Best way to represent a fraction in Java?
It just so happens that I wrote a BigFraction class not too long ago, for Project Euler problems. It keeps a BigInteger numerator and denominator, so it'll never overflow. But it'll be a tad slow for a lot of operations that you know will never overflow.. anyway, use it if you want it. I've been dying to show this off somehow. :)
Edit: Latest and greatest version of this code, including unit tests is now hosted on GitHub and also available via Maven Central. I'm leaving my original code here so that this answer isn't just a link...
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.
*/
public BigFraction add(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
//n1/d1 + n2/d2 = (n1*d2 + d1*n2)/(d1*d2)
return new BigFraction(numerator.multiply(f.denominator).add(denominator.multiply(f.numerator)),
denominator.multiply(f.denominator));
}
/**
* Returns this + b.
*/
public BigFraction add(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");
//n1/d1 + n2 = (n1 + d1*n2)/d1
return new BigFraction(numerator.add(denominator.multiply(b)),
denominator, true);
}
/**
* Returns this + n.
*/
public BigFraction add(long n)
{
return add(BigInteger.valueOf(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(); }
public double doubleValue() { return toBigDecimal(18).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;
return toBigDecimal(precision);
}
/**
* 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;
}
}
}
I'm trying to work with proper fractions in Java.
Apache Commons Math has had a Fraction class for quite some time. Most times the answer to, "Boy I wish Java had something like X in the core library!" can be found under the umbrella of the Apache Commons library.
- Make it immutable;
- Make it canonical, meaning 6/4 becomes 3/2 (greatest common divisor algorithm is useful for this);
- Call it Rational, since what you're representing is a rational number;
- You could use
BigIntegerto store arbitrarilyy-precise values. If not that thenlong, which has an easier implementation; - Make the denominator always positive. Sign should be carried by the numerator;
- Extend
Number; - Implement
Comparable<T>; - Implement
equals()andhashCode(); - Add factory method for a number represented by a
String; - Add some convenience factory methods;
- Add a
toString(); and - Make it
Serializable.
In fact, try this on for size. It runs but may have some issues:
public class BigRational extends Number implements Comparable<BigRational>, Serializable {
public final static BigRational ZERO = new BigRational(BigInteger.ZERO, BigInteger.ONE);
private final static long serialVersionUID = 1099377265582986378L;
private final BigInteger numerator, denominator;
private BigRational(BigInteger numerator, BigInteger denominator) {
this.numerator = numerator;
this.denominator = denominator;
}
private static BigRational canonical(BigInteger numerator, BigInteger denominator, boolean checkGcd) {
if (denominator.signum() == 0) {
throw new IllegalArgumentException("denominator is zero");
}
if (numerator.signum() == 0) {
return ZERO;
}
if (denominator.signum() < 0) {
numerator = numerator.negate();
denominator = denominator.negate();
}
if (checkGcd) {
BigInteger gcd = numerator.gcd(denominator);
if (!gcd.equals(BigInteger.ONE)) {
numerator = numerator.divide(gcd);
denominator = denominator.divide(gcd);
}
}
return new BigRational(numerator, denominator);
}
public static BigRational getInstance(BigInteger numerator, BigInteger denominator) {
return canonical(numerator, denominator, true);
}
public static BigRational getInstance(long numerator, long denominator) {
return canonical(new BigInteger("" + numerator), new BigInteger("" + denominator), true);
}
public static BigRational getInstance(String numerator, String denominator) {
return canonical(new BigInteger(numerator), new BigInteger(denominator), true);
}
public static BigRational valueOf(String s) {
Pattern p = Pattern.compile("(-?\\d+)(?:.(\\d+)?)?0*(?:e(-?\\d+))?");
Matcher m = p.matcher(s);
if (!m.matches()) {
throw new IllegalArgumentException("Unknown format '" + s + "'");
}
// this translates 23.123e5 to 25,123 / 1000 * 10^5 = 2,512,300 / 1 (GCD)
String whole = m.group(1);
String decimal = m.group(2);
String exponent = m.group(3);
String n = whole;
// 23.123 => 23123
if (decimal != null) {
n += decimal;
}
BigInteger numerator = new BigInteger(n);
// exponent is an int because BigInteger.pow() takes an int argument
// it gets more difficult if exponent needs to be outside {-2 billion,2 billion}
int exp = exponent == null ? 0 : Integer.valueOf(exponent);
int decimalPlaces = decimal == null ? 0 : decimal.length();
exp -= decimalPlaces;
BigInteger denominator;
if (exp < 0) {
denominator = BigInteger.TEN.pow(-exp);
} else {
numerator = numerator.multiply(BigInteger.TEN.pow(exp));
denominator = BigInteger.ONE;
}
// done
return canonical(numerator, denominator, true);
}
// Comparable
public int compareTo(BigRational o) {
// note: this is a bit of cheat, relying on BigInteger.compareTo() returning
// -1, 0 or 1. For the more general contract of compareTo(), you'd need to do
// more checking
if (numerator.signum() != o.numerator.signum()) {
return numerator.signum() - o.numerator.signum();
} else {
// oddly BigInteger has gcd() but no lcm()
BigInteger i1 = numerator.multiply(o.denominator);
BigInteger i2 = o.numerator.multiply(denominator);
return i1.compareTo(i2); // expensive!
}
}
public BigRational add(BigRational o) {
if (o.numerator.signum() == 0) {
return this;
} else if (numerator.signum() == 0) {
return o;
} else if (denominator.equals(o.denominator)) {
return new BigRational(numerator.add(o.numerator), denominator);
} else {
return canonical(numerator.multiply(o.denominator).add(o.numerator.multiply(denominator)), denominator.multiply(o.denominator), true);
}
}
public BigRational multiply(BigRational o) {
if (numerator.signum() == 0 || o.numerator.signum( )== 0) {
return ZERO;
} else if (numerator.equals(o.denominator)) {
return canonical(o.numerator, denominator, true);
} else if (o.numerator.equals(denominator)) {
return canonical(numerator, o.denominator, true);
} else if (numerator.negate().equals(o.denominator)) {
return canonical(o.numerator.negate(), denominator, true);
} else if (o.numerator.negate().equals(denominator)) {
return canonical(numerator.negate(), o.denominator, true);
} else {
return canonical(numerator.multiply(o.numerator), denominator.multiply(o.denominator), true);
}
}
public BigInteger getNumerator() { return numerator; }
public BigInteger getDenominator() { return denominator; }
public boolean isInteger() { return numerator.signum() == 0 || denominator.equals(BigInteger.ONE); }
public BigRational negate() { return new BigRational(numerator.negate(), denominator); }
public BigRational invert() { return canonical(denominator, numerator, false); }
public BigRational abs() { return numerator.signum() < 0 ? negate() : this; }
public BigRational pow(int exp) { return canonical(numerator.pow(exp), denominator.pow(exp), true); }
public BigRational subtract(BigRational o) { return add(o.negate()); }
public BigRational divide(BigRational o) { return multiply(o.invert()); }
public BigRational min(BigRational o) { return compareTo(o) <= 0 ? this : o; }
public BigRational max(BigRational o) { return compareTo(o) >= 0 ? this : o; }
public BigDecimal toBigDecimal(int scale, RoundingMode roundingMode) {
return isInteger() ? new BigDecimal(numerator) : new BigDecimal(numerator).divide(new BigDecimal(denominator), scale, roundingMode);
}
// Number
public int intValue() { return isInteger() ? numerator.intValue() : numerator.divide(denominator).intValue(); }
public long longValue() { return isInteger() ? numerator.longValue() : numerator.divide(denominator).longValue(); }
public float floatValue() { return (float)doubleValue(); }
public double doubleValue() { return isInteger() ? numerator.doubleValue() : numerator.doubleValue() / denominator.doubleValue(); }
@Override
public String toString() { return isInteger() ? String.format("%,d", numerator) : String.format("%,d / %,d", numerator, denominator); }
@Override
public boolean equals(Object o) {
if (this == o) return true;
if (o == null || getClass() != o.getClass()) return false;
BigRational that = (BigRational) o;
if (denominator != null ? !denominator.equals(that.denominator) : that.denominator != null) return false;
if (numerator != null ? !numerator.equals(that.numerator) : that.numerator != null) return false;
return true;
}
@Override
public int hashCode() {
int result = numerator != null ? numerator.hashCode() : 0;
result = 31 * result + (denominator != null ? denominator.hashCode() : 0);
return result;
}
public static void main(String args[]) {
BigRational r1 = BigRational.valueOf("3.14e4");
BigRational r2 = BigRational.getInstance(111, 7);
dump("r1", r1);
dump("r2", r2);
dump("r1 + r2", r1.add(r2));
dump("r1 - r2", r1.subtract(r2));
dump("r1 * r2", r1.multiply(r2));
dump("r1 / r2", r1.divide(r2));
dump("r2 ^ 2", r2.pow(2));
}
public static void dump(String name, BigRational r) {
System.out.printf("%s = %s%n", name, r);
System.out.printf("%s.negate() = %s%n", name, r.negate());
System.out.printf("%s.invert() = %s%n", name, r.invert());
System.out.printf("%s.intValue() = %,d%n", name, r.intValue());
System.out.printf("%s.longValue() = %,d%n", name, r.longValue());
System.out.printf("%s.floatValue() = %,f%n", name, r.floatValue());
System.out.printf("%s.doubleValue() = %,f%n", name, r.doubleValue());
System.out.println();
}
}
Output is:
r1 = 31,400
r1.negate() = -31,400
r1.invert() = 1 / 31,400
r1.intValue() = 31,400
r1.longValue() = 31,400
r1.floatValue() = 31,400.000000
r1.doubleValue() = 31,400.000000
r2 = 111 / 7
r2.negate() = -111 / 7
r2.invert() = 7 / 111
r2.intValue() = 15
r2.longValue() = 15
r2.floatValue() = 15.857142
r2.doubleValue() = 15.857143
r1 + r2 = 219,911 / 7
r1 + r2.negate() = -219,911 / 7
r1 + r2.invert() = 7 / 219,911
r1 + r2.intValue() = 31,415
r1 + r2.longValue() = 31,415
r1 + r2.floatValue() = 31,415.857422
r1 + r2.doubleValue() = 31,415.857143
r1 - r2 = 219,689 / 7
r1 - r2.negate() = -219,689 / 7
r1 - r2.invert() = 7 / 219,689
r1 - r2.intValue() = 31,384
r1 - r2.longValue() = 31,384
r1 - r2.floatValue() = 31,384.142578
r1 - r2.doubleValue() = 31,384.142857
r1 * r2 = 3,485,400 / 7
r1 * r2.negate() = -3,485,400 / 7
r1 * r2.invert() = 7 / 3,485,400
r1 * r2.intValue() = 497,914
r1 * r2.longValue() = 497,914
r1 * r2.floatValue() = 497,914.281250
r1 * r2.doubleValue() = 497,914.285714
r1 / r2 = 219,800 / 111
r1 / r2.negate() = -219,800 / 111
r1 / r2.invert() = 111 / 219,800
r1 / r2.intValue() = 1,980
r1 / r2.longValue() = 1,980
r1 / r2.floatValue() = 1,980.180176
r1 / r2.doubleValue() = 1,980.180180
r2 ^ 2 = 12,321 / 49
r2 ^ 2.negate() = -12,321 / 49
r2 ^ 2.invert() = 49 / 12,321
r2 ^ 2.intValue() = 251
r2 ^ 2.longValue() = 251
r2 ^ 2.floatValue() = 251.448975
r2 ^ 2.doubleValue() = 251.448980