Dining Philosophers Problem III

24 January 2022

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This post ends the mini-series about the dining philosophers problem by Andre Adrian. Today, he applies powerful locks and semaphores.

An illustration of the dining philosophers problem

By Benjamin D. Esham / Wikimedia Commons, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=56559

Here is a quick reminder about where Andre's analysis ended last time.

`std::lock_guard` and Synchronized Output with Resource Hierarchy

// dp_10.cpp
#include <iostream>
#include <thread>
#include <chrono>
#include <mutex>

int myrand(int min, int max) {
  return rand()%(max-min)+min;
}

std::mutex mo;

void phil(int ph, std::mutex& ma, std::mutex& mb) {
  while(true) {
    int duration=myrand(1000, 2000);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<ph<<" thinks "<<duration<<"ms\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(duration));

    std::lock_guard<std::mutex> ga(ma);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t"<<ph<<" got ma\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(1000));

    std::lock_guard<std::mutex> gb(mb);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t"<<ph<<" got mb\n";
    }

    duration=myrand(1000, 2000);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t\t\t"<<ph<<" eats "<<duration<<"ms\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(duration));
  }
}

int main() {
  std::cout<<"dp_10\n";
  srand(time(nullptr));

  std::mutex m1, m2, m3, m4;

  std::thread t1([&] {phil(1, m1, m2);});
  std::thread t2([&] {phil(2, m2, m3);});
  std::thread t3([&] {phil(3, m3, m4);});
  std::thread t4([&] {phil(4, m1, m4);});

  t1.join();
  t2.join();
  t3.join();
  t4.join();
}

The global mutex mo controls the console output resource. Every cout statement is in its block and the lock_guard() template ensures that console output is not garbled.

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A `std::unique_lock` using deferred locking

C++ offers alternative solutions next to resource hierarchy. We currently have two separate operations to acquire the two resources. If there is only one operation to acquire the two resources, there is no longer the danger of deadlock. The first "all or nothing" solution used unique_lock() with defer_lock. The actual resource acquire happens in the lock() statement. See dp_12.cpp:

int myrand(int min, int max) {
  static std::mt19937 rnd(std::time(nullptr));
  return std::uniform_int_distribution<>(min,max)(rnd);
}

std::mutex mo;

void phil(int ph, std::mutex& ma, std::mutex& mb) {
  while(true) {
    int duration=myrand(1000, 2000);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<ph<<" thinks "<<duration<<"ms\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(duration));

    std::unique_lock<std::mutex> ga(ma, std::defer_lock);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t"<<ph<<" got ma\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(1000));

    std::unique_lock<std::mutex> gb(mb,std::defer_lock);
    std::lock(ga, gb);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t"<<ph<<" got mb\n";
    }

    duration=myrand(1000, 2000);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t\t\t"<<ph<<" eats "<<duration<<"ms\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(duration));
  }
}

So far, we have generated random numbers using the rand() function. This function is not reentrant. Not reentrant means not threadable. This error is fixed with a modified myrand() function. The static function object rnd is a Mersenne Twister random number generator. With static, we avoid a global function object. Scaling to a value between min and max is now done with uniform_int_distribution<>. Using the library is better than writing your code. Who would have thought simple things like cout output and the random number are so tricky in programs with threads?

A `std::scoped_lock` with Resource Hierarchy

The second "all or nothing" solution is even more straightforward. The C++17 function scoped_lock() allows acquiring multiple resources. This powerful function gives us the shortest dining philosophers solution. See dp_13.cpp:

void phil(int ph, std::mutex& ma, std::mutex& mb) {
  while(true) {
    int duration=myrand(1000, 2000);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<ph<<" thinks "<<duration<<"ms\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(duration));

    std::this_thread::sleep_for(std::chrono::milliseconds(1000));
    std::scoped_lock sco(ma, mb);

    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t"<<ph<<" got ma, mb\n";
    }

    duration=myrand(1000, 2000);
    {
      std::lock_guard<std::mutex> g(mo);
      std::cout<<"\t\t\t\t"<<ph<<" eats "<<duration<<"ms\n";
    }
    std::this_thread::sleep_for(std::chrono::milliseconds(duration));
  }
}

There are more solutions. The original Dijkstra solution used one mutex, one semaphore per philosopher, and one state variable per philosopher. [ref 1971; Dijkstra; EWD310 Hierarchical Ordering of Sequential Processes; https://www.cs.utexas.edu/users/EWD/transcriptions/EWD03xx/EWD310.html]. Andrew S. Tanenbaum provided a C language solution. [ref 2006; Tanenbaum; Operating Systems. Design and Implementation, 3rd edition; chapter 2.3.1]

The Original Dining Philosopher's Problem using Semaphores

File dp_14.cpp is the Tanenbaum solution rewritten in C++20:

// dp_14.cpp
#include <iostream>
#include <chrono>
#include <thread>
#include <mutex>
#include <semaphore>
#include <random>

int myrand(int min, int max) {
  static std::mt19937 rnd(std::time(nullptr));
  return std::uniform_int_distribution<>(min,max)(rnd);
}

enum {
  N=5,                  // number of philosophers
  THINKING=0,           // philosopher is thinking
  HUNGRY=1,             // philosopher is trying to get forks
  EATING=2,             // philosopher is eating
};

#define LEFT (i+N-1)%N  // number of i's left neighbor
#define RIGHT (i+1)%N   // number of i's right neighbor

int state[N];           // array to keep track of everyone's state
std::mutex mutex_;      // mutual exclusion for critical regions
std::binary_semaphore s[N]{0, 0, 0, 0, 0};
                        // one semaphore per philosopher

void test(int i)        // i: philosopher number, from 0 to N-1
{
  if (state[i] == HUNGRY
   && state[LEFT] != EATING && state[RIGHT] != EATING) {
    state[i] = EATING;
    s[i].release();
  }
}

void take_forks(int i)  // i: philosopher number, from 0 to N-1
{
  mutex_.lock();        // enter critical region
  state[i] = HUNGRY;    // record fact that philosopher i is hungry
  test(i);              // try to acquire 2 forks
  mutex_.unlock();      // exit critical region
  s[i].acquire();       // block if forks were not acquired
}

void put_forks(int i)   // i: philosopher number, from 0 to N-1
{
  mutex_.lock();        // enter critical region
  state[i] = THINKING;  // philosopher has finished eating
  test(LEFT);           // see if left neighbor can now eat
  test(RIGHT);          // see if right neighbor can now eat
  mutex_.unlock();      // exit critical region
}

std::mutex mo;

void think(int i) {
  int duration = myrand(1000, 2000);
  {
		std::lock_guard<std::mutex> g(mo);
		std::cout<<i<<" thinks "<<duration<<"ms\n";
  }
  std::this_thread::sleep_for(std::chrono::milliseconds(duration));
}

void eat(int i) {
  int duration = myrand(1000, 2000);
  {
		std::lock_guard<std::mutex> g(mo);
		std::cout<<"\t\t\t\t"<<i<<" eats "<<duration<<"ms\n";
  }
  std::this_thread::sleep_for(std::chrono::milliseconds(duration));
}

void philosopher(int i) // i: philosopher number, from 0 to N-1
{
  while (true) {        // repeat forever
    think(i);           // philosopher is thinking
    take_forks(i);      // acquire two forks or block
    eat(i);             // yum-yum, spaghetti
    put_forks(i);       // put both forks back on table
  }
}

int main() {
  std::cout<<"dp_14\n";

  std::thread t0([&] {philosopher(0);});
  std::thread t1([&] {philosopher(1);});
  std::thread t2([&] {philosopher(2);});
  std::thread t3([&] {philosopher(3);});
  std::thread t4([&] {philosopher(4);});
  t0.join();
  t1.join();
  t2.join();
  t3.join();
  t4.join();
}

By the way, the semaphore is the oldest thread synchronization primitive. Dijkstra defined the P() and V() operation in 1965: "It is the P-operation, which represents the potential delay, viz. when a process initiates a P-operation on a semaphore, that at that moment is = 0, in that case, this P-operation cannot be completed until another process has performed a V-operation on the same semaphore and has given it the value '1'." Today P() is called release() and V() is called acquire(). [ref 1965; Dijkstra; EWD123 Cooperating sequential processes; https://www.cs.utexas.edu/users/EWD/transcriptions/EWD01xx/EWD123.html]

A C++20 Compatible Semaphore

You need a C++20 compiler like LLVM (clang++) version 13.0.0 or newer to compile dp_14.cpp. Or you change the #include <semaphore> into #include "semaphore.h" and provide the following header file. Then a C++11 compiler is sufficient.

// semaphore.h
#include <mutex>
#include <condition_variable>
#include <limits>

namespace std {
  template <std::ptrdiff_t least_max_value
   = std::numeric_limits<std::ptrdiff_t>::max()>
  class counting_semaphore {
  public:
    counting_semaphore(std::ptrdiff_t desired) : counter(desired) {}

    counting_semaphore(const counting_semaphore&) = delete;
    counting_semaphore& operator=(const counting_semaphore&) = delete;

    inline void release(ptrdiff_t update = 1) {
      std::unique_lock<std::mutex> lock(mutex_);
      counter += update;
      cv.notify_one();
    }

    inline void acquire() {
      std::unique_lock<std::mutex> lock(mutex_);
      while (0 == counter) cv.wait(lock);
      --counter;
    }

  private:
    ptrdiff_t counter;
    std::mutex mutex_;
    std::condition_variable cv;
  };

  using binary_semaphore = counting_semaphore<1>;
}

The C++ semaphore consists of a counter, a mutex, and a condition_variable. After 14 program versions, we leave this topic. The programs versions 1 to 6 have problems. I presented them to show bad multi-thread programming. Don't copy that!

What's next?

constexpr functions have much in common with templates and become more powerful with C++20. I will write about them in my next post.

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Tags: lock, semaphores, Dining Philosophers

Comments

0 #1 fred gannett 2023-04-19 09:20

I love the explanations of how parallel c++ works so sorry to ask the awkward questions but in all the examples up to and including dp_10.cpp there are only 4 or less dining philosophers. The original program description and the image you have at the start has 5 hungry thinkers.
The parallel nature of the answer changes when there are more than 4 diners chasing forks because there can, in a well ordered system, be 2 diners and 3 thinkers at one time. When there are only 4 diners someone will always be hungry and not thinking.
Also in dp_10.cpp there is a delay between a diner getting one fork and looking for the other.
std::this_thread::sleep_for(std::chrono::milliseconds(1000));

This seems unnecessary from the problem description and removing it allows for more parallelism.