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   * Copyright (C) 2014 The Android Open Source Project
   * Copyright (c) 1997, 2014, Oracle and/or its affiliates. All rights reserved.
   * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   *
   * This code is free software; you can redistribute it and/or modify it
   * under the terms of the GNU General Public License version 2 only, as
   * published by the Free Software Foundation.  Oracle designates this
   * particular file as subject to the "Classpath" exception as provided
   * by Oracle in the LICENSE file that accompanied this code.
   *
   * This code is distributed in the hope that it will be useful, but WITHOUT
   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
   * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   * version 2 for more details (a copy is included in the LICENSE file that
   * accompanied this code).
   *
   * You should have received a copy of the GNU General Public License version
   * 2 along with this work; if not, write to the Free Software Foundation,
   * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
   *
   * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
   * or visit www.oracle.com if you need additional information or have any
   * questions.
   */
  
  package java.util;
  
  import java.lang.reflect.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.
       * @hide
       */
      // Android-changed: Make MIN_ARRAY_SORT_GRAN public and @hide (used by harmony ArraysTest)
      public 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 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.
       */
  
      // Android-removed: LegacyMergeSort class (unused on Android).
  
      /**
       * 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) {
          // Android-removed: LegacyMergeSort support
          // if (LegacyMergeSort.userRequested)
          //     legacyMergeSort(a);
          // else
              ComparableTimSort.sort(a, 0, a.length, null, 0, 0);
      }
  
      // Android-removed: legacyMergeSort() (unused on Android)
  
      /**
       * 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);
          // Android-removed: LegacyMergeSort support
          // if (LegacyMergeSort.userRequested)
          //     legacyMergeSort(a, fromIndex, toIndex);
          // else
              ComparableTimSort.sort(a, fromIndex, toIndex, null, 0, 0);
      }
  
      // Android-removed: legacyMergeSort() (unused on Android)
  
      /**
       * 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 {
          // Android-removed: LegacyMergeSort support
              // if (LegacyMergeSort.userRequested)
              //     legacyMergeSort(a, c);
              // else
                  TimSort.sort(a, 0, a.length, c, null, 0, 0);
          }
      }
  
      // Android-removed: legacyMergeSort() (unused on Android)
  
      /**
       * 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);
              // Android-removed: LegacyMergeSort support
              // if (LegacyMergeSort.userRequested)
              //     legacyMergeSort(a, fromIndex, toIndex, c);
              // else
                  TimSort.sort(a, fromIndex, toIndex, c, null, 0, 0);
          }
      }
  
      // Android-removed: legacyMergeSort() (unused on Android)
      // Android-removed: mergeSort() (unused on Android)
  
      // 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;
              // BEGIN Android-changed: getComponentType() is faster than instanceof()
              if (element != null) {
                  Class<?> cl = element.getClass().getComponentType();
                  if (cl == null)
                      elementHash = element.hashCode();
                  else if (element instanceof Object[])
                      elementHash = deepHashCode((Object[]) element);
                  else if (cl == byte.class)
                      elementHash = hashCode((byte[]) element);
                  else if (cl == short.class)
                      elementHash = hashCode((short[]) element);
                  else if (cl == int.class)
                      elementHash = hashCode((int[]) element);
                  else if (cl == long.class)
                      elementHash = hashCode((long[]) element);
                  else if (cl == char.class)
                      elementHash = hashCode((char[]) element);
                  else if (cl == float.class)
                      elementHash = hashCode((float[]) element);
                  else if (cl == double.class)
                      elementHash = hashCode((double[]) element);
                  else if (cl == boolean.class)
                      elementHash = hashCode((boolean[]) element);
                  else
                      elementHash = element.hashCode();
              }
              // END Android-changed: getComponentType() is faster than instanceof()
              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);
      }
  }
  