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diff --git a/theory/paper_algs/paper.tex b/theory/paper_algs/paper.tex
index 1bc98c94f1c234f3859d926b18fbcc3257403102..413949b9ce27535253f1c3e0f47d39d9baceaa79 100644
--- a/theory/paper_algs/paper.tex
+++ b/theory/paper_algs/paper.tex
@@ -66,7 +66,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title, author and affiliations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\title{Fast Algorithms for Smoothed Particle Hydrodynamics on Multi-Core
+\title{Efficient and Scalable Algorithms for Smoothed Particle Hydrodynamics on Multi-Core
Architectures}
\author{Pedro Gonnet\thanks{School of Engineering and Computing Sciences,
Durham University, Durham, Untied Kingdom ({\tt pedro.gonnet@durham.ac.uk}).}}
@@ -95,7 +95,11 @@
% Abstract
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}
-Bla.
+A new framework for the parallelization of Smoothed Particle Hydrodynamics (SPH)
+simulations on shared-memory parallel architectures is described.
+This framework relies on fast and cache-efficient cell-based neighbour-finding
+algorithms, as well as task-based parallelism to achieve good scaling and
+parallel efficiency on mult-core computers.
\end{abstract}
@@ -115,7 +119,7 @@ multi-cores
\pagestyle{myheadings}
\thispagestyle{plain}
-\markboth{P. GONNET}{FAST ALGORITHMS FOR SPH}
+\markboth{P. GONNET}{EFFICIENT AND SCALABLE ALGORITHMS FOR SPH}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -627,21 +631,17 @@ The dependencies and conflicts between tasks are then given as follows:
\subsubsection{Task queues}
-\begin{itemize}
-
- \item If the dependencies and conflicts are defined correctly, then
- there is no risk of concurrency problems and thus each task
- can be implemented without special attention to the latter,
- e.g.~it can update data without using exclusinve access barriers
- or atomic memory updates.
-
- \item This, however, requires some care in how the individual tasks
- are allocated to the computing threads, i.e.~each task should
- be allocated once to a single thread, and should not have
- and unresolved dependencies, or conflict with any concurrently
- executing tasks.
-
- \item In the following, tasks will be stored in one or more {\em queues}:
+If the dependencies and conflicts are defined correctly, then
+there is no risk of concurrency problems and thus each task
+can be implemented without special attention to the latter,
+e.g.~it can update data without using exclusinve access barriers
+or atomic memory updates.
+This, however, requires some care in how the individual tasks
+are allocated to the computing threads, i.e.~each task should
+be allocated once to a single thread, and should not have
+and unresolved dependencies, or conflict with any concurrently
+executing tasks.
+In the following, tasks will be stored in one or more {\em queues}:
\begin{center}\begin{minipage}{0.8\textwidth}
\begin{lstlisting}
@@ -660,7 +660,7 @@ in the queue.
The {\tt pthread\_mutex\_t lock} is used to guarantee exclusive access
to the queue.
- \item Task IDs are retreived from the queue as follows:
+Task IDs are retreived from the queue as follows:
\begin{center}\begin{minipage}{0.8\textwidth}
\begin{lstlisting}
@@ -688,72 +688,145 @@ int queue_gettask ( struct queue *q , int steal ) {
\end{lstlisting}
\end{minipage}\end{center}
- \noindent i.e.~exclusive access to the queue is obtained by locking
- its mutex in line~2. In lines~3 to~6, the tasks are inspected
- in sequence until a task is found that has no unresolved
- dependencies or existing conflicts.
- If a task has been found, its ID is swapped with that at
- position {\tt next}, and {\tt next} is incremented by one
- (lines 8~to~11).
- The lock on the queue is then released (line~12) and
- the task ID, or {\tt -1} if no available task was found, is
- returned.
-
- \item The advantage of swapping the retreived task to the next
- position in the list is that if the queue is reset, e.g.~{\tt next}
- is set to zero, and used again with the same set of tasks,
- they will now be traversed in the order in which they were
- exectuted in the previous run.
- This provides a basic form of iterative refinement of the task
- order.
-
- \item The tasks can also be sorted topologically, according to their
- dependency graph, to help minimize the effort required to find
- a valid task.
-
- \item The mutex at the start of {\tt queue\_gettask} is a potential
- bottleneck if the time required to process a task is small
- compared to the time required for all the threads to obtain
- a task, e.g.~for large numbers of very small tasks and/or
- a large number of threads.
-
- \item One way of avoiding this problem is to use several concurrent
- queues, e.g.~one queue per thread, and spread the tasks over
- all queues.
-
- \item A fixed assignemnt of tasks to queues can, however,
- cause load balancing problems, e.g.~when a thread's queue is
- empty before the others have finished.
-
- \item In order to avoid such problems, {\em work-stealing} can be used:
- If a thread cannot obtain a task from its own queue, it picks
- another queue at random and tries to {\em steal} a task from it
- i.e. if it can obtain a task, it removes it from the queue and
- adds it to it's own queue, thus iteratively rebalancing
- the task queues if they are used repeatedly:
+\noindent i.e.~exclusive access to the queue is obtained by locking
+its mutex in line~2. In lines~3 to~6, the tasks are inspected
+in sequence until a task is found that has no unresolved
+dependencies or existing conflicts.
+If a task has been found, its ID is swapped with that at
+position {\tt next}, and {\tt next} is incremented by one
+(lines 8~to~11).
+The lock on the queue is then released (line~12) and
+the task ID, or {\tt -1} if no available task was found, is
+returned.
+
+The advantage of swapping the retreived task to the next
+position in the list is that if the queue is reset, e.g.~{\tt next}
+is set to zero, and used again with the same set of tasks,
+they will now be traversed in the order in which they were
+exectuted in the previous run.
+This provides a basic form of iterative refinement of the task
+order.
+The tasks can also be sorted topologically, according to their
+dependency graph, to help minimize the effort required to find
+a valid task.
+
+The mutex at the start of {\tt queue\_gettask} is a potential
+bottleneck if the time required to process a task is small
+compared to the time required for all the threads to obtain
+a task, e.g.~for large numbers of very small tasks and/or
+a large number of threads.
+One way of avoiding this problem is to use several concurrent
+queues, e.g.~one queue per thread, and spread the tasks over
+all queues.
+A fixed assignemnt of tasks to queues can, however,
+cause load balancing problems, e.g.~when a thread's queue is
+empty before the others have finished.
+In order to avoid such problems, {\em work-stealing} can be used:
+If a thread cannot obtain a task from its own queue, it picks
+another queue at random and tries to {\em steal} a task from it
+i.e. if it can obtain a task, it removes it from the queue and
+adds it to it's own queue, thus iteratively rebalancing
+the task queues if they are used repeatedly:
\begin{center}\begin{minipage}{0.8\textwidth}
\begin{lstlisting}
- while ( there is still a task in any of the queues ) {
-
+while ( there is still a task in any of the queues ) {
+ if ( ( tid = queue_gettask( myq , 0 ) ) < 0 ) {
+ randq = pick a non-empty queue at random.
+ if ( ( tid = queue_gettask( randq , 1 ) ) >= 0 )
+ queue_addtask( myq , tid );
}
+ if ( tid >= 0 )
+ execute task tid.
+ }
\end{lstlisting}
\end{minipage}\end{center}
-\end{itemize}
+\noindent where {\tt myq} is the queue associated with the
+current thread and {\tt queue\_addtask} adds a task ID
+to the given queue.
\subsubsection{Cell locking}
-\begin{itemize}
-
- \item Explain problem of hierarchical locking, i.e.~interactions
- involving higher-level cells exclude lower-level cells.
+Particles within a cell are also within that cell's hierarchical
+parents.
+Therefore, when working on the particles of a cell, tasks which
+operate on its parent's data should not be allowed to execute.
+One way to avoid this problem is to require that a task
+not only lock a cell, but also all of its hierarchical
+parents in order to operate on its data.
+This, however, would prevent tasks involving siblings,
+whose particle sets do not overlap, from executing.
+
+We avoid this problem by giving each cell both a {\em lock},
+and a {\em hold} counter:
- \item Two-phase locking up and down the cell hierarchy, with
- ``lock'' and ``hold'' states.
+\begin{center}\begin{minipage}{0.8\textwidth}
+ \begin{lstlisting}
+int cell_locktree ( struct cell c ) {
+ struct cell *c1, *c2;
+ if ( trylock( c->lock ) != 0 )
+ return 1;
+ if ( c->hold > 0 ) {
+ unlock( c->lock )
+ return 1;
+ }
+ for ( c1 = c->parent ; c1 != NULL ; c1 = c1->parent ) {
+ if ( trylock( c1->lock ) != 0 )
+ break;
+ atomic_add( c1->hold , 1 );
+ unlock( c1->lock );
+ }
+ if ( finger != NULL ) {
+ for ( c2 = c->parent ; c2 != c1 ; c2 = c2->parent )
+ atomic_sub( c2->hold , 1 );
+ unlock( c->lock );
+ return 1;
+ }
+ else
+ return 0;
+ }
+ \end{lstlisting}
+\end{minipage}\end{center}
-\end{itemize}
+\noindent When trying to lock a cell, we first check that it is neither
+locked (line 3) or held (line 5), i.e.~its hold counter is zero, and lock it.
+We then travel up the hierarchy increasing the
+hold counter of each cell on the way, up to the topmost cell (lines 9--14).
+If any cell along the hierarchy is locked (line 10), the locking is aborted
+and all locks and holds are undone (lines 15--20, see \fig{CellLocking}).
+The operations {\tt atomic\_add} and {\tt atomic\_sub} are understood,
+respectively, to increase or decrease a value atomically.
+
+When the cell is released, its lock is unlocked and the hold
+counter of all hierarchical parents is decreased by one:
+
+\begin{center}\begin{minipage}{0.8\textwidth}
+ \begin{lstlisting}
+void cell_unlocktree ( struct cell c ) {
+ struct cell *c1;
+ unlock( c->lock )
+ for ( c1 = c->parent ; c1 != NULL ; c1 = c1->parent ) {
+ atomic_sub( c1->hold , 1 );
+ }
+ \end{lstlisting}
+\end{minipage}\end{center}
+
+
+\begin{figure}[ht]
+ \centerline{\epsfig{file=figures/CellLocking.pdf,width=0.5\textwidth}}
+
+ \caption{Example of hierarchical cell locking. The cells marked in red
+ are ``locked'' while the cells marked in yellow have a ``hold'' count
+ larger than zero.
+ The hold count is shown inside each cell and corresponds to the number
+ of locked cells hierarchicaly below it.
+ All cells except for those locked or with a ``hold'' count larger than
+ zero can still be locked without causing concurrent data access.
+ }
+ \label{fig:CellLocking}
+\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -765,7 +838,14 @@ int queue_gettask ( struct queue *q , int steal ) {
\begin{itemize}
- \item Details of the task queues.
+ \item Implemented in C, compiled with {\tt gcc}.
+
+ \item Threading implemented with {\tt pthread}.
+
+ \item One task queue per thread.
+
+ \item As of yet, no use of SIMD capabilities to evaluate several
+ interactions at a time.
\item Details of the pair interactions.
@@ -778,7 +858,11 @@ int queue_gettask ( struct queue *q , int steal ) {
\begin{itemize}
- \item Show both large and small simulation setups.
+ \item Details of the simulation used, e.g. size, number of particles,
+ etc...
+
+ \item So far only considering density and force computation,
+ particles not moving.
\end{itemize}
@@ -801,7 +885,11 @@ int queue_gettask ( struct queue *q , int steal ) {
\begin{itemize}
- \item Bla.
+ \item Good scaling.
+
+ \item Computational model can easily be exported to other architectures,
+ including GPUs (reference task-based parallelism on GPUs with Aidan),
+ and other multi-core accelerators such as the Intel MIC.
\end{itemize}
@@ -811,7 +899,14 @@ int queue_gettask ( struct queue *q , int steal ) {
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\section*{Acknowledgments}
-ICC Durham, Nick Holliman's hardware, NVidia's hardware.
+\begin{itemize}
+
+ \item Collaboration with Matthieu Schaller and Tom Theums from the
+ Institute of Computational Cosmology (ICC) at Durham University.
+
+ \item Lydia Heck from the ICC for providing access to the infrastructure.
+
+\end{itemize}
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