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