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Re: commons-numbers git commit: Complex class [...]

Gilles Sadowski
Hi Eric.

A few comments below.

On Wed, 15 Mar 2017 16:07:26 +0000 (UTC), [hidden email]
wrote:
> Repository: commons-numbers
> Updated Branches:
>   refs/heads/master 39b5119cc -> 857033738

Overall, better let people a large set of changes in a "feature"
branch rather than modify "master" and then have to revert...

>
> Complex class references updated for numbers rather than math.
> Syntactical sugar added so all required c++11 syntax can be used with
> Complex() . Inverse hyperbolic funtions added using formulas from
> Complex.js to conform to c++11 standards.

Wouldn't it be nicer to have a shorter first line and provide the
details in a second paragraph?

>
>
> Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
> Commit:
>
> http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/85703373
> Tree:
> http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/85703373
> Diff:
> http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/85703373
>
> Branch: refs/heads/master
> Commit: 857033738c5f470289f3ff4ea325e5b7f6adae52
> Parents: 39b5119
> Author: Eric Barnhill <[hidden email]>
> Authored: Wed Mar 15 17:00:23 2017 +0100
> Committer: Eric Barnhill <[hidden email]>
> Committed: Wed Mar 15 17:00:23 2017 +0100
>
>
> ----------------------------------------------------------------------
>  .swp                                            | Bin 0 -> 16384
> bytes
>  .../apache/commons/numbers/complex/Complex.java | 420
> ++++++++++++++-----
>  .../numbers/core/.ArithmeticUtils.java.swp      | Bin 0 -> 16384
> bytes
>  .../numbers/fraction/.BigFraction.java.swp      | Bin 0 -> 16384
> bytes

What's this?

>  4 files changed, 321 insertions(+), 99 deletions(-)
>
> ----------------------------------------------------------------------
>
>
>
> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/85703373/.swp
>
> ----------------------------------------------------------------------
> diff --git a/.swp b/.swp
> new file mode 100644
> index 0000000..e5f142d
> Binary files /dev/null and b/.swp differ
>
>
> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/85703373/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
>
> ----------------------------------------------------------------------
> diff --git
>
> a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
>
> b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
> index 4e9022e..6e4639b 100644
> ---
>
> a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
> +++
>
> b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
> @@ -20,7 +20,9 @@ package org.apache.commons.numbers.complex;
>  import java.io.Serializable;
>  import java.util.ArrayList;
>  import java.util.List;
> +
>  import org.apache.commons.numbers.core.Precision;
> +
>  /**
>   * Representation of a Complex number, i.e. a number which has both
> a
>   * real and imaginary part.
> @@ -38,10 +40,10 @@ import org.apache.commons.numbers.core.Precision;
>   * Note that this contradicts the IEEE-754 standard for floating
>   * point numbers (according to which the test {@code x == x} must
> fail if
>   * {@code x} is {@code NaN}). The method
> - * {@link
> org.apache.commons.numbers.core.Precision#equals(double,double,int)
> - * equals for primitive double} in class {@code Precision} conforms
> with
> - * IEEE-754 while this class conforms with the standard behavior for
> Java
> - * object types.</p>
> + * {@link
> org.apache.commons.math4.util.Precision#equals(double,double,int)
> + * equals for primitive double} in {@link
> org.apache.commons.math4.util.Precision}
> + * conforms with IEEE-754 while this class conforms with the
> standard behavior
> + * for Java object types.</p>
>   *
>   */
>  public class Complex implements Serializable  {
> @@ -59,15 +61,15 @@ public class Complex implements Serializable  {
>      public static final Complex ZERO = new Complex(0.0, 0.0);
>
>      /** Serializable version identifier */
> -    private static final long serialVersionUID = 201701120L;
> +    private static final long serialVersionUID =
> -6195664516687396620L;

I'd prefer to keep the convention we adopted in Commons Math, i.e. the
date (of the incompatible change).

>
>      /** The imaginary part. */
>      private final double imaginary;
>      /** The real part. */
>      private final double real;
> -    /** Record whether this complex number is equal to NaN. */
> +    /** Record whether this Complex number is equal to NaN. */
>      private final transient boolean isNaN;
> -    /** Record whether this complex number is infinite. */
> +    /** Record whether this Complex number is infinite. */
>      private final transient boolean isInfinite;
>
>      /**
> @@ -79,7 +81,7 @@ public class Complex implements Serializable  {
>          this(real, 0.0);
>      }
>
> -    /**
> +     /**

Misalignment (introducing a spurious difference).

>       * Create a complex number given the real and imaginary parts.
>       *
>       * @param real Real part.
> @@ -94,8 +96,56 @@ public class Complex implements Serializable  {
>              (Double.isInfinite(real) ||
> Double.isInfinite(imaginary));
>      }
>
> +     /**
> +     * Creates a Complex from its polar representation.
> +     * <p>
> +     * If either {@code r} or {@code theta} is NaN, or {@code theta}
> is
> +     * infinite, {@link Complex#NaN} is returned.
> +     * <p>
> +     * If {@code r} is infinite and {@code theta} is finite,
> infinite or NaN
> +     * values may be returned in parts of the result, following the
> rules for
> +     * double arithmetic.
> +     *
> +     * <pre>
> +     * Examples:
> +     * {@code
> +     * polar2Complex(INFINITY, \(\pi\)) = INFINITY + INFINITY i
> +     * polar2Complex(INFINITY, 0) = INFINITY + NaN i
> +     * polar2Complex(INFINITY, \(-\frac{\pi}{4}\)) = INFINITY -
> INFINITY i
> +     * polar2Complex(INFINITY, \(5\frac{\pi}{4}\)) = -INFINITY -
> INFINITY i }
> +     * </pre>
> +     *
> +     * @param r the modulus of the complex number to create
> +     * @param theta the argument of the complex number to create
> +     * @return {@code Complex}
> +     * @since 1.1

There hasn't been a 1.0 release yet.

> +     */
> +    public Complex polar(double r, double theta) {
> +        checkNotNegative(r);
> +        return new Complex(r * Math.cos(theta), r *
> Math.sin(theta));
> +    }
> +
>      /**
> -     * Return the absolute value of this complex number.
> +     * Returns projection of this Complex number onto the Riemann
> sphere,
> +     * i.e. all infinities (including those with an NaN component)
> +     * project onto real infinity, as described in the
> +     * <a
>
> href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/cproj.html">
> +     * IEEE and ISO C standards</a>.
> +     * <p>
> +     *
> +     *
> +     * @return {@code Complex} projected onto the Riemann sphere.
> +     */
> +    public Complex proj() {
> +        if (isInfinite) {
> +            return new Complex(Double.POSITIVE_INFINITY);
> +        } else {
> +            return this;
> +        }
> +    }
> +
> +     /**
> +     * Return the absolute value of this Complex number.
>       * Returns {@code NaN} if either real or imaginary part is
> {@code NaN}
>       * and {@code Double.POSITIVE_INFINITY} if neither part is
> {@code NaN},
>       * but at least one part is infinite.
> @@ -124,6 +174,19 @@ public class Complex implements Serializable  {
>          }
>      }
>
> +     /**
> +     * Return the norm of this Complex number, defined as the square
> of the magnitude
> +     * (Matches C++ 11 standards.)

I would rather move that comment to the class Javadoc (with a link).
Or do you intend to have only partial compliance?

> +     * Returns {@code NaN} if either real or imaginary part is
> {@code NaN}
> +     * and {@code Double.POSITIVE_INFINITY} if neither part is
> {@code NaN},
> +     * but at least one part is infinite.
> +     *
> +     * @return the absolute value.
> +     */
> +    public double norm() {
> +        return abs()*abs();

There must be one space character around operators.

> +    }
> +
>      /**
>       * Returns a {@code Complex} whose value is
>       * {@code (this + addend)}.
> @@ -138,6 +201,7 @@ public class Complex implements Serializable  {
>       *
>       * @param  addend Value to be added to this {@code Complex}.
>       * @return {@code this + addend}.
> +     * @if {@code addend} is {@code null}.

@if ?

>       */
>      public Complex add(Complex addend) {
>          checkNotNull(addend);
> @@ -166,7 +230,7 @@ public class Complex implements Serializable  {
>      }
>
>       /**
> -     * Returns the conjugate of this complex number.
> +     * Returns the conjugate of this Complex number.
>       * The conjugate of {@code a + bi} is {@code a - bi}.
>       * <p>
>       * {@link #NaN} is returned if either the real or imaginary
> @@ -187,6 +251,17 @@ public class Complex implements Serializable  {
>          return createComplex(real, -imaginary);
>      }
>
> +     /**
> +     * Returns the conjugate of this Complex number.
> +     * C++11 grammar.

This is a new component: let's define _one_ convention; again you can
refer to the reason for the choice in the Javadoc. (Same for other
similar instances below).

> +     * </p>
> +     * @return the conjugate of this Complex object.
> +     */
> +    public Complex conj() {
> +        return conjugate();
> +    }
> +
> +
>      /**
>       * Returns a {@code Complex} whose value is
>       * {@code (this / divisor)}.
> @@ -227,8 +302,10 @@ public class Complex implements Serializable  {
>       *
>       * @param divisor Value by which this {@code Complex} is to be
> divided.
>       * @return {@code this / divisor}.
> +     * @if {@code divisor} is {@code null}.
>       */
> -    public Complex divide(Complex divisor) {
> +    public Complex divide(Complex divisor)
> +        {
>          checkNotNull(divisor);
>          if (isNaN || divisor.isNaN) {
>              return NaN;
> @@ -279,12 +356,7 @@ public class Complex implements Serializable  {
>                               imaginary  / divisor);
>      }
>
> -    /**
> -     * Returns the multiplicative inverse this instance.
> -     *
> -     * @return {@code 1 / this}.
> -     * @see #divide(Complex)
> -     */
> +    /** {@inheritDoc} */
>      public Complex reciprocal() {
>          if (isNaN) {
>              return NaN;
> @@ -343,8 +415,8 @@ public class Complex implements Serializable  {
>              if (c.isNaN) {
>                  return isNaN;
>              } else {
> -                return equals(real, c.real) &&
> -                    equals(imaginary, c.imaginary);
> +                return Precision.equals(real, c.real) &&
> +                    Precision.equals(imaginary, c.imaginary);
>              }
>          }
>          return false;
> @@ -365,6 +437,7 @@ public class Complex implements Serializable  {
>       * and {@code y}.
>       *
>       * @see Precision#equals(double,double,int)
> +     * @since 3.3
>       */
>      public static boolean equals(Complex x, Complex y, int maxUlps)
> {
>          return Precision.equals(x.real, y.real, maxUlps) &&
> @@ -378,6 +451,8 @@ public class Complex implements Serializable  {
>       * @param x First value (cannot be {@code null}).
>       * @param y Second value (cannot be {@code null}).
>       * @return {@code true} if the values are equal.
> +     *
> +     * @since 3.3

Wrong @since. (Several more below).

>       */
>      public static boolean equals(Complex x, Complex y) {
>          return equals(x, y, 1);
> @@ -396,6 +471,7 @@ public class Complex implements Serializable  {
>       * numbers or they are within range of each other.
>       *
>       * @see Precision#equals(double,double,double)
> +     * @since 3.3
>       */
>      public static boolean equals(Complex x, Complex y, double eps) {
>          return Precision.equals(x.real, y.real, eps) &&
> @@ -415,6 +491,7 @@ public class Complex implements Serializable  {
>       * numbers or they are within range of each other.
>       *
>       * @see
> Precision#equalsWithRelativeTolerance(double,double,double)
> +     * @since 3.3
>       */
>      public static boolean equalsWithRelativeTolerance(Complex x,
> Complex y,
>                                                        double eps) {
> @@ -434,8 +511,8 @@ public class Complex implements Serializable  {
>          if (isNaN) {
>              return 7;
>          }
> -        return 37 * (17 * hash(imaginary) +
> -            hash(real));
> +        return 37 * (17 * Precision.hash(imaginary) +
> +            Precision.hash(real));
>      }
>
>      /**
> @@ -446,6 +523,14 @@ public class Complex implements Serializable  {
>      public double getImaginary() {
>          return imaginary;
>      }
> +    /**
> +     * Access the imaginary part (C++ grammar)
> +     *
> +     * @return the imaginary part.
> +     */
> +    public double imag() {
> +        return imaginary;
> +    }
>
>      /**
>       * Access the real part.
> @@ -456,11 +541,20 @@ public class Complex implements Serializable  {
>          return real;
>      }
>
> -    /**
> -     * Checks whether either or both parts of this complex number is
> +     /**
> +     * Access the real part (C++ grammar)
> +     *
> +     * @return the real part.
> +     */
> +    public double real() {
> +        return real;
> +    }
> +
> +   /**
> +     * Checks whether either or both parts of this Complex number is
>       * {@code NaN}.
>       *
> -     * @return true if either or both parts of this complex number
> is
> +     * @return true if either or both parts of this Complex number
> is
>       * {@code NaN}; false otherwise.
>       */
>      public boolean isNaN() {
> @@ -468,12 +562,12 @@ public class Complex implements Serializable  {
>      }
>
>      /**
> -     * Checks whether either the real or imaginary part of this
> complex number
> +     * Checks whether either the real or imaginary part of this
> Complex number
>       * takes an infinite value (either {@code
> Double.POSITIVE_INFINITY} or
>       * {@code Double.NEGATIVE_INFINITY}) and neither part
>       * is {@code NaN}.
>       *
> -     * @return true if one or both parts of this complex number are
> infinite
> +     * @return true if one or both parts of this Complex number are
> infinite
>       * and neither part is {@code NaN}.
>       */
>      public boolean isInfinite() {
> @@ -500,8 +594,10 @@ public class Complex implements Serializable  {
>       *
>       * @param  factor value to be multiplied by this {@code
> Complex}.
>       * @return {@code this * factor}.
> +     * @if {@code factor} is {@code null}.
>       */
> -    public Complex multiply(Complex factor) {
> +    public Complex multiply(Complex factor)
> +        {
>          checkNotNull(factor);
>          if (isNaN || factor.isNaN) {
>              return NaN;
> @@ -586,8 +682,10 @@ public class Complex implements Serializable  {
>       *
>       * @param  subtrahend value to be subtracted from this {@code
> Complex}.
>       * @return {@code this - subtrahend}.
> +     * @if {@code subtrahend} is {@code null}.
>       */
> -    public Complex subtract(Complex subtrahend) {
> +    public Complex subtract(Complex subtrahend)
> +        {
>          checkNotNull(subtrahend);
>          if (isNaN || subtrahend.isNaN) {
>              return NaN;
> @@ -615,7 +713,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/InverseCosine.html"
> TARGET="_top">

TARGET ?
(Several other instances below.)

> -     * inverse cosine</a> of this complex number.
> +     * inverse cosine</a> of this Complex number.
>       * Implements the formula:
>       * <p>
>       *  {@code acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))}
> @@ -623,7 +721,8 @@ public class Complex implements Serializable  {
>       * Returns {@link Complex#NaN} if either real or imaginary part
> of the
>       * input argument is {@code NaN} or infinite.
>       *
> -     * @return the inverse cosine of this complex number.
> +     * @return the inverse cosine of this Complex number.
> +     * @since 1.2
>       */
>      public Complex acos() {
>          if (isNaN) {
> @@ -636,7 +735,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/InverseSine.html"
> TARGET="_top">
> -     * inverse sine</a> of this complex number.
> +     * inverse sine</a> of this Complex number.
>       * Implements the formula:
>       * <p>
>       *  {@code asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))}
> @@ -644,7 +743,8 @@ public class Complex implements Serializable  {
>       * Returns {@link Complex#NaN} if either real or imaginary part
> of the
>       * input argument is {@code NaN} or infinite.</p>
>       *
> -     * @return the inverse sine of this complex number.
> +     * @return the inverse sine of this Complex number.
> +     * @since 1.2
>       */
>      public Complex asin() {
>          if (isNaN) {
> @@ -657,7 +757,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/InverseTangent.html"
> TARGET="_top">
> -     * inverse tangent</a> of this complex number.
> +     * inverse tangent</a> of this Complex number.
>       * Implements the formula:
>       * <p>
>       * {@code atan(z) = (i/2) log((i + z)/(i - z))}
> @@ -665,7 +765,8 @@ public class Complex implements Serializable  {
>       * Returns {@link Complex#NaN} if either real or imaginary part
> of the
>       * input argument is {@code NaN} or infinite.</p>
>       *
> -     * @return the inverse tangent of this complex number
> +     * @return the inverse tangent of this Complex number
> +     * @since 1.2
>       */
>      public Complex atan() {
>          if (isNaN) {
> @@ -678,8 +779,86 @@ public class Complex implements Serializable  {
>
>      /**
>       * Compute the
> +     * <a
> href="http://mathworld.wolfram.com/InverseHyperbolicSine.html"
> TARGET="_top">
> +     * inverse hyperbolic sine</a> of this Complex number.
> +     * Implements the formula:
> +     * <p>
> +     * {@code asinh(z) = log(z+sqrt(z^2+1))}
> +     * </p><p>
> +     * Returns {@link Complex#NaN} if either real or imaginary part
> of the
> +     * input argument is {@code NaN} or infinite.</p>
> +     *
> +     * @return the inverse hyperbolic cosine of this Complex number
> +     * @since 1.2
> +     */
> +    public Complex asinh(){
> +        if (isNaN) {
> +            return NaN;
> +        }
> +
> +        return square().add(Complex.ONE).sqrt().add(this).log();
> +    }
> +
> +   /**
> +     * Compute the
> +     * <a
> href="http://mathworld.wolfram.com/InverseHyperbolicTangent.html"
> TARGET="_top">
> +     * inverse hyperbolic tangent</a> of this Complex number.
> +     * Implements the formula:
> +     * <p>
> +     * {@code atanh(z) = log((1+z)/(1-z))/2}
> +     * </p><p>
> +     * Returns {@link Complex#NaN} if either real or imaginary part
> of the
> +     * input argument is {@code NaN} or infinite.</p>
> +     *
> +     * @return the inverse hyperbolic cosine of this Complex number
> +     * @since 1.2
> +     */
> +    public Complex atanh(){
> +        if (isNaN) {
> +            return NaN;
> +        }
> +
> +        return
>
> this.add(Complex.ONE).divide(Complex.ONE.subtract(this)).log().divide(new
> Complex(2));
> +    }
> +   /**
> +     * Compute the
> +     * <a
> href="http://mathworld.wolfram.com/InverseHyperbolicCosine.html"
> TARGET="_top">
> +     * inverse hyperbolic cosine</a> of this Complex number.
> +     * Implements the formula:
> +     * <p>
> +     * {@code acosh(z) = log(z+sqrt(z^2-1))}
> +     * </p><p>
> +     * Returns {@link Complex#NaN} if either real or imaginary part
> of the
> +     * input argument is {@code NaN} or infinite.</p>
> +     *
> +     * @return the inverse hyperbolic cosine of this Complex number
> +     * @since 1.2
> +     */
> +    public Complex acosh() {
> +        if (isNaN) {
> +            return NaN;
> +        }
> +
> +        return
> square().subtract(Complex.ONE).sqrt().add(this).log();
> +    }
> +
> +    /**
> +     * Compute the square of this Complex number.
> +     *
> +     * @return square of this Complex number
> +     */
> +    public Complex square(){
> +        if (isNaN) {
> +            return NaN;
> +        }
> +
> +        return this.multiply(this);
> +    }
> +
> +    /**
> +     * Compute the
>       * <a href="http://mathworld.wolfram.com/Cosine.html"
> TARGET="_top">
> -     * cosine</a> of this complex number.
> +     * cosine</a> of this Complex number.
>       * Implements the formula:
>       * <p>
>       *  {@code cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i}
> @@ -702,7 +881,8 @@ public class Complex implements Serializable  {
>       *  </code>
>       * </pre>
>       *
> -     * @return the cosine of this complex number.
> +     * @return the cosine of this Complex number.
> +     * @since 1.2
>       */
>      public Complex cos() {
>          if (isNaN) {
> @@ -716,7 +896,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html"
> TARGET="_top">
> -     * hyperbolic cosine</a> of this complex number.
> +     * hyperbolic cosine</a> of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -741,7 +921,8 @@ public class Complex implements Serializable  {
>       *  </code>
>       * </pre>
>       *
> -     * @return the hyperbolic cosine of this complex number.
> +     * @return the hyperbolic cosine of this Complex number.
> +     * @since 1.2
>       */
>      public Complex cosh() {
>          if (isNaN) {
> @@ -755,7 +936,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a
> href="http://mathworld.wolfram.com/ExponentialFunction.html"
> TARGET="_top">
> -     * exponential function</a> of this complex number.
> +     * exponential function</a> of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -782,6 +963,7 @@ public class Complex implements Serializable  {
>       * </pre>
>       *
>       * @return <code><i>e</i><sup>this</sup></code>.
> +     * @since 1.2
>       */
>      public Complex exp() {
>          if (isNaN) {
> @@ -796,7 +978,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html"
> TARGET="_top">
> -     * natural logarithm</a> of this complex number.
> +     * natural logarithm</a> of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -826,6 +1008,7 @@ public class Complex implements Serializable  {
>       *
>       * @return the value <code>ln &nbsp; this</code>, the natural
> logarithm
>       * of {@code this}.
> +     * @since 1.2
>       */
>      public Complex log() {
>          if (isNaN) {
> @@ -837,7 +1020,19 @@ public class Complex implements Serializable  {
>      }
>
>      /**
> -     * Returns of value of this complex number raised to the power
> of {@code x}.
> +     * Compute the base 10 or
> +     * <a href="http://mathworld.wolfram.com/CommonLogarithm.html"
> TARGET="_top">
> +     * common logarithm</a> of this Complex number.
> +     *
> +     *  @return the base 10 logarithm of <code>this</code>.
> +    */
> +    public Complex log10() {
> +        return createComplex(Math.log(abs())/Math.log(10),
> +                             Math.atan2(imaginary, real));
> +    }
> +
> +    /**
> +     * Returns of value of this Complex number raised to the power
> of {@code x}.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -853,38 +1048,23 @@ public class Complex implements Serializable  
> {
>       *
>       * @param  x exponent to which this {@code Complex} is to be
> raised.
>       * @return <code> this<sup>x</sup></code>.
> +     * @if x is {@code null}.
> +     * @since 1.2
>       */
> -    public Complex pow(Complex x) {
> +    public Complex pow(Complex x)
> +        {
>          checkNotNull(x);
> -        if (real == 0 && imaginary == 0) {
> -            if (x.real > 0 && x.imaginary == 0) {
> -                // 0 raised to positive number is 0
> -                return ZERO;
> -            } else {
> -                // 0 raised to anything else is NaN
> -                return NaN;
> -            }
> -        }
>          return this.log().multiply(x).exp();
>      }
>
>      /**
> -     * Returns of value of this complex number raised to the power
> of {@code x}.
> +     * Returns of value of this Complex number raised to the power
> of {@code x}.
>       *
>       * @param  x exponent to which this {@code Complex} is to be
> raised.
>       * @return <code>this<sup>x</sup></code>.
>       * @see #pow(Complex)
>       */
>       public Complex pow(double x) {
> -        if (real == 0 && imaginary == 0) {
> -            if (x > 0) {
> -                // 0 raised to positive number is 0
> -                return ZERO;
> -            } else {
> -                // 0 raised to anything else is NaN
> -                return NaN;
> -            }
> -        }
>          return this.log().multiply(x).exp();
>      }
>
> @@ -892,7 +1072,7 @@ public class Complex implements Serializable  {
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/Sine.html"
> TARGET="_top">
>       * sine</a>
> -     * of this complex number.
> +     * of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -917,7 +1097,8 @@ public class Complex implements Serializable  {
>       *  </code>
>       * </pre>
>       *
> -     * @return the sine of this complex number.
> +     * @return the sine of this Complex number.
> +     * @since 1.2
>       */
>      public Complex sin() {
>          if (isNaN) {
> @@ -931,7 +1112,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/HyperbolicSine.html"
> TARGET="_top">
> -     * hyperbolic sine</a> of this complex number.
> +     * hyperbolic sine</a> of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -957,6 +1138,7 @@ public class Complex implements Serializable  {
>       * </pre>
>       *
>       * @return the hyperbolic sine of {@code this}.
> +     * @since 1.2
>       */
>      public Complex sinh() {
>          if (isNaN) {
> @@ -970,7 +1152,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/SquareRoot.html"
> TARGET="_top">
> -     * square root</a> of this complex number.
> +     * square root</a> of this Complex number.
>       * Implements the following algorithm to compute {@code sqrt(a +
> bi)}:
>       * <ol><li>Let {@code t = sqrt((|a| + |a + bi|) / 2)}</li>
>       * <li><pre>if {@code  a &#8805; 0} return {@code t + (b/2t)i}
> @@ -999,6 +1181,7 @@ public class Complex implements Serializable  {
>       * </pre>
>       *
>       * @return the square root of {@code this}.
> +     * @since 1.2
>       */
>      public Complex sqrt() {
>          if (isNaN) {
> @@ -1033,6 +1216,7 @@ public class Complex implements Serializable  {
>       * infinite or NaN values returned in parts of the result.
>       *
>       * @return the square root of <code>1 - this<sup>2</sup></code>.
> +     * @since 1.2
>       */
>      public Complex sqrt1z() {
>          return createComplex(1.0,
> 0.0).subtract(this.multiply(this)).sqrt();
> @@ -1041,7 +1225,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/Tangent.html"
> TARGET="_top">
> -     * tangent</a> of this complex number.
> +     * tangent</a> of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -1068,6 +1252,7 @@ public class Complex implements Serializable  {
>       * </pre>
>       *
>       * @return the tangent of {@code this}.
> +     * @since 1.2
>       */
>      public Complex tan() {
>          if (isNaN || Double.isInfinite(real)) {
> @@ -1091,7 +1276,7 @@ public class Complex implements Serializable  {
>      /**
>       * Compute the
>       * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html"
> TARGET="_top">
> -     * hyperbolic tangent</a> of this complex number.
> +     * hyperbolic tangent</a> of this Complex number.
>       * Implements the formula:
>       * <pre>
>       *  <code>
> @@ -1118,6 +1303,7 @@ public class Complex implements Serializable  {
>       * </pre>
>       *
>       * @return the hyperbolic tangent of {@code this}.
> +     * @since 1.2
>       */
>      public Complex tanh() {
>          if (isNaN || Double.isInfinite(imaginary)) {
> @@ -1137,10 +1323,8 @@ public class Complex implements Serializable  
> {
>                               Math.sin(imaginary2) / d);
>      }
>
> -
> -
>      /**
> -     * Compute the argument of this complex number.
> +     * Compute the argument of this Complex number.
>       * The argument is the angle phi between the positive real axis
> and
>       * the point representing this number in the complex plane.
>       * The value returned is between -PI (not inclusive)
> @@ -1157,11 +1341,32 @@ public class Complex implements Serializable  
> {
>       * @return the argument of {@code this}.
>       */
>      public double getArgument() {
> -        return Math.atan2(getImaginary(), getReal());
> +        return Math.atan2(imaginary, real);
>      }
>
>      /**
> -     * Computes the n-th roots of this complex number.
> +     * Compute the argument of this Complex number.
> +     * The argument is the angle phi between the positive real axis
> and
> +     * the point representing this number in the complex plane.
> +     * The value returned is between -PI (not inclusive)
> +     * and PI (inclusive), with negative values returned for numbers
> with
> +     * negative imaginary parts.
> +     * <p>
> +     * If either real or imaginary part (or both) is NaN, NaN is
> returned.
> +     * Infinite parts are handled as {@code Math.atan2} handles
> them,
> +     * essentially treating finite parts as zero in the presence of
> an
> +     * infinite coordinate and returning a multiple of pi/4
> depending on
> +     * the signs of the infinite parts.
> +     * See the javadoc for {@code Math.atan2} for full details.
> +     *
> +     * @return the argument of {@code this}.
> +     */
> +    public double arg() {
> +        return getArgument();
> +    }
> +
> +    /**
> +     * Computes the n-th roots of this Complex number.
>       * The nth roots are defined by the formula:
>       * <pre>
>       *  <code>
> @@ -1170,21 +1375,21 @@ public class Complex implements Serializable  
> {
>       * </pre>
>       * for <i>{@code k=0, 1, ..., n-1}</i>, where {@code abs} and
> {@code phi}
>       * are respectively the {@link #abs() modulus} and
> -     * {@link #getArgument() argument} of this complex number.
> +     * {@link #getArgument() argument} of this Complex number.
>       * <p>
> -     * If one or both parts of this complex number is NaN, a list
> with just
> +     * If one or both parts of this Complex number is NaN, a list
> with just
>       * one element, {@link #NaN} is returned.
>       * if neither part is NaN, but at least one part is infinite,
> the result
>       * is a one-element list containing {@link #INF}.
>       *
>       * @param n Degree of root.
>       * @return a List of all {@code n}-th roots of {@code this}.
> +     * @throws NotPositiveException if {@code n <= 0}.
> +     * @since 2.0
>       */
>      public List<Complex> nthRoot(int n) {
>
> -        if (n <= 0) {
> -            throw new RuntimeException("cannot compute nth root for
> null or negative n: {0}");
> -        }
> +        checkNotNegative(n);
>
>          final List<Complex> result = new ArrayList<Complex>();
>
> @@ -1221,6 +1426,7 @@ public class Complex implements Serializable  {
>       * @param realPart Real part.
>       * @param imaginaryPart Imaginary part.
>       * @return a new complex number instance.
> +     * @since 1.2
>       * @see #valueOf(double, double)
>       */
>      protected Complex createComplex(double realPart,
> @@ -1263,6 +1469,7 @@ public class Complex implements Serializable  {
>       * deserialize properly.
>       *
>       * @return A Complex instance with all fields resolved.
> +     * @since 2.0
>       */
>      protected final Object readResolve() {
>          return createComplex(real, imaginary);
> @@ -1274,36 +1481,51 @@ public class Complex implements Serializable  
> {
>          return "(" + real + ", " + imaginary + ")";
>      }
>
> -    /**
> -     * Checks that an object is not null.
> -     *
> -     * @param o Object to be checked.
> +     /**
> +     * Check that the argument is positive and throw a
> RuntimeException
> +     * if it is not.
> +     * @param arg {@code double} to check
>       */
> -    private static void checkNotNull(Object o) {
> -        if (o == null) {
> -            throw new RuntimeException("Null Argument to Complex
> Method");
> +    private static void checkNotNegative(double arg) {
> +        if (arg <= 0) {
> +            throw new RuntimeException("Complex: Non-positive
> argument");
>          }
>      }
>
> +
> +     /**
> +     * Check that the argument is positive and throw a
> RuntimeException
> +     * if it is not.
> +     * @param arg {@code int} to check
> +     */
> +    private static void checkNotNegative(int arg) {
> +        if (arg <= 0) {
> +            throw new RuntimeException("Complex: Non-positive
> argument");
> +        }
> +    }
> +
>      /**
> -     * Returns {@code true} if the values are equal according to
> semantics of
> -     * {@link Double#equals(Object)}.
> -     *
> -     * @param x Value
> -     * @param y Value
> -     * @return {@code new Double(x).equals(new Double(y))}
> +     * Check that the Complex is not null and throw a
> RuntimeException
> +     * if it is.
> +     * @param arg     the Complex to check
>       */
> -    private static boolean equals(double x, double y) {
> -        return new Double(x).equals(new Double(y));
> +    private static void checkNotNull(Complex arg) {
> +        if (arg == null) {
> +            throw new RuntimeException("Complex: Null argument");
> +        }
>      }
>
>      /**
> -     * Returns an integer hash code representing the given double
> value.
> -     *
> -     * @param value the value to be hashed
> -     * @return the hash code
> +     * Check that the argument is not null and throw a
> RuntimeException
> +     * if it is.
> +     * @param arg     the argument to check
> +     * @param argName the name of the argument
>       */
> -    private static int hash(double value) {
> -        return new Double(value).hashCode();
> +    private static void checkNotNull(Object arg, String argName) {
> +        if (arg == null) {
> +            throw new RuntimeException("Complex: Null argument");
> +        }
>      }
> -}
> +}
> +
> +
>
>
> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/85703373/commons-numbers-core/src/main/java/org/apache/commons/numbers/core/.ArithmeticUtils.java.swp
>
> ----------------------------------------------------------------------
> diff --git
>
> a/commons-numbers-core/src/main/java/org/apache/commons/numbers/core/.ArithmeticUtils.java.swp
>
> b/commons-numbers-core/src/main/java/org/apache/commons/numbers/core/.ArithmeticUtils.java.swp
> new file mode 100644
> index 0000000..cb08acb
> Binary files /dev/null and
>
> b/commons-numbers-core/src/main/java/org/apache/commons/numbers/core/.ArithmeticUtils.java.swp
> differ
>
>
> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/85703373/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/.BigFraction.java.swp
>
> ----------------------------------------------------------------------
> diff --git
>
> a/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/.BigFraction.java.swp
>
> b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/.BigFraction.java.swp
> new file mode 100644
> index 0000000..0321309
> Binary files /dev/null and
>
> b/commons-numbers-fraction/src/main/java/org/apache/commons/numbers/fraction/.BigFraction.java.swp
> differ



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Re: commons-numbers git commit: Complex class [...]

Eric Barnhill
Sorry Gilles I meant to push a new branch. Will fix tomorrow.
On 15 Mar 2017 17:34, "Gilles" <[hidden email]> wrote:

> Hi Eric.
>
> A few comments below.
>
> On Wed, 15 Mar 2017 16:07:26 +0000 (UTC), [hidden email] wrote:
>
>> Repository: commons-numbers
>> Updated Branches:
>>   refs/heads/master 39b5119cc -> 857033738
>>
>
> Overall, better let people a large set of changes in a "feature"
> branch rather than modify "master" and then have to revert...
>
>
>> Complex class references updated for numbers rather than math.
>> Syntactical sugar added so all required c++11 syntax can be used with
>> Complex() . Inverse hyperbolic funtions added using formulas from
>> Complex.js to conform to c++11 standards.
>>
>
> Wouldn't it be nicer to have a shorter first line and provide the
> details in a second paragraph?
>
>
>>
>> Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
>> Commit:
>>
>> http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/85703373
>> Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/
>> 85703373
>> Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/
>> 85703373
>>
>> Branch: refs/heads/master
>> Commit: 857033738c5f470289f3ff4ea325e5b7f6adae52
>> Parents: 39b5119
>> Author: Eric Barnhill <[hidden email]>
>> Authored: Wed Mar 15 17:00:23 2017 +0100
>> Committer: Eric Barnhill <[hidden email]>
>> Committed: Wed Mar 15 17:00:23 2017 +0100
>>
>>
>> ----------------------------------------------------------------------
>>  .swp                                            | Bin 0 -> 16384 bytes
>>  .../apache/commons/numbers/complex/Complex.java | 420
>> ++++++++++++++-----
>>  .../numbers/core/.ArithmeticUtils.java.swp      | Bin 0 -> 16384 bytes
>>  .../numbers/fraction/.BigFraction.java.swp      | Bin 0 -> 16384 bytes
>>
>
> What's this?
>
>  4 files changed, 321 insertions(+), 99 deletions(-)
>>
>> ----------------------------------------------------------------------
>>
>>
>>
>> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/85703373/.swp
>>
>> ----------------------------------------------------------------------
>> diff --git a/.swp b/.swp
>> new file mode 100644
>> index 0000000..e5f142d
>> Binary files /dev/null and b/.swp differ
>>
>>
>> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/
>> 85703373/commons-numbers-complex/src/main/java/org/apache/
>> commons/numbers/complex/Complex.java
>>
>> ----------------------------------------------------------------------
>> diff --git
>>
>> a/commons-numbers-complex/src/main/java/org/apache/commons/n
>> umbers/complex/Complex.java
>>
>> b/commons-numbers-complex/src/main/java/org/apache/commons/n
>> umbers/complex/Complex.java
>> index 4e9022e..6e4639b 100644
>> ---
>>
>> a/commons-numbers-complex/src/main/java/org/apache/commons/n
>> umbers/complex/Complex.java
>> +++
>>
>> b/commons-numbers-complex/src/main/java/org/apache/commons/n
>> umbers/complex/Complex.java
>> @@ -20,7 +20,9 @@ package org.apache.commons.numbers.complex;
>>  import java.io.Serializable;
>>  import java.util.ArrayList;
>>  import java.util.List;
>> +
>>  import org.apache.commons.numbers.core.Precision;
>> +
>>  /**
>>   * Representation of a Complex number, i.e. a number which has both a
>>   * real and imaginary part.
>> @@ -38,10 +40,10 @@ import org.apache.commons.numbers.core.Precision;
>>   * Note that this contradicts the IEEE-754 standard for floating
>>   * point numbers (according to which the test {@code x == x} must fail if
>>   * {@code x} is {@code NaN}). The method
>> - * {@link
>> org.apache.commons.numbers.core.Precision#equals(double,double,int)
>> - * equals for primitive double} in class {@code Precision} conforms with
>> - * IEEE-754 while this class conforms with the standard behavior for Java
>> - * object types.</p>
>> + * {@link org.apache.commons.math4.util.Precision#equals(double,double
>> ,int)
>> + * equals for primitive double} in {@link
>> org.apache.commons.math4.util.Precision}
>> + * conforms with IEEE-754 while this class conforms with the
>> standard behavior
>> + * for Java object types.</p>
>>   *
>>   */
>>  public class Complex implements Serializable  {
>> @@ -59,15 +61,15 @@ public class Complex implements Serializable  {
>>      public static final Complex ZERO = new Complex(0.0, 0.0);
>>
>>      /** Serializable version identifier */
>> -    private static final long serialVersionUID = 201701120L;
>> +    private static final long serialVersionUID = -6195664516687396620L;
>>
>
> I'd prefer to keep the convention we adopted in Commons Math, i.e. the
> date (of the incompatible change).
>
>
>>      /** The imaginary part. */
>>      private final double imaginary;
>>      /** The real part. */
>>      private final double real;
>> -    /** Record whether this complex number is equal to NaN. */
>> +    /** Record whether this Complex number is equal to NaN. */
>>      private final transient boolean isNaN;
>> -    /** Record whether this complex number is infinite. */
>> +    /** Record whether this Complex number is infinite. */
>>      private final transient boolean isInfinite;
>>
>>      /**
>> @@ -79,7 +81,7 @@ public class Complex implements Serializable  {
>>          this(real, 0.0);
>>      }
>>
>> -    /**
>> +     /**
>>
>
> Misalignment (introducing a spurious difference).
>
>       * Create a complex number given the real and imaginary parts.
>>       *
>>       * @param real Real part.
>> @@ -94,8 +96,56 @@ public class Complex implements Serializable  {
>>              (Double.isInfinite(real) || Double.isInfinite(imaginary));
>>      }
>>
>> +     /**
>> +     * Creates a Complex from its polar representation.
>> +     * <p>
>> +     * If either {@code r} or {@code theta} is NaN, or {@code theta} is
>> +     * infinite, {@link Complex#NaN} is returned.
>> +     * <p>
>> +     * If {@code r} is infinite and {@code theta} is finite, infinite or
>> NaN
>> +     * values may be returned in parts of the result, following the
>> rules for
>> +     * double arithmetic.
>> +     *
>> +     * <pre>
>> +     * Examples:
>> +     * {@code
>> +     * polar2Complex(INFINITY, \(\pi\)) = INFINITY + INFINITY i
>> +     * polar2Complex(INFINITY, 0) = INFINITY + NaN i
>> +     * polar2Complex(INFINITY, \(-\frac{\pi}{4}\)) = INFINITY - INFINITY
>> i
>> +     * polar2Complex(INFINITY, \(5\frac{\pi}{4}\)) = -INFINITY -
>> INFINITY i }
>> +     * </pre>
>> +     *
>> +     * @param r the modulus of the complex number to create
>> +     * @param theta the argument of the complex number to create
>> +     * @return {@code Complex}
>> +     * @since 1.1
>>
>
> There hasn't been a 1.0 release yet.
>
> +     */
>> +    public Complex polar(double r, double theta) {
>> +        checkNotNegative(r);
>> +        return new Complex(r * Math.cos(theta), r * Math.sin(theta));
>> +    }
>> +
>>      /**
>> -     * Return the absolute value of this complex number.
>> +     * Returns projection of this Complex number onto the Riemann sphere,
>> +     * i.e. all infinities (including those with an NaN component)
>> +     * project onto real infinity, as described in the
>> +     * <a
>>
>> href="http://pubs.opengroup.org/onlinepubs/9699919799/functi
>> ons/cproj.html">
>> +     * IEEE and ISO C standards</a>.
>> +     * <p>
>> +     *
>> +     *
>> +     * @return {@code Complex} projected onto the Riemann sphere.
>> +     */
>> +    public Complex proj() {
>> +        if (isInfinite) {
>> +            return new Complex(Double.POSITIVE_INFINITY);
>> +        } else {
>> +            return this;
>> +        }
>> +    }
>> +
>> +     /**
>> +     * Return the absolute value of this Complex number.
>>       * Returns {@code NaN} if either real or imaginary part is {@code
>> NaN}
>>       * and {@code Double.POSITIVE_INFINITY} if neither part is {@code
>> NaN},
>>       * but at least one part is infinite.
>> @@ -124,6 +174,19 @@ public class Complex implements Serializable  {
>>          }
>>      }
>>
>> +     /**
>> +     * Return the norm of this Complex number, defined as the square
>> of the magnitude
>> +     * (Matches C++ 11 standards.)
>>
>
> I would rather move that comment to the class Javadoc (with a link).
> Or do you intend to have only partial compliance?
>
> +     * Returns {@code NaN} if either real or imaginary part is {@code NaN}
>> +     * and {@code Double.POSITIVE_INFINITY} if neither part is {@code
>> NaN},
>> +     * but at least one part is infinite.
>> +     *
>> +     * @return the absolute value.
>> +     */
>> +    public double norm() {
>> +        return abs()*abs();
>>
>
> There must be one space character around operators.
>
> +    }
>> +
>>      /**
>>       * Returns a {@code Complex} whose value is
>>       * {@code (this + addend)}.
>> @@ -138,6 +201,7 @@ public class Complex implements Serializable  {
>>       *
>>       * @param  addend Value to be added to this {@code Complex}.
>>       * @return {@code this + addend}.
>> +     * @if {@code addend} is {@code null}.
>>
>
> @if ?
>
>       */
>>      public Complex add(Complex addend) {
>>          checkNotNull(addend);
>> @@ -166,7 +230,7 @@ public class Complex implements Serializable  {
>>      }
>>
>>       /**
>> -     * Returns the conjugate of this complex number.
>> +     * Returns the conjugate of this Complex number.
>>       * The conjugate of {@code a + bi} is {@code a - bi}.
>>       * <p>
>>       * {@link #NaN} is returned if either the real or imaginary
>> @@ -187,6 +251,17 @@ public class Complex implements Serializable  {
>>          return createComplex(real, -imaginary);
>>      }
>>
>> +     /**
>> +     * Returns the conjugate of this Complex number.
>> +     * C++11 grammar.
>>
>
> This is a new component: let's define _one_ convention; again you can
> refer to the reason for the choice in the Javadoc. (Same for other
> similar instances below).
>
> +     * </p>
>> +     * @return the conjugate of this Complex object.
>> +     */
>> +    public Complex conj() {
>> +        return conjugate();
>> +    }
>> +
>> +
>>      /**
>>       * Returns a {@code Complex} whose value is
>>       * {@code (this / divisor)}.
>> @@ -227,8 +302,10 @@ public class Complex implements Serializable  {
>>       *
>>       * @param divisor Value by which this {@code Complex} is to be
>> divided.
>>       * @return {@code this / divisor}.
>> +     * @if {@code divisor} is {@code null}.
>>       */
>> -    public Complex divide(Complex divisor) {
>> +    public Complex divide(Complex divisor)
>> +        {
>>          checkNotNull(divisor);
>>          if (isNaN || divisor.isNaN) {
>>              return NaN;
>> @@ -279,12 +356,7 @@ public class Complex implements Serializable  {
>>                               imaginary  / divisor);
>>      }
>>
>> -    /**
>> -     * Returns the multiplicative inverse this instance.
>> -     *
>> -     * @return {@code 1 / this}.
>> -     * @see #divide(Complex)
>> -     */
>> +    /** {@inheritDoc} */
>>      public Complex reciprocal() {
>>          if (isNaN) {
>>              return NaN;
>> @@ -343,8 +415,8 @@ public class Complex implements Serializable  {
>>              if (c.isNaN) {
>>                  return isNaN;
>>              } else {
>> -                return equals(real, c.real) &&
>> -                    equals(imaginary, c.imaginary);
>> +                return Precision.equals(real, c.real) &&
>> +                    Precision.equals(imaginary, c.imaginary);
>>              }
>>          }
>>          return false;
>> @@ -365,6 +437,7 @@ public class Complex implements Serializable  {
>>       * and {@code y}.
>>       *
>>       * @see Precision#equals(double,double,int)
>> +     * @since 3.3
>>       */
>>      public static boolean equals(Complex x, Complex y, int maxUlps) {
>>          return Precision.equals(x.real, y.real, maxUlps) &&
>> @@ -378,6 +451,8 @@ public class Complex implements Serializable  {
>>       * @param x First value (cannot be {@code null}).
>>       * @param y Second value (cannot be {@code null}).
>>       * @return {@code true} if the values are equal.
>> +     *
>> +     * @since 3.3
>>
>
> Wrong @since. (Several more below).
>
>       */
>>      public static boolean equals(Complex x, Complex y) {
>>          return equals(x, y, 1);
>> @@ -396,6 +471,7 @@ public class Complex implements Serializable  {
>>       * numbers or they are within range of each other.
>>       *
>>       * @see Precision#equals(double,double,double)
>> +     * @since 3.3
>>       */
>>      public static boolean equals(Complex x, Complex y, double eps) {
>>          return Precision.equals(x.real, y.real, eps) &&
>> @@ -415,6 +491,7 @@ public class Complex implements Serializable  {
>>       * numbers or they are within range of each other.
>>       *
>>       * @see Precision#equalsWithRelativeTolerance(double,double,double)
>> +     * @since 3.3
>>       */
>>      public static boolean equalsWithRelativeTolerance(Complex x,
>> Complex y,
>>                                                        double eps) {
>> @@ -434,8 +511,8 @@ public class Complex implements Serializable  {
>>          if (isNaN) {
>>              return 7;
>>          }
>> -        return 37 * (17 * hash(imaginary) +
>> -            hash(real));
>> +        return 37 * (17 * Precision.hash(imaginary) +
>> +            Precision.hash(real));
>>      }
>>
>>      /**
>> @@ -446,6 +523,14 @@ public class Complex implements Serializable  {
>>      public double getImaginary() {
>>          return imaginary;
>>      }
>> +    /**
>> +     * Access the imaginary part (C++ grammar)
>> +     *
>> +     * @return the imaginary part.
>> +     */
>> +    public double imag() {
>> +        return imaginary;
>> +    }
>>
>>      /**
>>       * Access the real part.
>> @@ -456,11 +541,20 @@ public class Complex implements Serializable  {
>>          return real;
>>      }
>>
>> -    /**
>> -     * Checks whether either or both parts of this complex number is
>> +     /**
>> +     * Access the real part (C++ grammar)
>> +     *
>> +     * @return the real part.
>> +     */
>> +    public double real() {
>> +        return real;
>> +    }
>> +
>> +   /**
>> +     * Checks whether either or both parts of this Complex number is
>>       * {@code NaN}.
>>       *
>> -     * @return true if either or both parts of this complex number is
>> +     * @return true if either or both parts of this Complex number is
>>       * {@code NaN}; false otherwise.
>>       */
>>      public boolean isNaN() {
>> @@ -468,12 +562,12 @@ public class Complex implements Serializable  {
>>      }
>>
>>      /**
>> -     * Checks whether either the real or imaginary part of this
>> complex number
>> +     * Checks whether either the real or imaginary part of this
>> Complex number
>>       * takes an infinite value (either {@code Double.POSITIVE_INFINITY}
>> or
>>       * {@code Double.NEGATIVE_INFINITY}) and neither part
>>       * is {@code NaN}.
>>       *
>> -     * @return true if one or both parts of this complex number are
>> infinite
>> +     * @return true if one or both parts of this Complex number are
>> infinite
>>       * and neither part is {@code NaN}.
>>       */
>>      public boolean isInfinite() {
>> @@ -500,8 +594,10 @@ public class Complex implements Serializable  {
>>       *
>>       * @param  factor value to be multiplied by this {@code Complex}.
>>       * @return {@code this * factor}.
>> +     * @if {@code factor} is {@code null}.
>>       */
>> -    public Complex multiply(Complex factor) {
>> +    public Complex multiply(Complex factor)
>> +        {
>>          checkNotNull(factor);
>>          if (isNaN || factor.isNaN) {
>>              return NaN;
>> @@ -586,8 +682,10 @@ public class Complex implements Serializable  {
>>       *
>>       * @param  subtrahend value to be subtracted from this {@code
>> Complex}.
>>       * @return {@code this - subtrahend}.
>> +     * @if {@code subtrahend} is {@code null}.
>>       */
>> -    public Complex subtract(Complex subtrahend) {
>> +    public Complex subtract(Complex subtrahend)
>> +        {
>>          checkNotNull(subtrahend);
>>          if (isNaN || subtrahend.isNaN) {
>>              return NaN;
>> @@ -615,7 +713,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/InverseCosine.html"
>> TARGET="_top">
>>
>
> TARGET ?
> (Several other instances below.)
>
> -     * inverse cosine</a> of this complex number.
>> +     * inverse cosine</a> of this Complex number.
>>       * Implements the formula:
>>       * <p>
>>       *  {@code acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))}
>> @@ -623,7 +721,8 @@ public class Complex implements Serializable  {
>>       * Returns {@link Complex#NaN} if either real or imaginary part of
>> the
>>       * input argument is {@code NaN} or infinite.
>>       *
>> -     * @return the inverse cosine of this complex number.
>> +     * @return the inverse cosine of this Complex number.
>> +     * @since 1.2
>>       */
>>      public Complex acos() {
>>          if (isNaN) {
>> @@ -636,7 +735,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/InverseSine.html"
>> TARGET="_top">
>> -     * inverse sine</a> of this complex number.
>> +     * inverse sine</a> of this Complex number.
>>       * Implements the formula:
>>       * <p>
>>       *  {@code asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))}
>> @@ -644,7 +743,8 @@ public class Complex implements Serializable  {
>>       * Returns {@link Complex#NaN} if either real or imaginary part of
>> the
>>       * input argument is {@code NaN} or infinite.</p>
>>       *
>> -     * @return the inverse sine of this complex number.
>> +     * @return the inverse sine of this Complex number.
>> +     * @since 1.2
>>       */
>>      public Complex asin() {
>>          if (isNaN) {
>> @@ -657,7 +757,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/InverseTangent.html"
>> TARGET="_top">
>> -     * inverse tangent</a> of this complex number.
>> +     * inverse tangent</a> of this Complex number.
>>       * Implements the formula:
>>       * <p>
>>       * {@code atan(z) = (i/2) log((i + z)/(i - z))}
>> @@ -665,7 +765,8 @@ public class Complex implements Serializable  {
>>       * Returns {@link Complex#NaN} if either real or imaginary part of
>> the
>>       * input argument is {@code NaN} or infinite.</p>
>>       *
>> -     * @return the inverse tangent of this complex number
>> +     * @return the inverse tangent of this Complex number
>> +     * @since 1.2
>>       */
>>      public Complex atan() {
>>          if (isNaN) {
>> @@ -678,8 +779,86 @@ public class Complex implements Serializable  {
>>
>>      /**
>>       * Compute the
>> +     * <a
>> href="http://mathworld.wolfram.com/InverseHyperbolicSine.html"
>> TARGET="_top">
>> +     * inverse hyperbolic sine</a> of this Complex number.
>> +     * Implements the formula:
>> +     * <p>
>> +     * {@code asinh(z) = log(z+sqrt(z^2+1))}
>> +     * </p><p>
>> +     * Returns {@link Complex#NaN} if either real or imaginary part of
>> the
>> +     * input argument is {@code NaN} or infinite.</p>
>> +     *
>> +     * @return the inverse hyperbolic cosine of this Complex number
>> +     * @since 1.2
>> +     */
>> +    public Complex asinh(){
>> +        if (isNaN) {
>> +            return NaN;
>> +        }
>> +
>> +        return square().add(Complex.ONE).sqrt().add(this).log();
>> +    }
>> +
>> +   /**
>> +     * Compute the
>> +     * <a
>> href="http://mathworld.wolfram.com/InverseHyperbolicTangent.html"
>> TARGET="_top">
>> +     * inverse hyperbolic tangent</a> of this Complex number.
>> +     * Implements the formula:
>> +     * <p>
>> +     * {@code atanh(z) = log((1+z)/(1-z))/2}
>> +     * </p><p>
>> +     * Returns {@link Complex#NaN} if either real or imaginary part of
>> the
>> +     * input argument is {@code NaN} or infinite.</p>
>> +     *
>> +     * @return the inverse hyperbolic cosine of this Complex number
>> +     * @since 1.2
>> +     */
>> +    public Complex atanh(){
>> +        if (isNaN) {
>> +            return NaN;
>> +        }
>> +
>> +        return
>>
>> this.add(Complex.ONE).divide(Complex.ONE.subtract(this)).log().divide(new
>> Complex(2));
>> +    }
>> +   /**
>> +     * Compute the
>> +     * <a
>> href="http://mathworld.wolfram.com/InverseHyperbolicCosine.html"
>> TARGET="_top">
>> +     * inverse hyperbolic cosine</a> of this Complex number.
>> +     * Implements the formula:
>> +     * <p>
>> +     * {@code acosh(z) = log(z+sqrt(z^2-1))}
>> +     * </p><p>
>> +     * Returns {@link Complex#NaN} if either real or imaginary part of
>> the
>> +     * input argument is {@code NaN} or infinite.</p>
>> +     *
>> +     * @return the inverse hyperbolic cosine of this Complex number
>> +     * @since 1.2
>> +     */
>> +    public Complex acosh() {
>> +        if (isNaN) {
>> +            return NaN;
>> +        }
>> +
>> +        return square().subtract(Complex.ONE).sqrt().add(this).log();
>> +    }
>> +
>> +    /**
>> +     * Compute the square of this Complex number.
>> +     *
>> +     * @return square of this Complex number
>> +     */
>> +    public Complex square(){
>> +        if (isNaN) {
>> +            return NaN;
>> +        }
>> +
>> +        return this.multiply(this);
>> +    }
>> +
>> +    /**
>> +     * Compute the
>>       * <a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top">
>> -     * cosine</a> of this complex number.
>> +     * cosine</a> of this Complex number.
>>       * Implements the formula:
>>       * <p>
>>       *  {@code cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i}
>> @@ -702,7 +881,8 @@ public class Complex implements Serializable  {
>>       *  </code>
>>       * </pre>
>>       *
>> -     * @return the cosine of this complex number.
>> +     * @return the cosine of this Complex number.
>> +     * @since 1.2
>>       */
>>      public Complex cos() {
>>          if (isNaN) {
>> @@ -716,7 +896,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html"
>> TARGET="_top">
>> -     * hyperbolic cosine</a> of this complex number.
>> +     * hyperbolic cosine</a> of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -741,7 +921,8 @@ public class Complex implements Serializable  {
>>       *  </code>
>>       * </pre>
>>       *
>> -     * @return the hyperbolic cosine of this complex number.
>> +     * @return the hyperbolic cosine of this Complex number.
>> +     * @since 1.2
>>       */
>>      public Complex cosh() {
>>          if (isNaN) {
>> @@ -755,7 +936,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a
>> href="http://mathworld.wolfram.com/ExponentialFunction.html"
>> TARGET="_top">
>> -     * exponential function</a> of this complex number.
>> +     * exponential function</a> of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -782,6 +963,7 @@ public class Complex implements Serializable  {
>>       * </pre>
>>       *
>>       * @return <code><i>e</i><sup>this</sup></code>.
>> +     * @since 1.2
>>       */
>>      public Complex exp() {
>>          if (isNaN) {
>> @@ -796,7 +978,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html"
>> TARGET="_top">
>> -     * natural logarithm</a> of this complex number.
>> +     * natural logarithm</a> of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -826,6 +1008,7 @@ public class Complex implements Serializable  {
>>       *
>>       * @return the value <code>ln &nbsp; this</code>, the natural
>> logarithm
>>       * of {@code this}.
>> +     * @since 1.2
>>       */
>>      public Complex log() {
>>          if (isNaN) {
>> @@ -837,7 +1020,19 @@ public class Complex implements Serializable  {
>>      }
>>
>>      /**
>> -     * Returns of value of this complex number raised to the power
>> of {@code x}.
>> +     * Compute the base 10 or
>> +     * <a href="http://mathworld.wolfram.com/CommonLogarithm.html"
>> TARGET="_top">
>> +     * common logarithm</a> of this Complex number.
>> +     *
>> +     *  @return the base 10 logarithm of <code>this</code>.
>> +    */
>> +    public Complex log10() {
>> +        return createComplex(Math.log(abs())/Math.log(10),
>> +                             Math.atan2(imaginary, real));
>> +    }
>> +
>> +    /**
>> +     * Returns of value of this Complex number raised to the power
>> of {@code x}.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -853,38 +1048,23 @@ public class Complex implements Serializable  {
>>       *
>>       * @param  x exponent to which this {@code Complex} is to be raised.
>>       * @return <code> this<sup>x</sup></code>.
>> +     * @if x is {@code null}.
>> +     * @since 1.2
>>       */
>> -    public Complex pow(Complex x) {
>> +    public Complex pow(Complex x)
>> +        {
>>          checkNotNull(x);
>> -        if (real == 0 && imaginary == 0) {
>> -            if (x.real > 0 && x.imaginary == 0) {
>> -                // 0 raised to positive number is 0
>> -                return ZERO;
>> -            } else {
>> -                // 0 raised to anything else is NaN
>> -                return NaN;
>> -            }
>> -        }
>>          return this.log().multiply(x).exp();
>>      }
>>
>>      /**
>> -     * Returns of value of this complex number raised to the power
>> of {@code x}.
>> +     * Returns of value of this Complex number raised to the power
>> of {@code x}.
>>       *
>>       * @param  x exponent to which this {@code Complex} is to be raised.
>>       * @return <code>this<sup>x</sup></code>.
>>       * @see #pow(Complex)
>>       */
>>       public Complex pow(double x) {
>> -        if (real == 0 && imaginary == 0) {
>> -            if (x > 0) {
>> -                // 0 raised to positive number is 0
>> -                return ZERO;
>> -            } else {
>> -                // 0 raised to anything else is NaN
>> -                return NaN;
>> -            }
>> -        }
>>          return this.log().multiply(x).exp();
>>      }
>>
>> @@ -892,7 +1072,7 @@ public class Complex implements Serializable  {
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top">
>>       * sine</a>
>> -     * of this complex number.
>> +     * of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -917,7 +1097,8 @@ public class Complex implements Serializable  {
>>       *  </code>
>>       * </pre>
>>       *
>> -     * @return the sine of this complex number.
>> +     * @return the sine of this Complex number.
>> +     * @since 1.2
>>       */
>>      public Complex sin() {
>>          if (isNaN) {
>> @@ -931,7 +1112,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/HyperbolicSine.html"
>> TARGET="_top">
>> -     * hyperbolic sine</a> of this complex number.
>> +     * hyperbolic sine</a> of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -957,6 +1138,7 @@ public class Complex implements Serializable  {
>>       * </pre>
>>       *
>>       * @return the hyperbolic sine of {@code this}.
>> +     * @since 1.2
>>       */
>>      public Complex sinh() {
>>          if (isNaN) {
>> @@ -970,7 +1152,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/SquareRoot.html"
>> TARGET="_top">
>> -     * square root</a> of this complex number.
>> +     * square root</a> of this Complex number.
>>       * Implements the following algorithm to compute {@code sqrt(a +
>> bi)}:
>>       * <ol><li>Let {@code t = sqrt((|a| + |a + bi|) / 2)}</li>
>>       * <li><pre>if {@code  a &#8805; 0} return {@code t + (b/2t)i}
>> @@ -999,6 +1181,7 @@ public class Complex implements Serializable  {
>>       * </pre>
>>       *
>>       * @return the square root of {@code this}.
>> +     * @since 1.2
>>       */
>>      public Complex sqrt() {
>>          if (isNaN) {
>> @@ -1033,6 +1216,7 @@ public class Complex implements Serializable  {
>>       * infinite or NaN values returned in parts of the result.
>>       *
>>       * @return the square root of <code>1 - this<sup>2</sup></code>.
>> +     * @since 1.2
>>       */
>>      public Complex sqrt1z() {
>>          return createComplex(1.0, 0.0).subtract(this.multiply(th
>> is)).sqrt();
>> @@ -1041,7 +1225,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/Tangent.html"
>> TARGET="_top">
>> -     * tangent</a> of this complex number.
>> +     * tangent</a> of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -1068,6 +1252,7 @@ public class Complex implements Serializable  {
>>       * </pre>
>>       *
>>       * @return the tangent of {@code this}.
>> +     * @since 1.2
>>       */
>>      public Complex tan() {
>>          if (isNaN || Double.isInfinite(real)) {
>> @@ -1091,7 +1276,7 @@ public class Complex implements Serializable  {
>>      /**
>>       * Compute the
>>       * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html"
>> TARGET="_top">
>> -     * hyperbolic tangent</a> of this complex number.
>> +     * hyperbolic tangent</a> of this Complex number.
>>       * Implements the formula:
>>       * <pre>
>>       *  <code>
>> @@ -1118,6 +1303,7 @@ public class Complex implements Serializable  {
>>       * </pre>
>>       *
>>       * @return the hyperbolic tangent of {@code this}.
>> +     * @since 1.2
>>       */
>>      public Complex tanh() {
>>          if (isNaN || Double.isInfinite(imaginary)) {
>> @@ -1137,10 +1323,8 @@ public class Complex implements Serializable  {
>>                               Math.sin(imaginary2) / d);
>>      }
>>
>> -
>> -
>>      /**
>> -     * Compute the argument of this complex number.
>> +     * Compute the argument of this Complex number.
>>       * The argument is the angle phi between the positive real axis and
>>       * the point representing this number in the complex plane.
>>       * The value returned is between -PI (not inclusive)
>> @@ -1157,11 +1341,32 @@ public class Complex implements Serializable  {
>>       * @return the argument of {@code this}.
>>       */
>>      public double getArgument() {
>> -        return Math.atan2(getImaginary(), getReal());
>> +        return Math.atan2(imaginary, real);
>>      }
>>
>>      /**
>> -     * Computes the n-th roots of this complex number.
>> +     * Compute the argument of this Complex number.
>> +     * The argument is the angle phi between the positive real axis and
>> +     * the point representing this number in the complex plane.
>> +     * The value returned is between -PI (not inclusive)
>> +     * and PI (inclusive), with negative values returned for numbers with
>> +     * negative imaginary parts.
>> +     * <p>
>> +     * If either real or imaginary part (or both) is NaN, NaN is
>> returned.
>> +     * Infinite parts are handled as {@code Math.atan2} handles them,
>> +     * essentially treating finite parts as zero in the presence of an
>> +     * infinite coordinate and returning a multiple of pi/4 depending on
>> +     * the signs of the infinite parts.
>> +     * See the javadoc for {@code Math.atan2} for full details.
>> +     *
>> +     * @return the argument of {@code this}.
>> +     */
>> +    public double arg() {
>> +        return getArgument();
>> +    }
>> +
>> +    /**
>> +     * Computes the n-th roots of this Complex number.
>>       * The nth roots are defined by the formula:
>>       * <pre>
>>       *  <code>
>> @@ -1170,21 +1375,21 @@ public class Complex implements Serializable  {
>>       * </pre>
>>       * for <i>{@code k=0, 1, ..., n-1}</i>, where {@code abs} and
>> {@code phi}
>>       * are respectively the {@link #abs() modulus} and
>> -     * {@link #getArgument() argument} of this complex number.
>> +     * {@link #getArgument() argument} of this Complex number.
>>       * <p>
>> -     * If one or both parts of this complex number is NaN, a list with
>> just
>> +     * If one or both parts of this Complex number is NaN, a list with
>> just
>>       * one element, {@link #NaN} is returned.
>>       * if neither part is NaN, but at least one part is infinite, the
>> result
>>       * is a one-element list containing {@link #INF}.
>>       *
>>       * @param n Degree of root.
>>       * @return a List of all {@code n}-th roots of {@code this}.
>> +     * @throws NotPositiveException if {@code n <= 0}.
>> +     * @since 2.0
>>       */
>>      public List<Complex> nthRoot(int n) {
>>
>> -        if (n <= 0) {
>> -            throw new RuntimeException("cannot compute nth root for
>> null or negative n: {0}");
>> -        }
>> +        checkNotNegative(n);
>>
>>          final List<Complex> result = new ArrayList<Complex>();
>>
>> @@ -1221,6 +1426,7 @@ public class Complex implements Serializable  {
>>       * @param realPart Real part.
>>       * @param imaginaryPart Imaginary part.
>>       * @return a new complex number instance.
>> +     * @since 1.2
>>       * @see #valueOf(double, double)
>>       */
>>      protected Complex createComplex(double realPart,
>> @@ -1263,6 +1469,7 @@ public class Complex implements Serializable  {
>>       * deserialize properly.
>>       *
>>       * @return A Complex instance with all fields resolved.
>> +     * @since 2.0
>>       */
>>      protected final Object readResolve() {
>>          return createComplex(real, imaginary);
>> @@ -1274,36 +1481,51 @@ public class Complex implements Serializable  {
>>          return "(" + real + ", " + imaginary + ")";
>>      }
>>
>> -    /**
>> -     * Checks that an object is not null.
>> -     *
>> -     * @param o Object to be checked.
>> +     /**
>> +     * Check that the argument is positive and throw a RuntimeException
>> +     * if it is not.
>> +     * @param arg {@code double} to check
>>       */
>> -    private static void checkNotNull(Object o) {
>> -        if (o == null) {
>> -            throw new RuntimeException("Null Argument to Complex
>> Method");
>> +    private static void checkNotNegative(double arg) {
>> +        if (arg <= 0) {
>> +            throw new RuntimeException("Complex: Non-positive argument");
>>          }
>>      }
>>
>> +
>> +     /**
>> +     * Check that the argument is positive and throw a RuntimeException
>> +     * if it is not.
>> +     * @param arg {@code int} to check
>> +     */
>> +    private static void checkNotNegative(int arg) {
>> +        if (arg <= 0) {
>> +            throw new RuntimeException("Complex: Non-positive argument");
>> +        }
>> +    }
>> +
>>      /**
>> -     * Returns {@code true} if the values are equal according to
>> semantics of
>> -     * {@link Double#equals(Object)}.
>> -     *
>> -     * @param x Value
>> -     * @param y Value
>> -     * @return {@code new Double(x).equals(new Double(y))}
>> +     * Check that the Complex is not null and throw a RuntimeException
>> +     * if it is.
>> +     * @param arg     the Complex to check
>>       */
>> -    private static boolean equals(double x, double y) {
>> -        return new Double(x).equals(new Double(y));
>> +    private static void checkNotNull(Complex arg) {
>> +        if (arg == null) {
>> +            throw new RuntimeException("Complex: Null argument");
>> +        }
>>      }
>>
>>      /**
>> -     * Returns an integer hash code representing the given double value.
>> -     *
>> -     * @param value the value to be hashed
>> -     * @return the hash code
>> +     * Check that the argument is not null and throw a RuntimeException
>> +     * if it is.
>> +     * @param arg     the argument to check
>> +     * @param argName the name of the argument
>>       */
>> -    private static int hash(double value) {
>> -        return new Double(value).hashCode();
>> +    private static void checkNotNull(Object arg, String argName) {
>> +        if (arg == null) {
>> +            throw new RuntimeException("Complex: Null argument");
>> +        }
>>      }
>> -}
>> +}
>> +
>> +
>>
>>
>> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/
>> 85703373/commons-numbers-core/src/main/java/org/apache/commo
>> ns/numbers/core/.ArithmeticUtils.java.swp
>>
>> ----------------------------------------------------------------------
>> diff --git
>>
>> a/commons-numbers-core/src/main/java/org/apache/commons/numb
>> ers/core/.ArithmeticUtils.java.swp
>>
>> b/commons-numbers-core/src/main/java/org/apache/commons/numb
>> ers/core/.ArithmeticUtils.java.swp
>> new file mode 100644
>> index 0000000..cb08acb
>> Binary files /dev/null and
>>
>> b/commons-numbers-core/src/main/java/org/apache/commons/numb
>> ers/core/.ArithmeticUtils.java.swp
>> differ
>>
>>
>> http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/
>> 85703373/commons-numbers-fraction/src/main/java/org/apache/
>> commons/numbers/fraction/.BigFraction.java.swp
>>
>> ----------------------------------------------------------------------
>> diff --git
>>
>> a/commons-numbers-fraction/src/main/java/org/apache/commons/
>> numbers/fraction/.BigFraction.java.swp
>>
>> b/commons-numbers-fraction/src/main/java/org/apache/commons/
>> numbers/fraction/.BigFraction.java.swp
>> new file mode 100644
>> index 0000000..0321309
>> Binary files /dev/null and
>>
>> b/commons-numbers-fraction/src/main/java/org/apache/commons/
>> numbers/fraction/.BigFraction.java.swp
>> differ
>>
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