| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.lang.math; |
| |
| import java.math.BigInteger; |
| |
| import org.apache.commons.lang.text.StrBuilder; |
| |
| /** |
| * <p><code>Fraction</code> is a <code>Number</code> implementation that |
| * stores fractions accurately.</p> |
| * |
| * <p>This class is immutable, and interoperable with most methods that accept |
| * a <code>Number</code>.</p> |
| * |
| * @author Apache Software Foundation |
| * @author Travis Reeder |
| * @author Tim O'Brien |
| * @author Pete Gieser |
| * @author C. Scott Ananian |
| * @since 2.0 |
| * @version $Id$ |
| */ |
| public final class Fraction extends Number implements Comparable { |
| |
| /** |
| * Required for serialization support. Lang version 2.0. |
| * |
| * @see java.io.Serializable |
| */ |
| private static final long serialVersionUID = 65382027393090L; |
| |
| /** |
| * <code>Fraction</code> representation of 0. |
| */ |
| public static final Fraction ZERO = new Fraction(0, 1); |
| /** |
| * <code>Fraction</code> representation of 1. |
| */ |
| public static final Fraction ONE = new Fraction(1, 1); |
| /** |
| * <code>Fraction</code> representation of 1/2. |
| */ |
| public static final Fraction ONE_HALF = new Fraction(1, 2); |
| /** |
| * <code>Fraction</code> representation of 1/3. |
| */ |
| public static final Fraction ONE_THIRD = new Fraction(1, 3); |
| /** |
| * <code>Fraction</code> representation of 2/3. |
| */ |
| public static final Fraction TWO_THIRDS = new Fraction(2, 3); |
| /** |
| * <code>Fraction</code> representation of 1/4. |
| */ |
| public static final Fraction ONE_QUARTER = new Fraction(1, 4); |
| /** |
| * <code>Fraction</code> representation of 2/4. |
| */ |
| public static final Fraction TWO_QUARTERS = new Fraction(2, 4); |
| /** |
| * <code>Fraction</code> representation of 3/4. |
| */ |
| public static final Fraction THREE_QUARTERS = new Fraction(3, 4); |
| /** |
| * <code>Fraction</code> representation of 1/5. |
| */ |
| public static final Fraction ONE_FIFTH = new Fraction(1, 5); |
| /** |
| * <code>Fraction</code> representation of 2/5. |
| */ |
| public static final Fraction TWO_FIFTHS = new Fraction(2, 5); |
| /** |
| * <code>Fraction</code> representation of 3/5. |
| */ |
| public static final Fraction THREE_FIFTHS = new Fraction(3, 5); |
| /** |
| * <code>Fraction</code> representation of 4/5. |
| */ |
| public static final Fraction FOUR_FIFTHS = new Fraction(4, 5); |
| |
| |
| /** |
| * The numerator number part of the fraction (the three in three sevenths). |
| */ |
| private final int numerator; |
| /** |
| * The denominator number part of the fraction (the seven in three sevenths). |
| */ |
| private final int denominator; |
| |
| /** |
| * Cached output hashCode (class is immutable). |
| */ |
| private transient int hashCode = 0; |
| /** |
| * Cached output toString (class is immutable). |
| */ |
| private transient String toString = null; |
| /** |
| * Cached output toProperString (class is immutable). |
| */ |
| private transient String toProperString = null; |
| |
| /** |
| * <p>Constructs a <code>Fraction</code> instance with the 2 parts |
| * of a fraction Y/Z.</p> |
| * |
| * @param numerator the numerator, for example the three in 'three sevenths' |
| * @param denominator the denominator, for example the seven in 'three sevenths' |
| */ |
| private Fraction(int numerator, int denominator) { |
| super(); |
| this.numerator = numerator; |
| this.denominator = denominator; |
| } |
| |
| /** |
| * <p>Creates a <code>Fraction</code> instance with the 2 parts |
| * of a fraction Y/Z.</p> |
| * |
| * <p>Any negative signs are resolved to be on the numerator.</p> |
| * |
| * @param numerator the numerator, for example the three in 'three sevenths' |
| * @param denominator the denominator, for example the seven in 'three sevenths' |
| * @return a new fraction instance |
| * @throws ArithmeticException if the denomiator is <code>zero</code> |
| */ |
| public static Fraction getFraction(int numerator, int denominator) { |
| if (denominator == 0) { |
| throw new ArithmeticException("The denominator must not be zero"); |
| } |
| if (denominator < 0) { |
| if (numerator==Integer.MIN_VALUE || |
| denominator==Integer.MIN_VALUE) { |
| throw new ArithmeticException("overflow: can't negate"); |
| } |
| numerator = -numerator; |
| denominator = -denominator; |
| } |
| return new Fraction(numerator, denominator); |
| } |
| |
| /** |
| * <p>Creates a <code>Fraction</code> instance with the 3 parts |
| * of a fraction X Y/Z.</p> |
| * |
| * <p>The negative sign must be passed in on the whole number part.</p> |
| * |
| * @param whole the whole number, for example the one in 'one and three sevenths' |
| * @param numerator the numerator, for example the three in 'one and three sevenths' |
| * @param denominator the denominator, for example the seven in 'one and three sevenths' |
| * @return a new fraction instance |
| * @throws ArithmeticException if the denomiator is <code>zero</code> |
| * @throws ArithmeticException if the denominator is negative |
| * @throws ArithmeticException if the numerator is negative |
| * @throws ArithmeticException if the resulting numerator exceeds |
| * <code>Integer.MAX_VALUE</code> |
| */ |
| public static Fraction getFraction(int whole, int numerator, int denominator) { |
| if (denominator == 0) { |
| throw new ArithmeticException("The denominator must not be zero"); |
| } |
| if (denominator < 0) { |
| throw new ArithmeticException("The denominator must not be negative"); |
| } |
| if (numerator < 0) { |
| throw new ArithmeticException("The numerator must not be negative"); |
| } |
| long numeratorValue; |
| if (whole < 0) { |
| numeratorValue = whole * (long)denominator - numerator; |
| } else { |
| numeratorValue = whole * (long)denominator + numerator; |
| } |
| if (numeratorValue < Integer.MIN_VALUE || |
| numeratorValue > Integer.MAX_VALUE) { |
| throw new ArithmeticException("Numerator too large to represent as an Integer."); |
| } |
| return new Fraction((int) numeratorValue, denominator); |
| } |
| |
| /** |
| * <p>Creates a reduced <code>Fraction</code> instance with the 2 parts |
| * of a fraction Y/Z.</p> |
| * |
| * <p>For example, if the input parameters represent 2/4, then the created |
| * fraction will be 1/2.</p> |
| * |
| * <p>Any negative signs are resolved to be on the numerator.</p> |
| * |
| * @param numerator the numerator, for example the three in 'three sevenths' |
| * @param denominator the denominator, for example the seven in 'three sevenths' |
| * @return a new fraction instance, with the numerator and denominator reduced |
| * @throws ArithmeticException if the denominator is <code>zero</code> |
| */ |
| public static Fraction getReducedFraction(int numerator, int denominator) { |
| if (denominator == 0) { |
| throw new ArithmeticException("The denominator must not be zero"); |
| } |
| if (numerator==0) { |
| return ZERO; // normalize zero. |
| } |
| // allow 2^k/-2^31 as a valid fraction (where k>0) |
| if (denominator==Integer.MIN_VALUE && (numerator&1)==0) { |
| numerator/=2; denominator/=2; |
| } |
| if (denominator < 0) { |
| if (numerator==Integer.MIN_VALUE || |
| denominator==Integer.MIN_VALUE) { |
| throw new ArithmeticException("overflow: can't negate"); |
| } |
| numerator = -numerator; |
| denominator = -denominator; |
| } |
| // simplify fraction. |
| int gcd = greatestCommonDivisor(numerator, denominator); |
| numerator /= gcd; |
| denominator /= gcd; |
| return new Fraction(numerator, denominator); |
| } |
| |
| /** |
| * <p>Creates a <code>Fraction</code> instance from a <code>double</code> value.</p> |
| * |
| * <p>This method uses the <a href="http://archives.math.utk.edu/articles/atuyl/confrac/"> |
| * continued fraction algorithm</a>, computing a maximum of |
| * 25 convergents and bounding the denominator by 10,000.</p> |
| * |
| * @param value the double value to convert |
| * @return a new fraction instance that is close to the value |
| * @throws ArithmeticException if <code>|value| > Integer.MAX_VALUE</code> |
| * or <code>value = NaN</code> |
| * @throws ArithmeticException if the calculated denominator is <code>zero</code> |
| * @throws ArithmeticException if the the algorithm does not converge |
| */ |
| public static Fraction getFraction(double value) { |
| int sign = (value < 0 ? -1 : 1); |
| value = Math.abs(value); |
| if (value > Integer.MAX_VALUE || Double.isNaN(value)) { |
| throw new ArithmeticException |
| ("The value must not be greater than Integer.MAX_VALUE or NaN"); |
| } |
| int wholeNumber = (int) value; |
| value -= wholeNumber; |
| |
| int numer0 = 0; // the pre-previous |
| int denom0 = 1; // the pre-previous |
| int numer1 = 1; // the previous |
| int denom1 = 0; // the previous |
| int numer2 = 0; // the current, setup in calculation |
| int denom2 = 0; // the current, setup in calculation |
| int a1 = (int) value; |
| int a2 = 0; |
| double x1 = 1; |
| double x2 = 0; |
| double y1 = value - a1; |
| double y2 = 0; |
| double delta1, delta2 = Double.MAX_VALUE; |
| double fraction; |
| int i = 1; |
| // System.out.println("---"); |
| do { |
| delta1 = delta2; |
| a2 = (int) (x1 / y1); |
| x2 = y1; |
| y2 = x1 - a2 * y1; |
| numer2 = a1 * numer1 + numer0; |
| denom2 = a1 * denom1 + denom0; |
| fraction = (double) numer2 / (double) denom2; |
| delta2 = Math.abs(value - fraction); |
| // System.out.println(numer2 + " " + denom2 + " " + fraction + " " + delta2 + " " + y1); |
| a1 = a2; |
| x1 = x2; |
| y1 = y2; |
| numer0 = numer1; |
| denom0 = denom1; |
| numer1 = numer2; |
| denom1 = denom2; |
| i++; |
| // System.out.println(">>" + delta1 +" "+ delta2+" "+(delta1 > delta2)+" "+i+" "+denom2); |
| } while ((delta1 > delta2) && (denom2 <= 10000) && (denom2 > 0) && (i < 25)); |
| if (i == 25) { |
| throw new ArithmeticException("Unable to convert double to fraction"); |
| } |
| return getReducedFraction((numer0 + wholeNumber * denom0) * sign, denom0); |
| } |
| |
| /** |
| * <p>Creates a Fraction from a <code>String</code>.</p> |
| * |
| * <p>The formats accepted are:</p> |
| * |
| * <ol> |
| * <li><code>double</code> String containing a dot</li> |
| * <li>'X Y/Z'</li> |
| * <li>'Y/Z'</li> |
| * <li>'X' (a simple whole number)</li> |
| * </ol> |
| * and a .</p> |
| * |
| * @param str the string to parse, must not be <code>null</code> |
| * @return the new <code>Fraction</code> instance |
| * @throws IllegalArgumentException if the string is <code>null</code> |
| * @throws NumberFormatException if the number format is invalid |
| */ |
| public static Fraction getFraction(String str) { |
| if (str == null) { |
| throw new IllegalArgumentException("The string must not be null"); |
| } |
| // parse double format |
| int pos = str.indexOf('.'); |
| if (pos >= 0) { |
| return getFraction(Double.parseDouble(str)); |
| } |
| |
| // parse X Y/Z format |
| pos = str.indexOf(' '); |
| if (pos > 0) { |
| int whole = Integer.parseInt(str.substring(0, pos)); |
| str = str.substring(pos + 1); |
| pos = str.indexOf('/'); |
| if (pos < 0) { |
| throw new NumberFormatException("The fraction could not be parsed as the format X Y/Z"); |
| } else { |
| int numer = Integer.parseInt(str.substring(0, pos)); |
| int denom = Integer.parseInt(str.substring(pos + 1)); |
| return getFraction(whole, numer, denom); |
| } |
| } |
| |
| // parse Y/Z format |
| pos = str.indexOf('/'); |
| if (pos < 0) { |
| // simple whole number |
| return getFraction(Integer.parseInt(str), 1); |
| } else { |
| int numer = Integer.parseInt(str.substring(0, pos)); |
| int denom = Integer.parseInt(str.substring(pos + 1)); |
| return getFraction(numer, denom); |
| } |
| } |
| |
| // Accessors |
| //------------------------------------------------------------------- |
| |
| /** |
| * <p>Gets the numerator part of the fraction.</p> |
| * |
| * <p>This method may return a value greater than the denominator, an |
| * improper fraction, such as the seven in 7/4.</p> |
| * |
| * @return the numerator fraction part |
| */ |
| public int getNumerator() { |
| return numerator; |
| } |
| |
| /** |
| * <p>Gets the denominator part of the fraction.</p> |
| * |
| * @return the denominator fraction part |
| */ |
| public int getDenominator() { |
| return denominator; |
| } |
| |
| /** |
| * <p>Gets the proper numerator, always positive.</p> |
| * |
| * <p>An improper fraction 7/4 can be resolved into a proper one, 1 3/4. |
| * This method returns the 3 from the proper fraction.</p> |
| * |
| * <p>If the fraction is negative such as -7/4, it can be resolved into |
| * -1 3/4, so this method returns the positive proper numerator, 3.</p> |
| * |
| * @return the numerator fraction part of a proper fraction, always positive |
| */ |
| public int getProperNumerator() { |
| return Math.abs(numerator % denominator); |
| } |
| |
| /** |
| * <p>Gets the proper whole part of the fraction.</p> |
| * |
| * <p>An improper fraction 7/4 can be resolved into a proper one, 1 3/4. |
| * This method returns the 1 from the proper fraction.</p> |
| * |
| * <p>If the fraction is negative such as -7/4, it can be resolved into |
| * -1 3/4, so this method returns the positive whole part -1.</p> |
| * |
| * @return the whole fraction part of a proper fraction, that includes the sign |
| */ |
| public int getProperWhole() { |
| return numerator / denominator; |
| } |
| |
| // Number methods |
| //------------------------------------------------------------------- |
| |
| /** |
| * <p>Gets the fraction as an <code>int</code>. This returns the whole number |
| * part of the fraction.</p> |
| * |
| * @return the whole number fraction part |
| */ |
| public int intValue() { |
| return numerator / denominator; |
| } |
| |
| /** |
| * <p>Gets the fraction as a <code>long</code>. This returns the whole number |
| * part of the fraction.</p> |
| * |
| * @return the whole number fraction part |
| */ |
| public long longValue() { |
| return (long) numerator / denominator; |
| } |
| |
| /** |
| * <p>Gets the fraction as a <code>float</code>. This calculates the fraction |
| * as the numerator divided by denominator.</p> |
| * |
| * @return the fraction as a <code>float</code> |
| */ |
| public float floatValue() { |
| return ((float) numerator) / ((float) denominator); |
| } |
| |
| /** |
| * <p>Gets the fraction as a <code>double</code>. This calculates the fraction |
| * as the numerator divided by denominator.</p> |
| * |
| * @return the fraction as a <code>double</code> |
| */ |
| public double doubleValue() { |
| return ((double) numerator) / ((double) denominator); |
| } |
| |
| // Calculations |
| //------------------------------------------------------------------- |
| |
| /** |
| * <p>Reduce the fraction to the smallest values for the numerator and |
| * denominator, returning the result.</p> |
| * |
| * <p>For example, if this fraction represents 2/4, then the result |
| * will be 1/2.</p> |
| * |
| * @return a new reduced fraction instance, or this if no simplification possible |
| */ |
| public Fraction reduce() { |
| if (numerator == 0) { |
| return equals(ZERO) ? this : ZERO; |
| } |
| int gcd = greatestCommonDivisor(Math.abs(numerator), denominator); |
| if (gcd == 1) { |
| return this; |
| } |
| return Fraction.getFraction(numerator / gcd, denominator / gcd); |
| } |
| |
| /** |
| * <p>Gets a fraction that is the inverse (1/fraction) of this one.</p> |
| * |
| * <p>The returned fraction is not reduced.</p> |
| * |
| * @return a new fraction instance with the numerator and denominator |
| * inverted. |
| * @throws ArithmeticException if the fraction represents zero. |
| */ |
| public Fraction invert() { |
| if (numerator == 0) { |
| throw new ArithmeticException("Unable to invert zero."); |
| } |
| if (numerator==Integer.MIN_VALUE) { |
| throw new ArithmeticException("overflow: can't negate numerator"); |
| } |
| if (numerator<0) { |
| return new Fraction(-denominator, -numerator); |
| } else { |
| return new Fraction(denominator, numerator); |
| } |
| } |
| |
| /** |
| * <p>Gets a fraction that is the negative (-fraction) of this one.</p> |
| * |
| * <p>The returned fraction is not reduced.</p> |
| * |
| * @return a new fraction instance with the opposite signed numerator |
| */ |
| public Fraction negate() { |
| // the positive range is one smaller than the negative range of an int. |
| if (numerator==Integer.MIN_VALUE) { |
| throw new ArithmeticException("overflow: too large to negate"); |
| } |
| return new Fraction(-numerator, denominator); |
| } |
| |
| /** |
| * <p>Gets a fraction that is the positive equivalent of this one.</p> |
| * <p>More precisely: <code>(fraction >= 0 ? this : -fraction)</code></p> |
| * |
| * <p>The returned fraction is not reduced.</p> |
| * |
| * @return <code>this</code> if it is positive, or a new positive fraction |
| * instance with the opposite signed numerator |
| */ |
| public Fraction abs() { |
| if (numerator >= 0) { |
| return this; |
| } |
| return negate(); |
| } |
| |
| /** |
| * <p>Gets a fraction that is raised to the passed in power.</p> |
| * |
| * <p>The returned fraction is in reduced form.</p> |
| * |
| * @param power the power to raise the fraction to |
| * @return <code>this</code> if the power is one, <code>ONE</code> if the power |
| * 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</code> |
| */ |
| public Fraction pow(int power) { |
| if (power == 1) { |
| return this; |
| } else if (power == 0) { |
| return ONE; |
| } else 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); |
| } else { |
| Fraction f = this.multiplyBy(this); |
| if ((power % 2) == 0) { // if even... |
| return f.pow(power/2); |
| } else { // if odd... |
| return f.pow(power/2).multiplyBy(this); |
| } |
| } |
| } |
| |
| /** |
| * <p>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).</p> |
| * |
| * @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) { |
| //if either op. is abs 0 or 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 |
| } |
| |
| // Arithmetic |
| //------------------------------------------------------------------- |
| |
| /** |
| * Multiply two integers, checking for overflow. |
| * |
| * @param x a factor |
| * @param y a factor |
| * @return the product <code>x*y</code> |
| * @throws ArithmeticException if the result can not be represented as |
| * an int |
| */ |
| private static int mulAndCheck(int x, int y) { |
| 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</code> |
| * @throws ArithmeticException if the result can not be represented as |
| * an int |
| */ |
| private static int mulPosAndCheck(int x, int y) { |
| /* assert x>=0 && y>=0; */ |
| 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</code> |
| * @throws ArithmeticException if the result can not be represented as |
| * an int |
| */ |
| private static int addAndCheck(int x, int y) { |
| 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</code> |
| * @throws ArithmeticException if the result can not be represented as |
| * an int |
| */ |
| private static int subAndCheck(int x, int y) { |
| long s = (long)x-(long)y; |
| if (s < Integer.MIN_VALUE || |
| s > Integer.MAX_VALUE) { |
| throw new ArithmeticException("overflow: add"); |
| } |
| return (int)s; |
| } |
| |
| /** |
| * <p>Adds the value of this fraction to another, returning the result in reduced form. |
| * The algorithm follows Knuth, 4.5.1.</p> |
| * |
| * @param fraction the fraction to add, must not be <code>null</code> |
| * @return a <code>Fraction</code> instance with the resulting values |
| * @throws IllegalArgumentException if the fraction is <code>null</code> |
| * @throws ArithmeticException if the resulting numerator or denominator exceeds |
| * <code>Integer.MAX_VALUE</code> |
| */ |
| public Fraction add(Fraction fraction) { |
| return addSub(fraction, true /* add */); |
| } |
| |
| /** |
| * <p>Subtracts the value of another fraction from the value of this one, |
| * returning the result in reduced form.</p> |
| * |
| * @param fraction the fraction to subtract, must not be <code>null</code> |
| * @return a <code>Fraction</code> instance with the resulting values |
| * @throws IllegalArgumentException if the fraction is <code>null</code> |
| * @throws ArithmeticException if the resulting numerator or denominator |
| * cannot be represented in an <code>int</code>. |
| */ |
| public Fraction subtract(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</code> |
| * @param isAdd true to add, false to subtract |
| * @return a <code>Fraction</code> instance with the resulting values |
| * @throws IllegalArgumentException if the fraction is <code>null</code> |
| * @throws ArithmeticException if the resulting numerator or denominator |
| * cannot be represented in an <code>int</code>. |
| */ |
| private Fraction addSub(Fraction fraction, boolean isAdd) { |
| if (fraction == null) { |
| throw new IllegalArgumentException("The fraction must not be null"); |
| } |
| // 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. |
| int d1 = greatestCommonDivisor(denominator, fraction.denominator); |
| if (d1==1) { |
| // result is ( (u*v' +/- u'v) / u'v') |
| int uvp = mulAndCheck(numerator, fraction.denominator); |
| 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) |
| BigInteger uvp = BigInteger.valueOf(numerator) |
| .multiply(BigInteger.valueOf(fraction.denominator/d1)); |
| BigInteger upv = BigInteger.valueOf(fraction.numerator) |
| .multiply(BigInteger.valueOf(denominator/d1)); |
| 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) |
| int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue(); |
| int d2 = (tmodd1==0)?d1:greatestCommonDivisor(tmodd1, d1); |
| |
| // result is (t/d2) / (u'/d1)(v'/d2) |
| 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)); |
| } |
| |
| /** |
| * <p>Multiplies the value of this fraction by another, returning the |
| * result in reduced form.</p> |
| * |
| * @param fraction the fraction to multiply by, must not be <code>null</code> |
| * @return a <code>Fraction</code> instance with the resulting values |
| * @throws IllegalArgumentException if the fraction is <code>null</code> |
| * @throws ArithmeticException if the resulting numerator or denominator exceeds |
| * <code>Integer.MAX_VALUE</code> |
| */ |
| public Fraction multiplyBy(Fraction fraction) { |
| if (fraction == null) { |
| throw new IllegalArgumentException("The fraction must not be null"); |
| } |
| if (numerator == 0 || fraction.numerator == 0) { |
| return ZERO; |
| } |
| // knuth 4.5.1 |
| // make sure we don't overflow unless the result *must* overflow. |
| int d1 = greatestCommonDivisor(numerator, fraction.denominator); |
| int d2 = greatestCommonDivisor(fraction.numerator, denominator); |
| return getReducedFraction |
| (mulAndCheck(numerator/d1, fraction.numerator/d2), |
| mulPosAndCheck(denominator/d2, fraction.denominator/d1)); |
| } |
| |
| /** |
| * <p>Divide the value of this fraction by another.</p> |
| * |
| * @param fraction the fraction to divide by, must not be <code>null</code> |
| * @return a <code>Fraction</code> instance with the resulting values |
| * @throws IllegalArgumentException if the fraction is <code>null</code> |
| * @throws ArithmeticException if the fraction to divide by is zero |
| * @throws ArithmeticException if the resulting numerator or denominator exceeds |
| * <code>Integer.MAX_VALUE</code> |
| */ |
| public Fraction divideBy(Fraction fraction) { |
| if (fraction == null) { |
| throw new IllegalArgumentException("The fraction must not be null"); |
| } |
| if (fraction.numerator == 0) { |
| throw new ArithmeticException("The fraction to divide by must not be zero"); |
| } |
| return multiplyBy(fraction.invert()); |
| } |
| |
| // Basics |
| //------------------------------------------------------------------- |
| |
| /** |
| * <p>Compares this fraction to another object to test if they are equal.</p>. |
| * |
| * <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</code> if this object is equal |
| */ |
| public boolean equals(Object obj) { |
| if (obj == this) { |
| return true; |
| } |
| if (obj instanceof Fraction == false) { |
| return false; |
| } |
| Fraction other = (Fraction) obj; |
| return (getNumerator() == other.getNumerator() && |
| getDenominator() == other.getDenominator()); |
| } |
| |
| /** |
| * <p>Gets a hashCode for the fraction.</p> |
| * |
| * @return a hash code value for this object |
| */ |
| public int hashCode() { |
| if (hashCode == 0) { |
| // hashcode update should be atomic. |
| hashCode = 37 * (37 * 17 + getNumerator()) + getDenominator(); |
| } |
| return hashCode; |
| } |
| |
| /** |
| * <p>Compares this object to another based on size.</p> |
| * |
| * <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 object 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 <code>Fraction</code> |
| * @throws NullPointerException if the object is <code>null</code> |
| */ |
| public int compareTo(Object object) { |
| Fraction other = (Fraction) object; |
| if (this==other) { |
| return 0; |
| } |
| if (numerator == other.numerator && denominator == other.denominator) { |
| return 0; |
| } |
| |
| // otherwise see which is less |
| long first = (long) numerator * (long) other.denominator; |
| long second = (long) other.numerator * (long) denominator; |
| if (first == second) { |
| return 0; |
| } else if (first < second) { |
| return -1; |
| } else { |
| return 1; |
| } |
| } |
| |
| /** |
| * <p>Gets the fraction as a <code>String</code>.</p> |
| * |
| * <p>The format used is '<i>numerator</i>/<i>denominator</i>' always. |
| * |
| * @return a <code>String</code> form of the fraction |
| */ |
| public String toString() { |
| if (toString == null) { |
| toString = new StrBuilder(32) |
| .append(getNumerator()) |
| .append('/') |
| .append(getDenominator()).toString(); |
| } |
| return toString; |
| } |
| |
| /** |
| * <p>Gets the fraction as a proper <code>String</code> in the format X Y/Z.</p> |
| * |
| * <p>The format used in '<i>wholeNumber</i> <i>numerator</i>/<i>denominator</i>'. |
| * If the whole number is zero it will be ommitted. If the numerator is zero, |
| * only the whole number is returned.</p> |
| * |
| * @return a <code>String</code> 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. |
| int properNumerator = getProperNumerator(); |
| if (properNumerator == 0) { |
| toProperString = Integer.toString(getProperWhole()); |
| } else { |
| toProperString = new StrBuilder(32) |
| .append(getProperWhole()).append(' ') |
| .append(properNumerator).append('/') |
| .append(getDenominator()).toString(); |
| } |
| } else { |
| toProperString = new StrBuilder(32) |
| .append(getNumerator()).append('/') |
| .append(getDenominator()).toString(); |
| } |
| } |
| return toProperString; |
| } |
| } |
