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  • java Arrays

    java Arrays

     * Copyright (c) 1997, 2014, Oracle and/or its affiliates. All rights reserved.
    
    package java.util;
    
    import java.lang.reflect.Array;
    import java.util.concurrent.ForkJoinPool;
    import java.util.function.BinaryOperator;
    import java.util.function.Consumer;
    import java.util.function.DoubleBinaryOperator;
    import java.util.function.IntBinaryOperator;
    import java.util.function.IntFunction;
    import java.util.function.IntToDoubleFunction;
    import java.util.function.IntToLongFunction;
    import java.util.function.IntUnaryOperator;
    import java.util.function.LongBinaryOperator;
    import java.util.function.UnaryOperator;
    import java.util.stream.DoubleStream;
    import java.util.stream.IntStream;
    import java.util.stream.LongStream;
    import java.util.stream.Stream;
    import java.util.stream.StreamSupport;
    
    /**
     * This class contains various methods for manipulating arrays (such as
     * sorting and searching). This class also contains a static factory
     * that allows arrays to be viewed as lists.
     *
     * <p>The methods in this class all throw a {@code NullPointerException},
     * if the specified array reference is null, except where noted.
     *
     * <p>The documentation for the methods contained in this class includes
     * briefs description of the <i>implementations</i>. Such descriptions should
     * be regarded as <i>implementation notes</i>, rather than parts of the
     * <i>specification</i>. Implementors should feel free to substitute other
     * algorithms, so long as the specification itself is adhered to. (For
     * example, the algorithm used by {@code sort(Object[])} does not have to be
     * a MergeSort, but it does have to be <i>stable</i>.)
     *
     * <p>This class is a member of the
     * <a href="{@docRoot}/../technotes/guides/collections/index.html">
     * Java Collections Framework</a>.
     *
     * @author Josh Bloch
     * @author Neal Gafter
     * @author John Rose
     * @since  1.2
     */
    public class Arrays {
    
        /**
         * The minimum array length below which a parallel sorting
         * algorithm will not further partition the sorting task. Using
         * smaller sizes typically results in memory contention across
         * tasks that makes parallel speedups unlikely.
         */
        private static final int MIN_ARRAY_SORT_GRAN = 1 << 13;
    
        // Suppresses default constructor, ensuring non-instantiability.
        private Arrays() {}
    
        /**
         * A comparator that implements the natural ordering of a group of
         * mutually comparable elements. May be used when a supplied
         * comparator is null. To simplify code-sharing within underlying
         * implementations, the compare method only declares type Object
         * for its second argument.
         *
         * Arrays class implementor's note: It is an empirical matter
         * whether ComparableTimSort offers any performance benefit over
         * TimSort used with this comparator.  If not, you are better off
         * deleting or bypassing ComparableTimSort.  There is currently no
         * empirical case for separating them for parallel sorting, so all
         * public Object parallelSort methods use the same comparator
         * based implementation.
         */
        static final class NaturalOrder implements Comparator<Object> {
            @SuppressWarnings("unchecked")
            public int compare(Object first, Object second) {
                return ((Comparable<Object>)first).compareTo(second);
            }
            static final NaturalOrder INSTANCE = new NaturalOrder();
        }
    
        /**
         * Checks that {@code fromIndex} and {@code toIndex} are in
         * the range and throws an exception if they aren't.
         */
        private static void rangeCheck(int arrayLength, int fromIndex, int toIndex) {
            if (fromIndex > toIndex) {
                throw new IllegalArgumentException(
                        "fromIndex(" + fromIndex + ") > toIndex(" + toIndex + ")");
            }
            if (fromIndex < 0) {
                throw new ArrayIndexOutOfBoundsException(fromIndex);
            }
            if (toIndex > arrayLength) {
                throw new ArrayIndexOutOfBoundsException(toIndex);
            }
        }
    
        /*
         * Sorting methods. Note that all public "sort" methods take the
         * same form: Performing argument checks if necessary, and then
         * expanding arguments into those required for the internal
         * implementation methods residing in other package-private
         * classes (except for legacyMergeSort, included in this class).
         */
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(int[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(int[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(long[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(long[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(short[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(short[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(char[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(char[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(byte[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(byte[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>The {@code <} relation does not provide a total order on all float
         * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
         * {@code 0.0f} and {@code Float.NaN} is considered greater than any
         * other value and all {@code Float.NaN} values are considered equal.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(float[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>The {@code <} relation does not provide a total order on all float
         * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
         * {@code 0.0f} and {@code Float.NaN} is considered greater than any
         * other value and all {@code Float.NaN} values are considered equal.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(float[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>The {@code <} relation does not provide a total order on all double
         * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
         * {@code 0.0d} and {@code Double.NaN} is considered greater than any
         * other value and all {@code Double.NaN} values are considered equal.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         */
        public static void sort(double[] a) {
            DualPivotQuicksort.sort(a, 0, a.length - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified range of the array into ascending order. The range
         * to be sorted extends from the index {@code fromIndex}, inclusive, to
         * the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
         * the range to be sorted is empty.
         *
         * <p>The {@code <} relation does not provide a total order on all double
         * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
         * {@code 0.0d} and {@code Double.NaN} is considered greater than any
         * other value and all {@code Double.NaN} values are considered equal.
         *
         * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort
         * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
         * offers O(n log(n)) performance on many data sets that cause other
         * quicksorts to degrade to quadratic performance, and is typically
         * faster than traditional (one-pivot) Quicksort implementations.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         */
        public static void sort(double[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(byte[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(byte[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(byte[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1);
            else
                new ArraysParallelSortHelpers.FJByte.Sorter
                    (null, a, new byte[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(byte[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(byte[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(byte[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
            else
                new ArraysParallelSortHelpers.FJByte.Sorter
                    (null, a, new byte[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(char[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(char[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(char[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJChar.Sorter
                    (null, a, new char[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
          @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(char[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(char[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(char[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJChar.Sorter
                    (null, a, new char[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(short[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(short[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(short[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJShort.Sorter
                    (null, a, new short[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(short[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(short[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(short[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJShort.Sorter
                    (null, a, new short[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(int[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(int[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(int[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJInt.Sorter
                    (null, a, new int[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(int[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(int[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(int[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJInt.Sorter
                    (null, a, new int[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(long[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(long[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(long[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJLong.Sorter
                    (null, a, new long[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(long[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(long[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(long[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJLong.Sorter
                    (null, a, new long[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>The {@code <} relation does not provide a total order on all float
         * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
         * {@code 0.0f} and {@code Float.NaN} is considered greater than any
         * other value and all {@code Float.NaN} values are considered equal.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(float[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(float[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(float[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJFloat.Sorter
                    (null, a, new float[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
         * <p>The {@code <} relation does not provide a total order on all float
         * values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Float#compareTo}: {@code -0.0f} is treated as less than value
         * {@code 0.0f} and {@code Float.NaN} is considered greater than any
         * other value and all {@code Float.NaN} values are considered equal.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(float[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(float[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(float[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJFloat.Sorter
                    (null, a, new float[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array into ascending numerical order.
         *
         * <p>The {@code <} relation does not provide a total order on all double
         * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
         * {@code 0.0d} and {@code Double.NaN} is considered greater than any
         * other value and all {@code Double.NaN} values are considered equal.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(double[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(double[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param a the array to be sorted
         *
         * @since 1.8
         */
        public static void parallelSort(double[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, 0, n - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJDouble.Sorter
                    (null, a, new double[n], 0, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified range of the array into ascending numerical order.
         * The range to be sorted extends from the index {@code fromIndex},
         * inclusive, to the index {@code toIndex}, exclusive. If
         * {@code fromIndex == toIndex}, the range to be sorted is empty.
         *
         * <p>The {@code <} relation does not provide a total order on all double
         * values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
         * value compares neither less than, greater than, nor equal to any value,
         * even itself. This method uses the total order imposed by the method
         * {@link Double#compareTo}: {@code -0.0d} is treated as less than value
         * {@code 0.0d} and {@code Double.NaN} is considered greater than any
         * other value and all {@code Double.NaN} values are considered equal.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(double[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(double[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element, inclusive, to be sorted
         * @param toIndex the index of the last element, exclusive, to be sorted
         *
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > a.length}
         *
         * @since 1.8
         */
        public static void parallelSort(double[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                DualPivotQuicksort.sort(a, fromIndex, toIndex - 1, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJDouble.Sorter
                    (null, a, new double[n], fromIndex, n, 0,
                     ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g).invoke();
        }
    
        /**
         * Sorts the specified array of objects into ascending order, according
         * to the {@linkplain Comparable natural ordering} of its elements.
         * All elements in the array must implement the {@link Comparable}
         * interface.  Furthermore, all elements in the array must be
         * <i>mutually comparable</i> (that is, {@code e1.compareTo(e2)} must
         * not throw a {@code ClassCastException} for any elements {@code e1}
         * and {@code e2} in the array).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param <T> the class of the objects to be sorted
         * @param a the array to be sorted
         *
         * @throws ClassCastException if the array contains elements that are not
         *         <i>mutually comparable</i> (for example, strings and integers)
         * @throws IllegalArgumentException (optional) if the natural
         *         ordering of the array elements is found to violate the
         *         {@link Comparable} contract
         *
         * @since 1.8
         */
        @SuppressWarnings("unchecked")
        public static <T extends Comparable<? super T>> void parallelSort(T[] a) {
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                TimSort.sort(a, 0, n, NaturalOrder.INSTANCE, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJObject.Sorter<T>
                    (null, a,
                     (T[])Array.newInstance(a.getClass().getComponentType(), n),
                     0, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g, NaturalOrder.INSTANCE).invoke();
        }
    
        /**
         * Sorts the specified range of the specified array of objects into
         * ascending order, according to the
         * {@linkplain Comparable natural ordering} of its
         * elements.  The range to be sorted extends from index
         * {@code fromIndex}, inclusive, to index {@code toIndex}, exclusive.
         * (If {@code fromIndex==toIndex}, the range to be sorted is empty.)  All
         * elements in this range must implement the {@link Comparable}
         * interface.  Furthermore, all elements in this range must be <i>mutually
         * comparable</i> (that is, {@code e1.compareTo(e2)} must not throw a
         * {@code ClassCastException} for any elements {@code e1} and
         * {@code e2} in the array).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param <T> the class of the objects to be sorted
         * @param a the array to be sorted
         * @param fromIndex the index of the first element (inclusive) to be
         *        sorted
         * @param toIndex the index of the last element (exclusive) to be sorted
         * @throws IllegalArgumentException if {@code fromIndex > toIndex} or
         *         (optional) if the natural ordering of the array elements is
         *         found to violate the {@link Comparable} contract
         * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
         *         {@code toIndex > a.length}
         * @throws ClassCastException if the array contains elements that are
         *         not <i>mutually comparable</i> (for example, strings and
         *         integers).
         *
         * @since 1.8
         */
        @SuppressWarnings("unchecked")
        public static <T extends Comparable<? super T>>
        void parallelSort(T[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                TimSort.sort(a, fromIndex, toIndex, NaturalOrder.INSTANCE, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJObject.Sorter<T>
                    (null, a,
                     (T[])Array.newInstance(a.getClass().getComponentType(), n),
                     fromIndex, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g, NaturalOrder.INSTANCE).invoke();
        }
    
        /**
         * Sorts the specified array of objects according to the order induced by
         * the specified comparator.  All elements in the array must be
         * <i>mutually comparable</i> by the specified comparator (that is,
         * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
         * for any elements {@code e1} and {@code e2} in the array).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a
         * working space no greater than the size of the original array. The
         * {@link ForkJoinPool#commonPool() ForkJoin common pool} is used to
         * execute any parallel tasks.
         *
         * @param <T> the class of the objects to be sorted
         * @param a the array to be sorted
         * @param cmp the comparator to determine the order of the array.  A
         *        {@code null} value indicates that the elements'
         *        {@linkplain Comparable natural ordering} should be used.
         * @throws ClassCastException if the array contains elements that are
         *         not <i>mutually comparable</i> using the specified comparator
         * @throws IllegalArgumentException (optional) if the comparator is
         *         found to violate the {@link java.util.Comparator} contract
         *
         * @since 1.8
         */
        @SuppressWarnings("unchecked")
        public static <T> void parallelSort(T[] a, Comparator<? super T> cmp) {
            if (cmp == null)
                cmp = NaturalOrder.INSTANCE;
            int n = a.length, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                TimSort.sort(a, 0, n, cmp, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJObject.Sorter<T>
                    (null, a,
                     (T[])Array.newInstance(a.getClass().getComponentType(), n),
                     0, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g, cmp).invoke();
        }
    
        /**
         * Sorts the specified range of the specified array of objects according
         * to the order induced by the specified comparator.  The range to be
         * sorted extends from index {@code fromIndex}, inclusive, to index
         * {@code toIndex}, exclusive.  (If {@code fromIndex==toIndex}, the
         * range to be sorted is empty.)  All elements in the range must be
         * <i>mutually comparable</i> by the specified comparator (that is,
         * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
         * for any elements {@code e1} and {@code e2} in the range).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * @implNote The sorting algorithm is a parallel sort-merge that breaks the
         * array into sub-arrays that are themselves sorted and then merged. When
         * the sub-array length reaches a minimum granularity, the sub-array is
         * sorted using the appropriate {@link Arrays#sort(Object[]) Arrays.sort}
         * method. If the length of the specified array is less than the minimum
         * granularity, then it is sorted using the appropriate {@link
         * Arrays#sort(Object[]) Arrays.sort} method. The algorithm requires a working
         * space no greater than the size of the specified range of the original
         * array. The {@link ForkJoinPool#commonPool() ForkJoin common pool} is
         * used to execute any parallel tasks.
         *
         * @param <T> the class of the objects to be sorted
         * @param a the array to be sorted
         * @param fromIndex the index of the first element (inclusive) to be
         *        sorted
         * @param toIndex the index of the last element (exclusive) to be sorted
         * @param cmp the comparator to determine the order of the array.  A
         *        {@code null} value indicates that the elements'
         *        {@linkplain Comparable natural ordering} should be used.
         * @throws IllegalArgumentException if {@code fromIndex > toIndex} or
         *         (optional) if the natural ordering of the array elements is
         *         found to violate the {@link Comparable} contract
         * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
         *         {@code toIndex > a.length}
         * @throws ClassCastException if the array contains elements that are
         *         not <i>mutually comparable</i> (for example, strings and
         *         integers).
         *
         * @since 1.8
         */
        @SuppressWarnings("unchecked")
        public static <T> void parallelSort(T[] a, int fromIndex, int toIndex,
                                            Comparator<? super T> cmp) {
            rangeCheck(a.length, fromIndex, toIndex);
            if (cmp == null)
                cmp = NaturalOrder.INSTANCE;
            int n = toIndex - fromIndex, p, g;
            if (n <= MIN_ARRAY_SORT_GRAN ||
                (p = ForkJoinPool.getCommonPoolParallelism()) == 1)
                TimSort.sort(a, fromIndex, toIndex, cmp, null, 0, 0);
            else
                new ArraysParallelSortHelpers.FJObject.Sorter<T>
                    (null, a,
                     (T[])Array.newInstance(a.getClass().getComponentType(), n),
                     fromIndex, n, 0, ((g = n / (p << 2)) <= MIN_ARRAY_SORT_GRAN) ?
                     MIN_ARRAY_SORT_GRAN : g, cmp).invoke();
        }
    
        /*
         * Sorting of complex type arrays.
         */
    
        /**
         * Old merge sort implementation can be selected (for
         * compatibility with broken comparators) using a system property.
         * Cannot be a static boolean in the enclosing class due to
         * circular dependencies. To be removed in a future release.
         */
        static final class LegacyMergeSort {
            private static final boolean userRequested =
                java.security.AccessController.doPrivileged(
                    new sun.security.action.GetBooleanAction(
                        "java.util.Arrays.useLegacyMergeSort")).booleanValue();
        }
    
        /**
         * Sorts the specified array of objects into ascending order, according
         * to the {@linkplain Comparable natural ordering} of its elements.
         * All elements in the array must implement the {@link Comparable}
         * interface.  Furthermore, all elements in the array must be
         * <i>mutually comparable</i> (that is, {@code e1.compareTo(e2)} must
         * not throw a {@code ClassCastException} for any elements {@code e1}
         * and {@code e2} in the array).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * <p>Implementation note: This implementation is a stable, adaptive,
         * iterative mergesort that requires far fewer than n lg(n) comparisons
         * when the input array is partially sorted, while offering the
         * performance of a traditional mergesort when the input array is
         * randomly ordered.  If the input array is nearly sorted, the
         * implementation requires approximately n comparisons.  Temporary
         * storage requirements vary from a small constant for nearly sorted
         * input arrays to n/2 object references for randomly ordered input
         * arrays.
         *
         * <p>The implementation takes equal advantage of ascending and
         * descending order in its input array, and can take advantage of
         * ascending and descending order in different parts of the the same
         * input array.  It is well-suited to merging two or more sorted arrays:
         * simply concatenate the arrays and sort the resulting array.
         *
         * <p>The implementation was adapted from Tim Peters's list sort for Python
         * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
         * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
         * Sorting and Information Theoretic Complexity", in Proceedings of the
         * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
         * January 1993.
         *
         * @param a the array to be sorted
         * @throws ClassCastException if the array contains elements that are not
         *         <i>mutually comparable</i> (for example, strings and integers)
         * @throws IllegalArgumentException (optional) if the natural
         *         ordering of the array elements is found to violate the
         *         {@link Comparable} contract
         */
        public static void sort(Object[] a) {
            if (LegacyMergeSort.userRequested)
                legacyMergeSort(a);
            else
                ComparableTimSort.sort(a, 0, a.length, null, 0, 0);
        }
    
        /** To be removed in a future release. */
        private static void legacyMergeSort(Object[] a) {
            Object[] aux = a.clone();
            mergeSort(aux, a, 0, a.length, 0);
        }
    
        /**
         * Sorts the specified range of the specified array of objects into
         * ascending order, according to the
         * {@linkplain Comparable natural ordering} of its
         * elements.  The range to be sorted extends from index
         * {@code fromIndex}, inclusive, to index {@code toIndex}, exclusive.
         * (If {@code fromIndex==toIndex}, the range to be sorted is empty.)  All
         * elements in this range must implement the {@link Comparable}
         * interface.  Furthermore, all elements in this range must be <i>mutually
         * comparable</i> (that is, {@code e1.compareTo(e2)} must not throw a
         * {@code ClassCastException} for any elements {@code e1} and
         * {@code e2} in the array).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * <p>Implementation note: This implementation is a stable, adaptive,
         * iterative mergesort that requires far fewer than n lg(n) comparisons
         * when the input array is partially sorted, while offering the
         * performance of a traditional mergesort when the input array is
         * randomly ordered.  If the input array is nearly sorted, the
         * implementation requires approximately n comparisons.  Temporary
         * storage requirements vary from a small constant for nearly sorted
         * input arrays to n/2 object references for randomly ordered input
         * arrays.
         *
         * <p>The implementation takes equal advantage of ascending and
         * descending order in its input array, and can take advantage of
         * ascending and descending order in different parts of the the same
         * input array.  It is well-suited to merging two or more sorted arrays:
         * simply concatenate the arrays and sort the resulting array.
         *
         * <p>The implementation was adapted from Tim Peters's list sort for Python
         * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
         * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
         * Sorting and Information Theoretic Complexity", in Proceedings of the
         * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
         * January 1993.
         *
         * @param a the array to be sorted
         * @param fromIndex the index of the first element (inclusive) to be
         *        sorted
         * @param toIndex the index of the last element (exclusive) to be sorted
         * @throws IllegalArgumentException if {@code fromIndex > toIndex} or
         *         (optional) if the natural ordering of the array elements is
         *         found to violate the {@link Comparable} contract
         * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
         *         {@code toIndex > a.length}
         * @throws ClassCastException if the array contains elements that are
         *         not <i>mutually comparable</i> (for example, strings and
         *         integers).
         */
        public static void sort(Object[] a, int fromIndex, int toIndex) {
            rangeCheck(a.length, fromIndex, toIndex);
            if (LegacyMergeSort.userRequested)
                legacyMergeSort(a, fromIndex, toIndex);
            else
                ComparableTimSort.sort(a, fromIndex, toIndex, null, 0, 0);
        }
    
        /** To be removed in a future release. */
        private static void legacyMergeSort(Object[] a,
                                            int fromIndex, int toIndex) {
            Object[] aux = copyOfRange(a, fromIndex, toIndex);
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
        }
    
        /**
         * Tuning parameter: list size at or below which insertion sort will be
         * used in preference to mergesort.
         * To be removed in a future release.
         */
        private static final int INSERTIONSORT_THRESHOLD = 7;
    
        /**
         * Src is the source array that starts at index 0
         * Dest is the (possibly larger) array destination with a possible offset
         * low is the index in dest to start sorting
         * high is the end index in dest to end sorting
         * off is the offset to generate corresponding low, high in src
         * To be removed in a future release.
         */
        @SuppressWarnings({"unchecked", "rawtypes"})
        private static void mergeSort(Object[] src,
                                      Object[] dest,
                                      int low,
                                      int high,
                                      int off) {
            int length = high - low;
    
            // Insertion sort on smallest arrays
            if (length < INSERTIONSORT_THRESHOLD) {
                for (int i=low; i<high; i++)
                    for (int j=i; j>low &&
                             ((Comparable) dest[j-1]).compareTo(dest[j])>0; j--)
                        swap(dest, j, j-1);
                return;
            }
    
            // Recursively sort halves of dest into src
            int destLow  = low;
            int destHigh = high;
            low  += off;
            high += off;
            int mid = (low + high) >>> 1;
            mergeSort(dest, src, low, mid, -off);
            mergeSort(dest, src, mid, high, -off);
    
            // If list is already sorted, just copy from src to dest.  This is an
            // optimization that results in faster sorts for nearly ordered lists.
            if (((Comparable)src[mid-1]).compareTo(src[mid]) <= 0) {
                System.arraycopy(src, low, dest, destLow, length);
                return;
            }
    
            // Merge sorted halves (now in src) into dest
            for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
                if (q >= high || p < mid && ((Comparable)src[p]).compareTo(src[q])<=0)
                    dest[i] = src[p++];
                else
                    dest[i] = src[q++];
            }
        }
    
        /**
         * Swaps x[a] with x[b].
         */
        private static void swap(Object[] x, int a, int b) {
            Object t = x[a];
            x[a] = x[b];
            x[b] = t;
        }
    
        /**
         * Sorts the specified array of objects according to the order induced by
         * the specified comparator.  All elements in the array must be
         * <i>mutually comparable</i> by the specified comparator (that is,
         * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
         * for any elements {@code e1} and {@code e2} in the array).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * <p>Implementation note: This implementation is a stable, adaptive,
         * iterative mergesort that requires far fewer than n lg(n) comparisons
         * when the input array is partially sorted, while offering the
         * performance of a traditional mergesort when the input array is
         * randomly ordered.  If the input array is nearly sorted, the
         * implementation requires approximately n comparisons.  Temporary
         * storage requirements vary from a small constant for nearly sorted
         * input arrays to n/2 object references for randomly ordered input
         * arrays.
         *
         * <p>The implementation takes equal advantage of ascending and
         * descending order in its input array, and can take advantage of
         * ascending and descending order in different parts of the the same
         * input array.  It is well-suited to merging two or more sorted arrays:
         * simply concatenate the arrays and sort the resulting array.
         *
         * <p>The implementation was adapted from Tim Peters's list sort for Python
         * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
         * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
         * Sorting and Information Theoretic Complexity", in Proceedings of the
         * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
         * January 1993.
         *
         * @param <T> the class of the objects to be sorted
         * @param a the array to be sorted
         * @param c the comparator to determine the order of the array.  A
         *        {@code null} value indicates that the elements'
         *        {@linkplain Comparable natural ordering} should be used.
         * @throws ClassCastException if the array contains elements that are
         *         not <i>mutually comparable</i> using the specified comparator
         * @throws IllegalArgumentException (optional) if the comparator is
         *         found to violate the {@link Comparator} contract
         */
        public static <T> void sort(T[] a, Comparator<? super T> c) {
            if (c == null) {
                sort(a);
            } else {
                if (LegacyMergeSort.userRequested)
                    legacyMergeSort(a, c);
                else
                    TimSort.sort(a, 0, a.length, c, null, 0, 0);
            }
        }
    
        /** To be removed in a future release. */
        private static <T> void legacyMergeSort(T[] a, Comparator<? super T> c) {
            T[] aux = a.clone();
            if (c==null)
                mergeSort(aux, a, 0, a.length, 0);
            else
                mergeSort(aux, a, 0, a.length, 0, c);
        }
    
        /**
         * Sorts the specified range of the specified array of objects according
         * to the order induced by the specified comparator.  The range to be
         * sorted extends from index {@code fromIndex}, inclusive, to index
         * {@code toIndex}, exclusive.  (If {@code fromIndex==toIndex}, the
         * range to be sorted is empty.)  All elements in the range must be
         * <i>mutually comparable</i> by the specified comparator (that is,
         * {@code c.compare(e1, e2)} must not throw a {@code ClassCastException}
         * for any elements {@code e1} and {@code e2} in the range).
         *
         * <p>This sort is guaranteed to be <i>stable</i>:  equal elements will
         * not be reordered as a result of the sort.
         *
         * <p>Implementation note: This implementation is a stable, adaptive,
         * iterative mergesort that requires far fewer than n lg(n) comparisons
         * when the input array is partially sorted, while offering the
         * performance of a traditional mergesort when the input array is
         * randomly ordered.  If the input array is nearly sorted, the
         * implementation requires approximately n comparisons.  Temporary
         * storage requirements vary from a small constant for nearly sorted
         * input arrays to n/2 object references for randomly ordered input
         * arrays.
         *
         * <p>The implementation takes equal advantage of ascending and
         * descending order in its input array, and can take advantage of
         * ascending and descending order in different parts of the the same
         * input array.  It is well-suited to merging two or more sorted arrays:
         * simply concatenate the arrays and sort the resulting array.
         *
         * <p>The implementation was adapted from Tim Peters's list sort for Python
         * (<a href="http://svn.python.org/projects/python/trunk/Objects/listsort.txt">
         * TimSort</a>).  It uses techniques from Peter McIlroy's "Optimistic
         * Sorting and Information Theoretic Complexity", in Proceedings of the
         * Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 467-474,
         * January 1993.
         *
         * @param <T> the class of the objects to be sorted
         * @param a the array to be sorted
         * @param fromIndex the index of the first element (inclusive) to be
         *        sorted
         * @param toIndex the index of the last element (exclusive) to be sorted
         * @param c the comparator to determine the order of the array.  A
         *        {@code null} value indicates that the elements'
         *        {@linkplain Comparable natural ordering} should be used.
         * @throws ClassCastException if the array contains elements that are not
         *         <i>mutually comparable</i> using the specified comparator.
         * @throws IllegalArgumentException if {@code fromIndex > toIndex} or
         *         (optional) if the comparator is found to violate the
         *         {@link Comparator} contract
         * @throws ArrayIndexOutOfBoundsException if {@code fromIndex < 0} or
         *         {@code toIndex > a.length}
         */
        public static <T> void sort(T[] a, int fromIndex, int toIndex,
                                    Comparator<? super T> c) {
            if (c == null) {
                sort(a, fromIndex, toIndex);
            } else {
                rangeCheck(a.length, fromIndex, toIndex);
                if (LegacyMergeSort.userRequested)
                    legacyMergeSort(a, fromIndex, toIndex, c);
                else
                    TimSort.sort(a, fromIndex, toIndex, c, null, 0, 0);
            }
        }
    
        /** To be removed in a future release. */
        private static <T> void legacyMergeSort(T[] a, int fromIndex, int toIndex,
                                                Comparator<? super T> c) {
            T[] aux = copyOfRange(a, fromIndex, toIndex);
            if (c==null)
                mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
            else
                mergeSort(aux, a, fromIndex, toIndex, -fromIndex, c);
        }
    
        /**
         * Src is the source array that starts at index 0
         * Dest is the (possibly larger) array destination with a possible offset
         * low is the index in dest to start sorting
         * high is the end index in dest to end sorting
         * off is the offset into src corresponding to low in dest
         * To be removed in a future release.
         */
        @SuppressWarnings({"rawtypes", "unchecked"})
        private static void mergeSort(Object[] src,
                                      Object[] dest,
                                      int low, int high, int off,
                                      Comparator c) {
            int length = high - low;
    
            // Insertion sort on smallest arrays
            if (length < INSERTIONSORT_THRESHOLD) {
                for (int i=low; i<high; i++)
                    for (int j=i; j>low && c.compare(dest[j-1], dest[j])>0; j--)
                        swap(dest, j, j-1);
                return;
            }
    
            // Recursively sort halves of dest into src
            int destLow  = low;
            int destHigh = high;
            low  += off;
            high += off;
            int mid = (low + high) >>> 1;
            mergeSort(dest, src, low, mid, -off, c);
            mergeSort(dest, src, mid, high, -off, c);
    
            // If list is already sorted, just copy from src to dest.  This is an
            // optimization that results in faster sorts for nearly ordered lists.
            if (c.compare(src[mid-1], src[mid]) <= 0) {
               System.arraycopy(src, low, dest, destLow, length);
               return;
            }
    
            // Merge sorted halves (now in src) into dest
            for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
                if (q >= high || p < mid && c.compare(src[p], src[q]) <= 0)
                    dest[i] = src[p++];
                else
                    dest[i] = src[q++];
            }
        }
    
        // Parallel prefix
    
        /**
         * Cumulates, in parallel, each element of the given array in place,
         * using the supplied function. For example if the array initially
         * holds {@code [2, 1, 0, 3]} and the operation performs addition,
         * then upon return the array holds {@code [2, 3, 3, 6]}.
         * Parallel prefix computation is usually more efficient than
         * sequential loops for large arrays.
         *
         * @param <T> the class of the objects in the array
         * @param array the array, which is modified in-place by this method
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static <T> void parallelPrefix(T[] array, BinaryOperator<T> op) {
            Objects.requireNonNull(op);
            if (array.length > 0)
                new ArrayPrefixHelpers.CumulateTask<>
                        (null, op, array, 0, array.length).invoke();
        }
    
        /**
         * Performs {@link #parallelPrefix(Object[], BinaryOperator)}
         * for the given subrange of the array.
         *
         * @param <T> the class of the objects in the array
         * @param array the array
         * @param fromIndex the index of the first element, inclusive
         * @param toIndex the index of the last element, exclusive
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > array.length}
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static <T> void parallelPrefix(T[] array, int fromIndex,
                                              int toIndex, BinaryOperator<T> op) {
            Objects.requireNonNull(op);
            rangeCheck(array.length, fromIndex, toIndex);
            if (fromIndex < toIndex)
                new ArrayPrefixHelpers.CumulateTask<>
                        (null, op, array, fromIndex, toIndex).invoke();
        }
    
        /**
         * Cumulates, in parallel, each element of the given array in place,
         * using the supplied function. For example if the array initially
         * holds {@code [2, 1, 0, 3]} and the operation performs addition,
         * then upon return the array holds {@code [2, 3, 3, 6]}.
         * Parallel prefix computation is usually more efficient than
         * sequential loops for large arrays.
         *
         * @param array the array, which is modified in-place by this method
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static void parallelPrefix(long[] array, LongBinaryOperator op) {
            Objects.requireNonNull(op);
            if (array.length > 0)
                new ArrayPrefixHelpers.LongCumulateTask
                        (null, op, array, 0, array.length).invoke();
        }
    
        /**
         * Performs {@link #parallelPrefix(long[], LongBinaryOperator)}
         * for the given subrange of the array.
         *
         * @param array the array
         * @param fromIndex the index of the first element, inclusive
         * @param toIndex the index of the last element, exclusive
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > array.length}
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static void parallelPrefix(long[] array, int fromIndex,
                                          int toIndex, LongBinaryOperator op) {
            Objects.requireNonNull(op);
            rangeCheck(array.length, fromIndex, toIndex);
            if (fromIndex < toIndex)
                new ArrayPrefixHelpers.LongCumulateTask
                        (null, op, array, fromIndex, toIndex).invoke();
        }
    
        /**
         * Cumulates, in parallel, each element of the given array in place,
         * using the supplied function. For example if the array initially
         * holds {@code [2.0, 1.0, 0.0, 3.0]} and the operation performs addition,
         * then upon return the array holds {@code [2.0, 3.0, 3.0, 6.0]}.
         * Parallel prefix computation is usually more efficient than
         * sequential loops for large arrays.
         *
         * <p> Because floating-point operations may not be strictly associative,
         * the returned result may not be identical to the value that would be
         * obtained if the operation was performed sequentially.
         *
         * @param array the array, which is modified in-place by this method
         * @param op a side-effect-free function to perform the cumulation
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static void parallelPrefix(double[] array, DoubleBinaryOperator op) {
            Objects.requireNonNull(op);
            if (array.length > 0)
                new ArrayPrefixHelpers.DoubleCumulateTask
                        (null, op, array, 0, array.length).invoke();
        }
    
        /**
         * Performs {@link #parallelPrefix(double[], DoubleBinaryOperator)}
         * for the given subrange of the array.
         *
         * @param array the array
         * @param fromIndex the index of the first element, inclusive
         * @param toIndex the index of the last element, exclusive
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > array.length}
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static void parallelPrefix(double[] array, int fromIndex,
                                          int toIndex, DoubleBinaryOperator op) {
            Objects.requireNonNull(op);
            rangeCheck(array.length, fromIndex, toIndex);
            if (fromIndex < toIndex)
                new ArrayPrefixHelpers.DoubleCumulateTask
                        (null, op, array, fromIndex, toIndex).invoke();
        }
    
        /**
         * Cumulates, in parallel, each element of the given array in place,
         * using the supplied function. For example if the array initially
         * holds {@code [2, 1, 0, 3]} and the operation performs addition,
         * then upon return the array holds {@code [2, 3, 3, 6]}.
         * Parallel prefix computation is usually more efficient than
         * sequential loops for large arrays.
         *
         * @param array the array, which is modified in-place by this method
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static void parallelPrefix(int[] array, IntBinaryOperator op) {
            Objects.requireNonNull(op);
            if (array.length > 0)
                new ArrayPrefixHelpers.IntCumulateTask
                        (null, op, array, 0, array.length).invoke();
        }
    
        /**
         * Performs {@link #parallelPrefix(int[], IntBinaryOperator)}
         * for the given subrange of the array.
         *
         * @param array the array
         * @param fromIndex the index of the first element, inclusive
         * @param toIndex the index of the last element, exclusive
         * @param op a side-effect-free, associative function to perform the
         * cumulation
         * @throws IllegalArgumentException if {@code fromIndex > toIndex}
         * @throws ArrayIndexOutOfBoundsException
         *     if {@code fromIndex < 0} or {@code toIndex > array.length}
         * @throws NullPointerException if the specified array or function is null
         * @since 1.8
         */
        public static void parallelPrefix(int[] array, int fromIndex,
                                          int toIndex, IntBinaryOperator op) {
            Objects.requireNonNull(op);
            rangeCheck(array.length, fromIndex, toIndex);
            if (fromIndex < toIndex)
                new ArrayPrefixHelpers.IntCumulateTask
                        (null, op, array, fromIndex, toIndex).invoke();
        }
    
        // Searching
    
        /**
         * Searches the specified array of longs for the specified value using the
         * binary search algorithm.  The array must be sorted (as
         * by the {@link #sort(long[])} method) prior to making this call.  If it
         * is not sorted, the results are undefined.  If the array contains
         * multiple elements with the specified value, there is no guarantee which
         * one will be found.
         *
         * @param a the array to be searched
         * @param key the value to be searched for
         * @return index of the search key, if it is contained in the array;
         *         otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
         *         <i>insertion point</i> is defined as the point at which the
         *         key would be inserted into the array: the index of the first
         *         element greater than the key, or <tt>a.length</tt> if all
         *         elements in the array are less than the specified key.  Note
         *         that this guarantees that the return value will be >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 >= 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > toIndex</tt>
         * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
         *         <tt>toIndex > 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 > 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 > 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 > 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 > 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 > 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 > 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 > 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 > 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 > 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 > 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<String> stooges = Arrays.asList("Larry", "Moe", "Curly");
         * </pre>
         *
         * @param <T> the class of the objects in the array
         * @param a the array by which the list will be backed
         * @return a list view of the specified array
         */
        @SafeVarargs
        @SuppressWarnings("varargs")
        public static <T> List<T> asList(T... a) {
            return new ArrayList<>(a);
        }
    
        /**
         * @serial include
         */
        private static class ArrayList<E> extends AbstractList<E>
            implements RandomAccess, java.io.Serializable
        {
            private static final long serialVersionUID = -2764017481108945198L;
            private final E[] a;
    
            ArrayList(E[] array) {
                a = Objects.requireNonNull(array);
            }
    
            @Override
            public int size() {
                return a.length;
            }
    
            @Override
            public Object[] toArray() {
                return a.clone();
            }
    
            @Override
            @SuppressWarnings("unchecked")
            public <T> T[] toArray(T[] a) {
                int size = size();
                if (a.length < size)
                    return Arrays.copyOf(this.a, size,
                                         (Class<? extends T[]>) a.getClass());
                System.arraycopy(this.a, 0, a, 0, size);
                if (a.length > size)
                    a[size] = null;
                return a;
            }
    
            @Override
            public E get(int index) {
                return a[index];
            }
    
            @Override
            public E set(int index, E element) {
                E oldValue = a[index];
                a[index] = element;
                return oldValue;
            }
    
            @Override
            public int indexOf(Object o) {
                E[] a = this.a;
                if (o == null) {
                    for (int i = 0; i < a.length; i++)
                        if (a[i] == null)
                            return i;
                } else {
                    for (int i = 0; i < a.length; i++)
                        if (o.equals(a[i]))
                            return i;
                }
                return -1;
            }
    
            @Override
            public boolean contains(Object o) {
                return indexOf(o) != -1;
            }
    
            @Override
            public Spliterator<E> spliterator() {
                return Spliterators.spliterator(a, Spliterator.ORDERED);
            }
    
            @Override
            public void forEach(Consumer<? super E> action) {
                Objects.requireNonNull(action);
                for (E e : a) {
                    action.accept(e);
                }
            }
    
            @Override
            public void replaceAll(UnaryOperator<E> operator) {
                Objects.requireNonNull(operator);
                E[] a = this.a;
                for (int i = 0; i < a.length; i++) {
                    a[i] = operator.apply(a[i]);
                }
            }
    
            @Override
            public void sort(Comparator<? super E> c) {
                Arrays.sort(a, c);
            }
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>long</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Long}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(long a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (long element : a) {
                int elementHash = (int)(element ^ (element >>> 32));
                result = 31 * result + elementHash;
            }
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two non-null <tt>int</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Integer}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(int a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (int element : a)
                result = 31 * result + element;
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>short</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Short}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(short a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (short element : a)
                result = 31 * result + element;
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>char</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Character}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(char a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (char element : a)
                result = 31 * result + element;
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>byte</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Byte}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(byte a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (byte element : a)
                result = 31 * result + element;
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>boolean</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Boolean}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(boolean a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (boolean element : a)
                result = 31 * result + (element ? 1231 : 1237);
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>float</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Float}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(float a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (float element : a)
                result = 31 * result + Float.floatToIntBits(element);
    
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.
         * For any two <tt>double</tt> arrays <tt>a</tt> and <tt>b</tt>
         * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is the same value that would be
         * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
         * method on a {@link List} containing a sequence of {@link Double}
         * instances representing the elements of <tt>a</tt> in the same order.
         * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
         *
         * @param a the array whose hash value to compute
         * @return a content-based hash code for <tt>a</tt>
         * @since 1.5
         */
        public static int hashCode(double a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
            for (double element : a) {
                long bits = Double.doubleToLongBits(element);
                result = 31 * result + (int)(bits ^ (bits >>> 32));
            }
            return result;
        }
    
        /**
         * Returns a hash code based on the contents of the specified array.  If
         * the array contains other arrays as elements, the hash code is based on
         * their identities rather than their contents.  It is therefore
         * acceptable to invoke this method on an array that contains itself as an
         * element,  either directly or indirectly through one or more levels of
         * arrays.
         *
         * <p>For any two arrays <tt>a</tt> and <tt>b</tt> such that
         * <tt>Arrays.equals(a, b)</tt>, it is also the case that
         * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
         *
         * <p>The value returned by this method is equal to the value that would
         * be returned by <tt>Arrays.asList(a).hashCode()</tt>, unless <tt>a</tt>
         * is <tt>null</tt>, in which case <tt>0</tt> is returned.
         *
         * @param a the array whose content-based hash code to compute
         * @return a content-based hash code for <tt>a</tt>
         * @see #deepHashCode(Object[])
         * @since 1.5
         */
        public static int hashCode(Object a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
    
            for (Object element : a)
                result = 31 * result + (element == null ? 0 : element.hashCode());
    
            return result;
        }
    
        /**
         * Returns a hash code based on the "deep contents" of the specified
         * array.  If the array contains other arrays as elements, the
         * hash code is based on their contents and so on, ad infinitum.
         * It is therefore unacceptable to invoke this method on an array that
         * contains itself as an element, either directly or indirectly through
         * one or more levels of arrays.  The behavior of such an invocation is
         * undefined.
         *
         * <p>For any two arrays <tt>a</tt> and <tt>b</tt> such that
         * <tt>Arrays.deepEquals(a, b)</tt>, it is also the case that
         * <tt>Arrays.deepHashCode(a) == Arrays.deepHashCode(b)</tt>.
         *
         * <p>The computation of the value returned by this method is similar to
         * that of the value returned by {@link List#hashCode()} on a list
         * containing the same elements as <tt>a</tt> in the same order, with one
         * difference: If an element <tt>e</tt> of <tt>a</tt> is itself an array,
         * its hash code is computed not by calling <tt>e.hashCode()</tt>, but as
         * by calling the appropriate overloading of <tt>Arrays.hashCode(e)</tt>
         * if <tt>e</tt> is an array of a primitive type, or as by calling
         * <tt>Arrays.deepHashCode(e)</tt> recursively if <tt>e</tt> is an array
         * of a reference type.  If <tt>a</tt> is <tt>null</tt>, this method
         * returns 0.
         *
         * @param a the array whose deep-content-based hash code to compute
         * @return a deep-content-based hash code for <tt>a</tt>
         * @see #hashCode(Object[])
         * @since 1.5
         */
        public static int deepHashCode(Object a[]) {
            if (a == null)
                return 0;
    
            int result = 1;
    
            for (Object element : a) {
                int elementHash = 0;
                if (element instanceof Object[])
                    elementHash = deepHashCode((Object[]) element);
                else if (element instanceof byte[])
                    elementHash = hashCode((byte[]) element);
                else if (element instanceof short[])
                    elementHash = hashCode((short[]) element);
                else if (element instanceof int[])
                    elementHash = hashCode((int[]) element);
                else if (element instanceof long[])
                    elementHash = hashCode((long[]) element);
                else if (element instanceof char[])
                    elementHash = hashCode((char[]) element);
                else if (element instanceof float[])
                    elementHash = hashCode((float[]) element);
                else if (element instanceof double[])
                    elementHash = hashCode((double[]) element);
                else if (element instanceof boolean[])
                    elementHash = hashCode((boolean[]) element);
                else if (element != null)
                    elementHash = element.hashCode();
    
                result = 31 * result + elementHash;
            }
    
            return result;
        }
    
        /**
         * Returns <tt>true</tt> if the two specified arrays are <i>deeply
         * equal</i> to one another.  Unlike the {@link #equals(Object[],Object[])}
         * method, this method is appropriate for use with nested arrays of
         * arbitrary depth.
         *
         * <p>Two array references are considered deeply equal if both
         * are <tt>null</tt>, or if they refer to arrays that contain the same
         * number of elements and all corresponding pairs of elements in the two
         * arrays are deeply equal.
         *
         * <p>Two possibly <tt>null</tt> elements <tt>e1</tt> and <tt>e2</tt> are
         * deeply equal if any of the following conditions hold:
         * <ul>
         *    <li> <tt>e1</tt> and <tt>e2</tt> are both arrays of object reference
         *         types, and <tt>Arrays.deepEquals(e1, e2) would return true</tt>
         *    <li> <tt>e1</tt> and <tt>e2</tt> are arrays of the same primitive
         *         type, and the appropriate overloading of
         *         <tt>Arrays.equals(e1, e2)</tt> would return true.
         *    <li> <tt>e1 == e2</tt>
         *    <li> <tt>e1.equals(e2)</tt> would return true.
         * </ul>
         * Note that this definition permits <tt>null</tt> elements at any depth.
         *
         * <p>If either of the specified arrays contain themselves as elements
         * either directly or indirectly through one or more levels of arrays,
         * the behavior of this method is undefined.
         *
         * @param a1 one array to be tested for equality
         * @param a2 the other array to be tested for equality
         * @return <tt>true</tt> if the two arrays are equal
         * @see #equals(Object[],Object[])
         * @see Objects#deepEquals(Object, Object)
         * @since 1.5
         */
        public static boolean deepEquals(Object[] a1, Object[] a2) {
            if (a1 == a2)
                return true;
            if (a1 == null || a2==null)
                return false;
            int length = a1.length;
            if (a2.length != length)
                return false;
    
            for (int i = 0; i < length; i++) {
                Object e1 = a1[i];
                Object e2 = a2[i];
    
                if (e1 == e2)
                    continue;
                if (e1 == null)
                    return false;
    
                // Figure out whether the two elements are equal
                boolean eq = deepEquals0(e1, e2);
    
                if (!eq)
                    return false;
            }
            return true;
        }
    
        static boolean deepEquals0(Object e1, Object e2) {
            assert e1 != null;
            boolean eq;
            if (e1 instanceof Object[] && e2 instanceof Object[])
                eq = deepEquals ((Object[]) e1, (Object[]) e2);
            else if (e1 instanceof byte[] && e2 instanceof byte[])
                eq = equals((byte[]) e1, (byte[]) e2);
            else if (e1 instanceof short[] && e2 instanceof short[])
                eq = equals((short[]) e1, (short[]) e2);
            else if (e1 instanceof int[] && e2 instanceof int[])
                eq = equals((int[]) e1, (int[]) e2);
            else if (e1 instanceof long[] && e2 instanceof long[])
                eq = equals((long[]) e1, (long[]) e2);
            else if (e1 instanceof char[] && e2 instanceof char[])
                eq = equals((char[]) e1, (char[]) e2);
            else if (e1 instanceof float[] && e2 instanceof float[])
                eq = equals((float[]) e1, (float[]) e2);
            else if (e1 instanceof double[] && e2 instanceof double[])
                eq = equals((double[]) e1, (double[]) e2);
            else if (e1 instanceof boolean[] && e2 instanceof boolean[])
                eq = equals((boolean[]) e1, (boolean[]) e2);
            else
                eq = e1.equals(e2);
            return eq;
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(long)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
         * is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(long[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(int)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt> is
         * <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(int[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(short)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
         * is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(short[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(char)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
         * is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(char[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements
         * are separated by the characters <tt>", "</tt> (a comma followed
         * by a space).  Elements are converted to strings as by
         * <tt>String.valueOf(byte)</tt>.  Returns <tt>"null"</tt> if
         * <tt>a</tt> is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(byte[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(boolean)</tt>.  Returns <tt>"null"</tt> if
         * <tt>a</tt> is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(boolean[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(float)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
         * is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(float[] a) {
            if (a == null)
                return "null";
    
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * The string representation consists of a list of the array's elements,
         * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
         * separated by the characters <tt>", "</tt> (a comma followed by a
         * space).  Elements are converted to strings as by
         * <tt>String.valueOf(double)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
         * is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @since 1.5
         */
        public static String toString(double[] a) {
            if (a == null)
                return "null";
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(a[i]);
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the contents of the specified array.
         * If the array contains other arrays as elements, they are converted to
         * strings by the {@link Object#toString} method inherited from
         * <tt>Object</tt>, which describes their <i>identities</i> rather than
         * their contents.
         *
         * <p>The value returned by this method is equal to the value that would
         * be returned by <tt>Arrays.asList(a).toString()</tt>, unless <tt>a</tt>
         * is <tt>null</tt>, in which case <tt>"null"</tt> is returned.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @see #deepToString(Object[])
         * @since 1.5
         */
        public static String toString(Object[] a) {
            if (a == null)
                return "null";
    
            int iMax = a.length - 1;
            if (iMax == -1)
                return "[]";
    
            StringBuilder b = new StringBuilder();
            b.append('[');
            for (int i = 0; ; i++) {
                b.append(String.valueOf(a[i]));
                if (i == iMax)
                    return b.append(']').toString();
                b.append(", ");
            }
        }
    
        /**
         * Returns a string representation of the "deep contents" of the specified
         * array.  If the array contains other arrays as elements, the string
         * representation contains their contents and so on.  This method is
         * designed for converting multidimensional arrays to strings.
         *
         * <p>The string representation consists of a list of the array's
         * elements, enclosed in square brackets (<tt>"[]"</tt>).  Adjacent
         * elements are separated by the characters <tt>", "</tt> (a comma
         * followed by a space).  Elements are converted to strings as by
         * <tt>String.valueOf(Object)</tt>, unless they are themselves
         * arrays.
         *
         * <p>If an element <tt>e</tt> is an array of a primitive type, it is
         * converted to a string as by invoking the appropriate overloading of
         * <tt>Arrays.toString(e)</tt>.  If an element <tt>e</tt> is an array of a
         * reference type, it is converted to a string as by invoking
         * this method recursively.
         *
         * <p>To avoid infinite recursion, if the specified array contains itself
         * as an element, or contains an indirect reference to itself through one
         * or more levels of arrays, the self-reference is converted to the string
         * <tt>"[...]"</tt>.  For example, an array containing only a reference
         * to itself would be rendered as <tt>"[[...]]"</tt>.
         *
         * <p>This method returns <tt>"null"</tt> if the specified array
         * is <tt>null</tt>.
         *
         * @param a the array whose string representation to return
         * @return a string representation of <tt>a</tt>
         * @see #toString(Object[])
         * @since 1.5
         */
        public static String deepToString(Object[] a) {
            if (a == null)
                return "null";
    
            int bufLen = 20 * a.length;
            if (a.length != 0 && bufLen <= 0)
                bufLen = Integer.MAX_VALUE;
            StringBuilder buf = new StringBuilder(bufLen);
            deepToString(a, buf, new HashSet<Object[]>());
            return buf.toString();
        }
    
        private static void deepToString(Object[] a, StringBuilder buf,
                                         Set<Object[]> dejaVu) {
            if (a == null) {
                buf.append("null");
                return;
            }
            int iMax = a.length - 1;
            if (iMax == -1) {
                buf.append("[]");
                return;
            }
    
            dejaVu.add(a);
            buf.append('[');
            for (int i = 0; ; i++) {
    
                Object element = a[i];
                if (element == null) {
                    buf.append("null");
                } else {
                    Class<?> eClass = element.getClass();
    
                    if (eClass.isArray()) {
                        if (eClass == byte[].class)
                            buf.append(toString((byte[]) element));
                        else if (eClass == short[].class)
                            buf.append(toString((short[]) element));
                        else if (eClass == int[].class)
                            buf.append(toString((int[]) element));
                        else if (eClass == long[].class)
                            buf.append(toString((long[]) element));
                        else if (eClass == char[].class)
                            buf.append(toString((char[]) element));
                        else if (eClass == float[].class)
                            buf.append(toString((float[]) element));
                        else if (eClass == double[].class)
                            buf.append(toString((double[]) element));
                        else if (eClass == boolean[].class)
                            buf.append(toString((boolean[]) element));
                        else { // element is an array of object references
                            if (dejaVu.contains(element))
                                buf.append("[...]");
                            else
                                deepToString((Object[])element, buf, dejaVu);
                        }
                    } else {  // element is non-null and not an array
                        buf.append(element.toString());
                    }
                }
                if (i == iMax)
                    break;
                buf.append(", ");
            }
            buf.append(']');
            dejaVu.remove(a);
        }
    
    
        /**
         * Set all elements of the specified array, using the provided
         * generator function to compute each element.
         *
         * <p>If the generator function throws an exception, it is relayed to
         * the caller and the array is left in an indeterminate state.
         *
         * @param <T> type of elements of the array
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static <T> void setAll(T[] array, IntFunction<? extends T> generator) {
            Objects.requireNonNull(generator);
            for (int i = 0; i < array.length; i++)
                array[i] = generator.apply(i);
        }
    
        /**
         * Set all elements of the specified array, in parallel, using the
         * provided generator function to compute each element.
         *
         * <p>If the generator function throws an exception, an unchecked exception
         * is thrown from {@code parallelSetAll} and the array is left in an
         * indeterminate state.
         *
         * @param <T> type of elements of the array
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static <T> void parallelSetAll(T[] array, IntFunction<? extends T> generator) {
            Objects.requireNonNull(generator);
            IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.apply(i); });
        }
    
        /**
         * Set all elements of the specified array, using the provided
         * generator function to compute each element.
         *
         * <p>If the generator function throws an exception, it is relayed to
         * the caller and the array is left in an indeterminate state.
         *
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static void setAll(int[] array, IntUnaryOperator generator) {
            Objects.requireNonNull(generator);
            for (int i = 0; i < array.length; i++)
                array[i] = generator.applyAsInt(i);
        }
    
        /**
         * Set all elements of the specified array, in parallel, using the
         * provided generator function to compute each element.
         *
         * <p>If the generator function throws an exception, an unchecked exception
         * is thrown from {@code parallelSetAll} and the array is left in an
         * indeterminate state.
         *
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         * value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static void parallelSetAll(int[] array, IntUnaryOperator generator) {
            Objects.requireNonNull(generator);
            IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.applyAsInt(i); });
        }
    
        /**
         * Set all elements of the specified array, using the provided
         * generator function to compute each element.
         *
         * <p>If the generator function throws an exception, it is relayed to
         * the caller and the array is left in an indeterminate state.
         *
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static void setAll(long[] array, IntToLongFunction generator) {
            Objects.requireNonNull(generator);
            for (int i = 0; i < array.length; i++)
                array[i] = generator.applyAsLong(i);
        }
    
        /**
         * Set all elements of the specified array, in parallel, using the
         * provided generator function to compute each element.
         *
         * <p>If the generator function throws an exception, an unchecked exception
         * is thrown from {@code parallelSetAll} and the array is left in an
         * indeterminate state.
         *
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static void parallelSetAll(long[] array, IntToLongFunction generator) {
            Objects.requireNonNull(generator);
            IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.applyAsLong(i); });
        }
    
        /**
         * Set all elements of the specified array, using the provided
         * generator function to compute each element.
         *
         * <p>If the generator function throws an exception, it is relayed to
         * the caller and the array is left in an indeterminate state.
         *
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static void setAll(double[] array, IntToDoubleFunction generator) {
            Objects.requireNonNull(generator);
            for (int i = 0; i < array.length; i++)
                array[i] = generator.applyAsDouble(i);
        }
    
        /**
         * Set all elements of the specified array, in parallel, using the
         * provided generator function to compute each element.
         *
         * <p>If the generator function throws an exception, an unchecked exception
         * is thrown from {@code parallelSetAll} and the array is left in an
         * indeterminate state.
         *
         * @param array array to be initialized
         * @param generator a function accepting an index and producing the desired
         *        value for that position
         * @throws NullPointerException if the generator is null
         * @since 1.8
         */
        public static void parallelSetAll(double[] array, IntToDoubleFunction generator) {
            Objects.requireNonNull(generator);
            IntStream.range(0, array.length).parallel().forEach(i -> { array[i] = generator.applyAsDouble(i); });
        }
    
        /**
         * Returns a {@link Spliterator} covering all of the specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param <T> type of elements
         * @param array the array, assumed to be unmodified during use
         * @return a spliterator for the array elements
         * @since 1.8
         */
        public static <T> Spliterator<T> spliterator(T[] array) {
            return Spliterators.spliterator(array,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator} covering the specified range of the
         * specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param <T> type of elements
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a spliterator for the array elements
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static <T> Spliterator<T> spliterator(T[] array, int startInclusive, int endExclusive) {
            return Spliterators.spliterator(array, startInclusive, endExclusive,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator.OfInt} covering all of the specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param array the array, assumed to be unmodified during use
         * @return a spliterator for the array elements
         * @since 1.8
         */
        public static Spliterator.OfInt spliterator(int[] array) {
            return Spliterators.spliterator(array,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator.OfInt} covering the specified range of the
         * specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a spliterator for the array elements
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static Spliterator.OfInt spliterator(int[] array, int startInclusive, int endExclusive) {
            return Spliterators.spliterator(array, startInclusive, endExclusive,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator.OfLong} covering all of the specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param array the array, assumed to be unmodified during use
         * @return the spliterator for the array elements
         * @since 1.8
         */
        public static Spliterator.OfLong spliterator(long[] array) {
            return Spliterators.spliterator(array,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator.OfLong} covering the specified range of the
         * specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a spliterator for the array elements
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static Spliterator.OfLong spliterator(long[] array, int startInclusive, int endExclusive) {
            return Spliterators.spliterator(array, startInclusive, endExclusive,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator.OfDouble} covering all of the specified
         * array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param array the array, assumed to be unmodified during use
         * @return a spliterator for the array elements
         * @since 1.8
         */
        public static Spliterator.OfDouble spliterator(double[] array) {
            return Spliterators.spliterator(array,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a {@link Spliterator.OfDouble} covering the specified range of
         * the specified array.
         *
         * <p>The spliterator reports {@link Spliterator#SIZED},
         * {@link Spliterator#SUBSIZED}, {@link Spliterator#ORDERED}, and
         * {@link Spliterator#IMMUTABLE}.
         *
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a spliterator for the array elements
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static Spliterator.OfDouble spliterator(double[] array, int startInclusive, int endExclusive) {
            return Spliterators.spliterator(array, startInclusive, endExclusive,
                                            Spliterator.ORDERED | Spliterator.IMMUTABLE);
        }
    
        /**
         * Returns a sequential {@link Stream} with the specified array as its
         * source.
         *
         * @param <T> The type of the array elements
         * @param array The array, assumed to be unmodified during use
         * @return a {@code Stream} for the array
         * @since 1.8
         */
        public static <T> Stream<T> stream(T[] array) {
            return stream(array, 0, array.length);
        }
    
        /**
         * Returns a sequential {@link Stream} with the specified range of the
         * specified array as its source.
         *
         * @param <T> the type of the array elements
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a {@code Stream} for the array range
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static <T> Stream<T> stream(T[] array, int startInclusive, int endExclusive) {
            return StreamSupport.stream(spliterator(array, startInclusive, endExclusive), false);
        }
    
        /**
         * Returns a sequential {@link IntStream} with the specified array as its
         * source.
         *
         * @param array the array, assumed to be unmodified during use
         * @return an {@code IntStream} for the array
         * @since 1.8
         */
        public static IntStream stream(int[] array) {
            return stream(array, 0, array.length);
        }
    
        /**
         * Returns a sequential {@link IntStream} with the specified range of the
         * specified array as its source.
         *
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return an {@code IntStream} for the array range
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static IntStream stream(int[] array, int startInclusive, int endExclusive) {
            return StreamSupport.intStream(spliterator(array, startInclusive, endExclusive), false);
        }
    
        /**
         * Returns a sequential {@link LongStream} with the specified array as its
         * source.
         *
         * @param array the array, assumed to be unmodified during use
         * @return a {@code LongStream} for the array
         * @since 1.8
         */
        public static LongStream stream(long[] array) {
            return stream(array, 0, array.length);
        }
    
        /**
         * Returns a sequential {@link LongStream} with the specified range of the
         * specified array as its source.
         *
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a {@code LongStream} for the array range
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static LongStream stream(long[] array, int startInclusive, int endExclusive) {
            return StreamSupport.longStream(spliterator(array, startInclusive, endExclusive), false);
        }
    
        /**
         * Returns a sequential {@link DoubleStream} with the specified array as its
         * source.
         *
         * @param array the array, assumed to be unmodified during use
         * @return a {@code DoubleStream} for the array
         * @since 1.8
         */
        public static DoubleStream stream(double[] array) {
            return stream(array, 0, array.length);
        }
    
        /**
         * Returns a sequential {@link DoubleStream} with the specified range of the
         * specified array as its source.
         *
         * @param array the array, assumed to be unmodified during use
         * @param startInclusive the first index to cover, inclusive
         * @param endExclusive index immediately past the last index to cover
         * @return a {@code DoubleStream} for the array range
         * @throws ArrayIndexOutOfBoundsException if {@code startInclusive} is
         *         negative, {@code endExclusive} is less than
         *         {@code startInclusive}, or {@code endExclusive} is greater than
         *         the array size
         * @since 1.8
         */
        public static DoubleStream stream(double[] array, int startInclusive, int endExclusive) {
            return StreamSupport.doubleStream(spliterator(array, startInclusive, endExclusive), false);
        }
    }
    

      

    #####################################

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  • 原文地址:https://www.cnblogs.com/herd/p/15532016.html
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