org.apache.commons.math3.util.ArithmeticUtils Java Examples

private synchronized void configureSinks() {
  sinkConfigs = config.getInstanceConfigs(SINK_KEY);
  int confPeriod = 0;
  for (Entry<String, MetricsConfig> entry : sinkConfigs.entrySet()) {
    MetricsConfig conf = entry.getValue();
    int sinkPeriod = conf.getInt(PERIOD_KEY, PERIOD_DEFAULT);
    confPeriod = confPeriod == 0 ? sinkPeriod
                                 : ArithmeticUtils.gcd(confPeriod, sinkPeriod);
    String clsName = conf.getClassName("");
    if (clsName == null) continue;  // sink can be registered later on
    String sinkName = entry.getKey();
    try {
      MetricsSinkAdapter sa = newSink(sinkName,
          conf.getString(DESC_KEY, sinkName), conf);
      sa.start();
      sinks.put(sinkName, sa);
    }
    catch (Exception e) {
      LOG.warn("Error creating sink '"+ sinkName +"'", e);
    }
  }
  period = confPeriod > 0 ? confPeriod
                          : config.getInt(PERIOD_KEY, PERIOD_DEFAULT);
}
 

/** Evaluate Taylor expansion of a derivative structure.
 * @param ds array holding the derivative structure
 * @param dsOffset offset of the derivative structure in its array
 * @param delta parameters offsets (Δx, Δy, ...)
 * @return value of the Taylor expansion at x + Δx, y + Δy, ...
 * @throws MathArithmeticException if factorials becomes too large
 */
public double taylor(final double[] ds, final int dsOffset, final double ... delta)
   throws MathArithmeticException {
    double value = 0;
    for (int i = getSize() - 1; i >= 0; --i) {
        final int[] orders = getPartialDerivativeOrders(i);
        double term = ds[dsOffset + i];
        for (int k = 0; k < orders.length; ++k) {
            if (orders[k] > 0) {
                try {
                    term *= FastMath.pow(delta[k], orders[k]) /
                            ArithmeticUtils.factorial(orders[k]);
                } catch (NotPositiveException e) {
                    // this cannot happen
                    throw new MathInternalError(e);
                }
            }
        }
        value += term;
    }
    return value;
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

private synchronized void configureSinks() {
  sinkConfigs = config.getInstanceConfigs(SINK_KEY);
  int confPeriod = 0;
  for (Entry<String, MetricsConfig> entry : sinkConfigs.entrySet()) {
    MetricsConfig conf = entry.getValue();
    int sinkPeriod = conf.getInt(PERIOD_KEY, PERIOD_DEFAULT);
    confPeriod = confPeriod == 0 ? sinkPeriod
                                 : ArithmeticUtils.gcd(confPeriod, sinkPeriod);
    String clsName = conf.getClassName("");
    if (clsName == null) continue;  // sink can be registered later on
    String sinkName = entry.getKey();
    try {
      MetricsSinkAdapter sa = newSink(sinkName,
          conf.getString(DESC_KEY, sinkName), conf);
      sa.start();
      sinks.put(sinkName, sa);
    }
    catch (Exception e) {
      LOG.warn("Error creating sink '"+ sinkName +"'", e);
    }
  }
  period = confPeriod > 0 ? confPeriod
                          : config.getInt(PERIOD_KEY, PERIOD_DEFAULT);
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * <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 NullArgumentException if the fraction is {@code null}
 * @throws MathArithmeticException if the resulting numerator or denominator exceeds
 *  {@code Integer.MAX_VALUE}
 */
public Fraction multiply(Fraction fraction) {
    if (fraction == null) {
        throw new NullArgumentException(LocalizedFormats.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));
}
 

/**
 * Create a fraction given the numerator and denominator.  The fraction is
 * reduced to lowest terms.
 * @param num the numerator.
 * @param den the denominator.
 * @throws MathArithmeticException if the denominator is {@code zero}
 */
public Fraction(int num, int den) {
    if (den == 0) {
        throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR_IN_FRACTION,
                                          num, den);
    }
    if (den < 0) {
        if (num == Integer.MIN_VALUE ||
            den == Integer.MIN_VALUE) {
            throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_FRACTION,
                                              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;
}
 

private void sum(int bufferLength) throws StandardException {
		long newSum = sum;
		try {
                  for (int i = 0; i < bufferLength; i++) {
                      newSum = ArithmeticUtils.addAndCheck(newSum, buffer[i]);
                  }
              }
		catch (MathArithmeticException e) {
			throw StandardException.newException(SQLState.LANG_OUTSIDE_RANGE_FOR_DATATYPE,"BIGINT");
		}
		sum = newSum;
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = CombinatoricsUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = CombinatoricsUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = CombinatoricsUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

@Test
public void testReciprocal() {
    for (double x = 0.1; x < 1.2; x += 0.1) {
        DerivativeStructure r = new DerivativeStructure(1, 6, 0, x).reciprocal();
        Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);
        for (int i = 1; i < r.getOrder(); ++i) {
            double expected = ArithmeticUtils.pow(-1, i) * ArithmeticUtils.factorial(i) /
                              FastMath.pow(x, i + 1);
            Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));
        }
    }
}
 

/**
 * <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 MathArithmeticException if the denominator is {@code zero}
 */
public static Fraction getReducedFraction(int numerator, int denominator) {
    if (denominator == 0) {
        throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR_IN_FRACTION,
                                          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 MathArithmeticException(LocalizedFormats.OVERFLOW_IN_FRACTION,
                                              numerator, denominator);
        }
        numerator = -numerator;
        denominator = -denominator;
    }
    // simplify fraction.
    int gcd = ArithmeticUtils.gcd(numerator, denominator);
    numerator /= gcd;
    denominator /= gcd;
    return new Fraction(numerator, denominator);
}
 

@Test
public void testSize() {
    for (int i = 0; i < 6; ++i) {
        for (int j = 0; j < 6; ++j) {
            long expected = ArithmeticUtils.binomialCoefficient(i + j, i);
            Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
            Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
        }
    }
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

protected SlidingWindowAssigner(long size, long slide, long offset, boolean isEventTime) {
	if (size <= 0 || slide <= 0) {
		throw new IllegalArgumentException(
			"SlidingWindowAssigner parameters must satisfy slide > 0 and size > 0");
	}

	this.size = size;
	this.slide = slide;
	this.offset = offset;
	this.isEventTime = isEventTime;
	this.paneSize = ArithmeticUtils.gcd(size, slide);
	this.numPanesPerWindow = MathUtils.checkedDownCast(size / paneSize);
}
 

/** {@inheritDoc} */
public double probability(int x) {
    double ret;
    if (x < 0) {
        ret = 0.0;
    } else {
        ret = ArithmeticUtils.binomialCoefficientDouble(x +
              numberOfSuccesses - 1, numberOfSuccesses - 1) *
              FastMath.pow(probabilityOfSuccess, numberOfSuccesses) *
              FastMath.pow(1.0 - probabilityOfSuccess, x);
    }
    return ret;
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

@Test
public void testSize() {
    for (int i = 0; i < 6; ++i) {
        for (int j = 0; j < 6; ++j) {
            long expected = ArithmeticUtils.binomialCoefficient(i + j, i);
            Assert.assertEquals(expected, DSCompiler.getCompiler(i, j).getSize());
            Assert.assertEquals(expected, DSCompiler.getCompiler(j, i).getSize());
        }
    }
}
 

/** Evaluate Taylor expansion of a derivative structure.
 * @param ds array holding the derivative structure
 * @param dsOffset offset of the derivative structure in its array
 * @param delta parameters offsets (Δx, Δy, ...)
 * @return value of the Taylor expansion at x + Δx, y + Δy, ...
 */
public double taylor(final double[] ds, final int dsOffset, final double ... delta) {
    double value = 0;
    for (int i = getSize() - 1; i >= 0; --i) {
        final int[] orders = getPartialDerivativeOrders(i);
        double term = ds[dsOffset + i];
        for (int k = 0; k < orders.length; ++k) {
            if (orders[k] > 0) {
                term *= FastMath.pow(delta[k], orders[k]) / ArithmeticUtils.factorial(orders[k]);
            }
        }
        value += term;
    }
    return value;
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = CombinatoricsUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = CombinatoricsUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = CombinatoricsUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}
 

/** {@inheritDoc} */
public double probability(int x) {
    double ret;
    if (x < 0) {
        ret = 0.0;
    } else {
        ret = ArithmeticUtils.binomialCoefficientDouble(x +
              numberOfSuccesses - 1, numberOfSuccesses - 1) *
              FastMath.pow(probabilityOfSuccess, numberOfSuccesses) *
              FastMath.pow(1.0 - probabilityOfSuccess, x);
    }
    return ret;
}
 

/**
 * Create a fraction given the numerator and denominator.  The fraction is
 * reduced to lowest terms.
 * @param num the numerator.
 * @param den the denominator.
 * @throws MathArithmeticException if the denominator is {@code zero}
 */
public Fraction(int num, int den) {
    if (den == 0) {
        throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR_IN_FRACTION,
                                          num, den);
    }
    if (den < 0) {
        if (num == Integer.MIN_VALUE ||
            den == Integer.MIN_VALUE) {
            throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_FRACTION,
                                              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;
}
 

@Test
public void testReciprocal() {
    for (double x = 0.1; x < 1.2; x += 0.1) {
        DerivativeStructure r = new DerivativeStructure(1, 6, 0, x).reciprocal();
        Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);
        for (int i = 1; i < r.getOrder(); ++i) {
            double expected = ArithmeticUtils.pow(-1, i) * CombinatoricsUtils.factorial(i) /
                              FastMath.pow(x, i + 1);
            Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));
        }
    }
}
 

/**
 * <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 MathArithmeticException if the denominator is {@code zero}
 */
public static Fraction getReducedFraction(int numerator, int denominator) {
    if (denominator == 0) {
        throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR_IN_FRACTION,
                                          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 MathArithmeticException(LocalizedFormats.OVERFLOW_IN_FRACTION,
                                              numerator, denominator);
        }
        numerator = -numerator;
        denominator = -denominator;
    }
    // simplify fraction.
    int gcd = ArithmeticUtils.gcd(numerator, denominator);
    numerator /= gcd;
    denominator /= gcd;
    return new Fraction(numerator, denominator);
}
 

/** {@inheritDoc} */
public double probability(int x) {
    double ret;
    if (x < 0) {
        ret = 0.0;
    } else {
        ret = ArithmeticUtils.binomialCoefficientDouble(x +
              numberOfSuccesses - 1, numberOfSuccesses - 1) *
              FastMath.pow(probabilityOfSuccess, numberOfSuccesses) *
              FastMath.pow(1.0 - probabilityOfSuccess, x);
    }
    return ret;
}
 

/**
 * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact
 * arithmetic is used; in case of overflow, an exception is thrown.
 *
 * @param i Row index (starts at 0).
 * @param j Column index (starts at 0).
 * @return The coefficient of the inverse Hilbert matrix.
 */
public long getEntry(final int i, final int j) {
    long val = i + j + 1;
    long aux = ArithmeticUtils.binomialCoefficient(n + i, n - j - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(n + j, n - i - 1);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    aux = ArithmeticUtils.binomialCoefficient(i + j, i);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    val = ArithmeticUtils.mulAndCheck(val, aux);
    return ((i + j) & 1) == 0 ? val : -val;
}