/*
 * Copyright (c) 1997, 2007, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.util;

import java.lang.reflect.*;

This class contains various methods for manipulating arrays (such as
sorting and searching).  This class also contains a static factory
that allows arrays to be viewed as lists.
The methods in this class all throw a NullPointerException if
the specified array reference is null, except where noted.
The documentation for the methods contained in this class includes
briefs description of the implementations.  Such descriptions should
be regarded as implementation notes, rather than parts of the
specification.  Implementors should feel free to substitute other
algorithms, so long as the specification itself is adhered to.  (For
example, the algorithm used by sort(Object[]) does not have to be
a mergesort, but it does have to be stable.)
This class is a member of the

Java Collections Framework.
Author:
 Josh Bloch,  Neal Gafter,  John Rose
Since:
  1.2/**
 * This class contains various methods for manipulating arrays (such as
 * sorting and searching).  This class also contains a static factory
 * that allows arrays to be viewed as lists.
 *
 * <p>The methods in this class all throw a <tt>NullPointerException</tt> if
 * the specified array reference is null, except where noted.
 *
 * <p>The documentation for the methods contained in this class includes
 * briefs description of the <i>implementations</i>.  Such descriptions should
 * be regarded as <i>implementation notes</i>, rather than parts of the
 * <i>specification</i>.  Implementors should feel free to substitute other
 * algorithms, so long as the specification itself is adhered to.  (For
 * example, the algorithm used by <tt>sort(Object[])</tt> does not have to be
 * a mergesort, but it does have to be <i>stable</i>.)
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/../technotes/guides/collections/index.html">
 * Java Collections Framework</a>.
 *
 * @author  Josh Bloch
 * @author  Neal Gafter
 * @author  John Rose
 * @since   1.2
 */

public class Arrays {
    // Suppresses default constructor, ensuring non-instantiability.
    private Arrays() {
    }

    // Sorting

    
Sorts the specified array of longs into ascending numerical order.
The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of longs into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(long[] a) {
        sort1(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of longs into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)
The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
toIndex > a.length/**
     * Sorts the specified range of the specified array of longs into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
     *
     * <p>The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     * <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(long[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort1(a, fromIndex, toIndex-fromIndex);
    }

    
Sorts the specified array of ints into ascending numerical order.
The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of ints into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(int[] a) {
        sort1(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of ints into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of ints into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(int[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort1(a, fromIndex, toIndex-fromIndex);
    }

    
Sorts the specified array of shorts into ascending numerical order.
The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of shorts into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(short[] a) {
        sort1(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of shorts into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of shorts into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(short[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort1(a, fromIndex, toIndex-fromIndex);
    }

    
Sorts the specified array of chars into ascending numerical order.
The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of chars into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(char[] a) {
        sort1(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of chars into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of chars into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(char[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort1(a, fromIndex, toIndex-fromIndex);
    }

    
Sorts the specified array of bytes into ascending numerical order.
The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of bytes into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(byte[] a) {
        sort1(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of bytes into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of bytes into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(byte[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort1(a, fromIndex, toIndex-fromIndex);
    }

    
Sorts the specified array of doubles into ascending numerical order.

The < relation does not provide a total order on
all floating-point values; although they are distinct numbers
-0.0 == 0.0 is true and a NaN value
compares neither less than, greater than, nor equal to any
floating-point value, even itself.  To allow the sort to
proceed, instead of using the < relation to determine ascending numerical order, this method uses the total order imposed by Double.compareTo. This ordering differs from the < relation in that
-0.0 is treated as less than 0.0 and
NaN is considered greater than any other floating-point value.
For the purposes of sorting, all NaN values are considered
equivalent and equal.

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of doubles into ascending numerical order.
     * <p>
     * The <code>&lt;</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0 == 0.0</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code>&lt;</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Double#compareTo}.  This ordering
     * differs from the <code>&lt;</code> relation in that
     * <code>-0.0</code> is treated as less than <code>0.0</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(double[] a) {
        sort2(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of doubles into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)

The < relation does not provide a total order on
all floating-point values; although they are distinct numbers
-0.0 == 0.0 is true and a NaN value
compares neither less than, greater than, nor equal to any
floating-point value, even itself.  To allow the sort to
proceed, instead of using the < relation to determine ascending numerical order, this method uses the total order imposed by Double.compareTo. This ordering differs from the < relation in that
-0.0 is treated as less than 0.0 and
NaN is considered greater than any other floating-point value.
For the purposes of sorting, all NaN values are considered
equivalent and equal.

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of doubles into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
     * <p>
     * The <code>&lt;</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0 == 0.0</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code>&lt;</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Double#compareTo}.  This ordering
     * differs from the <code>&lt;</code> relation in that
     * <code>-0.0</code> is treated as less than <code>0.0</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(double[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort2(a, fromIndex, toIndex);
    }

    
Sorts the specified array of floats into ascending numerical order.

The < relation does not provide a total order on
all floating-point values; although they are distinct numbers
-0.0f == 0.0f is true and a NaN value
compares neither less than, greater than, nor equal to any
floating-point value, even itself.  To allow the sort to
proceed, instead of using the < relation to determine ascending numerical order, this method uses the total order imposed by Float.compareTo. This ordering differs from the < relation in that
-0.0f is treated as less than 0.0f and
NaN is considered greater than any other floating-point value.
For the purposes of sorting, all NaN values are considered
equivalent and equal.

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted/**
     * Sorts the specified array of floats into ascending numerical order.
     * <p>
     * The <code>&lt;</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0f == 0.0f</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code>&lt;</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Float#compareTo}.  This ordering
     * differs from the <code>&lt;</code> relation in that
     * <code>-0.0f</code> is treated as less than <code>0.0f</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     */
    public static void sort(float[] a) {
        sort2(a, 0, a.length);
    }

    
Sorts the specified range of the specified array of floats into
ascending numerical order.  The range to be sorted extends from index
fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.)

The < relation does not provide a total order on
all floating-point values; although they are distinct numbers
-0.0f == 0.0f is true and a NaN value
compares neither less than, greater than, nor equal to any
floating-point value, even itself.  To allow the sort to
proceed, instead of using the < relation to determine ascending numerical order, this method uses the total order imposed by Float.compareTo. This ordering differs from the < relation in that
-0.0f is treated as less than 0.0f and
NaN is considered greater than any other floating-point value.
For the purposes of sorting, all NaN values are considered
equivalent and equal.

The sorting algorithm is a tuned quicksort, adapted from Jon
L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
1993).  This algorithm offers n*log(n) performance on many data sets
that cause other quicksorts to degrade to quadratic performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of floats into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
     * <p>
     * The <code>&lt;</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0f == 0.0f</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code>&lt;</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Float#compareTo}.  This ordering
     * differs from the <code>&lt;</code> relation in that
     * <code>-0.0f</code> is treated as less than <code>0.0f</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void sort(float[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        sort2(a, fromIndex, toIndex);
    }

    private static void sort2(double a[], int fromIndex, int toIndex) {
        final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * Preprocessing phase:  Move any NaN's to end of array, count the
         * number of -0.0's, and turn them into 0.0's.
         */
        int numNegZeros = 0;
        int i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
                swap(a, i, --n);
            } else {
                if (a[i]==0 && Double.doubleToLongBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0d;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
        sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch0(a, fromIndex, n, 0.0d); // posn of ANY zero
            do {
                j--;
            } while (j>=fromIndex && a[j]==0.0d);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0d;
        }
    }


    private static void sort2(float a[], int fromIndex, int toIndex) {
        final int NEG_ZERO_BITS = Float.floatToIntBits(-0.0f);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * Preprocessing phase:  Move any NaN's to end of array, count the
         * number of -0.0's, and turn them into 0.0's.
         */
        int numNegZeros = 0;
        int i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
                swap(a, i, --n);
            } else {
                if (a[i]==0 && Float.floatToIntBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0f;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
        sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch0(a, fromIndex, n, 0.0f); // posn of ANY zero
            do {
                j--;
            } while (j>=fromIndex && a[j]==0.0f);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0f;
        }
    }


    /*
     * The code for each of the seven primitive types is largely identical.
     * C'est la vie.
     */

    
Sorts the specified sub-array of longs into ascending order.
/**
     * Sorts the specified sub-array of longs into ascending order.
     */
    private static void sort1(long x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        long v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(long x[], int a, int b) {
        long t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(long x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed longs.
/**
     * Returns the index of the median of the three indexed longs.
     */
    private static int med3(long x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }

    
Sorts the specified sub-array of integers into ascending order.
/**
     * Sorts the specified sub-array of integers into ascending order.
     */
    private static void sort1(int x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        int v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(int x[], int a, int b) {
        int t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(int x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed integers.
/**
     * Returns the index of the median of the three indexed integers.
     */
    private static int med3(int x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }

    
Sorts the specified sub-array of shorts into ascending order.
/**
     * Sorts the specified sub-array of shorts into ascending order.
     */
    private static void sort1(short x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        short v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(short x[], int a, int b) {
        short t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(short x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed shorts.
/**
     * Returns the index of the median of the three indexed shorts.
     */
    private static int med3(short x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    
Sorts the specified sub-array of chars into ascending order.
/**
     * Sorts the specified sub-array of chars into ascending order.
     */
    private static void sort1(char x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        char v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(char x[], int a, int b) {
        char t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(char x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed chars.
/**
     * Returns the index of the median of the three indexed chars.
     */
    private static int med3(char x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    
Sorts the specified sub-array of bytes into ascending order.
/**
     * Sorts the specified sub-array of bytes into ascending order.
     */
    private static void sort1(byte x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        byte v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(byte x[], int a, int b) {
        byte t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(byte x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed bytes.
/**
     * Returns the index of the median of the three indexed bytes.
     */
    private static int med3(byte x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    
Sorts the specified sub-array of doubles into ascending order.
/**
     * Sorts the specified sub-array of doubles into ascending order.
     */
    private static void sort1(double x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        double v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(double x[], int a, int b) {
        double t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(double x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed doubles.
/**
     * Returns the index of the median of the three indexed doubles.
     */
    private static int med3(double x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    
Sorts the specified sub-array of floats into ascending order.
/**
     * Sorts the specified sub-array of floats into ascending order.
     */
    private static void sort1(float x[], int off, int len) {
        // Insertion sort on smallest arrays
        if (len < 7) {
            for (int i=off; i<len+off; i++)
                for (int j=i; j>off && x[j-1]>x[j]; j--)
                    swap(x, j, j-1);
            return;
        }

        // Choose a partition element, v
        int m = off + (len >> 1);       // Small arrays, middle element
        if (len > 7) {
            int l = off;
            int n = off + len - 1;
            if (len > 40) {        // Big arrays, pseudomedian of 9
                int s = len/8;
                l = med3(x, l,     l+s, l+2*s);
                m = med3(x, m-s,   m,   m+s);
                n = med3(x, n-2*s, n-s, n);
            }
            m = med3(x, l, m, n); // Mid-size, med of 3
        }
        float v = x[m];

        // Establish Invariant: v* (<v)* (>v)* v*
        int a = off, b = a, c = off + len - 1, d = c;
        while(true) {
            while (b <= c && x[b] <= v) {
                if (x[b] == v)
                    swap(x, a++, b);
                b++;
            }
            while (c >= b && x[c] >= v) {
                if (x[c] == v)
                    swap(x, c, d--);
                c--;
            }
            if (b > c)
                break;
            swap(x, b++, c--);
        }

        // Swap partition elements back to middle
        int s, n = off + len;
        s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
        s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

        // Recursively sort non-partition-elements
        if ((s = b-a) > 1)
            sort1(x, off, s);
        if ((s = d-c) > 1)
            sort1(x, n-s, s);
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(float x[], int a, int b) {
        float t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
/**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(float x[], int a, int b, int n) {
        for (int i=0; i<n; i++, a++, b++)
            swap(x, a, b);
    }

    
Returns the index of the median of the three indexed floats.
/**
     * Returns the index of the median of the three indexed floats.
     */
    private static int med3(float x[], int a, int b, int c) {
        return (x[a] < x[b] ?
                (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
                (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    
Sorts the specified array of objects into ascending order, according to the natural ordering of its elements. All elements in the array must implement the Comparable interface. Furthermore, all elements in the array must be mutually comparable (that is,
e1.compareTo(e2) must not throw a ClassCastException
for any elements e1 and e2 in the array).

This sort is guaranteed to be stable:  equal elements will
not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is
omitted if the highest element in the low sublist is less than the
lowest element in the high sublist).  This algorithm offers guaranteed
n*log(n) performance.
Params:
a – the array to be sorted
Throws:
ClassCastException – if the array contains elements that are not
         mutually comparable (for example, strings and integers)./**
     * Sorts the specified array of objects into ascending order, according to
     * the {@linkplain Comparable natural ordering}
     * of its elements.  All elements in the array
     * must implement the {@link Comparable} interface.  Furthermore, all
     * elements in the array must be <i>mutually comparable</i> (that is,
     * <tt>e1.compareTo(e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance.
     *
     * @param a the array to be sorted
     * @throws  ClassCastException if the array contains elements that are not
     *          <i>mutually comparable</i> (for example, strings and integers).
     */
    public static void sort(Object[] a) {
        Object[] aux = a.clone();
        mergeSort(aux, a, 0, a.length, 0);
    }

    
Sorts the specified range of the specified array of objects into ascending order, according to the natural ordering of its elements. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive.
(If fromIndex==toIndex, the range to be sorted is empty.) All elements in this range must implement the Comparable interface. Furthermore, all elements in this range must be mutually
comparable (that is, e1.compareTo(e2) must not throw a
ClassCastException for any elements e1 and
e2 in the array).

This sort is guaranteed to be stable:  equal elements will
not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is
omitted if the highest element in the low sublist is less than the
lowest element in the high sublist).  This algorithm offers guaranteed
n*log(n) performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length
ClassCastException – if the array contains elements that are
           not mutually comparable (for example, strings and
           integers)./**
     * Sorts the specified range of the specified array of objects into
     * ascending order, according to the
     * {@linkplain Comparable natural ordering} of its
     * elements.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)  All
     * elements in this range must implement the {@link Comparable}
     * interface.  Furthermore, all elements in this range must be <i>mutually
     * comparable</i> (that is, <tt>e1.compareTo(e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     * @throws    ClassCastException if the array contains elements that are
     *            not <i>mutually comparable</i> (for example, strings and
     *            integers).
     */
    public static void sort(Object[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        Object[] aux = copyOfRange(a, fromIndex, toIndex);
        mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
    }

    
Tuning parameter: list size at or below which insertion sort will be
used in preference to mergesort or quicksort.
/**
     * Tuning parameter: list size at or below which insertion sort will be
     * used in preference to mergesort or quicksort.
     */
    private static final int INSERTIONSORT_THRESHOLD = 7;

    
Src is the source array that starts at index 0
Dest is the (possibly larger) array destination with a possible offset
low is the index in dest to start sorting
high is the end index in dest to end sorting
off is the offset to generate corresponding low, high in src
/**
     * Src is the source array that starts at index 0
     * Dest is the (possibly larger) array destination with a possible offset
     * low is the index in dest to start sorting
     * high is the end index in dest to end sorting
     * off is the offset to generate corresponding low, high in src
     */
    private static void mergeSort(Object[] src,
                                  Object[] dest,
                                  int low,
                                  int high,
                                  int off) {
        int length = high - low;

        // Insertion sort on smallest arrays
        if (length < INSERTIONSORT_THRESHOLD) {
            for (int i=low; i<high; i++)
                for (int j=i; j>low &&
                         ((Comparable) dest[j-1]).compareTo(dest[j])>0; j--)
                    swap(dest, j, j-1);
            return;
        }

        // Recursively sort halves of dest into src
        int destLow  = low;
        int destHigh = high;
        low  += off;
        high += off;
        int mid = (low + high) >>> 1;
        mergeSort(dest, src, low, mid, -off);
        mergeSort(dest, src, mid, high, -off);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (((Comparable)src[mid-1]).compareTo(src[mid]) <= 0) {
            System.arraycopy(src, low, dest, destLow, length);
            return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
            if (q >= high || p < mid && ((Comparable)src[p]).compareTo(src[q])<=0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    }

    
Swaps x[a] with x[b].
/**
     * Swaps x[a] with x[b].
     */
    private static void swap(Object[] x, int a, int b) {
        Object t = x[a];
        x[a] = x[b];
        x[b] = t;
    }

    
Sorts the specified array of objects according to the order induced by
the specified comparator.  All elements in the array must be
mutually comparable by the specified comparator (that is,
c.compare(e1, e2) must not throw a ClassCastException
for any elements e1 and e2 in the array).

This sort is guaranteed to be stable:  equal elements will
not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is
omitted if the highest element in the low sublist is less than the
lowest element in the high sublist).  This algorithm offers guaranteed
n*log(n) performance.
Params:
a – the array to be sorted
c – the comparator to determine the order of the array.  A
       null value indicates that the elements' natural ordering should be used.
Throws:
ClassCastException – if the array contains elements that are
         not mutually comparable using the specified comparator./**
     * Sorts the specified array of objects according to the order induced by
     * the specified comparator.  All elements in the array must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * <tt>c.compare(e1, e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance.
     *
     * @param a the array to be sorted
     * @param c the comparator to determine the order of the array.  A
     *        <tt>null</tt> value indicates that the elements'
     *        {@linkplain Comparable natural ordering} should be used.
     * @throws  ClassCastException if the array contains elements that are
     *          not <i>mutually comparable</i> using the specified comparator.
     */
    public static <T> void sort(T[] a, Comparator<? super T> c) {
        T[] aux = a.clone();
        if (c==null)
            mergeSort(aux, a, 0, a.length, 0);
        else
            mergeSort(aux, a, 0, a.length, 0, c);
    }

    
Sorts the specified range of the specified array of objects according
to the order induced by the specified comparator.  The range to be
sorted extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be sorted is empty.)  All elements in the range must be
mutually comparable by the specified comparator (that is,
c.compare(e1, e2) must not throw a ClassCastException
for any elements e1 and e2 in the range).

This sort is guaranteed to be stable:  equal elements will
not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is
omitted if the highest element in the low sublist is less than the
lowest element in the high sublist).  This algorithm offers guaranteed
n*log(n) performance.
Params:
a – the array to be sorted
fromIndex – the index of the first element (inclusive) to be
       sorted
toIndex – the index of the last element (exclusive) to be sorted
c – the comparator to determine the order of the array.  A
       null value indicates that the elements' natural ordering should be used.
Throws:
ClassCastException – if the array contains elements that are not
        mutually comparable using the specified comparator.
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Sorts the specified range of the specified array of objects according
     * to the order induced by the specified comparator.  The range to be
     * sorted extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be sorted is empty.)  All elements in the range must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * <tt>c.compare(e1, e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the range).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance.
     *
     * @param a the array to be sorted
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted
     * @param toIndex the index of the last element (exclusive) to be sorted
     * @param c the comparator to determine the order of the array.  A
     *        <tt>null</tt> value indicates that the elements'
     *        {@linkplain Comparable natural ordering} should be used.
     * @throws ClassCastException if the array contains elements that are not
     *         <i>mutually comparable</i> using the specified comparator.
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static <T> void sort(T[] a, int fromIndex, int toIndex,
                                Comparator<? super T> c) {
        rangeCheck(a.length, fromIndex, toIndex);
        T[] aux = copyOfRange(a, fromIndex, toIndex);
        if (c==null)
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
        else
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex, c);
    }

    
Src is the source array that starts at index 0
Dest is the (possibly larger) array destination with a possible offset
low is the index in dest to start sorting
high is the end index in dest to end sorting
off is the offset into src corresponding to low in dest
/**
     * Src is the source array that starts at index 0
     * Dest is the (possibly larger) array destination with a possible offset
     * low is the index in dest to start sorting
     * high is the end index in dest to end sorting
     * off is the offset into src corresponding to low in dest
     */
    private static void mergeSort(Object[] src,
                                  Object[] dest,
                                  int low, int high, int off,
                                  Comparator c) {
        int length = high - low;

        // Insertion sort on smallest arrays
        if (length < INSERTIONSORT_THRESHOLD) {
            for (int i=low; i<high; i++)
                for (int j=i; j>low && c.compare(dest[j-1], dest[j])>0; j--)
                    swap(dest, j, j-1);
            return;
        }

        // Recursively sort halves of dest into src
        int destLow  = low;
        int destHigh = high;
        low  += off;
        high += off;
        int mid = (low + high) >>> 1;
        mergeSort(dest, src, low, mid, -off, c);
        mergeSort(dest, src, mid, high, -off, c);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (c.compare(src[mid-1], src[mid]) <= 0) {
           System.arraycopy(src, low, dest, destLow, length);
           return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
            if (q >= high || p < mid && c.compare(src[p], src[q]) <= 0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    }

    
Check that fromIndex and toIndex are in range, and throw an
appropriate exception if they aren't.
/**
     * Check that fromIndex and toIndex are in range, and throw an
     * appropriate exception if they aren't.
     */
    private static void rangeCheck(int arrayLen, int fromIndex, int toIndex) {
        if (fromIndex > toIndex)
            throw new IllegalArgumentException("fromIndex(" + fromIndex +
                       ") > toIndex(" + toIndex+")");
        if (fromIndex < 0)
            throw new ArrayIndexOutOfBoundsException(fromIndex);
        if (toIndex > arrayLen)
            throw new ArrayIndexOutOfBoundsException(toIndex);
    }

    // Searching

    
Searches the specified array of longs for the specified value using the binary search algorithm. The array must be sorted (as by the sort(long[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of longs for the specified value using the
     * binary search algorithm.  The array must be sorted (as
     * by the {@link #sort(long[])} method) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(long[] a, long key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of longs for the specified value using the binary search algorithm. The range must be sorted (as by the sort(long[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of longs for the specified value using the
     * binary search algorithm.
     * The range must be sorted (as
     * by the {@link #sort(long[], int, int)} method)
     * prior to making this call.  If it
     * is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(long[] a, int fromIndex, int toIndex,
                                   long key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(long[] a, int fromIndex, int toIndex,
                                     long key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            long midVal = a[mid];

            if (midVal < key)
                low = mid + 1;
            else if (midVal > key)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array of ints for the specified value using the binary search algorithm. The array must be sorted (as by the sort(int[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of ints for the specified value using the
     * binary search algorithm.  The array must be sorted (as
     * by the {@link #sort(int[])} method) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(int[] a, int key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of ints for the specified value using the binary search algorithm. The range must be sorted (as by the sort(int[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of ints for the specified value using the
     * binary search algorithm.
     * The range must be sorted (as
     * by the {@link #sort(int[], int, int)} method)
     * prior to making this call.  If it
     * is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(int[] a, int fromIndex, int toIndex,
                                   int key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(int[] a, int fromIndex, int toIndex,
                                     int key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            int midVal = a[mid];

            if (midVal < key)
                low = mid + 1;
            else if (midVal > key)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array of shorts for the specified value using the binary search algorithm. The array must be sorted (as by the sort(short[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of shorts for the specified value using
     * the binary search algorithm.  The array must be sorted
     * (as by the {@link #sort(short[])} method) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(short[] a, short key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of shorts for the specified value using the binary search algorithm. The range must be sorted (as by the sort(short[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of shorts for the specified value using
     * the binary search algorithm.
     * The range must be sorted
     * (as by the {@link #sort(short[], int, int)} method)
     * prior to making this call.  If
     * it is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(short[] a, int fromIndex, int toIndex,
                                   short key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(short[] a, int fromIndex, int toIndex,
                                     short key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            short midVal = a[mid];

            if (midVal < key)
                low = mid + 1;
            else if (midVal > key)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array of chars for the specified value using the binary search algorithm. The array must be sorted (as by the sort(char[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of chars for the specified value using the
     * binary search algorithm.  The array must be sorted (as
     * by the {@link #sort(char[])} method) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(char[] a, char key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of chars for the specified value using the binary search algorithm. The range must be sorted (as by the sort(char[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of chars for the specified value using the
     * binary search algorithm.
     * The range must be sorted (as
     * by the {@link #sort(char[], int, int)} method)
     * prior to making this call.  If it
     * is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(char[] a, int fromIndex, int toIndex,
                                   char key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(char[] a, int fromIndex, int toIndex,
                                     char key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            char midVal = a[mid];

            if (midVal < key)
                low = mid + 1;
            else if (midVal > key)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array of bytes for the specified value using the binary search algorithm. The array must be sorted (as by the sort(byte[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of bytes for the specified value using the
     * binary search algorithm.  The array must be sorted (as
     * by the {@link #sort(byte[])} method) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(byte[] a, byte key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of bytes for the specified value using the binary search algorithm. The range must be sorted (as by the sort(byte[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of bytes for the specified value using the
     * binary search algorithm.
     * The range must be sorted (as
     * by the {@link #sort(byte[], int, int)} method)
     * prior to making this call.  If it
     * is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(byte[] a, int fromIndex, int toIndex,
                                   byte key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(byte[] a, int fromIndex, int toIndex,
                                     byte key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            byte midVal = a[mid];

            if (midVal < key)
                low = mid + 1;
            else if (midVal > key)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array of doubles for the specified value using the binary search algorithm. The array must be sorted (as by the sort(double[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. This method considers all NaN values to be equivalent and equal. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of doubles for the specified value using
     * the binary search algorithm.  The array must be sorted
     * (as by the {@link #sort(double[])} method) prior to making this call.
     * If it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.  This method considers all NaN values to be
     * equivalent and equal.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(double[] a, double key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of doubles for the specified value using the binary search algorithm. The range must be sorted (as by the sort(double[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. This method considers all NaN values to be equivalent and equal. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of doubles for the specified value using
     * the binary search algorithm.
     * The range must be sorted
     * (as by the {@link #sort(double[], int, int)} method)
     * prior to making this call.
     * If it is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.  This method considers all NaN values to be
     * equivalent and equal.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(double[] a, int fromIndex, int toIndex,
                                   double key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(double[] a, int fromIndex, int toIndex,
                                     double key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            double midVal = a[mid];

            if (midVal < key)
                low = mid + 1;  // Neither val is NaN, thisVal is smaller
            else if (midVal > key)
                high = mid - 1; // Neither val is NaN, thisVal is larger
            else {
                long midBits = Double.doubleToLongBits(midVal);
                long keyBits = Double.doubleToLongBits(key);
                if (midBits == keyBits)     // Values are equal
                    return mid;             // Key found
                else if (midBits < keyBits) // (-0.0, 0.0) or (!NaN, NaN)
                    low = mid + 1;
                else                        // (0.0, -0.0) or (NaN, !NaN)
                    high = mid - 1;
            }
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array of floats for the specified value using the binary search algorithm. The array must be sorted (as by the sort(float[]) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. This method considers all NaN values to be equivalent and equal. 
Params:
a – the array to be searched
key – the value to be searched for
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array of floats for the specified value using
     * the binary search algorithm.  The array must be sorted
     * (as by the {@link #sort(float[])} method) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.  This method considers all NaN values to be
     * equivalent and equal.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     */
    public static int binarySearch(float[] a, float key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array of floats for the specified value using the binary search algorithm. The range must be sorted (as by the sort(float[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements with the specified value, there is no guarantee which one will be found. This method considers all NaN values to be equivalent and equal. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array of floats for the specified value using
     * the binary search algorithm.
     * The range must be sorted
     * (as by the {@link #sort(float[], int, int)} method)
     * prior to making this call.  If
     * it is not sorted, the results are undefined.  If the range contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.  This method considers all NaN values to be
     * equivalent and equal.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(float[] a, int fromIndex, int toIndex,
                                   float key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(float[] a, int fromIndex, int toIndex,
                                     float key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            float midVal = a[mid];

            if (midVal < key)
                low = mid + 1;  // Neither val is NaN, thisVal is smaller
            else if (midVal > key)
                high = mid - 1; // Neither val is NaN, thisVal is larger
            else {
                int midBits = Float.floatToIntBits(midVal);
                int keyBits = Float.floatToIntBits(key);
                if (midBits == keyBits)     // Values are equal
                    return mid;             // Key found
                else if (midBits < keyBits) // (-0.0, 0.0) or (!NaN, NaN)
                    low = mid + 1;
                else                        // (0.0, -0.0) or (NaN, !NaN)
                    high = mid - 1;
            }
        }
        return -(low + 1);  // key not found.
    }


    
Searches the specified array for the specified object using the binary search algorithm. The array must be sorted into ascending order according to the natural ordering of its elements (as by the sort(Object[]) method) prior to making this call. If it is not sorted, the results are undefined. (If the array contains elements that are not mutually comparable (for example, strings and integers), it cannot be sorted according
to the natural ordering of its elements, hence results are undefined.)
If the array contains multiple
elements equal to the specified object, there is no guarantee which
one will be found.
Params:
a – the array to be searched
key – the value to be searched for
Throws:
ClassCastException – if the search key is not comparable to the
        elements of the array.
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array for the specified object using the binary
     * search algorithm.  The array must be sorted into ascending order
     * according to the
     * {@linkplain Comparable natural ordering}
     * of its elements (as by the
     * {@link #sort(Object[])} method) prior to making this call.
     * If it is not sorted, the results are undefined.
     * (If the array contains elements that are not mutually comparable (for
     * example, strings and integers), it <i>cannot</i> be sorted according
     * to the natural ordering of its elements, hence results are undefined.)
     * If the array contains multiple
     * elements equal to the specified object, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws ClassCastException if the search key is not comparable to the
     *         elements of the array.
     */
    public static int binarySearch(Object[] a, Object key) {
        return binarySearch0(a, 0, a.length, key);
    }

    
Searches a range of the specified array for the specified object using the binary search algorithm. The range must be sorted into ascending order according to the natural ordering of its elements (as by the sort(Object[], int, int) method) prior to making this call. If it is not sorted, the results are undefined. (If the range contains elements that are not mutually comparable (for example, strings and integers), it cannot be sorted according
to the natural ordering of its elements, hence results are undefined.)
If the range contains multiple
elements equal to the specified object, there is no guarantee which
one will be found.
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
Throws:
ClassCastException – if the search key is not comparable to the
        elements of the array within the specified range.
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array for the specified object using the binary
     * search algorithm.
     * The range must be sorted into ascending order
     * according to the
     * {@linkplain Comparable natural ordering}
     * of its elements (as by the
     * {@link #sort(Object[], int, int)} method) prior to making this
     * call.  If it is not sorted, the results are undefined.
     * (If the range contains elements that are not mutually comparable (for
     * example, strings and integers), it <i>cannot</i> be sorted according
     * to the natural ordering of its elements, hence results are undefined.)
     * If the range contains multiple
     * elements equal to the specified object, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws ClassCastException if the search key is not comparable to the
     *         elements of the array within the specified range.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static int binarySearch(Object[] a, int fromIndex, int toIndex,
                                   Object key) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key);
    }

    // Like public version, but without range checks.
    private static int binarySearch0(Object[] a, int fromIndex, int toIndex,
                                     Object key) {
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            Comparable midVal = (Comparable)a[mid];
            int cmp = midVal.compareTo(key);

            if (cmp < 0)
                low = mid + 1;
            else if (cmp > 0)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }

    
Searches the specified array for the specified object using the binary search algorithm. The array must be sorted into ascending order according to the specified comparator (as by the sort(T[], Comparator) method) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements equal to the specified object, there is no guarantee which one will be found. 
Params:
a – the array to be searched
key – the value to be searched for
c – the comparator by which the array is ordered.  A
       null value indicates that the elements' natural ordering should be used.
Throws:
ClassCastException – if the array contains elements that are not
        mutually comparable using the specified comparator,
        or the search key is not comparable to the
        elements of the array using this comparator.
Returns:
index of the search key, if it is contained in the array;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element greater than the key, or a.length if all
        elements in the array are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found./**
     * Searches the specified array for the specified object using the binary
     * search algorithm.  The array must be sorted into ascending order
     * according to the specified comparator (as by the
     * {@link #sort(Object[], Comparator) sort(T[], Comparator)}
     * method) prior to making this call.  If it is
     * not sorted, the results are undefined.
     * If the array contains multiple
     * elements equal to the specified object, there is no guarantee which one
     * will be found.
     *
     * @param a the array to be searched
     * @param key the value to be searched for
     * @param c the comparator by which the array is ordered.  A
     *        <tt>null</tt> value indicates that the elements'
     *        {@linkplain Comparable natural ordering} should be used.
     * @return index of the search key, if it is contained in the array;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element greater than the key, or <tt>a.length</tt> if all
     *         elements in the array are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws ClassCastException if the array contains elements that are not
     *         <i>mutually comparable</i> using the specified comparator,
     *         or the search key is not comparable to the
     *         elements of the array using this comparator.
     */
    public static <T> int binarySearch(T[] a, T key, Comparator<? super T> c) {
        return binarySearch0(a, 0, a.length, key, c);
    }

    
Searches a range of the specified array for the specified object using the binary search algorithm. The range must be sorted into ascending order according to the specified comparator (as by the 
sort(T[], int, int, Comparator) method) prior to making this call. If it is not sorted, the results are undefined. If the range contains multiple elements equal to the specified object, there is no guarantee which one will be found. 
Params:
a – the array to be searched
fromIndex – the index of the first element (inclusive) to be
         searched
toIndex – the index of the last element (exclusive) to be searched
key – the value to be searched for
c – the comparator by which the array is ordered.  A
       null value indicates that the elements' natural ordering should be used.
Throws:
ClassCastException – if the range contains elements that are not
        mutually comparable using the specified comparator,
        or the search key is not comparable to the
        elements in the range using this comparator.
IllegalArgumentException –  if fromIndex > toIndex
ArrayIndexOutOfBoundsException –  if fromIndex < 0 or toIndex > a.length
Returns:
index of the search key, if it is contained in the array
        within the specified range;
        otherwise, (-(insertion point) - 1).  The
        insertion point is defined as the point at which the
        key would be inserted into the array: the index of the first
        element in the range greater than the key,
        or toIndex if all
        elements in the range are less than the specified key.  Note
        that this guarantees that the return value will be >= 0 if
        and only if the key is found.
Since:
1.6/**
     * Searches a range of
     * the specified array for the specified object using the binary
     * search algorithm.
     * The range must be sorted into ascending order
     * according to the specified comparator (as by the
     * {@link #sort(Object[], int, int, Comparator)
     * sort(T[], int, int, Comparator)}
     * method) prior to making this call.
     * If it is not sorted, the results are undefined.
     * If the range contains multiple elements equal to the specified object,
     * there is no guarantee which one will be found.
     *
     * @param a the array to be searched
     * @param fromIndex the index of the first element (inclusive) to be
     *          searched
     * @param toIndex the index of the last element (exclusive) to be searched
     * @param key the value to be searched for
     * @param c the comparator by which the array is ordered.  A
     *        <tt>null</tt> value indicates that the elements'
     *        {@linkplain Comparable natural ordering} should be used.
     * @return index of the search key, if it is contained in the array
     *         within the specified range;
     *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *         <i>insertion point</i> is defined as the point at which the
     *         key would be inserted into the array: the index of the first
     *         element in the range greater than the key,
     *         or <tt>toIndex</tt> if all
     *         elements in the range are less than the specified key.  Note
     *         that this guarantees that the return value will be &gt;= 0 if
     *         and only if the key is found.
     * @throws ClassCastException if the range contains elements that are not
     *         <i>mutually comparable</i> using the specified comparator,
     *         or the search key is not comparable to the
     *         elements in the range using this comparator.
     * @throws IllegalArgumentException
     *         if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *         if {@code fromIndex < 0 or toIndex > a.length}
     * @since 1.6
     */
    public static <T> int binarySearch(T[] a, int fromIndex, int toIndex,
                                       T key, Comparator<? super T> c) {
        rangeCheck(a.length, fromIndex, toIndex);
        return binarySearch0(a, fromIndex, toIndex, key, c);
    }

    // Like public version, but without range checks.
    private static <T> int binarySearch0(T[] a, int fromIndex, int toIndex,
                                         T key, Comparator<? super T> c) {
        if (c == null) {
            return binarySearch0(a, fromIndex, toIndex, key);
        }
        int low = fromIndex;
        int high = toIndex - 1;

        while (low <= high) {
            int mid = (low + high) >>> 1;
            T midVal = a[mid];
            int cmp = c.compare(midVal, key);

            if (cmp < 0)
                low = mid + 1;
            else if (cmp > 0)
                high = mid - 1;
            else
                return mid; // key found
        }
        return -(low + 1);  // key not found.
    }


    // Equality Testing

    
Returns true if the two specified arrays of longs are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of longs are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(long[] a, long[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    
Returns true if the two specified arrays of ints are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of ints are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(int[] a, int[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    
Returns true if the two specified arrays of shorts are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of shorts are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(short[] a, short a2[]) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    
Returns true if the two specified arrays of chars are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of chars are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(char[] a, char[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    
Returns true if the two specified arrays of bytes are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of bytes are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(byte[] a, byte[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    
Returns true if the two specified arrays of booleans are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of booleans are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(boolean[] a, boolean[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    
Returns true if the two specified arrays of doubles are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Two doubles d1 and d2 are considered equal if:
    new Double(d1).equals(new Double(d2))
(Unlike the == operator, this method considers
NaN equals to itself, and 0.0d unequal to -0.0d.)
Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
See Also:
Double.equals(Object)
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of doubles are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * Two doubles <tt>d1</tt> and <tt>d2</tt> are considered equal if:
     * <pre>    <tt>new Double(d1).equals(new Double(d2))</tt></pre>
     * (Unlike the <tt>==</tt> operator, this method considers
     * <tt>NaN</tt> equals to itself, and 0.0d unequal to -0.0d.)
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     * @see Double#equals(Object)
     */
    public static boolean equals(double[] a, double[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (Double.doubleToLongBits(a[i])!=Double.doubleToLongBits(a2[i]))
                return false;

        return true;
    }

    
Returns true if the two specified arrays of floats are
equal to one another.  Two arrays are considered equal if both
arrays contain the same number of elements, and all corresponding pairs
of elements in the two arrays are equal.  In other words, two arrays
are equal if they contain the same elements in the same order.  Also,
two array references are considered equal if both are null.

Two floats f1 and f2 are considered equal if:
    new Float(f1).equals(new Float(f2))
(Unlike the == operator, this method considers
NaN equals to itself, and 0.0f unequal to -0.0f.)
Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
See Also:
Float.equals(Object)
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of floats are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * Two floats <tt>f1</tt> and <tt>f2</tt> are considered equal if:
     * <pre>    <tt>new Float(f1).equals(new Float(f2))</tt></pre>
     * (Unlike the <tt>==</tt> operator, this method considers
     * <tt>NaN</tt> equals to itself, and 0.0f unequal to -0.0f.)
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     * @see Float#equals(Object)
     */
    public static boolean equals(float[] a, float[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (Float.floatToIntBits(a[i])!=Float.floatToIntBits(a2[i]))
                return false;

        return true;
    }


    
Returns true if the two specified arrays of Objects are
equal to one another.  The two arrays are considered equal if
both arrays contain the same number of elements, and all corresponding
pairs of elements in the two arrays are equal.  Two objects e1
and e2 are considered equal if (e1==null ? e2==null
: e1.equals(e2)).  In other words, the two arrays are equal if
they contain the same elements in the same order.  Also, two array
references are considered equal if both are null.

Params:
a – one array to be tested for equality
a2 – the other array to be tested for equality
Returns:
true if the two arrays are equal/**
     * Returns <tt>true</tt> if the two specified arrays of Objects are
     * <i>equal</i> to one another.  The two arrays are considered equal if
     * both arrays contain the same number of elements, and all corresponding
     * pairs of elements in the two arrays are equal.  Two objects <tt>e1</tt>
     * and <tt>e2</tt> are considered <i>equal</i> if <tt>(e1==null ? e2==null
     * : e1.equals(e2))</tt>.  In other words, the two arrays are equal if
     * they contain the same elements in the same order.  Also, two array
     * references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     */
    public static boolean equals(Object[] a, Object[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++) {
            Object o1 = a[i];
            Object o2 = a2[i];
            if (!(o1==null ? o2==null : o1.equals(o2)))
                return false;
        }

        return true;
    }


    // Filling

    
Assigns the specified long value to each element of the specified array
of longs.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified long value to each element of the specified array
     * of longs.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(long[] a, long val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified long value to each element of the specified
range of the specified array of longs.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified long value to each element of the specified
     * range of the specified array of longs.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(long[] a, int fromIndex, int toIndex, long val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified int value to each element of the specified array
of ints.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified int value to each element of the specified array
     * of ints.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(int[] a, int val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified int value to each element of the specified
range of the specified array of ints.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified int value to each element of the specified
     * range of the specified array of ints.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(int[] a, int fromIndex, int toIndex, int val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified short value to each element of the specified array
of shorts.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified short value to each element of the specified array
     * of shorts.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(short[] a, short val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified short value to each element of the specified
range of the specified array of shorts.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified short value to each element of the specified
     * range of the specified array of shorts.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(short[] a, int fromIndex, int toIndex, short val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified char value to each element of the specified array
of chars.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified char value to each element of the specified array
     * of chars.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(char[] a, char val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified char value to each element of the specified
range of the specified array of chars.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified char value to each element of the specified
     * range of the specified array of chars.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(char[] a, int fromIndex, int toIndex, char val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified byte value to each element of the specified array
of bytes.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified byte value to each element of the specified array
     * of bytes.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(byte[] a, byte val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified byte value to each element of the specified
range of the specified array of bytes.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified byte value to each element of the specified
     * range of the specified array of bytes.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(byte[] a, int fromIndex, int toIndex, byte val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified boolean value to each element of the specified
array of booleans.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified boolean value to each element of the specified
     * array of booleans.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(boolean[] a, boolean val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified boolean value to each element of the specified
range of the specified array of booleans.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified boolean value to each element of the specified
     * range of the specified array of booleans.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(boolean[] a, int fromIndex, int toIndex,
                            boolean val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified double value to each element of the specified
array of doubles.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified double value to each element of the specified
     * array of doubles.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(double[] a, double val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified double value to each element of the specified
range of the specified array of doubles.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified double value to each element of the specified
     * range of the specified array of doubles.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(double[] a, int fromIndex, int toIndex,double val){
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified float value to each element of the specified array
of floats.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array/**
     * Assigns the specified float value to each element of the specified array
     * of floats.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     */
    public static void fill(float[] a, float val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified float value to each element of the specified
range of the specified array of floats.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length/**
     * Assigns the specified float value to each element of the specified
     * range of the specified array of floats.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     */
    public static void fill(float[] a, int fromIndex, int toIndex, float val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }

    
Assigns the specified Object reference to each element of the specified
array of Objects.
Params:
a – the array to be filled
val – the value to be stored in all elements of the array
Throws:
ArrayStoreException – if the specified value is not of a
        runtime type that can be stored in the specified array/**
     * Assigns the specified Object reference to each element of the specified
     * array of Objects.
     *
     * @param a the array to be filled
     * @param val the value to be stored in all elements of the array
     * @throws ArrayStoreException if the specified value is not of a
     *         runtime type that can be stored in the specified array
     */
    public static void fill(Object[] a, Object val) {
        for (int i = 0, len = a.length; i < len; i++)
            a[i] = val;
    }

    
Assigns the specified Object reference to each element of the specified
range of the specified array of Objects.  The range to be filled
extends from index fromIndex, inclusive, to index
toIndex, exclusive.  (If fromIndex==toIndex, the
range to be filled is empty.)
Params:
a – the array to be filled
fromIndex – the index of the first element (inclusive) to be
       filled with the specified value
toIndex – the index of the last element (exclusive) to be
       filled with the specified value
val – the value to be stored in all elements of the array
Throws:
IllegalArgumentException – if fromIndex > toIndex
ArrayIndexOutOfBoundsException – if fromIndex < 0 or
        toIndex > a.length
ArrayStoreException – if the specified value is not of a
        runtime type that can be stored in the specified array/**
     * Assigns the specified Object reference to each element of the specified
     * range of the specified array of Objects.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be filled is empty.)
     *
     * @param a the array to be filled
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value
     * @param val the value to be stored in all elements of the array
     * @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
     *         <tt>toIndex &gt; a.length</tt>
     * @throws ArrayStoreException if the specified value is not of a
     *         runtime type that can be stored in the specified array
     */
    public static void fill(Object[] a, int fromIndex, int toIndex, Object val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i = fromIndex; i < toIndex; i++)
            a[i] = val;
    }


    // Cloning
    
Copies the specified array, truncating or padding with nulls (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain null.
Such indices will exist if and only if the specified length
is greater than that of the original array.
The resulting array is of exactly the same class as the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with nulls
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with nulls (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>null</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     * The resulting array is of exactly the same class as the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with nulls
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static <T> T[] copyOf(T[] original, int newLength) {
        return (T[]) copyOf(original, newLength, original.getClass());
    }

    
Copies the specified array, truncating or padding with nulls (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain null.
Such indices will exist if and only if the specified length
is greater than that of the original array.
The resulting array is of the class newType.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
newType – the class of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
ArrayStoreException – if an element copied from
    original is not of a runtime type that can be stored in
    an array of class newType
Returns:
a copy of the original array, truncated or padded with nulls
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with nulls (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>null</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     * The resulting array is of the class <tt>newType</tt>.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @param newType the class of the copy to be returned
     * @return a copy of the original array, truncated or padded with nulls
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @throws ArrayStoreException if an element copied from
     *     <tt>original</tt> is not of a runtime type that can be stored in
     *     an array of class <tt>newType</tt>
     * @since 1.6
     */
    public static <T,U> T[] copyOf(U[] original, int newLength, Class<? extends T[]> newType) {
        T[] copy = ((Object)newType == (Object)Object[].class)
            ? (T[]) new Object[newLength]
            : (T[]) Array.newInstance(newType.getComponentType(), newLength);
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with zeros (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain (byte)0.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with zeros
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with zeros (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>(byte)0</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with zeros
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static byte[] copyOf(byte[] original, int newLength) {
        byte[] copy = new byte[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with zeros (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain (short)0.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with zeros
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with zeros (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>(short)0</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with zeros
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static short[] copyOf(short[] original, int newLength) {
        short[] copy = new short[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with zeros (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain 0.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with zeros
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with zeros (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>0</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with zeros
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static int[] copyOf(int[] original, int newLength) {
        int[] copy = new int[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with zeros (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain 0L.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with zeros
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with zeros (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>0L</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with zeros
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static long[] copyOf(long[] original, int newLength) {
        long[] copy = new long[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with null characters (if necessary)
so the copy has the specified length.  For all indices that are valid
in both the original array and the copy, the two arrays will contain
identical values.  For any indices that are valid in the copy but not
the original, the copy will contain '\\u000'.  Such indices
will exist if and only if the specified length is greater than that of
the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with null characters
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with null characters (if necessary)
     * so the copy has the specified length.  For all indices that are valid
     * in both the original array and the copy, the two arrays will contain
     * identical values.  For any indices that are valid in the copy but not
     * the original, the copy will contain <tt>'\\u000'</tt>.  Such indices
     * will exist if and only if the specified length is greater than that of
     * the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with null characters
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static char[] copyOf(char[] original, int newLength) {
        char[] copy = new char[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with zeros (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain 0f.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with zeros
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with zeros (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>0f</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with zeros
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static float[] copyOf(float[] original, int newLength) {
        float[] copy = new float[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with zeros (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain 0d.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with zeros
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with zeros (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>0d</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with zeros
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static double[] copyOf(double[] original, int newLength) {
        double[] copy = new double[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified array, truncating or padding with false (if necessary)
so the copy has the specified length.  For all indices that are
valid in both the original array and the copy, the two arrays will
contain identical values.  For any indices that are valid in the
copy but not the original, the copy will contain false.
Such indices will exist if and only if the specified length
is greater than that of the original array.
Params:
original – the array to be copied
newLength – the length of the copy to be returned
Throws:
NegativeArraySizeException – if newLength is negative
NullPointerException – if original is null
Returns:
a copy of the original array, truncated or padded with false elements
    to obtain the specified length
Since:
1.6/**
     * Copies the specified array, truncating or padding with <tt>false</tt> (if necessary)
     * so the copy has the specified length.  For all indices that are
     * valid in both the original array and the copy, the two arrays will
     * contain identical values.  For any indices that are valid in the
     * copy but not the original, the copy will contain <tt>false</tt>.
     * Such indices will exist if and only if the specified length
     * is greater than that of the original array.
     *
     * @param original the array to be copied
     * @param newLength the length of the copy to be returned
     * @return a copy of the original array, truncated or padded with false elements
     *     to obtain the specified length
     * @throws NegativeArraySizeException if <tt>newLength</tt> is negative
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static boolean[] copyOf(boolean[] original, int newLength) {
        boolean[] copy = new boolean[newLength];
        System.arraycopy(original, 0, copy, 0,
                         Math.min(original.length, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
null is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.

The resulting array is of exactly the same class as the original array.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with nulls to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>null</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     * <p>
     * The resulting array is of exactly the same class as the original array.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with nulls to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static <T> T[] copyOfRange(T[] original, int from, int to) {
        return copyOfRange(original, from, to, (Class<T[]>) original.getClass());
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
null is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
The resulting array is of the class newType.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
newType – the class of the copy to be returned
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
ArrayStoreException – if an element copied from
    original is not of a runtime type that can be stored in
    an array of class newType.
Returns:
a new array containing the specified range from the original array,
    truncated or padded with nulls to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>null</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     * The resulting array is of the class <tt>newType</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @param newType the class of the copy to be returned
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with nulls to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @throws ArrayStoreException if an element copied from
     *     <tt>original</tt> is not of a runtime type that can be stored in
     *     an array of class <tt>newType</tt>.
     * @since 1.6
     */
    public static <T,U> T[] copyOfRange(U[] original, int from, int to, Class<? extends T[]> newType) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        T[] copy = ((Object)newType == (Object)Object[].class)
            ? (T[]) new Object[newLength]
            : (T[]) Array.newInstance(newType.getComponentType(), newLength);
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
(byte)0 is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with zeros to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>(byte)0</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with zeros to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static byte[] copyOfRange(byte[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        byte[] copy = new byte[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
(short)0 is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with zeros to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>(short)0</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with zeros to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static short[] copyOfRange(short[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        short[] copy = new short[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
0 is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with zeros to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>0</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with zeros to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static int[] copyOfRange(int[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        int[] copy = new int[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
0L is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with zeros to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>0L</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with zeros to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static long[] copyOfRange(long[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        long[] copy = new long[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
'\\u000' is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with null characters to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>'\\u000'</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with null characters to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static char[] copyOfRange(char[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        char[] copy = new char[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
0f is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with zeros to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>0f</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with zeros to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static float[] copyOfRange(float[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        float[] copy = new float[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
0d is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with zeros to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>0d</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with zeros to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static double[] copyOfRange(double[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        double[] copy = new double[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }

    
Copies the specified range of the specified array into a new array.
The initial index of the range (from) must lie between zero
and original.length, inclusive.  The value at
original[from] is placed into the initial element of the copy
(unless from == original.length or from == to).
Values from subsequent elements in the original array are placed into
subsequent elements in the copy.  The final index of the range
(to), which must be greater than or equal to from,
may be greater than original.length, in which case
false is placed in all elements of the copy whose index is
greater than or equal to original.length - from.  The length
of the returned array will be to - from.
Params:
original – the array from which a range is to be copied
from – the initial index of the range to be copied, inclusive
to – the final index of the range to be copied, exclusive.
    (This index may lie outside the array.)
Throws:
ArrayIndexOutOfBoundsException – if from < 0 or from > original.length
IllegalArgumentException – if from > to
NullPointerException – if original is null
Returns:
a new array containing the specified range from the original array,
    truncated or padded with false elements to obtain the required length
Since:
1.6/**
     * Copies the specified range of the specified array into a new array.
     * The initial index of the range (<tt>from</tt>) must lie between zero
     * and <tt>original.length</tt>, inclusive.  The value at
     * <tt>original[from]</tt> is placed into the initial element of the copy
     * (unless <tt>from == original.length</tt> or <tt>from == to</tt>).
     * Values from subsequent elements in the original array are placed into
     * subsequent elements in the copy.  The final index of the range
     * (<tt>to</tt>), which must be greater than or equal to <tt>from</tt>,
     * may be greater than <tt>original.length</tt>, in which case
     * <tt>false</tt> is placed in all elements of the copy whose index is
     * greater than or equal to <tt>original.length - from</tt>.  The length
     * of the returned array will be <tt>to - from</tt>.
     *
     * @param original the array from which a range is to be copied
     * @param from the initial index of the range to be copied, inclusive
     * @param to the final index of the range to be copied, exclusive.
     *     (This index may lie outside the array.)
     * @return a new array containing the specified range from the original array,
     *     truncated or padded with false elements to obtain the required length
     * @throws ArrayIndexOutOfBoundsException if {@code from < 0}
     *     or {@code from > original.length}
     * @throws IllegalArgumentException if <tt>from &gt; to</tt>
     * @throws NullPointerException if <tt>original</tt> is null
     * @since 1.6
     */
    public static boolean[] copyOfRange(boolean[] original, int from, int to) {
        int newLength = to - from;
        if (newLength < 0)
            throw new IllegalArgumentException(from + " > " + to);
        boolean[] copy = new boolean[newLength];
        System.arraycopy(original, from, copy, 0,
                         Math.min(original.length - from, newLength));
        return copy;
    }


    // Misc

    
Returns a fixed-size list backed by the specified array. (Changes to the returned list "write through" to the array.) This method acts as bridge between array-based and collection-based APIs, in combination with Collection.toArray. The returned list is serializable and implements RandomAccess. 
This method also provides a convenient way to create a fixed-size
list initialized to contain several elements:
    List<String> stooges = Arrays.asList("Larry", "Moe", "Curly");

Params:
a – the array by which the list will be backed
Returns:
a list view of the specified array/**
     * Returns a fixed-size list backed by the specified array.  (Changes to
     * the returned list "write through" to the array.)  This method acts
     * as bridge between array-based and collection-based APIs, in
     * combination with {@link Collection#toArray}.  The returned list is
     * serializable and implements {@link RandomAccess}.
     *
     * <p>This method also provides a convenient way to create a fixed-size
     * list initialized to contain several elements:
     * <pre>
     *     List&lt;String&gt; stooges = Arrays.asList("Larry", "Moe", "Curly");
     * </pre>
     *
     * @param a the array by which the list will be backed
     * @return a list view of the specified array
     */
    public static <T> List<T> asList(T... a) {
        return new ArrayList<T>(a);
    }

    
@serial
include/**
     * @serial include
     */
    private static class ArrayList<E> extends AbstractList<E>
        implements RandomAccess, java.io.Serializable
    {
        private static final long serialVersionUID = -2764017481108945198L;
        private final E[] a;

        ArrayList(E[] array) {
            if (array==null)
                throw new NullPointerException();
            a = array;
        }

        public int size() {
            return a.length;
        }

        public Object[] toArray() {
            return a.clone();
        }

        public <T> T[] toArray(T[] a) {
            int size = size();
            if (a.length < size)
                return Arrays.copyOf(this.a, size,
                                     (Class<? extends T[]>) a.getClass());
            System.arraycopy(this.a, 0, a, 0, size);
            if (a.length > size)
                a[size] = null;
            return a;
        }

        public E get(int index) {
            return a[index];
        }

        public E set(int index, E element) {
            E oldValue = a[index];
            a[index] = element;
            return oldValue;
        }

        public int indexOf(Object o) {
            if (o==null) {
                for (int i=0; i<a.length; i++)
                    if (a[i]==null)
                        return i;
            } else {
                for (int i=0; i<a.length; i++)
                    if (o.equals(a[i]))
                        return i;
            }
            return -1;
        }

        public boolean contains(Object o) {
            return indexOf(o) != -1;
        }
    }

    
Returns a hash code based on the contents of the specified array.
For any two long arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Long instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>long</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Long}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(long a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (long element : a) {
            int elementHash = (int)(element ^ (element >>> 32));
            result = 31 * result + elementHash;
        }

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two non-null int arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Integer instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two non-null <tt>int</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Integer}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(int a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (int element : a)
            result = 31 * result + element;

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two short arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Short instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>short</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Short}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(short a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (short element : a)
            result = 31 * result + element;

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two char arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Character instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>char</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Character}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(char a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (char element : a)
            result = 31 * result + element;

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two byte arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Byte instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>byte</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Byte}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(byte a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (byte element : a)
            result = 31 * result + element;

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two boolean arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Boolean instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>boolean</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Boolean}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(boolean a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (boolean element : a)
            result = 31 * result + (element ? 1231 : 1237);

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two float arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Float instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>float</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Float}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(float a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (float element : a)
            result = 31 * result + Float.floatToIntBits(element);

        return result;
    }

    
Returns a hash code based on the contents of the specified array.
For any two double arrays a and b
such that Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is the same value that would be obtained by invoking the hashCode method on a List containing a sequence of Double instances representing the elements of a in the same order.
If a is null, this method returns 0.
Params:
a – the array whose hash value to compute
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>double</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Double}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(double a[]) {
        if (a == null)
            return 0;

        int result = 1;
        for (double element : a) {
            long bits = Double.doubleToLongBits(element);
            result = 31 * result + (int)(bits ^ (bits >>> 32));
        }
        return result;
    }

    
Returns a hash code based on the contents of the specified array.  If
the array contains other arrays as elements, the hash code is based on
their identities rather than their contents.  It is therefore
acceptable to invoke this method on an array that contains itself as an
element,  either directly or indirectly through one or more levels of
arrays.
For any two arrays a and b such that
Arrays.equals(a, b), it is also the case that
Arrays.hashCode(a) == Arrays.hashCode(b).
The value returned by this method is equal to the value that would
be returned by Arrays.asList(a).hashCode(), unless a
is null, in which case 0 is returned.
Params:
a – the array whose content-based hash code to compute
See Also:
deepHashCode(Object[])
Returns:
a content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the contents of the specified array.  If
     * the array contains other arrays as elements, the hash code is based on
     * their identities rather than their contents.  It is therefore
     * acceptable to invoke this method on an array that contains itself as an
     * element,  either directly or indirectly through one or more levels of
     * arrays.
     *
     * <p>For any two arrays <tt>a</tt> and <tt>b</tt> such that
     * <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is equal to the value that would
     * be returned by <tt>Arrays.asList(a).hashCode()</tt>, unless <tt>a</tt>
     * is <tt>null</tt>, in which case <tt>0</tt> is returned.
     *
     * @param a the array whose content-based hash code to compute
     * @return a content-based hash code for <tt>a</tt>
     * @see #deepHashCode(Object[])
     * @since 1.5
     */
    public static int hashCode(Object a[]) {
        if (a == null)
            return 0;

        int result = 1;

        for (Object element : a)
            result = 31 * result + (element == null ? 0 : element.hashCode());

        return result;
    }

    
Returns a hash code based on the "deep contents" of the specified
array.  If the array contains other arrays as elements, the
hash code is based on their contents and so on, ad infinitum.
It is therefore unacceptable to invoke this method on an array that
contains itself as an element, either directly or indirectly through
one or more levels of arrays.  The behavior of such an invocation is
undefined.
For any two arrays a and b such that
Arrays.deepEquals(a, b), it is also the case that
Arrays.deepHashCode(a) == Arrays.deepHashCode(b).
The computation of the value returned by this method is similar to that of the value returned by List.hashCode() on a list containing the same elements as a in the same order, with one
difference: If an element e of a is itself an array,
its hash code is computed not by calling e.hashCode(), but as
by calling the appropriate overloading of Arrays.hashCode(e)
if e is an array of a primitive type, or as by calling
Arrays.deepHashCode(e) recursively if e is an array
of a reference type.  If a is null, this method
returns 0.
Params:
a – the array whose deep-content-based hash code to compute
See Also:
hashCode(Object[])
Returns:
a deep-content-based hash code for a
Since:
1.5/**
     * Returns a hash code based on the "deep contents" of the specified
     * array.  If the array contains other arrays as elements, the
     * hash code is based on their contents and so on, ad infinitum.
     * It is therefore unacceptable to invoke this method on an array that
     * contains itself as an element, either directly or indirectly through
     * one or more levels of arrays.  The behavior of such an invocation is
     * undefined.
     *
     * <p>For any two arrays <tt>a</tt> and <tt>b</tt> such that
     * <tt>Arrays.deepEquals(a, b)</tt>, it is also the case that
     * <tt>Arrays.deepHashCode(a) == Arrays.deepHashCode(b)</tt>.
     *
     * <p>The computation of the value returned by this method is similar to
     * that of the value returned by {@link List#hashCode()} on a list
     * containing the same elements as <tt>a</tt> in the same order, with one
     * difference: If an element <tt>e</tt> of <tt>a</tt> is itself an array,
     * its hash code is computed not by calling <tt>e.hashCode()</tt>, but as
     * by calling the appropriate overloading of <tt>Arrays.hashCode(e)</tt>
     * if <tt>e</tt> is an array of a primitive type, or as by calling
     * <tt>Arrays.deepHashCode(e)</tt> recursively if <tt>e</tt> is an array
     * of a reference type.  If <tt>a</tt> is <tt>null</tt>, this method
     * returns 0.
     *
     * @param a the array whose deep-content-based hash code to compute
     * @return a deep-content-based hash code for <tt>a</tt>
     * @see #hashCode(Object[])
     * @since 1.5
     */
    public static int deepHashCode(Object a[]) {
        if (a == null)
            return 0;

        int result = 1;

        for (Object element : a) {
            int elementHash = 0;
            if (element instanceof Object[])
                elementHash = deepHashCode((Object[]) element);
            else if (element instanceof byte[])
                elementHash = hashCode((byte[]) element);
            else if (element instanceof short[])
                elementHash = hashCode((short[]) element);
            else if (element instanceof int[])
                elementHash = hashCode((int[]) element);
            else if (element instanceof long[])
                elementHash = hashCode((long[]) element);
            else if (element instanceof char[])
                elementHash = hashCode((char[]) element);
            else if (element instanceof float[])
                elementHash = hashCode((float[]) element);
            else if (element instanceof double[])
                elementHash = hashCode((double[]) element);
            else if (element instanceof boolean[])
                elementHash = hashCode((boolean[]) element);
            else if (element != null)
                elementHash = element.hashCode();

            result = 31 * result + elementHash;
        }

        return result;
    }

    
Returns true if the two specified arrays are deeply
equal to one another. Unlike the equals(Object[], Object[]) method, this method is appropriate for use with nested arrays of arbitrary depth. 
Two array references are considered deeply equal if both
are null, or if they refer to arrays that contain the same
number of elements and all corresponding pairs of elements in the two
arrays are deeply equal.
Two possibly null elements e1 and e2 are
deeply equal if any of the following conditions hold:

   
 e1 and e2 are both arrays of object reference
        types, and Arrays.deepEquals(e1, e2) would return true
   
 e1 and e2 are arrays of the same primitive
        type, and the appropriate overloading of
        Arrays.equals(e1, e2) would return true.
   
 e1 == e2
   
 e1.equals(e2) would return true.

Note that this definition permits null elements at any depth.
If either of the specified arrays contain themselves as elements
either directly or indirectly through one or more levels of arrays,
the behavior of this method is undefined.
Params:
a1 – one array to be tested for equality
a2 – the other array to be tested for equality
See Also:
equals(Object[], Object[])
Returns:
true if the two arrays are equal
Since:
1.5/**
     * Returns <tt>true</tt> if the two specified arrays are <i>deeply
     * equal</i> to one another.  Unlike the {@link #equals(Object[],Object[])}
     * method, this method is appropriate for use with nested arrays of
     * arbitrary depth.
     *
     * <p>Two array references are considered deeply equal if both
     * are <tt>null</tt>, or if they refer to arrays that contain the same
     * number of elements and all corresponding pairs of elements in the two
     * arrays are deeply equal.
     *
     * <p>Two possibly <tt>null</tt> elements <tt>e1</tt> and <tt>e2</tt> are
     * deeply equal if any of the following conditions hold:
     * <ul>
     *    <li> <tt>e1</tt> and <tt>e2</tt> are both arrays of object reference
     *         types, and <tt>Arrays.deepEquals(e1, e2) would return true</tt>
     *    <li> <tt>e1</tt> and <tt>e2</tt> are arrays of the same primitive
     *         type, and the appropriate overloading of
     *         <tt>Arrays.equals(e1, e2)</tt> would return true.
     *    <li> <tt>e1 == e2</tt>
     *    <li> <tt>e1.equals(e2)</tt> would return true.
     * </ul>
     * Note that this definition permits <tt>null</tt> elements at any depth.
     *
     * <p>If either of the specified arrays contain themselves as elements
     * either directly or indirectly through one or more levels of arrays,
     * the behavior of this method is undefined.
     *
     * @param a1 one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     * @see #equals(Object[],Object[])
     * @since 1.5
     */
    public static boolean deepEquals(Object[] a1, Object[] a2) {
        if (a1 == a2)
            return true;
        if (a1 == null || a2==null)
            return false;
        int length = a1.length;
        if (a2.length != length)
            return false;

        for (int i = 0; i < length; i++) {
            Object e1 = a1[i];
            Object e2 = a2[i];

            if (e1 == e2)
                continue;
            if (e1 == null)
                return false;

            // Figure out whether the two elements are equal
            boolean eq;
            if (e1 instanceof Object[] && e2 instanceof Object[])
                eq = deepEquals ((Object[]) e1, (Object[]) e2);
            else if (e1 instanceof byte[] && e2 instanceof byte[])
                eq = equals((byte[]) e1, (byte[]) e2);
            else if (e1 instanceof short[] && e2 instanceof short[])
                eq = equals((short[]) e1, (short[]) e2);
            else if (e1 instanceof int[] && e2 instanceof int[])
                eq = equals((int[]) e1, (int[]) e2);
            else if (e1 instanceof long[] && e2 instanceof long[])
                eq = equals((long[]) e1, (long[]) e2);
            else if (e1 instanceof char[] && e2 instanceof char[])
                eq = equals((char[]) e1, (char[]) e2);
            else if (e1 instanceof float[] && e2 instanceof float[])
                eq = equals((float[]) e1, (float[]) e2);
            else if (e1 instanceof double[] && e2 instanceof double[])
                eq = equals((double[]) e1, (double[]) e2);
            else if (e1 instanceof boolean[] && e2 instanceof boolean[])
                eq = equals((boolean[]) e1, (boolean[]) e2);
            else
                eq = e1.equals(e2);

            if (!eq)
                return false;
        }
        return true;
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(long).  Returns "null" if a
is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(long)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(long[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(int).  Returns "null" if a is
null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(int)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt> is
     * <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(int[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(short).  Returns "null" if a
is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(short)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(short[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(char).  Returns "null" if a
is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(char)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(char[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements
are separated by the characters ", " (a comma followed
by a space).  Elements are converted to strings as by
String.valueOf(byte).  Returns "null" if
a is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements
     * are separated by the characters <tt>", "</tt> (a comma followed
     * by a space).  Elements are converted to strings as by
     * <tt>String.valueOf(byte)</tt>.  Returns <tt>"null"</tt> if
     * <tt>a</tt> is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(byte[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(boolean).  Returns "null" if
a is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(boolean)</tt>.  Returns <tt>"null"</tt> if
     * <tt>a</tt> is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(boolean[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(float).  Returns "null" if a
is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(float)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(float[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array.
The string representation consists of a list of the array's elements,
enclosed in square brackets ("[]").  Adjacent elements are
separated by the characters ", " (a comma followed by a
space).  Elements are converted to strings as by
String.valueOf(double).  Returns "null" if a
is null.
Params:
a – the array whose string representation to return
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(double)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(double[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(a[i]);
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the contents of the specified array. If the array contains other arrays as elements, they are converted to strings by the Object.toString method inherited from Object, which describes their identities rather than
their contents.
The value returned by this method is equal to the value that would
be returned by Arrays.asList(a).toString(), unless a
is null, in which case "null" is returned.
Params:
a – the array whose string representation to return
See Also:
deepToString(Object[])
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the contents of the specified array.
     * If the array contains other arrays as elements, they are converted to
     * strings by the {@link Object#toString} method inherited from
     * <tt>Object</tt>, which describes their <i>identities</i> rather than
     * their contents.
     *
     * <p>The value returned by this method is equal to the value that would
     * be returned by <tt>Arrays.asList(a).toString()</tt>, unless <tt>a</tt>
     * is <tt>null</tt>, in which case <tt>"null"</tt> is returned.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @see #deepToString(Object[])
     * @since 1.5
     */
    public static String toString(Object[] a) {
        if (a == null)
            return "null";
        int iMax = a.length - 1;
        if (iMax == -1)
            return "[]";

        StringBuilder b = new StringBuilder();
        b.append('[');
        for (int i = 0; ; i++) {
            b.append(String.valueOf(a[i]));
            if (i == iMax)
                return b.append(']').toString();
            b.append(", ");
        }
    }

    
Returns a string representation of the "deep contents" of the specified
array.  If the array contains other arrays as elements, the string
representation contains their contents and so on.  This method is
designed for converting multidimensional arrays to strings.
The string representation consists of a list of the array's
elements, enclosed in square brackets ("[]").  Adjacent
elements are separated by the characters ", " (a comma
followed by a space).  Elements are converted to strings as by
String.valueOf(Object), unless they are themselves
arrays.
If an element e is an array of a primitive type, it is
converted to a string as by invoking the appropriate overloading of
Arrays.toString(e).  If an element e is an array of a
reference type, it is converted to a string as by invoking
this method recursively.
To avoid infinite recursion, if the specified array contains itself
as an element, or contains an indirect reference to itself through one
or more levels of arrays, the self-reference is converted to the string
"[...]".  For example, an array containing only a reference
to itself would be rendered as "[[...]]".
This method returns "null" if the specified array
is null.
Params:
a – the array whose string representation to return
See Also:
toString(Object[])
Returns:
a string representation of a
Since:
1.5/**
     * Returns a string representation of the "deep contents" of the specified
     * array.  If the array contains other arrays as elements, the string
     * representation contains their contents and so on.  This method is
     * designed for converting multidimensional arrays to strings.
     *
     * <p>The string representation consists of a list of the array's
     * elements, enclosed in square brackets (<tt>"[]"</tt>).  Adjacent
     * elements are separated by the characters <tt>", "</tt> (a comma
     * followed by a space).  Elements are converted to strings as by
     * <tt>String.valueOf(Object)</tt>, unless they are themselves
     * arrays.
     *
     * <p>If an element <tt>e</tt> is an array of a primitive type, it is
     * converted to a string as by invoking the appropriate overloading of
     * <tt>Arrays.toString(e)</tt>.  If an element <tt>e</tt> is an array of a
     * reference type, it is converted to a string as by invoking
     * this method recursively.
     *
     * <p>To avoid infinite recursion, if the specified array contains itself
     * as an element, or contains an indirect reference to itself through one
     * or more levels of arrays, the self-reference is converted to the string
     * <tt>"[...]"</tt>.  For example, an array containing only a reference
     * to itself would be rendered as <tt>"[[...]]"</tt>.
     *
     * <p>This method returns <tt>"null"</tt> if the specified array
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @see #toString(Object[])
     * @since 1.5
     */
    public static String deepToString(Object[] a) {
        if (a == null)
            return "null";

        int bufLen = 20 * a.length;
        if (a.length != 0 && bufLen <= 0)
            bufLen = Integer.MAX_VALUE;
        StringBuilder buf = new StringBuilder(bufLen);
        deepToString(a, buf, new HashSet<Object[]>());
        return buf.toString();
    }

    private static void deepToString(Object[] a, StringBuilder buf,
                                     Set<Object[]> dejaVu) {
        if (a == null) {
            buf.append("null");
            return;
        }
        int iMax = a.length - 1;
        if (iMax == -1) {
            buf.append("[]");
            return;
        }

        dejaVu.add(a);
        buf.append('[');
        for (int i = 0; ; i++) {

            Object element = a[i];
            if (element == null) {
                buf.append("null");
            } else {
                Class eClass = element.getClass();

                if (eClass.isArray()) {
                    if (eClass == byte[].class)
                        buf.append(toString((byte[]) element));
                    else if (eClass == short[].class)
                        buf.append(toString((short[]) element));
                    else if (eClass == int[].class)
                        buf.append(toString((int[]) element));
                    else if (eClass == long[].class)
                        buf.append(toString((long[]) element));
                    else if (eClass == char[].class)
                        buf.append(toString((char[]) element));
                    else if (eClass == float[].class)
                        buf.append(toString((float[]) element));
                    else if (eClass == double[].class)
                        buf.append(toString((double[]) element));
                    else if (eClass == boolean[].class)
                        buf.append(toString((boolean[]) element));
                    else { // element is an array of object references
                        if (dejaVu.contains(element))
                            buf.append("[...]");
                        else
                            deepToString((Object[])element, buf, dejaVu);
                    }
                } else {  // element is non-null and not an array
                    buf.append(element.toString());
                }
            }
            if (i == iMax)
                break;
            buf.append(", ");
        }
        buf.append(']');
        dejaVu.remove(a);
    }
}