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 % ======================================================================
+The mutex statement is a concurrent language feature that aims to support easy lock usage.
+The mutex statement is in the form of a clause and following statement, similar to a loop or conditional statement.
+In the clause the mutex statement accepts a number of lockable objects, and then locks them for the duration of the following statement.
+The locks are acquired in a deadlock free manner and released using \gls{raii}.
+The mutex statement provides an avenue for easy lock usage in the common case where locks are used to wrap a critical section.
+Additionally, it provides the safety guarantee of deadlock-freedom, both by acquiring the locks in a deadlock-free manner, and by ensuring that the locks release on error, or normal program execution via \gls{raii}.
+\begin{cfa}[tabsize=3,caption={\CFA mutex statement usage},label={l:cfa_mutex_ex}]
+The mutual exclusion problem was introduced by Dijkstra in 1965~\cite{Dijkstra65,Dijkstra65a}.
+There are several concurrent processes or threads that communicate by shared variables and from time to time need exclusive access to shared resources.
+A shared resource and code manipulating it form a pairing called a \Newterm{critical section (CS)}, which is a many-to-one relationship;
+\eg if multiple files are being written to by multiple threads, only the pairings of simultaneous writes to the same files are CSs.
+Regions of code where the thread is not interested in the resource are combined into the \Newterm{non-critical section (NCS)}.
+Exclusive access to a resource is provided by \Newterm{mutual exclusion (MX)}.
+MX is implemented by some form of \emph{lock}, where the CS is bracketed by lock procedures @acquire@ and @release@.
+Threads execute a loop of the form:
+\begin{cfa}
+loop of $thread$ p:
+        NCS;
+        acquire( lock );  CS;  release( lock ); // protected critical section with MX
+end loop.
+\end{cfa}
+MX guarantees there is never more than one thread in the CS.
+MX must also guarantee eventual progress: when there are competing threads attempting access, eventually some competing thread succeeds, \ie acquires the CS, releases it, and returns to the NCS.
+% Lamport \cite[p.~329]{Lam86mx} extends this requirement to the exit protocol.
+A stronger constraint is that every thread that calls @acquire@ eventually succeeds after some reasonable bounded time.
+\section{Monitor}
+\CFA provides a high-level locking object, called a \Newterm{monitor}, an elegant, efficient, high-level mechanisms for mutual exclusion and synchronization for shared-memory systems.
+First proposed by Brinch Hansen~\cite{Hansen73} and later described and extended by C.A.R.~Hoare~\cite{Hoare74}, several concurrent programming languages provide monitors as an explicit language construct: \eg Concurrent Pascal~\cite{ConcurrentPascal}, Mesa~\cite{Mesa}, Turing~\cite{Turing:old}, Modula-3~\cite{Modula-3}, \uC~\cite{Buhr92a} and Java~\cite{Java}.
+In addition, operating-system kernels and device drivers have a monitor-like structure, although they often use lower-level primitives such as mutex locks or semaphores to manually implement a monitor.
+Figure~\ref{f:AtomicCounter} shows a \CFA and Java monitor implementing an atomic counter.
+A \Newterm{monitor} is a programming technique that implicitly binds mutual exclusion to static function scope by call and return.
+Lock mutual exclusion, defined by acquire/release calls, is independent of lexical context (analogous to block versus heap storage allocation).
+Restricting acquire and release points in a monitor eases programming, comprehension, and maintenance, at a slight cost in flexibility and efficiency.
+Ultimately, a monitor is implemented using a combination of basic locks and atomic instructions.
+\begin{figure}
+\centering
+\begin{lrbox}{\myboxA}
+\begin{cfa}[aboveskip=0pt,belowskip=0pt]
+@monitor@ Aint {
+        int cnt;
+};
+int ++?( Aint & @mutex@ m ) { return ++m.cnt; }
+int ?=?( Aint & @mutex@ l, int r ) { l.cnt = r; }
+int ?=?(int & l, Aint & r) { l = r.cnt; }
+int i = 0, j = 0;
+Aint x = { 0 }, y = { 0 };      $\C[1.5in]{// no mutex}$
+++x;  ++y;                      $\C{// mutex}$
+x = 2;  y = i;          $\C{// mutex}$
+i = x;  j = y;          $\C{// no mutex}\CRT$
+\end{cfa}
+\end{lrbox}
+\begin{lrbox}{\myboxB}
+\begin{java}[aboveskip=0pt,belowskip=0pt]
+class Aint {
+        private int cnt;
+        public Aint( int init ) { cnt = init; }
+        @synchronized@ public int inc() { return ++cnt; }
+        @synchronized@ public void set( int r ) {cnt = r;}
+        public int get() { return cnt; }
+}
+int i = 0, j = 0;
+Aint x = new Aint( 0 ), y = new Aint( 0 );
+x.inc();  y.inc();
+x.set( 2 );  y.set( i );
+i = x.get();  j = y.get();
+\end{java}
+\end{lrbox}
+\subfloat[\CFA]{\label{f:AtomicCounterCFA}\usebox\myboxA}
+\hspace*{3pt}
+\vrule
+\hspace*{3pt}
+\subfloat[Java]{\label{f:AtomicCounterJava}\usebox\myboxB}
+\caption{Atomic integer counter}
+\label{f:AtomicCounter}
+\end{figure}
+Like Java, \CFA monitors have \Newterm{multi-acquire} semantics so the thread in the monitor may acquire it multiple times without deadlock, allowing recursion and calling other MX functions.
+For robustness, \CFA monitors ensure the monitor lock is released regardless of how an acquiring function ends, normal or exceptional, and returning a shared variable is safe via copying before the lock is released.
+Monitor objects can be passed through multiple helper functions without acquiring mutual exclusion, until a designated function associated with the object is called.
+\CFA functions are designated MX by one or more pointer/reference parameters having qualifier @mutex@.
+Java members are designated MX with \lstinline[language=java]{synchronized}, which applies only to the implicit receiver parameter.
+In the example, the increment and setter operations need mutual exclusion, while the read-only getter operation is not MX because reading an integer is atomic.
+As stated, the non-object-oriented nature of \CFA monitors allows a function to acquire multiple mutex objects.
+For example, the bank-transfer problem requires locking two bank accounts to safely debit and credit money between accounts.
+\begin{cfa}
+monitor BankAccount {
+        int balance;
+};
+void deposit( BankAccount & mutex b, int deposit ) with( b ) {
+        balance += deposit;
+}
+void transfer( BankAccount & mutex my, BankAccount & mutex your, int me2you ) {
+        deposit( my, -me2you );         $\C{// debit}$
+        deposit( your, me2you );        $\C{// credit}$
+}
+\end{cfa}
+The \CFA monitor implementation ensures multi-lock acquisition is done in a deadlock-free manner regardless of the number of MX parameters and monitor arguments.
+\section{\lstinline{mutex} statement}
+Restricting implicit lock acquisition to function entry and exit can be awkward for certain problems.
+To increase locking flexibility, some languages introduce a mutex statement.
+\VRef[Figure]{f:ReadersWriter} shows the outline of a reader/writer lock written as a \CFA monitor and mutex statements.
+(The exact lock implement is irrelevant.)
+The @read@ and @write@ functions are called with a reader/write lock and any arguments to perform reading or writing.
+The @read@ function is not MX because multiple readers can read simultaneously.
+MX is acquired within @read@ by calling the (nested) helper functions @StartRead@ and @EndRead@ or executing the mutex statements.
+Between the calls or statements, reads can execute simultaneous within the body of @read@.
+The @write@ function does not require refactoring because writing is a CS.
+The mutex-statement version is better because it has fewer names, less argument/parameter passing, and can possibly hold MX for a shorter duration.
+\begin{figure}
+\centering
+\begin{lrbox}{\myboxA}
+\begin{cfa}[aboveskip=0pt,belowskip=0pt]
+monitor RWlock { ... };
+void read( RWlock & rw, ... ) {
+        void StartRead( RWlock & @mutex@ rw ) { ... }
+        void EndRead( RWlock & @mutex@ rw ) { ... }
+        StartRead( rw );
+        ... // read without MX
+        EndRead( rw );
+}
+void write( RWlock & @mutex@ rw, ... ) {
+        ... // write with MX
+}
+\end{cfa}
+\end{lrbox}
+\begin{lrbox}{\myboxB}
+\begin{cfa}[aboveskip=0pt,belowskip=0pt]
+void read( RWlock & rw, ... ) {
+        @mutex@( rw ) { ... }
+        ... // read without MX
+        @mutex@{ rw ) { ... }
+}
+void write( RWlock & @mutex@ rw, ... ) {
+        ... // write with MX
+}
+\end{cfa}
+\end{lrbox}
+\subfloat[monitor]{\label{f:RWmonitor}\usebox\myboxA}
+\hspace*{3pt}
+\vrule
+\hspace*{3pt}
+\subfloat[mutex statement]{\label{f:RWmutexstmt}\usebox\myboxB}
+\caption{Readers writer problem}
+\label{f:ReadersWriter}
+\end{figure}
+This work adds a mutex statement to \CFA, but generalizes it beyond implicit monitor locks.
+In detail, the mutex statement has a clause and statement block, similar to a conditional or loop statement.
+The clause accepts any number of lockable objects (like a \CFA MX function prototype), and locks them for the duration of the statement.
+The locks are acquired in a deadlock free manner and released regardless of how control-flow exits the statement.
+The mutex statement provides easy lock usage in the common case of lexically wrapping a CS.
+Examples of \CFA mutex statement are shown in \VRef[Listing]{l:cfa_mutex_ex}.
+\begin{cfa}[caption={\CFA mutex statement usage},label={l:cfa_mutex_ex}]
 owner_lock lock1, lock2, lock3;
+int count = 0;
+mutex( lock1, lock2, lock3 ) {
+    // can use block statement
+    // ...
+}
+mutex( lock2, lock3 ) count++; // or inline statement
+@mutex@( lock2, lock3 ) ...;    $\C{// inline statement}$
+@mutex@( lock1, lock2, lock3 ) { ... }  $\C{// statement block}$
+void transfer( BankAccount & my, BankAccount & your, int me2you ) {
+        ... // check values, no MX
+        @mutex@( my, your ) { // MX is shorter duration that function body
+                deposit( my, -me2you );  $\C{// debit}$
+                deposit( your, me2you ); $\C{// credit}$
+        }
+}
 \end{cfa}
 \section{Other Languages}
+There are similar concepts to the mutex statement that exist in other languages.
+Java has a feature called a synchronized statement, which looks identical to \CFA's mutex statement, but it has some differences.
+The synchronized statement only accepts a single object in its clause.
+Any object can be passed to the synchronized statement in Java since all objects in Java are monitors, and the synchronized statement acquires that object's monitor.
+In \CC there is a feature in the standard library \code{<mutex>} header called scoped\_lock, which is also similar to the mutex statement.
+The scoped\_lock is a class that takes in any number of locks in its constructor, and acquires them in a deadlock-free manner.
+It then releases them when the scoped\_lock object is deallocated, thus using \gls{raii}.
+An example of \CC scoped\_lock usage is shown in Listing~\ref{l:cc_scoped_lock}.
+\begin{cfa}[tabsize=3,caption={\CC scoped\_lock usage},label={l:cc_scoped_lock}]
+std::mutex lock1, lock2, lock3;
+{
+    scoped_lock s( lock1, lock2, lock3 )
+    // locks are released via raii at end of scope
+}
+There are similar constructs to the mutex statement in other programming languages.
+Java has a feature called a synchronized statement, which looks like the \CFA's mutex statement, but only accepts a single object in the clause and only handles monitor locks.
+The \CC standard library has a @scoped_lock@, which is also similar to the mutex statement.
+The @scoped_lock@ takes any number of locks in its constructor, and acquires them in a deadlock-free manner.
+It then releases them when the @scoped_lock@ object is deallocated using \gls{raii}.
+An example of \CC @scoped_lock@ is shown in \VRef[Listing]{l:cc_scoped_lock}.
+\begin{cfa}[caption={\CC \lstinline{scoped_lock} usage},label={l:cc_scoped_lock}]
+struct BankAccount {
+        @recursive_mutex m;@            $\C{// must be recursive}$
+        int balance = 0;
+};
+void deposit( BankAccount & b, int deposit ) {
+        @scoped_lock lock( b.m );@      $\C{// RAII acquire}$
+        b.balance += deposit;
+}                                                               $\C{// RAII release}$
+void transfer( BankAccount & my, BankAccount & your, int me2you ) {
+        @scoped_lock lock( my.m, your.m );@     $\C{// RAII acquire}$
+        deposit( my, -me2you );         $\C{// debit}$
+        deposit( your, me2you );        $\C{// credit}$
+}                                                               $\C{// RAII release}$
 \end{cfa}
 \section{\CFA implementation}
+The \CFA mutex statement takes some ideas from both the Java and \CC features.
+The mutex statement can acquire more that one lock in a deadlock-free manner, and releases them via \gls{raii} like \CC, however the syntax is identical to the Java synchronized statement.
+This syntactic choice was made so that the body of the mutex statement is its own scope.
+Compared to the scoped\_lock, which relies on its enclosing scope, the mutex statement's introduced scope can provide visual clarity as to what code is being protected by the mutex statement, and where the mutual exclusion ends.
+\CFA's mutex statement and \CC's scoped\_lock both use parametric polymorphism to allow user defined types to work with the feature.
+\CFA's implementation requires types to support the routines \code{lock()} and \code{unlock()}, whereas \CC requires those routines, plus \code{try_lock()}.
+The scoped\_lock requires an additional routine since it differs from the mutex statement in how it implements deadlock avoidance.
+The parametric polymorphism allows for locking to be defined for types that may want convenient mutual exclusion.
+An example of one such use case in \CFA is \code{sout}.
+The output stream in \CFA is called \code{sout}, and functions similarly to \CC's \code{cout}.
+\code{sout} has routines that satisfy the mutex statement trait, so the mutex statement can be used to lock the output stream while producing output.
+In this case, the mutex statement allows the programmer to acquire mutual exclusion over an object without having to know the internals of the object or what locks need to be acquired.
+The ability to do so provides both improves safety and programmer productivity since it abstracts away the concurrent details and provides an interface for optional thread-safety.
+This is a commonly used feature when producing output from a concurrent context, since producing output is not thread safe by default.
+This use case is shown in Listing~\ref{l:sout}.
+\begin{cfa}[tabsize=3,caption={\CFA sout with mutex statement},label={l:sout}]
+mutex( sout )
+    sout | "This output is protected by mutual exclusion!";
+\end{cfa}
+\section{Deadlock Avoidance}
+The mutex statement uses the deadlock prevention technique of lock ordering, where the circular-wait condition of a deadlock cannot occur if all locks are acquired in the same order.
+The scoped\_lock uses a deadlock avoidance algorithm where all locks after the first are acquired using \code{try_lock} and if any of the attempts to lock fails, all locks so far are released.
+This repeats until all locks are acquired successfully.
+The deadlock avoidance algorithm used by scoped\_lock is shown in Listing~\ref{l:cc_deadlock_avoid}.
+The algorithm presented is taken directly from the source code of the \code{<mutex>} header, with some renaming and comments for clarity.
+\begin{cfa}[caption={\CC scoped\_lock deadlock avoidance algorithm},label={l:cc_deadlock_avoid}]
+The \CFA mutex statement takes some ideas from both the Java and \CC features.
+Like Java, \CFA introduces a new statement rather than building from existing language features.
+(\CFA has sufficient language features to mimic \CC RAII locking.)
+This syntactic choice makes MX explicit rather than implicit via object declarations.
+Hence, it is easier for programmers and language tools to identify MX points in a program, \eg scan for all @mutex@ parameters and statements in a body of code.
+Furthermore, concurrent safety is provided across an entire program for the complex operation of acquiring multiple locks in a deadlock-free manner.
+Unlike Java, \CFA's mutex statement and \CC's @scoped_lock@ both use parametric polymorphism to allow user defined types to work with this feature.
+In this case, the polymorphism allows a locking mechanism to acquire MX over an object without having to know the object internals or what kind of lock it is using.
+\CFA's provides and uses this locking trait:
+\begin{cfa}
+forall( L & | sized(L) )
+trait is_lock {
+        void lock( L & );
+        void unlock( L & );
+};
+\end{cfa}
+\CC @scoped_lock@ has this trait implicitly based on functions accessed in a template.
+@scoped_lock@ also requires @try_lock@ because of its technique for deadlock avoidance \see{\VRef{s:DeadlockAvoidance}}.
+The following shows how the @mutex@ statement is used with \CFA streams to eliminate unpredictable results when printing in a concurrent program.
+For example, if two threads execute:
+\begin{cfa}
+thread$\(_1\)$ : sout | "abc" | "def";
+thread$\(_2\)$ : sout | "uvw" | "xyz";
+\end{cfa}
+any of the outputs can appear, included a segment fault due to I/O buffer corruption:
+\begin{cquote}
+\small\tt
+\begin{tabular}{@{}l|l|l|l|l@{}}
+abc def & abc uvw xyz & uvw abc xyz def & abuvwc dexf &  uvw abc def \\
+uvw xyz & def & & yz & xyz
+\end{tabular}
+\end{cquote}
+The stream type for @sout@ is defined to satisfy the @is_lock@ trait, so the @mutex@ statement can be used to lock an output stream while producing output.
+From the programmer's perspective, it is sufficient to know an object can be locked and then any necessary MX is easily available via the @mutex@ statement.
+This ability improves safety and programmer productivity since it abstracts away the concurrent details.
+Hence, a  programmer can easily protect cascaded I/O expressions:
+\begin{cfa}
+thread$\(_1\)$ : mutex( sout )  sout | "abc" | "def";
+thread$\(_2\)$ : mutex( sout )  sout | "uvw" | "xyz";
+\end{cfa}
+constraining the output to two different lines in either order:
+\begin{cquote}
+\small\tt
+\begin{tabular}{@{}l|l@{}}
+abc def & uvw xyz \\
+uvw xyz & abc def
+\end{tabular}
+\end{cquote}
+where this level of safe nondeterministic output is acceptable.
+Alternatively, multiple I/O statements can be protected using the mutex statement block:
+\begin{cfa}
+mutex( sout ) { // acquire stream lock for sout for block duration
+        sout | "abc";
+        mutex( sout ) sout | "uvw" | "xyz"; // OK because sout lock is recursive
+        sout | "def";
+} // implicitly release sout lock
+\end{cfa}
+The inner lock acquire is likely to occur through a function call that does a thread-safe print.
+\section{Deadlock Avoidance}\label{s:DeadlockAvoidance}
+The mutex statement uses the deadlock avoidance technique of lock ordering, where the circular-wait condition of a deadlock cannot occur if all locks are acquired in the same order.
+The @scoped_lock@ uses a deadlock avoidance algorithm where all locks after the first are acquired using @try_lock@ and if any of the lock attempts fail, all acquired locks are released.
+This repeats after selecting a new starting point in a cyclic manner until all locks are acquired successfully.
+This deadlock avoidance algorithm is shown in Listing~\ref{l:cc_deadlock_avoid}.
+The algorithm is taken directly from the source code of the @<mutex>@ header, with some renaming and comments for clarity.
+\begin{cfa}[caption={\CC \lstinline{scoped_lock} deadlock avoidance algorithm},label={l:cc_deadlock_avoid}]
 int first = 0;  // first lock to attempt to lock
 do {
     // locks is the array of locks to acquire
+    locks[first].lock();    // lock first lock
+    for (int i = 1; i < Num_Locks; ++i) {   // iterate over rest of locks
         const int idx = (first + i) % Num_Locks;
+        if (!locks[idx].try_lock()) {       // try lock each one
+            for (int j = i; j != 0; --j)    // release all locks
                 locks[(first + j - 1) % Num_Locks].unlock();
+            first = idx;    // rotate which lock to acquire first
             break;
+        }
+    }
+        // locks is the array of locks to acquire
+        locks[first].lock();                            $\C{// lock first lock}$
+        for ( int i = 1; i < Num_Locks; i += 1 ) { $\C{// iterate over rest of locks}$
+                const int idx = (first + i) % Num_Locks;
+                if ( ! locks[idx].try_lock() ) {   $\C{// try lock each one}$
+                        for ( int j = i; j != 0; j -= 1 )       $\C{// release all locks}$
+                                locks[(first + j - 1) % Num_Locks].unlock();
+                        first = idx;                            $\C{// rotate which lock to acquire first}$
+                        break;
+                }
+        }
 // if first lock is still held then all have been acquired
+} while (!locks[first].owns_lock());  // is first lock held?
+\end{cfa}
+The algorithm in \ref{l:cc_deadlock_avoid} successfully avoids deadlock, however there is a potential livelock scenario.
+Given two threads $A$ and $B$, who create a scoped\_lock with two locks $L1$ and $L2$, a livelock can form as follows.
+Thread $A$ creates a scoped\_lock with $L1$, $L2$, and $B$ creates a scoped lock with the order $L2$, $L1$.
+Both threads acquire the first lock in their order and then fail the try\_lock since the other lock is held.
+They then reset their start lock to be their 2nd lock and try again.
+This time $A$ has order $L2$, $L1$, and $B$ has order $L1$, $L2$.
+This is identical to the starting setup, but with the ordering swapped among threads.
+As such, if they each acquire their first lock before the other acquires their second, they can livelock indefinitely.
+The lock ordering algorithm used in the mutex statement in \CFA is both deadlock and livelock free.
+It sorts the locks based on memory address and then acquires them.
+For locks fewer than 7, it sorts using hard coded sorting methods that perform the minimum number of swaps for a given number of locks.
+For 7 or more locks insertion sort is used.
+These sorting algorithms were chosen since it is rare to have to hold more than  a handful of locks at a time.
+It is worth mentioning that the downside to the sorting approach is that it is not fully compatible with usages of the same locks outside the mutex statement.
+If more than one lock is held by a mutex statement, if more than one lock is to be held elsewhere, it must be acquired via the mutex statement, or else the required ordering will not occur.
+Comparitively, if the scoped\_lock is used and the same locks are acquired elsewhere, there is no concern of the scoped\_lock deadlocking, due to its avoidance scheme, but it may livelock.
+} while ( ! locks[first].owns_lock() );  $\C{// is first lock held?}$
+\end{cfa}
+While the algorithm in \ref{l:cc_deadlock_avoid} successfully avoids deadlock, there is a livelock scenario.
+Assume two threads, $A$ and $B$, create a @scoped_lock@ accessing two locks, $L1$ and $L2$.
+A livelock can form as follows.
+Thread $A$ creates a @scoped_lock@ with arguments $L1$, $L2$, and $B$ creates a scoped lock with the lock arguments in the opposite order $L2$, $L1$.
+Both threads acquire the first lock in their order and then fail the @try_lock@ since the other lock is held.
+Both threads then reset their starting lock to be their second lock and try again.
+This time $A$ has order $L2$, $L1$, and $B$ has order $L1$, $L2$, which is identical to the starting setup but with the ordering swapped between threads.
+If the threads perform this action in lock-step, they cycle indefinitely without entering the CS, \ie livelock.
+Hence, to use @scoped_lock@ safely, a programmer must manually construct and maintain a global ordering of lock arguments passed to @scoped_lock@.
+The lock ordering algorithm used in \CFA mutex functions and statements is deadlock and livelock free.
+The algorithm uses the lock memory addresses as keys, sorts the keys, and then acquires the locks in sorted order.
+For fewer than 7 locks ($2^3-1$), the sort is unrolled performing the minimum number of compare and swaps for the given number of locks;
+for 7 or more locks, insertion sort is used.
+Since it is extremely rare to hold more than 6 locks at a time, the algorithm is fast and executes in $O(1)$ time.
+Furthermore, lock addresses are unique across program execution, even for dynamically allocated locks, so the algorithm is safe across the entire program execution.
+The downside to the sorting approach is that it is not fully compatible with manual usages of the same locks outside the @mutex@ statement, \ie the lock are acquired without using the @mutex@ statement.
+The following scenario is a classic deadlock.
+\begin{cquote}
+\begin{tabular}{@{}l@{\hspace{30pt}}l@{}}
+\begin{cfa}
+lock L1, L2; // assume &L1 < &L2
+        $\textbf{thread\(_1\)}$
+acquire( L2 );
+        acquire( L1 );
+                CS
+        release( L1 );
+release( L2 );
+\end{cfa}
+&
+\begin{cfa}
+        $\textbf{thread\(_2\)}$
+mutex( L1, L2 ) {
+        CS
+}
+\end{cfa}
+\end{tabular}
+\end{cquote}
+Comparatively, if the @scoped_lock@ is used and the same locks are acquired elsewhere, there is no concern of the @scoped_lock@ deadlocking, due to its avoidance scheme, but it may livelock.
+The convenience and safety of the @mutex@ statement, \eg guaranteed lock release with exceptions, should encourage programmers to always use it for locking, mitigating any deadlock scenario.
+\section{Performance}
+Given the two multi-acquisition algorithms in \CC and \CFA, each with differing advantages and disadvantages, it interesting to compare their performance.
+Comparison with Java is not possible, since it only takes a single lock.
+The comparison starts with a baseline that acquires the locks directly without a mutex statement or @scoped_lock@ in a fixed ordering and then releases them.
+The baseline helps highlight the cost of the deadlock avoidance/prevention algorithms for each implementation.
+The benchmark used to evaluate the avoidance algorithms repeatedly acquires a fixed number of locks in a random order and then releases them.
+The pseudo code for the deadlock avoidance benchmark is shown in \VRef[Listing]{l:deadlock_avoid_pseudo}.
+To ensure the comparison exercises the implementation of each lock avoidance algorithm, an identical spinlock is implemented in each language using a set of builtin atomics available in both \CC and \CFA.
+The benchmarks are run for a fixed duration of 10 seconds and then terminate.
+The total number of times the group of locks is acquired is returned for each thread.
+Each variation is run 11 times on 2, 4, 8, 16, 24, 32 cores and with 2, 4, and 8 locks being acquired.
+The median is calculated and is plotted alongside the 95\% confidence intervals for each point.
+\begin{cfa}[caption={Deadlock avoidance bendchmark pseudo code},label={l:deadlock_avoid_pseudo}]
+$\PAB{// add pseudo code}$
+\end{cfa}
+The performance experiments were run on the following multi-core hardware systems to determine differences across platforms:
+\begin{list}{\arabic{enumi}.}{\usecounter{enumi}\topsep=5pt\parsep=5pt\itemsep=0pt}
+% sudo dmidecode -t system
+\item
+Supermicro AS--1123US--TR4 AMD EPYC 7662 64--core socket, hyper-threading $\times$ 2 sockets (256 processing units) 2.0 GHz, TSO memory model, running Linux v5.8.0--55--generic, gcc--10 compiler
+\item
+Supermicro SYS--6029U--TR4 Intel Xeon Gold 5220R 24--core socket, hyper-threading $\times$ 2 sockets (48 processing units) 2.2GHz, TSO memory model, running Linux v5.8.0--59--generic, gcc--10 compiler
+\end{list}
+%The hardware architectures are different in threading (multithreading vs hyper), cache structure (MESI or MESIF), NUMA layout (QPI vs HyperTransport), memory model (TSO vs WO), and energy/thermal mechanisms (turbo-boost).
+%Software that runs well on one architecture may run poorly or not at all on another.
+Figure~\ref{f:mutex_bench} shows the results of the benchmark experiments.
+\PAB{Make the points in the graphs for each line different.
+Also, make the text in the graphs larger.}
+The baseline results for both languages are mostly comparable, except for the 8 locks results in \ref{f:mutex_bench8_AMD} and \ref{f:mutex_bench8_Intel}, where the \CFA baseline is slightly slower.
+The avoidance result for both languages is significantly different, where \CFA's mutex statement achieves throughput that is magnitudes higher than \CC's @scoped_lock@.
+The slowdown for @scoped_lock@ is likely due to its deadlock-avoidance implementation.
+Since it uses a retry based mechanism, it can take a long time for threads to progress.
+Additionally the potential for livelock in the algorithm can result in very little throughput under high contention.
+For example, on the AMD machine with 32 threads and 8 locks, the benchmarks would occasionally livelock indefinitely, with no threads making any progress for 3 hours before the experiment was terminated manually.
+It is likely that shorter bouts of livelock occurred in many of the experiments, which would explain large confidence intervals for some of the data points in the \CC data.
+In Figures~\ref{f:mutex_bench8_AMD} and \ref{f:mutex_bench8_Intel} the mutex statement performs better than the baseline.
+At 7 locks and above the mutex statement switches from a hard coded sort to insertion sort.
+It is likely that the improvement in throughput compared to baseline is due to the time spent in the insertion sort, which decreases contention on the locks.
 \begin{figure}
+    \centering
+    \begin{subfigure}{0.5\textwidth}
+        \centering
+        \scalebox{0.5}{\input{figures/nasus_Aggregate_Lock_2.pgf}}
+        \subcaption{AMD}
+    \end{subfigure}\hfill
+    \begin{subfigure}{0.5\textwidth}
+        \centering
+        \scalebox{0.5}{\input{figures/pyke_Aggregate_Lock_2.pgf}}
+        \subcaption{Intel}
+    \end{subfigure}
+    \begin{subfigure}{0.5\textwidth}
+        \centering
+        \scalebox{0.5}{\input{figures/nasus_Aggregate_Lock_4.pgf}}
+        \subcaption{AMD}
+    \end{subfigure}\hfill
+    \begin{subfigure}{0.5\textwidth}
+        \centering
+        \scalebox{0.5}{\input{figures/pyke_Aggregate_Lock_4.pgf}}
+        \subcaption{Intel}
+    \end{subfigure}
+    \begin{subfigure}{0.5\textwidth}
+        \centering
+        \scalebox{0.5}{\input{figures/nasus_Aggregate_Lock_8.pgf}}
+        \subcaption{AMD}\label{f:mutex_bench8_AMD}
+    \end{subfigure}\hfill
+    \begin{subfigure}{0.5\textwidth}
+        \centering
+        \scalebox{0.5}{\input{figures/pyke_Aggregate_Lock_8.pgf}}
+        \subcaption{Intel}\label{f:mutex_bench8_Intel}
+    \end{subfigure}
+    \caption{The aggregate lock benchmark comparing \CC scoped\_lock and \CFA mutex statement throughput (higher is better).}
+    \label{f:mutex_bench}
+        \centering
+        \subfloat[AMD]{
+                \resizebox{0.5\textwidth}{!}{\input{figures/nasus_Aggregate_Lock_2.pgf}}
+        }
+        \subfloat[Intel]{
+                \resizebox{0.5\textwidth}{!}{\input{figures/pyke_Aggregate_Lock_2.pgf}}
+        }
+        \subfloat[AMD]{
+                \resizebox{0.5\textwidth}{!}{\input{figures/nasus_Aggregate_Lock_4.pgf}}
+        }
+        \subfloat[Intel]{
+                \resizebox{0.5\textwidth}{!}{\input{figures/pyke_Aggregate_Lock_4.pgf}}
+        }
+        \subfloat[AMD]{
+                \resizebox{0.5\textwidth}{!}{\input{figures/nasus_Aggregate_Lock_8.pgf}}
+                \label{f:mutex_bench8_AMD}
+        }
+        \subfloat[Intel]{
+                \resizebox{0.5\textwidth}{!}{\input{figures/pyke_Aggregate_Lock_8.pgf}}
+                \label{f:mutex_bench8_Intel}
+        }
+        \caption{The aggregate lock benchmark comparing \CC \lstinline{scoped_lock} and \CFA mutex statement throughput (higher is better).}
+        \label{f:mutex_bench}
 \end{figure}
+\section{Performance}
+Performance is compared between \CC's scoped\_lock and \CFA's mutex statement.
+Comparison with Java is omitted, since it only takes a single lock.
+To ensure that the comparison between \CC and \CFA exercises the implementation of each feature, an identical spinlock is implemented in each language using a set of builtin atomics available in both \CFA and \CC.
+Each feature is evaluated on a benchmark which acquires a fixed number of locks in a random order and then releases them.
+A baseline is included that acquires the locks directly without a mutex statement or scoped\_lock in a fixed ordering and then releases them.
+The baseline helps highlight the cost of the deadlock avoidance/prevention algorithms for each implementation.
+The benchmarks are run for a fixed duration of 10 seconds and then terminate and return the total number of times the group of locks were acquired.
+Each variation is run 11 times on a variety up to 32 cores and with 2, 4, and 8 locks being acquired.
+The median is calculated and is plotted alongside the 95\% confidence intervals for each point.
+Figure~\ref{f:mutex_bench} shows the results of the benchmark.
+The baseline runs for both languages are mostly comparable, except for the 8 locks results in \ref{f:mutex_bench8_AMD} and \ref{f:mutex_bench8_Intel}, where the \CFA baseline is slower.
+\CFA's mutex statement achieves throughput that is magnitudes higher than \CC's scoped\_lock.
+This is likely due to the scoped\_lock deadlock avoidance implementation.
+Since it uses a retry based mechanism, it can take a long time for threads to progress.
+Additionally the potential for livelock in the algorithm can result in very little throughput under high contention.
+It was observed on the AMD machine that with 32 threads and 8 locks the benchmarks would occasionally livelock indefinitely, with no threads making any progress for 3 hours before the experiment was terminated manually.
+It is likely that shorter bouts of livelock occured in many of the experiments, which would explain large confidence intervals for some of the data points in the \CC data.
+In Figures~\ref{f:mutex_bench8_AMD} and \ref{f:mutex_bench8_Intel} the mutex statement performs better than the baseline.
+At 7 locks and above the mutex statement switches from a hard coded sort to insertion sort.
+It is likely that the improvement in throughput compared to baseline is due to the time spent in the insertion sort, which decreases contention on the locks.
+% Local Variables: %
+% tab-width: 4 %
+% End: %

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