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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.fraction;
import java.io.Serializable;
import java.math.BigDecimal;
import java.math.BigInteger;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
/**
* Representation of a rational number without any overflow. This class is
* immutable.
*
* @since 2.0
*/
public class BigFraction
extends Number
implements FieldElement, Comparable, Serializable {
/** A fraction representing "2 / 1". */
public static final BigFraction TWO = new BigFraction(2);
/** A fraction representing "1". */
public static final BigFraction ONE = new BigFraction(1);
/** A fraction representing "0". */
public static final BigFraction ZERO = new BigFraction(0);
/** A fraction representing "-1 / 1". */
public static final BigFraction MINUS_ONE = new BigFraction(-1);
/** A fraction representing "4/5". */
public static final BigFraction FOUR_FIFTHS = new BigFraction(4, 5);
/** A fraction representing "1/5". */
public static final BigFraction ONE_FIFTH = new BigFraction(1, 5);
/** A fraction representing "1/2". */
public static final BigFraction ONE_HALF = new BigFraction(1, 2);
/** A fraction representing "1/4". */
public static final BigFraction ONE_QUARTER = new BigFraction(1, 4);
/** A fraction representing "1/3". */
public static final BigFraction ONE_THIRD = new BigFraction(1, 3);
/** A fraction representing "3/5". */
public static final BigFraction THREE_FIFTHS = new BigFraction(3, 5);
/** A fraction representing "3/4". */
public static final BigFraction THREE_QUARTERS = new BigFraction(3, 4);
/** A fraction representing "2/5". */
public static final BigFraction TWO_FIFTHS = new BigFraction(2, 5);
/** A fraction representing "2/4". */
public static final BigFraction TWO_QUARTERS = new BigFraction(2, 4);
/** A fraction representing "2/3". */
public static final BigFraction TWO_THIRDS = new BigFraction(2, 3);
/** Serializable version identifier. */
private static final long serialVersionUID = -5630213147331578515L;
/** BigInteger representation of 100. */
private static final BigInteger ONE_HUNDRED = BigInteger.valueOf(100);
/** The numerator. */
private final BigInteger numerator;
/** The denominator. */
private final BigInteger denominator;
/**
*
* Create a {@link BigFraction} equivalent to the passed {@code BigInteger}, ie
* "num / 1".
*
*
* @param num
* the numerator.
*/
public BigFraction(final BigInteger num) {
this(num, BigInteger.ONE);
}
/**
* Create a {@link BigFraction} given the numerator and denominator as
* {@code BigInteger}. The {@link BigFraction} is reduced to lowest terms.
*
* @param num the numerator, must not be {@code null}.
* @param den the denominator, must not be {@code null}.
* @throws ZeroException if the denominator is zero.
* @throws NullArgumentException if either of the arguments is null
*/
public BigFraction(BigInteger num, BigInteger den) {
MathUtils.checkNotNull(num, LocalizedFormats.NUMERATOR);
MathUtils.checkNotNull(den, LocalizedFormats.DENOMINATOR);
if (den.signum() == 0) {
throw new ZeroException(LocalizedFormats.ZERO_DENOMINATOR);
}
if (num.signum() == 0) {
numerator = BigInteger.ZERO;
denominator = BigInteger.ONE;
} else {
// reduce numerator and denominator by greatest common denominator
final BigInteger gcd = num.gcd(den);
if (BigInteger.ONE.compareTo(gcd) < 0) {
num = num.divide(gcd);
den = den.divide(gcd);
}
// move sign to numerator
if (den.signum() == -1) {
num = num.negate();
den = den.negate();
}
// store the values in the final fields
numerator = num;
denominator = den;
}
}
/**
* Create a fraction given the double value.
*
* This constructor behaves differently from
* {@link #BigFraction(double, double, int)}. It converts the double value
* exactly, considering its internal bits representation. This works for all
* values except NaN and infinities and does not requires any loop or
* convergence threshold.
*
*
* Since this conversion is exact and since double numbers are sometimes
* approximated, the fraction created may seem strange in some cases. For example,
* calling new BigFraction(1.0 / 3.0) does not create
* the fraction 1/3, but the fraction 6004799503160661 / 18014398509481984
* because the double number passed to the constructor is not exactly 1/3
* (this number cannot be stored exactly in IEEE754).
*
* @see #BigFraction(double, double, int)
* @param value the double value to convert to a fraction.
* @exception MathIllegalArgumentException if value is NaN or infinite
*/
public BigFraction(final double value) throws MathIllegalArgumentException {
if (Double.isNaN(value)) {
throw new MathIllegalArgumentException(LocalizedFormats.NAN_VALUE_CONVERSION);
}
if (Double.isInfinite(value)) {
throw new MathIllegalArgumentException(LocalizedFormats.INFINITE_VALUE_CONVERSION);
}
// compute m and k such that value = m * 2^k
final long bits = Double.doubleToLongBits(value);
final long sign = bits & 0x8000000000000000L;
final long exponent = bits & 0x7ff0000000000000L;
long m = bits & 0x000fffffffffffffL;
if (exponent != 0) {
// this was a normalized number, add the implicit most significant bit
m |= 0x0010000000000000L;
}
if (sign != 0) {
m = -m;
}
int k = ((int) (exponent >> 52)) - 1075;
while (((m & 0x001ffffffffffffeL) != 0) && ((m & 0x1) == 0)) {
m >>= 1;
++k;
}
if (k < 0) {
numerator = BigInteger.valueOf(m);
denominator = BigInteger.ZERO.flipBit(-k);
} else {
numerator = BigInteger.valueOf(m).multiply(BigInteger.ZERO.flipBit(k));
denominator = BigInteger.ONE;
}
}
/**
* Create a fraction given the double value and maximum error allowed.
*
* References:
*
* -
* Continued Fraction equations (11) and (22)-(26)
*
*
*
* @param value
* the double value to convert to a fraction.
* @param epsilon
* maximum error allowed. The resulting fraction is within
* epsilon of value, in absolute terms.
* @param maxIterations
* maximum number of convergents.
* @throws FractionConversionException
* if the continued fraction failed to converge.
* @see #BigFraction(double)
*/
public BigFraction(final double value, final double epsilon,
final int maxIterations)
throws FractionConversionException {
this(value, epsilon, Integer.MAX_VALUE, maxIterations);
}
/**
* Create a fraction given the double value and either the maximum error
* allowed or the maximum number of denominator digits.
*
*
* NOTE: This constructor is called with EITHER - a valid epsilon value and
* the maxDenominator set to Integer.MAX_VALUE (that way the maxDenominator
* has no effect). OR - a valid maxDenominator value and the epsilon value
* set to zero (that way epsilon only has effect if there is an exact match
* before the maxDenominator value is reached).
*
*
*
* It has been done this way so that the same code can be (re)used for both
* scenarios. However this could be confusing to users if it were part of
* the public API and this constructor should therefore remain PRIVATE.
*
*
* See JIRA issue ticket MATH-181 for more details:
*
* https://issues.apache.org/jira/browse/MATH-181
*
* @param value
* the double value to convert to a fraction.
* @param epsilon
* maximum error allowed. The resulting fraction is within
* epsilon of value, in absolute terms.
* @param maxDenominator
* maximum denominator value allowed.
* @param maxIterations
* maximum number of convergents.
* @throws FractionConversionException
* if the continued fraction failed to converge.
*/
private BigFraction(final double value, final double epsilon,
final int maxDenominator, int maxIterations)
throws FractionConversionException {
long overflow = Integer.MAX_VALUE;
double r0 = value;
long a0 = (long) FastMath.floor(r0);
if (FastMath.abs(a0) > overflow) {
throw new FractionConversionException(value, a0, 1l);
}
// check for (almost) integer arguments, which should not go
// to iterations.
if (FastMath.abs(a0 - value) < epsilon) {
numerator = BigInteger.valueOf(a0);
denominator = BigInteger.ONE;
return;
}
long p0 = 1;
long q0 = 0;
long p1 = a0;
long q1 = 1;
long p2 = 0;
long q2 = 1;
int n = 0;
boolean stop = false;
do {
++n;
final double r1 = 1.0 / (r0 - a0);
final long a1 = (long) FastMath.floor(r1);
p2 = (a1 * p1) + p0;
q2 = (a1 * q1) + q0;
if ((p2 > overflow) || (q2 > overflow)) {
// in maxDenominator mode, if the last fraction was very close to the actual value
// q2 may overflow in the next iteration; in this case return the last one.
if (epsilon == 0.0 && FastMath.abs(q1) < maxDenominator) {
break;
}
throw new FractionConversionException(value, p2, q2);
}
final double convergent = (double) p2 / (double) q2;
if ((n < maxIterations) &&
(FastMath.abs(convergent - value) > epsilon) &&
(q2 < maxDenominator)) {
p0 = p1;
p1 = p2;
q0 = q1;
q1 = q2;
a0 = a1;
r0 = r1;
} else {
stop = true;
}
} while (!stop);
if (n >= maxIterations) {
throw new FractionConversionException(value, maxIterations);
}
if (q2 < maxDenominator) {
numerator = BigInteger.valueOf(p2);
denominator = BigInteger.valueOf(q2);
} else {
numerator = BigInteger.valueOf(p1);
denominator = BigInteger.valueOf(q1);
}
}
/**
* Create a fraction given the double value and maximum denominator.
*
* References:
*
* -
* Continued Fraction equations (11) and (22)-(26)
*
*
*
* @param value
* the double value to convert to a fraction.
* @param maxDenominator
* The maximum allowed value for denominator.
* @throws FractionConversionException
* if the continued fraction failed to converge.
*/
public BigFraction(final double value, final int maxDenominator)
throws FractionConversionException {
this(value, 0, maxDenominator, 100);
}
/**
*
* Create a {@link BigFraction} equivalent to the passed {@code int}, ie
* "num / 1".
*
*
* @param num
* the numerator.
*/
public BigFraction(final int num) {
this(BigInteger.valueOf(num), BigInteger.ONE);
}
/**
*
* Create a {@link BigFraction} given the numerator and denominator as simple
* {@code int}. The {@link BigFraction} is reduced to lowest terms.
*
*
* @param num
* the numerator.
* @param den
* the denominator.
*/
public BigFraction(final int num, final int den) {
this(BigInteger.valueOf(num), BigInteger.valueOf(den));
}
/**
*
* Create a {@link BigFraction} equivalent to the passed long, ie "num / 1".
*
*
* @param num
* the numerator.
*/
public BigFraction(final long num) {
this(BigInteger.valueOf(num), BigInteger.ONE);
}
/**
*
* Create a {@link BigFraction} given the numerator and denominator as simple
* {@code long}. The {@link BigFraction} is reduced to lowest terms.
*
*
* @param num
* the numerator.
* @param den
* the denominator.
*/
public BigFraction(final long num, final long den) {
this(BigInteger.valueOf(num), BigInteger.valueOf(den));
}
/**
*
* Creates a BigFraction instance with the 2 parts of a fraction
* Y/Z.
*
*
*
* Any negative signs are resolved to be on the numerator.
*
*
* @param numerator
* the numerator, for example the three in 'three sevenths'.
* @param denominator
* the denominator, for example the seven in 'three sevenths'.
* @return a new fraction instance, with the numerator and denominator
* reduced.
* @throws ArithmeticException
* if the denominator is zero.
*/
public static BigFraction getReducedFraction(final int numerator,
final int denominator) {
if (numerator == 0) {
return ZERO; // normalize zero.
}
return new BigFraction(numerator, denominator);
}
/**
*
* Returns the absolute value of this {@link BigFraction}.
*
*
* @return the absolute value as a {@link BigFraction}.
*/
public BigFraction abs() {
return (numerator.signum() == 1) ? this : negate();
}
/**
*
* Adds the value of this fraction to the passed {@link BigInteger},
* returning the result in reduced form.
*
*
* @param bg
* the {@link BigInteger} to add, must'nt be null.
* @return a BigFraction instance with the resulting values.
* @throws NullArgumentException
* if the {@link BigInteger} is null.
*/
public BigFraction add(final BigInteger bg) throws NullArgumentException {
MathUtils.checkNotNull(bg);
if (numerator.signum() == 0) {
return new BigFraction(bg);
}
if (bg.signum() == 0) {
return this;
}
return new BigFraction(numerator.add(denominator.multiply(bg)), denominator);
}
/**
*
* Adds the value of this fraction to the passed {@code integer}, returning
* the result in reduced form.
*
*
* @param i
* the {@code integer} to add.
* @return a BigFraction instance with the resulting values.
*/
public BigFraction add(final int i) {
return add(BigInteger.valueOf(i));
}
/**
*
* Adds the value of this fraction to the passed {@code long}, returning
* the result in reduced form.
*
*
* @param l
* the {@code long} to add.
* @return a BigFraction instance with the resulting values.
*/
public BigFraction add(final long l) {
return add(BigInteger.valueOf(l));
}
/**
*
* Adds the value of this fraction to another, returning the result in
* reduced form.
*
*
* @param fraction
* the {@link BigFraction} to add, must not be null.
* @return a {@link BigFraction} instance with the resulting values.
* @throws NullArgumentException if the {@link BigFraction} is {@code null}.
*/
public BigFraction add(final BigFraction fraction) {
if (fraction == null) {
throw new NullArgumentException(LocalizedFormats.FRACTION);
}
if (fraction.numerator.signum() == 0) {
return this;
}
if (numerator.signum() == 0) {
return fraction;
}
BigInteger num = null;
BigInteger den = null;
if (denominator.equals(fraction.denominator)) {
num = numerator.add(fraction.numerator);
den = denominator;
} else {
num = (numerator.multiply(fraction.denominator)).add((fraction.numerator).multiply(denominator));
den = denominator.multiply(fraction.denominator);
}
if (num.signum() == 0) {
return ZERO;
}
return new BigFraction(num, den);
}
/**
*
* Gets the fraction as a BigDecimal. This calculates the
* fraction as the numerator divided by denominator.
*
*
* @return the fraction as a BigDecimal.
* @throws ArithmeticException
* if the exact quotient does not have a terminating decimal
* expansion.
* @see BigDecimal
*/
public BigDecimal bigDecimalValue() {
return new BigDecimal(numerator).divide(new BigDecimal(denominator));
}
/**
*
* Gets the fraction as a BigDecimal following the passed
* rounding mode. This calculates the fraction as the numerator divided by
* denominator.
*
*
* @param roundingMode
* rounding mode to apply. see {@link BigDecimal} constants.
* @return the fraction as a BigDecimal.
* @throws IllegalArgumentException
* if {@code roundingMode} does not represent a valid rounding
* mode.
* @see BigDecimal
*/
public BigDecimal bigDecimalValue(final int roundingMode) {
return new BigDecimal(numerator).divide(new BigDecimal(denominator), roundingMode);
}
/**
*
* Gets the fraction as a BigDecimal following the passed scale
* and rounding mode. This calculates the fraction as the numerator divided
* by denominator.
*
*
* @param scale
* scale of the BigDecimal quotient to be returned.
* see {@link BigDecimal} for more information.
* @param roundingMode
* rounding mode to apply. see {@link BigDecimal} constants.
* @return the fraction as a BigDecimal.
* @see BigDecimal
*/
public BigDecimal bigDecimalValue(final int scale, final int roundingMode) {
return new BigDecimal(numerator).divide(new BigDecimal(denominator), scale, roundingMode);
}
/**
*
* Compares this object to another based on size.
*
*
* @param object
* the object to compare to, must not be null.
* @return -1 if this is less than {@code object}, +1 if this is greater
* than {@code object}, 0 if they are equal.
* @see java.lang.Comparable#compareTo(java.lang.Object)
*/
public int compareTo(final BigFraction object) {
int lhsSigNum = numerator.signum();
int rhsSigNum = object.numerator.signum();
if (lhsSigNum != rhsSigNum) {
return (lhsSigNum > rhsSigNum) ? 1 : -1;
}
if (lhsSigNum == 0) {
return 0;
}
BigInteger nOd = numerator.multiply(object.denominator);
BigInteger dOn = denominator.multiply(object.numerator);
return nOd.compareTo(dOn);
}
/**
*
* Divide the value of this fraction by the passed {@code BigInteger},
* ie {@code this * 1 / bg}, returning the result in reduced form.
*
*
* @param bg the {@code BigInteger} to divide by, must not be {@code null}
* @return a {@link BigFraction} instance with the resulting values
* @throws NullArgumentException if the {@code BigInteger} is {@code null}
* @throws MathArithmeticException if the fraction to divide by is zero
*/
public BigFraction divide(final BigInteger bg) {
if (bg == null) {
throw new NullArgumentException(LocalizedFormats.FRACTION);
}
if (bg.signum() == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
}
if (numerator.signum() == 0) {
return ZERO;
}
return new BigFraction(numerator, denominator.multiply(bg));
}
/**
*
* Divide the value of this fraction by the passed {@code int}, ie
* {@code this * 1 / i}, returning the result in reduced form.
*
*
* @param i the {@code int} to divide by
* @return a {@link BigFraction} instance with the resulting values
* @throws MathArithmeticException if the fraction to divide by is zero
*/
public BigFraction divide(final int i) {
return divide(BigInteger.valueOf(i));
}
/**
*
* Divide the value of this fraction by the passed {@code long}, ie
* {@code this * 1 / l}, returning the result in reduced form.
*
*
* @param l the {@code long} to divide by
* @return a {@link BigFraction} instance with the resulting values
* @throws MathArithmeticException if the fraction to divide by is zero
*/
public BigFraction divide(final long l) {
return divide(BigInteger.valueOf(l));
}
/**
*
* Divide the value of this fraction by another, returning the result in
* reduced form.
*
*
* @param fraction Fraction to divide by, must not be {@code null}.
* @return a {@link BigFraction} instance with the resulting values.
* @throws NullArgumentException if the {@code fraction} is {@code null}.
* @throws MathArithmeticException if the fraction to divide by is zero
*/
public BigFraction divide(final BigFraction fraction) {
if (fraction == null) {
throw new NullArgumentException(LocalizedFormats.FRACTION);
}
if (fraction.numerator.signum() == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
}
if (numerator.signum() == 0) {
return ZERO;
}
return multiply(fraction.reciprocal());
}
/**
*
* Gets the fraction as a {@code double}. This calculates the fraction as
* the numerator divided by denominator.
*
*
* @return the fraction as a {@code double}
* @see java.lang.Number#doubleValue()
*/
@Override
public double doubleValue() {
double result = numerator.doubleValue() / denominator.doubleValue();
if (Double.isNaN(result)) {
// Numerator and/or denominator must be out of range:
// Calculate how far to shift them to put them in range.
int shift = FastMath.max(numerator.bitLength(),
denominator.bitLength()) - FastMath.getExponent(Double.MAX_VALUE);
result = numerator.shiftRight(shift).doubleValue() /
denominator.shiftRight(shift).doubleValue();
}
return result;
}
/**
*
* Test for the equality of two fractions. If the lowest term numerator and
* denominators are the same for both fractions, the two fractions are
* considered to be equal.
*
*
* @param other
* fraction to test for equality to this fraction, can be
* null.
* @return true if two fractions are equal, false if object is
* null, not an instance of {@link BigFraction}, or not
* equal to this fraction instance.
* @see java.lang.Object#equals(java.lang.Object)
*/
@Override
public boolean equals(final Object other) {
boolean ret = false;
if (this == other) {
ret = true;
} else if (other instanceof BigFraction) {
BigFraction rhs = ((BigFraction) other).reduce();
BigFraction thisOne = this.reduce();
ret = thisOne.numerator.equals(rhs.numerator) && thisOne.denominator.equals(rhs.denominator);
}
return ret;
}
/**
*
* Gets the fraction as a {@code float}. This calculates the fraction as
* the numerator divided by denominator.
*
*
* @return the fraction as a {@code float}.
* @see java.lang.Number#floatValue()
*/
@Override
public float floatValue() {
float result = numerator.floatValue() / denominator.floatValue();
if (Double.isNaN(result)) {
// Numerator and/or denominator must be out of range:
// Calculate how far to shift them to put them in range.
int shift = FastMath.max(numerator.bitLength(),
denominator.bitLength()) - FastMath.getExponent(Float.MAX_VALUE);
result = numerator.shiftRight(shift).floatValue() /
denominator.shiftRight(shift).floatValue();
}
return result;
}
/**
*
* Access the denominator as a BigInteger.
*
*
* @return the denominator as a BigInteger.
*/
public BigInteger getDenominator() {
return denominator;
}
/**
*
* Access the denominator as a {@code int}.
*
*
* @return the denominator as a {@code int}.
*/
public int getDenominatorAsInt() {
return denominator.intValue();
}
/**
*
* Access the denominator as a {@code long}.
*
*
* @return the denominator as a {@code long}.
*/
public long getDenominatorAsLong() {
return denominator.longValue();
}
/**
*
* Access the numerator as a BigInteger.
*
*
* @return the numerator as a BigInteger.
*/
public BigInteger getNumerator() {
return numerator;
}
/**
*
* Access the numerator as a {@code int}.
*
*
* @return the numerator as a {@code int}.
*/
public int getNumeratorAsInt() {
return numerator.intValue();
}
/**
*
* Access the numerator as a {@code long}.
*
*
* @return the numerator as a {@code long}.
*/
public long getNumeratorAsLong() {
return numerator.longValue();
}
/**
*
* Gets a hashCode for the fraction.
*
*
* @return a hash code value for this object.
* @see java.lang.Object#hashCode()
*/
@Override
public int hashCode() {
return 37 * (37 * 17 + numerator.hashCode()) + denominator.hashCode();
}
/**
*
* Gets the fraction as an {@code int}. This returns the whole number part
* of the fraction.
*
*
* @return the whole number fraction part.
* @see java.lang.Number#intValue()
*/
@Override
public int intValue() {
return numerator.divide(denominator).intValue();
}
/**
*
* Gets the fraction as a {@code long}. This returns the whole number part
* of the fraction.
*
*
* @return the whole number fraction part.
* @see java.lang.Number#longValue()
*/
@Override
public long longValue() {
return numerator.divide(denominator).longValue();
}
/**
*
* Multiplies the value of this fraction by the passed
* BigInteger, returning the result in reduced form.
*
*
* @param bg the {@code BigInteger} to multiply by.
* @return a {@code BigFraction} instance with the resulting values.
* @throws NullArgumentException if {@code bg} is {@code null}.
*/
public BigFraction multiply(final BigInteger bg) {
if (bg == null) {
throw new NullArgumentException();
}
if (numerator.signum() == 0 || bg.signum() == 0) {
return ZERO;
}
return new BigFraction(bg.multiply(numerator), denominator);
}
/**
*
* Multiply the value of this fraction by the passed {@code int}, returning
* the result in reduced form.
*
*
* @param i
* the {@code int} to multiply by.
* @return a {@link BigFraction} instance with the resulting values.
*/
public BigFraction multiply(final int i) {
if (i == 0 || numerator.signum() == 0) {
return ZERO;
}
return multiply(BigInteger.valueOf(i));
}
/**
*
* Multiply the value of this fraction by the passed {@code long},
* returning the result in reduced form.
*
*
* @param l
* the {@code long} to multiply by.
* @return a {@link BigFraction} instance with the resulting values.
*/
public BigFraction multiply(final long l) {
if (l == 0 || numerator.signum() == 0) {
return ZERO;
}
return multiply(BigInteger.valueOf(l));
}
/**
*
* Multiplies the value of this fraction by another, returning the result in
* reduced form.
*
*
* @param fraction Fraction to multiply by, must not be {@code null}.
* @return a {@link BigFraction} instance with the resulting values.
* @throws NullArgumentException if {@code fraction} is {@code null}.
*/
public BigFraction multiply(final BigFraction fraction) {
if (fraction == null) {
throw new NullArgumentException(LocalizedFormats.FRACTION);
}
if (numerator.signum() == 0 ||
fraction.numerator.signum() == 0) {
return ZERO;
}
return new BigFraction(numerator.multiply(fraction.numerator),
denominator.multiply(fraction.denominator));
}
/**
*
* Return the additive inverse of this fraction, returning the result in
* reduced form.
*
*
* @return the negation of this fraction.
*/
public BigFraction negate() {
return new BigFraction(numerator.negate(), denominator);
}
/**
*
* Gets the fraction percentage as a {@code double}. This calculates the
* fraction as the numerator divided by denominator multiplied by 100.
*
*
* @return the fraction percentage as a {@code double}.
*/
public double percentageValue() {
return multiply(ONE_HUNDRED).doubleValue();
}
/**
*
* Returns a {@code BigFraction} whose value is
* {@code (thisexponent)}, returning the result in reduced form.
*
*
* @param exponent
* exponent to which this {@code BigFraction} is to be
* raised.
* @return thisexponent.
*/
public BigFraction pow(final int exponent) {
if (exponent == 0) {
return ONE;
}
if (numerator.signum() == 0) {
return this;
}
if (exponent < 0) {
return new BigFraction(denominator.pow(-exponent), numerator.pow(-exponent));
}
return new BigFraction(numerator.pow(exponent), denominator.pow(exponent));
}
/**
*
* Returns a BigFraction whose value is
* (thisexponent), returning the result in reduced form.
*
*
* @param exponent
* exponent to which this BigFraction is to be raised.
* @return thisexponent as a BigFraction.
*/
public BigFraction pow(final long exponent) {
if (exponent == 0) {
return ONE;
}
if (numerator.signum() == 0) {
return this;
}
if (exponent < 0) {
return new BigFraction(ArithmeticUtils.pow(denominator, -exponent),
ArithmeticUtils.pow(numerator, -exponent));
}
return new BigFraction(ArithmeticUtils.pow(numerator, exponent),
ArithmeticUtils.pow(denominator, exponent));
}
/**
*
* Returns a BigFraction whose value is
* (thisexponent), returning the result in reduced form.
*
*
* @param exponent
* exponent to which this BigFraction is to be raised.
* @return thisexponent as a BigFraction.
*/
public BigFraction pow(final BigInteger exponent) {
if (exponent.signum() == 0) {
return ONE;
}
if (numerator.signum() == 0) {
return this;
}
if (exponent.signum() == -1) {
final BigInteger eNeg = exponent.negate();
return new BigFraction(ArithmeticUtils.pow(denominator, eNeg),
ArithmeticUtils.pow(numerator, eNeg));
}
return new BigFraction(ArithmeticUtils.pow(numerator, exponent),
ArithmeticUtils.pow(denominator, exponent));
}
/**
*
* Returns a double whose value is
* (thisexponent), returning the result in reduced form.
*
*
* @param exponent
* exponent to which this BigFraction is to be raised.
* @return thisexponent.
*/
public double pow(final double exponent) {
return FastMath.pow(numerator.doubleValue(), exponent) /
FastMath.pow(denominator.doubleValue(), exponent);
}
/**
*
* Return the multiplicative inverse of this fraction.
*
*
* @return the reciprocal fraction.
*/
public BigFraction reciprocal() {
return new BigFraction(denominator, numerator);
}
/**
*
* Reduce this BigFraction to its lowest terms.
*
*
* @return the reduced BigFraction. It doesn't change anything if
* the fraction can be reduced.
*/
public BigFraction reduce() {
final BigInteger gcd = numerator.gcd(denominator);
if (BigInteger.ONE.compareTo(gcd) < 0) {
return new BigFraction(numerator.divide(gcd), denominator.divide(gcd));
} else {
return this;
}
}
/**
*
* Subtracts the value of an {@link BigInteger} from the value of this
* {@code BigFraction}, returning the result in reduced form.
*
*
* @param bg the {@link BigInteger} to subtract, cannot be {@code null}.
* @return a {@code BigFraction} instance with the resulting values.
* @throws NullArgumentException if the {@link BigInteger} is {@code null}.
*/
public BigFraction subtract(final BigInteger bg) {
if (bg == null) {
throw new NullArgumentException();
}
if (bg.signum() == 0) {
return this;
}
if (numerator.signum() == 0) {
return new BigFraction(bg.negate());
}
return new BigFraction(numerator.subtract(denominator.multiply(bg)), denominator);
}
/**
*
* Subtracts the value of an {@code integer} from the value of this
* {@code BigFraction}, returning the result in reduced form.
*
*
* @param i the {@code integer} to subtract.
* @return a {@code BigFraction} instance with the resulting values.
*/
public BigFraction subtract(final int i) {
return subtract(BigInteger.valueOf(i));
}
/**
*
* Subtracts the value of a {@code long} from the value of this
* {@code BigFraction}, returning the result in reduced form.
*
*
* @param l the {@code long} to subtract.
* @return a {@code BigFraction} instance with the resulting values.
*/
public BigFraction subtract(final long l) {
return subtract(BigInteger.valueOf(l));
}
/**
*
* Subtracts the value of another fraction from the value of this one,
* returning the result in reduced form.
*
*
* @param fraction {@link BigFraction} to subtract, must not be {@code null}.
* @return a {@link BigFraction} instance with the resulting values
* @throws NullArgumentException if the {@code fraction} is {@code null}.
*/
public BigFraction subtract(final BigFraction fraction) {
if (fraction == null) {
throw new NullArgumentException(LocalizedFormats.FRACTION);
}
if (fraction.numerator.signum() == 0) {
return this;
}
if (numerator.signum() == 0) {
return fraction.negate();
}
BigInteger num = null;
BigInteger den = null;
if (denominator.equals(fraction.denominator)) {
num = numerator.subtract(fraction.numerator);
den = denominator;
} else {
num = (numerator.multiply(fraction.denominator)).subtract((fraction.numerator).multiply(denominator));
den = denominator.multiply(fraction.denominator);
}
return new BigFraction(num, den);
}
/**
*
* Returns the String representing this fraction, ie
* "num / dem" or just "num" if the denominator is one.
*
*
* @return a string representation of the fraction.
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
String str = null;
if (BigInteger.ONE.equals(denominator)) {
str = numerator.toString();
} else if (BigInteger.ZERO.equals(numerator)) {
str = "0";
} else {
str = numerator + " / " + denominator;
}
return str;
}
/** {@inheritDoc} */
public BigFractionField getField() {
return BigFractionField.getInstance();
}
}