/*
* Rational.java
*
* This class is public domain software - that is, you can do whatever you want
* with it, and include it software that is licensed under the GNU or the
* BSD license, or whatever other licence you choose, including proprietary
* closed source licenses. Similarly, I release this Java version under the
* same license, though I do ask that you leave this header in tact.
*
* If you make modifications to this code that you think would benefit the
* wider community, please send me a copy and I'll post it on my site.
*
* If you make use of this code, I'd appreciate hearing about it.
* drew.noakes@drewnoakes.com
* Latest version of this software kept at
* http://drewnoakes.com/
*
* Created on 6 May 2002, 18:06
* Updated 26 Aug 2002 by Drew
* - Added toSimpleString() method, which returns a simplified and hopefully more
* readable version of the Rational. i.e. 2/10 -> 1/5, and 10/2 -> 5
* Modified 29 Oct 2002 (v1.2)
* - Improved toSimpleString() to factor more complex rational numbers into
* a simpler form
* i.e.
* 10/15 -> 2/3
* - toSimpleString() now accepts a boolean flag, 'allowDecimals' which will
* display the rational number in decimal form if it fits within 5 digits
* i.e.
* 3/4 -> 0.75 when allowDecimal == true
*/
import java.io.Serializable;
/**
* Immutable class for holding a rational number without loss of precision. Provides
* a familiar representation via toString() in form numerator/denominator.
*
* @author Drew Noakes http://drewnoakes.com
*/
public class Rational extends java.lang.Number implements Serializable
{
/**
* Holds the numerator.
*/
private final int numerator;
/**
* Holds the denominator.
*/
private final int denominator;
private int maxSimplificationCalculations = 1000;
/**
* Creates a new instance of Rational. Rational objects are immutable, so
* once you've set your numerator and denominator values here, you're stuck
* with them!
*/
public Rational(int numerator, int denominator)
{
this.numerator = numerator;
this.denominator = denominator;
}
/**
* Returns the value of the specified number as a double.
* This may involve rounding.
*
* @return the numeric value represented by this object after conversion
* to type double.
*/
public double doubleValue()
{
return (double)numerator / (double)denominator;
}
/**
* Returns the value of the specified number as a float.
* This may involve rounding.
*
* @return the numeric value represented by this object after conversion
* to type float.
*/
public float floatValue()
{
return (float)numerator / (float)denominator;
}
/**
* Returns the value of the specified number as a byte.
* This may involve rounding or truncation. This implementation simply
* casts the result of doubleValue() to byte.
*
* @return the numeric value represented by this object after conversion
* to type byte.
*/
public final byte byteValue()
{
return (byte)doubleValue();
}
/**
* Returns the value of the specified number as an int.
* This may involve rounding or truncation. This implementation simply
* casts the result of doubleValue() to int.
*
* @return the numeric value represented by this object after conversion
* to type int.
*/
public final int intValue()
{
return (int)doubleValue();
}
/**
* Returns the value of the specified number as a long.
* This may involve rounding or truncation. This implementation simply
* casts the result of doubleValue() to long.
*
* @return the numeric value represented by this object after conversion
* to type long.
*/
public final long longValue()
{
return (long)doubleValue();
}
/**
* Returns the value of the specified number as a short.
* This may involve rounding or truncation. This implementation simply
* casts the result of doubleValue() to short.
*
* @return the numeric value represented by this object after conversion
* to type short.
*/
public final short shortValue()
{
return (short)doubleValue();
}
/**
* Returns the denominator.
*/
public final int getDenominator()
{
return this.denominator;
}
/**
* Returns the numerator.
*/
public final int getNumerator()
{
return this.numerator;
}
/**
* Returns the reciprocal value of this obejct as a new Rational.
* @return the reciprocal in a new object
*/
public Rational getReciprocal()
{
return new Rational(this.denominator, this.numerator);
}
/**
* Checks if this rational number is an Integer, either positive or negative.
*/
public boolean isInteger()
{
if (denominator == 1 ||
(denominator != 0 && (numerator % denominator == 0)) ||
(denominator == 0 && numerator == 0)
) {
return true;
} else {
return false;
}
}
/**
* Returns a string representation of the object of form numerator/denominator.
* @return a string representation of the object.
*/
public String toString()
{
return numerator + "/" + denominator;
}
/**
* Returns the simplest represenation of this Rational's value possible.
*/
public String toSimpleString(boolean allowDecimal)
{
if (denominator == 0 && numerator != 0) {
return toString();
} else if (isInteger()) {
return Integer.toString(intValue());
} else if (numerator != 1 && denominator % numerator == 0) {
// common factor between denominator and numerator
int newDenominator = denominator / numerator;
return new Rational(1, newDenominator).toSimpleString(allowDecimal);
} else {
Rational simplifiedInstance = getSimplifiedInstance();
if (allowDecimal) {
String doubleString = Double.toString(simplifiedInstance.doubleValue());
if (doubleString.length() < 5) {
return doubleString;
}
}
return simplifiedInstance.toString();
}
}
/**
* Decides whether a brute-force simplification calculation should be avoided
* by comparing the maximum number of possible calculations with some threshold.
* @return true if the simplification should be performed, otherwise false
*/
private boolean tooComplexForSimplification()
{
double maxPossibleCalculations = (((double)(Math.min(denominator, numerator) - 1) / 5d) + 2);
return maxPossibleCalculations > maxSimplificationCalculations;
}
/**
* Compares two Rational instances, returning true if they are mathematically
* equivalent.
* @param obj the Rational to compare this instance to.
* @return true if instances are mathematically equivalent, otherwise false. Will also
* return false if obj is not an instance of Rational.
*/
public boolean equals(Object obj)
{
if (!(obj instanceof Rational)) {
return false;
}
Rational that = (Rational)obj;
return this.doubleValue() == that.doubleValue();
}
/**
*
* Simplifies the Rational number.
*
* Prime number series: 1, 2, 3, 5, 7, 9, 11, 13, 17
*
* To reduce a rational, need to see if both numerator and denominator are divisible
* by a common factor. Using the prime number series in ascending order guarantees
* the minimun number of checks required.
*
* However, generating the prime number series seems to be a hefty task. Perhaps
* it's simpler to check if both d & n are divisible by all numbers from 2 ->
* (Math.min(denominator, numerator) / 2). In doing this, one can check for 2
* and 5 once, then ignore all even numbers, and all numbers ending in 0 or 5.
* This leaves four numbers from every ten to check.
*
* Therefore, the max number of pairs of modulus divisions required will be:
*
* 4 Math.min(denominator, numerator) - 1
* -- * ------------------------------------ + 2
* 10 2
*
* Math.min(denominator, numerator) - 1
* = ------------------------------------ + 2
* 5
*
* @return a simplified instance, or if the Rational could not be simpliffied,
* returns itself (unchanged)
*/
public Rational getSimplifiedInstance()
{
if (tooComplexForSimplification()) {
return this;
}
for (int factor = 2; factor <= Math.min(denominator, numerator); factor++) {
if ((factor % 2 == 0 && factor > 2) || (factor % 5 == 0 && factor > 5)) {
continue;
}
if (denominator % factor == 0 && numerator % factor == 0) {
// found a common factor
return new Rational(numerator / factor, denominator / factor);
}
}
return this;
}
}