ArrayDeque 源码分析

Posted 2020-12-04 zhuxudong

package java.util;

import java.io.Serializable;
import java.util.function.Consumer;
import java.util.function.Predicate;

import jdk.internal.misc.SharedSecrets;

/**
 * 1）Deque 接口的循环可变数组实现，ArrayDeque 没有容量限制并会按需增长。
 * 2）ArrayDeque 不是线程安全的，ArrayDeque 不允许使用 null 元素。
 * 3）ArrayDeque 用作栈时，性能优于 Stack，用作队列时，性能优于 LinkedList.
 * 4）ArrayDeque 的大多数操作基于平摊常数时间，除了 remove* 和 contains。
 * 5）ArrayDeque 返回的 iterator 是快速失败的。
 */
public class ArrayDeque<E> extends AbstractCollection<E>
                           implements Deque<E>, Cloneable, Serializable
{
    /*
     * VMs excel at optimizing simple array loops where indices are
     * incrementing or decrementing over a valid slice, e.g.
     *
     * for (int i = start; i < end; i++) ... elements[i]
     *
     * Because in a circular array, elements are in general stored in
     * two disjoint such slices, we help the VM by writing unusual
     * nested loops for all traversals over the elements.  Having only
     * one hot inner loop body instead of two or three eases human
     * maintenance and encourages VM loop inlining into the caller.
     */

    /**
     * 存储元素的底层对象数组，尾部的位置总为 null
     */
    transient Object[] elements;

    /**
     * 头部元素索引
     */
    transient int head;

    /**
     * 尾部元素索引，此处的元素一直为 null
     */
    transient int tail;

    /**
     * 最大的对象数组长度
     */
    private static final int MAX_ARRAY_SIZE = Integer.MAX_VALUE - 8;

    /**
     * 底层数组扩容
     */
    private void grow(int needed) {
        final int oldCapacity = elements.length;
        int newCapacity;
        // Double capacity if small; else grow by 50%
        /**
         * 如果容量小于 64，则执行【双倍+2】扩容，否则执行 1.5 倍向下取整扩容。
         */
        int jump = (oldCapacity < 64) ? (oldCapacity + 2) : (oldCapacity >> 1);
        /**
         * 扩容增量小于所需的空间或总容量大于 Integer.MAX_VALUE - 8
         */
        if (jump < needed
            || (newCapacity = (oldCapacity + jump)) - MAX_ARRAY_SIZE > 0)
            newCapacity = newCapacity(needed, jump);
        // 创建新的数组并拷贝原有元素
        final Object[] es = elements = Arrays.copyOf(elements, newCapacity);
        // Exceptionally, here tail == head needs to be disambiguated
        /**
         * 尾部索引小于头部索引，尾部索引等于头部索引并且头部元素不为 null
         */
        if (tail < head || (tail == head && es[head] != null)) {
            // wrap around; slide first leg forward to end of array
            int newSpace = newCapacity - oldCapacity;
            /**
             * 将头部元素拷贝到数组的尾部，并将那些空间置为 null
             */
            System.arraycopy(es, head,
                             es, head + newSpace,
                             oldCapacity - head);
            for (int i = head, to = (head += newSpace); i < to; i++)
                es[i] = null;
        }
    }

    /** Capacity calculation for edge conditions, especially overflow. */
    private int newCapacity(int needed, int jump) {
        final int oldCapacity = elements.length, minCapacity;
        if ((minCapacity = oldCapacity + needed) - MAX_ARRAY_SIZE > 0) {
            if (minCapacity < 0)
                throw new IllegalStateException("Sorry, deque too big");
            return Integer.MAX_VALUE;
        }
        if (needed > jump)
            return minCapacity;
        return (oldCapacity + jump - MAX_ARRAY_SIZE < 0)
            ? oldCapacity + jump
            : MAX_ARRAY_SIZE;
    }

    /**
     * 创建容量为 16 的 ArrayDeque
     */
    public ArrayDeque() {
        elements = new Object[16];
    }

    /**
     * 创建指定初始容量的 ArrayDeque
     */
    public ArrayDeque(int numElements) {
        elements =
            new Object[(numElements < 1) ? 1 :
                       (numElements == Integer.MAX_VALUE) ? Integer.MAX_VALUE :
                       numElements + 1];
    }

    /**
     * 创建包含集合中所有元素的 ArrayDeque
     */
    public ArrayDeque(Collection<? extends E> c) {
        this(c.size());
        addAll(c);
    }

    /**
     * Circularly increments i, mod modulus.
     * Precondition and postcondition: 0 <= i < modulus.
     * 基于 modulus 计算循环递增索引
     */
    static final int inc(int i, int modulus) {
        if (++i >= modulus) i = 0;
        return i;
    }

    /**
     * Circularly decrements i, mod modulus.
     * Precondition and postcondition: 0 <= i < modulus.
     * 基于 modulus 计算循环递减索引
     */
    static final int dec(int i, int modulus) {
        if (--i < 0) i = modulus - 1;
        return i;
    }

    /**
     * Circularly adds the given distance to index i, mod modulus.
     * Precondition: 0 <= i < modulus, 0 <= distance <= modulus.
     * @return index 0 <= i < modulus
     * 基于指定的增量，计算循环索引
     */
    static final int inc(int i, int distance, int modulus) {
        if ((i += distance) - modulus >= 0) i -= modulus;
        return i;
    }

    /**
     * Subtracts j from i, mod modulus.
     * Index i must be logically ahead of index j.
     * Precondition: 0 <= i < modulus, 0 <= j < modulus.
     * @return the "circular distance" from j to i; corner case i == j
     * is disambiguated to "empty", returning 0.
     * 基于指定的递减值，计算循环索引
     */
    static final int sub(int i, int j, int modulus) {
        if ((i -= j) < 0) i += modulus;
        return i;
    }

    /**
     * 获取指定索引处的元素
     */
    @SuppressWarnings("unchecked")
    static final <E> E elementAt(Object[] es, int i) {
        return (E) es[i];
    }

    /**
     * 获取指定索引处的元素，如果元素为空，则抛出 ConcurrentModificationException
     */
    static final <E> E nonNullElementAt(Object[] es, int i) {
        @SuppressWarnings("unchecked") E e = (E) es[i];
        if (e == null)
            throw new ConcurrentModificationException();
        return e;
    }

    // The main insertion and extraction methods are addFirst,
    // addLast, pollFirst, pollLast. The other methods are defined in
    // terms of these.

    /**
     * 将元素插入到双端队列的头部
     */
    public void addFirst(E e) {
        if (e == null)
            throw new NullPointerException();
        final Object[] es = elements;
        es[head = dec(head, es.length)] = e;
        if (head == tail)
            grow(1);
    }

    /**
     * 将元素插入到双端队列的尾部
     */
    public void addLast(E e) {
        if (e == null)
            throw new NullPointerException();
        final Object[] es = elements;
        es[tail] = e;
        if (head == (tail = inc(tail, es.length)))
            grow(1);
    }

    /**
     * 通过 addLast 方法将集合中的所有元素插入到 ArrayDeque 的尾部
     */
    public boolean addAll(Collection<? extends E> c) {
        final int s, needed;
        if ((needed = (s = size()) + c.size() + 1 - elements.length) > 0)
            grow(needed);
        c.forEach(this::addLast);
        return size() > s;
    }

    /**
     * 将元素插入到 ArrayDeque 的头部
     */
    public boolean offerFirst(E e) {
        addFirst(e);
        return true;
    }

    /**
     * 将元素插入到 ArrayDeque 的尾部
     */
    public boolean offerLast(E e) {
        addLast(e);
        return true;
    }

    /**
     * 移除并返回头部元素，如果 ArrayDeque 为空，则抛出 NoSuchElementException 异常
     * @throws NoSuchElementException {@inheritDoc}
     */
    public E removeFirst() {
        E e = pollFirst();
        if (e == null)
            throw new NoSuchElementException();
        return e;
    }

    /**
     * 移除并返回尾部元素，如果 ArrayDeque 为空，则抛出 NoSuchElementException 异常
     * @throws NoSuchElementException {@inheritDoc}
     */
    public E removeLast() {
        E e = pollLast();
        if (e == null)
            throw new NoSuchElementException();
        return e;
    }

    /**
     * 移除并返回头部元素，如果 ArrayDeque 为空，则返回 null。
     */
    public E pollFirst() {
        final Object[] es;
        final int h;
        E e = elementAt(es = elements, h = head);
        if (e != null) {
            es[h] = null;
            head = inc(h, es.length);
        }
        return e;
    }

    /**
     * 移除并返回尾部元素，如果 ArrayDeque 为空，则返回 null。
     */
    public E pollLast() {
        final Object[] es;
        final int t;
        E e = elementAt(es = elements, t = dec(tail, es.length));
        if (e != null)
            es[tail = t] = null;
        return e;
    }
    
    /**
     * 获取头部元素，如果 ArrayDeque 为空，则抛出 NoSuchElementException 异常。
     */
    public E getFirst() {
        E e = elementAt(elements, head);
        if (e == null)
            throw new NoSuchElementException();
        return e;
    }

    /**
     * 获取尾部元素，如果 ArrayDeque 为空，则抛出 NoSuchElementException 异常。
     */
    public E getLast() {
        final Object[] es = elements;
        E e = elementAt(es, dec(tail, es.length));
        if (e == null)
            throw new NoSuchElementException();
        return e;
    }

    /**
     * 获取头部元素，如果 ArrayDeque 为空，则返回 null
     */
    public E peekFirst() {
        return elementAt(elements, head);
    }

    /**
     * 获取尾部元素，如果 ArrayDeque 为空，则返回 null
     */
    public E peekLast() {
        final Object[] es;
        return elementAt(es = elements, dec(tail, es.length));
    }

    /**
     * 移除和形参相等的第一个元素，通过 {@link Object#equals(Object)} 进行相等性判断。
     */
    public boolean removeFirstOccurrence(Object o) {
        if (o != null) {
            final Object[] es = elements;
            for (int i = head, end = tail, to = (i <= end) ? end : es.length;
                 ; i = 0, to = end) {
                for (; i < to; i++)
                    if (o.equals(es[i])) {
                        delete(i);
                        return true;
                    }
                if (to == end) break;
            }
        }
        return false;
    }

    /**
     * 移除和形参相等的最后一个元素，通过 {@link Object#equals(Object)} 进行相等性判断。
     */
    public boolean removeLastOccurrence(Object o) {
        if (o != null) {
            final Object[] es = elements;
            for (int i = tail, end = head, to = (i >= end) ? end : 0;
                 ; i = es.length, to = end) {
                for (i--; i > to - 1; i--)
                    if (o.equals(es[i])) {
                        delete(i);
                        return true;
                    }
                if (to == end) break;
            }
        }
        return false;
    }

    // *** Queue methods ***

    /**
     * 将目标元素插入到 ArrayDeque 的尾部
     */
    public boolean add(E e) {
        addLast(e);
        return true;
    }

    /**
     * 将目标元素插入到 ArrayDeque 的尾部
     */
    public boolean offer(E e) {
        return offerLast(e);
    }

    public E remove() {
        return removeFirst();
    }

    public E poll() {
        return pollFirst();
    }

    public E element() {
        return getFirst();
    }

    public E peek() {
        return peekFirst();
    }

    // *** Stack methods ***

    /**
     * 将元素加入到 ArrayDeque 栈顶
     */
    public void push(E e) {
        addFirst(e);
    }

    /**
     * 将元素从 ArrayDeque 栈顶移除并返回
     */
    public E pop() {
        return removeFirst();
    }

    /**
     * 删除指定索引处的元素
     */
    boolean delete(int i) {
        final Object[] es = elements;
        final int capacity = es.length;
        final int h, t;
        // number of elements before to-be-deleted elt
        final int front = sub(i, h = head, capacity);
        // number of elements after to-be-deleted elt
        final int back = sub(t = tail, i, capacity) - 1;
        if (front < back) {
            // move front elements forwards
            if (h <= i) {
                System.arraycopy(es, h, es, h + 1, front);
            } else { // Wrap around
                System.arraycopy(es, 0, es, 1, i);
                es[0] = es[capacity - 1];
                System.arraycopy(es, h, es, h + 1, front - (i + 1));
            }
            es[h] = null;
            head = inc(h, capacity);
            return false;
        } else {
            // move back elements backwards
            tail = dec(t, capacity);
            if (i <= tail) {
                System.arraycopy(es, i + 1, es, i, back);
            } else { // Wrap around
                System.arraycopy(es, i + 1, es, i, capacity - (i + 1));
                es[capacity - 1] = es[0];
                System.arraycopy(es, 1, es, 0, t - 1);
            }
            es[tail] = null;
            return true;
        }
    }

    // *** Collection Methods ***

    /**
     * 返回 ArrayDeque 的元素个数
     */
    public int size() {
        return sub(tail, head, elements.length);
    }

    /**
     * ArrayDeque 是否为空
     */
    public boolean isEmpty() {
        return head == tail;
    }

    /**
     * 返回 ArrayDeque 的顺序迭代器
     */
    public Iterator<E> iterator() {
        return new DeqIterator();
    }

    /**
     * 返回 ArrayDeque 的降序迭代器
     */
    public Iterator<E> descendingIterator() {
        return new DescendingIterator();
    }

    private class DeqIterator implements Iterator<E> {
        /** Index of element to be returned by subsequent call to next. */
        int cursor;

        /** Number of elements yet to be returned. */
        int remaining = size();

        /**
         * Index of element returned by most recent call to next.
         * Reset to -1 if element is deleted by a call to remove.
         */
        int lastRet = -1;

        DeqIterator() { cursor = head; }

        public final boolean hasNext() {
            return remaining > 0;
        }

        public E next() {
            if (remaining <= 0)
                throw new NoSuchElementException();
            final Object[] es = elements;
            E e = nonNullElementAt(es, cursor);
            cursor = inc(lastRet = cursor, es.length);
            remaining--;
            return e;
        }

        void postDelete(boolean leftShifted) {
            if (leftShifted)
                cursor = dec(cursor, elements.length);
        }

        public final void remove() {
            if (lastRet < 0)
                throw new IllegalStateException();
            postDelete(delete(lastRet));
            lastRet = -1;
        }

        public void forEachRemaining(Consumer<? super E> action) {
            Objects.requireNonNull(action);
            int r;
            if ((r = remaining) <= 0)
                return;
            remaining = 0;
            final Object[] es = elements;
            if (es[cursor] == null || sub(tail, cursor, es.length) != r)
                throw new ConcurrentModificationException();
            for (int i = cursor, end = tail, to = (i <= end) ? end : es.length;
                 ; i = 0, to = end) {
                for (; i < to; i++)
                    action.accept(elementAt(es, i));
                if (to == end) {
                    if (end != tail)
                        throw new ConcurrentModificationException();
                    lastRet = dec(end, es.length);
                    break;
                }
            }
        }
    }

    private class DescendingIterator extends DeqIterator {
        DescendingIterator() { cursor = dec(tail, elements.length); }

        public final E next() {
            if (remaining <= 0)
                throw new NoSuchElementException();
            final Object[] es = elements;
            E e = nonNullElementAt(es, cursor);
            cursor = dec(lastRet = cursor, es.length);
            remaining--;
            return e;
        }

        void postDelete(boolean leftShifted) {
            if (!leftShifted)
                cursor = inc(cursor, elements.length);
        }

        public final void forEachRemaining(Consumer<? super E> action) {
            Objects.requireNonNull(action);
            int r;
            if ((r = remaining) <= 0)
                return;
            remaining = 0;
            final Object[] es = elements;
            if (es[cursor] == null || sub(cursor, head, es.length) + 1 != r)
                throw new ConcurrentModificationException();
            for (int i = cursor, end = head, to = (i >= end) ? end : 0;
                 ; i = es.length - 1, to = end) {
                // hotspot generates faster code than for: i >= to !
                for (; i > to - 1; i--)
                    action.accept(elementAt(es, i));
                if (to == end) {
                    if (end != head)
                        throw new ConcurrentModificationException();
                    lastRet = end;
                    break;
                }
            }
        }
    }

    /**
     * 返回后期绑定和快速失败的分割迭代器
     */
    public Spliterator<E> spliterator() {
        return new DeqSpliterator();
    }

    final class DeqSpliterator implements Spliterator<E> {
        private int fence;      // -1 until first use
        private int cursor;     // current index, modified on traverse/split

        /** Constructs late-binding spliterator over all elements. */
        DeqSpliterator() {
            this.fence = -1;
        }

        /** Constructs spliterator over the given range. */
        DeqSpliterator(int origin, int fence) {
            // assert 0 <= origin && origin < elements.length;
            // assert 0 <= fence && fence < elements.length;
            this.cursor = origin;
            this.fence = fence;
        }

        /** Ensures late-binding initialization; then returns fence. */
        private int getFence() { // force initialization
            int t;
            if ((t = fence) < 0) {
                t = fence = tail;
                cursor = head;
            }
            return t;
        }

        public DeqSpliterator trySplit() {
            final Object[] es = elements;
            final int i, n;
            return ((n = sub(getFence(), i = cursor, es.length) >> 1) <= 0)
                ? null
                : new DeqSpliterator(i, cursor = inc(i, n, es.length));
        }

        public void forEachRemaining(Consumer<? super E> action) {
            if (action == null)
                throw new NullPointerException();
            final int end = getFence(), cursor = this.cursor;
            final Object[] es = elements;
            if (cursor != end) {
                this.cursor = end;
                // null check at both ends of range is sufficient
                if (es[cursor] == null || es[dec(end, es.length)] == null)
                    throw new ConcurrentModificationException();
                for (int i = cursor, to = (i <= end) ? end : es.length;
                     ; i = 0, to = end) {
                    for (; i < to; i++)
                        action.accept(elementAt(es, i));
                    if (to == end) break;
                }
            }
        }

        public boolean tryAdvance(Consumer<? super E> action) {
            Objects.requireNonNull(action);
            final Object[] es = elements;
            if (fence < 0) { fence = tail; cursor = head; } // late-binding
            final int i;
            if ((i = cursor) == fence)
                return false;
            E e = nonNullElementAt(es, i);
            cursor = inc(i, es.length);
            action.accept(e);
            return true;
        }

        public long estimateSize() {
            return sub(getFence(), cursor, elements.length);
        }

        public int characteristics() {
            return Spliterator.NONNULL
                | Spliterator.ORDERED
                | Spliterator.SIZED
                | Spliterator.SUBSIZED;
        }
    }

    /**
     * 顺序消费 ArrayDeque 中的每个元素
     */
    public void forEach(Consumer<? super E> action) {
        Objects.requireNonNull(action);
        final Object[] es = elements;
        for (int i = head, end = tail, to = (i <= end) ? end : es.length;
             ; i = 0, to = end) {
            for (; i < to; i++)
                action.accept(elementAt(es, i));
            if (to == end) {
                if (end != tail) throw new ConcurrentModificationException();
                break;
            }
        }
    }

    /**
     * 根据函数式断言移除满足条件的所有元素
     */
    public boolean removeIf(Predicate<? super E> filter) {
        Objects.requireNonNull(filter);
        return bulkRemove(filter);
    }

    /**
     * 移除 ArrayDeque 包含在集合 c 中的所有元素，集合差集
     */
    public boolean removeAll(Collection<?> c) {
        Objects.requireNonNull(c);
        return bulkRemove(e -> c.contains(e));
    }

    /**
     * 保留 ArrayDeque 包含在集合 c 中的所有元素，集合交集
     */
    public boolean retainAll(Collection<?> c) {
        Objects.requireNonNull(c);
        return bulkRemove(e -> !c.contains(e));
    }

    private boolean bulkRemove(Predicate<? super E> filter) {
        final Object[] es = elements;
        // Optimize for initial run of survivors
        for (int i = head, end = tail, to = (i <= end) ? end : es.length;
             ; i = 0, to = end) {
            for (; i < to; i++)
                if (filter.test(elementAt(es, i)))
                    return bulkRemoveModified(filter, i);
            if (to == end) {
                if (end != tail) throw new ConcurrentModificationException();
                break;
            }
        }
        return false;
    }

    // A tiny bit set implementation
    private static long[] nBits(int n) {
        return new long[((n - 1) >> 6) + 1];
    }
    private static void setBit(long[] bits, int i) {
        bits[i >> 6] |= 1L << i;
    }
    private static boolean isClear(long[] bits, int i) {
        return (bits[i >> 6] & (1L << i)) == 0;
    }

    /**
     * Helper for bulkRemove, in case of at least one deletion.
     * Tolerate predicates that reentrantly access the collection for
     * read (but writers still get CME), so traverse once to find
     * elements to delete, a second pass to physically expunge.
     *
     * @param beg valid index of first element to be deleted
     */
    private boolean bulkRemoveModified(
        Predicate<? super E> filter, final int beg) {
        final Object[] es = elements;
        final int capacity = es.length;
        final int end = tail;
        final long[] deathRow = nBits(sub(end, beg, capacity));
        deathRow[0] = 1L;   // set bit 0
        for (int i = beg + 1, to = (i <= end) ? end : es.length, k = beg;
             ; i = 0, to = end, k -= capacity) {
            for (; i < to; i++)
                if (filter.test(elementAt(es, i)))
                    setBit(deathRow, i - k);
            if (to == end) break;
        }
        // a two-finger traversal, with hare i reading, tortoise w writing
        int w = beg;
        for (int i = beg + 1, to = (i <= end) ? end : es.length, k = beg;
             ; w = 0) { // w rejoins i on second leg
            // In this loop, i and w are on the same leg, with i > w
            for (; i < to; i++)
                if (isClear(deathRow, i - k))
                    es[w++] = es[i];
            if (to == end) break;
            // In this loop, w is on the first leg, i on the second
            for (i = 0, to = end, k -= capacity; i < to && w < capacity; i++)
                if (isClear(deathRow, i - k))
                    es[w++] = es[i];
            if (i >= to) {
                if (w == capacity) w = 0; // "corner" case
                break;
            }
        }
        if (end != tail) throw new ConcurrentModificationException();
        circularClear(es, tail = w, end);
        return true;
    }

    /**
     * ArrayDeque 是否包含目标元素
     */
    public boolean contains(Object o) {
        if (o != null) {
            final Object[] es = elements;
            for (int i = head, end = tail, to = (i <= end) ? end : es.length;
                 ; i = 0, to = end) {
                for (; i < to; i++)
                    if (o.equals(es[i]))
                        return true;
                if (to == end) break;
            }
        }
        return false;
    }

    /**
     * 移除在 ArrayDeque 中第一次匹配形参的目标元素
     */
    public boolean remove(Object o) {
        return removeFirstOccurrence(o);
    }

    /**
     * 清空 ArrayDeque，head 和 tail 指针都置为 0
     */
    public void clear() {
        circularClear(elements, head, tail);
        head = tail = 0;
    }

    /**
     * Nulls out slots starting at array index i, upto index end.
     * Condition i == end means "empty" - nothing to do.
     */
    private static void circularClear(Object[] es, int i, int end) {
        // assert 0 <= i && i < es.length;
        // assert 0 <= end && end < es.length;
        for (int to = (i <= end) ? end : es.length;
             ; i = 0, to = end) {
            for (; i < to; i++) es[i] = null;
            if (to == end) break;
        }
    }

    /**
     * 返回包含 ArrayDeque 所有元素的对象数组
     */
    public Object[] toArray() {
        return toArray(Object[].class);
    }

    private <T> T[] toArray(Class<T[]> klazz) {
        final Object[] es = elements;
        final T[] a;
        final int head = this.head, tail = this.tail, end;
        if ((end = tail + ((head <= tail) ? 0 : es.length)) >= 0) {
            // Uses null extension feature of copyOfRange
            a = Arrays.copyOfRange(es, head, end, klazz);
        } else {
            // integer overflow!
            a = Arrays.copyOfRange(es, 0, end - head, klazz);
            System.arraycopy(es, head, a, 0, es.length - head);
        }
        if (end != tail)
            System.arraycopy(es, 0, a, es.length - head, tail);
        return a;
    }

    @SuppressWarnings("unchecked")
    public <T> T[] toArray(T[] a) {
        final int size;
        if ((size = size()) > a.length)
            return toArray((Class<T[]>) a.getClass());
        final Object[] es = elements;
        for (int i = head, j = 0, len = Math.min(size, es.length - i);
             ; i = 0, len = tail) {
            System.arraycopy(es, i, a, j, len);
            if ((j += len) == size) break;
        }
        if (size < a.length)
            a[size] = null;
        return a;
    }

    // *** Object methods ***
    /**
     * Returns a copy of this deque.
     */
    public ArrayDeque<E> clone() {
        try {
            @SuppressWarnings("unchecked")
            ArrayDeque<E> result = (ArrayDeque<E>) super.clone();
            result.elements = Arrays.copyOf(elements, elements.length);
            return result;
        } catch (CloneNotSupportedException e) {
            throw new AssertionError();
        }
    }

    private static final long serialVersionUID = 2340985798034038923L;

    /**
     * Saves this deque to a stream (that is, serializes it).
     */
    private void writeObject(java.io.ObjectOutputStream s)
            throws java.io.IOException {
        s.defaultWriteObject();

        // Write out size
        s.writeInt(size());

        // Write out elements in order.
        final Object[] es = elements;
        for (int i = head, end = tail, to = (i <= end) ? end : es.length;
             ; i = 0, to = end) {
            for (; i < to; i++)
                s.writeObject(es[i]);
            if (to == end) break;
        }
    }

    /**
     * Reconstitutes this deque from a stream (that is, deserializes it).
     */
    private void readObject(java.io.ObjectInputStream s)
            throws java.io.IOException, ClassNotFoundException {
        s.defaultReadObject();

        // Read in size and allocate array
        int size = s.readInt();
        SharedSecrets.getJavaObjectInputStreamAccess().checkArray(s, Object[].class, size + 1);
        elements = new Object[size + 1];
        this.tail = size;

        // Read in all elements in the proper order.
        for (int i = 0; i < size; i++)
            elements[i] = s.readObject();
    }

    /** debugging */
    void checkInvariants() {
        // Use head and tail fields with empty slot at tail strategy.
        // head == tail disambiguates to "empty".
        try {
            int capacity = elements.length;
            // assert 0 <= head && head < capacity;
            // assert 0 <= tail && tail < capacity;
            // assert capacity > 0;
            // assert size() < capacity;
            // assert head == tail || elements[head] != null;
            // assert elements[tail] == null;
            // assert head == tail || elements[dec(tail, capacity)] != null;
        } catch (Throwable t) {
            System.err.printf("head=%d tail=%d capacity=%d%n",
                              head, tail, elements.length);
            System.err.printf("elements=%s%n",
                              Arrays.toString(elements));
            throw t;
        }
    }
}