Inconvenient truth(s)

• Moore's Law
  • Coined in 1965 by Gordon Moore from Intel
  • Chip complexity increases by a factor of 2 every year

• State-of-the-art processors are clocked at 4 GHz

  • Light travels 7.5 cm every clock tick
  • Not possible to clock the whole large system using the same clock
  • Events that happen in different parts of the system close in time are simultaneous

• Back to the 80s

  • Intel's 80386 was released in 1986
  • Initial clock rate was 12 MHz (1 tick every 83 ns)
  • RAM latency: 70 ns
  • No cache (cache added with 33 MHz version)

• Intel Skylake (2015) die

• Intel Skylake (2015)

  • Max ca. 4 GHz
  • Cache (64 B/line)
    • 32+32 KB L1 cache
    • 2056 KB L2 cache
    • 8 MB L3 cache (shared by 2 cores)
  • Latencies
    • L1: 4/5 cycles
    • L2: 12 cycles
    • L3: 42 cycles (if the same core)
    • RAM: 42 cycles + 51 ns
  • Bandwidth
    • L1, L2: probably maxed
    • L3: ~200 GB/s
    • RAM: ~30 GB/s (one benchmark)

• Hitting the memory wall

• In the 80s

  • Computation was expensive
    • i386 32-bit division: up to 43 clock cycles
  • Transfer from memory was cheap
    • i386: 3-4 cycles

• Now

  • Computation is cheap
    • Skylake 32-bit division: 26 cycles (throughput: every 6 cycles)
  • Transfer from memory is expensive
    • Skylake: about 246 cycles

• Caches and I/O take most od the die area

  • Communication takes most of the energy

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• 80s: Instruction saved is instruction earned
• Now: Memory access saved is memory access earned
• It all gets worse when different cores are competing for the same memory

Back-of-the-envelope calculations

• It's difficult to predict the exact performance of individual instructions

• Memory latency is hidden by caches, so it's also difficult to predict

• Cache/memory bandwidth can be predicted more easily if you know the working set of your computation

• You can't tell how fast your code will go, but you can tell how fast it won't go:)

• You probably want to think about other I/O bandwidth (network, disk, etc.)

How to tune your application

• Concurrent/parallel code will often behave not in the way you expect

• Use benchmarking: if you cannot measure something, it does not exist!

• Unrolling all loops will make my program faster - are you sure? Do it only if you can demonstrate its usefulness using benchmarks

• We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3% - Donald Knuth

• Concentrate on finding the bottlenecks - the critical 3% - they might be not where you think they are

Sawzall

• Domain-specific language created to compute statistics based on large quantities of data at Google (2005)

• Average job 100 GB

• Although Sawzall is interpreted, that is rarely the limiting factor in its performance. Most Sawzall jobs do very little processing per record and are therefore I/O bound; for most of the rest, the CPU spends the majority of its time in various run-time operations such as parsing protocol buffers.

  • from Interpreting the Data: Parallel Analysis with Sawzall

• Last year Sawzall has been retired in favour of Go (compiled)

Parallelizing computations

• Embarrasingly parallel problems

  • MapReduce

• Sequential dependencies

  • Amdahl's law: speedup due parallelization is limited by critical paths in the dependency graph of the computation

int c = 0;
for(int i = 0; i < n; ++i) {
  c += a[i];
}

int c = 0;
int[] tmp = new int[4];
pfor (int j = 0; j < 4; ++j) { // This is pseudocode
  for(int i = 0; i < n; ++i) {
    tmp[j] += a[i];
  }
}
for (int i = 0; i < 4; ++i) { c += tmp[i];}

• Associative operation (+) allows for easy parallelization

• The CBC block cipher mode cannot be parallelized

• Parallelizing encryption requires choosing a different mode, such as CTR

• Removing dependencies gives more benefits than just parallelizing opportunity

Multicore

Aspects

• Applications to run faster if we have multicore CPUs

  • Alternatively, several CPUs in a distributed setting

• Is the code going to run faster just by having more cores?

  • No!

  • It might if it has lots of non-interferent processes and no sequential bottlenecks

• Erlang uses all the cores on the SMP machine by default

  • Symmetric MultiProcessing

    erl -smp +S N 
    

  • The number N indicates how many schedulers (govern Erlang virtual machines)

  • Useful to test how the program works on different amount of cores

• Programming Erlang - Chapter 20

Speeding up programs on a multicore CPU

General guidelines

• Use lots of processes

  • To keep cores busy!

• Avoid side effects

  • Their order might change in the parallel version

• Avoid sequential bottlenecks

  • If the algorithm is intrinsically sequential, then larger changes are needed

• Write “small messages, big computations” code.

  • If computations are very small, it might be bigger the cost of spawning and messaging among processes

Making code run in parallel

code

• Definition of map

map(_, []) -> [];
map(F, [H|T]) -> [F(H)|map(F, T)].

• Can the application for each element be done in parallel?

pmap(F, Xs) ->
   S = self(),
   Ref = make_ref(),
   Pids = map(fun(X) -> spawn( fun() -> 
                                  S ! {self(), Ref, F(X)} 
                               end )
              end, Xs),
   gather(Pids, Ref).

gather([Pid|T], Ref) -> 
   receive
       {Pid, Ref, Ret} -> [Ret|gather(T, Ref)]
   end ;
gather([], _) -> [].

• map(F,L) =:= pmap(F,L)

  • Order of elements?

  • Side-effects?

  • What if the list is very big and the computation F very small?

Workers

code

• What would it happen if you use pmap with a list of 1.000.000.000 elements?

• When doing X, a question arises: how many threads should I spawn here?

  • Too few: wasted parallelisation opportunity
  • Too many: overloaded system
    • Threads expensive
    • Subcomputations may use significant resources (files, memory, network)
  • You are willing to give up the control on what to run exactly when

• The workers model is designed for that goal

• Ideal: system-wide queue

  • Application-wide/component-wide queues also useful

Workers example

• We have tasks (computations) divided among a number of workers

  • Workers are simple processes

• Workers can be active or passive.

  • An active worker is a process already performing computations related to a task(s),
  • A passive worker is waiting to be assigned to a task(s).

• There is a server, called a pool, that keeps track of the tasks to be performed and has a fix number of workers willing to take those tasks.

• Server behavior

  • The initial state of the server is a queue of tasks and a list of passive workers

  • A worker can take more than a single task

  • An active worker becomes passive after finishing with the assigned task(s)

  • A passive worker becomes active when being assigned a task(s).

  • The server finishes execution when the queue of tasks is empty and there are no active workers

  • The server waits for a worker to return a result when the queue is empty or there are no more passive workers

  • When the task queue is not empty, the server gets a passive worker and assign some chunk of tasks to perform, i.e., the worker is now active

Implementation of workers

   worker(Compute) ->
       spawn (fun () -> worker_body(Compute) end ).

   worker_body(Compute) ->
            receive {Pid, Tasks} ->
                    Result = Compute(Tasks),
                    Pid ! {self(), Result},
                    worker_body(Compute)
            end.
  

• Implementation of the server

  -record(st, { tasks, aworkers, pworkers, 
                 get, combine } ). 
  
   %% Done
   work_load(#st{tasks = [], aworkers = []}, Results) -> Results;
  
   %% There are tasks to give to a passive worker
   work_load(St = #st{tasks = [Task | Tasks], 
                      pworkers = [PWorker | PWorkers], 
                      aworkers = AWorkers, 
                      get = Get} 
             , Results) ->
       {Chunk, TTasks} = Get([Task | Tasks]),
       PWorker ! {self(), Chunk},
       work_load(St#st{tasks = TTasks, 
                       pworkers = PWorkers, 
                       aworkers = [PWorker | AWorkers] }
                 , Results) ;
  
   %% No more passive workers or empty tasks, then 
   %% wait for results
   work_load(St = #st{pworkers = PWorkers, 
                      aworkers = AWorkers, 
                      combine  = Combine } 
             , Results) ->
       receive {Worker, Result} -> 
                work_load (St#st{ pworkers = [Worker | PWorkers],
                                  aworkers = lists:delete(Worker, AWorkers) } 
                           , Combine(Result, Results))
       end. 
  
  start(Tasks, Workers, Get, Combine, InitialResult) ->
      St = #st{tasks = Tasks,
               pworkers = Workers,
               aworkers = [],
               get = Get, combine = Combine},
      work_load(St, InitialResult).
  

Function pmap using workers

• Limit the resources to two workers only

• Tasks are the elements in the list, i.e., [X1,X2,X3] has three tasks.

• The computation of the worker is just to apply F to its tasks, e.g., F(X).

• Getting a task is simply taking the first task

  get_pmap([X | Xs]) -> {X, Xs}.
  

• Combine a new result is simply to add it to the lists of computed results

  combine_pmap(R, Rs) -> [R | Rs]. 
  

• The initial result is the empty list

• pmap with two workers

  pmap(F, Xs) ->
     W1 = worker(F),
     W2 = worker(F), 
     start(Xs, [W1, W2], fun get_pmap/1, fun combine_pmap/2, []).
  

On lock based programming

• Lock-based programming is difficult

• There are many potential problems:

  • Deadlock

  • Starvation

  • Non-compositionality

• Is there some way to eliminate at least some of these problems?

• Lock-based programming does not compose

  • Suppose you have two thread safe buffers and you want to atomically take an element from one of them and put it in the other

    class Buffer<Elem> {
         Elem get() {} ;
         void put(Elem) {} ;
    }
    

• A not so nice solution

  • Expose the the locks of the buffers

    class Buffer<Elem> {
          void aquireLock();
          void releaseLock();
          Elem get();
          void put(Elem);
    }
    

  • Lock both buffers before moving the element

    class TwoBuffer<Elem> {
          private Buffer<Elem> b1 ;
          private Buffer<Elem> b2 ;
    
          void copy_elem()
          {
             b1.aquireLock() ;
             b2.aquireLock() ;
             b2.put(b1.get()) ;
             b2.releaseLock() ;
             b1.releaseLock() ;
          }
        }
    

  • Alternatively: use one more lock that is locked in addition

  • Problems with lock granularity

    • Too few locks: reduces opportunities for concurrency
    • Too many locks: race conditions may occur

  • Deadlocks (however, we know how to avoid them)

  • It breaks abstraction!

  • What is you need to involved 3 buffers?

    • The number of locks grows as we compose algorithms

    • Increases the risk of programming errors

Solution: atomic blocks

• What we want

    class TwoBuffer<Elem> {
  
          void copy_elem()
          {
             atomic {
               b2.put(b1.get()) ;
             }
          }
        }
    

• We want blocks that are globally atomic (not only synchronized on a particular lock)

• We don't want to 'lock the world' at every state modification

• We will use a trick

  do {
    int old = shared;
    int new = old + 1;
  } while (compare-and-swap(shared, old, new) != old);
  

  • STM is like extending compare-and-swap to work on many variables a the same time

  • The loop will execute more than once only if there is a conflict between two threads

• Lock-based synchronization can be seen as pessimistic concurrency: ”We always assume that we need mutual exclusion”

• Another option would be optimistic concurrency

  • Assume we have mutual exclusion
  • Perform our critical section
  • Check if everything was OK
  • Revert our actions if it was not (rollback/retry)
  • Otherwise proceed

Software Transactional Memories (STM)

• A concept to allow easy lock-free programming and optimistic concurrency

• Although the programming model is lock-free implementations uses locks

  • Hardware or software level
  • Programmer does not need to know about it!

• Transactions: standard database concept

  • A group of operations should execute atomically,

  • Or not at all

• One possible implementation of transactions

  • When writing to variables, do not actually modify them, instead the system keeps a log over all the reads and writes that are made

  • When the transaction is done the system checks that the read variables still have the same value as in the beginning of the transaction

  • If that is the case, make the changes permanent (known as commit)

  • Otherwise, rerun the transaction (known as rollback or retry)

  • To detect if a variable has changed, we assume a version number for each variable in the transaction

• Example

We have two processes with two different transactions.

Now, both transactions read their corresponding variables. Each transaction recalls the version number of the read variables.

The transaction on the left firstly writes into variable x, and the transaction on the right follows but it fails (Why?) and retry.

The transaction on the right retries.

At the time of writing, it succeeds (Why?).

• Benefits of transactions:

  • Many processes can be in the critical section at the same time

    • More parallelism

    • They only need to rerun if there is an actual runtime conflict

    • Deadlocks cannot occur

    • Easy to compose

• What is more: retry may block!

  • We can program everything that is possible with locks and condition variables

  get() { if (beg == end) retry; T x = buf[beg]; beg = beg + 1 % S; }

  ...

  atomic { ... x = m.get(); ... }

• Implementations may provide an orElse conditional construction for nested transactions

  • Try executing the first branch; if it succeeds without retrying then ignore the second branch
  • Otherwise, roll back the effects run the second branch

• Drawbacks of transactions:

  • Cannot guarantee fairness

    • A large transaction can be starved by many small ones

  • All the book keeping can be expensive

• STM are still a subject of reseach!

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