Java多线程系列--“JUC集合”05之 ConcurrentSkipListMap

概要

本章对Java.util.concurrent包中的ConcurrentSkipListMap类进行详细的介绍。内容包括:
ConcurrentSkipListMap介绍
ConcurrentSkipListMap原理和数据结构
ConcurrentSkipListMap函数列表
ConcurrentSkipListMap源码分析(JDK1.7.0_40版本)
ConcurrentSkipListMap示例

转载请注明出处:http://www.cnblogs.com/skywang12345/p/3498556.html

 

ConcurrentSkipListMap介绍

ConcurrentSkipListMap是线程安全的有序的哈希表,适用于高并发的场景。
ConcurrentSkipListMap和TreeMap,它们虽然都是有序的哈希表。但是,第一,它们的线程安全机制不同,TreeMap是非线程安全的,而ConcurrentSkipListMap是线程安全的。第二,ConcurrentSkipListMap是通过跳表实现的,而TreeMap是通过红黑树实现的。
关于跳表(Skip List),它是平衡树的一种替代的数据结构,但是和红黑树不相同的是,跳表对于树的平衡的实现是基于一种随机化的算法的,这样也就是说跳表的插入和删除的工作是比较简单的。

 

ConcurrentSkipListMap原理和数据结构

ConcurrentSkipListMap的数据结构,如下图所示:

说明

先以数据“7,14,21,32,37,71,85”序列为例,来对跳表进行简单说明。

跳表分为许多层(level),每一层都可以看作是数据的索引,这些索引的意义就是加快跳表查找数据速度。每一层的数据都是有序的,上一层数据是下一层数据的子集,并且第一层(level 1)包含了全部的数据;层次越高,跳跃性越大,包含的数据越少。
跳表包含一个表头,它查找数据时,是从上往下,从左往右进行查找。现在“需要找出值为32的节点”为例,来对比说明跳表和普遍的链表。

情况1:链表中查找“32”节点
路径如下图1-02所示:

需要4步(红色部分表示路径)。

 

情况2:跳表中查找“32”节点
路径如下图1-03所示:

忽略索引垂直线路上路径的情况下,只需要2步(红色部分表示路径)。


下面说说Java中ConcurrentSkipListMap的数据结构。
(01) ConcurrentSkipListMap继承于AbstractMap类,也就意味着它是一个哈希表。
(02) Index是ConcurrentSkipListMap的内部类,它与“跳表中的索引相对应”。HeadIndex继承于Index,ConcurrentSkipListMap中含有一个HeadIndex的对象head,head是“跳表的表头”。
(03) Index是跳表中的索引,它包含“右索引的指针(right)”,“下索引的指针(down)”和“哈希表节点node”。node是Node的对象,Node也是ConcurrentSkipListMap中的内部类。

 

ConcurrentSkipListMap函数列表

// 构造一个新的空映射,该映射按照键的自然顺序进行排序。
ConcurrentSkipListMap()
// 构造一个新的空映射,该映射按照指定的比较器进行排序。
ConcurrentSkipListMap(Comparator<? super K> comparator)
// 构造一个新映射,该映射所包含的映射关系与给定映射包含的映射关系相同,并按照键的自然顺序进行排序。
ConcurrentSkipListMap(Map<? extends K,? extends V> m)
// 构造一个新映射,该映射所包含的映射关系与指定的有序映射包含的映射关系相同,使用的顺序也相同。
ConcurrentSkipListMap(SortedMap<K,? extends V> m)

// 返回与大于等于给定键的最小键关联的键-值映射关系;如果不存在这样的条目,则返回 null。
Map.Entry<K,V> ceilingEntry(K key)
// 返回大于等于给定键的最小键;如果不存在这样的键,则返回 null。
K ceilingKey(K key)
// 从此映射中移除所有映射关系。
void clear()
// 返回此 ConcurrentSkipListMap 实例的浅表副本。
ConcurrentSkipListMap<K,V> clone()
// 返回对此映射中的键进行排序的比较器;如果此映射使用键的自然顺序,则返回 null。
Comparator<? super K> comparator()
// 如果此映射包含指定键的映射关系,则返回 true。
boolean containsKey(Object key)
// 如果此映射为指定值映射一个或多个键,则返回 true。
boolean containsValue(Object value)
// 返回此映射中所包含键的逆序 NavigableSet 视图。
NavigableSet<K> descendingKeySet()
// 返回此映射中所包含映射关系的逆序视图。
ConcurrentNavigableMap<K,V> descendingMap()
// 返回此映射中所包含的映射关系的 Set 视图。
Set<Map.Entry<K,V>> entrySet()
// 比较指定对象与此映射的相等性。
boolean equals(Object o)
// 返回与此映射中的最小键关联的键-值映射关系;如果该映射为空,则返回 null。
Map.Entry<K,V> firstEntry()
// 返回此映射中当前第一个(最低)键。
K firstKey()
// 返回与小于等于给定键的最大键关联的键-值映射关系;如果不存在这样的键,则返回 null。
Map.Entry<K,V> floorEntry(K key)
// 返回小于等于给定键的最大键;如果不存在这样的键,则返回 null。
K floorKey(K key)
// 返回指定键所映射到的值;如果此映射不包含该键的映射关系,则返回 null。
V get(Object key)
// 返回此映射的部分视图,其键值严格小于 toKey。
ConcurrentNavigableMap<K,V> headMap(K toKey)
// 返回此映射的部分视图,其键小于(或等于,如果 inclusive 为 true)toKey。
ConcurrentNavigableMap<K,V> headMap(K toKey, boolean inclusive)
// 返回与严格大于给定键的最小键关联的键-值映射关系;如果不存在这样的键,则返回 null。
Map.Entry<K,V> higherEntry(K key)
// 返回严格大于给定键的最小键;如果不存在这样的键,则返回 null。
K higherKey(K key)
// 如果此映射未包含键-值映射关系,则返回 true。
boolean isEmpty()
// 返回此映射中所包含键的 NavigableSet 视图。
NavigableSet<K> keySet()
// 返回与此映射中的最大键关联的键-值映射关系;如果该映射为空,则返回 null。
Map.Entry<K,V> lastEntry()
// 返回映射中当前最后一个(最高)键。
K lastKey()
// 返回与严格小于给定键的最大键关联的键-值映射关系;如果不存在这样的键,则返回 null。
Map.Entry<K,V> lowerEntry(K key)
// 返回严格小于给定键的最大键;如果不存在这样的键,则返回 null。
K lowerKey(K key)
// 返回此映射中所包含键的 NavigableSet 视图。
NavigableSet<K> navigableKeySet()
// 移除并返回与此映射中的最小键关联的键-值映射关系;如果该映射为空,则返回 null。
Map.Entry<K,V> pollFirstEntry()
// 移除并返回与此映射中的最大键关联的键-值映射关系;如果该映射为空,则返回 null。
Map.Entry<K,V> pollLastEntry()
// 将指定值与此映射中的指定键关联。
V put(K key, V value)
// 如果指定键已经不再与某个值相关联,则将它与给定值关联。
V putIfAbsent(K key, V value)
// 从此映射中移除指定键的映射关系(如果存在)。
V remove(Object key)
// 只有目前将键的条目映射到给定值时,才移除该键的条目。
boolean remove(Object key, Object value)
// 只有目前将键的条目映射到某一值时,才替换该键的条目。
V replace(K key, V value)
// 只有目前将键的条目映射到给定值时,才替换该键的条目。
boolean replace(K key, V oldValue, V newValue)
// 返回此映射中的键-值映射关系数。
int size()
// 返回此映射的部分视图,其键的范围从 fromKey 到 toKey。
ConcurrentNavigableMap<K,V> subMap(K fromKey, boolean fromInclusive, K toKey, boolean toInclusive)
// 返回此映射的部分视图,其键值的范围从 fromKey(包括)到 toKey(不包括)。
ConcurrentNavigableMap<K,V> subMap(K fromKey, K toKey)
// 返回此映射的部分视图,其键大于等于 fromKey。
ConcurrentNavigableMap<K,V> tailMap(K fromKey)
// 返回此映射的部分视图,其键大于(或等于,如果 inclusive 为 true)fromKey。
ConcurrentNavigableMap<K,V> tailMap(K fromKey, boolean inclusive)
// 返回此映射中所包含值的 Collection 视图。
Collection<V> values()

 

ConcurrentSkipListMap源码分析(JDK1.7.0_40版本)

ConcurrentSkipListMap.java的完整源码如下:

/*
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
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 *
 *
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 */

/*
 *
 *
 *
 *
 *
 * Written by Doug Lea with assistance from members of JCP JSR-166
 * Expert Group and released to the public domain, as explained at
 * http://creativecommons.org/publicdomain/zero/1.0/
 */

package java.util.concurrent;
import java.util.*;
import java.util.concurrent.atomic.*;

/**
 * A scalable concurrent {@link ConcurrentNavigableMap} implementation.
 * The map is sorted according to the {@linkplain Comparable natural
 * ordering} of its keys, or by a {@link Comparator} provided at map
 * creation time, depending on which constructor is used.
 *
 * <p>This class implements a concurrent variant of <a
 * href="http://en.wikipedia.org/wiki/Skip_list" target="_top">SkipLists</a>
 * providing expected average <i>log(n)</i> time cost for the
 * <tt>containsKey</tt>, <tt>get</tt>, <tt>put</tt> and
 * <tt>remove</tt> operations and their variants.  Insertion, removal,
 * update, and access operations safely execute concurrently by
 * multiple threads.  Iterators are <i>weakly consistent</i>, returning
 * elements reflecting the state of the map at some point at or since
 * the creation of the iterator.  They do <em>not</em> throw {@link
 * ConcurrentModificationException}, and may proceed concurrently with
 * other operations. Ascending key ordered views and their iterators
 * are faster than descending ones.
 *
 * <p>All <tt>Map.Entry</tt> pairs returned by methods in this class
 * and its views represent snapshots of mappings at the time they were
 * produced. They do <em>not</em> support the <tt>Entry.setValue</tt>
 * method. (Note however that it is possible to change mappings in the
 * associated map using <tt>put</tt>, <tt>putIfAbsent</tt>, or
 * <tt>replace</tt>, depending on exactly which effect you need.)
 *
 * <p>Beware that, unlike in most collections, the <tt>size</tt>
 * method is <em>not</em> a constant-time operation. Because of the
 * asynchronous nature of these maps, determining the current number
 * of elements requires a traversal of the elements, and so may report
 * inaccurate results if this collection is modified during traversal.
 * Additionally, the bulk operations <tt>putAll</tt>, <tt>equals</tt>,
 * <tt>toArray</tt>, <tt>containsValue</tt>, and <tt>clear</tt> are
 * <em>not</em> guaranteed to be performed atomically. For example, an
 * iterator operating concurrently with a <tt>putAll</tt> operation
 * might view only some of the added elements.
 *
 * <p>This class and its views and iterators implement all of the
 * <em>optional</em> methods of the {@link Map} and {@link Iterator}
 * interfaces. Like most other concurrent collections, this class does
 * <em>not</em> permit the use of <tt>null</tt> keys or values because some
 * null return values cannot be reliably distinguished from the absence of
 * elements.
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/../technotes/guides/collections/index.html">
 * Java Collections Framework</a>.
 *
 * @author Doug Lea
 * @param <K> the type of keys maintained by this map
 * @param <V> the type of mapped values
 * @since 1.6
 */
public class ConcurrentSkipListMap<K,V> extends AbstractMap<K,V>
    implements ConcurrentNavigableMap<K,V>,
               Cloneable,
               java.io.Serializable {
    /*
     * This class implements a tree-like two-dimensionally linked skip
     * list in which the index levels are represented in separate
     * nodes from the base nodes holding data.  There are two reasons
     * for taking this approach instead of the usual array-based
     * structure: 1) Array based implementations seem to encounter
     * more complexity and overhead 2) We can use cheaper algorithms
     * for the heavily-traversed index lists than can be used for the
     * base lists.  Here's a picture of some of the basics for a
     * possible list with 2 levels of index:
     *
     * Head nodes          Index nodes
     * +-+    right        +-+                      +-+
     * |2|---------------->| |--------------------->| |->null
     * +-+                 +-+                      +-+
     *  | down              |                        |
     *  v                   v                        v
     * +-+            +-+  +-+       +-+            +-+       +-+
     * |1|----------->| |->| |------>| |----------->| |------>| |->null
     * +-+            +-+  +-+       +-+            +-+       +-+
     *  v              |    |         |              |         |
     * Nodes  next     v    v         v              v         v
     * +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+
     * | |->|A|->|B|->|C|->|D|->|E|->|F|->|G|->|H|->|I|->|J|->|K|->null
     * +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+  +-+
     *
     * The base lists use a variant of the HM linked ordered set
     * algorithm. See Tim Harris, "A pragmatic implementation of
     * non-blocking linked lists"
     * http://www.cl.cam.ac.uk/~tlh20/publications.html and Maged
     * Michael "High Performance Dynamic Lock-Free Hash Tables and
     * List-Based Sets"
     * http://www.research.ibm.com/people/m/michael/pubs.htm.  The
     * basic idea in these lists is to mark the "next" pointers of
     * deleted nodes when deleting to avoid conflicts with concurrent
     * insertions, and when traversing to keep track of triples
     * (predecessor, node, successor) in order to detect when and how
     * to unlink these deleted nodes.
     *
     * Rather than using mark-bits to mark list deletions (which can
     * be slow and space-intensive using AtomicMarkedReference), nodes
     * use direct CAS'able next pointers.  On deletion, instead of
     * marking a pointer, they splice in another node that can be
     * thought of as standing for a marked pointer (indicating this by
     * using otherwise impossible field values).  Using plain nodes
     * acts roughly like "boxed" implementations of marked pointers,
     * but uses new nodes only when nodes are deleted, not for every
     * link.  This requires less space and supports faster
     * traversal. Even if marked references were better supported by
     * JVMs, traversal using this technique might still be faster
     * because any search need only read ahead one more node than
     * otherwise required (to check for trailing marker) rather than
     * unmasking mark bits or whatever on each read.
     *
     * This approach maintains the essential property needed in the HM
     * algorithm of changing the next-pointer of a deleted node so
     * that any other CAS of it will fail, but implements the idea by
     * changing the pointer to point to a different node, not by
     * marking it.  While it would be possible to further squeeze
     * space by defining marker nodes not to have key/value fields, it
     * isn't worth the extra type-testing overhead.  The deletion
     * markers are rarely encountered during traversal and are
     * normally quickly garbage collected. (Note that this technique
     * would not work well in systems without garbage collection.)
     *
     * In addition to using deletion markers, the lists also use
     * nullness of value fields to indicate deletion, in a style
     * similar to typical lazy-deletion schemes.  If a node's value is
     * null, then it is considered logically deleted and ignored even
     * though it is still reachable. This maintains proper control of
     * concurrent replace vs delete operations -- an attempted replace
     * must fail if a delete beat it by nulling field, and a delete
     * must return the last non-null value held in the field. (Note:
     * Null, rather than some special marker, is used for value fields
     * here because it just so happens to mesh with the Map API
     * requirement that method get returns null if there is no
     * mapping, which allows nodes to remain concurrently readable
     * even when deleted. Using any other marker value here would be
     * messy at best.)
     *
     * Here's the sequence of events for a deletion of node n with
     * predecessor b and successor f, initially:
     *
     *        +------+       +------+      +------+
     *   ...  |   b  |------>|   n  |----->|   f  | ...
     *        +------+       +------+      +------+
     *
     * 1. CAS n's value field from non-null to null.
     *    From this point on, no public operations encountering
     *    the node consider this mapping to exist. However, other
     *    ongoing insertions and deletions might still modify
     *    n's next pointer.
     *
     * 2. CAS n's next pointer to point to a new marker node.
     *    From this point on, no other nodes can be appended to n.
     *    which avoids deletion errors in CAS-based linked lists.
     *
     *        +------+       +------+      +------+       +------+
     *   ...  |   b  |------>|   n  |----->|marker|------>|   f  | ...
     *        +------+       +------+      +------+       +------+
     *
     * 3. CAS b's next pointer over both n and its marker.
     *    From this point on, no new traversals will encounter n,
     *    and it can eventually be GCed.
     *        +------+                                    +------+
     *   ...  |   b  |----------------------------------->|   f  | ...
     *        +------+                                    +------+
     *
     * A failure at step 1 leads to simple retry due to a lost race
     * with another operation. Steps 2-3 can fail because some other
     * thread noticed during a traversal a node with null value and
     * helped out by marking and/or unlinking.  This helping-out
     * ensures that no thread can become stuck waiting for progress of
     * the deleting thread.  The use of marker nodes slightly
     * complicates helping-out code because traversals must track
     * consistent reads of up to four nodes (b, n, marker, f), not
     * just (b, n, f), although the next field of a marker is
     * immutable, and once a next field is CAS'ed to point to a
     * marker, it never again changes, so this requires less care.
     *
     * Skip lists add indexing to this scheme, so that the base-level
     * traversals start close to the locations being found, inserted
     * or deleted -- usually base level traversals only traverse a few
     * nodes. This doesn't change the basic algorithm except for the
     * need to make sure base traversals start at predecessors (here,
     * b) that are not (structurally) deleted, otherwise retrying
     * after processing the deletion.
     *
     * Index levels are maintained as lists with volatile next fields,
     * using CAS to link and unlink.  Races are allowed in index-list
     * operations that can (rarely) fail to link in a new index node
     * or delete one. (We can't do this of course for data nodes.)
     * However, even when this happens, the index lists remain sorted,
     * so correctly serve as indices.  This can impact performance,
     * but since skip lists are probabilistic anyway, the net result
     * is that under contention, the effective "p" value may be lower
     * than its nominal value. And race windows are kept small enough
     * that in practice these failures are rare, even under a lot of
     * contention.
     *
     * The fact that retries (for both base and index lists) are
     * relatively cheap due to indexing allows some minor
     * simplifications of retry logic. Traversal restarts are
     * performed after most "helping-out" CASes. This isn't always
     * strictly necessary, but the implicit backoffs tend to help
     * reduce other downstream failed CAS's enough to outweigh restart
     * cost.  This worsens the worst case, but seems to improve even
     * highly contended cases.
     *
     * Unlike most skip-list implementations, index insertion and
     * deletion here require a separate traversal pass occuring after
     * the base-level action, to add or remove index nodes.  This adds
     * to single-threaded overhead, but improves contended
     * multithreaded performance by narrowing interference windows,
     * and allows deletion to ensure that all index nodes will be made
     * unreachable upon return from a public remove operation, thus
     * avoiding unwanted garbage retention. This is more important
     * here than in some other data structures because we cannot null
     * out node fields referencing user keys since they might still be
     * read by other ongoing traversals.
     *
     * Indexing uses skip list parameters that maintain good search
     * performance while using sparser-than-usual indices: The
     * hardwired parameters k=1, p=0.5 (see method randomLevel) mean
     * that about one-quarter of the nodes have indices. Of those that
     * do, half have one level, a quarter have two, and so on (see
     * Pugh's Skip List Cookbook, sec 3.4).  The expected total space
     * requirement for a map is slightly less than for the current
     * implementation of java.util.TreeMap.
     *
     * Changing the level of the index (i.e, the height of the
     * tree-like structure) also uses CAS. The head index has initial
     * level/height of one. Creation of an index with height greater
     * than the current level adds a level to the head index by
     * CAS'ing on a new top-most head. To maintain good performance
     * after a lot of removals, deletion methods heuristically try to
     * reduce the height if the topmost levels appear to be empty.
     * This may encounter races in which it possible (but rare) to
     * reduce and "lose" a level just as it is about to contain an
     * index (that will then never be encountered). This does no
     * structural harm, and in practice appears to be a better option
     * than allowing unrestrained growth of levels.
     *
     * The code for all this is more verbose than you'd like. Most
     * operations entail locating an element (or position to insert an
     * element). The code to do this can't be nicely factored out
     * because subsequent uses require a snapshot of predecessor
     * and/or successor and/or value fields which can't be returned
     * all at once, at least not without creating yet another object
     * to hold them -- creating such little objects is an especially
     * bad idea for basic internal search operations because it adds
     * to GC overhead.  (This is one of the few times I've wished Java
     * had macros.) Instead, some traversal code is interleaved within
     * insertion and removal operations.  The control logic to handle
     * all the retry conditions is sometimes twisty. Most search is
     * broken into 2 parts. findPredecessor() searches index nodes
     * only, returning a base-level predecessor of the key. findNode()
     * finishes out the base-level search. Even with this factoring,
     * there is a fair amount of near-duplication of code to handle
     * variants.
     *
     * For explanation of algorithms sharing at least a couple of
     * features with this one, see Mikhail Fomitchev's thesis
     * (http://www.cs.yorku.ca/~mikhail/), Keir Fraser's thesis
     * (http://www.cl.cam.ac.uk/users/kaf24/), and Hakan Sundell's
     * thesis (http://www.cs.chalmers.se/~phs/).
     *
     * Given the use of tree-like index nodes, you might wonder why
     * this doesn't use some kind of search tree instead, which would
     * support somewhat faster search operations. The reason is that
     * there are no known efficient lock-free insertion and deletion
     * algorithms for search trees. The immutability of the "down"
     * links of index nodes (as opposed to mutable "left" fields in
     * true trees) makes this tractable using only CAS operations.
     *
     * Notation guide for local variables
     * Node:         b, n, f    for  predecessor, node, successor
     * Index:        q, r, d    for index node, right, down.
     *               t          for another index node
     * Head:         h
     * Levels:       j
     * Keys:         k, key
     * Values:       v, value
     * Comparisons:  c
     */

    private static final long serialVersionUID = -8627078645895051609L;

    /**
     * Generates the initial random seed for the cheaper per-instance
     * random number generators used in randomLevel.
     */
    private static final Random seedGenerator = new Random();

    /**
     * Special value used to identify base-level header
     */
    private static final Object BASE_HEADER = new Object();

    /**
     * The topmost head index of the skiplist.
     */
    private transient volatile HeadIndex<K,V> head;

    /**
     * The comparator used to maintain order in this map, or null
     * if using natural ordering.
     * @serial
     */
    private final Comparator<? super K> comparator;

    /**
     * Seed for simple random number generator.  Not volatile since it
     * doesn't matter too much if different threads don't see updates.
     */
    private transient int randomSeed;

    /** Lazily initialized key set */
    private transient KeySet keySet;
    /** Lazily initialized entry set */
    private transient EntrySet entrySet;
    /** Lazily initialized values collection */
    private transient Values values;
    /** Lazily initialized descending key set */
    private transient ConcurrentNavigableMap<K,V> descendingMap;

    /**
     * Initializes or resets state. Needed by constructors, clone,
     * clear, readObject. and ConcurrentSkipListSet.clone.
     * (Note that comparator must be separately initialized.)
     */
    final void initialize() {
        keySet = null;
        entrySet = null;
        values = null;
        descendingMap = null;
        randomSeed = seedGenerator.nextInt() | 0x0100; // ensure nonzero
        head = new HeadIndex<K,V>(new Node<K,V>(null, BASE_HEADER, null),
                                  null, null, 1);
    }

    /**
     * compareAndSet head node
     */
    private boolean casHead(HeadIndex<K,V> cmp, HeadIndex<K,V> val) {
        return UNSAFE.compareAndSwapObject(this, headOffset, cmp, val);
    }

    /* ---------------- Nodes -------------- */

    /**
     * Nodes hold keys and values, and are singly linked in sorted
     * order, possibly with some intervening marker nodes. The list is
     * headed by a dummy node accessible as head.node. The value field
     * is declared only as Object because it takes special non-V
     * values for marker and header nodes.
     */
    static final class Node<K,V> {
        final K key;
        volatile Object value;
        volatile Node<K,V> next;

        /**
         * Creates a new regular node.
         */
        Node(K key, Object value, Node<K,V> next) {
            this.key = key;
            this.value = value;
            this.next = next;
        }

        /**
         * Creates a new marker node. A marker is distinguished by
         * having its value field point to itself.  Marker nodes also
         * have null keys, a fact that is exploited in a few places,
         * but this doesn't distinguish markers from the base-level
         * header node (head.node), which also has a null key.
         */
        Node(Node<K,V> next) {
            this.key = null;
            this.value = this;
            this.next = next;
        }

        /**
         * compareAndSet value field
         */
        boolean casValue(Object cmp, Object val) {
            return UNSAFE.compareAndSwapObject(this, valueOffset, cmp, val);
        }

        /**
         * compareAndSet next field
         */
        boolean casNext(Node<K,V> cmp, Node<K,V> val) {
            return UNSAFE.compareAndSwapObject(this, nextOffset, cmp, val);
        }

        /**
         * Returns true if this node is a marker. This method isn't
         * actually called in any current code checking for markers
         * because callers will have already read value field and need
         * to use that read (not another done here) and so directly
         * test if value points to node.
         * @param n a possibly null reference to a node
         * @return true if this node is a marker node
         */
        boolean isMarker() {
            return value == this;
        }

        /**
         * Returns true if this node is the header of base-level list.
         * @return true if this node is header node
         */
        boolean isBaseHeader() {
            return value == BASE_HEADER;
        }

        /**
         * Tries to append a deletion marker to this node.
         * @param f the assumed current successor of this node
         * @return true if successful
         */
        boolean appendMarker(Node<K,V> f) {
            return casNext(f, new Node<K,V>(f));
        }

        /**
         * Helps out a deletion by appending marker or unlinking from
         * predecessor. This is called during traversals when value
         * field seen to be null.
         * @param b predecessor
         * @param f successor
         */
        void helpDelete(Node<K,V> b, Node<K,V> f) {
            /*
             * Rechecking links and then doing only one of the
             * help-out stages per call tends to minimize CAS
             * interference among helping threads.
             */
            if (f == next && this == b.next) {
                if (f == null || f.value != f) // not already marked
                    appendMarker(f);
                else
                    b.casNext(this, f.next);
            }
        }

        /**
         * Returns value if this node contains a valid key-value pair,
         * else null.
         * @return this node's value if it isn't a marker or header or
         * is deleted, else null.
         */
        V getValidValue() {
            Object v = value;
            if (v == this || v == BASE_HEADER)
                return null;
            return (V)v;
        }

        /**
         * Creates and returns a new SimpleImmutableEntry holding current
         * mapping if this node holds a valid value, else null.
         * @return new entry or null
         */
        AbstractMap.SimpleImmutableEntry<K,V> createSnapshot() {
            V v = getValidValue();
            if (v == null)
                return null;
            return new AbstractMap.SimpleImmutableEntry<K,V>(key, v);
        }

        // UNSAFE mechanics

        private static final sun.misc.Unsafe UNSAFE;
        private static final long valueOffset;
        private static final long nextOffset;

        static {
            try {
                UNSAFE = sun.misc.Unsafe.getUnsafe();
                Class k = Node.class;
                valueOffset = UNSAFE.objectFieldOffset
                    (k.getDeclaredField("value"));
                nextOffset = UNSAFE.objectFieldOffset
                    (k.getDeclaredField("next"));
            } catch (Exception e) {
                throw new Error(e);
            }
        }
    }

    /* ---------------- Indexing -------------- */

    /**
     * Index nodes represent the levels of the skip list.  Note that
     * even though both Nodes and Indexes have forward-pointing
     * fields, they have different types and are handled in different
     * ways, that can't nicely be captured by placing field in a
     * shared abstract class.
     */
    static class Index<K,V> {
        final Node<K,V> node;
        final Index<K,V> down;
        volatile Index<K,V> right;

        /**
         * Creates index node with given values.
         */
        Index(Node<K,V> node, Index<K,V> down, Index<K,V> right) {
            this.node = node;
            this.down = down;
            this.right = right;
        }

        /**
         * compareAndSet right field
         */
        final boolean casRight(Index<K,V> cmp, Index<K,V> val) {
            return UNSAFE.compareAndSwapObject(this, rightOffset, cmp, val);
        }

        /**
         * Returns true if the node this indexes has been deleted.
         * @return true if indexed node is known to be deleted
         */
        final boolean indexesDeletedNode() {
            return node.value == null;
        }

        /**
         * Tries to CAS newSucc as successor.  To minimize races with
         * unlink that may lose this index node, if the node being
         * indexed is known to be deleted, it doesn't try to link in.
         * @param succ the expected current successor
         * @param newSucc the new successor
         * @return true if successful
         */
        final boolean link(Index<K,V> succ, Index<K,V> newSucc) {
            Node<K,V> n = node;
            newSucc.right = succ;
            return n.value != null && casRight(succ, newSucc);
        }

        /**
         * Tries to CAS right field to skip over apparent successor
         * succ.  Fails (forcing a retraversal by caller) if this node
         * is known to be deleted.
         * @param succ the expected current successor
         * @return true if successful
         */
        final boolean unlink(Index<K,V> succ) {
            return !indexesDeletedNode() && casRight(succ, succ.right);
        }

        // Unsafe mechanics
        private static final sun.misc.Unsafe UNSAFE;
        private static final long rightOffset;
        static {
            try {
                UNSAFE = sun.misc.Unsafe.getUnsafe();
                Class k = Index.class;
                rightOffset = UNSAFE.objectFieldOffset
                    (k.getDeclaredField("right"));
            } catch (Exception e) {
                throw new Error(e);
            }
        }
    }

    /* ---------------- Head nodes -------------- */

    /**
     * Nodes heading each level keep track of their level.
     */
    static final class HeadIndex<K,V> extends Index<K,V> {
        final int level;
        HeadIndex(Node<K,V> node, Index<K,V> down, Index<K,V> right, int level) {
            super(node, down, right);
            this.level = level;
        }
    }

    /* ---------------- Comparison utilities -------------- */

    /**
     * Represents a key with a comparator as a Comparable.
     *
     * Because most sorted collections seem to use natural ordering on
     * Comparables (Strings, Integers, etc), most internal methods are
     * geared to use them. This is generally faster than checking
     * per-comparison whether to use comparator or comparable because
     * it doesn't require a (Comparable) cast for each comparison.
     * (Optimizers can only sometimes remove such redundant checks
     * themselves.) When Comparators are used,
     * ComparableUsingComparators are created so that they act in the
     * same way as natural orderings. This penalizes use of
     * Comparators vs Comparables, which seems like the right
     * tradeoff.
     */
    static final class ComparableUsingComparator<K> implements Comparable<K> {
        final K actualKey;
        final Comparator<? super K> cmp;
        ComparableUsingComparator(K key, Comparator<? super K> cmp) {
            this.actualKey = key;
            this.cmp = cmp;
        }
        public int compareTo(K k2) {
            return cmp.compare(actualKey, k2);
        }
    }

    /**
     * If using comparator, return a ComparableUsingComparator, else
     * cast key as Comparable, which may cause ClassCastException,
     * which is propagated back to caller.
     */
    private Comparable<? super K> comparable(Object key)
            throws ClassCastException {
        if (key == null)
            throw new NullPointerException();
        if (comparator != null)
            return new ComparableUsingComparator<K>((K)key, comparator);
        else
            return (Comparable<? super K>)key;
    }

    /**
     * Compares using comparator or natural ordering. Used when the
     * ComparableUsingComparator approach doesn't apply.
     */
    int compare(K k1, K k2) throws ClassCastException {
        Comparator<? super K> cmp = comparator;
        if (cmp != null)
            return cmp.compare(k1, k2);
        else
            return ((Comparable<? super K>)k1).compareTo(k2);
    }

    /**
     * Returns true if given key greater than or equal to least and
     * strictly less than fence, bypassing either test if least or
     * fence are null. Needed mainly in submap operations.
     */
    boolean inHalfOpenRange(K key, K least, K fence) {
        if (key == null)
            throw new NullPointerException();
        return ((least == null || compare(key, least) >= 0) &&
                (fence == null || compare(key, fence) <  0));
    }

    /**
     * Returns true if given key greater than or equal to least and less
     * or equal to fence. Needed mainly in submap operations.
     */
    boolean inOpenRange(K key, K least, K fence) {
        if (key == null)
            throw new NullPointerException();
        return ((least == null || compare(key, least) >= 0) &&
                (fence == null || compare(key, fence) <= 0));
    }

    /* ---------------- Traversal -------------- */

    /**
     * Returns a base-level node with key strictly less than given key,
     * or the base-level header if there is no such node.  Also
     * unlinks indexes to deleted nodes found along the way.  Callers
     * rely on this side-effect of clearing indices to deleted nodes.
     * @param key the key
     * @return a predecessor of key
     */
    private Node<K,V> findPredecessor(Comparable<? super K> key) {
        if (key == null)
            throw new NullPointerException(); // don't postpone errors
        for (;;) {
            Index<K,V> q = head;
            Index<K,V> r = q.right;
            for (;;) {
                if (r != null) {
                    Node<K,V> n = r.node;
                    K k = n.key;
                    if (n.value == null) {
                        if (!q.unlink(r))
                            break;           // restart
                        r = q.right;         // reread r
                        continue;
                    }
                    if (key.compareTo(k) > 0) {
                        q = r;
                        r = r.right;
                        continue;
                    }
                }
                Index<K,V> d = q.down;
                if (d != null) {
                    q = d;
                    r = d.right;
                } else
                    return q.node;
            }
        }
    }

    /**
     * Returns node holding key or null if no such, clearing out any
     * deleted nodes seen along the way.  Repeatedly traverses at
     * base-level looking for key starting at predecessor returned
     * from findPredecessor, processing base-level deletions as
     * encountered. Some callers rely on this side-effect of clearing
     * deleted nodes.
     *
     * Restarts occur, at traversal step centered on node n, if:
     *
     *   (1) After reading n's next field, n is no longer assumed
     *       predecessor b's current successor, which means that
     *       we don't have a consistent 3-node snapshot and so cannot
     *       unlink any subsequent deleted nodes encountered.
     *
     *   (2) n's value field is null, indicating n is deleted, in
     *       which case we help out an ongoing structural deletion
     *       before retrying.  Even though there are cases where such
     *       unlinking doesn't require restart, they aren't sorted out
     *       here because doing so would not usually outweigh cost of
     *       restarting.
     *
     *   (3) n is a marker or n's predecessor's value field is null,
     *       indicating (among other possibilities) that
     *       findPredecessor returned a deleted node. We can't unlink
     *       the node because we don't know its predecessor, so rely
     *       on another call to findPredecessor to notice and return
     *       some earlier predecessor, which it will do. This check is
     *       only strictly needed at beginning of loop, (and the
     *       b.value check isn't strictly needed at all) but is done
     *       each iteration to help avoid contention with other
     *       threads by callers that will fail to be able to change
     *       links, and so will retry anyway.
     *
     * The traversal loops in doPut, doRemove, and findNear all
     * include the same three kinds of checks. And specialized
     * versions appear in findFirst, and findLast and their
     * variants. They can't easily share code because each uses the
     * reads of fields held in locals occurring in the orders they
     * were performed.
     *
     * @param key the key
     * @return node holding key, or null if no such
     */
    private Node<K,V> findNode(Comparable<? super K> key) {
        for (;;) {
            Node<K,V> b = findPredecessor(key);
            Node<K,V> n = b.next;
            for (;;) {
                if (n == null)
                    return null;
                Node<K,V> f = n.next;
                if (n != b.next)                // inconsistent read
                    break;
                Object v = n.value;
                if (v == null) {                // n is deleted
                    n.helpDelete(b, f);
                    break;
                }
                if (v == n || b.value == null)  // b is deleted
                    break;
                int c = key.compareTo(n.key);
                if (c == 0)
                    return n;
                if (c < 0)
                    return null;
                b = n;
                n = f;
            }
        }
    }

    /**
     * Gets value for key using findNode.
     * @param okey the key
     * @return the value, or null if absent
     */
    private V doGet(Object okey) {
        Comparable<? super K> key = comparable(okey);
        /*
         * Loop needed here and elsewhere in case value field goes
         * null just as it is about to be returned, in which case we
         * lost a race with a deletion, so must retry.
         */
        for (;;) {
            Node<K,V> n = findNode(key);
            if (n == null)
                return null;
            Object v = n.value;
            if (v != null)
                return (V)v;
        }
    }

    /* ---------------- Insertion -------------- */

    /**
     * Main insertion method.  Adds element if not present, or
     * replaces value if present and onlyIfAbsent is false.
     * @param kkey the key
     * @param value  the value that must be associated with key
     * @param onlyIfAbsent if should not insert if already present
     * @return the old value, or null if newly inserted
     */
    private V doPut(K kkey, V value, boolean onlyIfAbsent) {
        Comparable<? super K> key = comparable(kkey);
        for (;;) {
            Node<K,V> b = findPredecessor(key);
            Node<K,V> n = b.next;
            for (;;) {
                if (n != null) {
                    Node<K,V> f = n.next;
                    if (n != b.next)               // inconsistent read
                        break;
                    Object v = n.value;
                    if (v == null) {               // n is deleted
                        n.helpDelete(b, f);
                        break;
                    }
                    if (v == n || b.value == null) // b is deleted
                        break;
                    int c = key.compareTo(n.key);
                    if (c > 0) {
                        b = n;
                        n = f;
                        continue;
                    }
                    if (c == 0) {
                        if (onlyIfAbsent || n.casValue(v, value))
                            return (V)v;
                        else
                            break; // restart if lost race to replace value
                    }
                    // else c < 0; fall through
                }

                Node<K,V> z = new Node<K,V>(kkey, value, n);
                if (!b.casNext(n, z))
                    break;         // restart if lost race to append to b
                int level = randomLevel();
                if (level > 0)
                    insertIndex(z, level);
                return null;
            }
        }
    }

    /**
     * Returns a random level for inserting a new node.
     * Hardwired to k=1, p=0.5, max 31 (see above and
     * Pugh's "Skip List Cookbook", sec 3.4).
     *
     * This uses the simplest of the generators described in George
     * Marsaglia's "Xorshift RNGs" paper.  This is not a high-quality
     * generator but is acceptable here.
     */
    private int randomLevel() {
        int x = randomSeed;
        x ^= x << 13;
        x ^= x >>> 17;
        randomSeed = x ^= x << 5;
        if ((x & 0x80000001) != 0) // test highest and lowest bits
            return 0;
        int level = 1;
        while (((x >>>= 1) & 1) != 0) ++level;
        return level;
    }

    /**
     * Creates and adds index nodes for the given node.
     * @param z the node
     * @param level the level of the index
     */
    private void insertIndex(Node<K,V> z, int level) {
        HeadIndex<K,V> h = head;
        int max = h.level;

        if (level <= max) {
            Index<K,V> idx = null;
            for (int i = 1; i <= level; ++i)
                idx = new Index<K,V>(z, idx, null);
            addIndex(idx, h, level);

        } else { // Add a new level
            /*
             * To reduce interference by other threads checking for
             * empty levels in tryReduceLevel, new levels are added
             * with initialized right pointers. Which in turn requires
             * keeping levels in an array to access them while
             * creating new head index nodes from the opposite
             * direction.
             */
            level = max + 1;
            Index<K,V>[] idxs = (Index<K,V>[])new Index[level+1];
            Index<K,V> idx = null;
            for (int i = 1; i <= level; ++i)
                idxs[i] = idx = new Index<K,V>(z, idx, null);

            HeadIndex<K,V> oldh;
            int k;
            for (;;) {
                oldh = head;
                int oldLevel = oldh.level;
                if (level <= oldLevel) { // lost race to add level
                    k = level;
                    break;
                }
                HeadIndex<K,V> newh = oldh;
                Node<K,V> oldbase = oldh.node;
                for (int j = oldLevel+1; j <= level; ++j)
                    newh = new HeadIndex<K,V>(oldbase, newh, idxs[j], j);
                if (casHead(oldh, newh)) {
                    k = oldLevel;
                    break;
                }
            }
            addIndex(idxs[k], oldh, k);
        }
    }

    /**
     * Adds given index nodes from given level down to 1.
     * @param idx the topmost index node being inserted
     * @param h the value of head to use to insert. This must be
     * snapshotted by callers to provide correct insertion level
     * @param indexLevel the level of the index
     */
    private void addIndex(Index<K,V> idx, HeadIndex<K,V> h, int indexLevel) {
        // Track next level to insert in case of retries
        int insertionLevel = indexLevel;
        Comparable<? super K> key = comparable(idx.node.key);
        if (key == null) throw new NullPointerException();

        // Similar to findPredecessor, but adding index nodes along
        // path to key.
        for (;;) {
            int j = h.level;
            Index<K,V> q = h;
            Index<K,V> r = q.right;
            Index<K,V> t = idx;
            for (;;) {
                if (r != null) {
                    Node<K,V> n = r.node;
                    // compare before deletion check avoids needing recheck
                    int c = key.compareTo(n.key);
                    if (n.value == null) {
                        if (!q.unlink(r))
                            break;
                        r = q.right;
                        continue;
                    }
                    if (c > 0) {
                        q = r;
                        r = r.right;
                        continue;
                    }
                }

                if (j == insertionLevel) {
                    // Don't insert index if node already deleted
                    if (t.indexesDeletedNode()) {
                        findNode(key); // cleans up
                        return;
                    }
                    if (!q.link(r, t))
                        break; // restart
                    if (--insertionLevel == 0) {
                        // need final deletion check before return
                        if (t.indexesDeletedNode())
                            findNode(key);
                        return;
                    }
                }

                if (--j >= insertionLevel && j < indexLevel)
                    t = t.down;
                q = q.down;
                r = q.right;
            }
        }
    }

    /* ---------------- Deletion -------------- */

    /**
     * Main deletion method. Locates node, nulls value, appends a
     * deletion marker, unlinks predecessor, removes associated index
     * nodes, and possibly reduces head index level.
     *
     * Index nodes are cleared out simply by calling findPredecessor.
     * which unlinks indexes to deleted nodes found along path to key,
     * which will include the indexes to this node.  This is done
     * unconditionally. We can't check beforehand whether there are
     * index nodes because it might be the case that some or all
     * indexes hadn't been inserted yet for this node during initial
     * search for it, and we'd like to ensure lack of garbage
     * retention, so must call to be sure.
     *
     * @param okey the key
     * @param value if non-null, the value that must be
     * associated with key
     * @return the node, or null if not found
     */
    final V doRemove(Object okey, Object value) {
        Comparable<? super K> key = comparable(okey);
        for (;;) {
            Node<K,V> b = findPredecessor(key);
            Node<K,V> n = b.next;
            for (;;) {
                if (n == null)
                    return null;
                Node<K,V> f = n.next;
                if (n != b.next)                    // inconsistent read
                    break;
                Object v = n.value;
                if (v == null) {                    // n is deleted
                    n.helpDelete(b, f);
                    break;
                }
                if (v == n || b.value == null)      // b is deleted
                    break;
                int c = key.compareTo(n.key);
                if (c < 0)
                    return null;
                if (c > 0) {
                    b = n;
                    n = f;
                    continue;
                }
                if (value != null && !value.equals(v))
                    return null;
                if (!n.casValue(v, null))
                    break;
                if (!n.appendMarker(f) || !b.casNext(n, f))
                    findNode(key);                  // Retry via findNode
                else {
                    findPredecessor(key);           // Clean index
                    if (head.right == null)
                        tryReduceLevel();
                }
                return (V)v;
            }
        }
    }

    /**
     * Possibly reduce head level if it has no nodes.  This method can
     * (rarely) make mistakes, in which case levels can disappear even
     * though they are about to contain index nodes. This impacts
     * performance, not correctness.  To minimize mistakes as well as
     * to reduce hysteresis, the level is reduced by one only if the
     * topmost three levels look empty. Also, if the removed level
     * looks non-empty after CAS, we try to change it back quick
     * before anyone notices our mistake! (This trick works pretty
     * well because this method will practically never make mistakes
     * unless current thread stalls immediately before first CAS, in
     * which case it is very unlikely to stall again immediately
     * afterwards, so will recover.)
     *
     * We put up with all this rather than just let levels grow
     * because otherwise, even a small map that has undergone a large
     * number of insertions and removals will have a lot of levels,
     * slowing down access more than would an occasional unwanted
     * reduction.
     */
    private void tryReduceLevel() {
        HeadIndex<K,V> h = head;
        HeadIndex<K,V> d;
        HeadIndex<K,V> e;
        if (h.level > 3 &&
            (d = (HeadIndex<K,V>)h.down) != null &&
            (e = (HeadIndex<K,V>)d.down) != null &&
            e.right == null &&
            d.right == null &&
            h.right == null &&
            casHead(h, d) && // try to set
            h.right != null) // recheck
            casHead(d, h);   // try to backout
    }

    /* ---------------- Finding and removing first element -------------- */

    /**
     * Specialized variant of findNode to get first valid node.
     * @return first node or null if empty
     */
    Node<K,V> findFirst() {
        for (;;) {
            Node<K,V> b = head.node;
            Node<K,V> n = b.next;
            if (n == null)
                return null;
            if (n.value != null)
                return n;
            n.helpDelete(b, n.next);
        }
    }

    /**
     * Removes first entry; returns its snapshot.
     * @return null if empty, else snapshot of first entry
     */
    Map.Entry<K,V> doRemoveFirstEntry() {
        for (;;) {
            Node<K,V> b = head.node;
            Node<K,V> n = b.next;
            if (n == null)
                return null;
            Node<K,V> f = n.next;
            if (n != b.next)
                continue;
            Object v = n.value;
            if (v == null) {
                n.helpDelete(b, f);
                continue;
            }
            if (!n.casValue(v, null))
                continue;
            if (!n.appendMarker(f) || !b.casNext(n, f))
                findFirst(); // retry
            clearIndexToFirst();
            return new AbstractMap.SimpleImmutableEntry<K,V>(n.key, (V)v);
        }
    }

    /**
     * Clears out index nodes associated with deleted first entry.
     */
    private void clearIndexToFirst() {
        for (;;) {
            Index<K,V> q = head;
            for (;;) {
                Index<K,V> r = q.right;
                if (r != null && r.indexesDeletedNode() && !q.unlink(r))
                    break;
                if ((q = q.down) == null) {
                    if (head.right == null)
                        tryReduceLevel();
                    return;
                }
            }
        }
    }


    /* ---------------- Finding and removing last element -------------- */

    /**
     * Specialized version of find to get last valid node.
     * @return last node or null if empty
     */
    Node<K,V> findLast() {
        /*
         * findPredecessor can't be used to traverse index level
         * because this doesn't use comparisons.  So traversals of
         * both levels are folded together.
         */
        Index<K,V> q = head;
        for (;;) {
            Index<K,V> d, r;
            if ((r = q.right) != null) {
                if (r.indexesDeletedNode()) {
                    q.unlink(r);
                    q = head; // restart
                }
                else
                    q = r;
            } else if ((d = q.down) != null) {
                q = d;
            } else {
                Node<K,V> b = q.node;
                Node<K,V> n = b.next;
                for (;;) {
                    if (n == null)
                        return b.isBaseHeader() ? null : b;
                    Node<K,V> f = n.next;            // inconsistent read
                    if (n != b.next)
                        break;
                    Object v = n.value;
                    if (v == null) {                 // n is deleted
                        n.helpDelete(b, f);
                        break;
                    }
                    if (v == n || b.value == null)   // b is deleted
                        break;
                    b = n;
                    n = f;
                }
                q = head; // restart
            }
        }
    }

    /**
     * Specialized variant of findPredecessor to get predecessor of last
     * valid node.  Needed when removing the last entry.  It is possible
     * that all successors of returned node will have been deleted upon
     * return, in which case this method can be retried.
     * @return likely predecessor of last node
     */
    private Node<K,V> findPredecessorOfLast() {
        for (;;) {
            Index<K,V> q = head;
            for (;;) {
                Index<K,V> d, r;
                if ((r = q.right) != null) {
                    if (r.indexesDeletedNode()) {
                        q.unlink(r);
                        break;    // must restart
                    }
                    // proceed as far across as possible without overshooting
                    if (r.node.next != null) {
                        q = r;
                        continue;
                    }
                }
                if ((d = q.down) != null)
                    q = d;
                else
                    return q.node;
            }
        }
    }

    /**
     * Removes last entry; returns its snapshot.
     * Specialized variant of doRemove.
     * @return null if empty, else snapshot of last entry
     */
    Map.Entry<K,V> doRemoveLastEntry() {
        for (;;) {
            Node<K,V> b = findPredecessorOfLast();
            Node<K,V> n = b.next;
            if (n == null) {
                if (b.isBaseHeader())               // empty
                    return null;
                else
                    continue; // all b's successors are deleted; retry
            }
            for (;;) {
                Node<K,V> f = n.next;
                if (n != b.next)                    // inconsistent read
                    break;
                Object v = n.value;
                if (v == null) {                    // n is deleted
                    n.helpDelete(b, f);
                    break;
                }
                if (v == n || b.value == null)      // b is deleted
                    break;
                if (f != null) {
                    b = n;
                    n = f;
                    continue;
                }
                if (!n.casValue(v, null))
                    break;
                K key = n.key;
                Comparable<? super K> ck = comparable(key);
                if (!n.appendMarker(f) || !b.casNext(n, f))
                    findNode(ck);                  // Retry via findNode
                else {
                    findPredecessor(ck);           // Clean index
                    if (head.right == null)
                        tryReduceLevel();
                }
                return new AbstractMap.SimpleImmutableEntry<K,V>(key, (V)v);
            }
        }
    }

    /* ---------------- Relational operations -------------- */

    // Control values OR'ed as arguments to findNear

    private static final int EQ = 1;
    private static final int LT = 2;
    private static final int GT = 0; // Actually checked as !LT

    /**
     * Utility for ceiling, floor, lower, higher methods.
     * @param kkey the key
     * @param rel the relation -- OR'ed combination of EQ, LT, GT
     * @return nearest node fitting relation, or null if no such
     */
    Node<K,V> findNear(K kkey, int rel) {
        Comparable<? super K> key = comparable(kkey);
        for (;;) {
            Node<K,V> b = findPredecessor(key);
            Node<K,V> n = b.next;
            for (;;) {
                if (n == null)
                    return ((rel & LT) == 0 || b.isBaseHeader()) ? null : b;
                Node<K,V> f = n.next;
                if (n != b.next)                  // inconsistent read
                    break;
                Object v = n.value;
                if (v == null) {                  // n is deleted
                    n.helpDelete(b, f);
                    break;
                }
                if (v == n || b.value == null)    // b is deleted
                    break;
                int c = key.compareTo(n.key);
                if ((c == 0 && (rel & EQ) != 0) ||
                    (c <  0 && (rel & LT) == 0))
                    return n;
                if ( c <= 0 && (rel & LT) != 0)
                    return b.isBaseHeader() ? null : b;
                b = n;
                n = f;
            }
        }
    }

    /**
     * Returns SimpleImmutableEntry for results of findNear.
     * @param key the key
     * @param rel the relation -- OR'ed combination of EQ, LT, GT
     * @return Entry fitting relation, or null if no such
     */
    AbstractMap.SimpleImmutableEntry<K,V> getNear(K key, int rel) {
        for (;;) {
            Node<K,V> n = findNear(key, rel);
            if (n == null)
                return null;
            AbstractMap.SimpleImmutableEntry<K,V> e = n.createSnapshot();
            if (e != null)
                return e;
        }
    }


    /* ---------------- Constructors -------------- */

    /**
     * Constructs a new, empty map, sorted according to the
     * {@linkplain Comparable natural ordering} of the keys.
     */
    public ConcurrentSkipListMap() {
        this.comparator = null;
        initialize();
    }

    /**
     * Constructs a new, empty map, sorted according to the specified
     * comparator.
     *
     * @param comparator the comparator that will be used to order this map.
     *        If <tt>null</tt>, the {@linkplain Comparable natural
     *        ordering} of the keys will be used.
     */
    public ConcurrentSkipListMap(Comparator<? super K> comparator) {
        this.comparator = comparator;
        initialize();
    }

    /**
     * Constructs a new map containing the same mappings as the given map,
     * sorted according to the {@linkplain Comparable natural ordering} of
     * the keys.
     *
     * @param  m the map whose mappings are to be placed in this map
     * @throws ClassCastException if the keys in <tt>m</tt> are not
     *         {@link Comparable}, or are not mutually comparable
     * @throws NullPointerException if the specified map or any of its keys
     *         or values are null
     */
    public ConcurrentSkipListMap(Map<? extends K, ? extends V> m) {
        this.comparator = null;
        initialize();
        putAll(m);
    }

    /**
     * Constructs a new map containing the same mappings and using the
     * same ordering as the specified sorted map.
     *
     * @param m the sorted map whose mappings are to be placed in this
     *        map, and whose comparator is to be used to sort this map
     * @throws NullPointerException if the specified sorted map or any of
     *         its keys or values are null
     */
    public ConcurrentSkipListMap(SortedMap<K, ? extends V> m) {
        this.comparator = m.comparator();
        initialize();
        buildFromSorted(m);
    }

    /**
     * Returns a shallow copy of this <tt>ConcurrentSkipListMap</tt>
     * instance. (The keys and values themselves are not cloned.)
     *
     * @return a shallow copy of this map
     */
    public ConcurrentSkipListMap<K,V> clone() {
        ConcurrentSkipListMap<K,V> clone = null;
        try {
            clone = (ConcurrentSkipListMap<K,V>) super.clone();
        } catch (CloneNotSupportedException e) {
            throw new InternalError();
        }

        clone.initialize();
        clone.buildFromSorted(this);
        return clone;
    }

    /**
     * Streamlined bulk insertion to initialize from elements of
     * given sorted map.  Call only from constructor or clone
     * method.
     */
    private void buildFromSorted(SortedMap<K, ? extends V> map) {
        if (map == null)
            throw new NullPointerException();

        HeadIndex<K,V> h = head;
        Node<K,V> basepred = h.node;

        // Track the current rightmost node at each level. Uses an
        // ArrayList to avoid committing to initial or maximum level.
        ArrayList<Index<K,V>> preds = new ArrayList<Index<K,V>>();

        // initialize
        for (int i = 0; i <= h.level; ++i)
            preds.add(null);
        Index<K,V> q = h;
        for (int i = h.level; i > 0; --i) {
            preds.set(i, q);
            q = q.down;
        }

        Iterator<? extends Map.Entry<? extends K, ? extends V>> it =
            map.entrySet().iterator();
        while (it.hasNext()) {
            Map.Entry<? extends K, ? extends V> e = it.next();
            int j = randomLevel();
            if (j > h.level) j = h.level + 1;
            K k = e.getKey();
            V v = e.getValue();
            if (k == null || v == null)
                throw new NullPointerException();
            Node<K,V> z = new Node<K,V>(k, v, null);
            basepred.next = z;
            basepred = z;
            if (j > 0) {
                Index<K,V> idx = null;
                for (int i = 1; i <= j; ++i) {
                    idx = new Index<K,V>(z, idx, null);
                    if (i > h.level)
                        h = new HeadIndex<K,V>(h.node, h, idx, i);

                    if (i < preds.size()) {
                        preds.get(i).right = idx;
                        preds.set(i, idx);
                    } else
                        preds.add(idx);
                }
            }
        }
        head = h;
    }

    /* ---------------- Serialization -------------- */

    /**
     * Save the state of this map to a stream.
     *
     * @serialData The key (Object) and value (Object) for each
     * key-value mapping represented by the map, followed by
     * <tt>null</tt>. The key-value mappings are emitted in key-order
     * (as determined by the Comparator, or by the keys' natural
     * ordering if no Comparator).
     */
    private void writeObject(java.io.ObjectOutputStream s)
        throws java.io.IOException {
        // Write out the Comparator and any hidden stuff
        s.defaultWriteObject();

        // Write out keys and values (alternating)
        for (Node<K,V> n = findFirst(); n != null; n = n.next) {
            V v = n.getValidValue();
            if (v != null) {
                s.writeObject(n.key);
                s.writeObject(v);
            }
        }
        s.writeObject(null);
    }

    /**
     * Reconstitute the map from a stream.
     */
    private void readObject(final java.io.ObjectInputStream s)
        throws java.io.IOException, ClassNotFoundException {
        // Read in the Comparator and any hidden stuff
        s.defaultReadObject();
        // Reset transients
        initialize();

        /*
         * This is nearly identical to buildFromSorted, but is
         * distinct because readObject calls can't be nicely adapted
         * as the kind of iterator needed by buildFromSorted. (They
         * can be, but doing so requires type cheats and/or creation
         * of adaptor classes.) It is simpler to just adapt the code.
         */

        HeadIndex<K,V> h = head;
        Node<K,V> basepred = h.node;
        ArrayList<Index<K,V>> preds = new ArrayList<Index<K,V>>();
        for (int i = 0; i <= h.level; ++i)
            preds.add(null);
        Index<K,V> q = h;
        for (int i = h.level; i > 0; --i) {
            preds.set(i, q);
            q = q.down;
        }

        for (;;) {
            Object k = s.readObject();
            if (k == null)
                break;
            Object v = s.readObject();
            if (v == null)
                throw new NullPointerException();
            K key = (K) k;
            V val = (V) v;
            int j = randomLevel();
            if (j > h.level) j = h.level + 1;
            Node<K,V> z = new Node<K,V>(key, val, null);
            basepred.next = z;
            basepred = z;
            if (j > 0) {
                Index<K,V> idx = null;
                for (int i = 1; i <= j; ++i) {
                    idx = new Index<K,V>(z, idx, null);
                    if (i > h.level)
                        h = new HeadIndex<K,V>(h.node, h, idx, i);

                    if (i < preds.size()) {
                        preds.get(i).right = idx;
                        preds.set(i, idx);
                    } else
                        preds.add(idx);
                }
            }
        }
        head = h;
    }

    /* ------ Map API methods ------ */

    /**
     * Returns <tt>true</tt> if this map contains a mapping for the specified
     * key.
     *
     * @param key key whose presence in this map is to be tested
     * @return <tt>true</tt> if this map contains a mapping for the specified key
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key is null
     */
    public boolean containsKey(Object key) {
        return doGet(key) != null;
    }

    /**
     * Returns the value to which the specified key is mapped,
     * or {@code null} if this map contains no mapping for the key.
     *
     * <p>More formally, if this map contains a mapping from a key
     * {@code k} to a value {@code v} such that {@code key} compares
     * equal to {@code k} according to the map's ordering, then this
     * method returns {@code v}; otherwise it returns {@code null}.
     * (There can be at most one such mapping.)
     *
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key is null
     */
    public V get(Object key) {
        return doGet(key);
    }

    /**
     * Associates the specified value with the specified key in this map.
     * If the map previously contained a mapping for the key, the old
     * value is replaced.
     *
     * @param key key with which the specified value is to be associated
     * @param value value to be associated with the specified key
     * @return the previous value associated with the specified key, or
     *         <tt>null</tt> if there was no mapping for the key
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key or value is null
     */
    public V put(K key, V value) {
        if (value == null)
            throw new NullPointerException();
        return doPut(key, value, false);
    }

    /**
     * Removes the mapping for the specified key from this map if present.
     *
     * @param  key key for which mapping should be removed
     * @return the previous value associated with the specified key, or
     *         <tt>null</tt> if there was no mapping for the key
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key is null
     */
    public V remove(Object key) {
        return doRemove(key, null);
    }

    /**
     * Returns <tt>true</tt> if this map maps one or more keys to the
     * specified value.  This operation requires time linear in the
     * map size. Additionally, it is possible for the map to change
     * during execution of this method, in which case the returned
     * result may be inaccurate.
     *
     * @param value value whose presence in this map is to be tested
     * @return <tt>true</tt> if a mapping to <tt>value</tt> exists;
     *         <tt>false</tt> otherwise
     * @throws NullPointerException if the specified value is null
     */
    public boolean containsValue(Object value) {
        if (value == null)
            throw new NullPointerException();
        for (Node<K,V> n = findFirst(); n != null; n = n.next) {
            V v = n.getValidValue();
            if (v != null && value.equals(v))
                return true;
        }
        return false;
    }

    /**
     * Returns the number of key-value mappings in this map.  If this map
     * contains more than <tt>Integer.MAX_VALUE</tt> elements, it
     * returns <tt>Integer.MAX_VALUE</tt>.
     *
     * <p>Beware that, unlike in most collections, this method is
     * <em>NOT</em> a constant-time operation. Because of the
     * asynchronous nature of these maps, determining the current
     * number of elements requires traversing them all to count them.
     * Additionally, it is possible for the size to change during
     * execution of this method, in which case the returned result
     * will be inaccurate. Thus, this method is typically not very
     * useful in concurrent applications.
     *
     * @return the number of elements in this map
     */
    public int size() {
        long count = 0;
        for (Node<K,V> n = findFirst(); n != null; n = n.next) {
            if (n.getValidValue() != null)
                ++count;
        }
        return (count >= Integer.MAX_VALUE) ? Integer.MAX_VALUE : (int) count;
    }

    /**
     * Returns <tt>true</tt> if this map contains no key-value mappings.
     * @return <tt>true</tt> if this map contains no key-value mappings
     */
    public boolean isEmpty() {
        return findFirst() == null;
    }

    /**
     * Removes all of the mappings from this map.
     */
    public void clear() {
        initialize();
    }

    /* ---------------- View methods -------------- */

    /*
     * Note: Lazy initialization works for views because view classes
     * are stateless/immutable so it doesn't matter wrt correctness if
     * more than one is created (which will only rarely happen).  Even
     * so, the following idiom conservatively ensures that the method
     * returns the one it created if it does so, not one created by
     * another racing thread.
     */

    /**
     * Returns a {@link NavigableSet} view of the keys contained in this map.
     * The set's iterator returns the keys in ascending order.
     * The set is backed by the map, so changes to the map are
     * reflected in the set, and vice-versa.  The set supports element
     * removal, which removes the corresponding mapping from the map,
     * via the {@code Iterator.remove}, {@code Set.remove},
     * {@code removeAll}, {@code retainAll}, and {@code clear}
     * operations.  It does not support the {@code add} or {@code addAll}
     * operations.
     *
     * <p>The view's {@code iterator} is a "weakly consistent" iterator
     * that will never throw {@link ConcurrentModificationException},
     * and guarantees to traverse elements as they existed upon
     * construction of the iterator, and may (but is not guaranteed to)
     * reflect any modifications subsequent to construction.
     *
     * <p>This method is equivalent to method {@code navigableKeySet}.
     *
     * @return a navigable set view of the keys in this map
     */
    public NavigableSet<K> keySet() {
        KeySet ks = keySet;
        return (ks != null) ? ks : (keySet = new KeySet(this));
    }

    public NavigableSet<K> navigableKeySet() {
        KeySet ks = keySet;
        return (ks != null) ? ks : (keySet = new KeySet(this));
    }

    /**
     * Returns a {@link Collection} view of the values contained in this map.
     * The collection's iterator returns the values in ascending order
     * of the corresponding keys.
     * The collection is backed by the map, so changes to the map are
     * reflected in the collection, and vice-versa.  The collection
     * supports element removal, which removes the corresponding
     * mapping from the map, via the <tt>Iterator.remove</tt>,
     * <tt>Collection.remove</tt>, <tt>removeAll</tt>,
     * <tt>retainAll</tt> and <tt>clear</tt> operations.  It does not
     * support the <tt>add</tt> or <tt>addAll</tt> operations.
     *
     * <p>The view's <tt>iterator</tt> is a "weakly consistent" iterator
     * that will never throw {@link ConcurrentModificationException},
     * and guarantees to traverse elements as they existed upon
     * construction of the iterator, and may (but is not guaranteed to)
     * reflect any modifications subsequent to construction.
     */
    public Collection<V> values() {
        Values vs = values;
        return (vs != null) ? vs : (values = new Values(this));
    }

    /**
     * Returns a {@link Set} view of the mappings contained in this map.
     * The set's iterator returns the entries in ascending key order.
     * The set is backed by the map, so changes to the map are
     * reflected in the set, and vice-versa.  The set supports element
     * removal, which removes the corresponding mapping from the map,
     * via the <tt>Iterator.remove</tt>, <tt>Set.remove</tt>,
     * <tt>removeAll</tt>, <tt>retainAll</tt> and <tt>clear</tt>
     * operations.  It does not support the <tt>add</tt> or
     * <tt>addAll</tt> operations.
     *
     * <p>The view's <tt>iterator</tt> is a "weakly consistent" iterator
     * that will never throw {@link ConcurrentModificationException},
     * and guarantees to traverse elements as they existed upon
     * construction of the iterator, and may (but is not guaranteed to)
     * reflect any modifications subsequent to construction.
     *
     * <p>The <tt>Map.Entry</tt> elements returned by
     * <tt>iterator.next()</tt> do <em>not</em> support the
     * <tt>setValue</tt> operation.
     *
     * @return a set view of the mappings contained in this map,
     *         sorted in ascending key order
     */
    public Set<Map.Entry<K,V>> entrySet() {
        EntrySet es = entrySet;
        return (es != null) ? es : (entrySet = new EntrySet(this));
    }

    public ConcurrentNavigableMap<K,V> descendingMap() {
        ConcurrentNavigableMap<K,V> dm = descendingMap;
        return (dm != null) ? dm : (descendingMap = new SubMap<K,V>
                                    (this, null, false, null, false, true));
    }

    public NavigableSet<K> descendingKeySet() {
        return descendingMap().navigableKeySet();
    }

    /* ---------------- AbstractMap Overrides -------------- */

    /**
     * Compares the specified object with this map for equality.
     * Returns <tt>true</tt> if the given object is also a map and the
     * two maps represent the same mappings.  More formally, two maps
     * <tt>m1</tt> and <tt>m2</tt> represent the same mappings if
     * <tt>m1.entrySet().equals(m2.entrySet())</tt>.  This
     * operation may return misleading results if either map is
     * concurrently modified during execution of this method.
     *
     * @param o object to be compared for equality with this map
     * @return <tt>true</tt> if the specified object is equal to this map
     */
    public boolean equals(Object o) {
        if (o == this)
            return true;
        if (!(o instanceof Map))
            return false;
        Map<?,?> m = (Map<?,?>) o;
        try {
            for (Map.Entry<K,V> e : this.entrySet())
                if (! e.getValue().equals(m.get(e.getKey())))
                    return false;
            for (Map.Entry<?,?> e : m.entrySet()) {
                Object k = e.getKey();
                Object v = e.getValue();
                if (k == null || v == null || !v.equals(get(k)))
                    return false;
            }
            return true;
        } catch (ClassCastException unused) {
            return false;
        } catch (NullPointerException unused) {
            return false;
        }
    }

    /* ------ ConcurrentMap API methods ------ */

    /**
     * {@inheritDoc}
     *
     * @return the previous value associated with the specified key,
     *         or <tt>null</tt> if there was no mapping for the key
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key or value is null
     */
    public V putIfAbsent(K key, V value) {
        if (value == null)
            throw new NullPointerException();
        return doPut(key, value, true);
    }

    /**
     * {@inheritDoc}
     *
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key is null
     */
    public boolean remove(Object key, Object value) {
        if (key == null)
            throw new NullPointerException();
        if (value == null)
            return false;
        return doRemove(key, value) != null;
    }

    /**
     * {@inheritDoc}
     *
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if any of the arguments are null
     */
    public boolean replace(K key, V oldValue, V newValue) {
        if (oldValue == null || newValue == null)
            throw new NullPointerException();
        Comparable<? super K> k = comparable(key);
        for (;;) {
            Node<K,V> n = findNode(k);
            if (n == null)
                return false;
            Object v = n.value;
            if (v != null) {
                if (!oldValue.equals(v))
                    return false;
                if (n.casValue(v, newValue))
                    return true;
            }
        }
    }

    /**
     * {@inheritDoc}
     *
     * @return the previous value associated with the specified key,
     *         or <tt>null</tt> if there was no mapping for the key
     * @throws ClassCastException if the specified key cannot be compared
     *         with the keys currently in the map
     * @throws NullPointerException if the specified key or value is null
     */
    public V replace(K key, V value) {
        if (value == null)
            throw new NullPointerException();
        Comparable<? super K> k = comparable(key);
        for (;;) {
            Node<K,V> n = findNode(k);
            if (n == null)
                return null;
            Object v = n.value;
            if (v != null && n.casValue(v, value))
                return (V)v;
        }
    }

    /* ------ SortedMap API methods ------ */

    public Comparator<? super K> comparator() {
        return comparator;
    }

    /**
     * @throws NoSuchElementException {@inheritDoc}
     */
    public K firstKey() {
        Node<K,V> n = findFirst();
        if (n == null)
            throw new NoSuchElementException();
        return n.key;
    }

    /**
     * @throws NoSuchElementException {@inheritDoc}
     */
    public K lastKey() {
        Node<K,V> n = findLast();
        if (n == null)
            throw new NoSuchElementException();
        return n.key;
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if {@code fromKey} or {@code toKey} is null
     * @throws IllegalArgumentException {@inheritDoc}
     */
    public ConcurrentNavigableMap<K,V> subMap(K fromKey,
                                              boolean fromInclusive,
                                              K toKey,
                                              boolean toInclusive) {
        if (fromKey == null || toKey == null)
            throw new NullPointerException();
        return new SubMap<K,V>
            (this, fromKey, fromInclusive, toKey, toInclusive, false);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if {@code toKey} is null
     * @throws IllegalArgumentException {@inheritDoc}
     */
    public ConcurrentNavigableMap<K,V> headMap(K toKey,
                                               boolean inclusive) {
        if (toKey == null)
            throw new NullPointerException();
        return new SubMap<K,V>
            (this, null, false, toKey, inclusive, false);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if {@code fromKey} is null
     * @throws IllegalArgumentException {@inheritDoc}
     */
    public ConcurrentNavigableMap<K,V> tailMap(K fromKey,
                                               boolean inclusive) {
        if (fromKey == null)
            throw new NullPointerException();
        return new SubMap<K,V>
            (this, fromKey, inclusive, null, false, false);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if {@code fromKey} or {@code toKey} is null
     * @throws IllegalArgumentException {@inheritDoc}
     */
    public ConcurrentNavigableMap<K,V> subMap(K fromKey, K toKey) {
        return subMap(fromKey, true, toKey, false);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if {@code toKey} is null
     * @throws IllegalArgumentException {@inheritDoc}
     */
    public ConcurrentNavigableMap<K,V> headMap(K toKey) {
        return headMap(toKey, false);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if {@code fromKey} is null
     * @throws IllegalArgumentException {@inheritDoc}
     */
    public ConcurrentNavigableMap<K,V> tailMap(K fromKey) {
        return tailMap(fromKey, true);
    }

    /* ---------------- Relational operations -------------- */

    /**
     * Returns a key-value mapping associated with the greatest key
     * strictly less than the given key, or <tt>null</tt> if there is
     * no such key. The returned entry does <em>not</em> support the
     * <tt>Entry.setValue</tt> method.
     *
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public Map.Entry<K,V> lowerEntry(K key) {
        return getNear(key, LT);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public K lowerKey(K key) {
        Node<K,V> n = findNear(key, LT);
        return (n == null) ? null : n.key;
    }

    /**
     * Returns a key-value mapping associated with the greatest key
     * less than or equal to the given key, or <tt>null</tt> if there
     * is no such key. The returned entry does <em>not</em> support
     * the <tt>Entry.setValue</tt> method.
     *
     * @param key the key
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public Map.Entry<K,V> floorEntry(K key) {
        return getNear(key, LT|EQ);
    }

    /**
     * @param key the key
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public K floorKey(K key) {
        Node<K,V> n = findNear(key, LT|EQ);
        return (n == null) ? null : n.key;
    }

    /**
     * Returns a key-value mapping associated with the least key
     * greater than or equal to the given key, or <tt>null</tt> if
     * there is no such entry. The returned entry does <em>not</em>
     * support the <tt>Entry.setValue</tt> method.
     *
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public Map.Entry<K,V> ceilingEntry(K key) {
        return getNear(key, GT|EQ);
    }

    /**
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public K ceilingKey(K key) {
        Node<K,V> n = findNear(key, GT|EQ);
        return (n == null) ? null : n.key;
    }

    /**
     * Returns a key-value mapping associated with the least key
     * strictly greater than the given key, or <tt>null</tt> if there
     * is no such key. The returned entry does <em>not</em> support
     * the <tt>Entry.setValue</tt> method.
     *
     * @param key the key
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public Map.Entry<K,V> higherEntry(K key) {
        return getNear(key, GT);
    }

    /**
     * @param key the key
     * @throws ClassCastException {@inheritDoc}
     * @throws NullPointerException if the specified key is null
     */
    public K higherKey(K key) {
        Node<K,V> n = findNear(key, GT);
        return (n == null) ? null : n.key;
    }

    /**
     * Returns a key-value mapping associated with the least
     * key in this map, or <tt>null</tt> if the map is empty.
     * The returned entry does <em>not</em> support
     * the <tt>Entry.setValue</tt> method.
     */
    public Map.Entry<K,V> firstEntry() {
        for (;;) {
            Node<K,V> n = findFirst();
            if (n == null)
                return null;
            AbstractMap.SimpleImmutableEntry<K,V> e = n.createSnapshot();
            if (e != null)
                return e;
        }
    }

    /**
     * Returns a key-value mapping associated with the greatest
     * key in this map, or <tt>null</tt> if the map is empty.
     * The returned entry does <em>not</em> support
     * the <tt>Entry.setValue</tt> method.
     */
    public Map.Entry<K,V> lastEntry() {
        for (;;) {
            Node<K,V> n = findLast();
            if (n == null)
                return null;
            AbstractMap.SimpleImmutableEntry<K,V> e = n.createSnapshot();
            if (e != null)
                return e;
        }
    }

    /**
     * Removes and returns a key-value mapping associated with
     * the least key in this map, or <tt>null</tt> if the map is empty.
     * The returned entry does <em>not</em> support
     * the <tt>Entry.setValue</tt> method.
     */
    public Map.Entry<K,V> pollFirstEntry() {
        return doRemoveFirstEntry();
    }

    /**
     * Removes and returns a key-value mapping associated with
     * the greatest key in this map, or <tt>null</tt> if the map is empty.
     * The returned entry does <em>not</em> support
     * the <tt>Entry.setValue</tt> method.
     */
    public Map.Entry<K,V> pollLastEntry() {
        return doRemoveLastEntry();
    }


    /* ---------------- Iterators -------------- */

    /**
     * Base of iterator classes:
     */
    abstract class Iter<T> implements Iterator<T> {
        /** the last node returned by next() */
        Node<K,V> lastReturned;
        /** the next node to return from next(); */
        Node<K,V> next;
        /** Cache of next value field to maintain weak consistency */
        V nextValue;

        /** Initializes ascending iterator for entire range. */
        Iter() {
            for (;;) {
                next = findFirst();
                if (next == null)
                    break;
                Object x = next.value;
                if (x != null && x != next) {
                    nextValue = (V) x;
                    break;
                }
            }
        }

        public final boolean hasNext() {
            return next != null;
        }

        /** Advances next to higher entry. */
        final void advance() {
            if (next == null)
                throw new NoSuchElementException();
            lastReturned = next;
            for (;;) {
                next = next.next;
                if (next == null)
                    break;
                Object x = next.value;
                if (x != null && x != next) {
                    nextValue = (V) x;
                    break;
                }
            }
        }

        public void remove() {
            Node<K,V> l = lastReturned;
            if (l == null)
                throw new IllegalStateException();
            // It would not be worth all of the overhead to directly
            // unlink from here. Using remove is fast enough.
            ConcurrentSkipListMap.this.remove(l.key);
            lastReturned = null;
        }

    }

    final class ValueIterator extends Iter<V> {
        public V next() {
            V v = nextValue;
            advance();
            return v;
        }
    }

    final class KeyIterator extends Iter<K> {
        public K next() {
            Node<K,V> n = next;
            advance();
            return n.key;
        }
    }

    final class EntryIterator extends Iter<Map.Entry<K,V>> {
        public Map.Entry<K,V> next() {
            Node<K,V> n = next;
            V v = nextValue;
            advance();
            return new AbstractMap.SimpleImmutableEntry<K,V>(n.key, v);
        }
    }

    // Factory methods for iterators needed by ConcurrentSkipListSet etc

    Iterator<K> keyIterator() {
        return new KeyIterator();
    }

    Iterator<V> valueIterator() {
        return new ValueIterator();
    }

    Iterator<Map.Entry<K,V>> entryIterator() {
        return new EntryIterator();
    }

    /* ---------------- View Classes -------------- */

    /*
     * View classes are static, delegating to a ConcurrentNavigableMap
     * to allow use by SubMaps, which outweighs the ugliness of
     * needing type-tests for Iterator methods.
     */

    static final <E> List<E> toList(Collection<E> c) {
        // Using size() here would be a pessimization.
        List<E> list = new ArrayList<E>();
        for (E e : c)
            list.add(e);
        return list;
    }

    static final class KeySet<E>
            extends AbstractSet<E> implements NavigableSet<E> {
        private final ConcurrentNavigableMap<E,Object> m;
        KeySet(ConcurrentNavigableMap<E,Object> map) { m = map; }
        public int size() { return m.size(); }
        public boolean isEmpty() { return m.isEmpty(); }
        public boolean contains(Object o) { return m.containsKey(o); }
        public boolean remove(Object o) { return m.remove(o) != null; }
        public void clear() { m.clear(); }
        public E lower(E e) { return m.lowerKey(e); }
        public E floor(E e) { return m.floorKey(e); }
        public E ceiling(E e) { return m.ceilingKey(e); }
        public E higher(E e) { return m.higherKey(e); }
        public Comparator<? super E> comparator() { return m.comparator(); }
        public E first() { return m.firstKey(); }
        public E last() { return m.lastKey(); }
        public E pollFirst() {
            Map.Entry<E,Object> e = m.pollFirstEntry();
            return (e == null) ? null : e.getKey();
        }
        public E pollLast() {
            Map.Entry<E,Object> e = m.pollLastEntry();
            return (e == null) ? null : e.getKey();
        }
        public Iterator<E> iterator() {
            if (m instanceof ConcurrentSkipListMap)
                return ((ConcurrentSkipListMap<E,Object>)m).keyIterator();
            else
                return ((ConcurrentSkipListMap.SubMap<E,Object>)m).keyIterator();
        }
        public boolean equals(Object o) {
            if (o == this)
                return true;
            if (!(o instanceof Set))
                return false;
            Collection<?> c = (Collection<?>) o;
            try {
                return containsAll(c) && c.containsAll(this);
            } catch (ClassCastException unused)   {
                return false;
            } catch (NullPointerException unused) {
                return false;
            }
        }
        public Object[] toArray()     { return toList(this).toArray();  }
        public <T> T[] toArray(T[] a) { return toList(this).toArray(a); }
        public Iterator<E> descendingIterator() {
            return descendingSet().iterator();
        }
        public NavigableSet<E> subSet(E fromElement,
                                      boolean fromInclusive,
                                      E toElement,
                                      boolean toInclusive) {
            return new KeySet<E>(m.subMap(fromElement, fromInclusive,
                                          toElement,   toInclusive));
        }
        public NavigableSet<E> headSet(E toElement, boolean inclusive) {
            return new KeySet<E>(m.headMap(toElement, inclusive));
        }
        public NavigableSet<E> tailSet(E fromElement, boolean inclusive) {
            return new KeySet<E>(m.tailMap(fromElement, inclusive));
        }
        public NavigableSet<E> subSet(E fromElement, E toElement) {
            return subSet(fromElement, true, toElement, false);
        }
        public NavigableSet<E> headSet(E toElement) {
            return headSet(toElement, false);
        }
        public NavigableSet<E> tailSet(E fromElement) {
            return tailSet(fromElement, true);
        }
        public NavigableSet<E> descendingSet() {
            return new KeySet(m.descendingMap());
        }
    }

    static final class Values<E> extends AbstractCollection<E> {
        private final ConcurrentNavigableMap<Object, E> m;
        Values(ConcurrentNavigableMap<Object, E> map) {
            m = map;
        }
        public Iterator<E> iterator() {
            if (m instanceof ConcurrentSkipListMap)
                return ((ConcurrentSkipListMap<Object,E>)m).valueIterator();
            else
                return ((SubMap<Object,E>)m).valueIterator();
        }
        public boolean isEmpty() {
            return m.isEmpty();
        }
        public int size() {
            return m.size();
        }
        public boolean contains(Object o) {
            return m.containsValue(o);
        }
        public void clear() {
            m.clear();
        }
        public Object[] toArray()     { return toList(this).toArray();  }
        public <T> T[] toArray(T[] a) { return toList(this).toArray(a); }
    }

    static final class EntrySet<K1,V1> extends AbstractSet<Map.Entry<K1,V1>> {
        private final ConcurrentNavigableMap<K1, V1> m;
        EntrySet(ConcurrentNavigableMap<K1, V1> map) {
            m = map;
        }

        public Iterator<Map.Entry<K1,V1>> iterator() {
            if (m instanceof ConcurrentSkipListMap)
                return ((ConcurrentSkipListMap<K1,V1>)m).entryIterator();
            else
                return ((SubMap<K1,V1>)m).entryIterator();
        }

        public boolean contains(Object o) {
            if (!(o instanceof Map.Entry))
                return false;
            Map.Entry<K1,V1> e = (Map.Entry<K1,V1>)o;
            V1 v = m.get(e.getKey());
            return v != null && v.equals(e.getValue());
        }
        public boolean remove(Object o) {
            if (!(o instanceof Map.Entry))
                return false;
            Map.Entry<K1,V1> e = (Map.Entry<K1,V1>)o;
            return m.remove(e.getKey(),
                            e.getValue());
        }
        public boolean isEmpty() {
            return m.isEmpty();
        }
        public int size() {
            return m.size();
        }
        public void clear() {
            m.clear();
        }
        public boolean equals(Object o) {
            if (o == this)
                return true;
            if (!(o instanceof Set))
                return false;
            Collection<?> c = (Collection<?>) o;
            try {
                return containsAll(c) && c.containsAll(this);
            } catch (ClassCastException unused)   {
                return false;
            } catch (NullPointerException unused) {
                return false;
            }
        }
        public Object[] toArray()     { return toList(this).toArray();  }
        public <T> T[] toArray(T[] a) { return toList(this).toArray(a); }
    }

    /**
     * Submaps returned by {@link ConcurrentSkipListMap} submap operations
     * represent a subrange of mappings of their underlying
     * maps. Instances of this class support all methods of their
     * underlying maps, differing in that mappings outside their range are
     * ignored, and attempts to add mappings outside their ranges result
     * in {@link IllegalArgumentException}.  Instances of this class are
     * constructed only using the <tt>subMap</tt>, <tt>headMap</tt>, and
     * <tt>tailMap</tt> methods of their underlying maps.
     *
     * @serial include
     */
    static final class SubMap<K,V> extends AbstractMap<K,V>
        implements ConcurrentNavigableMap<K,V>, Cloneable,
                   java.io.Serializable {
        private static final long serialVersionUID = -7647078645895051609L;

        /** Underlying map */
        private final ConcurrentSkipListMap<K,V> m;
        /** lower bound key, or null if from start */
        private final K lo;
        /** upper bound key, or null if to end */
        private final K hi;
        /** inclusion flag for lo */
        private final boolean loInclusive;
        /** inclusion flag for hi */
        private final boolean hiInclusive;
        /** direction */
        private final boolean isDescending;

        // Lazily initialized view holders
        private transient KeySet<K> keySetView;
        private transient Set<Map.Entry<K,V>> entrySetView;
        private transient Collection<V> valuesView;

        /**
         * Creates a new submap, initializing all fields
         */
        SubMap(ConcurrentSkipListMap<K,V> map,
               K fromKey, boolean fromInclusive,
               K toKey, boolean toInclusive,
               boolean isDescending) {
            if (fromKey != null && toKey != null &&
                map.compare(fromKey, toKey) > 0)
                throw new IllegalArgumentException("inconsistent range");
            this.m = map;
            this.lo = fromKey;
            this.hi = toKey;
            this.loInclusive = fromInclusive;
            this.hiInclusive = toInclusive;
            this.isDescending = isDescending;
        }

        /* ----------------  Utilities -------------- */

        private boolean tooLow(K key) {
            if (lo != null) {
                int c = m.compare(key, lo);
                if (c < 0 || (c == 0 && !loInclusive))
                    return true;
            }
            return false;
        }

        private boolean tooHigh(K key) {
            if (hi != null) {
                int c = m.compare(key, hi);
                if (c > 0 || (c == 0 && !hiInclusive))
                    return true;
            }
            return false;
        }

        private boolean inBounds(K key) {
            return !tooLow(key) && !tooHigh(key);
        }

        private void checkKeyBounds(K key) throws IllegalArgumentException {
            if (key == null)
                throw new NullPointerException();
            if (!inBounds(key))
                throw new IllegalArgumentException("key out of range");
        }

        /**
         * Returns true if node key is less than upper bound of range
         */
        private boolean isBeforeEnd(ConcurrentSkipListMap.Node<K,V> n) {
            if (n == null)
                return false;
            if (hi == null)
                return true;
            K k = n.key;
            if (k == null) // pass by markers and headers
                return true;
            int c = m.compare(k, hi);
            if (c > 0 || (c == 0 && !hiInclusive))
                return false;
            return true;
        }

        /**
         * Returns lowest node. This node might not be in range, so
         * most usages need to check bounds
         */
        private ConcurrentSkipListMap.Node<K,V> loNode() {
            if (lo == null)
                return m.findFirst();
            else if (loInclusive)
                return m.findNear(lo, m.GT|m.EQ);
            else
                return m.findNear(lo, m.GT);
        }

        /**
         * Returns highest node. This node might not be in range, so
         * most usages need to check bounds
         */
        private ConcurrentSkipListMap.Node<K,V> hiNode() {
            if (hi == null)
                return m.findLast();
            else if (hiInclusive)
                return m.findNear(hi, m.LT|m.EQ);
            else
                return m.findNear(hi, m.LT);
        }

        /**
         * Returns lowest absolute key (ignoring directonality)
         */
        private K lowestKey() {
            ConcurrentSkipListMap.Node<K,V> n = loNode();
            if (isBeforeEnd(n))
                return n.key;
            else
                throw new NoSuchElementException();
        }

        /**
         * Returns highest absolute key (ignoring directonality)
         */
        private K highestKey() {
            ConcurrentSkipListMap.Node<K,V> n = hiNode();
            if (n != null) {
                K last = n.key;
                if (inBounds(last))
                    return last;
            }
            throw new NoSuchElementException();
        }

        private Map.Entry<K,V> lowestEntry() {
            for (;;) {
                ConcurrentSkipListMap.Node<K,V> n = loNode();
                if (!isBeforeEnd(n))
                    return null;
                Map.Entry<K,V> e = n.createSnapshot();
                if (e != null)
                    return e;
            }
        }

        private Map.Entry<K,V> highestEntry() {
            for (;;) {
                ConcurrentSkipListMap.Node<K,V> n = hiNode();
                if (n == null || !inBounds(n.key))
                    return null;
                Map.Entry<K,V> e = n.createSnapshot();
                if (e != null)
                    return e;
            }
        }

        private Map.Entry<K,V> removeLowest() {
            for (;;) {
                Node<K,V> n = loNode();
                if (n == null)
                    return null;
                K k = n.key;
                if (!inBounds(k))
                    return null;
                V v = m.doRemove(k, null);
                if (v != null)
                    return new AbstractMap.SimpleImmutableEntry<K,V>(k, v);
            }
        }

        private Map.Entry<K,V> removeHighest() {
            for (;;) {
                Node<K,V> n = hiNode();
                if (n == null)
                    return null;
                K k = n.key;
                if (!inBounds(k))
                    return null;
                V v = m.doRemove(k, null);
                if (v != null)
                    return new AbstractMap.SimpleImmutableEntry<K,V>(k, v);
            }
        }

        /**
         * Submap version of ConcurrentSkipListMap.getNearEntry
         */
        private Map.Entry<K,V> getNearEntry(K key, int rel) {
            if (isDescending) { // adjust relation for direction
                if ((rel & m.LT) == 0)
                    rel |= m.LT;
                else
                    rel &= ~m.LT;
            }
            if (tooLow(key))
                return ((rel & m.LT) != 0) ? null : lowestEntry();
            if (tooHigh(key))
                return ((rel & m.LT) != 0) ? highestEntry() : null;
            for (;;) {
                Node<K,V> n = m.findNear(key, rel);
                if (n == null || !inBounds(n.key))
                    return null;
                K k = n.key;
                V v = n.getValidValue();
                if (v != null)
                    return new AbstractMap.SimpleImmutableEntry<K,V>(k, v);
            }
        }

        // Almost the same as getNearEntry, except for keys
        private K getNearKey(K key, int rel) {
            if (isDescending) { // adjust relation for direction
                if ((rel & m.LT) == 0)
                    rel |= m.LT;
                else
                    rel &= ~m.LT;
            }
            if (tooLow(key)) {
                if ((rel & m.LT) == 0) {
                    ConcurrentSkipListMap.Node<K,V> n = loNode();
                    if (isBeforeEnd(n))
                        return n.key;
                }
                return null;
            }
            if (tooHigh(key)) {
                if ((rel & m.LT) != 0) {
                    ConcurrentSkipListMap.Node<K,V> n = hiNode();
                    if (n != null) {
                        K last = n.key;
                        if (inBounds(last))
                            return last;
                    }
                }
                return null;
            }
            for (;;) {
                Node<K,V> n = m.findNear(key, rel);
                if (n == null || !inBounds(n.key))
                    return null;
                K k = n.key;
                V v = n.getValidValue();
                if (v != null)
                    return k;
            }
        }

        /* ----------------  Map API methods -------------- */

        public boolean containsKey(Object key) {
            if (key == null) throw new NullPointerException();
            K k = (K)key;
            return inBounds(k) && m.containsKey(k);
        }

        public V get(Object key) {
            if (key == null) throw new NullPointerException();
            K k = (K)key;
            return ((!inBounds(k)) ? null : m.get(k));
        }

        public V put(K key, V value) {
            checkKeyBounds(key);
            return m.put(key, value);
        }

        public V remove(Object key) {
            K k = (K)key;
            return (!inBounds(k)) ? null : m.remove(k);
        }

        public int size() {
            long count = 0;
            for (ConcurrentSkipListMap.Node<K,V> n = loNode();
                 isBeforeEnd(n);
                 n = n.next) {
                if (n.getValidValue() != null)
                    ++count;
            }
            return count >= Integer.MAX_VALUE ? Integer.MAX_VALUE : (int)count;
        }

        public boolean isEmpty() {
            return !isBeforeEnd(loNode());
        }

        public boolean containsValue(Object value) {
            if (value == null)
                throw new NullPointerException();
            for (ConcurrentSkipListMap.Node<K,V> n = loNode();
                 isBeforeEnd(n);
                 n = n.next) {
                V v = n.getValidValue();
                if (v != null && value.equals(v))
                    return true;
            }
            return false;
        }

        public void clear() {
            for (ConcurrentSkipListMap.Node<K,V> n = loNode();
                 isBeforeEnd(n);
                 n = n.next) {
                if (n.getValidValue() != null)
                    m.remove(n.key);
            }
        }

        /* ----------------  ConcurrentMap API methods -------------- */

        public V putIfAbsent(K key, V value) {
            checkKeyBounds(key);
            return m.putIfAbsent(key, value);
        }

        public boolean remove(Object key, Object value) {
            K k = (K)key;
            return inBounds(k) && m.remove(k, value);
        }

        public boolean replace(K key, V oldValue, V newValue) {
            checkKeyBounds(key);
            return m.replace(key, oldValue, newValue);
        }

        public V replace(K key, V value) {
            checkKeyBounds(key);
            return m.replace(key, value);
        }

        /* ----------------  SortedMap API methods -------------- */

        public Comparator<? super K> comparator() {
            Comparator<? super K> cmp = m.comparator();
            if (isDescending)
                return Collections.reverseOrder(cmp);
            else
                return cmp;
        }

        /**
         * Utility to create submaps, where given bounds override
         * unbounded(null) ones and/or are checked against bounded ones.
         */
        private SubMap<K,V> newSubMap(K fromKey,
                                      boolean fromInclusive,
                                      K toKey,
                                      boolean toInclusive) {
            if (isDescending) { // flip senses
                K tk = fromKey;
                fromKey = toKey;
                toKey = tk;
                boolean ti = fromInclusive;
                fromInclusive = toInclusive;
                toInclusive = ti;
            }
            if (lo != null) {
                if (fromKey == null) {
                    fromKey = lo;
                    fromInclusive = loInclusive;
                }
                else {
                    int c = m.compare(fromKey, lo);
                    if (c < 0 || (c == 0 && !loInclusive && fromInclusive))
                        throw new IllegalArgumentException("key out of range");
                }
            }
            if (hi != null) {
                if (toKey == null) {
                    toKey = hi;
                    toInclusive = hiInclusive;
                }
                else {
                    int c = m.compare(toKey, hi);
                    if (c > 0 || (c == 0 && !hiInclusive && toInclusive))
                        throw new IllegalArgumentException("key out of range");
                }
            }
            return new SubMap<K,V>(m, fromKey, fromInclusive,
                                   toKey, toInclusive, isDescending);
        }

        public SubMap<K,V> subMap(K fromKey,
                                  boolean fromInclusive,
                                  K toKey,
                                  boolean toInclusive) {
            if (fromKey == null || toKey == null)
                throw new NullPointerException();
            return newSubMap(fromKey, fromInclusive, toKey, toInclusive);
        }

        public SubMap<K,V> headMap(K toKey,
                                   boolean inclusive) {
            if (toKey == null)
                throw new NullPointerException();
            return newSubMap(null, false, toKey, inclusive);
        }

        public SubMap<K,V> tailMap(K fromKey,
                                   boolean inclusive) {
            if (fromKey == null)
                throw new NullPointerException();
            return newSubMap(fromKey, inclusive, null, false);
        }

        public SubMap<K,V> subMap(K fromKey, K toKey) {
            return subMap(fromKey, true, toKey, false);
        }

        public SubMap<K,V> headMap(K toKey) {
            return headMap(toKey, false);
        }

        public SubMap<K,V> tailMap(K fromKey) {
            return tailMap(fromKey, true);
        }

        public SubMap<K,V> descendingMap() {
            return new SubMap<K,V>(m, lo, loInclusive,
                                   hi, hiInclusive, !isDescending);
        }

        /* ----------------  Relational methods -------------- */

        public Map.Entry<K,V> ceilingEntry(K key) {
            return getNearEntry(key, (m.GT|m.EQ));
        }

        public K ceilingKey(K key) {
            return getNearKey(key, (m.GT|m.EQ));
        }

        public Map.Entry<K,V> lowerEntry(K key) {
            return getNearEntry(key, (m.LT));
        }

        public K lowerKey(K key) {
            return getNearKey(key, (m.LT));
        }

        public Map.Entry<K,V> floorEntry(K key) {
            return getNearEntry(key, (m.LT|m.EQ));
        }

        public K floorKey(K key) {
            return getNearKey(key, (m.LT|m.EQ));
        }

        public Map.Entry<K,V> higherEntry(K key) {
            return getNearEntry(key, (m.GT));
        }

        public K higherKey(K key) {
            return getNearKey(key, (m.GT));
        }

        public K firstKey() {
            return isDescending ? highestKey() : lowestKey();
        }

        public K lastKey() {
            return isDescending ? lowestKey() : highestKey();
        }

        public Map.Entry<K,V> firstEntry() {
            return isDescending ? highestEntry() : lowestEntry();
        }

        public Map.Entry<K,V> lastEntry() {
            return isDescending ? lowestEntry() : highestEntry();
        }

        public Map.Entry<K,V> pollFirstEntry() {
            return isDescending ? removeHighest() : removeLowest();
        }

        public Map.Entry<K,V> pollLastEntry() {
            return isDescending ? removeLowest() : removeHighest();
        }

        /* ---------------- Submap Views -------------- */

        public NavigableSet<K> keySet() {
            KeySet<K> ks = keySetView;
            return (ks != null) ? ks : (keySetView = new KeySet(this));
        }

        public NavigableSet<K> navigableKeySet() {
            KeySet<K> ks = keySetView;
            return (ks != null) ? ks : (keySetView = new KeySet(this));
        }

        public Collection<V> values() {
            Collection<V> vs = valuesView;
            return (vs != null) ? vs : (valuesView = new Values(this));
        }

        public Set<Map.Entry<K,V>> entrySet() {
            Set<Map.Entry<K,V>> es = entrySetView;
            return (es != null) ? es : (entrySetView = new EntrySet(this));
        }

        public NavigableSet<K> descendingKeySet() {
            return descendingMap().navigableKeySet();
        }

        Iterator<K> keyIterator() {
            return new SubMapKeyIterator();
        }

        Iterator<V> valueIterator() {
            return new SubMapValueIterator();
        }

        Iterator<Map.Entry<K,V>> entryIterator() {
            return new SubMapEntryIterator();
        }

        /**
         * Variant of main Iter class to traverse through submaps.
         */
        abstract class SubMapIter<T> implements Iterator<T> {
            /** the last node returned by next() */
            Node<K,V> lastReturned;
            /** the next node to return from next(); */
            Node<K,V> next;
            /** Cache of next value field to maintain weak consistency */
            V nextValue;

            SubMapIter() {
                for (;;) {
                    next = isDescending ? hiNode() : loNode();
                    if (next == null)
                        break;
                    Object x = next.value;
                    if (x != null && x != next) {
                        if (! inBounds(next.key))
                            next = null;
                        else
                            nextValue = (V) x;
                        break;
                    }
                }
            }

            public final boolean hasNext() {
                return next != null;
            }

            final void advance() {
                if (next == null)
                    throw new NoSuchElementException();
                lastReturned = next;
                if (isDescending)
                    descend();
                else
                    ascend();
            }

            private void ascend() {
                for (;;) {
                    next = next.next;
                    if (next == null)
                        break;
                    Object x = next.value;
                    if (x != null && x != next) {
                        if (tooHigh(next.key))
                            next = null;
                        else
                            nextValue = (V) x;
                        break;
                    }
                }
            }

            private void descend() {
                for (;;) {
                    next = m.findNear(lastReturned.key, LT);
                    if (next == null)
                        break;
                    Object x = next.value;
                    if (x != null && x != next) {
                        if (tooLow(next.key))
                            next = null;
                        else
                            nextValue = (V) x;
                        break;
                    }
                }
            }

            public void remove() {
                Node<K,V> l = lastReturned;
                if (l == null)
                    throw new IllegalStateException();
                m.remove(l.key);
                lastReturned = null;
            }

        }

        final class SubMapValueIterator extends SubMapIter<V> {
            public V next() {
                V v = nextValue;
                advance();
                return v;
            }
        }

        final class SubMapKeyIterator extends SubMapIter<K> {
            public K next() {
                Node<K,V> n = next;
                advance();
                return n.key;
            }
        }

        final class SubMapEntryIterator extends SubMapIter<Map.Entry<K,V>> {
            public Map.Entry<K,V> next() {
                Node<K,V> n = next;
                V v = nextValue;
                advance();
                return new AbstractMap.SimpleImmutableEntry<K,V>(n.key, v);
            }
        }
    }

    // Unsafe mechanics
    private static final sun.misc.Unsafe UNSAFE;
    private static final long headOffset;
    static {
        try {
            UNSAFE = sun.misc.Unsafe.getUnsafe();
            Class k = ConcurrentSkipListMap.class;
            headOffset = UNSAFE.objectFieldOffset
                (k.getDeclaredField("head"));
        } catch (Exception e) {
            throw new Error(e);
        }
    }
}

  

下面从ConcurrentSkipListMap的添加,删除,获取这3个方面对它进行分析。

1. 添加

下面以put(K key, V value)为例,对ConcurrentSkipListMap的添加方法进行说明。

public V put(K key, V value) {
    if (value == null)
        throw new NullPointerException();
    return doPut(key, value, false);
}

实际上,put()是通过doPut()将key-value键值对添加到ConcurrentSkipListMap中的。

doPut()的源码如下:

private V doPut(K kkey, V value, boolean onlyIfAbsent) {
    Comparable<? super K> key = comparable(kkey);
    for (;;) {
        // 找到key的前继节点
        Node<K,V> b = findPredecessor(key);
        // 设置n为“key的前继节点的后继节点”,即n应该是“插入节点”的“后继节点”
        Node<K,V> n = b.next;
        for (;;) {
            if (n != null) {
                Node<K,V> f = n.next;
                // 如果两次获得的b.next不是相同的Node,就跳转到”外层for循环“,重新获得b和n后再遍历。
                if (n != b.next)
                    break;
                // v是“n的值”
                Object v = n.value;
                // 当n的值为null(意味着其它线程删除了n);此时删除b的下一个节点,然后跳转到”外层for循环“,重新获得b和n后再遍历。
                if (v == null) {               // n is deleted
                    n.helpDelete(b, f);
                    break;
                }
                // 如果其它线程删除了b;则跳转到”外层for循环“,重新获得b和n后再遍历。
                if (v == n || b.value == null) // b is deleted
                    break;
                // 比较key和n.key
                int c = key.compareTo(n.key);
                if (c > 0) {
                    b = n;
                    n = f;
                    continue;
                }
                if (c == 0) {
                    if (onlyIfAbsent || n.casValue(v, value))
                        return (V)v;
                    else
                        break; // restart if lost race to replace value
                }
                // else c < 0; fall through
            }

            // 新建节点(对应是“要插入的键值对”)
            Node<K,V> z = new Node<K,V>(kkey, value, n);
            // 设置“b的后继节点”为z
            if (!b.casNext(n, z))
                break;         // 多线程情况下,break才可能发生(其它线程对b进行了操作)
            // 随机获取一个level
            // 然后在“第1层”到“第level层”的链表中都插入新建节点
            int level = randomLevel();
            if (level > 0)
                insertIndex(z, level);
            return null;
        }
    }
}

说明:doPut() 的作用就是将键值对添加到“跳表”中。
要想搞清doPut(),首先要弄清楚它的主干部分 —— 我们先单纯的只考虑“单线程的情况下,将key-value添加到跳表中”,即忽略“多线程相关的内容”。它的流程如下:
第1步:找到“插入位置”。
即,找到“key的前继节点(b)”和“key的后继节点(n)”;key是要插入节点的键。
第2步:新建并插入节点。
即,新建节点z(key对应的节点),并将新节点z插入到“跳表”中(设置“b的后继节点为z”,“z的后继节点为n”)。
第3步:更新跳表。
即,随机获取一个level,然后在“跳表”的第1层~第level层之间,每一层都插入节点z;在第level层之上就不再插入节点了。若level数值大于“跳表的层次”,则新建一层。
主干部分“对应的精简后的doPut()的代码”如下(仅供参考):

private V doPut(K kkey, V value, boolean onlyIfAbsent) {
    Comparable<? super K> key = comparable(kkey);
    for (;;) {
        // 找到key的前继节点
        Node<K,V> b = findPredecessor(key);
        // 设置n为key的后继节点
        Node<K,V> n = b.next;
        for (;;) {
            
            // 新建节点(对应是“要被插入的键值对”)
            Node<K,V> z = new Node<K,V>(kkey, value, n);
            // 设置“b的后继节点”为z
            b.casNext(n, z);

            // 随机获取一个level
            // 然后在“第1层”到“第level层”的链表中都插入新建节点
            int level = randomLevel();
            if (level > 0)
                insertIndex(z, level);
            return null;
        }
    }
}

理清主干之后,剩余的工作就相对简单了。主要是上面几步的对应算法的具体实现,以及多线程相关情况的处理!

 

2. 删除

下面以remove(Object key)为例,对ConcurrentSkipListMap的删除方法进行说明。

public V remove(Object key) {
    return doRemove(key, null);
}

实际上,remove()是通过doRemove()将ConcurrentSkipListMap中的key对应的键值对删除的。

doRemove()的源码如下:

 

final V doRemove(Object okey, Object value) {
    Comparable<? super K> key = comparable(okey);
    for (;;) {
        // 找到“key的前继节点”
        Node<K,V> b = findPredecessor(key);
        // 设置n为“b的后继节点”(即若key存在于“跳表中”,n就是key对应的节点)
        Node<K,V> n = b.next;
        for (;;) {
            if (n == null)
                return null;
            // f是“当前节点n的后继节点”
            Node<K,V> f = n.next;
            // 如果两次读取到的“b的后继节点”不同(其它线程操作了该跳表),则返回到“外层for循环”重新遍历。
            if (n != b.next)                    // inconsistent read
                break;
            // 如果“当前节点n的值”变为null(其它线程操作了该跳表),则返回到“外层for循环”重新遍历。
            Object v = n.value;
            if (v == null) {                    // n is deleted
                n.helpDelete(b, f);
                break;
            }
            // 如果“前继节点b”被删除(其它线程操作了该跳表),则返回到“外层for循环”重新遍历。
            if (v == n || b.value == null)      // b is deleted
                break;
            int c = key.compareTo(n.key);
            if (c < 0)
                return null;
            if (c > 0) {
                b = n;
                n = f;
                continue;
            }

            // 以下是c=0的情况
            if (value != null && !value.equals(v))
                return null;
            // 设置“当前节点n”的值为null
            if (!n.casValue(v, null))
                break;
            // 设置“b的后继节点”为f
            if (!n.appendMarker(f) || !b.casNext(n, f))
                findNode(key);                  // Retry via findNode
            else {
                // 清除“跳表”中每一层的key节点
                findPredecessor(key);           // Clean index
                // 如果“表头的右索引为空”,则将“跳表的层次”-1。
                if (head.right == null)
                    tryReduceLevel();
            }
            return (V)v;
        }
    }
}

说明:doRemove()的作用是删除跳表中的节点。
和doPut()一样,我们重点看doRemove()的主干部分,了解主干部分之后,其余部分就非常容易理解了。下面是“单线程的情况下,删除跳表中键值对的步骤”:
第1步:找到“被删除节点的位置”。
即,找到“key的前继节点(b)”,“key所对应的节点(n)”,“n的后继节点f”;key是要删除节点的键。
第2步:删除节点。
即,将“key所对应的节点n”从跳表中移除 -- 将“b的后继节点”设为“f”!
第3步:更新跳表。
即,遍历跳表,删除每一层的“key节点”(如果存在的话)。如果删除“key节点”之后,跳表的层次需要-1;则执行相应的操作!
主干部分“对应的精简后的doRemove()的代码”如下(仅供参考):

 

final V doRemove(Object okey, Object value) {
    Comparable<? super K> key = comparable(okey);
    for (;;) {
        // 找到“key的前继节点”
        Node<K,V> b = findPredecessor(key);
        // 设置n为“b的后继节点”(即若key存在于“跳表中”,n就是key对应的节点)
        Node<K,V> n = b.next;
        for (;;) {
            // f是“当前节点n的后继节点”
            Node<K,V> f = n.next;

            // 设置“当前节点n”的值为null
            n.casValue(v, null);

            // 设置“b的后继节点”为f
            b.casNext(n, f);
            // 清除“跳表”中每一层的key节点
            findPredecessor(key);
            // 如果“表头的右索引为空”,则将“跳表的层次”-1。
            if (head.right == null)
                tryReduceLevel();
            return (V)v;
        }
    }
}

 

3. 获取

下面以get(Object key)为例,对ConcurrentSkipListMap的获取方法进行说明。

public V get(Object key) {
    return doGet(key);
}

doGet的源码如下:

private V doGet(Object okey) {
    Comparable<? super K> key = comparable(okey);
    for (;;) {
        // 找到“key对应的节点”
        Node<K,V> n = findNode(key);
        if (n == null)
            return null;
        Object v = n.value;
        if (v != null)
            return (V)v;
    }
}

说明:doGet()是通过findNode()找到并返回节点的。

private Node<K,V> findNode(Comparable<? super K> key) {
    for (;;) {
        // 找到key的前继节点
        Node<K,V> b = findPredecessor(key);
        // 设置n为“b的后继节点”(即若key存在于“跳表中”,n就是key对应的节点)
        Node<K,V> n = b.next;
        for (;;) {
            // 如果“n为null”,则跳转中不存在key对应的节点,直接返回null。
            if (n == null)
                return null;
            Node<K,V> f = n.next;
            // 如果两次读取到的“b的后继节点”不同(其它线程操作了该跳表),则返回到“外层for循环”重新遍历。
            if (n != b.next)                // inconsistent read
                break;
            Object v = n.value;
            // 如果“当前节点n的值”变为null(其它线程操作了该跳表),则返回到“外层for循环”重新遍历。
            if (v == null) {                // n is deleted
                n.helpDelete(b, f);
                break;
            }
            if (v == n || b.value == null)  // b is deleted
                break;
            // 若n是当前节点,则返回n。
            int c = key.compareTo(n.key);
            if (c == 0)
                return n;
            // 若“节点n的key”小于“key”,则说明跳表中不存在key对应的节点,返回null
            if (c < 0)
                return null;
            // 若“节点n的key”大于“key”,则更新b和n,继续查找。
            b = n;
            n = f;
        }
    }
}

说明:findNode(key)的作用是在返回跳表中key对应的节点;存在则返回节点,不存在则返回null。
先弄清函数的主干部分,即抛开“多线程相关内容”,单纯的考虑单线程情况下,从跳表获取节点的算法。
第1步:找到“被删除节点的位置”。
根据findPredecessor()定位key所在的层次以及找到key的前继节点(b),然后找到b的后继节点n。
第2步:根据“key的前继节点(b)”和“key的前继节点的后继节点(n)”来定位“key对应的节点”。
具体是通过比较“n的键值”和“key”的大小。如果相等,则n就是所要查找的键。

 

ConcurrentSkipListMap示例

import java.util.*;
import java.util.concurrent.*;

/*
 *   ConcurrentSkipListMap是“线程安全”的哈希表,而TreeMap是非线程安全的。
 *
 *   下面是“多个线程同时操作并且遍历map”的示例
 *   (01) 当map是ConcurrentSkipListMap对象时,程序能正常运行。
 *   (02) 当map是TreeMap对象时,程序会产生ConcurrentModificationException异常。
 *
 * @author skywang
 */
public class ConcurrentSkipListMapDemo1 {

    // TODO: map是TreeMap对象时,程序会出错。
    //private static Map<String, String> map = new TreeMap<String, String>();
    private static Map<String, String> map = new ConcurrentSkipListMap<String, String>();
    public static void main(String[] args) {
    
        // 同时启动两个线程对map进行操作!
        new MyThread("a").start();
        new MyThread("b").start();
    }

    private static void printAll() {
        String key, value;
        Iterator iter = map.entrySet().iterator();
        while(iter.hasNext()) {
            Map.Entry entry = (Map.Entry)iter.next();
            key = (String)entry.getKey();
            value = (String)entry.getValue();
            System.out.print("("+key+", "+value+"), ");
        }
        System.out.println();
    }

    private static class MyThread extends Thread {
        MyThread(String name) {
            super(name);
        }
        @Override
        public void run() {
                int i = 0;
            while (i++ < 6) {
                // “线程名” + "序号"
                String val = Thread.currentThread().getName()+i;
                map.put(val, "0");
                // 通过“Iterator”遍历map。
                printAll();
            }
        }
    }
}

(某一次)运行结果

 

(a1, 0), (a1, 0), (b1, 0), (b1, 0),

(a1, 0), (b1, 0), (b2, 0), 
(a1, 0), (a1, 0), (a2, 0), (a2, 0), (b1, 0), (b1, 0), (b2, 0), (b2, 0), (b3, 0), 
(b3, 0), (a1, 0), 
(a2, 0), (a3, 0), (a1, 0), (b1, 0), (a2, 0), (b2, 0), (a3, 0), (b3, 0), (b1, 0), (b4, 0), 
(b2, 0), (a1, 0), (b3, 0), (a2, 0), (b4, 0), 
(a3, 0), (a1, 0), (a4, 0), (a2, 0), (b1, 0), (a3, 0), (b2, 0), (a4, 0), (b3, 0), (b1, 0), (b4, 0), (b2, 0), (b5, 0), 
(b3, 0), (a1, 0), (b4, 0), (a2, 0), (b5, 0), 
(a3, 0), (a1, 0), (a4, 0), (a2, 0), (a5, 0), (a3, 0), (b1, 0), (a4, 0), (b2, 0), (a5, 0), (b3, 0), (b1, 0), (b4, 0), (b2, 0), (b5, 0), (b3, 0), (b6, 0), 
(b4, 0), (a1, 0), (b5, 0), (a2, 0), (b6, 0), 
(a3, 0), (a4, 0), (a5, 0), (a6, 0), (b1, 0), (b2, 0), (b3, 0), (b4, 0), (b5, 0), (b6, 0), 

结果说明
示例程序中,启动两个线程(线程a和线程b)分别对ConcurrentSkipListMap进行操作。以线程a而言,它会先获取“线程名”+“序号”,然后将该字符串作为key,将“0”作为value,插入到ConcurrentSkipListMap中;接着,遍历并输出ConcurrentSkipListMap中的全部元素。 线程b的操作和线程a一样,只不过线程b的名字和线程a的名字不同。
当map是ConcurrentSkipListMap对象时,程序能正常运行。如果将map改为TreeMap时,程序会产生ConcurrentModificationException异常。

posted @ 2020-05-03 23:06  跃小云  阅读(223)  评论(0编辑  收藏  举报