//****************************************************************************** // // File: Rational.java // Package: edu.rit.numeric // Unit: Class edu.rit.numeric.Rational // // This Java source file is copyright (C) 2002-2004 by Alan Kaminsky. All rights // reserved. For further information, contact the author, Alan Kaminsky, at // ark@cs.rit.edu. // // This Java source file is part of the Parallel Java Library ("PJ"). PJ is free // software; you can redistribute it and/or modify it under the terms of the GNU // General Public License as published by the Free Software Foundation; either // version 3 of the License, or (at your option) any later version. // // PJ is distributed in the hope that it will be useful, but WITHOUT ANY // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR // A PARTICULAR PURPOSE. See the GNU General Public License for more details. // // A copy of the GNU General Public License is provided in the file gpl.txt. You // may also obtain a copy of the GNU General Public License on the World Wide // Web at http://www.gnu.org/licenses/gpl.html. // //****************************************************************************** package edu.rit.numeric; import java.io.Serializable; /** * Class Rational provides a 32-bit rational number. A 32-bit rational number is * the ratio of two 32-bit integers (type int). Operations are provided * for exact arithmetic and comparison with rational numbers. *HashMap* Class Rational overrides the equals() and hashCode() * methods, making it suitable for use as a key in a hashed data structure like * a {@link java.util.HashMap
} or {@link java.util.HashSet *HashSet}. However, a Rational object is mutable. Take care not * to change the value of a Rational object if it is used as a key in a hashed * data structure. ** Class Rational is not multiple thread safe. * * @author Alan Kaminsky * @version 01-Dec-2004 */ public class Rational implements Comparable, Serializable { // Hidden data members. private int numer; private int denom; // Exported constructors. /** * Construct a new rational number. Its value is 0. */ public Rational() { numer = 0; denom = 1; } /** * Construct a new rational number. Its value is value. * * @param value Value. */ public Rational (int value) { numer = value; denom = 1; } /** * Construct a new rational number. Its value is numer/denom. * * @param numer Numerator. * @param denom Denominator. * * @exception ArithmeticException * (unchecked exception) Thrown if denom is 0. */ public Rational (int numer, int denom) { if (denom == 0) { throw new ArithmeticException ("Divide by zero"); } this.numer = numer; this.denom = denom; normalize(); } /** * Construct a new rational number. Its value is value. * * @param value Rational number. */ public Rational (Rational value) { this.numer = value.numer; this.denom = value.denom; } /** * Construct a new rational number. Its value comes from the string * s. The string must obey this syntax: optional minus sign * (-), numerator (decimal integer), slash (/), * denominator (decimal integer). The slash-and-denominator is optional. If * present, the denominator must be greater than 0. There is no whitespace * within the string. * * @param s String. * * @exception NumberFormatException * (unchecked exception) Thrown if s cannot be parsed into a * rational number. */ public Rational (String s) { assign (s); } // Exported operations. /** * Set this rational number to the given number. * * @param x Rational number. * * @return This rational number, with its value set to x. */ public Rational assign (Rational x) { this.numer = x.numer; this.denom = x.denom; return this; } /** * Set this rational number to the given number. * * @param x Integer. * * @return This rational number, with its value set to x. */ public Rational assign (int x) { this.numer = x; this.denom = 1; return this; } /** * Set this rational number to the value parsed from the given string. The * string must obey this syntax: optional minus sign (-), numerator * (decimal integer), slash (/), denominator (decimal integer). The * slash-and-denominator is optional. If present, the denominator must be * greater than 0. There is no whitespace within the string. * * @param s String. * * @return This rational number, with its value set to s. * * @exception NumberFormatException * (unchecked exception) Thrown if s cannot be parsed into a * rational number. */ public Rational assign (String s) { int numer, denom; int iSlash = s.indexOf ('/'); if (iSlash == -1) { // No denominator. numer = Integer.parseInt (s); denom = 1; } else if (iSlash+1 < s.length()) { // Slash and denominator. numer = Integer.parseInt (s.substring (0, iSlash)); denom = Integer.parseInt (s.substring (iSlash+1)); if (denom <= 0) { throw new NumberFormatException(); } } else { // Slash but no denominator. throw new NumberFormatException(); } this.numer = numer; this.denom = denom; normalize(); return this; } /** * Set this rational number to the negative of the given number. * * @param x Rational number. * * @return This rational number, with its value set to -x. */ public Rational neg (Rational x) { this.numer = -x.numer; this.denom = x.denom; return this; } /** * Set this rational number to the negative of the given number. * * @param x Integer. * * @return This rational number, with its value set to -x. */ public Rational neg (int x) { this.numer = -x; this.denom = 1; return this; } /** * Set this rational number to the absolute value of the given number. * * @param x Rational number. * * @return This rational number, with its value set to abs(x). */ public Rational abs (Rational x) { this.numer = absval (x.numer); this.denom = x.denom; return this; } /** * Set this rational number to the absolute value of the given number. * * @param x Integer. * * @return This rational number, with its value set to abs(x). */ public Rational abs (int x) { this.numer = absval (x); this.denom = 1; return this; } /** * Set this rational number to the integer part of the given rational * number. * * @param x Rational number. * * @return This rational number, with its value set to int(x). */ public Rational intPart (Rational x) { this.numer = x.numer / x.denom; this.denom = 1; return this; } /** * Set this rational number to the fractional part of the given rational * number. * * @param x Rational number. * * @return This rational number, with its value set to frac(x). */ public Rational fracPart (Rational x) { this.numer = x.numer % x.denom; this.denom = x.denom; normalize(); return this; } /** * Set this rational number to the sum of the given numbers. * * @param x Rational number. * @param y Rational number. * * @return This rational number, with its value set to x+y. */ public Rational add (Rational x, Rational y) { int lcm = leastCommonMultiple (x.denom, y.denom); this.numer = (lcm / x.denom) * x.numer + (lcm / y.denom) * y.numer; this.denom = lcm; normalize(); return this; } /** * Set this rational number to the sum of the given numbers. * * @param x Rational number. * @param y Integer. * * @return This rational number, with its value set to x+y. */ public Rational add (Rational x, int y) { this.numer = x.numer + y * x.denom; this.denom = x.denom; normalize(); return this; } /** * Set this rational number to the sum of the given numbers. * * @param x Integer. * @param y Rational number. * * @return This rational number, with its value set to x+y. */ public Rational add (int x, Rational y) { this.numer = x * y.denom + y.numer; this.denom = y.denom; normalize(); return this; } /** * Set this rational number to the sum of the given numbers. * * @param x Integer. * @param y Integer. * * @return This rational number, with its value set to x+y. */ public Rational add (int x, int y) { this.numer = x + y; this.denom = 1; return this; } /** * Set this rational number to the difference of the given numbers. * * @param x Rational number. * @param y Rational number. * * @return This rational number, with its value set to x-y. */ public Rational sub (Rational x, Rational y) { int lcm = leastCommonMultiple (x.denom, y.denom); this.numer = (lcm / x.denom) * x.numer - (lcm / y.denom) * y.numer; this.denom = lcm; normalize(); return this; } /** * Set this rational number to the difference of the given numbers. * * @param x Rational number. * @param y Integer. * * @return This rational number, with its value set to x-y. */ public Rational sub (Rational x, int y) { this.numer = x.numer - y * x.denom; this.denom = x.denom; normalize(); return this; } /** * Set this rational number to the difference of the given numbers. * * @param x Integer. * @param y Rational number. * * @return This rational number, with its value set to x-y. */ public Rational sub (int x, Rational y) { this.numer = x * y.denom - y.numer; this.denom = y.denom; normalize(); return this; } /** * Set this rational number to the difference of the given numbers. * * @param x Integer. * @param y Integer. * * @return This rational number, with its value set to x-y. */ public Rational sub (int x, int y) { this.numer = x - y; this.denom = 1; return this; } /** * Set this rational number to the product of the given numbers. * * @param x Rational number. * @param y Rational number. * * @return This rational number, with its value set to x*y. */ public Rational mul (Rational x, Rational y) { this.numer = x.numer * y.numer; this.denom = x.denom * y.denom; normalize(); return this; } /** * Set this rational number to the product of the given numbers. * * @param x Rational number. * @param y Integer. * * @return This rational number, with its value set to x*y. */ public Rational mul (Rational x, int y) { this.numer = x.numer * y; this.denom = x.denom; normalize(); return this; } /** * Set this rational number to the product of the given numbers. * * @param x Integer. * @param y Rational number. * * @return This rational number, with its value set to x*y. */ public Rational mul (int x, Rational y) { this.numer = x * y.numer; this.denom = y.denom; normalize(); return this; } /** * Set this rational number to the product of the given numbers. * * @param x Integer. * @param y Integer. * * @return This rational number, with its value set to x*y. */ public Rational mul (int x, int y) { this.numer = x * y; this.denom = 1; return this; } /** * Set this rational number to the quotient of the given numbers. * * @param x Rational number. * @param y Rational number. * * @return This rational number, with its value set to x/y. * * @exception ArithmeticException * (unchecked exception) Thrown if y is 0. */ public Rational div (Rational x, Rational y) { if (y.numer == 0) { throw new ArithmeticException ("Divide by zero"); } int numer = x.numer * y.denom; int denom = x.denom * y.numer; this.numer = numer; this.denom = denom; normalize(); return this; } /** * Set this rational number to the quotient of the given numbers. * * @param x Rational number. * @param y Integer. * * @return This rational number, with its value set to x/y. * * @exception ArithmeticException * (unchecked exception) Thrown if y is 0. */ public Rational div (Rational x, int y) { if (y == 0) { throw new ArithmeticException ("Divide by zero"); } this.numer = x.numer; this.denom = x.denom * y; normalize(); return this; } /** * Set this rational number to the quotient of the given numbers. * * @param x Integer. * @param y Rational number. * * @return This rational number, with its value set to x/y. * * @exception ArithmeticException * (unchecked exception) Thrown if y is 0. */ public Rational div (int x, Rational y) { if (y.numer == 0) { throw new ArithmeticException ("Divide by zero"); } int numer = x * y.denom; int denom = y.numer; this.numer = numer; this.denom = denom; normalize(); return this; } /** * Set this rational number to the quotient of the given numbers. * * @param x Integer. * @param y Integer. * * @return This rational number, with its value set to x/y. * * @exception ArithmeticException * (unchecked exception) Thrown if y is 0. */ public Rational div (int x, int y) { if (y == 0) { throw new ArithmeticException ("Divide by zero"); } this.numer = x; this.denom = y; normalize(); return this; } /** * Set this rational number to the minimum of the given numbers. * * @param x Rational number. * @param y Rational number. * * @return This rational number, with its value set to the smaller of * x and y. */ public Rational min (Rational x, Rational y) { if (x.lt (y)) { this.assign (x); } else { this.assign (y); } return this; } /** * Set this rational number to the minimum of the given numbers. * * @param x Rational number. * @param y Integer. * * @return This rational number, with its value set to the smaller of * x and y. */ public Rational min (Rational x, int y) { if (x.lt (y)) { this.assign (x); } else { this.assign (y); } return this; } /** * Set this rational number to the minimum of the given numbers. * * @param x Integer. * @param y Rational number. * * @return This rational number, with its value set to the smaller of * x and y. */ public Rational min (int x, Rational y) { if (y.gt (x)) { this.assign (x); } else { this.assign (y); } return this; } /** * Set this rational number to the minimum of the given numbers. * * @param x Integer. * @param y Integer. * * @return This rational number, with its value set to the smaller of * x and y. */ public Rational min (int x, int y) { this.assign (Math.min (x, y)); return this; } /** * Set this rational number to the maximum of the given numbers. * * @param x Rational number. * @param y Rational number. * * @return This rational number, with its value set to the larger of * x and y. */ public Rational max (Rational x, Rational y) { if (x.gt (y)) { this.assign (x); } else { this.assign (y); } return this; } /** * Set this rational number to the maximum of the given numbers. * * @param x Rational number. * @param y Integer. * * @return This rational number, with its value set to the larger of * x and y. */ public Rational max (Rational x, int y) { if (x.gt (y)) { this.assign (x); } else { this.assign (y); } return this; } /** * Set this rational number to the maximum of the given numbers. * * @param x Integer. * @param y Rational number. * * @return This rational number, with its value set to the larger of * x and y. */ public Rational max (int x, Rational y) { if (y.lt (x)) { this.assign (x); } else { this.assign (y); } return this; } /** * Set this rational number to the maximum of the given numbers. * * @param x Integer. * @param y Integer. * * @return This rational number, with its value set to the larger of * x and y. */ public Rational max (int x, int y) { this.assign (Math.max (x, y)); return this; } /** * Determine if this rational number is equal to zero. * * @return True if this rational number is equal to 0, false otherwise. */ public boolean eqZero() { return this.numer == 0; } /** * Determine if this rational number is not equal to zero. * * @return True if this rational number is not equal to 0, false otherwise. */ public boolean neZero() { return this.numer != 0; } /** * Determine if this rational number is less than zero. * * @return True if this rational number is less than 0, false otherwise. */ public boolean ltZero() { return this.numer < 0; } /** * Determine if this rational number is less than or equal to zero. * * @return True if this rational number is less than or equal to 0, false * otherwise. */ public boolean leZero() { return this.numer <= 0; } /** * Determine if this rational number is greater than zero. * * @return True if this rational number is greater than 0, false otherwise. */ public boolean gtZero() { return this.numer > 0; } /** * Determine if this rational number is greater than or equal to zero. * * @return True if this rational number is greater than or equal to 0, * false otherwise. */ public boolean geZero() { return this.numer >= 0; } /** * Determine if this rational number is equal to the given number. * * @param x Rational number. * * @return True if this rational number is equal to x, false * otherwise. */ public boolean eq (Rational x) { return this.numer == x.numer && this.denom == x.denom; } /** * Determine if this rational number is equal to the given number. * * @param x Integer. * * @return True if this rational number is equal to x, false * otherwise. */ public boolean eq (int x) { return this.numer == x && this.denom == 1; } /** * Determine if this rational number is not equal to the given number. * * @param x Rational number. * * @return True if this rational number is not equal to x, false * otherwise. */ public boolean ne (Rational x) { return this.numer != x.numer || this.denom != x.denom; } /** * Determine if this rational number is not equal to the given number. * * @param x Integer. * * @return True if this rational number is not equal to x, false * otherwise. */ public boolean ne (int x) { return this.numer != x || this.denom != 1; } /** * Determine if this rational number is less than the given number. * * @param x Rational number. * * @return True if this rational number is less than x, false * otherwise. */ public boolean lt (Rational x) { return new Rational() .sub (this, x) .ltZero(); } /** * Determine if this rational number is less than the given number. * * @param x Integer. * * @return True if this rational number is less than x, false * otherwise. */ public boolean lt (int x) { return new Rational() .sub (this, x) .ltZero(); } /** * Determine if this rational number is less than or equal to the given * number. * * @param x Rational number. * * @return True if this rational number is less than or equal to * x, false otherwise. */ public boolean le (Rational x) { return new Rational() .sub (this, x) .leZero(); } /** * Determine if this rational number is less than or equal to the given * number. * * @param x Integer. * * @return True if this rational number is less than or equal to * x, false otherwise. */ public boolean le (int x) { return new Rational() .sub (this, x) .leZero(); } /** * Determine if this rational number is greater than the given number. * * @param x Rational number. * * @return True if this rational number is greater than x, false * otherwise. */ public boolean gt (Rational x) { return new Rational() .sub (this, x) .gtZero(); } /** * Determine if this rational number is greater than the given number. * * @param x Integer. * * @return True if this rational number is greater than x, false * otherwise. */ public boolean gt (int x) { return new Rational() .sub (this, x) .gtZero(); } /** * Determine if this rational number is greater than or equal to the given * number. * * @param x Rational number. * * @return True if this rational number is greater than or equal to * x, false otherwise. */ public boolean ge (Rational x) { return new Rational() .sub (this, x) .geZero(); } /** * Determine if this rational number is greater than or equal to the given * number. * * @param x Integer. * * @return True if this rational number is greater than or equal to * x, false otherwise. */ public boolean ge (int x) { return new Rational() .sub (this, x) .geZero(); } /** * Converts this rational number to an integer. If this rational number is * not an exact integer, any fractional part is truncated. * * @return Integer value of this rational number. */ public int intValue() { return this.numer / this.denom; } /** * Converts this rational number to a long integer. If this rational number * is not an exact integer, any fractional part is truncated. * * @return Long integer value of this rational number. */ public long longValue() { return ((long) this.numer) / ((long) this.denom); } /** * Converts this rational number to a single precision floating point * number. * * @return Single precision floating point value of this rational number. */ public float floatValue() { return ((float) this.numer) / ((float) this.denom); } /** * Converts this rational number to a double precision floating point * number. * * @return Double precision floating point value of this rational number. */ public double doubleValue() { return ((double) this.numer) / ((double) this.denom); } /** * Returns a string version of this rational number. If this rational number * is an exact integer, the string is in the form "<numer>", * otherwise the string is in the form * "<numer>/<denom>". If this rational number is less * than 0, the string begins with a minus sign (-). */ public String toString() { if (this.denom == 1) { return Integer.toString (this.numer); } else { return this.numer + "/" + this.denom; } } /** * Determine if this rational number is equal to the given object. To be * equal, obj must be a non-null instance of class Rational whose * value is the same as this rational number's value. * * @param obj Object to test. * * @return True if this rational number is equal to obj, false * otherwise. */ public boolean equals (Object obj) { return obj instanceof Rational && eq ((Rational) obj); } /** * Returns a hash code for this rational number. */ public int hashCode() { return this.numer + this.denom; } /** * Compare this rational number to the given object. * * @param obj Object to compare to. * * @return A number less than, equal to, or greater than 0 if this rational * number is less than, equal to, or greater than obj, * respectively. * * @exception NullPointerException * (unchecked exception) Thrown if obj is null. * @exception ClassCastException * (unchecked exception) Thrown if obj is not an instance of * class Rational. */ public int compareTo (Object obj) { return new Rational() .sub (this, (Rational) obj) .numer; } // Hidden operations. /** * Normalize this rational number. Afterwards, the denominator is greater * than 0, and the denominator does not divide the numerator. */ private void normalize() { int sign = signum (numer) * signum (denom); numer = absval (numer); denom = absval (denom); int gcd = greatestCommonDivisor (numer, denom); numer = sign * numer / gcd; denom = denom / gcd; } /** * Returns the signum of the given number. */ private static int signum (int x) { return x < 0 ? -1 : 1; } /** * Returns the absolute value of the given number. */ private static int absval (int x) { return x < 0 ? -x : x; } /** * Returns the greatest common divisor of the given numbers. x and * y are assumed to be greater than 0. */ private static int greatestCommonDivisor (int x, int y) { int r; while (y != 0) { r = x % y; x = y; y = r; } return x; } /** * Returns the least common multiple of the given numbers. x and * y are assumed to be greater than 0. */ private static int leastCommonMultiple (int x, int y) { return (x / greatestCommonDivisor (x, y)) * y; } }
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