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Posted to commits@commons.apache.org by ra...@apache.org on 2017/02/06 12:52:24 UTC
[03/13] commons-numbers git commit: NUMBERS-6: Create structure for
fraction module within commons-numbers.
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/ca71f355/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/AbstractFormat.java
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diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/AbstractFormat.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/AbstractFormat.java
new file mode 100644
index 0000000..b77b522
--- /dev/null
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/AbstractFormat.java
@@ -0,0 +1,206 @@
+/*
+ * 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.numbers.fraction;
+
+import java.io.Serializable;
+import java.text.FieldPosition;
+import java.text.NumberFormat;
+import java.text.ParsePosition;
+import java.util.Locale;
+
+/**
+ * Common part shared by both {@link FractionFormat} and {@link BigFractionFormat}.
+ * @since 2.0
+ */
+public abstract class AbstractFormat extends NumberFormat implements Serializable {
+
+ /** Serializable version identifier. */
+ private static final long serialVersionUID = -6981118387974191891L;
+
+ /** The format used for the denominator. */
+ private NumberFormat denominatorFormat;
+
+ /** The format used for the numerator. */
+ private NumberFormat numeratorFormat;
+
+ /**
+ * Create an improper formatting instance with the default number format
+ * for the numerator and denominator.
+ */
+ protected AbstractFormat() {
+ this(getDefaultNumberFormat());
+ }
+
+ /**
+ * Create an improper formatting instance with a custom number format for
+ * both the numerator and denominator.
+ * @param format the custom format for both the numerator and denominator.
+ */
+ protected AbstractFormat(final NumberFormat format) {
+ this(format, (NumberFormat) format.clone());
+ }
+
+ /**
+ * Create an improper formatting instance with a custom number format for
+ * the numerator and a custom number format for the denominator.
+ * @param numeratorFormat the custom format for the numerator.
+ * @param denominatorFormat the custom format for the denominator.
+ */
+ protected AbstractFormat(final NumberFormat numeratorFormat,
+ final NumberFormat denominatorFormat) {
+ this.numeratorFormat = numeratorFormat;
+ this.denominatorFormat = denominatorFormat;
+ }
+
+ /**
+ * Create a default number format. The default number format is based on
+ * {@link NumberFormat#getNumberInstance(java.util.Locale)}. The only
+ * customization is the maximum number of BigFraction digits, which is set to 0.
+ * @return the default number format.
+ */
+ protected static NumberFormat getDefaultNumberFormat() {
+ return getDefaultNumberFormat(Locale.getDefault());
+ }
+
+ /**
+ * Create a default number format. The default number format is based on
+ * {@link NumberFormat#getNumberInstance(java.util.Locale)}. The only
+ * customization is the maximum number of BigFraction digits, which is set to 0.
+ * @param locale the specific locale used by the format.
+ * @return the default number format specific to the given locale.
+ */
+ protected static NumberFormat getDefaultNumberFormat(final Locale locale) {
+ final NumberFormat nf = NumberFormat.getNumberInstance(locale);
+ nf.setMaximumFractionDigits(0);
+ nf.setParseIntegerOnly(true);
+ return nf;
+ }
+
+ /**
+ * Access the denominator format.
+ * @return the denominator format.
+ */
+ public NumberFormat getDenominatorFormat() {
+ return denominatorFormat;
+ }
+
+ /**
+ * Access the numerator format.
+ * @return the numerator format.
+ */
+ public NumberFormat getNumeratorFormat() {
+ return numeratorFormat;
+ }
+
+ /**
+ * Modify the denominator format.
+ * @param format the new denominator format value.
+ * @throws NullPointerException if {@code format} is {@code null}.
+ */
+ public void setDenominatorFormat(final NumberFormat format) {
+ if (format == null) {
+ throw new NullPointerException("denominator format");
+ }
+ this.denominatorFormat = format;
+ }
+
+ /**
+ * Modify the numerator format.
+ * @param format the new numerator format value.
+ * @throws NullPointerException if {@code format} is {@code null}.
+ */
+ public void setNumeratorFormat(final NumberFormat format) {
+ if (format == null) {
+ throw new NullPointerException("numerator format");
+ }
+ this.numeratorFormat = format;
+ }
+
+ /**
+ * Parses <code>source</code> until a non-whitespace character is found.
+ * @param source the string to parse
+ * @param pos input/output parsing parameter. On output, <code>pos</code>
+ * holds the index of the next non-whitespace character.
+ */
+ protected static void parseAndIgnoreWhitespace(final String source,
+ final ParsePosition pos) {
+ parseNextCharacter(source, pos);
+ pos.setIndex(pos.getIndex() - 1);
+ }
+
+ /**
+ * Parses <code>source</code> until a non-whitespace character is found.
+ * @param source the string to parse
+ * @param pos input/output parsing parameter.
+ * @return the first non-whitespace character.
+ */
+ protected static char parseNextCharacter(final String source,
+ final ParsePosition pos) {
+ int index = pos.getIndex();
+ final int n = source.length();
+ char ret = 0;
+
+ if (index < n) {
+ char c;
+ do {
+ c = source.charAt(index++);
+ } while (Character.isWhitespace(c) && index < n);
+ pos.setIndex(index);
+
+ if (index < n) {
+ ret = c;
+ }
+ }
+
+ return ret;
+ }
+
+ /**
+ * Formats a double value as a fraction and appends the result to a StringBuffer.
+ *
+ * @param value the double value to format
+ * @param buffer StringBuffer to append to
+ * @param position On input: an alignment field, if desired. On output: the
+ * offsets of the alignment field
+ * @return a reference to the appended buffer
+ * @see #format(Object, StringBuffer, FieldPosition)
+ */
+ @Override
+ public StringBuffer format(final double value,
+ final StringBuffer buffer, final FieldPosition position) {
+ return format(Double.valueOf(value), buffer, position);
+ }
+
+
+ /**
+ * Formats a long value as a fraction and appends the result to a StringBuffer.
+ *
+ * @param value the long value to format
+ * @param buffer StringBuffer to append to
+ * @param position On input: an alignment field, if desired. On output: the
+ * offsets of the alignment field
+ * @return a reference to the appended buffer
+ * @see #format(Object, StringBuffer, FieldPosition)
+ */
+ @Override
+ public StringBuffer format(final long value,
+ final StringBuffer buffer, final FieldPosition position) {
+ return format(Long.valueOf(value), buffer, position);
+ }
+
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/ca71f355/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFraction.java
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diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFraction.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFraction.java
new file mode 100644
index 0000000..9c1a571
--- /dev/null
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFraction.java
@@ -0,0 +1,1199 @@
+/*
+ * 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.numbers.fraction;
+
+import java.io.Serializable;
+import java.math.BigDecimal;
+import java.math.BigInteger;
+import org.apache.commons.numbers.core.ArithmeticUtils;
+
+/**
+ * Representation of a rational number without any overflow. This class is
+ * immutable.
+ *
+ * @since 2.0
+ */
+public class BigFraction
+ extends Number
+ implements /*FieldElement<BigFraction>, */Comparable<BigFraction>, 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;
+
+ /** <code>BigInteger</code> representation of 100. */
+ private static final BigInteger ONE_HUNDRED = BigInteger.valueOf(100);
+
+ /** The numerator. */
+ private final BigInteger numerator;
+
+ /** The denominator. */
+ private final BigInteger denominator;
+
+ /**
+ * <p>
+ * Create a {@link BigFraction} equivalent to the passed {@code BigInteger}, ie
+ * "num / 1".
+ * </p>
+ *
+ * @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 ZeroDenominatorException if the denominator is zero.
+ */
+ public BigFraction(BigInteger num, BigInteger den) {
+ checkNotNull(num, "numerator");
+ checkNotNull(den, "denominator");
+ if (den.signum() == 0) {
+ throw new ZeroDenominatorException();
+ }
+ 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.
+ * <p>
+ * This constructor behaves <em>differently</em> 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.
+ * </p>
+ * <p>
+ * Since this conversion is exact and since double numbers are sometimes
+ * approximated, the fraction created may seem strange in some cases. For example,
+ * calling <code>new BigFraction(1.0 / 3.0)</code> does <em>not</em> 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).
+ * </p>
+ * @see #BigFraction(double, double, int)
+ * @param value the double value to convert to a fraction.
+ * @exception IllegalArgumentException if value is NaN or infinite
+ */
+ public BigFraction(final double value) throws IllegalArgumentException {
+ if (Double.isNaN(value)) {
+ throw new IllegalArgumentException("cannot convert NaN value");
+ }
+ if (Double.isInfinite(value)) {
+ throw new IllegalArgumentException("cannot convert infinite value");
+ }
+
+ // 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.
+ * <p>
+ * References:
+ * <ul>
+ * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
+ * Continued Fraction</a> equations (11) and (22)-(26)</li>
+ * </ul>
+ * </p>
+ *
+ * @param value
+ * the double value to convert to a fraction.
+ * @param epsilon
+ * maximum error allowed. The resulting fraction is within
+ * <code>epsilon</code> of <code>value</code>, 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.
+ * <p>
+ *
+ * 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).
+ * </p>
+ * <p>
+ *
+ * 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.
+ * </p>
+ *
+ * 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
+ * <code>epsilon</code> of <code>value</code>, 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) Math.floor(r0);
+
+ if (Math.abs(a0) > overflow) {
+ throw new FractionConversionException(value, a0, 1l);
+ }
+
+ // check for (almost) integer arguments, which should not go
+ // to iterations.
+ if (Math.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) Math.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 && Math.abs(q1) < maxDenominator) {
+ break;
+ }
+ throw new FractionConversionException(value, p2, q2);
+ }
+
+ final double convergent = (double) p2 / (double) q2;
+ if ((n < maxIterations) &&
+ (Math.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.
+ * <p>
+ * References:
+ * <ul>
+ * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
+ * Continued Fraction</a> equations (11) and (22)-(26)</li>
+ * </ul>
+ * </p>
+ *
+ * @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);
+ }
+
+ /**
+ * <p>
+ * Create a {@link BigFraction} equivalent to the passed {@code int}, ie
+ * "num / 1".
+ * </p>
+ *
+ * @param num
+ * the numerator.
+ */
+ public BigFraction(final int num) {
+ this(BigInteger.valueOf(num), BigInteger.ONE);
+ }
+
+ /**
+ * <p>
+ * Create a {@link BigFraction} given the numerator and denominator as simple
+ * {@code int}. The {@link BigFraction} is reduced to lowest terms.
+ * </p>
+ *
+ * @param num
+ * the numerator.
+ * @param den
+ * the denominator.
+ */
+ public BigFraction(final int num, final int den) {
+ this(BigInteger.valueOf(num), BigInteger.valueOf(den));
+ }
+
+ /**
+ * <p>
+ * Create a {@link BigFraction} equivalent to the passed long, ie "num / 1".
+ * </p>
+ *
+ * @param num
+ * the numerator.
+ */
+ public BigFraction(final long num) {
+ this(BigInteger.valueOf(num), BigInteger.ONE);
+ }
+
+ /**
+ * <p>
+ * Create a {@link BigFraction} given the numerator and denominator as simple
+ * {@code long}. The {@link BigFraction} is reduced to lowest terms.
+ * </p>
+ *
+ * @param num
+ * the numerator.
+ * @param den
+ * the denominator.
+ */
+ public BigFraction(final long num, final long den) {
+ this(BigInteger.valueOf(num), BigInteger.valueOf(den));
+ }
+
+ /**
+ * <p>
+ * Creates a <code>BigFraction</code> instance with the 2 parts of a fraction
+ * Y/Z.
+ * </p>
+ *
+ * <p>
+ * Any negative signs are resolved to be on the numerator.
+ * </p>
+ *
+ * @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 <code>zero</code>.
+ */
+ public static BigFraction getReducedFraction(final int numerator,
+ final int denominator) {
+ if (numerator == 0) {
+ return ZERO; // normalize zero.
+ }
+
+ return new BigFraction(numerator, denominator);
+ }
+
+ /**
+ * <p>
+ * Returns the absolute value of this {@link BigFraction}.
+ * </p>
+ *
+ * @return the absolute value as a {@link BigFraction}.
+ */
+ public BigFraction abs() {
+ return (numerator.signum() == 1) ? this : negate();
+ }
+
+ /**
+ * <p>
+ * Adds the value of this fraction to the passed {@link BigInteger},
+ * returning the result in reduced form.
+ * </p>
+ *
+ * @param bg
+ * the {@link BigInteger} to add, must'nt be <code>null</code>.
+ * @return a <code>BigFraction</code> instance with the resulting values.
+ */
+ public BigFraction add(final BigInteger bg) throws NullPointerException {
+ checkNotNull(bg, "bg");
+
+ if (numerator.signum() == 0) {
+ return new BigFraction(bg);
+ }
+ if (bg.signum() == 0) {
+ return this;
+ }
+
+ return new BigFraction(numerator.add(denominator.multiply(bg)), denominator);
+ }
+
+ /**
+ * <p>
+ * Adds the value of this fraction to the passed {@code integer}, returning
+ * the result in reduced form.
+ * </p>
+ *
+ * @param i
+ * the {@code integer} to add.
+ * @return a <code>BigFraction</code> instance with the resulting values.
+ */
+ public BigFraction add(final int i) {
+ return add(BigInteger.valueOf(i));
+ }
+
+ /**
+ * <p>
+ * Adds the value of this fraction to the passed {@code long}, returning
+ * the result in reduced form.
+ * </p>
+ *
+ * @param l
+ * the {@code long} to add.
+ * @return a <code>BigFraction</code> instance with the resulting values.
+ */
+ public BigFraction add(final long l) {
+ return add(BigInteger.valueOf(l));
+ }
+
+ /**
+ * <p>
+ * Adds the value of this fraction to another, returning the result in
+ * reduced form.
+ * </p>
+ *
+ * @param fraction
+ * the {@link BigFraction} to add, must not be <code>null</code>.
+ * @return a {@link BigFraction} instance with the resulting values.
+ */
+ public BigFraction add(final BigFraction fraction) {
+ checkNotNull(fraction, "fraction");
+ if (fraction.numerator.signum() == 0) {
+ return this;
+ }
+ if (numerator.signum() == 0) {
+ return fraction;
+ }
+
+ final BigInteger num;
+ final BigInteger den;
+
+ 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);
+
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as a <code>BigDecimal</code>. This calculates the
+ * fraction as the numerator divided by denominator.
+ * </p>
+ *
+ * @return the fraction as a <code>BigDecimal</code>.
+ * @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));
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as a <code>BigDecimal</code> following the passed
+ * rounding mode. This calculates the fraction as the numerator divided by
+ * denominator.
+ * </p>
+ *
+ * @param roundingMode
+ * rounding mode to apply. see {@link BigDecimal} constants.
+ * @return the fraction as a <code>BigDecimal</code>.
+ * @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);
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as a <code>BigDecimal</code> following the passed scale
+ * and rounding mode. This calculates the fraction as the numerator divided
+ * by denominator.
+ * </p>
+ *
+ * @param scale
+ * scale of the <code>BigDecimal</code> 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 <code>BigDecimal</code>.
+ * @see BigDecimal
+ */
+ public BigDecimal bigDecimalValue(final int scale, final int roundingMode) {
+ return new BigDecimal(numerator).divide(new BigDecimal(denominator), scale, roundingMode);
+ }
+
+ /**
+ * <p>
+ * Compares this object to another based on size.
+ * </p>
+ *
+ * @param object
+ * the object to compare to, must not be <code>null</code>.
+ * @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)
+ */
+ @Override
+ 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);
+ }
+
+ /**
+ * <p>
+ * Divide the value of this fraction by the passed {@code BigInteger},
+ * ie {@code this * 1 / bg}, returning the result in reduced form.
+ * </p>
+ *
+ * @param bg the {@code BigInteger} to divide by, must not be {@code null}
+ * @return a {@link BigFraction} instance with the resulting values
+ * @throws ZeroDenominatorException if the fraction to divide by is zero
+ */
+ public BigFraction divide(final BigInteger bg) {
+ checkNotNull(bg, "bg");
+ if (bg.signum() == 0) {
+ throw new ZeroDenominatorException();
+ }
+ if (numerator.signum() == 0) {
+ return ZERO;
+ }
+ return new BigFraction(numerator, denominator.multiply(bg));
+ }
+
+ /**
+ * <p>
+ * Divide the value of this fraction by the passed {@code int}, ie
+ * {@code this * 1 / i}, returning the result in reduced form.
+ * </p>
+ *
+ * @param i the {@code int} to divide by
+ * @return a {@link BigFraction} instance with the resulting values
+ * @throws ArithmeticException if the fraction to divide by is zero
+ */
+ public BigFraction divide(final int i) {
+ return divide(BigInteger.valueOf(i));
+ }
+
+ /**
+ * <p>
+ * Divide the value of this fraction by the passed {@code long}, ie
+ * {@code this * 1 / l}, returning the result in reduced form.
+ * </p>
+ *
+ * @param l the {@code long} to divide by
+ * @return a {@link BigFraction} instance with the resulting values
+ * @throws ArithmeticException if the fraction to divide by is zero
+ */
+ public BigFraction divide(final long l) {
+ return divide(BigInteger.valueOf(l));
+ }
+
+ /**
+ * <p>
+ * Divide the value of this fraction by another, returning the result in
+ * reduced form.
+ * </p>
+ *
+ * @param fraction Fraction to divide by, must not be {@code null}.
+ * @return a {@link BigFraction} instance with the resulting values.
+ * @throws ZeroDenominatorException if the fraction to divide by is zero
+ */
+ public BigFraction divide(final BigFraction fraction) {
+ checkNotNull(fraction, "fraction");
+ if (fraction.numerator.signum() == 0) {
+ throw new ZeroDenominatorException(fraction.denominator, fraction.numerator);
+ }
+ if (numerator.signum() == 0) {
+ return ZERO;
+ }
+
+ return multiply(fraction.reciprocal());
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as a {@code double}. This calculates the fraction as
+ * the numerator divided by denominator.
+ * </p>
+ *
+ * @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 = Math.max(numerator.bitLength(),
+ denominator.bitLength()) - Math.getExponent(Double.MAX_VALUE);
+ result = numerator.shiftRight(shift).doubleValue() /
+ denominator.shiftRight(shift).doubleValue();
+ }
+ return result;
+ }
+
+ /**
+ * <p>
+ * 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.
+ * </p>
+ *
+ * @param other
+ * fraction to test for equality to this fraction, can be
+ * <code>null</code>.
+ * @return true if two fractions are equal, false if object is
+ * <code>null</code>, 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;
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as a {@code float}. This calculates the fraction as
+ * the numerator divided by denominator.
+ * </p>
+ *
+ * @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 = Math.max(numerator.bitLength(),
+ denominator.bitLength()) - Math.getExponent(Float.MAX_VALUE);
+ result = numerator.shiftRight(shift).floatValue() /
+ denominator.shiftRight(shift).floatValue();
+ }
+ return result;
+ }
+
+ /**
+ * <p>
+ * Access the denominator as a <code>BigInteger</code>.
+ * </p>
+ *
+ * @return the denominator as a <code>BigInteger</code>.
+ */
+ public BigInteger getDenominator() {
+ return denominator;
+ }
+
+ /**
+ * <p>
+ * Access the denominator as a {@code int}.
+ * </p>
+ *
+ * @return the denominator as a {@code int}.
+ */
+ public int getDenominatorAsInt() {
+ return denominator.intValue();
+ }
+
+ /**
+ * <p>
+ * Access the denominator as a {@code long}.
+ * </p>
+ *
+ * @return the denominator as a {@code long}.
+ */
+ public long getDenominatorAsLong() {
+ return denominator.longValue();
+ }
+
+ /**
+ * <p>
+ * Access the numerator as a <code>BigInteger</code>.
+ * </p>
+ *
+ * @return the numerator as a <code>BigInteger</code>.
+ */
+ public BigInteger getNumerator() {
+ return numerator;
+ }
+
+ /**
+ * <p>
+ * Access the numerator as a {@code int}.
+ * </p>
+ *
+ * @return the numerator as a {@code int}.
+ */
+ public int getNumeratorAsInt() {
+ return numerator.intValue();
+ }
+
+ /**
+ * <p>
+ * Access the numerator as a {@code long}.
+ * </p>
+ *
+ * @return the numerator as a {@code long}.
+ */
+ public long getNumeratorAsLong() {
+ return numerator.longValue();
+ }
+
+ /**
+ * <p>
+ * Gets a hashCode for the fraction.
+ * </p>
+ *
+ * @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();
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as an {@code int}. This returns the whole number part
+ * of the fraction.
+ * </p>
+ *
+ * @return the whole number fraction part.
+ * @see java.lang.Number#intValue()
+ */
+ @Override
+ public int intValue() {
+ return numerator.divide(denominator).intValue();
+ }
+
+ /**
+ * <p>
+ * Gets the fraction as a {@code long}. This returns the whole number part
+ * of the fraction.
+ * </p>
+ *
+ * @return the whole number fraction part.
+ * @see java.lang.Number#longValue()
+ */
+ @Override
+ public long longValue() {
+ return numerator.divide(denominator).longValue();
+ }
+
+ /**
+ * <p>
+ * Multiplies the value of this fraction by the passed
+ * <code>BigInteger</code>, returning the result in reduced form.
+ * </p>
+ *
+ * @param bg the {@code BigInteger} to multiply by.
+ * @return a {@code BigFraction} instance with the resulting values.
+ */
+ public BigFraction multiply(final BigInteger bg) {
+ checkNotNull(bg, "bg");
+ if (numerator.signum() == 0 || bg.signum() == 0) {
+ return ZERO;
+ }
+ return new BigFraction(bg.multiply(numerator), denominator);
+ }
+
+ /**
+ * <p>
+ * Multiply the value of this fraction by the passed {@code int}, returning
+ * the result in reduced form.
+ * </p>
+ *
+ * @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));
+ }
+
+ /**
+ * <p>
+ * Multiply the value of this fraction by the passed {@code long},
+ * returning the result in reduced form.
+ * </p>
+ *
+ * @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));
+ }
+
+ /**
+ * <p>
+ * Multiplies the value of this fraction by another, returning the result in
+ * reduced form.
+ * </p>
+ *
+ * @param fraction Fraction to multiply by, must not be {@code null}.
+ * @return a {@link BigFraction} instance with the resulting values.
+ */
+ public BigFraction multiply(final BigFraction fraction) {
+ checkNotNull(fraction, "fraction");
+ if (numerator.signum() == 0 ||
+ fraction.numerator.signum() == 0) {
+ return ZERO;
+ }
+ return new BigFraction(numerator.multiply(fraction.numerator),
+ denominator.multiply(fraction.denominator));
+ }
+
+ /**
+ * <p>
+ * Return the additive inverse of this fraction, returning the result in
+ * reduced form.
+ * </p>
+ *
+ * @return the negation of this fraction.
+ */
+ public BigFraction negate() {
+ return new BigFraction(numerator.negate(), denominator);
+ }
+
+ /**
+ * <p>
+ * Gets the fraction percentage as a {@code double}. This calculates the
+ * fraction as the numerator divided by denominator multiplied by 100.
+ * </p>
+ *
+ * @return the fraction percentage as a {@code double}.
+ */
+ public double percentageValue() {
+ return multiply(ONE_HUNDRED).doubleValue();
+ }
+
+ /**
+ * <p>
+ * Returns a {@code BigFraction} whose value is
+ * {@code (this<sup>exponent</sup>)}, returning the result in reduced form.
+ * </p>
+ *
+ * @param exponent
+ * exponent to which this {@code BigFraction} is to be
+ * raised.
+ * @return <tt>this<sup>exponent</sup></tt>.
+ */
+ 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));
+ }
+
+ /**
+ * <p>
+ * Returns a <code>BigFraction</code> whose value is
+ * <tt>(this<sup>exponent</sup>)</tt>, returning the result in reduced form.
+ * </p>
+ *
+ * @param exponent
+ * exponent to which this <code>BigFraction</code> is to be raised.
+ * @return <tt>this<sup>exponent</sup></tt> as a <code>BigFraction</code>.
+ */
+ 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));
+ }
+
+ /**
+ * <p>
+ * Returns a <code>BigFraction</code> whose value is
+ * <tt>(this<sup>exponent</sup>)</tt>, returning the result in reduced form.
+ * </p>
+ *
+ * @param exponent
+ * exponent to which this <code>BigFraction</code> is to be raised.
+ * @return <tt>this<sup>exponent</sup></tt> as a <code>BigFraction</code>.
+ */
+ 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));
+ }
+
+ /**
+ * <p>
+ * Returns a <code>double</code> whose value is
+ * <tt>(this<sup>exponent</sup>)</tt>, returning the result in reduced form.
+ * </p>
+ *
+ * @param exponent
+ * exponent to which this <code>BigFraction</code> is to be raised.
+ * @return <tt>this<sup>exponent</sup></tt>.
+ */
+ public double pow(final double exponent) {
+ return Math.pow(numerator.doubleValue(), exponent) /
+ Math.pow(denominator.doubleValue(), exponent);
+ }
+
+ /**
+ * <p>
+ * Return the multiplicative inverse of this fraction.
+ * </p>
+ *
+ * @return the reciprocal fraction.
+ */
+ public BigFraction reciprocal() {
+ return new BigFraction(denominator, numerator);
+ }
+
+ /**
+ * <p>
+ * Reduce this <code>BigFraction</code> to its lowest terms.
+ * </p>
+ *
+ * @return the reduced <code>BigFraction</code>. 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;
+ }
+ }
+
+ /**
+ * <p>
+ * Subtracts the value of an {@link BigInteger} from the value of this
+ * {@code BigFraction}, returning the result in reduced form.
+ * </p>
+ *
+ * @param bg the {@link BigInteger} to subtract, cannot be {@code null}.
+ * @return a {@code BigFraction} instance with the resulting values.
+ */
+ public BigFraction subtract(final BigInteger bg) {
+ checkNotNull(bg, "bg");
+ if (bg.signum() == 0) {
+ return this;
+ }
+ if (numerator.signum() == 0) {
+ return new BigFraction(bg.negate());
+ }
+
+ return new BigFraction(numerator.subtract(denominator.multiply(bg)), denominator);
+ }
+
+ /**
+ * <p>
+ * Subtracts the value of an {@code integer} from the value of this
+ * {@code BigFraction}, returning the result in reduced form.
+ * </p>
+ *
+ * @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));
+ }
+
+ /**
+ * <p>
+ * Subtracts the value of a {@code long} from the value of this
+ * {@code BigFraction}, returning the result in reduced form.
+ * </p>
+ *
+ * @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));
+ }
+
+ /**
+ * <p>
+ * Subtracts the value of another fraction from the value of this one,
+ * returning the result in reduced form.
+ * </p>
+ *
+ * @param fraction {@link BigFraction} to subtract, must not be {@code null}.
+ * @return a {@link BigFraction} instance with the resulting values
+ */
+ public BigFraction subtract(final BigFraction fraction) {
+ checkNotNull(fraction, "fraction");
+ if (fraction.numerator.signum() == 0) {
+ return this;
+ }
+ if (numerator.signum() == 0) {
+ return fraction.negate();
+ }
+
+ final BigInteger num;
+ final BigInteger den;
+ 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);
+
+ }
+
+ /**
+ * <p>
+ * Returns the <code>String</code> representing this fraction, ie
+ * "num / dem" or just "num" if the denominator is one.
+ * </p>
+ *
+ * @return a string representation of the fraction.
+ * @see java.lang.Object#toString()
+ */
+ @Override
+ public String toString() {
+ final String str;
+ if (BigInteger.ONE.equals(denominator)) {
+ str = numerator.toString();
+ } else if (BigInteger.ZERO.equals(numerator)) {
+ str = "0";
+ } else {
+ str = numerator + " / " + denominator;
+ }
+ return str;
+ }
+
+ public BigFractionField getField() {
+ return BigFractionField.getInstance();
+ }
+
+ private static void checkNotNull(Object arg, String argName) {
+ if (arg == null) {
+ throw new NullPointerException(argName);
+ }
+ }
+
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/ca71f355/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionField.java
----------------------------------------------------------------------
diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionField.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionField.java
new file mode 100644
index 0000000..7a12b16
--- /dev/null
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionField.java
@@ -0,0 +1,83 @@
+/*
+ * 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.numbers.fraction;
+
+import java.io.Serializable;
+
+
+/**
+ * Representation of the fractional numbers without any overflow field.
+ * <p>
+ * This class is a singleton.
+ * </p>
+ * @see Fraction
+ * @since 2.0
+ */
+public class BigFractionField implements /*Field<BigFraction>, */Serializable {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = -1699294557189741703L;
+
+ /** Private constructor for the singleton.
+ */
+ private BigFractionField() {
+ }
+
+ /** Get the unique instance.
+ * @return the unique instance
+ */
+ public static BigFractionField getInstance() {
+ return LazyHolder.INSTANCE;
+ }
+
+ /** {@inheritDoc} */
+ public BigFraction getOne() {
+ return BigFraction.ONE;
+ }
+
+ /** {@inheritDoc} */
+ public BigFraction getZero() {
+ return BigFraction.ZERO;
+ }
+
+ /** {@inheritDoc} */
+/*
+ @Override
+ public Class<? extends FieldElement<BigFraction>> getRuntimeClass() {
+ return BigFraction.class;
+ }
+*/
+ // CHECKSTYLE: stop HideUtilityClassConstructor
+ /** Holder for the instance.
+ * <p>We use here the Initialization On Demand Holder Idiom.</p>
+ */
+ private static class LazyHolder {
+ /** Cached field instance. */
+ private static final BigFractionField INSTANCE = new BigFractionField();
+ }
+ // CHECKSTYLE: resume HideUtilityClassConstructor
+
+ /** Handle deserialization of the singleton.
+ * @return the singleton instance
+ */
+ private Object readResolve() {
+ // return the singleton instance
+ return LazyHolder.INSTANCE;
+ }
+
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/ca71f355/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionFormat.java
----------------------------------------------------------------------
diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionFormat.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionFormat.java
new file mode 100644
index 0000000..8b68d02
--- /dev/null
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/BigFractionFormat.java
@@ -0,0 +1,283 @@
+/*
+ * 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.numbers.fraction;
+
+import java.io.Serializable;
+import java.math.BigInteger;
+import java.text.FieldPosition;
+import java.text.NumberFormat;
+import java.text.ParsePosition;
+import java.util.Locale;
+
+/**
+ * Formats a BigFraction number in proper format or improper format.
+ * <p>
+ * The number format for each of the whole number, numerator and,
+ * denominator can be configured.
+ * </p>
+ *
+ * @since 2.0
+ */
+public class BigFractionFormat extends AbstractFormat implements Serializable {
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = -2932167925527338976L;
+
+ /**
+ * Create an improper formatting instance with the default number format
+ * for the numerator and denominator.
+ */
+ public BigFractionFormat() {
+ }
+
+ /**
+ * Create an improper formatting instance with a custom number format for
+ * both the numerator and denominator.
+ * @param format the custom format for both the numerator and denominator.
+ */
+ public BigFractionFormat(final NumberFormat format) {
+ super(format);
+ }
+
+ /**
+ * Create an improper formatting instance with a custom number format for
+ * the numerator and a custom number format for the denominator.
+ * @param numeratorFormat the custom format for the numerator.
+ * @param denominatorFormat the custom format for the denominator.
+ */
+ public BigFractionFormat(final NumberFormat numeratorFormat,
+ final NumberFormat denominatorFormat) {
+ super(numeratorFormat, denominatorFormat);
+ }
+
+ /**
+ * Get the set of locales for which complex formats are available. This
+ * is the same set as the {@link NumberFormat} set.
+ * @return available complex format locales.
+ */
+ public static Locale[] getAvailableLocales() {
+ return NumberFormat.getAvailableLocales();
+ }
+
+ /**
+ * This static method calls formatBigFraction() on a default instance of
+ * BigFractionFormat.
+ *
+ * @param f BigFraction object to format
+ * @return A formatted BigFraction in proper form.
+ */
+ public static String formatBigFraction(final BigFraction f) {
+ return getImproperInstance().format(f);
+ }
+
+ /**
+ * Returns the default complex format for the current locale.
+ * @return the default complex format.
+ */
+ public static BigFractionFormat getImproperInstance() {
+ return getImproperInstance(Locale.getDefault());
+ }
+
+ /**
+ * Returns the default complex format for the given locale.
+ * @param locale the specific locale used by the format.
+ * @return the complex format specific to the given locale.
+ */
+ public static BigFractionFormat getImproperInstance(final Locale locale) {
+ return new BigFractionFormat(getDefaultNumberFormat(locale));
+ }
+
+ /**
+ * Returns the default complex format for the current locale.
+ * @return the default complex format.
+ */
+ public static BigFractionFormat getProperInstance() {
+ return getProperInstance(Locale.getDefault());
+ }
+
+ /**
+ * Returns the default complex format for the given locale.
+ * @param locale the specific locale used by the format.
+ * @return the complex format specific to the given locale.
+ */
+ public static BigFractionFormat getProperInstance(final Locale locale) {
+ return new ProperBigFractionFormat(getDefaultNumberFormat(locale));
+ }
+
+ /**
+ * Formats a {@link BigFraction} object to produce a string. The BigFraction is
+ * output in improper format.
+ *
+ * @param BigFraction the object to format.
+ * @param toAppendTo where the text is to be appended
+ * @param pos On input: an alignment field, if desired. On output: the
+ * offsets of the alignment field
+ * @return the value passed in as toAppendTo.
+ */
+ public StringBuffer format(final BigFraction BigFraction,
+ final StringBuffer toAppendTo, final FieldPosition pos) {
+
+ pos.setBeginIndex(0);
+ pos.setEndIndex(0);
+
+ getNumeratorFormat().format(BigFraction.getNumerator(), toAppendTo, pos);
+ toAppendTo.append(" / ");
+ getDenominatorFormat().format(BigFraction.getDenominator(), toAppendTo, pos);
+
+ return toAppendTo;
+ }
+
+ /**
+ * Formats an object and appends the result to a StringBuffer.
+ * <code>obj</code> must be either a {@link BigFraction} object or a
+ * {@link BigInteger} object or a {@link Number} object. Any other type of
+ * object will result in an {@link IllegalArgumentException} being thrown.
+ *
+ * @param obj the object to format.
+ * @param toAppendTo where the text is to be appended
+ * @param pos On input: an alignment field, if desired. On output: the
+ * offsets of the alignment field
+ * @return the value passed in as toAppendTo.
+ * @see java.text.Format#format(java.lang.Object, java.lang.StringBuffer, java.text.FieldPosition)
+ * @throws IllegalArgumentException if <code>obj</code> is not a valid type.
+ */
+ @Override
+ public StringBuffer format(final Object obj,
+ final StringBuffer toAppendTo, final FieldPosition pos) {
+
+ final StringBuffer ret;
+ if (obj instanceof BigFraction) {
+ ret = format((BigFraction) obj, toAppendTo, pos);
+ } else if (obj instanceof BigInteger) {
+ ret = format(new BigFraction((BigInteger) obj), toAppendTo, pos);
+ } else if (obj instanceof Number) {
+ ret = format(new BigFraction(((Number) obj).doubleValue()),
+ toAppendTo, pos);
+ } else {
+ throw new IllegalArgumentException("cannot format given object as a fraction number");
+ }
+
+ return ret;
+ }
+
+ /**
+ * Parses a string to produce a {@link BigFraction} object.
+ * @param source the string to parse
+ * @return the parsed {@link BigFraction} object.
+ * @exception FractionParseException if the beginning of the specified string
+ * cannot be parsed.
+ */
+ @Override
+ public BigFraction parse(final String source) throws FractionParseException {
+ final ParsePosition parsePosition = new ParsePosition(0);
+ final BigFraction result = parse(source, parsePosition);
+ if (parsePosition.getIndex() == 0) {
+ throw new FractionParseException(source, parsePosition.getErrorIndex(), BigFraction.class);
+ }
+ return result;
+ }
+
+ /**
+ * Parses a string to produce a {@link BigFraction} object.
+ * This method expects the string to be formatted as an improper BigFraction.
+ * @param source the string to parse
+ * @param pos input/output parsing parameter.
+ * @return the parsed {@link BigFraction} object.
+ */
+ @Override
+ public BigFraction parse(final String source, final ParsePosition pos) {
+ final int initialIndex = pos.getIndex();
+
+ // parse whitespace
+ parseAndIgnoreWhitespace(source, pos);
+
+ // parse numerator
+ final BigInteger num = parseNextBigInteger(source, pos);
+ if (num == null) {
+ // invalid integer number
+ // set index back to initial, error index should already be set
+ // character examined.
+ pos.setIndex(initialIndex);
+ return null;
+ }
+
+ // parse '/'
+ final int startIndex = pos.getIndex();
+ final char c = parseNextCharacter(source, pos);
+ switch (c) {
+ case 0 :
+ // no '/'
+ // return num as a BigFraction
+ return new BigFraction(num);
+ case '/' :
+ // found '/', continue parsing denominator
+ break;
+ default :
+ // invalid '/'
+ // set index back to initial, error index should be the last
+ // character examined.
+ pos.setIndex(initialIndex);
+ pos.setErrorIndex(startIndex);
+ return null;
+ }
+
+ // parse whitespace
+ parseAndIgnoreWhitespace(source, pos);
+
+ // parse denominator
+ final BigInteger den = parseNextBigInteger(source, pos);
+ if (den == null) {
+ // invalid integer number
+ // set index back to initial, error index should already be set
+ // character examined.
+ pos.setIndex(initialIndex);
+ return null;
+ }
+
+ return new BigFraction(num, den);
+ }
+
+ /**
+ * Parses a string to produce a <code>BigInteger</code>.
+ * @param source the string to parse
+ * @param pos input/output parsing parameter.
+ * @return a parsed <code>BigInteger</code> or null if string does not
+ * contain a BigInteger at the specified position
+ */
+ protected BigInteger parseNextBigInteger(final String source,
+ final ParsePosition pos) {
+
+ final int start = pos.getIndex();
+ int end = (source.charAt(start) == '-') ? (start + 1) : start;
+ while((end < source.length()) &&
+ Character.isDigit(source.charAt(end))) {
+ ++end;
+ }
+
+ try {
+ BigInteger n = new BigInteger(source.substring(start, end));
+ pos.setIndex(end);
+ return n;
+ } catch (NumberFormatException nfe) {
+ pos.setErrorIndex(start);
+ return null;
+ }
+
+ }
+
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/ca71f355/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/Fraction.java
----------------------------------------------------------------------
diff --git a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/Fraction.java b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/Fraction.java
new file mode 100644
index 0000000..b4ed6b0
--- /dev/null
+++ b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/Fraction.java
@@ -0,0 +1,664 @@
+/*
+ * 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.numbers.fraction;
+
+import java.io.Serializable;
+import java.math.BigInteger;
+import org.apache.commons.numbers.core.ArithmeticUtils;
+
+/**
+ * Representation of a rational number.
+ *
+ * implements Serializable since 2.0
+ *
+ * @since 1.1
+ */
+public class Fraction
+ extends Number
+ implements /*FieldElement<Fraction>,*/ Comparable<Fraction>, Serializable {
+
+ /** A fraction representing "2 / 1". */
+ public static final Fraction TWO = new Fraction(2, 1);
+
+ /** A fraction representing "1". */
+ public static final Fraction ONE = new Fraction(1, 1);
+
+ /** A fraction representing "0". */
+ public static final Fraction ZERO = new Fraction(0, 1);
+
+ /** A fraction representing "4/5". */
+ public static final Fraction FOUR_FIFTHS = new Fraction(4, 5);
+
+ /** A fraction representing "1/5". */
+ public static final Fraction ONE_FIFTH = new Fraction(1, 5);
+
+ /** A fraction representing "1/2". */
+ public static final Fraction ONE_HALF = new Fraction(1, 2);
+
+ /** A fraction representing "1/4". */
+ public static final Fraction ONE_QUARTER = new Fraction(1, 4);
+
+ /** A fraction representing "1/3". */
+ public static final Fraction ONE_THIRD = new Fraction(1, 3);
+
+ /** A fraction representing "3/5". */
+ public static final Fraction THREE_FIFTHS = new Fraction(3, 5);
+
+ /** A fraction representing "3/4". */
+ public static final Fraction THREE_QUARTERS = new Fraction(3, 4);
+
+ /** A fraction representing "2/5". */
+ public static final Fraction TWO_FIFTHS = new Fraction(2, 5);
+
+ /** A fraction representing "2/4". */
+ public static final Fraction TWO_QUARTERS = new Fraction(2, 4);
+
+ /** A fraction representing "2/3". */
+ public static final Fraction TWO_THIRDS = new Fraction(2, 3);
+
+ /** A fraction representing "-1 / 1". */
+ public static final Fraction MINUS_ONE = new Fraction(-1, 1);
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = 3698073679419233275L;
+
+ /** The default epsilon used for convergence. */
+ private static final double DEFAULT_EPSILON = 1e-5;
+
+ /** The denominator. */
+ private final int denominator;
+
+ /** The numerator. */
+ private final int numerator;
+
+ /**
+ * Create a fraction given the double value.
+ * @param value the double value to convert to a fraction.
+ * @throws FractionConversionException if the continued fraction failed to
+ * converge.
+ */
+ public Fraction(double value) throws FractionConversionException {
+ this(value, DEFAULT_EPSILON, 100);
+ }
+
+ /**
+ * Create a fraction given the double value and maximum error allowed.
+ * <p>
+ * References:
+ * <ul>
+ * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
+ * Continued Fraction</a> equations (11) and (22)-(26)</li>
+ * </ul>
+ * </p>
+ * @param value the double value to convert to a fraction.
+ * @param epsilon maximum error allowed. The resulting fraction is within
+ * {@code epsilon} of {@code value}, in absolute terms.
+ * @param maxIterations maximum number of convergents
+ * @throws FractionConversionException if the continued fraction failed to
+ * converge.
+ */
+ public Fraction(double value, double epsilon, int maxIterations)
+ throws FractionConversionException
+ {
+ this(value, epsilon, Integer.MAX_VALUE, maxIterations);
+ }
+
+ /**
+ * Create a fraction given the double value and maximum denominator.
+ * <p>
+ * References:
+ * <ul>
+ * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
+ * Continued Fraction</a> equations (11) and (22)-(26)</li>
+ * </ul>
+ * </p>
+ * @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 Fraction(double value, int maxDenominator)
+ throws FractionConversionException
+ {
+ this(value, 0, maxDenominator, 100);
+ }
+
+ /**
+ * Create a fraction given the double value and either the maximum error
+ * allowed or the maximum number of denominator digits.
+ * <p>
+ *
+ * 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).
+ * </p><p>
+ *
+ * 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.
+ * </p>
+ *
+ * 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
+ * {@code epsilon} of {@code 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 Fraction(double value, double epsilon, int maxDenominator, int maxIterations)
+ throws FractionConversionException, FractionOverflowException
+ {
+ long overflow = Integer.MAX_VALUE;
+ double r0 = value;
+ long a0 = (long)Math.floor(r0);
+ if (Math.abs(a0) > overflow) {
+ throw new FractionConversionException(value, a0, 1l);
+ }
+
+ // check for (almost) integer arguments, which should not go to iterations.
+ if (Math.abs(a0 - value) < epsilon) {
+ this.numerator = (int) a0;
+ this.denominator = 1;
+ 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;
+ double r1 = 1.0 / (r0 - a0);
+ long a1 = (long)Math.floor(r1);
+ p2 = (a1 * p1) + p0;
+ q2 = (a1 * q1) + q0;
+
+ if ((Math.abs(p2) > overflow) || (Math.abs(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 && Math.abs(q1) < maxDenominator) {
+ break;
+ }
+ throw new FractionConversionException(value, p2, q2);
+ }
+
+ double convergent = (double)p2 / (double)q2;
+ if (n < maxIterations && Math.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) {
+ this.numerator = (int) p2;
+ this.denominator = (int) q2;
+ } else {
+ this.numerator = (int) p1;
+ this.denominator = (int) q1;
+ }
+
+ }
+
+ /**
+ * Create a fraction from an int.
+ * The fraction is num / 1.
+ * @param num the numerator.
+ */
+ public Fraction(int num) {
+ this(num, 1);
+ }
+
+ /**
+ * Create a fraction given the numerator and denominator. The fraction is
+ * reduced to lowest terms.
+ * @param num the numerator.
+ * @param den the denominator.
+ * @throws FractionException if the denominator is {@code zero}
+ */
+ public Fraction(int num, int den) {
+ if (den == 0) {
+ throw new ZeroDenominatorException(num, den);
+ }
+ if (den < 0) {
+ if (num == Integer.MIN_VALUE ||
+ den == Integer.MIN_VALUE) {
+ throw new FractionOverflowException(num, den);
+ }
+ num = -num;
+ den = -den;
+ }
+ // reduce numerator and denominator by greatest common denominator.
+ final int d = ArithmeticUtils.gcd(num, den);
+ if (d > 1) {
+ num /= d;
+ den /= d;
+ }
+
+ // move sign to numerator.
+ if (den < 0) {
+ num = -num;
+ den = -den;
+ }
+ this.numerator = num;
+ this.denominator = den;
+ }
+
+ /**
+ * Returns the absolute value of this fraction.
+ * @return the absolute value.
+ */
+ public Fraction abs() {
+ Fraction ret;
+ if (numerator >= 0) {
+ ret = this;
+ } else {
+ ret = negate();
+ }
+ return ret;
+ }
+
+ /**
+ * Compares this object to another based on size.
+ * @param object the object to compare to
+ * @return -1 if this is less than {@code object}, +1 if this is greater
+ * than {@code object}, 0 if they are equal.
+ */
+ @Override
+ public int compareTo(Fraction object) {
+ long nOd = ((long) numerator) * object.denominator;
+ long dOn = ((long) denominator) * object.numerator;
+ return (nOd < dOn) ? -1 : ((nOd > dOn) ? +1 : 0);
+ }
+
+ /**
+ * Gets the fraction as a {@code double}. This calculates the fraction as
+ * the numerator divided by denominator.
+ * @return the fraction as a {@code double}
+ */
+ @Override
+ public double doubleValue() {
+ return (double)numerator / (double)denominator;
+ }
+
+ /**
+ * 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
+ * @return true if two fractions are equal, false if object is
+ * {@code null}, not an instance of {@link Fraction}, or not equal
+ * to this fraction instance.
+ */
+ @Override
+ public boolean equals(Object other) {
+ if (this == other) {
+ return true;
+ }
+ if (other instanceof Fraction) {
+ // since fractions are always in lowest terms, numerators and
+ // denominators can be compared directly for equality.
+ Fraction rhs = (Fraction)other;
+ return (numerator == rhs.numerator) &&
+ (denominator == rhs.denominator);
+ }
+ return false;
+ }
+
+ /**
+ * Gets the fraction as a {@code float}. This calculates the fraction as
+ * the numerator divided by denominator.
+ * @return the fraction as a {@code float}
+ */
+ @Override
+ public float floatValue() {
+ return (float)doubleValue();
+ }
+
+ /**
+ * Access the denominator.
+ * @return the denominator.
+ */
+ public int getDenominator() {
+ return denominator;
+ }
+
+ /**
+ * Access the numerator.
+ * @return the numerator.
+ */
+ public int getNumerator() {
+ return numerator;
+ }
+
+ /**
+ * Gets a hashCode for the fraction.
+ * @return a hash code value for this object
+ */
+ @Override
+ public int hashCode() {
+ return 37 * (37 * 17 + numerator) + denominator;
+ }
+
+ /**
+ * Gets the fraction as an {@code int}. This returns the whole number part
+ * of the fraction.
+ * @return the whole number fraction part
+ */
+ @Override
+ public int intValue() {
+ return (int)doubleValue();
+ }
+
+ /**
+ * Gets the fraction as a {@code long}. This returns the whole number part
+ * of the fraction.
+ * @return the whole number fraction part
+ */
+ @Override
+ public long longValue() {
+ return (long)doubleValue();
+ }
+
+ /**
+ * Return the additive inverse of this fraction.
+ * @return the negation of this fraction.
+ */
+ public Fraction negate() {
+ if (numerator==Integer.MIN_VALUE) {
+ throw new FractionOverflowException(numerator, denominator);
+ }
+ return new Fraction(-numerator, denominator);
+ }
+
+ /**
+ * Return the multiplicative inverse of this fraction.
+ * @return the reciprocal fraction
+ */
+ public Fraction reciprocal() {
+ return new Fraction(denominator, numerator);
+ }
+
+ /**
+ * <p>Adds the value of this fraction to another, returning the result in reduced form.
+ * The algorithm follows Knuth, 4.5.1.</p>
+ *
+ * @param fraction the fraction to add, must not be {@code null}
+ * @return a {@code Fraction} instance with the resulting values
+ * @throws NullPointerException if the fraction is {@code null}
+ * @throws NumbersArithmeticException if the resulting numerator or denominator exceeds
+ * {@code Integer.MAX_VALUE}
+ */
+ public Fraction add(Fraction fraction) {
+ return addSub(fraction, true /* add */);
+ }
+
+ /**
+ * Add an integer to the fraction.
+ * @param i the {@code integer} to add.
+ * @return this + i
+ */
+ public Fraction add(final int i) {
+ return new Fraction(numerator + i * denominator, denominator);
+ }
+
+ /**
+ * <p>Subtracts the value of another fraction from the value of this one,
+ * returning the result in reduced form.</p>
+ *
+ * @param fraction the fraction to subtract, must not be {@code null}
+ * @return a {@code Fraction} instance with the resulting values
+ * @throws NullPointerException if the fraction is {@code null}
+ * @throws NumbersArithmeticException if the resulting numerator or denominator
+ * cannot be represented in an {@code int}.
+ */
+ public Fraction subtract(Fraction fraction) {
+ return addSub(fraction, false /* subtract */);
+ }
+
+ /**
+ * Subtract an integer from the fraction.
+ * @param i the {@code integer} to subtract.
+ * @return this - i
+ */
+ public Fraction subtract(final int i) {
+ return new Fraction(numerator - i * denominator, denominator);
+ }
+
+ /**
+ * Implement add and subtract using algorithm described in Knuth 4.5.1.
+ *
+ * @param fraction the fraction to subtract, must not be {@code null}
+ * @param isAdd true to add, false to subtract
+ * @return a {@code Fraction} instance with the resulting values
+ * @throws NullPointerException if the fraction is {@code null}
+ * @throws NumbersArithmeticException if the resulting numerator or denominator
+ * cannot be represented in an {@code int}.
+ */
+ private Fraction addSub(Fraction fraction, boolean isAdd) {
+ if (fraction == null) {
+ throw new NullPointerException("fraction");
+ }
+ // zero is identity for addition.
+ if (numerator == 0) {
+ return isAdd ? fraction : fraction.negate();
+ }
+ if (fraction.numerator == 0) {
+ return this;
+ }
+ // if denominators are randomly distributed, d1 will be 1 about 61%
+ // of the time.
+ int d1 = ArithmeticUtils.gcd(denominator, fraction.denominator);
+ if (d1==1) {
+ // result is ( (u*v' +/- u'v) / u'v')
+ int uvp = ArithmeticUtils.mulAndCheck(numerator, fraction.denominator);
+ int upv = ArithmeticUtils.mulAndCheck(fraction.numerator, denominator);
+ return new Fraction
+ (isAdd ? ArithmeticUtils.addAndCheck(uvp, upv) :
+ ArithmeticUtils.subAndCheck(uvp, upv),
+ ArithmeticUtils.mulAndCheck(denominator, fraction.denominator));
+ }
+ // the quantity 't' requires 65 bits of precision; see knuth 4.5.1
+ // exercise 7. we're going to use a BigInteger.
+ // t = u(v'/d1) +/- v(u'/d1)
+ BigInteger uvp = BigInteger.valueOf(numerator)
+ .multiply(BigInteger.valueOf(fraction.denominator/d1));
+ BigInteger upv = BigInteger.valueOf(fraction.numerator)
+ .multiply(BigInteger.valueOf(denominator/d1));
+ BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
+ // but d2 doesn't need extra precision because
+ // d2 = gcd(t,d1) = gcd(t mod d1, d1)
+ int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
+ int d2 = (tmodd1==0)?d1:ArithmeticUtils.gcd(tmodd1, d1);
+
+ // result is (t/d2) / (u'/d1)(v'/d2)
+ BigInteger w = t.divide(BigInteger.valueOf(d2));
+ if (w.bitLength() > 31) {
+ throw new FractionOverflowException(
+ "overflow, numerator too large after multiply: {0}", w.toString(), "");
+ }
+ return new Fraction (w.intValue(),
+ ArithmeticUtils.mulAndCheck(denominator/d1,
+ fraction.denominator/d2));
+ }
+
+ /**
+ * <p>Multiplies the value of this fraction by another, returning the
+ * result in reduced form.</p>
+ *
+ * @param fraction the fraction to multiply by, must not be {@code null}
+ * @return a {@code Fraction} instance with the resulting values
+ * @throws NullPointerException if the fraction is {@code null}
+ * @throws NumbersArithmeticException if the resulting numerator or denominator exceeds
+ * {@code Integer.MAX_VALUE}
+ */
+ public Fraction multiply(Fraction fraction) {
+ if (fraction == null) {
+ throw new NullPointerException("fraction");
+ }
+ if (numerator == 0 || fraction.numerator == 0) {
+ return ZERO;
+ }
+ // knuth 4.5.1
+ // make sure we don't overflow unless the result *must* overflow.
+ int d1 = ArithmeticUtils.gcd(numerator, fraction.denominator);
+ int d2 = ArithmeticUtils.gcd(fraction.numerator, denominator);
+ return getReducedFraction
+ (ArithmeticUtils.mulAndCheck(numerator/d1, fraction.numerator/d2),
+ ArithmeticUtils.mulAndCheck(denominator/d2, fraction.denominator/d1));
+ }
+
+ /**
+ * Multiply the fraction by an integer.
+ * @param i the {@code integer} to multiply by.
+ * @return this * i
+ */
+ public Fraction multiply(final int i) {
+ return multiply(new Fraction(i));
+ }
+
+ /**
+ * <p>Divide the value of this fraction by another.</p>
+ *
+ * @param fraction the fraction to divide by, must not be {@code null}
+ * @return a {@code Fraction} instance with the resulting values
+ * @throws IllegalArgumentException if the fraction is {@code null}
+ * @throws FractionException if the fraction to divide by is zero
+ * @throws NumbersArithmeticException if the resulting numerator or denominator exceeds
+ * {@code Integer.MAX_VALUE}
+ */
+ public Fraction divide(Fraction fraction) {
+ if (fraction == null) {
+ throw new NullPointerException("fraction");
+ }
+ if (fraction.numerator == 0) {
+ throw new FractionException("the fraction to divide by must not be zero: {0}/{1}",
+ fraction.numerator, fraction.denominator);
+ }
+ return multiply(fraction.reciprocal());
+ }
+
+ /**
+ * Divide the fraction by an integer.
+ * @param i the {@code integer} to divide by.
+ * @return this * i
+ */
+ public Fraction divide(final int i) {
+ return divide(new Fraction(i));
+ }
+
+ /**
+ * <p>
+ * Gets the fraction percentage as a {@code double}. This calculates the
+ * fraction as the numerator divided by denominator multiplied by 100.
+ * </p>
+ *
+ * @return the fraction percentage as a {@code double}.
+ */
+ public double percentageValue() {
+ return 100 * doubleValue();
+ }
+
+ /**
+ * <p>Creates a {@code Fraction} instance with the 2 parts
+ * of a fraction Y/Z.</p>
+ *
+ * <p>Any negative signs are resolved to be on the numerator.</p>
+ *
+ * @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 NumbersArithmeticException if the denominator is {@code zero}
+ */
+ public static Fraction getReducedFraction(int numerator, int denominator) {
+ if (denominator == 0) {
+ throw new ZeroDenominatorException(numerator, denominator);
+ }
+ if (numerator==0) {
+ return ZERO; // normalize zero.
+ }
+ // allow 2^k/-2^31 as a valid fraction (where k>0)
+ if (denominator==Integer.MIN_VALUE && (numerator&1)==0) {
+ numerator/=2; denominator/=2;
+ }
+ if (denominator < 0) {
+ if (numerator==Integer.MIN_VALUE ||
+ denominator==Integer.MIN_VALUE) {
+ throw new FractionOverflowException(numerator, denominator);
+ }
+ numerator = -numerator;
+ denominator = -denominator;
+ }
+ // simplify fraction.
+ int gcd = ArithmeticUtils.gcd(numerator, denominator);
+ numerator /= gcd;
+ denominator /= gcd;
+ return new Fraction(numerator, denominator);
+ }
+
+ /**
+ * <p>
+ * Returns the {@code String} representing this fraction, ie
+ * "num / dem" or just "num" if the denominator is one.
+ * </p>
+ *
+ * @return a string representation of the fraction.
+ * @see java.lang.Object#toString()
+ */
+ @Override
+ public String toString() {
+ final String str;
+ if (denominator == 1) {
+ str = Integer.toString(numerator);
+ } else if (numerator == 0) {
+ str = "0";
+ } else {
+ str = numerator + " / " + denominator;
+ }
+ return str;
+ }
+
+ /** {@inheritDoc} */
+ public FractionField getField() {
+ return FractionField.getInstance();
+ }
+
+}