java 比較 有効桁数 - Javaで端数を表現する最も良い方法は?

あまりにもずっと前に、 プロジェクトオイラー問題のためにBigFractionクラスを書きました。 BigIntegerの分子と分母を保持しているので、オーバーフローすることはありません。 しかし、それはあなたがそれを必要とする場合は、とにかく、それを使用してオーバーフローしないことを知っている多くの操作のために少し遅いでしょう。 私は何とかこれを見せたくありませんでした。 :)

``````import java.math.*;

/**
* Arbitrary-precision fractions, utilizing BigIntegers for numerator and
* denominator.  Fraction is always kept in lowest terms.  Fraction is
* immutable, and guaranteed not to have a null numerator or denominator.
* Denominator will always be positive (so sign is carried by numerator,
* and a zero-denominator is impossible).
*/
public final class BigFraction extends Number implements Comparable<BigFraction>
{
private static final long serialVersionUID = 1L; //because Number is Serializable
private final BigInteger numerator;
private final BigInteger denominator;

public final static BigFraction ZERO = new BigFraction(BigInteger.ZERO, BigInteger.ONE, true);
public final static BigFraction ONE = new BigFraction(BigInteger.ONE, BigInteger.ONE, true);

/**
* Constructs a BigFraction with given numerator and denominator.  Fraction
* will be reduced to lowest terms.  If fraction is negative, negative sign will
* be carried on numerator, regardless of how the values were passed in.
*/
public BigFraction(BigInteger numerator, BigInteger denominator)
{
if(numerator == null)
throw new IllegalArgumentException("Numerator is null");
if(denominator == null)
throw new IllegalArgumentException("Denominator is null");
if(denominator.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero.");

//only numerator should be negative.
if(denominator.signum() < 0)
{
numerator = numerator.negate();
denominator = denominator.negate();
}

//create a reduced fraction
BigInteger gcd = numerator.gcd(denominator);
this.numerator = numerator.divide(gcd);
this.denominator = denominator.divide(gcd);
}

/**
* Constructs a BigFraction from a whole number.
*/
public BigFraction(BigInteger numerator)
{
this(numerator, BigInteger.ONE, true);
}

public BigFraction(long numerator, long denominator)
{
this(BigInteger.valueOf(numerator), BigInteger.valueOf(denominator));
}

public BigFraction(long numerator)
{
this(BigInteger.valueOf(numerator), BigInteger.ONE, true);
}

/**
* Constructs a BigFraction from a floating-point number.
*
* Warning: round-off error in IEEE floating point numbers can result
* in answers that are unexpected.  For example,
*     System.out.println(new BigFraction(1.1))
* will print:
*     2476979795053773/2251799813685248
*
* This is because 1.1 cannot be expressed exactly in binary form.  The
* given fraction is exactly equal to the internal representation of
* the double-precision floating-point number.  (Which, for 1.1, is:
* (-1)^0 * 2^0 * (1 + 0x199999999999aL / 0x10000000000000L).)
*
* NOTE: In many cases, BigFraction(Double.toString(d)) may give a result
* closer to what the user expects.
*/
public BigFraction(double d)
{
if(Double.isInfinite(d))
throw new IllegalArgumentException("double val is infinite");
if(Double.isNaN(d))
throw new IllegalArgumentException("double val is NaN");

//special case - math below won't work right for 0.0 or -0.0
if(d == 0)
{
numerator = BigInteger.ZERO;
denominator = BigInteger.ONE;
return;
}

final long bits = Double.doubleToLongBits(d);
final int sign = (int)(bits >> 63) & 0x1;
final int exponent = ((int)(bits >> 52) & 0x7ff) - 0x3ff;
final long mantissa = bits & 0xfffffffffffffL;

//number is (-1)^sign * 2^(exponent) * 1.mantissa
BigInteger tmpNumerator = BigInteger.valueOf(sign==0 ? 1 : -1);
BigInteger tmpDenominator = BigInteger.ONE;

//use shortcut: 2^x == 1 << x.  if x is negative, shift the denominator
if(exponent >= 0)
tmpNumerator = tmpNumerator.multiply(BigInteger.ONE.shiftLeft(exponent));
else
tmpDenominator = tmpDenominator.multiply(BigInteger.ONE.shiftLeft(-exponent));

//1.mantissa == 1 + mantissa/2^52 == (2^52 + mantissa)/2^52
tmpDenominator = tmpDenominator.multiply(BigInteger.valueOf(0x10000000000000L));
tmpNumerator = tmpNumerator.multiply(BigInteger.valueOf(0x10000000000000L + mantissa));

BigInteger gcd = tmpNumerator.gcd(tmpDenominator);
numerator = tmpNumerator.divide(gcd);
denominator = tmpDenominator.divide(gcd);
}

/**
* Constructs a BigFraction from two floating-point numbers.
*
* Warning: round-off error in IEEE floating point numbers can result
* in answers that are unexpected.  See BigFraction(double) for more
* information.
*
* NOTE: In many cases, BigFraction(Double.toString(numerator) + "/" + Double.toString(denominator))
* may give a result closer to what the user expects.
*/
public BigFraction(double numerator, double denominator)
{
if(denominator == 0)
throw new ArithmeticException("Divide by zero.");

BigFraction tmp = new BigFraction(numerator).divide(new BigFraction(denominator));
this.numerator = tmp.numerator;
this.denominator = tmp.denominator;
}

/**
* Constructs a new BigFraction from the given BigDecimal object.
*/
public BigFraction(BigDecimal d)
{
this(d.scale() < 0 ? d.unscaledValue().multiply(BigInteger.TEN.pow(-d.scale())) : d.unscaledValue(),
d.scale() < 0 ? BigInteger.ONE                                             : BigInteger.TEN.pow(d.scale()));
}

public BigFraction(BigDecimal numerator, BigDecimal denominator)
{
if(denominator.equals(BigDecimal.ZERO))
throw new ArithmeticException("Divide by zero.");

BigFraction tmp = new BigFraction(numerator).divide(new BigFraction(denominator));
this.numerator = tmp.numerator;
this.denominator = tmp.denominator;
}

/**
* Constructs a BigFraction from a String.  Expected format is numerator/denominator,
* but /denominator part is optional.  Either numerator or denominator may be a floating-
* point decimal number, which in the same format as a parameter to the
* <code>BigDecimal(String)</code> constructor.
*
* @throws NumberFormatException  if the string cannot be properly parsed.
*/
public BigFraction(String s)
{
int slashPos = s.indexOf('/');
if(slashPos < 0)
{
BigFraction res = new BigFraction(new BigDecimal(s));
this.numerator = res.numerator;
this.denominator = res.denominator;
}
else
{
BigDecimal num = new BigDecimal(s.substring(0, slashPos));
BigDecimal den = new BigDecimal(s.substring(slashPos+1, s.length()));
BigFraction res = new BigFraction(num, den);
this.numerator = res.numerator;
this.denominator = res.denominator;
}
}

/**
* Returns this + f.
*/
{
if(f == null)
throw new IllegalArgumentException("Null argument");

//n1/d1 + n2/d2 = (n1*d2 + d1*n2)/(d1*d2)
denominator.multiply(f.denominator));
}

/**
* Returns this + b.
*/
{
if(b == null)
throw new IllegalArgumentException("Null argument");

//n1/d1 + n2 = (n1 + d1*n2)/d1
denominator, true);
}

/**
* Returns this + n.
*/
{
}

/**
* Returns this - f.
*/
public BigFraction subtract(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");

return new BigFraction(numerator.multiply(f.denominator).subtract(denominator.multiply(f.numerator)),
denominator.multiply(f.denominator));
}

/**
* Returns this - b.
*/
public BigFraction subtract(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");

return new BigFraction(numerator.subtract(denominator.multiply(b)),
denominator, true);
}

/**
* Returns this - n.
*/
public BigFraction subtract(long n)
{
return subtract(BigInteger.valueOf(n));
}

/**
* Returns this * f.
*/
public BigFraction multiply(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");

return new BigFraction(numerator.multiply(f.numerator), denominator.multiply(f.denominator));
}

/**
* Returns this * b.
*/
public BigFraction multiply(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");

return new BigFraction(numerator.multiply(b), denominator);
}

/**
* Returns this * n.
*/
public BigFraction multiply(long n)
{
return multiply(BigInteger.valueOf(n));
}

/**
* Returns this / f.
*/
public BigFraction divide(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");

if(f.numerator.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");

return new BigFraction(numerator.multiply(f.denominator), denominator.multiply(f.numerator));
}

/**
* Returns this / b.
*/
public BigFraction divide(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");

if(b.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");

return new BigFraction(numerator, denominator.multiply(b));
}

/**
* Returns this / n.
*/
public BigFraction divide(long n)
{
return divide(BigInteger.valueOf(n));
}

/**
* Returns this^exponent.
*/
public BigFraction pow(int exponent)
{
if(exponent == 0)
return BigFraction.ONE;
else if (exponent == 1)
return this;
else if (exponent < 0)
return new BigFraction(denominator.pow(-exponent), numerator.pow(-exponent), true);
else
return new BigFraction(numerator.pow(exponent), denominator.pow(exponent), true);
}

/**
* Returns 1/this.
*/
public BigFraction reciprocal()
{
if(this.numerator.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");

return new BigFraction(denominator, numerator, true);
}

/**
* Returns the complement of this fraction, which is equal to 1 - this.
* Useful for probabilities/statistics.

*/
public BigFraction complement()
{
return new BigFraction(denominator.subtract(numerator), denominator, true);
}

/**
* Returns -this.
*/
public BigFraction negate()
{
return new BigFraction(numerator.negate(), denominator, true);
}

/**
* Returns -1, 0, or 1, representing the sign of this fraction.
*/
public int signum()
{
return numerator.signum();
}

/**
* Returns the absolute value of this.
*/
public BigFraction abs()
{
return (signum() < 0 ? negate() : this);
}

/**
* Returns a string representation of this, in the form
* numerator/denominator.
*/
public String toString()
{
return numerator.toString() + "/" + denominator.toString();
}

/**
* Returns if this object is equal to another object.
*/
public boolean equals(Object o)
{
if(!(o instanceof BigFraction))
return false;

BigFraction f = (BigFraction)o;
return numerator.equals(f.numerator) && denominator.equals(f.denominator);
}

/**
* Returns a hash code for this object.
*/
public int hashCode()
{
//using the method generated by Eclipse, but streamlined a bit..
return (31 + numerator.hashCode())*31 + denominator.hashCode();
}

/**
* Returns a negative, zero, or positive number, indicating if this object
* is less than, equal to, or greater than f, respectively.
*/
public int compareTo(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");

//easy case: this and f have different signs
if(signum() != f.signum())
return signum() - f.signum();

//next easy case: this and f have the same denominator
if(denominator.equals(f.denominator))
return numerator.compareTo(f.numerator);

//not an easy case, so first make the denominators equal then compare the numerators
return numerator.multiply(f.denominator).compareTo(denominator.multiply(f.numerator));
}

/**
* Returns the smaller of this and f.
*/
public BigFraction min(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");

return (this.compareTo(f) <= 0 ? this : f);
}

/**
* Returns the maximum of this and f.
*/
public BigFraction max(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");

return (this.compareTo(f) >= 0 ? this : f);
}

/**
* Returns a positive BigFraction, greater than or equal to zero, and less than one.
*/
public static BigFraction random()
{
return new BigFraction(Math.random());
}

public final BigInteger getNumerator() { return numerator; }
public final BigInteger getDenominator() { return denominator; }

//implementation of Number class.  may cause overflow.
public byte   byteValue()   { return (byte) Math.max(Byte.MIN_VALUE,    Math.min(Byte.MAX_VALUE,    longValue())); }
public short  shortValue()  { return (short)Math.max(Short.MIN_VALUE,   Math.min(Short.MAX_VALUE,   longValue())); }
public int    intValue()    { return (int)  Math.max(Integer.MIN_VALUE, Math.min(Integer.MAX_VALUE, longValue())); }
public long   longValue()   { return Math.round(doubleValue()); }
public float  floatValue()  { return (float)doubleValue(); }

/**
* Returns a BigDecimal representation of this fraction.  If possible, the
* returned value will be exactly equal to the fraction.  If not, the BigDecimal
* will have a scale large enough to hold the same number of significant figures
* as both numerator and denominator, or the equivalent of a double-precision
* number, whichever is more.
*/
public BigDecimal toBigDecimal()
{
//Implementation note:  A fraction can be represented exactly in base-10 iff its
//denominator is of the form 2^a * 5^b, where a and b are nonnegative integers.
//(In other words, if there are no prime factors of the denominator except for
//2 and 5, or if the denominator is 1).  So to determine if this denominator is
//of this form, continually divide by 2 to get the number of 2's, and then
//continually divide by 5 to get the number of 5's.  Afterward, if the denominator
//is 1 then there are no other prime factors.

//Note: number of 2's is given by the number of trailing 0 bits in the number
int twos = denominator.getLowestSetBit();
BigInteger tmpDen = denominator.shiftRight(twos); // x / 2^n === x >> n

final BigInteger FIVE = BigInteger.valueOf(5);
int fives = 0;
BigInteger[] divMod = null;

//while(tmpDen % 5 == 0) { fives++; tmpDen /= 5; }
while(BigInteger.ZERO.equals((divMod = tmpDen.divideAndRemainder(FIVE))[1]))
{
fives++;
tmpDen = divMod[0];
}

if(BigInteger.ONE.equals(tmpDen))
{
//This fraction will terminate in base 10, so it can be represented exactly as
//a BigDecimal.  We would now like to make the fraction of the form
//unscaled / 10^scale.  We know that 2^x * 5^x = 10^x, and our denominator is
//in the form 2^twos * 5^fives.  So use max(twos, fives) as the scale, and
//multiply the numerator and deminator by the appropriate number of 2's or 5's
//such that the denominator is of the form 2^scale * 5^scale.  (Of course, we
//only have to actually multiply the numerator, since all we need for the
//BigDecimal constructor is the scale.
BigInteger unscaled = numerator;
int scale = Math.max(twos, fives);

if(twos < fives)
unscaled = unscaled.shiftLeft(fives - twos); //x * 2^n === x << n
else if (fives < twos)
unscaled = unscaled.multiply(FIVE.pow(twos - fives));

return new BigDecimal(unscaled, scale);
}

//else: this number will repeat infinitely in base-10.  So try to figure out
//a good number of significant digits.  Start with the number of digits required
//to represent the numerator and denominator in base-10, which is given by
//bitLength / log[2](10).  (bitLenth is the number of digits in base-2).
final double LG10 = 3.321928094887362; //Precomputed ln(10)/ln(2), a.k.a. log[2](10)
int precision = Math.max(numerator.bitLength(), denominator.bitLength());
precision = (int)Math.ceil(precision / LG10);

//If the precision is less than 18 digits, use 18 digits so that the number
//will be at least as accurate as a cast to a double.  For example, with
//the fraction 1/3, precision will be 1, giving a result of 0.3.  This is
//quite a bit different from what a user would expect.
if(precision < 18)
precision = 18;

}

/**
* Returns a BigDecimal representation of this fraction, with a given precision.
* @param precision  the number of significant figures to be used in the result.
*/
public BigDecimal toBigDecimal(int precision)
{
return new BigDecimal(numerator).divide(new BigDecimal(denominator), new MathContext(precision, RoundingMode.HALF_EVEN));
}

//--------------------------------------------------------------------------
//  PRIVATE FUNCTIONS
//--------------------------------------------------------------------------

/**
* Private constructor, used when you can be certain that the fraction is already in
* lowest terms.  No check is done to reduce numerator/denominator.  A check is still
* done to maintain a positive denominator.
*
* @param throwaway  unused variable, only here to signal to the compiler that this
*                   constructor should be used.
*/
private BigFraction(BigInteger numerator, BigInteger denominator, boolean throwaway)
{
if(denominator.signum() < 0)
{
this.numerator = numerator.negate();
this.denominator = denominator.negate();
}
else
{
this.numerator = numerator;
this.denominator = denominator;
}
}

}
``````

バージョン8（ hstoerrおかげで）：

• equals（）メソッドはcompareTo（）メソッドと一貫しています
``````final class Fraction extends Number {
private int numerator;
private int denominator;

public Fraction(int numerator, int denominator) {
if(denominator == 0) {
throw new IllegalArgumentException("denominator is zero");
}
if(denominator < 0) {
numerator *= -1;
denominator *= -1;
}
this.numerator = numerator;
this.denominator = denominator;
}

public Fraction(int numerator) {
this.numerator = numerator;
this.denominator = 1;
}

public int getNumerator() {
return this.numerator;
}

public int getDenominator() {
return this.denominator;
}

public byte byteValue() {
return (byte) this.doubleValue();
}

public double doubleValue() {
return ((double) numerator)/((double) denominator);
}

public float floatValue() {
return (float) this.doubleValue();
}

public int intValue() {
return (int) this.doubleValue();
}

public long longValue() {
return (long) this.doubleValue();
}

public short shortValue() {
return (short) this.doubleValue();
}

public boolean equals(Fraction frac) {
return this.compareTo(frac) == 0;
}

public int compareTo(Fraction frac) {
long t = this.getNumerator() * frac.getDenominator();
long f = frac.getNumerator() * this.getDenominator();
int result = 0;
if(t>f) {
result = 1;
}
else if(f>t) {
result = -1;
}
return result;
}
}
``````

• デイブレイ
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まあ、1つは、私はセッターを取り除き、分数を不変にします。

おそらく、さまざまなString形式で表現を取得するための方法を追加したり、減算したりする方法が必要になるでしょう。

I will need to order them from smallest to largest, so eventually I will need to represent them as a double also

Not strictly necessary. (In fact if you want to handle equality correctly, don't rely on double to work properly.) If b*d is positive, a/b < c/d if ad < bc. If there are negative integers involved, that can be handled appropriately...

I might rewrite as:

``````public int compareTo(Fraction frac)
{
// we are comparing this=a/b with frac=c/d
// by multiplying both sides by bd.
// If bd is positive, then a/b < c/d <=> ad < bc.
// If bd is negative, then a/b < c/d <=> ad > bc.
// If bd is 0, then you've got other problems (either b=0 or d=0)
int d = frac.getDenominator();
long ad = (long)this.numerator * d;
long bc = (long)this.denominator * frac.getNumerator();
return (diff > 0 ? 1 : (diff < 0 ? -1 : 0));
}
``````

The use of `long` here is to ensure there's not an overflow if you multiply two large `int` s. handle If you can guarantee that the denominator is always nonnegative (if it's negative, just negate both numerator and denominator), then you can get rid of having to check whether b*d is positive and save a few steps. I'm not sure what behavior you're looking for with zero denominator.

Not sure how performance compares to using doubles to compare. (that is, if you care about performance that much) Here's a test method I used to check. (Appears to work properly.)

``````public static void main(String[] args)
{
int a = Integer.parseInt(args[0]);
int b = Integer.parseInt(args[1]);
int c = Integer.parseInt(args[2]);
int d = Integer.parseInt(args[3]);
Fraction f1 = new Fraction(a,b);
Fraction f2 = new Fraction(c,d);
int rel = f1.compareTo(f2);
String relstr = "<=>";
System.out.println(a+"/"+b+" "+relstr.charAt(rel+1)+" "+c+"/"+d);
}
``````

(ps you might consider restructuring to implement `Comparable` or `Comparator` for your class.)

There are several ways to improve this or any value type:

• Make your class immutable , including making numerator and denominator final
• Automatically convert fractions to a canonical form , eg 2/4 -> 1/2
• Implement toString()
• Implement "public static Fraction valueOf(String s)" to convert from strings to fractions. Implement similar factory methods for converting from int, double, etc.
• Add constructor from whole numbers
• Override equals/hashCode
• Consider making Fraction an interface with an implementation that switches to BigInteger as necessary
• Consider sub-classing Number
• Consider including named constants for common values like 0 and 1
• Consider making it serializable
• Test for division by zero

Basically, take a look at the API for other value classes like Double , Integer and do what they do :)

how I would improve that code:

1. a constructor based on String Fraction(String s) //expect "number/number"
2. a copy constructor Fraction(Fraction copy)
3. override the clone method
4. implements the equals, toString and hashcode methods
5. implements the interface java.io.Serializable, Comparable
6. a method "double getDoubleValue()"
8. I would make that class as immutable (no setters)

Once you've created a fraction object why would you want to allow other objects to set the numerator or the denominator? I would think these should be read only. It makes the object immutable...

Also...setting the denominator to zero should throw an invalid argument exception (I don't know what it is in Java)

I'll third or fifth or whatever the recommendation for making your fraction immutable. I'd also recommend that you have it extend the Number class. I'd probably look at the Double class, since you're probably going to want to implement many of the same methods.

You should probably also implement Comparable<T> and Serializable since this behavior will probably be expected. Thus, you will need to implement compareTo(). You will also need to override equals() and I cannot stress strongly enough that you also override hashCode(). This might be one of the few cases though where you don't want compareTo() and equals() to be consistent since fractions reducable to each other are not necessarily equal.

Use Rational class from JScience library. It's the best thing for fractional arithmetic I seen in Java.

Initial remark:

Never write this:

``````if ( condition ) statement;
``````

This is much better

``````if ( condition ) { statement };
``````

Just create to create a good habit.

By making the class immutable as suggested, you can also take advantage of the double to perform the equals and hashCode and compareTo operations

Here's my quick dirty version:

``````public final class Fraction implements Comparable {

private final int numerator;
private final int denominator;
private final Double internal;

public static Fraction createFraction( int numerator, int denominator ) {
return new Fraction( numerator, denominator );
}

private Fraction(int numerator, int denominator) {
this.numerator   = numerator;
this.denominator = denominator;
this.internal = ((double) numerator)/((double) denominator);
}

public int getNumerator() {
return this.numerator;
}

public int getDenominator() {
return this.denominator;
}

private double doubleValue() {
return internal;
}

public int compareTo( Object o ) {
if ( o instanceof Fraction ) {
return internal.compareTo( ((Fraction)o).internal );
}
return 1;
}

public boolean equals( Object o ) {
if ( o instanceof Fraction ) {
return this.internal.equals( ((Fraction)o).internal );
}
return false;
}

public int hashCode() {
return internal.hashCode();
}

public String toString() {
return String.format("%d/%d", numerator, denominator );
}

public static void main( String [] args ) {
System.out.println( Fraction.createFraction( 1 , 2 ) ) ;
System.out.println( Fraction.createFraction( 1 , 2 ).hashCode() ) ;
System.out.println( Fraction.createFraction( 1 , 2 ).compareTo( Fraction.createFraction(2,4) ) ) ;
System.out.println( Fraction.createFraction( 1 , 2 ).equals( Fraction.createFraction(4,8) ) ) ;
System.out.println( Fraction.createFraction( 3 , 9 ).equals( Fraction.createFraction(1,3) ) ) ;
}

}
``````

About the static factory method, it may be useful later, if you subclass the Fraction to handle more complex things, or if you decide to use a pool for the most frequently used objects.

It may not be the case, I just wanted to point it out. :)

See Effective Java first item.

Even though you have the methods compareTo(), if you want to make use of utilities like Collections.sort(), then you should also implement Comparable.

``````public class Fraction extends Number implements Comparable<Fraction> {
...
}
``````

Also, for pretty display I recommend overriding toString()

``````public String toString() {
return this.getNumerator() + "/" + this.getDenominator();
}
``````

And finally, I'd make the class public so that you can use it from different packages.

For industry-grade Fraction/Rational implementation, I would implement it so it can represent NaN, positive infinity, negative infinity, and optionally negative zero with operational semantics exactly the same as the IEEE 754 standard states for floating point arithmetics (it also eases the conversion to/from floating point values). Plus, since comparison to zero, one, and the special values above only needs simple, but combined comparison of the numerator and denominator against 0 and 1 - i would add several isXXX and compareToXXX methods for ease of use (eg. eq0() would use numerator == 0 && denominator != 0 behind the scenes instead of letting the client to compare against a zero valued instance). Some statically predefined values (ZERO, ONE, TWO, TEN, ONE_TENTH, NAN, etc.) are also useful, since they appear at several places as constant values. This is the best way IMHO.

Tags

java   math   fractions