【JUC源码解析】Exchanger
简介
Exchanger,并发工具类,用于线程间的数据交换。
使用
两个线程,两个缓冲区,一个线程往一个缓冲区里面填数据,另一个线程从另一个缓冲区里面取数据。当填数据的线程将缓冲区填满时,或者取数据的线程将缓冲区里的数据取空时,就主动向对方发起交换缓冲区的动作,而交换的时机是,一个缓冲区满,另一个缓冲区空。代码如下,很简单,没有加注释。
public class FillAndEmpty {
Exchanger<DataBuffer> exchanger = new Exchanger<DataBuffer>();
DataBuffer initialEmptyBuffer = DataBuffer.allocate(1024);
DataBuffer initialFullBuffer = DataBuffer.allocate(1024); class FillingLoop implements Runnable {
public void run() {
DataBuffer currentBuffer = initialEmptyBuffer;
try {
while (currentBuffer != null) {
addToBuffer(currentBuffer);
if (currentBuffer.isFull()) {
System.out.println("[FillingLoop](Before)" + currentBuffer);
currentBuffer = exchanger.exchange(currentBuffer);
System.out.println("[FillingLoop](After)" + currentBuffer);
}
}
} catch (InterruptedException ex) {
Thread.currentThread().interrupt();
}
}
} class EmptyingLoop implements Runnable {
public void run() {
DataBuffer currentBuffer = initialFullBuffer;
try {
while (currentBuffer != null) {
takeFromBuffer(currentBuffer);
if (currentBuffer.isEmpty()) {
System.out.println("[EmptyingLoop](Before)" + currentBuffer);
currentBuffer = exchanger.exchange(currentBuffer);
System.out.println("[EmptyingLoop](After)" + currentBuffer);
}
}
} catch (InterruptedException ex) {
Thread.currentThread().interrupt();
}
}
} void start() {
Thread fillingLoopThread = new Thread(new FillingLoop());
Thread emptyingLoopThread = new Thread(new EmptyingLoop()); fillingLoopThread.start();
emptyingLoopThread.start(); try {
Thread.sleep(10);
} catch (InterruptedException e) {
// do nothing
}
fillingLoopThread.interrupt();
emptyingLoopThread.interrupt();
} public void takeFromBuffer(DataBuffer buf) {
buf.take();
} public void addToBuffer(DataBuffer buf) {
buf.add(1);
} private static class DataBuffer {
private final int[] buf;
private final int size;
private int index; private DataBuffer(int size) {
this.size = size;
this.buf = new int[size];
} public static DataBuffer allocate(int size) {
return new DataBuffer(size);
} public boolean isEmpty() {
return index == 0;
} public boolean isFull() {
return index == size - 1;
} public int take() {
if (index > 0) {
return buf[index--];
} return -1;
} public void add(int data) {
if (index < size - 1) {
buf[index++] = data;
}
}
} public static void main(String[] args) {
FillAndEmpty fae = new FillAndEmpty();
fae.start();
}
}
输出如下,交换前后,两个线程所持的数据缓冲区对调。(部分输出未给出)
[EmptyingLoop](Before)com.luoluo.exchanger.FillAndEmpty$DataBuffer@1733c6a5
[FillingLoop](Before)com.luoluo.exchanger.FillAndEmpty$DataBuffer@39bcfec1
[FillingLoop](After)com.luoluo.exchanger.FillAndEmpty$DataBuffer@1733c6a5
[EmptyingLoop](After)com.luoluo.exchanger.FillAndEmpty$DataBuffer@39bcfec1
......
源码解析
常量介绍
private static final int ASHIFT = 7; // 两个有效槽(slot -> Node)之间的字节地址长度(内存地址,以字节为单位),1 << 7至少为缓存行的大小,防止伪共享
private static final int MMASK = 0xff; // 场地(一排槽,arena -> Node[])的可支持的最大索引,可分配的大小为 MMASK + 1
private static final int SEQ = MMASK + 1; // bound的递增单元,确立其唯一性
private static final int NCPU = Runtime.getRuntime().availableProcessors(); // CPU的个数,用于场地大小和自旋控制
static final int FULL = (NCPU >= (MMASK << 1)) ? MMASK : NCPU >>> 1; // 最大的arena索引
private static final int SPINS = 1 << 10; // 自旋次数,NCPU = 1时,禁用
private static final Object NULL_ITEM = new Object();// 空对象,对应null
private static final Object TIMED_OUT = new Object();// 超时对象,对应timeout
ASHIFT,两个有效的槽之间的地址长度是1 << 7(至少为缓存行的大小,避免伪共享问题,见下面说明)
MMASK,多槽交换可支持的最大索引,大小为MMASK + 1(index从0开始)
SEQ,bound的递增单元,确定其唯一性(高位)
NCPU,CPU的个数
FULL,最大的arena索引,不大于MMASK;arena,一排slot,为的是获得良好的伸缩性,避免所有的线程争用同一个槽位。
SPINS,自旋次数,用于自旋等待,是最轻量的等待,依次是 spin -> yield -> block
伪共享,高速缓存与内存之间是以缓存行为单位交换数据的,根据局部性原理,相邻地址空间的数据会被加载到高速缓存的同一个数据块上(缓存行),而数组是连续的(逻辑,涉及到虚拟内存)内存地址空间,因此,多个slot会被加载到同一个缓存行上,当一个slot改变时,会导致这个slot所在的缓存行上所有的数据(包括其他的slot)无效,需要从内存重新加载,影响性能。
所以,为了避免这种情况,需要填充数据,使得有效的slot不被加载到同一个缓存行上。填充的大小即为1 << 7,如下图所示
数据结构Node
static final class Node {
int index; // arena的索引
int bound; // 记录上次的bound
int collides; // 当前bound下CAS失败的次数
int hash; // 伪随机,用于自旋
Object item; // 当前线程携带的数据
volatile Object match; // 存放释放线程携带的数据
volatile Thread parked; // 挂在此结点上阻塞着的线程
}
index,arena的索引
bound,记录上次的bound
collides,当前bound下CAS失败的次数,最大为m,m(bound & MMASK)为当前bound下最大有效索引,从右往左遍历,等到collides == m时,有效索引的槽位也已经遍历完了,这时需要增长槽位,增长的方式是重置bound(依赖SEQ更新其版本,高位;+1,低位),同时collides重置
hash,伪随机,用于自旋
item,当前线程携带的数据
match,存放释放线程(来交换的线程)携带的数据
parked,挂在此结点上阻塞着的线程,等待被释放
见下图
数据结构Participant
// 每个线程携带一个Node
static final class Participant extends ThreadLocal<Node> {
public Node initialValue() {
return new Node();
}
}
Participant直接继承自ThreadLocal保存当前线程携带的Node,交换操作主要依赖Node的行为
属性介绍
private final Participant participant;// 每个线程携带一个Node
private volatile Node[] arena; // 场地,Node数组
private volatile Node slot;// 槽,单个Node
private volatile int bound;// 当前最大有效arena索引,高8位+SEQ确立其唯一性,低8位记录有效索引
bound,记录最大有效的arena索引,动态变化,竞争激烈时(槽位全满)增加, 槽位空旷时减小。bound + SEQ +/- 1,其高位+ 1(SEQ,oxff + 1)确定其版本唯一性(比如,+1后,又-1,实际上是两个版本的bound,collides要重置的,而且从右向左遍历的索引也要更新,一般来讲,左边槽位比右边槽位竞争激烈,所以要从右向左找,为的是快速找到一个空位置,并尝试占领它,当bound加一又减一后,遍历索引右侧的槽位应该就空出来了,因为大家都往左边靠拢,所以要更新到最右侧,如果没有bound的版本唯一性,便没有索引更新,就一直往左遍历竞争激烈的槽位,还会误判,本来bound应该缩减的,反而又使其增加,于是会很影响效率的。),低位+/-1实际有效的索引(&MMASK)
如下图
exchange方法
public V exchange(V x) throws InterruptedException {
Object v;
Object item = (x == null) ? NULL_ITEM : x; // 转换成空对象
// arena == null, 路由到slotExchange(单槽交换), 如果arena != null或者单槽交换失败,且线程没有被中断,则路由到arenaExchange(多槽交换),返回null,则抛出中断异常
if ((arena != null || (v = slotExchange(item, false, 0L)) == null)
&& ((Thread.interrupted() || (v = arenaExchange(item, false, 0L)) == null)))
throw new InterruptedException();
return (v == NULL_ITEM) ? null : (V) v;
}
首先判断arena是否为null,如果为null,则调用slotExchange方法,如果arena不为null,或者slotExchange方法返回null,然后判断当前线程是否被中断(中断标记),有则抛出中断异常,没有则继续调用arenaExchange方法,如果该方法返回null,抛出中断异常,最后返回结果。
带超时的exchange方法
public V exchange(V x, long timeout, TimeUnit unit) throws InterruptedException, TimeoutException {
Object v;
Object item = (x == null) ? NULL_ITEM : x;// 转换成空对象
long ns = unit.toNanos(timeout);
// arena == null, 路由到slotExchange(单槽交换), 如果arena != null或者单槽交换失败,且线程没有被中断,则路由到arenaExchange(多槽交换),返回null,则抛出中断异常
if ((arena != null || (v = slotExchange(item, true, ns)) == null)
&& ((Thread.interrupted() || (v = arenaExchange(item, true, ns)) == null)))
throw new InterruptedException();
if (v == TIMED_OUT)// 超时
throw new TimeoutException();
return (v == NULL_ITEM) ? null : (V) v;
}
同上,加了超时的判断。
slotExchange方法
private final Object slotExchange(Object item, boolean timed, long ns) {
Node p = participant.get(); // 获取当前线程携带的Node
Thread t = Thread.currentThread(); // 当前线程
if (t.isInterrupted()) // 保留中断状态,以便调用者可以重新检查,Thread.interrupted() 会清除中断状态标记
return null;
for (Node q;;) {
if ((q = slot) != null) { // slot不为null, 说明已经有线程在这里等待了
if (U.compareAndSwapObject(this, SLOT, q, null)) { // 将slot重新设置为null, CAS操作
Object v = q.item; // 取出等待线程携带的数据
q.match = item; // 将当前线程的携带的数据交给等待线程
Thread w = q.parked; // 可能存在的等待线程(可能中断,不等了)
if (w != null)
U.unpark(w); // 唤醒等待线程
return v; // 返回结果,交易成功
}
// CPU的个数多于1个,并且bound为0时创建 arena,并将bound设置为SEQ大小
if (NCPU > 1 && bound == 0 && U.compareAndSwapInt(this, BOUND, 0, SEQ))
arena = new Node[(FULL + 2) << ASHIFT]; // 根据CPU的个数估计Node的数量
} else if (arena != null)
return null; // 如果slot为null, 但arena不为null, 则转而路由到arenaExchange方法
else { // 最后一种情况,说明当前线程先到,则占用此slot
p.item = item; // 将携带的数据卸下,等待别的线程来交易
if (U.compareAndSwapObject(this, SLOT, null, p)) // 将slot的设为当前线程携带的Node
break; // 成功则跳出循环
p.item = null; // 失败,将数据清除,继续循环
}
}
// 当前线程等待被释放, spin -> yield -> block/cancel
int h = p.hash; // 伪随机,用于自旋
long end = timed ? System.nanoTime() + ns : 0L; // 如果timed为true,等待超时的时间点; 0表示没有设置超时
int spins = (NCPU > 1) ? SPINS : 1; // 自旋次数
Object v;
while ((v = p.match) == null) { // 一直循环,直到有线程来交易
if (spins > 0) { // 自旋,直至spins不大于0
h ^= h << 1; // 伪随机算法, 目的是等h小于0(随机的)
h ^= h >>> 3;
h ^= h << 10;
if (h == 0) // 初始值
h = SPINS | (int) t.getId();
else if (h < 0 && (--spins & ((SPINS >>> 1) - 1)) == 0)
Thread.yield(); // 等到h < 0, 而spins的低9位也为0(防止spins过大,CPU空转过久),让出CPU时间片,每一次等待有两次让出CPU的时机(SPINS >>> 1)
} else if (slot != p) // 别的线程已经到来,正在准备数据,自旋等待一会儿,马上就好
spins = SPINS;
// 如果线程没被中断,且arena还没被创建,并且没有超时
else if (!t.isInterrupted() && arena == null && (!timed || (ns = end - System.nanoTime()) > 0L)) {
U.putObject(t, BLOCKER, this); // 设置当前线程将阻塞在当前对象上
p.parked = t; // 挂在此结点上的阻塞着的线程
if (slot == p)
U.park(false, ns); // 阻塞, 等着被唤醒或中断
p.parked = null; // 醒来后,解除与结点的联系
U.putObject(t, BLOCKER, null); // 解除阻塞对象
} else if (U.compareAndSwapObject(this, SLOT, p, null)) { // 超时或其他(取消),给其他线程腾出slot
v = timed && ns <= 0L && !t.isInterrupted() ? TIMED_OUT : null;
break;
}
}
// 归位
U.putOrderedObject(p, MATCH, null);
p.item = null;
p.hash = h;
return v;
}
总结
1. 检查slot是否为空(null),不为空,说明已经有线程在此等待,尝试占领该槽位,如果占领成功,与等待线程交换数据,并唤醒等待线程,交易结束,返回。
2. 如果占领槽位失败,创建arena,但要继续【步骤1】尝试抢占slot,直至slot为空,或者抢占成功,交易结束返回。
3. 如果slot为空,则判断arena是否为空,如果arena不为空,返回null,重新路由到arenaExchange方法
4. 如果arena为空,说明当前线程是先到达的,尝试占有slot,如果成功,将slot标记为自己占用,跳出循环,继续【步骤5】,如果失败,则继续【步骤1】
5 当前线程等待被释放,等待的顺序是先自旋(spin),不成功则让出CPU时间片(yield),最后还不行就阻塞(block),spin -> yield -> block
6. 如果超时(设置超时的话)或被中断,则退出循环。
7. 最后,重置数据,下次重用,返回结果,结束。
见下图
arenaExchange方法
private final Object arenaExchange(Object item, boolean timed, long ns) {
Node[] a = arena; // 交换场地,一排slot
Node p = participant.get(); // 获取当前线程携带的Node
for (int i = p.index;;) { // arena的索引,数组下标
int b, m, c;
long j; // 原数组偏移量,包括填充值
// 从场地中选出偏移地址为(i << ASHIFT) + ABASE的内存值,也即真正可用的Node
Node q = (Node) U.getObjectVolatile(a, j = (i << ASHIFT) + ABASE);
if (q != null && U.compareAndSwapObject(a, j, q, null)) { // 此槽位不为null, 说明已经有线程在这里等了,重新将其设置为null, CAS操作
Object v = q.item; // 取出等待线程携带的数据
q.match = item; // 将当前线程携带的数据交给等待线程
Thread w = q.parked; // 可能存在的等待线程
if (w != null)
U.unpark(w); // 唤醒等待线程
return v; // 返回结果, 交易成功
} else if (i <= (m = (b = bound) & MMASK) && q == null) { // 有效交换位置,且槽位为空
p.item = item; // 将携带的数据卸下,等待别的线程来交易
if (U.compareAndSwapObject(a, j, null, p)) { // 槽位占领成功
long end = (timed && m == 0) ? System.nanoTime() + ns : 0L; // 计算出超时结束时间点
Thread t = Thread.currentThread(); // 当前线程
for (int h = p.hash, spins = SPINS;;) { // 一直循环,直到有别的线程来交易,或超时,或中断
Object v = p.match; // 检查是否有别的线程来交换数据
if (v != null) { // 有则返回
U.putOrderedObject(p, MATCH, null); // match重置,等着下次使用
p.item = null; // 清空,下次接着使用
p.hash = h;
return v; // 返回结果,交易结束
} else if (spins > 0) { // 自旋
h ^= h << 1;
h ^= h >>> 3;
h ^= h << 10; // 移位加异或,伪随机
if (h == 0) // 初始值
h = SPINS | (int) t.getId();
else if (h < 0 && // SPINS >>> 1, 一半的概率
(--spins & ((SPINS >>> 1) - 1)) == 0)
Thread.yield(); // 每一次等待有两次让出CPU的时机
} else if (U.getObjectVolatile(a, j) != p)
spins = SPINS; // 别的线程已经到来,正在准备数据,自旋等待一会儿,马上就好
else if (!t.isInterrupted() && m == 0 && (!timed || (ns = end - System.nanoTime()) > 0L)) {
U.putObject(t, BLOCKER, this); // 设置当前线程将阻塞在当前对象上
p.parked = t; // 挂在此结点上的阻塞着的线程
if (U.getObjectVolatile(a, j) == p)
U.park(false, ns); // 阻塞, 等着被唤醒或中断
p.parked = null; // 醒来后,解除与结点的联系
U.putObject(t, BLOCKER, null); // 解除阻塞对象
} else if (U.getObjectVolatile(a, j) == p && U.compareAndSwapObject(a, j, p, null)) {
if (m != 0) // 尝试缩减
U.compareAndSwapInt(this, BOUND, b, b + SEQ - 1); // 更新bound, 高位递增,低位 -1
p.item = null; // 重置
p.hash = h;
i = p.index >>>= 1; // 索引减半,为的是快速找到汇合点(最左侧)
if (Thread.interrupted())// 保留中断状态,以便调用者可以重新检查,Thread.interrupted() 会清除中断状态标记
return null;
if (timed && m == 0 && ns <= 0L) // 超时
return TIMED_OUT;
break; // 重新开始
}
}
} else
p.item = null; // 重置
} else {
if (p.bound != b) { // 别的线程更改了bound,重置collides为0, i的情况如下:当i != m, 或者m = 0时,i = m; 否则,i = m-1; 从右往左遍历
p.bound = b;
p.collides = 0;
i = (i != m || m == 0) ? m : m - 1; // index 左移
} else if ((c = p.collides) < m || m == FULL || !U.compareAndSwapInt(this, BOUND, b, b + SEQ + 1)) { // 更新bound, 高位递增,低位 +1
p.collides = c + 1;
i = (i == 0) ? m : i - 1; // 左移,遍历槽位,m == FULL时,i == 0(最左侧),重置i = m, 重新从右往左循环遍历
} else
i = m + 1; // 槽位增长
p.index = i;
}
}
}
总结
1. 从场地中选出偏移地址为(i << ASHIFT) + ABASE的内存值,也即第i个真正可用的Node,判断其槽位是否为空,为空,进入【步骤2】;不为空,说明有线程在此等待,尝试抢占该槽位,抢占成功,交换数据,并唤醒等待线程,返回,结束;没有抢占成功,进入【步骤9】
2. 检查索引(i vs m)是否越界,越界,进入【步骤9】;没有越界,进入下一步。
3. 尝试占有该槽位,抢占失败,进入【步骤1】;抢占成功,进入下一步。
4. 检查match,是否有线程来交换数据,如果有,交换数据,结束;如果没有,进入下一步。
5. 检查spin是否大于0,如果不大于0,进入下一步;如果大于0,检查hash是否小于0,并且spin减半或为0,如果不是,进入【步骤4】;如果是,让出CPU时间,过一会儿,进入【步骤4】
6. 检查是否中断,m达到最小值,是否超时,如果没有中断,没有超时,并且m达到最小值,阻塞,过一会儿进入【步骤4】;否则,下一步。
7. 没有线程来交换数据,尝试丢弃原有的槽位重新开始,丢弃失败,进入【步骤4】;否则,下一步。
8. bound减1(m>0),索引减半;检查是否中断或超时,如果没有,进入【步骤1】;否则,返回,结束。
9. 检查bound是否发生变化,如果变化了,重置collides,索引重置为m或左移,转向【步骤1】;否则,进入下一步。
10. 检查collides是否达到最大值,如果没有,进入【步骤13】,否则下一步。
11. m是否达到FULL,是,进入【步骤13】;否则,下一步。
12. CAS bound加1是否成功,如果成功,i置为m+1,槽位增长,进入【步骤1】;否则,下一步。
13. collides加1,索引左移,进入【步骤1】
见下图(看不清图片?鼠标放在图片上面,【右键】 -> 【在新标签页中打开图片(I)】 -> 【点击(+)矢量放大】)
Unsafe
private static final sun.misc.Unsafe U;
private static final long BOUND;
private static final long SLOT;
private static final long MATCH;
private static final long BLOCKER;
private static final int ABASE;
static {
int s;
try {
U = sun.misc.Unsafe.getUnsafe();
Class<?> ek = Exchanger.class;
Class<?> nk = Node.class;
Class<?> ak = Node[].class;
Class<?> tk = Thread.class;
BOUND = U.objectFieldOffset(ek.getDeclaredField("bound"));
SLOT = U.objectFieldOffset(ek.getDeclaredField("slot"));
MATCH = U.objectFieldOffset(nk.getDeclaredField("match"));
BLOCKER = U.objectFieldOffset(tk.getDeclaredField("parkBlocker"));
s = U.arrayIndexScale(ak); // 数组增量地址
ABASE = U.arrayBaseOffset(ak) + (1 << ASHIFT); // 数组首元素偏移地址
} catch (Exception e) {
throw new Error(e);
}
if ((s & (s - 1)) != 0 || s > (1 << ASHIFT))
throw new Error("Unsupported array scale");
}
s为数组中每个元素占用的地址空间大小,ABASE为数组首元素偏移地址,防止伪共享
最后,arena = new Node[(FULL + 2) << ASHIFT],FULL,<= MMASK,scale,<= 1 << ASHIFT,说明(FULL + 2)<< ASHIFT 个Node,真正可用的是FULL + 2个,实际上是FULL + 1 个,最后一个没有用,也是为了防止伪共享,如果最后一个也使用,那么,其右边并没有填充,别的数据修改可能会影响到它,也即是发生伪共享问题。最大的有效索引是MMASK(bound & MMASK),但m(实际的最大索引)增长到FULL时,不再增长,会循环遍历槽位,尝试交换数据。
伪随机
h ^= h << 1; h ^= h >>> 3; h ^= h << 10;
实际上是xorshift算法,T = (I + La)(I + Rb)(I + Lc),其中,L代表左移,R代表右移,a, b, c分别代表上式的1,3,10,I代表矩阵{0,1}共32位(int),也即是二进制int,T代表的就是随机算法。翻译过来就是上面的式子:h ^= h << 1; h ^= h >>> 3; h ^= h << 10.
为什么要选用1,3,10呢?
其实,伪随机数,并不是真正的随机,而是通过算法模拟出来的,为了达到随机的效果,希望是周期越大越好。所谓周期指的是,当给定一个输入,得到的输出再作为下一次的输入,如此反复,直到某次输出恰巧等于最初的输入,可以作为随机算法关于随机数的周期。有了这个概念,我们就可以写代码测试下。
直观地推测,int类型最大周期应该是遍历该类型所有的值(0除外,【奇异矩阵】,如果是0的话,输出便一直是0,谈不上随机了),即是max - min = 232 - 1
Java代码
public class PseudoRandom {
private static final Map<Long, StringBuilder> map = new ConcurrentHashMap<>(); public static void random(int a, int b, int c) {
long cnt = 0;
int h = 1;
do {
h ^= h << a;
h ^= h >>> b;
h ^= h << c;
cnt++;
} while (h != 1); StringBuilder builder = map.get(cnt);
if (builder == null) {
builder = new StringBuilder();
map.put(cnt, builder);
} builder.append(" (" + a + ", " + b + ", " + c + ")");
} public static void main(String[] args) {
CountDownLatch latch = new CountDownLatch(11 * 11 * 11);
ExecutorService s = Executors.newFixedThreadPool(10);
for (int i = 1; i < 11; i++) { // i, j ,k实际上应该是31,这里仅为了说明问题,当改成31时,CountDownLatch应该初始化为31 * 31 * 31
for (int j = 1; j < 11; j++) {
for (int k = 1; k < 11; k++) {
final int ii = i;
final int jj = j;
final int kk = k;
s.execute(new Runnable() {
@Override
public void run() {
random(ii, jj, kk);
latch.countDown();
}
});
}
}
} s.shutdown();
try {
latch.await(300, TimeUnit.SECONDS);
} catch (InterruptedException e) {
Thread.currentThread().interrupt();
} TreeMap<Long, StringBuilder> t = new TreeMap<Long, StringBuilder>(Collections.reverseOrder());
t.putAll(map); for (Map.Entry<Long, StringBuilder> entry : t.entrySet()) {
System.out.println("[" + entry.getKey() + "]" + entry.getValue().toString());
}
}
}
输出,按周期次数倒序排列,即最大的在前
[4294967295] (1, 3, 10) (2, 7, 7) (2, 7, 9) (5, 9, 7) (7, 1, 9) (7, 7, 2) (7, 9, 5)
[4160749537] (1, 7, 9) (4, 1, 9) (6, 5, 9)
[3900702255] (1, 3, 4) (5, 5, 7) (7, 5, 5)
[3758096377] (1, 9, 2) (2, 9, 1) (7, 7, 9)
[2147483647] (1, 5, 5) (1, 9, 6) (2, 5, 5) (2, 5, 7) (5, 5, 1) (5, 5, 2) (6, 5, 7) (6, 9, 1) (7, 5, 2) (7, 5, 6)
[2147483644] (1, 9, 10)
[2147213313] (2, 5, 3) (3, 5, 2)
[2147188740] (4, 5, 5) (4, 9, 1) (5, 5, 4)
[2145385473] (7, 9, 9)
[2145382404] (1, 5, 9)
[2143288833] (5, 1, 6) (6, 1, 5)
[2139094020] (1, 7, 6)
[2113929153] (1, 5, 4) (4, 5, 1)
[2080374753] (2, 3, 3) (3, 3, 2)
[1997533470] (2, 9, 9)
[1879048185] (2, 5, 9) (4, 7, 9)
[1747831785] (8, 9, 5)
[1610612733] (7, 3, 10)
[1560280902] (3, 5, 5) (5, 5, 3)
[1431655765] (1, 7, 7) (2, 9, 5) (5, 1, 8) (5, 9, 2) (7, 7, 1) (8, 1, 5)
[1431562923] (1, 1, 2) (2, 1, 1)
[1430257323] (3, 9, 7) (7, 9, 3)
[1409286123] (5, 3, 7) (7, 3, 5) (9, 1, 10)
[1339553285] (1, 9, 5) (5, 9, 1)
[1242911789] (3, 7, 10) (5, 3, 10)
[1174405085] (1, 3, 5) (5, 3, 1) (9, 3, 4)
[1073741823] (3, 1, 6) (6, 1, 3)
[1073594370] (1, 9, 4)
[1064182911] (4, 3, 7) (7, 3, 4)
[1006632930] (3, 1, 10)
[714429611] (3, 1, 4) (4, 1, 3)
[713031595] (1, 7, 5) (5, 7, 1) (7, 7, 10)
[704642988] (3, 9, 10)
[626349395] (9, 5, 3)
[621455450] (2, 3, 9)
[613543351] (1, 5, 3) (3, 5, 1)
[602795529] (1, 1, 9) (7, 3, 9) (9, 1, 1) (9, 3, 7)
[536870911] (3, 5, 7) (6, 9, 7) (7, 5, 3) (7, 9, 6)
[536772612] (1, 1, 3)
[534773505] (6, 7, 1)
[528482241] (8, 3, 9)
[520093634] (1, 5, 10)
[469762041] (1, 7, 4) (4, 1, 7) (7, 1, 4)
[459276069] (4, 7, 5)
[453248985] (1, 3, 7)
[429286605] (5, 7, 6) (6, 7, 5)
[426141261] (1, 3, 8) (8, 3, 1)
[390070086] (1, 1, 6)
[389118324] (3, 3, 10)
[352321494] (6, 7, 9)
[352106517] (3, 7, 5) (5, 7, 3)
[341310837] (8, 7, 1)
[335544315] (4, 9, 7) (7, 7, 8) (7, 9, 4) (8, 7, 7)
[335360010] (3, 9, 5)
[310727725] (9, 3, 2)
[286331153] (5, 3, 8) (8, 3, 5)
[268435455] (1, 9, 3) (3, 9, 1)
[268435454] (3, 1, 8) (7, 9, 8) (8, 9, 7)
[268435452] (3, 1, 7) (7, 1, 3)
[268435448] (2, 3, 7)
[267386370] (5, 7, 7) (7, 7, 5)
[260046817] (4, 3, 1)
[259507262] (9, 5, 5)
[252645135] (3, 1, 5) (5, 1, 3)
[249690255] (5, 9, 8)
[234637326] (4, 1, 5)
[201326586] (5, 3, 6) (5, 7, 9) (6, 3, 5)
[201222147] (3, 7, 8) (8, 7, 3)
[195225786] (8, 1, 7)
[178924204] (3, 1, 1)
[167772155] (4, 3, 9)
[167680005] (5, 9, 3)
[153391689] (1, 5, 2) (2, 5, 1)
[153092023] (5, 7, 4)
[142501905] (2, 3, 5) (5, 3, 2)
[134217727] (8, 1, 3)
[134217726] (7, 5, 8)
[134150145] (3, 7, 9)
[134085633] (3, 7, 6) (6, 7, 3)
[133693185] (1, 9, 7) (7, 9, 1)
[129753631] (3, 9, 4) (4, 9, 3) (5, 5, 9)
[117318663] (5, 1, 4)
[100663293] (8, 9, 9)
[97612893] (7, 1, 8)
[97517382] (1, 7, 8)
[94371795] (1, 7, 3) (3, 7, 1)
[93323175] (6, 1, 7) (7, 1, 6)
[89478485] (3, 5, 9)
[87951402] (5, 9, 10)
[82993665] (4, 3, 5) (5, 3, 4)
[78212442] (1, 7, 10) (7, 5, 9) (9, 5, 7)
[75497463] (9, 3, 8)
[69273666] (7, 5, 1)
[67108863] (4, 7, 1) (5, 9, 9)
[67108862] (7, 3, 2)
[67084290] (9, 5, 10)
[66584449] (9, 3, 10)
[66059784] (4, 5, 9) (9, 5, 4)
[65536191] (2, 1, 5) (5, 1, 2)
[65011681] (6, 1, 1)
[62914530] (1, 7, 2) (2, 7, 1)
[58260615] (2, 9, 3) (3, 9, 2)
[57252195] (3, 5, 4) (4, 5, 3)
[56884380] (1, 1, 5) (5, 1, 1)
[55050135] (3, 1, 9) (9, 1, 3)
[47439707] (1, 5, 8) (8, 5, 1)
[44739242] (8, 5, 7)
[42105595] (1, 9, 8) (8, 9, 1)
[41287365] (5, 9, 6)
[34636833] (1, 3, 6) (1, 5, 7) (6, 3, 1)
[33554430] (3, 3, 8) (8, 3, 3)
[33554416] (6, 5, 3)
[30593745] (6, 7, 7) (7, 7, 6)
[23194290] (7, 3, 6)
[22282155] (1, 3, 2) (2, 3, 1)
[19473111] (1, 1, 4) (4, 1, 1)
[19168695] (1, 1, 8) (8, 1, 1)
[17284575] (5, 7, 8) (8, 7, 5)
[16777215] (1, 3, 3) (3, 3, 1) (5, 3, 9) (9, 3, 5)
[16777208] (3, 5, 6)
[16129169] (5, 1, 7) (7, 1, 5)
[14351946] (3, 7, 7)
[11597145] (6, 3, 7)
[11184810] (2, 7, 5) (5, 7, 2)
[11180715] (3, 7, 4) (4, 7, 3)
[9266985] (3, 3, 7) (7, 3, 3)
[8382465] (1, 1, 10)
[8257473] (6, 9, 5)
[7798308] (5, 5, 6)
[7427385] (4, 9, 9)
[7339976] (8, 1, 9) (9, 1, 8)
[5963685] (4, 9, 5) (5, 9, 4)
[5832615] (7, 1, 10)
[5592405] (2, 1, 3) (3, 1, 2)
[5374005] (5, 1, 9) (9, 1, 5)
[5332341] (7, 3, 1)
[5158440] (2, 1, 9)
[4783982] (7, 7, 3)
[3997791] (1, 9, 9)
[2936010] (5, 1, 10)
[2790571] (2, 9, 7) (7, 9, 2)
[2579220] (9, 1, 2)
[2162622] (3, 3, 5)
[2149602] (2, 1, 7) (7, 1, 2)
[1179612] (5, 5, 8) (8, 5, 5)
[1081311] (5, 3, 3)
[1048575] (1, 3, 9) (1, 5, 6) (6, 5, 1) (9, 3, 1)
[1043970] (8, 5, 3)
[1016379] (7, 9, 10)
[1003935] (6, 1, 9) (9, 1, 6)
[573405] (2, 7, 3) (3, 7, 2)
[557039] (1, 1, 7) (7, 1, 1)
[522753] (3, 3, 4) (4, 3, 3)
[521985] (3, 5, 8)
[458724] (7, 3, 8) (8, 3, 7)
[390915] (4, 5, 7) (7, 5, 4)
[278511] (6, 5, 5)
[131070] (1, 4, 7) (1, 8, 9) (1, 10, 10) (2, 4, 9) (2, 5, 6) (2, 7, 4) (2, 7, 8) (2, 7, 10) (2, 8, 7) (4, 6, 7) (4, 7, 2) (4, 9, 4) (5, 2, 9) (5, 4, 7) (5, 6, 8) (5, 8, 7) (5, 8, 10) (6, 5, 2) (6, 8, 7) (7, 4, 1) (7, 4, 5) (7, 6, 4) (7, 8, 2) (7, 8, 5) (7, 8, 6) (8, 6, 5) (8, 7, 2) (8, 7, 10) (9, 2, 5) (9, 4, 2)
[129794] (2, 5, 4) (2, 9, 8) (3, 5, 3) (4, 5, 2) (4, 5, 6) (5, 8, 9) (6, 5, 4) (8, 9, 2)
[128961] (7, 5, 10)
[126914] (6, 3, 10) (7, 6, 9) (7, 10, 9) (8, 6, 9) (9, 6, 7) (9, 6, 8)
[114674] (1, 2, 7) (1, 2, 9) (3, 4, 10) (5, 10, 7) (7, 2, 1) (7, 2, 8) (7, 10, 5) (8, 2, 7) (9, 2, 1)
[110670] (3, 2, 5) (5, 2, 3)
[98301] (4, 7, 7) (7, 7, 4)
[95046] (4, 4, 7) (5, 2, 2) (5, 6, 10) (7, 4, 4)
[85974] (2, 4, 7) (6, 6, 1) (7, 4, 2)
[65535] (2, 10, 4) (4, 10, 2) (5, 7, 10)
[65534] (1, 3, 1) (1, 6, 5) (3, 4, 9) (3, 10, 5) (4, 7, 4) (5, 6, 1) (5, 6, 7) (5, 10, 3) (6, 3, 8) (7, 6, 5) (8, 3, 6) (9, 4, 3)
[65532] (4, 10, 3)
[65528] (1, 2, 3) (4, 5, 10) (7, 4, 9) (9, 4, 7)
[64770] (1, 4, 9) (9, 4, 1)
[63240] (3, 4, 4) (4, 4, 3) (8, 2, 9) (9, 2, 8)
[61410] (2, 2, 7) (7, 2, 2)
[61320] (9, 2, 10)
[57316] (2, 3, 2) (6, 5, 8) (8, 5, 6)
[57288] (3, 8, 7) (7, 8, 3)
[55335] (4, 2, 6) (6, 2, 4) (8, 7, 9)
[55118] (3, 8, 8) (8, 8, 3)
[49146] (1, 8, 7) (2, 3, 8) (3, 4, 5) (5, 4, 3) (7, 8, 1) (8, 3, 2)
[47523] (2, 2, 8) (8, 2, 2)
[47244] (4, 7, 6) (6, 7, 4) (6, 10, 9)
[43690] (1, 2, 5) (1, 10, 3) (3, 10, 1) (3, 10, 7) (5, 2, 1) (5, 4, 6) (6, 4, 5) (7, 2, 9) (7, 8, 8) (7, 10, 3) (8, 8, 7) (9, 2, 7) (9, 4, 10)
[42966] (1, 8, 3) (2, 8, 5) (3, 8, 1) (3, 8, 5) (5, 8, 2) (5, 8, 3) (6, 7, 10)
[40955] (3, 9, 8) (8, 9, 3)
[39370] (5, 2, 6) (6, 2, 5)
[32767] (2, 2, 6) (6, 2, 2)
[32766] (2, 3, 6) (2, 9, 10) (2, 10, 9) (3, 2, 9) (3, 8, 6) (3, 10, 4) (3, 10, 10) (4, 4, 5) (4, 7, 10) (4, 9, 10) (5, 4, 4) (6, 3, 2) (6, 8, 3) (9, 2, 3)
[32764] (3, 2, 1)
[32752] (2, 6, 7) (4, 8, 5) (5, 8, 4) (7, 6, 2)
[31682] (2, 2, 5)
[31248] (6, 6, 5)
[30660] (3, 7, 3)
[28658] (1, 6, 6) (5, 4, 8) (8, 4, 5) (8, 10, 6)
[28644] (3, 2, 10)
[26670] (2, 10, 3) (3, 10, 2) (5, 10, 8) (8, 10, 5)
[26214] (2, 2, 9) (2, 9, 4) (4, 9, 2) (9, 2, 2)
[26040] (2, 8, 3)
[24573] (2, 6, 10)
[24528] (2, 5, 10) (5, 3, 5)
[23622] (7, 6, 1)
[22134] (3, 8, 4) (4, 8, 3)
[21844] (3, 2, 4) (4, 2, 3)
[21590] (3, 10, 9)
[21483] (4, 6, 6) (6, 6, 4)
[21420] (5, 2, 8) (8, 2, 5)
[21336] (1, 10, 9)
[20470] (7, 10, 10) (8, 10, 9)
[20460] (7, 8, 9)
[16383] (4, 6, 10) (4, 10, 10)
[16002] (5, 10, 6) (6, 10, 5)
[15810] (3, 5, 10)
[15748] (1, 6, 7)
[15624] (5, 6, 6)
[15330] (1, 4, 10) (3, 10, 6) (4, 9, 6) (6, 9, 4) (6, 10, 3)
[14329] (6, 10, 8)
[14322] (2, 10, 10) (3, 6, 10) (4, 3, 6) (4, 6, 9) (6, 3, 4) (9, 6, 4) (9, 6, 10)
[14280] (8, 6, 10)
[13020] (3, 8, 2)
[10922] (2, 4, 5) (5, 4, 2)
[10710] (6, 6, 7) (7, 6, 6)
[10668] (2, 10, 8)
[10416] (4, 3, 4)
[10230] (1, 5, 1)
[9362] (1, 4, 6) (2, 3, 4) (3, 6, 7) (3, 10, 8) (4, 3, 2) (6, 4, 1) (6, 9, 8) (7, 6, 3) (8, 9, 6) (8, 10, 3)
[9198] (3, 2, 6) (4, 10, 7) (6, 2, 3) (7, 10, 4)
[9052] (2, 8, 9)
[8190] (1, 6, 10) (1, 10, 6) (2, 6, 9) (4, 3, 10) (5, 4, 10) (5, 8, 6) (6, 4, 7) (6, 8, 5) (6, 10, 1) (6, 10, 7) (7, 2, 10) (7, 4, 6) (7, 10, 6) (9, 6, 2)
[8184] (4, 2, 5) (5, 4, 9) (7, 6, 7) (9, 4, 5)
[7905] (8, 6, 2)
[7710] (2, 10, 7) (7, 10, 2)
[7140] (6, 2, 9) (9, 2, 6)
[7112] (5, 8, 1)
[6510] (6, 10, 10)
[5460] (3, 8, 10)
[5334] (1, 10, 5) (5, 10, 1) (6, 8, 9)
[5208] (3, 2, 7)
[4774] (1, 2, 10)
[4526] (4, 10, 6)
[4284] (8, 3, 10)
[4095] (6, 2, 10) (7, 2, 7)
[4094] (2, 2, 10)
[4092] (3, 2, 8) (5, 2, 4) (7, 10, 7) (8, 2, 3)
[4088] (8, 8, 9)
[3906] (4, 10, 9)
[3810] (3, 6, 8) (8, 6, 3)
[3556] (2, 5, 2) (9, 2, 9)
[3472] (2, 6, 3) (3, 6, 2)
[3276] (1, 4, 3) (3, 4, 1)
[3069] (3, 10, 3) (5, 6, 5)
[3066] (7, 8, 10)
[2920] (2, 5, 8) (8, 5, 2)
[2730] (1, 8, 10) (5, 2, 7) (6, 10, 2) (7, 2, 5) (7, 6, 10)
[2570] (4, 8, 9)
[2520] (4, 8, 7) (7, 8, 4)
[2286] (1, 6, 9) (9, 6, 1)
[2263] (6, 10, 4)
[2142] (1, 10, 7) (2, 4, 3) (3, 4, 2) (7, 10, 1)
[2114] (3, 4, 7) (7, 4, 3)
[2044] (6, 5, 10)
[1953] (3, 6, 3) (3, 9, 3) (6, 6, 8) (6, 9, 6) (8, 6, 6)
[1778] (1, 8, 5)
[1533] (3, 9, 9) (6, 6, 10) (9, 6, 3)
[1530] (3, 4, 6) (5, 2, 10) (6, 4, 3)
[1524] (2, 2, 3) (3, 2, 2) (7, 10, 8)
[1365] (1, 10, 1) (2, 10, 6) (5, 2, 5)
[1302] (3, 6, 5) (5, 6, 3) (7, 2, 3) (8, 2, 6)
[1190] (2, 6, 4) (4, 6, 2)
[1116] (5, 10, 9)
[1068] (3, 4, 8) (8, 4, 3)
[1023] (3, 3, 6) (6, 3, 3)
[1022] (8, 2, 10)
[1020] (4, 4, 9) (4, 10, 5) (5, 8, 8) (5, 10, 4) (6, 2, 7) (7, 2, 6) (8, 8, 5) (9, 4, 4)
[1008] (1, 2, 6) (6, 2, 1)
[930] (3, 6, 4) (4, 2, 7) (4, 6, 3) (7, 2, 4)
[889] (8, 10, 2)
[868] (1, 6, 2) (1, 10, 4) (2, 6, 1) (4, 2, 9) (4, 10, 1) (9, 2, 4)
[840] (8, 6, 7)
[762] (1, 4, 5) (5, 4, 1) (8, 10, 7)
[682] (7, 4, 10)
[630] (1, 6, 3) (2, 3, 10) (3, 6, 1) (5, 6, 9) (6, 4, 9) (9, 4, 6) (9, 6, 5)
[511] (3, 6, 9)
[510] (2, 6, 5) (2, 6, 8) (2, 8, 10) (2, 9, 6) (3, 8, 9) (4, 6, 5) (5, 6, 2) (5, 6, 4) (6, 9, 2)
[508] (1, 2, 2) (1, 10, 8) (2, 2, 1) (4, 3, 8) (4, 9, 8) (6, 7, 8) (6, 9, 9) (8, 3, 4) (8, 7, 6) (8, 9, 4) (8, 10, 1) (9, 3, 9)
[496] (1, 2, 8) (8, 2, 1)
[476] (2, 7, 6) (6, 7, 2)
[434] (6, 2, 8)
[420] (7, 6, 8)
[315] (8, 10, 10)
[280] (8, 5, 10)
[255] (4, 4, 8) (8, 4, 4)
[254] (3, 8, 3) (4, 4, 10) (4, 6, 4) (4, 10, 8) (6, 8, 10) (8, 10, 4)
[252] (1, 7, 1) (1, 10, 2) (2, 7, 2) (2, 10, 1) (4, 8, 10) (6, 4, 10) (7, 3, 7) (8, 8, 10) (8, 9, 10)
[248] (4, 6, 8) (6, 6, 9) (9, 6, 6)
[240] (1, 2, 4) (4, 2, 1)
[234] (4, 5, 8) (8, 5, 4)
[210] (1, 8, 6) (2, 6, 6) (6, 6, 2) (6, 8, 1)
[186] (2, 8, 6) (2, 10, 2) (5, 4, 5) (6, 8, 2)
[170] (3, 3, 9)
[146] (3, 6, 6) (6, 6, 3)
[127] (6, 9, 3)
[126] (6, 4, 8) (7, 4, 7) (7, 4, 8) (8, 4, 6) (8, 4, 7)
[124] (8, 6, 4)
[120] (1, 4, 8) (1, 6, 4) (1, 6, 8) (4, 6, 1) (5, 7, 5) (5, 9, 5) (6, 5, 6) (6, 7, 6) (8, 4, 1) (8, 6, 1) (9, 6, 9)
[105] (5, 10, 10)
[102] (4, 8, 6) (6, 8, 4) (6, 8, 8) (6, 9, 10) (8, 8, 6)
[93] (1, 6, 1) (3, 2, 3) (6, 3, 6)
[85] (4, 2, 10) (9, 3, 3)
[84] (2, 4, 6) (2, 6, 2) (2, 10, 5) (3, 4, 3) (5, 10, 2) (6, 4, 2) (8, 4, 10)
[63] (6, 4, 6)
[60] (2, 4, 4) (2, 4, 8) (4, 4, 2) (4, 10, 4) (5, 8, 5) (8, 4, 2)
[56] (1, 4, 4) (4, 4, 1)
[51] (6, 3, 9) (9, 3, 6)
[48] (4, 4, 6) (4, 7, 8) (6, 4, 4) (8, 7, 4)
[42] (2, 4, 10) (5, 5, 10)
[35] (5, 5, 5)
[32] (1, 1, 1) (1, 4, 2) (1, 8, 2) (1, 8, 4) (1, 9, 1) (2, 1, 2) (2, 1, 4) (2, 1, 6) (2, 1, 8) (2, 1, 10) (2, 4, 1) (2, 8, 1) (2, 9, 2) (3, 1, 3) (4, 1, 2) (4, 1, 4) (4, 1, 6) (4, 1, 8) (4, 1, 10) (4, 5, 4) (4, 8, 1) (5, 1, 5) (6, 1, 2) (6, 1, 4) (6, 1, 6) (6, 1, 8) (6, 1, 10) (7, 1, 7) (7, 5, 7) (7, 9, 7) (8, 1, 2) (8, 1, 4) (8, 1, 6) (8, 1, 8) (8, 1, 10) (8, 3, 8) (8, 4, 9) (8, 5, 8) (9, 1, 9) (9, 4, 8) (9, 5, 9)
[31] (1, 2, 1) (3, 3, 3) (7, 7, 7)
[30] (6, 8, 6)
[24] (2, 8, 8)
[21] (2, 2, 4) (4, 2, 2)
[16] (1, 4, 1) (1, 8, 1) (1, 8, 8) (2, 2, 2) (4, 2, 8) (6, 2, 6) (6, 10, 6) (8, 2, 4) (8, 2, 8) (8, 8, 1) (9, 4, 9)
[15] (2, 4, 2)
[14] (6, 6, 6)
[12] (4, 8, 8) (8, 8, 2) (8, 8, 4)
[8] (2, 8, 2) (2, 8, 4) (4, 2, 4) (4, 4, 4) (4, 8, 2) (7, 8, 7) (8, 4, 8) (8, 6, 8) (8, 9, 8) (8, 10, 8)
[7] (4, 8, 4) (5, 10, 5)
[5] (3, 9, 6)
[4] (8, 7, 8)
[2] (8, 8, 8)
......5min timeout
可以看到,排在第一的恰巧是(1,3,10)周期为4294967295,正好是 232 - 1
一排多组,表示周期相等。
问题,为什么要有两次左移和一次右移呢?其实只一次左移加异或就能达到随机的效果。
猜测,之所以这样,大概是因为,第一次左移,是为了让高位多1,右移,是为了让低位多1,这样,高位低位都参与进来,增加随机性,第二次左移,便是真正的随机了。
行文至此结束。
尊重他人的劳动,转载请注明出处:http://www.cnblogs.com/aniao/p/aniao_exchanger.html
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