Integer.MIN_VALUE || denominator == Integer.MIN_VALUE) {
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throw new ArithmeticException("overflow: can't negate");
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}
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numerator = -numerator;
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denominator = -denominator;
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}
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// simplify fraction.
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final int gcd = greatestCommonDivisor(numerator, denominator);
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numerator /= gcd;
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denominator /= gcd;
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return new Fraction(numerator, denominator);
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}
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/**
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* Creates a {@link Fraction} instance from a {@code double} value.
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*
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* <p>This method uses the <a href="https://web.archive.org/web/20210516065058/http%3A//archives.math.utk.edu/articles/atuyl/confrac/">
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* continued fraction algorithm</a>, computing a maximum of
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* 25 convergents and bounding the denominator by 10,000.</p>
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*
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* @param value the double value to convert
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* @return a new fraction instance that is close to the value
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* @throws ArithmeticException if {@code |value| > Integer.MAX_VALUE}
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* or {@code value = NaN}
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* @throws ArithmeticException if the calculated denominator is {@code zero}
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* @throws ArithmeticException if the algorithm does not converge
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*/
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public static Fraction getFraction(double value) {
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final int sign = value < 0 ? -1 : 1;
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value = Math.abs(value);
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if (value > Integer.MAX_VALUE || Double.isNaN(value)) {
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throw new ArithmeticException("The value must not be greater than Integer.MAX_VALUE or NaN");
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}
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final int wholeNumber = (int) value;
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value -= wholeNumber;
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int numer0 = 0; // the pre-previous
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int denom0 = 1; // the pre-previous
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int numer1 = 1; // the previous
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int denom1 = 0; // the previous
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int numer2; // the current, setup in calculation
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int denom2; // the current, setup in calculation
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int a1 = (int) value;
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int a2;
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double x1 = 1;
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double x2;
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double y1 = value - a1;
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double y2;
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double delta1, delta2 = Double.MAX_VALUE;
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double fraction;
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int i = 1;
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do {
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delta1 = delta2;
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a2 = (int) (x1 / y1);
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x2 = y1;
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y2 = x1 - a2 * y1;
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numer2 = a1 * numer1 + numer0;
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denom2 = a1 * denom1 + denom0;
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fraction = (double) numer2 / (double) denom2;
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delta2 = Math.abs(value - fraction);
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a1 = a2;
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x1 = x2;
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y1 = y2;
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numer0 = numer1;
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denom0 = denom1;
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numer1 = numer2;
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denom1 = denom2;
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i++;
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} while (delta1 > delta2 && denom2 <= 10000 && denom2 > 0 && i < 25);
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if (i == 25) {
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throw new ArithmeticException("Unable to convert double to fraction");
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}
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return getReducedFraction((numer0 + wholeNumber * denom0) * sign, denom0);
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}
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/**
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* Creates a Fraction from a {@link String}.
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*
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* <p>The formats accepted are:</p>
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*
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* <ol>
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* <li>{@code double} String containing a dot</li>
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* <li>'X Y/Z'</li>
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* <li>'Y/Z'</li>
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* <li>'X' (a simple whole number)</li>
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* </ol>
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* <p>and a .</p>
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*
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* @param str the string to parse, must not be {@code null}
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* @return the new {@link Fraction} instance
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* @throws NullPointerException if the string is {@code null}
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* @throws NumberFormatException if the number format is invalid
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*/
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public static Fraction getFraction(String str) {
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Objects.requireNonNull(str, "str");
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// parse double format
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int pos = str.indexOf('.');
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if (pos >= 0) {
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return getFraction(Double.parseDouble(str));
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}
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// parse X Y/Z format
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pos = str.indexOf(' ');
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if (pos > 0) {
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final int whole = Integer.parseInt(str.substring(0, pos));
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str = str.substring(pos + 1);
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pos = str.indexOf('/');
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if (pos < 0) {
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throw new NumberFormatException("The fraction could not be parsed as the format X Y/Z");
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}
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final int numer = Integer.parseInt(str.substring(0, pos));
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final int denom = Integer.parseInt(str.substring(pos + 1));
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return getFraction(whole, numer, denom);
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}
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// parse Y/Z format
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pos = str.indexOf('/');
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if (pos < 0) {
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// simple whole number
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return getFraction(Integer.parseInt(str), 1);
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}
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final int numer = Integer.parseInt(str.substring(0, pos));
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final int denom = Integer.parseInt(str.substring(pos + 1));
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return getFraction(numer, denom);
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}
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/**
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* Gets the numerator part of the fraction.
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*
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* <p>This method may return a value greater than the denominator, an
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* improper fraction, such as the seven in 7/4.</p>
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*
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* @return the numerator fraction part
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*/
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public int getNumerator() {
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return numerator;
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}
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/**
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* Gets the denominator part of the fraction.
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*
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* @return the denominator fraction part
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*/
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public int getDenominator() {
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return denominator;
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}
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/**
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* Gets the proper numerator, always positive.
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*
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* <p>An improper fraction 7/4 can be resolved into a proper one, 1 3/4.
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* This method returns the 3 from the proper fraction.</p>
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*
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* <p>If the fraction is negative such as -7/4, it can be resolved into
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* -1 3/4, so this method returns the positive proper numerator, 3.</p>
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*
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* @return the numerator fraction part of a proper fraction, always positive
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*/
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public int getProperNumerator() {
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return Math.abs(numerator % denominator);
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}
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/**
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* Gets the proper whole part of the fraction.
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*
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* <p>An improper fraction 7/4 can be resolved into a proper one, 1 3/4.
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* This method returns the 1 from the proper fraction.</p>
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*
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* <p>If the fraction is negative such as -7/4, it can be resolved into
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* -1 3/4, so this method returns the positive whole part -1.</p>
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*
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* @return the whole fraction part of a proper fraction, that includes the sign
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*/
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public int getProperWhole() {
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return numerator / denominator;
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}
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/**
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* Gets the fraction as an {@code int}. This returns the whole number
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* part of the fraction.
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*
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* @return the whole number fraction part
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*/
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@Override
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public int intValue() {
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return numerator / denominator;
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}
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/**
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* Gets the fraction as a {@code long}. This returns the whole number
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* part of the fraction.
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*
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* @return the whole number fraction part
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*/
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@Override
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public long longValue() {
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return (long) numerator / denominator;
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}
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/**
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* Gets the fraction as a {@code float}. This calculates the fraction
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* as the numerator divided by denominator.
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*
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* @return the fraction as a {@code float}
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*/
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@Override
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public float floatValue() {
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return (float) numerator / (float) denominator;
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}
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/**
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* Gets the fraction as a {@code double}. This calculates the fraction
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* as the numerator divided by denominator.
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*
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* @return the fraction as a {@code double}
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*/
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@Override
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public double doubleValue() {
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return (double) numerator / (double) denominator;
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}
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/**
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* Reduce the fraction to the smallest values for the numerator and
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* denominator, returning the result.
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*
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* <p>For example, if this fraction represents 2/4, then the result
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* will be 1/2.</p>
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*
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* @return a new reduced fraction instance, or this if no simplification possible
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*/
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public Fraction reduce() {
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if (numerator == 0) {
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return equals(ZERO) ? this : ZERO;
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}
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final int gcd = greatestCommonDivisor(Math.abs(numerator), denominator);
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if (gcd == 1) {
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return this;
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}
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return getFraction(numerator / gcd, denominator / gcd);
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}
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/**
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* Gets a fraction that is the inverse (1/fraction) of this one.
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*
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* <p>The returned fraction is not reduced.</p>
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*
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* @return a new fraction instance with the numerator and denominator
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* inverted.
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* @throws ArithmeticException if the fraction represents zero.
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*/
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public Fraction invert() {
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if (numerator == 0) {
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throw new ArithmeticException("Unable to invert zero.");
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}
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if (numerator==Integer.MIN_VALUE) {
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throw new ArithmeticException("overflow: can't negate numerator");
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}
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if (numerator<0) {
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return new Fraction(-denominator, -numerator);
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}
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return new Fraction(denominator, numerator);
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}
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/**
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* Gets a fraction that is the negative (-fraction) of this one.
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*
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* <p>The returned fraction is not reduced.</p>
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*
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* @return a new fraction instance with the opposite signed numerator
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*/
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public Fraction negate() {
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// the positive range is one smaller than the negative range of an int.
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if (numerator==Integer.MIN_VALUE) {
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throw new ArithmeticException("overflow: too large to negate");
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}
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return new Fraction(-numerator, denominator);
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}
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/**
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* Gets a fraction that is the positive equivalent of this one.
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* <p>More precisely: {@code (fraction >= 0 ? this : -fraction)}</p>
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*
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* <p>The returned fraction is not reduced.</p>
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*
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* @return {@code this} if it is positive, or a new positive fraction
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* instance with the opposite signed numerator
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*/
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public Fraction abs() {
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if (numerator >= 0) {
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return this;
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}
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return negate();
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}
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/**
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* Gets a fraction that is raised to the passed in power.
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*
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* <p>The returned fraction is in reduced form.</p>
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*
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* @param power the power to raise the fraction to
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* @return {@code this} if the power is one, {@link #ONE} if the power
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* is zero (even if the fraction equals ZERO) or a new fraction instance
|
|
* raised to the appropriate power
|
|
* @throws ArithmeticException if the resulting numerator or denominator exceeds
|
|
* {@code Integer.MAX_VALUE}
|
|
*/
|
|
public Fraction pow(final int power) {
|
|
if (power == 1) {
|
|
return this;
|
|
}
|
|
if (power == 0) {
|
|
return ONE;
|
|
}
|
|
if (power < 0) {
|
|
if (power == Integer.MIN_VALUE) { // MIN_VALUE can't be negated.
|
|
return this.invert().pow(2).pow(-(power / 2));
|
|
}
|
|
return this.invert().pow(-power);
|
|
}
|
|
final Fraction f = this.multiplyBy(this);
|
|
if (power % 2 == 0) { // if even...
|
|
return f.pow(power / 2);
|
|
}
|
|
return f.pow(power / 2).multiplyBy(this);
|
|
}
|
|
|
|
/**
|
|
* Gets the greatest common divisor of the absolute value of
|
|
* two numbers, using the "binary gcd" method which avoids
|
|
* division and modulo operations. See Knuth 4.5.2 algorithm B.
|
|
* This algorithm is due to Josef Stein (1961).
|
|
*
|
|
* @param u a non-zero number
|
|
* @param v a non-zero number
|
|
* @return the greatest common divisor, never zero
|
|
*/
|
|
private static int greatestCommonDivisor(int u, int v) {
|
|
// From Commons Math:
|
|
if (u == 0 || v == 0) {
|
|
if (u == Integer.MIN_VALUE || v == Integer.MIN_VALUE) {
|
|
throw new ArithmeticException("overflow: gcd is 2^31");
|
|
}
|
|
return Math.abs(u) + Math.abs(v);
|
|
}
|
|
// if either operand is abs 1, return 1:
|
|
if (Math.abs(u) == 1 || Math.abs(v) == 1) {
|
|
return 1;
|
|
}
|
|
// keep u and v negative, as negative integers range down to
|
|
// -2^31, while positive numbers can only be as large as 2^31-1
|
|
// (i.e. we can't necessarily negate a negative number without
|
|
// overflow)
|
|
if (u > 0) {
|
|
u = -u;
|
|
} // make u negative
|
|
if (v > 0) {
|
|
v = -v;
|
|
} // make v negative
|
|
// B1. [Find power of 2]
|
|
int k = 0;
|
|
while ((u & 1) == 0 && (v & 1) == 0 && k < 31) { // while u and v are both even...
|
|
u /= 2;
|
|
v /= 2;
|
|
k++; // cast out twos.
|
|
}
|
|
if (k == 31) {
|
|
throw new ArithmeticException("overflow: gcd is 2^31");
|
|
}
|
|
// B2. Initialize: u and v have been divided by 2^k and at least
|
|
// one is odd.
|
|
int t = (u & 1) == 1 ? v : -(u / 2)/* B3 */;
|
|
// t negative: u was odd, v may be even (t replaces v)
|
|
// t positive: u was even, v is odd (t replaces u)
|
|
do {
|
|
/* assert u<0 && v<0; */
|
|
// B4/B3: cast out twos from t.
|
|
while ((t & 1) == 0) { // while t is even.
|
|
t /= 2; // cast out twos
|
|
}
|
|
// B5 [reset max(u,v)]
|
|
if (t > 0) {
|
|
u = -t;
|
|
} else {
|
|
v = t;
|
|
}
|
|
// B6/B3. at this point both u and v should be odd.
|
|
t = (v - u) / 2;
|
|
// |u| larger: t positive (replace u)
|
|
// |v| larger: t negative (replace v)
|
|
} while (t != 0);
|
|
return -u * (1 << k); // gcd is u*2^k
|
|
}
|
|
|
|
/**
|
|
* Multiply two integers, checking for overflow.
|
|
*
|
|
* @param x a factor
|
|
* @param y a factor
|
|
* @return the product {@code x*y}
|
|
* @throws ArithmeticException if the result can not be represented as
|
|
* an int
|
|
*/
|
|
private static int mulAndCheck(final int x, final int y) {
|
|
final long m = (long) x * (long) y;
|
|
if (m < Integer.MIN_VALUE || m > Integer.MAX_VALUE) {
|
|
throw new ArithmeticException("overflow: mul");
|
|
}
|
|
return (int) m;
|
|
}
|
|
|
|
/**
|
|
* Multiply two non-negative integers, checking for overflow.
|
|
*
|
|
* @param x a non-negative factor
|
|
* @param y a non-negative factor
|
|
* @return the product {@code x*y}
|
|
* @throws ArithmeticException if the result can not be represented as
|
|
* an int
|
|
*/
|
|
private static int mulPosAndCheck(final int x, final int y) {
|
|
/* assert x>=0 && y>=0; */
|
|
final long m = (long) x * (long) y;
|
|
if (m > Integer.MAX_VALUE) {
|
|
throw new ArithmeticException("overflow: mulPos");
|
|
}
|
|
return (int) m;
|
|
}
|
|
|
|
/**
|
|
* Add two integers, checking for overflow.
|
|
*
|
|
* @param x an addend
|
|
* @param y an addend
|
|
* @return the sum {@code x+y}
|
|
* @throws ArithmeticException if the result can not be represented as
|
|
* an int
|
|
*/
|
|
private static int addAndCheck(final int x, final int y) {
|
|
final long s = (long) x + (long) y;
|
|
if (s < Integer.MIN_VALUE || s > Integer.MAX_VALUE) {
|
|
throw new ArithmeticException("overflow: add");
|
|
}
|
|
return (int) s;
|
|
}
|
|
|
|
/**
|
|
* Subtract two integers, checking for overflow.
|
|
*
|
|
* @param x the minuend
|
|
* @param y the subtrahend
|
|
* @return the difference {@code x-y}
|
|
* @throws ArithmeticException if the result can not be represented as
|
|
* an int
|
|
*/
|
|
private static int subAndCheck(final int x, final int y) {
|
|
final long s = (long) x - (long) y;
|
|
if (s < Integer.MIN_VALUE || s > Integer.MAX_VALUE) {
|
|
throw new ArithmeticException("overflow: add");
|
|
}
|
|
return (int) s;
|
|
}
|
|
|
|
/**
|
|
* Adds the value of this fraction to another, returning the result in reduced form.
|
|
* The algorithm follows Knuth, 4.5.1.
|
|
*
|
|
* @param fraction the fraction to add, must not be {@code null}
|
|
* @return a {@link Fraction} instance with the resulting values
|
|
* @throws IllegalArgumentException if the fraction is {@code null}
|
|
* @throws ArithmeticException if the resulting numerator or denominator exceeds
|
|
* {@code Integer.MAX_VALUE}
|
|
*/
|
|
public Fraction add(final Fraction fraction) {
|
|
return addSub(fraction, true /* add */);
|
|
}
|
|
|
|
/**
|
|
* Subtracts the value of another fraction from the value of this one,
|
|
* returning the result in reduced form.
|
|
*
|
|
* @param fraction the fraction to subtract, must not be {@code null}
|
|
* @return a {@link Fraction} instance with the resulting values
|
|
* @throws IllegalArgumentException if the fraction is {@code null}
|
|
* @throws ArithmeticException if the resulting numerator or denominator
|
|
* cannot be represented in an {@code int}.
|
|
*/
|
|
public Fraction subtract(final Fraction fraction) {
|
|
return addSub(fraction, false /* subtract */);
|
|
}
|
|
|
|
/**
|
|
* Implement add and subtract using algorithm described in Knuth 4.5.1.
|
|
*
|
|
* @param fraction the fraction to subtract, must not be {@code null}
|
|
* @param isAdd true to add, false to subtract
|
|
* @return a {@link Fraction} instance with the resulting values
|
|
* @throws IllegalArgumentException if the fraction is {@code null}
|
|
* @throws ArithmeticException if the resulting numerator or denominator
|
|
* cannot be represented in an {@code int}.
|
|
*/
|
|
private Fraction addSub(final Fraction fraction, final boolean isAdd) {
|
|
Objects.requireNonNull(fraction, "fraction");
|
|
// zero is identity for addition.
|
|
if (numerator == 0) {
|
|
return isAdd ? fraction : fraction.negate();
|
|
}
|
|
if (fraction.numerator == 0) {
|
|
return this;
|
|
}
|
|
// if denominators are randomly distributed, d1 will be 1 about 61%
|
|
// of the time.
|
|
final int d1 = greatestCommonDivisor(denominator, fraction.denominator);
|
|
if (d1 == 1) {
|
|
// result is ( (u*v' +/- u'v) / u'v')
|
|
final int uvp = mulAndCheck(numerator, fraction.denominator);
|
|
final int upv = mulAndCheck(fraction.numerator, denominator);
|
|
return new Fraction(isAdd ? addAndCheck(uvp, upv) : subAndCheck(uvp, upv), mulPosAndCheck(denominator,
|
|
fraction.denominator));
|
|
}
|
|
// the quantity 't' requires 65 bits of precision; see knuth 4.5.1
|
|
// exercise 7. we're going to use a BigInteger.
|
|
// t = u(v'/d1) +/- v(u'/d1)
|
|
final BigInteger uvp = BigInteger.valueOf(numerator).multiply(BigInteger.valueOf(fraction.denominator / d1));
|
|
final BigInteger upv = BigInteger.valueOf(fraction.numerator).multiply(BigInteger.valueOf(denominator / d1));
|
|
final BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
|
|
// but d2 doesn't need extra precision because
|
|
// d2 = gcd(t,d1) = gcd(t mod d1, d1)
|
|
final int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
|
|
final int d2 = tmodd1 == 0 ? d1 : greatestCommonDivisor(tmodd1, d1);
|
|
|
|
// result is (t/d2) / (u'/d1)(v'/d2)
|
|
final BigInteger w = t.divide(BigInteger.valueOf(d2));
|
|
if (w.bitLength() > 31) {
|
|
throw new ArithmeticException("overflow: numerator too large after multiply");
|
|
}
|
|
return new Fraction(w.intValue(), mulPosAndCheck(denominator / d1, fraction.denominator / d2));
|
|
}
|
|
|
|
/**
|
|
* Multiplies the value of this fraction by another, returning the
|
|
* result in reduced form.
|
|
*
|
|
* @param fraction the fraction to multiply by, must not be {@code null}
|
|
* @return a {@link Fraction} instance with the resulting values
|
|
* @throws NullPointerException if the fraction is {@code null}
|
|
* @throws ArithmeticException if the resulting numerator or denominator exceeds
|
|
* {@code Integer.MAX_VALUE}
|
|
*/
|
|
public Fraction multiplyBy(final Fraction fraction) {
|
|
Objects.requireNonNull(fraction, "fraction");
|
|
if (numerator == 0 || fraction.numerator == 0) {
|
|
return ZERO;
|
|
}
|
|
// knuth 4.5.1
|
|
// make sure we don't overflow unless the result *must* overflow.
|
|
final int d1 = greatestCommonDivisor(numerator, fraction.denominator);
|
|
final int d2 = greatestCommonDivisor(fraction.numerator, denominator);
|
|
return getReducedFraction(mulAndCheck(numerator / d1, fraction.numerator / d2),
|
|
mulPosAndCheck(denominator / d2, fraction.denominator / d1));
|
|
}
|
|
|
|
/**
|
|
* Divide the value of this fraction by another.
|
|
*
|
|
* @param fraction the fraction to divide by, must not be {@code null}
|
|
* @return a {@link Fraction} instance with the resulting values
|
|
* @throws NullPointerException if the fraction is {@code null}
|
|
* @throws ArithmeticException if the fraction to divide by is zero
|
|
* @throws ArithmeticException if the resulting numerator or denominator exceeds
|
|
* {@code Integer.MAX_VALUE}
|
|
*/
|
|
public Fraction divideBy(final Fraction fraction) {
|
|
Objects.requireNonNull(fraction, "fraction");
|
|
if (fraction.numerator == 0) {
|
|
throw new ArithmeticException("The fraction to divide by must not be zero");
|
|
}
|
|
return multiplyBy(fraction.invert());
|
|
}
|
|
|
|
/**
|
|
* Compares this fraction to another object to test if they are equal..
|
|
*
|
|
* <p>To be equal, both values must be equal. Thus 2/4 is not equal to 1/2.</p>
|
|
*
|
|
* @param obj the reference object with which to compare
|
|
* @return {@code true} if this object is equal
|
|
*/
|
|
@Override
|
|
public boolean equals(final Object obj) {
|
|
if (obj == this) {
|
|
return true;
|
|
}
|
|
if (!(obj instanceof Fraction)) {
|
|
return false;
|
|
}
|
|
final Fraction other = (Fraction) obj;
|
|
return getNumerator() == other.getNumerator() && getDenominator() == other.getDenominator();
|
|
}
|
|
|
|
/**
|
|
* Gets a hashCode for the fraction.
|
|
*
|
|
* @return a hash code value for this object
|
|
*/
|
|
@Override
|
|
public int hashCode() {
|
|
if (hashCode == 0) {
|
|
// hash code update should be atomic.
|
|
hashCode = 37 * (37 * 17 + getNumerator()) + getDenominator();
|
|
}
|
|
return hashCode;
|
|
}
|
|
|
|
/**
|
|
* Compares this object to another based on size.
|
|
*
|
|
* <p>Note: this class has a natural ordering that is inconsistent
|
|
* with equals, because, for example, equals treats 1/2 and 2/4 as
|
|
* different, whereas compareTo treats them as equal.
|
|
*
|
|
* @param other the object to compare to
|
|
* @return -1 if this is less, 0 if equal, +1 if greater
|
|
* @throws ClassCastException if the object is not a {@link Fraction}
|
|
* @throws NullPointerException if the object is {@code null}
|
|
*/
|
|
@Override
|
|
public int compareTo(final Fraction other) {
|
|
if (this == other) {
|
|
return 0;
|
|
}
|
|
if (numerator == other.numerator && denominator == other.denominator) {
|
|
return 0;
|
|
}
|
|
|
|
// otherwise see which is less
|
|
final long first = (long) numerator * (long) other.denominator;
|
|
final long second = (long) other.numerator * (long) denominator;
|
|
return Long.compare(first, second);
|
|
}
|
|
|
|
/**
|
|
* Gets the fraction as a {@link String}.
|
|
*
|
|
* <p>The format used is '<i>numerator</i>/<i>denominator</i>' always.
|
|
*
|
|
* @return a {@link String} form of the fraction
|
|
*/
|
|
@Override
|
|
public String toString() {
|
|
if (toString == null) {
|
|
toString = getNumerator() + "/" + getDenominator();
|
|
}
|
|
return toString;
|
|
}
|
|
|
|
/**
|
|
* Gets the fraction as a proper {@link String} in the format X Y/Z.
|
|
*
|
|
* <p>The format used in '<i>wholeNumber</i> <i>numerator</i>/<i>denominator</i>'.
|
|
* If the whole number is zero it will be omitted. If the numerator is zero,
|
|
* only the whole number is returned.</p>
|
|
*
|
|
* @return a {@link String} form of the fraction
|
|
*/
|
|
public String toProperString() {
|
|
if (toProperString == null) {
|
|
if (numerator == 0) {
|
|
toProperString = "0";
|
|
} else if (numerator == denominator) {
|
|
toProperString = "1";
|
|
} else if (numerator == -1 * denominator) {
|
|
toProperString = "-1";
|
|
} else if ((numerator > 0 ? -numerator : numerator) < -denominator) {
|
|
// note that we do the magnitude comparison test above with
|
|
// NEGATIVE (not positive) numbers, since negative numbers
|
|
// have a larger range. otherwise numerator==Integer.MIN_VALUE
|
|
// is handled incorrectly.
|
|
final int properNumerator = getProperNumerator();
|
|
if (properNumerator == 0) {
|
|
toProperString = Integer.toString(getProperWhole());
|
|
} else {
|
|
toProperString = getProperWhole() + " " + properNumerator + "/" + getDenominator();
|
|
}
|
|
} else {
|
|
toProperString = getNumerator() + "/" + getDenominator();
|
|
}
|
|
}
|
|
return toProperString;
|
|
}
|
|
}
|