From 3cadbfcf07dbf9f3acff17b1eb5dafee06bd8a40 Mon Sep 17 00:00:00 2001 From: Shine wOng <1551885@tongji.edu.cn> Date: Sun, 22 Sep 2019 20:56:39 +0800 Subject: [PATCH] create eisenberg.md. --- thu_os/eisenberg.md | 152 ++++++++++++++++++++++++++++++++++ thu_os/images/nproc_mutex.png | Bin 0 -> 77310 bytes 2 files changed, 152 insertions(+) create mode 100644 thu_os/eisenberg.md create mode 100644 thu_os/images/nproc_mutex.png diff --git a/thu_os/eisenberg.md b/thu_os/eisenberg.md new file mode 100644 index 0000000..a0dadb7 --- /dev/null +++ b/thu_os/eisenberg.md @@ -0,0 +1,152 @@ +多进程互斥问题的软件实现方法 +========================== + +在前面[进程管理(3):同步互斥](chp17.md)中,已经就两个进程情况下互斥问题的软件实现方法进行了讨论,最终介绍了两种算法,即`Peterson`算法和`Dekkers`算法,这两种算法的基本思路是相同的,但是`Dekkers`算法更容易推广到多进程的情况。因此,以下我们将尝试以`Dekkers`算法为基础,实现多进程的互斥访问。 + +## 一些简单尝试 + +首先还是先来回顾一下`Dekkers`算法,它的代码描述如下: + +```c +flag[i] = true; +while(flag[j] == true){ + if(turn != i){ + flag[i] = false + while(turn != i); + flag[i] = true + } +} +critical_section +turn = j +flag[i] = false; +``` + +在两个进程的情况下,该算法是通过设置一个`turn`标志位来表示当前应该由哪个进程进入临界区,每个进程都拥有一个`flag[i]`标志位,表示当前进程是否想要进入临界区。 + +因此,可以简明的将`Dekkers`算法推广到多进程的情况下,即为每一个进程都设置一个`flag`标志位来表示该进程是否想要进入临界区,继续沿用`turn`标志位表示获得了进入临界区权限的进程。在进入临界区之前,每个进程都需要首先判断所有其他进程的`flag`标志,保证没有其他进程想要进入临界区时,当前进程才进入。在进程退出临界区时,将`turn`标志设置为当前进程的下一个进程。这样,就形成了下面的代码: + +```c +//code for process pid +flag[pid] = true; +while(1){ + for(idx = pid; idx != pid; idx = (idx + 1) % n) + if(flag[idx] == true) break; + if(idx = pid) break; + if(turn != pid){ + flag[pid] = false; + while(turn != pid); + flag[pid] = true; + } +} +critical_section +turn = (pid + 1) % n; +flag[pid] = false; +``` + +和双进程的`Dekkers`算法比较,该版本的主要区别只是在`while`循环处,需要判断所有其他进程的标志位,一旦有一个进程的标志位为`true`,就会进入循环内部。 + +乍一看这个算法好像是挺好的,但它还具有致命性的缺陷。考虑一种情况,同时有多个进程请求进入临界区,但是当前`turn`所指向的那个进程并不想要进入临界区。那些想要进入临界区的进程都会因为互相判断到对方而进入循环体,由于它们都不拥有`turn`,它们都将陷入等待`turn`的循环,但是拥有`turn`的进程却并不进入临界区,因此也无法释放`turn`标志。可见,这种实现方法不满足`空闲则入`原则。 + +## 另一种尝试 + +然后看了看向勇老师的网课,他说所有可能进入临界区的进程是排成了一个环。想要进入临界区的进程只需要等待介于`turn`和自己之间的进程。进程退出临界区时,将`turn`设置为下一个请求进入的进程。整体的流程如下图所示: + +![nproc_mutex](nproc_mutex.png) + +因此,我就根据这个简单的描述修改了上面第一种尝试的代码,形成了下面的代码: + +```c +//code for process pid +flag[pid] = true; +while(1){ + for(idx = turn; idx != pid; idx = (idx + 1) % n) + if(flag[idx] = true) break; + if(idx == pid) break; + if(turn != pid){ + flag[pid] = false; + while(turn != pid); + flag[pid] = true; + } +} +critical_section +for(idx = pid + 1; idx != pid; idx = (idx + 1) % n) + if(flag[idx] == true) break; +turn = idx; +flag[pid] = false; +``` + +看起来这种实现方法似乎规避了第一次尝试的不足,因为总存在第一个离`turn`最近的请求进程,它只需要等待`turn`进程即可,不可能出现多个想要进入临界区的进程互相等待的情况,并且如果`turn`进程并没有请求进入临界区,离`turn`最近的进程可以直接通过循环进入临界区,满足了`空闲则入`原则。 + +但是通过深入的分析,我们可以构造出一种特殊情况。当前拥有`turn`的进程也没有请求进入临界区,距离`turn`为1的进程没有请求临界区,距离`turn`为3的进程发出了请求,因此它进入`for`循环判断在`turn`和它之间的进程是否还有发出请求的。然后这个循环还没有结束,刚刚判断完了距离`turn`为1的进程,就发生了进程的调度。此时,距离`turn`为1的进程也发出了进入临界区的请求,这样,这两个进程就同时进入临界区了,就违背了`忙则等待`原则。 + +## `eisenberg`算法 + +`eisenberg`算法是在上面算法的基础上的又一次改进,它的伪代码如下: + +```c +repeat { + /* announce that we need the resource */ + flags[i] := WAITING; + + /* scan processes from the one with the turn up to ourselves. */ + /* repeat if necessary until the scan finds all processes idle */ +CYCLE1: + index := turn; + while (index != i) { + if (flags[index] != IDLE) index := turn; + else index := (index+1) mod n; + } + + /* now tentatively claim the resource */ + flags[i] := ACTIVE; +CYCLE2: + /* find the first active process besides ourselves, if any */ + index := 0; + while ((index < n) && ((index = i) || (flags[index] != ACTIVE))) { + index := index+1; + } + + /* if there were no other active processes, AND if we have the turn + or else whoever has it is idle, then proceed. Otherwise, repeat + the whole sequence. */ + } until ((index >= n) && ((turn = i) || (flags[turn] = IDLE))); + + /* Start of CRITICAL SECTION */ + + /* claim the turn and proceed */ + turn := i; + + /* Critical Section Code of the Process */ + + /* End of CRITICAL SECTION */ + + /* find a process which is not IDLE */ + /* (if there are no others, we will find ourselves) */ + + index := (turn+1) mod n; + while (flags[index] = IDLE) { + index := (index+1) mod n; + } + + /* give the turn to someone that needs it, or keep it */ + turn := index; + + /* we're finished now */ + flags[i] := IDLE; + + /* REMAINDER Section */ +``` + +可以看得到,这个算法也太复杂了,下面直接给出对该算法的分析。 + +在`eisenberg`算法中,进程被分成了三个状态,分别为`IDLE`, `WAITING`, `ACTIVE`。`IDLE`表示进程没有请求进入临界区,`WAITING`表示发出了请求,在等待进入临界区,`ACTIVE`表示可能进入了临界区,也可能还没有。进入区主要是分成两个部分,分别是`CYCLE1`和`CYCLE2`。 + +在`CYCLE1`中的操作与我们第二次尝试的`for`循环一致,即判断从`turn`到当前进程之间是否存在请求进程,若存在,则不断循环`CYCLE1`,直至不存在这样的进程,将当前进程标记为`ACTIVE`。可以看出,所有标记为`ACTIVE`的进程,在循环中都判断自己是距离`turn`最近的请求进程,但是由于进程的调度,这样的进程仍然有多个,而这正是导致我们第二次尝试失败的原因。 + +在`CYCLE2`中,对所有`ACTIVE`的进程做进一步的判断,主要操作就是判断除了当前进程以外,是否还存在其他`ACTIVE`的进程。需要注意的是,这里是对所有其他进程做判断,而不仅限于判断从`turn`到当前进程。 + +进入临界区的条件是,当前进程是唯一的`ACTIVE`进程,并且当前进程获得了`turn`,或者获得`turn`的进程处于`IDLE`状态。否则,退回到`CYCLE1`重新进行上面的判断。 + +首先证明,`eisenberg`算法是满足`忙则等待`原则的,这是通过`CYCLE2`来实现的。在第一次尝试中已经说明过,对所有进程做遍历并且保证当前进程是唯一的请求进程或者`ACTIVE`进程是一种更强的互斥条件,它甚至会导致`空闲则入`原则的不满足。 + +下面说明一定会有进程可以进入临界区,即`空闲则入`原则是满足的。设一次循环中,所有`ACTIVE`状态的进程中,距离`turn`最近的进程为`pid_min`,距离`turn`最远的进程为`pid_max`。在`CYCLE2`中,由于同时存在多个`ACTIVE`进程,所有这些进程都会重新进入`WAITING`状态并且退回到`CYCLE1`。第二次循环,根据`CYCLE1`的性质,这些进程中只有`pid_min`可以通过`CYCLE1`进入`ACTIVE`状态,此时进入`ACTIVE`状态的进程至多只有`pid_min - turn`个。这样,在每次循环以后,可以进入`ACTIVE`状态的进程数量是递减的,最终只会有一个进程可以通过`CYCLE1`进入`ACTIVE`状态,并且获得临界区的访问权限。 \ No newline at end of file diff --git a/thu_os/images/nproc_mutex.png b/thu_os/images/nproc_mutex.png new 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