Java tutorial
/* * 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; /** * <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 Travis Reeder * @author Stephen Colebourne * @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 StringBuffer(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 StringBuffer(32).append(getProperWhole()).append(' ') .append(properNumerator).append('/').append(getDenominator()).toString(); } } else { toProperString = new StringBuffer(32).append(getNumerator()).append('/').append(getDenominator()) .toString(); } } return toProperString; } }