Arrays.java

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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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package java.util;

import java.lang.reflect.Array;
import java.util.concurrent.ForkJoinPool;
import java.util.function.BinaryOperator;
import java.util.function.Consumer;
import java.util.function.DoubleBinaryOperator;
import java.util.function.IntBinaryOperator;
import java.util.function.IntFunction;
import java.util.function.IntToDoubleFunction;
import java.util.function.IntToLongFunction;
import java.util.function.IntUnaryOperator;
import java.util.function.LongBinaryOperator;
import java.util.function.UnaryOperator;
import java.util.stream.DoubleStream;
import java.util.stream.IntStream;
import java.util.stream.LongStream;
import java.util.stream.Stream;
import java.util.stream.StreamSupport;

/**
 * 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 {@code NullPointerException},
 * 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 {@code sort(Object[])} 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 {

    /**
     * The minimum array length below which a parallel sorting
     * algorithm will not further partition the sorting task. Using
     * smaller sizes typically results in memory contention across
     * tasks that makes parallel speedups unlikely.
     */
    private static final int MIN_ARRAY_SORT_GRAN = 1 << 13;

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

    /**
     * A comparator that implements the natural ordering of a group of
     * mutually comparable elements. May be used when a supplied
     * comparator is null. To simplify code-sharing within underlying
     * implementations, the compare method only declares type Object
     * for its second argument.
     *
     * Arrays class implementor's note: It is an empirical matter
     * whether ComparableTimSort offers any performance benefit over
     * TimSort used with this comparator.  If not, you are better off
     * deleting or bypassing ComparableTimSort.  There is currently no
     * empirical case for separating them for parallel sorting, so all
     * public Object parallelSort methods use the same comparator
     * based implementation.
     */
    static final class NaturalOrder implements Comparator<Object> {
        @SuppressWarnings("unchecked")
        public int compare(Object first, Object second) {
            return ((Comparable<Object>)first).compareTo(second);
        }
        static final NaturalOrder INSTANCE = new NaturalOrder();
    }

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

    /*
     * Sorting methods. Note that all public "sort" methods take the
     * same form: Performing argument checks if necessary, and then
     * expanding arguments into those required for the internal
     * implementation methods residing in other package-private
     * classes (except for legacyMergeSort, included in this class).
     */

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(int[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(int[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(long[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(long[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(short[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(short[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(char[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(char[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(byte[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(byte[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>The {@code <} relation does not provide a total order on all float
     * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
     * {@code 0.0f} and {@code Float.NaN} is considered greater than any
     * other value and all {@code Float.NaN} values are considered equal.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(float[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>The {@code <} relation does not provide a total order on all float
     * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
     * {@code 0.0f} and {@code Float.NaN} is considered greater than any
     * other value and all {@code Float.NaN} values are considered equal.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(float[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>The {@code <} relation does not provide a total order on all double
     * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
     * {@code 0.0d} and {@code Double.NaN} is considered greater than any
     * other value and all {@code Double.NaN} values are considered equal.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @param a the array to be sorted
     */
    public static void sort(double[] a) {
        DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
    }

    /**
     * Sorts the specified range of the array into ascending order. The range
     * to be sorted extends from the index {@code fromIndex}, inclusive, to
     * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
     * the range to be sorted is empty.
     *
     * <p>The {@code <} relation does not provide a total order on all double
     * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
     * {@code 0.0d} and {@code Double.NaN} is considered greater than any
     * other value and all {@code Double.NaN} values are considered equal.
     *
     * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
     * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
     * offers O(n log(n)) performance on many data sets that cause other
     * quicksorts to degrade to quadratic performance, and is typically
     * faster than traditional (one-pivot) Quicksort implementations.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     */
    public static void sort(double[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(byte[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(byte[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(byte[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1);
        else
            new ArraysParallelSortHelpers.FJByte.Sorter
                (null, a, new byte[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(byte[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(byte[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(byte[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
        else
            new ArraysParallelSortHelpers.FJByte.Sorter
                (null, a, new byte[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(char[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(char[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(char[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJChar.Sorter
                (null, a, new char[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
      @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(char[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(char[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(char[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJChar.Sorter
                (null, a, new char[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(short[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(short[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(short[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJShort.Sorter
                (null, a, new short[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(short[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(short[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(short[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJShort.Sorter
                (null, a, new short[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(int[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(int[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(int[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJInt.Sorter
                (null, a, new int[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(int[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(int[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(int[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJInt.Sorter
                (null, a, new int[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(long[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(long[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(long[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJLong.Sorter
                (null, a, new long[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(long[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(long[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(long[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJLong.Sorter
                (null, a, new long[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>The {@code <} relation does not provide a total order on all float
     * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
     * {@code 0.0f} and {@code Float.NaN} is considered greater than any
     * other value and all {@code Float.NaN} values are considered equal.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(float[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(float[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(float[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJFloat.Sorter
                (null, a, new float[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
     * <p>The {@code <} relation does not provide a total order on all float
     * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
     * {@code 0.0f} and {@code Float.NaN} is considered greater than any
     * other value and all {@code Float.NaN} values are considered equal.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(float[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(float[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(float[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJFloat.Sorter
                (null, a, new float[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified array into ascending numerical order.
     *
     * <p>The {@code <} relation does not provide a total order on all double
     * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
     * {@code 0.0d} and {@code Double.NaN} is considered greater than any
     * other value and all {@code Double.NaN} values are considered equal.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(double[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(double[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param a the array to be sorted
     *
     * @since 1.8
     */
    public static void parallelSort(double[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJDouble.Sorter
                (null, a, new double[n], 0, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * Sorts the specified range of the array into ascending numerical order.
     * The range to be sorted extends from the index {@code fromIndex},
     * inclusive, to the index {@code toIndex}, exclusive. If
     * {@code fromIndex == toIndex}, the range to be sorted is empty.
     *
     * <p>The {@code <} relation does not provide a total order on all double
     * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
     * value compares neither less than, greater than, nor equal to any value,
     * even itself. This method uses the total order imposed by the method
     * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
     * {@code 0.0d} and {@code Double.NaN} is considered greater than any
     * other value and all {@code Double.NaN} values are considered equal.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(double[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(double[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @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 {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > a.length}
     *
     * @since 1.8
     */
    public static void parallelSort(double[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJDouble.Sorter
                (null, a, new double[n], fromIndex, n, 0,
                 ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g).invoke();
    }

    /**
     * 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, {@code e1.compareTo(e2)} must
     * not throw a {@code ClassCastException} for any elements {@code e1}
     * and {@code e2} 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.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param <T> the class of the objects to be sorted
     * @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)
     * @throws IllegalArgumentException (optional) if the natural
     *         ordering of the array elements is found to violate the
     *         {@link Comparable} contract
     *
     * @since 1.8
     */
    @SuppressWarnings("unchecked")
    public static <T extends Comparable<? super T>> void parallelSort(T[] a) {
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            TimSort.sort(a, 0, n, NaturalOrder.INSTANCE, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJObject.Sorter<T>
                (null, a,
                 (T[])Array.newInstance(a.getClass().getComponentType(), n),
                 0, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g, NaturalOrder.INSTANCE).invoke();
    }

    /**
     * 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
     * {@code fromIndex}, inclusive, to index {@code toIndex}, exclusive.
     * (If {@code fromIndex==toIndex}, 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, {@code e1.compareTo(e2)} must not throw a
     * {@code ClassCastException} for any elements {@code e1} and
     * {@code e2} 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.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @param <T> the class of the objects to be sorted
     * @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 {@code fromIndex > toIndex} or
     *         (optional) if the natural ordering of the array elements is
     *         found to violate the {@link Comparable} contract
     * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
     *         {@code toIndex > a.length}
     * @throws ClassCastException if the array contains elements that are
     *         not <i>mutually comparable</i> (for example, strings and
     *         integers).
     *
     * @since 1.8
     */
    @SuppressWarnings("unchecked")
    public static <T extends Comparable<? super T>>
    void parallelSort(T[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            TimSort.sort(a, fromIndex, toIndex, NaturalOrder.INSTANCE, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJObject.Sorter<T>
                (null, a,
                 (T[])Array.newInstance(a.getClass().getComponentType(), n),
                 fromIndex, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g, NaturalOrder.INSTANCE).invoke();
    }

    /**
     * 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,
     * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
     * for any elements {@code e1} and {@code e2} 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.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a
     * working space no greater than the size of the original array. The
     * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
     * execute any parallel tasks.
     *
     * @param <T> the class of the objects to be sorted
     * @param a the array to be sorted
     * @param cmp the comparator to determine the order of the array.  A
     *        {@code null} 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 (optional) if the comparator is
     *         found to violate the {@link java.util.Comparator} contract
     *
     * @since 1.8
     */
    @SuppressWarnings("unchecked")
    public static <T> void parallelSort(T[] a, Comparator<? super T> cmp) {
        if (cmp == null)
            cmp = NaturalOrder.INSTANCE;
        int n = a.length, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            TimSort.sort(a, 0, n, cmp, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJObject.Sorter<T>
                (null, a,
                 (T[])Array.newInstance(a.getClass().getComponentType(), n),
                 0, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g, cmp).invoke();
    }

    /**
     * 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 {@code fromIndex}, inclusive, to index
     * {@code toIndex}, exclusive.  (If {@code fromIndex==toIndex}, the
     * range to be sorted is empty.)  All elements in the range must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
     * for any elements {@code e1} and {@code e2} 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.
     *
     * @implNote The sorting algorithm is a parallel sort-merge that breaks the
     * array into sub-arrays that are themselves sorted and then merged. When
     * the sub-array length reaches a minimum granularity, the sub-array is
     * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
     * method. If the length of the specified array is less than the minimum
     * granularity, then it is sorted using the appropriate {@link
     * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a working
     * space no greater than the size of the specified range of the original
     * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
     * used to execute any parallel tasks.
     *
     * @param <T> the class of the objects to be sorted
     * @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 cmp the comparator to determine the order of the array.  A
     *        {@code null} value indicates that the elements'
     *        {@linkplain Comparable natural ordering} should be used.
     * @throws IllegalArgumentException if {@code fromIndex > toIndex} or
     *         (optional) if the natural ordering of the array elements is
     *         found to violate the {@link Comparable} contract
     * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
     *         {@code toIndex > a.length}
     * @throws ClassCastException if the array contains elements that are
     *         not <i>mutually comparable</i> (for example, strings and
     *         integers).
     *
     * @since 1.8
     */
    @SuppressWarnings("unchecked")
    public static <T> void parallelSort(T[] a, int fromIndex, int toIndex,
                                        Comparator<? super T> cmp) {
        rangeCheck(a.length, fromIndex, toIndex);
        if (cmp == null)
            cmp = NaturalOrder.INSTANCE;
        int n = toIndex - fromIndex, p, g;
        if (n <= MIN_ARRAY_SORT_GRAN ||
            (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
            TimSort.sort(a, fromIndex, toIndex, cmp, null, 0, 0);
        else
            new ArraysParallelSortHelpers.FJObject.Sorter<T>
                (null, a,
                 (T[])Array.newInstance(a.getClass().getComponentType(), n),
                 fromIndex, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                 MIN_ARRAY_SORT_GRAN : g, cmp).invoke();
    }

    /*
     * Sorting of complex type arrays.
     */

    /**
     * Old merge sort implementation can be selected (for
     * compatibility with broken comparators) using a system property.
     * Cannot be a static boolean in the enclosing class due to
     * circular dependencies. To be removed in a future release.
     */
    static final class LegacyMergeSort {
        private static final boolean userRequested =
            java.security.AccessController.doPrivileged(
                new sun.security.action.GetBooleanAction(
                    "java.util.Arrays.useLegacyMergeSort")).booleanValue();
    }

    /**
     * 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, {@code e1.compareTo(e2)} must
     * not throw a {@code ClassCastException} for any elements {@code e1}
     * and {@code e2} 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>Implementation note: This implementation is a stable, adaptive,
     * iterative mergesort that requires far fewer than n lg(n) comparisons
     * when the input array is partially sorted, while offering the
     * performance of a traditional mergesort when the input array is
     * randomly ordered.  If the input array is nearly sorted, the
     * implementation requires approximately n comparisons.  Temporary
     * storage requirements vary from a small constant for nearly sorted
     * input arrays to n/2 object references for randomly ordered input
     * arrays.
     *
     * <p>The implementation takes equal advantage of ascending and
     * descending order in its input array, and can take advantage of
     * ascending and descending order in different parts of the the same
     * input array.  It is well-suited to merging two or more sorted arrays:
     * simply concatenate the arrays and sort the resulting array.
     *
     * <p>The implementation was adapted from Tim Peters's list sort for Python
     * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
     * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
     * Sorting and Information Theoretic Complexity", in Proceedings of the
     * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
     * January 1993.
     *
     * @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)
     * @throws IllegalArgumentException (optional) if the natural
     *         ordering of the array elements is found to violate the
     *         {@link Comparable} contract
     */
    public static void sort(Object[] a) {
        if (LegacyMergeSort.userRequested)
            legacyMergeSort(a);
        else
            ComparableTimSort.sort(a, 0, a.length, null, 0, 0);
    }

    /** To be removed in a future release. */
    private static void legacyMergeSort(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
     * {@linkplain Comparable natural ordering} of its
     * elements.  The range to be sorted extends from index
     * {@code fromIndex}, inclusive, to index {@code toIndex}, exclusive.
     * (If {@code fromIndex==toIndex}, 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, {@code e1.compareTo(e2)} must not throw a
     * {@code ClassCastException} for any elements {@code e1} and
     * {@code e2} 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>Implementation note: This implementation is a stable, adaptive,
     * iterative mergesort that requires far fewer than n lg(n) comparisons
     * when the input array is partially sorted, while offering the
     * performance of a traditional mergesort when the input array is
     * randomly ordered.  If the input array is nearly sorted, the
     * implementation requires approximately n comparisons.  Temporary
     * storage requirements vary from a small constant for nearly sorted
     * input arrays to n/2 object references for randomly ordered input
     * arrays.
     *
     * <p>The implementation takes equal advantage of ascending and
     * descending order in its input array, and can take advantage of
     * ascending and descending order in different parts of the the same
     * input array.  It is well-suited to merging two or more sorted arrays:
     * simply concatenate the arrays and sort the resulting array.
     *
     * <p>The implementation was adapted from Tim Peters's list sort for Python
     * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
     * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
     * Sorting and Information Theoretic Complexity", in Proceedings of the
     * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
     * January 1993.
     *
     * @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 {@code fromIndex > toIndex} or
     *         (optional) if the natural ordering of the array elements is
     *         found to violate the {@link Comparable} contract
     * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
     *         {@code toIndex > a.length}
     * @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);
        if (LegacyMergeSort.userRequested)
            legacyMergeSort(a, fromIndex, toIndex);
        else
            ComparableTimSort.sort(a, fromIndex, toIndex, null, 0, 0);
    }

    /** To be removed in a future release. */
    private static void legacyMergeSort(Object[] a,
                                        int fromIndex, int 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.
     * To be removed in a future release.
     */
    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
     * To be removed in a future release.
     */
    @SuppressWarnings({"unchecked", "rawtypes"})
    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].
     */
    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
     * <i>mutually comparable</i> by the specified comparator (that is,
     * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
     * for any elements {@code e1} and {@code e2} 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>Implementation note: This implementation is a stable, adaptive,
     * iterative mergesort that requires far fewer than n lg(n) comparisons
     * when the input array is partially sorted, while offering the
     * performance of a traditional mergesort when the input array is
     * randomly ordered.  If the input array is nearly sorted, the
     * implementation requires approximately n comparisons.  Temporary
     * storage requirements vary from a small constant for nearly sorted
     * input arrays to n/2 object references for randomly ordered input
     * arrays.
     *
     * <p>The implementation takes equal advantage of ascending and
     * descending order in its input array, and can take advantage of
     * ascending and descending order in different parts of the the same
     * input array.  It is well-suited to merging two or more sorted arrays:
     * simply concatenate the arrays and sort the resulting array.
     *
     * <p>The implementation was adapted from Tim Peters's list sort for Python
     * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
     * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
     * Sorting and Information Theoretic Complexity", in Proceedings of the
     * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
     * January 1993.
     *
     * @param <T> the class of the objects to be sorted
     * @param a the array to be sorted
     * @param c the comparator to determine the order of the array.  A
     *        {@code null} 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 (optional) if the comparator is
     *         found to violate the {@link Comparator} contract
     */
    public static <T> void sort(T[] a, Comparator<? super T> c) {
        if (c == null) {
            sort(a);
        } else {
            if (LegacyMergeSort.userRequested)
                legacyMergeSort(a, c);
            else
                TimSort.sort(a, 0, a.length, c, null, 0, 0);
        }
    }

    /** To be removed in a future release. */
    private static <T> void legacyMergeSort(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 {@code fromIndex}, inclusive, to index
     * {@code toIndex}, exclusive.  (If {@code fromIndex==toIndex}, the
     * range to be sorted is empty.)  All elements in the range must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
     * for any elements {@code e1} and {@code e2} 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>Implementation note: This implementation is a stable, adaptive,
     * iterative mergesort that requires far fewer than n lg(n) comparisons
     * when the input array is partially sorted, while offering the
     * performance of a traditional mergesort when the input array is
     * randomly ordered.  If the input array is nearly sorted, the
     * implementation requires approximately n comparisons.  Temporary
     * storage requirements vary from a small constant for nearly sorted
     * input arrays to n/2 object references for randomly ordered input
     * arrays.
     *
     * <p>The implementation takes equal advantage of ascending and
     * descending order in its input array, and can take advantage of
     * ascending and descending order in different parts of the the same
     * input array.  It is well-suited to merging two or more sorted arrays:
     * simply concatenate the arrays and sort the resulting array.
     *
     * <p>The implementation was adapted from Tim Peters's list sort for Python
     * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
     * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
     * Sorting and Information Theoretic Complexity", in Proceedings of the
     * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
     * January 1993.
     *
     * @param <T> the class of the objects to be sorted
     * @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
     *        {@code null} 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 {@code fromIndex > toIndex} or
     *         (optional) if the comparator is found to violate the
     *         {@link Comparator} contract
     * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
     *         {@code toIndex > a.length}
     */
    public static <T> void sort(T[] a, int fromIndex, int toIndex,
                                Comparator<? super T> c) {
        if (c == null) {
            sort(a, fromIndex, toIndex);
        } else {
            rangeCheck(a.length, fromIndex, toIndex);
            if (LegacyMergeSort.userRequested)
                legacyMergeSort(a, fromIndex, toIndex, c);
            else
                TimSort.sort(a, fromIndex, toIndex, c, null, 0, 0);
        }
    }

    /** To be removed in a future release. */
    private static <T> void legacyMergeSort(T[] a, int fromIndex, int toIndex,
                                            Comparator<? super T> c) {
        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
     * To be removed in a future release.
     */
    @SuppressWarnings({"rawtypes", "unchecked"})
    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++];
        }
    }

    // Parallel prefix

    /**
     * Cumulates, in parallel, each element of the given array in place,
     * using the supplied function. For example if the array initially
     * holds {@code [2, 1, 0, 3]} and the operation performs addition,
     * then upon return the array holds {@code [2, 3, 3, 6]}.
     * Parallel prefix computation is usually more efficient than
     * sequential loops for large arrays.
     *
     * @param <T> the class of the objects in the array
     * @param array the array, which is modified in-place by this method
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static <T> void parallelPrefix(T[] array, BinaryOperator<T> op) {
        Objects.requireNonNull(op);
        if (array.length > 0)
            new ArrayPrefixHelpers.CumulateTask<>
                    (null, op, array, 0, array.length).invoke();
    }

    /**
     * Performs {@link #parallelPrefix(Object[], BinaryOperator)}
     * for the given subrange of the array.
     *
     * @param <T> the class of the objects in the array
     * @param array the array
     * @param fromIndex the index of the first element, inclusive
     * @param toIndex the index of the last element, exclusive
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws IllegalArgumentException if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > array.length}
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static <T> void parallelPrefix(T[] array, int fromIndex,
                                          int toIndex, BinaryOperator<T> op) {
        Objects.requireNonNull(op);
        rangeCheck(array.length, fromIndex, toIndex);
        if (fromIndex < toIndex)
            new ArrayPrefixHelpers.CumulateTask<>
                    (null, op, array, fromIndex, toIndex).invoke();
    }

    /**
     * Cumulates, in parallel, each element of the given array in place,
     * using the supplied function. For example if the array initially
     * holds {@code [2, 1, 0, 3]} and the operation performs addition,
     * then upon return the array holds {@code [2, 3, 3, 6]}.
     * Parallel prefix computation is usually more efficient than
     * sequential loops for large arrays.
     *
     * @param array the array, which is modified in-place by this method
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static void parallelPrefix(long[] array, LongBinaryOperator op) {
        Objects.requireNonNull(op);
        if (array.length > 0)
            new ArrayPrefixHelpers.LongCumulateTask
                    (null, op, array, 0, array.length).invoke();
    }

    /**
     * Performs {@link #parallelPrefix(long[], LongBinaryOperator)}
     * for the given subrange of the array.
     *
     * @param array the array
     * @param fromIndex the index of the first element, inclusive
     * @param toIndex the index of the last element, exclusive
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws IllegalArgumentException if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > array.length}
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static void parallelPrefix(long[] array, int fromIndex,
                                      int toIndex, LongBinaryOperator op) {
        Objects.requireNonNull(op);
        rangeCheck(array.length, fromIndex, toIndex);
        if (fromIndex < toIndex)
            new ArrayPrefixHelpers.LongCumulateTask
                    (null, op, array, fromIndex, toIndex).invoke();
    }

    /**
     * Cumulates, in parallel, each element of the given array in place,
     * using the supplied function. For example if the array initially
     * holds {@code [2.0, 1.0, 0.0, 3.0]} and the operation performs addition,
     * then upon return the array holds {@code [2.0, 3.0, 3.0, 6.0]}.
     * Parallel prefix computation is usually more efficient than
     * sequential loops for large arrays.
     *
     * <p> Because floating-point operations may not be strictly associative,
     * the returned result may not be identical to the value that would be
     * obtained if the operation was performed sequentially.
     *
     * @param array the array, which is modified in-place by this method
     * @param op a side-effect-free function to perform the cumulation
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static void parallelPrefix(double[] array, DoubleBinaryOperator op) {
        Objects.requireNonNull(op);
        if (array.length > 0)
            new ArrayPrefixHelpers.DoubleCumulateTask
                    (null, op, array, 0, array.length).invoke();
    }

    /**
     * Performs {@link #parallelPrefix(double[], DoubleBinaryOperator)}
     * for the given subrange of the array.
     *
     * @param array the array
     * @param fromIndex the index of the first element, inclusive
     * @param toIndex the index of the last element, exclusive
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws IllegalArgumentException if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > array.length}
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static void parallelPrefix(double[] array, int fromIndex,
                                      int toIndex, DoubleBinaryOperator op) {
        Objects.requireNonNull(op);
        rangeCheck(array.length, fromIndex, toIndex);
        if (fromIndex < toIndex)
            new ArrayPrefixHelpers.DoubleCumulateTask
                    (null, op, array, fromIndex, toIndex).invoke();
    }

    /**
     * Cumulates, in parallel, each element of the given array in place,
     * using the supplied function. For example if the array initially
     * holds {@code [2, 1, 0, 3]} and the operation performs addition,
     * then upon return the array holds {@code [2, 3, 3, 6]}.
     * Parallel prefix computation is usually more efficient than
     * sequential loops for large arrays.
     *
     * @param array the array, which is modified in-place by this method
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static void parallelPrefix(int[] array, IntBinaryOperator op) {
        Objects.requireNonNull(op);
        if (array.length > 0)
            new ArrayPrefixHelpers.IntCumulateTask
                    (null, op, array, 0, array.length).invoke();
    }

    /**
     * Performs {@link #parallelPrefix(int[], IntBinaryOperator)}
     * for the given subrange of the array.
     *
     * @param array the array
     * @param fromIndex the index of the first element, inclusive
     * @param toIndex the index of the last element, exclusive
     * @param op a side-effect-free, associative function to perform the
     * cumulation
     * @throws IllegalArgumentException if {@code fromIndex > toIndex}
     * @throws ArrayIndexOutOfBoundsException
     *     if {@code fromIndex < 0} or {@code toIndex > array.length}
     * @throws NullPointerException if the specified array or function is null
     * @since 1.8
     */
    public static void parallelPrefix(int[] array, int fromIndex,
                                      int toIndex, IntBinaryOperator op) {
        Objects.requireNonNull(op);
        rangeCheck(array.length, fromIndex, toIndex);
        if (fromIndex < toIndex)
            new ArrayPrefixHelpers.IntCumulateTask
                    (null, op, array, fromIndex, toIndex).invoke();
    }

    // Searching

    /**
     * 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 {@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 {@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 {@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 {@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 {@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 {@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 {@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 {@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 {@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 {@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 {@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 {@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 {@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
     * {@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
     * {@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;
            @SuppressWarnings("rawtypes")
            Comparable midVal = (Comparable)a[mid];
            @SuppressWarnings("unchecked")
            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
     * {@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 <T> the class of the objects in the array
     * @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
     * {@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 <T> the class of the objects in the array
     * @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 <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 <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 <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 <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 <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 <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 <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 <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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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.
     *
     * @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 <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 <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 <T> the class of the objects in the 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
     */
    @SuppressWarnings("unchecked")
    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 <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 <U> the class of the objects in the original array
     * @param <T> the class of the objects in the returned array
     * @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) {
        @SuppressWarnings("unchecked")
        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 <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 <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 <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 <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 <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 <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 <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 <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 (<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 <T> the class of the objects in the 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
     */
    @SuppressWarnings("unchecked")
    public static <T> T[] copyOfRange(T[] original, int from, int to) {
        return copyOfRange(original, from, to, (Class<? extends T[]>) original.getClass());
    }

    /**
     * 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 <U> the class of the objects in the original array
     * @param <T> the class of the objects in the returned 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.)
     * @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);
        @SuppressWarnings("unchecked")
        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 (<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 (<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 (<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 (<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 (<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 (<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 (<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 (<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 {@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 <T> the class of the objects in the array
     * @param a the array by which the list will be backed
     * @return a list view of the specified array
     */
    @SafeVarargs
    @SuppressWarnings("varargs")
    public static <T> List<T> asList(T... a) {
        return new ArrayList<>(a);
    }

    /**
     * @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) {
            a = Objects.requireNonNull(array);
        }

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

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

        @Override
        @SuppressWarnings("unchecked")
        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;
        }

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

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

        @Override
        public int indexOf(Object o) {
            E[] a = this.a;
            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;
        }

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

        @Override
        public Spliterator<E> spliterator() {
            return Spliterators.spliterator(a, Spliterator.ORDERED);
        }

        @Override
        public void forEach(Consumer<? super E> action) {
            Objects.requireNonNull(action);
            for (E e : a) {
                action.accept(e);
            }
        }

        @Override
        public void replaceAll(UnaryOperator<E> operator) {
            Objects.requireNonNull(operator);
            E[] a = this.a;
            for (int i = 0; i < a.length; i++) {
                a[i] = operator.apply(a[i]);
            }
        }

        @Override
        public void sort(Comparator<? super E> c) {
            Arrays.sort(a, c);
        }
    }

    /**
     * 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 <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 <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 <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 <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 <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 <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 <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.
     *
     * <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.
     *
     * <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 <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[])
     * @see Objects#deepEquals(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 = deepEquals0(e1, e2);

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

    static boolean deepEquals0(Object e1, Object e2) {
        assert e1 != null;
        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);
        return eq;
    }

    /**
     * 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 (<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 (<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 (<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 (<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 (<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 (<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 (<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 {@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.
     *
     * <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);
    }


    /**
     * Set all elements of the specified array, using the provided
     * generator function to compute each element.
     *
     * <p>If the generator function throws an exception, it is relayed to
     * the caller and the array is left in an indeterminate state.
     *
     * @param <T> type of elements of the array
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static <T> void setAll(T[] array, IntFunction<? extends T> generator) {
        Objects.requireNonNull(generator);
        for (int i = 0; i < array.length; i++)
            array[i] = generator.apply(i);
    }

    /**
     * Set all elements of the specified array, in parallel, using the
     * provided generator function to compute each element.
     *
     * <p>If the generator function throws an exception, an unchecked exception
     * is thrown from {@code parallelSetAll} and the array is left in an
     * indeterminate state.
     *
     * @param <T> type of elements of the array
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static <T> void parallelSetAll(T[] array, IntFunction<? extends T> generator) {
        Objects.requireNonNull(generator);
        IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.apply(i); });
    }

    /**
     * Set all elements of the specified array, using the provided
     * generator function to compute each element.
     *
     * <p>If the generator function throws an exception, it is relayed to
     * the caller and the array is left in an indeterminate state.
     *
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static void setAll(int[] array, IntUnaryOperator generator) {
        Objects.requireNonNull(generator);
        for (int i = 0; i < array.length; i++)
            array[i] = generator.applyAsInt(i);
    }

    /**
     * Set all elements of the specified array, in parallel, using the
     * provided generator function to compute each element.
     *
     * <p>If the generator function throws an exception, an unchecked exception
     * is thrown from {@code parallelSetAll} and the array is left in an
     * indeterminate state.
     *
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     * value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static void parallelSetAll(int[] array, IntUnaryOperator generator) {
        Objects.requireNonNull(generator);
        IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.applyAsInt(i); });
    }

    /**
     * Set all elements of the specified array, using the provided
     * generator function to compute each element.
     *
     * <p>If the generator function throws an exception, it is relayed to
     * the caller and the array is left in an indeterminate state.
     *
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static void setAll(long[] array, IntToLongFunction generator) {
        Objects.requireNonNull(generator);
        for (int i = 0; i < array.length; i++)
            array[i] = generator.applyAsLong(i);
    }

    /**
     * Set all elements of the specified array, in parallel, using the
     * provided generator function to compute each element.
     *
     * <p>If the generator function throws an exception, an unchecked exception
     * is thrown from {@code parallelSetAll} and the array is left in an
     * indeterminate state.
     *
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static void parallelSetAll(long[] array, IntToLongFunction generator) {
        Objects.requireNonNull(generator);
        IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.applyAsLong(i); });
    }

    /**
     * Set all elements of the specified array, using the provided
     * generator function to compute each element.
     *
     * <p>If the generator function throws an exception, it is relayed to
     * the caller and the array is left in an indeterminate state.
     *
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static void setAll(double[] array, IntToDoubleFunction generator) {
        Objects.requireNonNull(generator);
        for (int i = 0; i < array.length; i++)
            array[i] = generator.applyAsDouble(i);
    }

    /**
     * Set all elements of the specified array, in parallel, using the
     * provided generator function to compute each element.
     *
     * <p>If the generator function throws an exception, an unchecked exception
     * is thrown from {@code parallelSetAll} and the array is left in an
     * indeterminate state.
     *
     * @param array array to be initialized
     * @param generator a function accepting an index and producing the desired
     *        value for that position
     * @throws NullPointerException if the generator is null
     * @since 1.8
     */
    public static void parallelSetAll(double[] array, IntToDoubleFunction generator) {
        Objects.requireNonNull(generator);
        IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.applyAsDouble(i); });
    }

    /**
     * Returns a {@link Spliterator} covering all of the specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param <T> type of elements
     * @param array the array, assumed to be unmodified during use
     * @return a spliterator for the array elements
     * @since 1.8
     */
    public static <T> Spliterator<T> spliterator(T[] array) {
        return Spliterators.spliterator(array,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator} covering the specified range of the
     * specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param <T> type of elements
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a spliterator for the array elements
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static <T> Spliterator<T> spliterator(T[] array, int startInclusive, int endExclusive) {
        return Spliterators.spliterator(array, startInclusive, endExclusive,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator.OfInt} covering all of the specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param array the array, assumed to be unmodified during use
     * @return a spliterator for the array elements
     * @since 1.8
     */
    public static Spliterator.OfInt spliterator(int[] array) {
        return Spliterators.spliterator(array,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator.OfInt} covering the specified range of the
     * specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a spliterator for the array elements
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static Spliterator.OfInt spliterator(int[] array, int startInclusive, int endExclusive) {
        return Spliterators.spliterator(array, startInclusive, endExclusive,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator.OfLong} covering all of the specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param array the array, assumed to be unmodified during use
     * @return the spliterator for the array elements
     * @since 1.8
     */
    public static Spliterator.OfLong spliterator(long[] array) {
        return Spliterators.spliterator(array,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator.OfLong} covering the specified range of the
     * specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a spliterator for the array elements
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static Spliterator.OfLong spliterator(long[] array, int startInclusive, int endExclusive) {
        return Spliterators.spliterator(array, startInclusive, endExclusive,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator.OfDouble} covering all of the specified
     * array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param array the array, assumed to be unmodified during use
     * @return a spliterator for the array elements
     * @since 1.8
     */
    public static Spliterator.OfDouble spliterator(double[] array) {
        return Spliterators.spliterator(array,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a {@link Spliterator.OfDouble} covering the specified range of
     * the specified array.
     *
     * <p>The spliterator reports {@link Spliterator#SIZED},
     * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
     * {@link Spliterator#IMMUTABLE}.
     *
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a spliterator for the array elements
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static Spliterator.OfDouble spliterator(double[] array, int startInclusive, int endExclusive) {
        return Spliterators.spliterator(array, startInclusive, endExclusive,
                                        Spliterator.ORDERED | Spliterator.IMMUTABLE);
    }

    /**
     * Returns a sequential {@link Stream} with the specified array as its
     * source.
     *
     * @param <T> The type of the array elements
     * @param array The array, assumed to be unmodified during use
     * @return a {@code Stream} for the array
     * @since 1.8
     */
    public static <T> Stream<T> stream(T[] array) {
        return stream(array, 0, array.length);
    }

    /**
     * Returns a sequential {@link Stream} with the specified range of the
     * specified array as its source.
     *
     * @param <T> the type of the array elements
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a {@code Stream} for the array range
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static <T> Stream<T> stream(T[] array, int startInclusive, int endExclusive) {
        return StreamSupport.stream(spliterator(array, startInclusive, endExclusive), false);
    }

    /**
     * Returns a sequential {@link IntStream} with the specified array as its
     * source.
     *
     * @param array the array, assumed to be unmodified during use
     * @return an {@code IntStream} for the array
     * @since 1.8
     */
    public static IntStream stream(int[] array) {
        return stream(array, 0, array.length);
    }

    /**
     * Returns a sequential {@link IntStream} with the specified range of the
     * specified array as its source.
     *
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return an {@code IntStream} for the array range
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static IntStream stream(int[] array, int startInclusive, int endExclusive) {
        return StreamSupport.intStream(spliterator(array, startInclusive, endExclusive), false);
    }

    /**
     * Returns a sequential {@link LongStream} with the specified array as its
     * source.
     *
     * @param array the array, assumed to be unmodified during use
     * @return a {@code LongStream} for the array
     * @since 1.8
     */
    public static LongStream stream(long[] array) {
        return stream(array, 0, array.length);
    }

    /**
     * Returns a sequential {@link LongStream} with the specified range of the
     * specified array as its source.
     *
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a {@code LongStream} for the array range
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static LongStream stream(long[] array, int startInclusive, int endExclusive) {
        return StreamSupport.longStream(spliterator(array, startInclusive, endExclusive), false);
    }

    /**
     * Returns a sequential {@link DoubleStream} with the specified array as its
     * source.
     *
     * @param array the array, assumed to be unmodified during use
     * @return a {@code DoubleStream} for the array
     * @since 1.8
     */
    public static DoubleStream stream(double[] array) {
        return stream(array, 0, array.length);
    }

    /**
     * Returns a sequential {@link DoubleStream} with the specified range of the
     * specified array as its source.
     *
     * @param array the array, assumed to be unmodified during use
     * @param startInclusive the first index to cover, inclusive
     * @param endExclusive index immediately past the last index to cover
     * @return a {@code DoubleStream} for the array range
     * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
     *         negative, {@code endExclusive} is less than
     *         {@code startInclusive}, or {@code endExclusive} is greater than
     *         the array size
     * @since 1.8
     */
    public static DoubleStream stream(double[] array, int startInclusive, int endExclusive) {
        return StreamSupport.doubleStream(spliterator(array, startInclusive, endExclusive), false);
    }
}