# source:doc/theses/fangren_yu_COOP_F20/Report.tex@417e8ea

Last change on this file since 417e8ea was 735b627, checked in by Peter A. Buhr <pabuhr@…>, 20 months ago

update to new common macros, incorporate Thierry's fixes

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1\documentclass[twoside,12pt]{article}
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3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4
5% Latex packages used in the document.
6\usepackage{fullpage,times,comment}
7\usepackage{epic,eepic}
8\usepackage{upquote}                                                                    % switch curled '" to straight
9\usepackage{calc}
10\usepackage{varioref}                                                                   % extended references
11\usepackage[labelformat=simple,aboveskip=0pt,farskip=0pt]{subfig}
12\renewcommand{\thesubfigure}{\alph{subfigure})}
13\usepackage[flushmargin]{footmisc}                                              % support label/reference in footnote
14\usepackage{latexsym}                                   % \Box glyph
15\usepackage{mathptmx}                                   % better math font with "times"
16\usepackage[toc]{appendix}                                                              % article does not have appendix
17\usepackage[usenames]{color}
18\input{common}                                          % common CFA document macros
20\usepackage{breakurl}
21\urlstyle{sf}
22
23
24% reduce spacing
25\setlist[itemize]{topsep=5pt,parsep=0pt}% global
26\setlist[enumerate]{topsep=5pt,parsep=0pt}% global
27
28\usepackage[pagewise]{lineno}
29\renewcommand{\linenumberfont}{\scriptsize\sffamily}
30
31% Default underscore is too low and wide. Cannot use lstlisting "literate" as replacing underscore
32% removes it as a variable-name character so keywords in variables are highlighted. MUST APPEAR
33% AFTER HYPERREF.
34\renewcommand{\textunderscore}{\leavevmode\makebox[1.2ex][c]{\rule{1ex}{0.075ex}}}
35\newcommand{\NOTE}{\textbf{NOTE}}
36\newcommand{\TODO}[1]{{\color{Purple}#1}}
37
38\setlength{\topmargin}{-0.45in}                                                 % move running title into header
40
41%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
42
43\CFAStyle                                                                                               % CFA code-style for all languages
44%\lstset{
45%language=C++,moredelim=**[is][\color{red}]{@}{@}               % make C++ the default language
46%}% lstset
47%\lstnewenvironment{C++}[1][]                            % use C++ style
48%{\lstset{language=C++,moredelim=**[is][\color{red}]{@}{@}}\lstset{#1}}{}
49
50%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
51
52\setcounter{secnumdepth}{3}                             % number subsubsections
54\makeindex
55
56%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
57
58\title{\LARGE
59Optimization of \CFA Compiler with Case Studies
60}% title
61
62\author{\LARGE
63Fangren Yu -- University of Waterloo
64}% author
65
66\date{
67\today
68}% date
69
70%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
71
72\begin{document}
74% changed after setting pagestyle
77\pagenumbering{roman}
78%\linenumbers                                            % comment out to turn off line numbering
79
80\maketitle
81\pdfbookmark[1]{Contents}{section}
82
83\thispagestyle{plain}
84\pagenumbering{arabic}
85
86\begin{abstract}
87\CFA is an evolutionary, non-object-oriented extension of the C programming language, featuring a parametric type-system, and is currently under active development. The reference compiler for the \CFA language, @cfa-cc@, has some of its major components dated back to the early 2000s, which are based on inefficient data structures and algorithms. This report introduces improvements targeting the expression resolution algorithm, suggested by a recent prototype experiment on a simplified model, which are implemented in @cfa-cc@ to support the full \CFA language. These optimizations speed up the compiler by a factor of 20 across the existing \CFA codebase, bringing the compilation time of a mid-sized \CFA source file down to the 10-second level. A few problem cases derived from realistic code examples are analyzed in detail, with proposed solutions. This work is a critical step in the \CFA project development to achieve its eventual goal of being used alongside C for large software systems.
88\end{abstract}
89
90\clearpage
91\section*{Acknowledgements}
92\begin{sloppypar}
93I would like to thank everyone in the \CFA team for their contribution towards this project. Programming language design and development is a tough subject and requires a lot of teamwork. Without the collaborative efforts from the team, this project could not have been a success. Specifically, I would like to thank Andrew Beach for introducing me to the \CFA codebase, Thierry Delisle for maintaining the test and build automation framework, Michael Brooks for providing example programs of various experimental language and type system features, and most importantly, Professor Martin Karsten for recommending me to the \CFA team, and my supervisor, Professor Peter Buhr for encouraging me to explore deeply into intricate compiler algorithms. Finally, I gratefully acknowledge the help from Aaron Moss, former graduate from the team and the author of the precedent thesis work, to participate in the \CFA team's virtual conferences and email correspondence, and provide many critical arguments and suggestions. 2020 had been an unusually challenging year for everyone and we managed to keep a steady pace.
94\end{sloppypar}
95
96\clearpage
97\tableofcontents
98
99\clearpage
100\section{Introduction}
101
102\CFA language, developed by the Programming Language Group at the University of Waterloo, has a long history, with the initial language design in 1992 by Glen Ditchfield~\cite{Ditchfield92} and the first proof-of-concept compiler built in 2003 by Richard Bilson~\cite{Bilson03}. Many new features have been added to the language over time, but the core of \CFA's type-system --- parametric functions introduced by the @forall@ clause (hence the name of the language) providing parametric overloading --- remains mostly unchanged.
103
104The current \CFA reference compiler, @cfa-cc@, is designed using the visitor pattern~\cite{vistorpattern} over an abstract syntax tree (AST), where multiple passes over the AST modify it for subsequent passes. @cfa-cc@ still includes many parts taken directly from the original Bilson implementation, which served as the starting point for this enhancement work to the type system. Unfortunately, the prior implementation did not provide the efficiency required for the language to be practical: a \CFA source file of approximately 1000 lines of code can take multiple minutes to compile. The cause of the problem is that the old compiler used inefficient data structures and algorithms for expression resolution, which involved significant copying and redundant work.
105
106This report presents a series of optimizations to the performance-critical parts of the resolver, with a major rework of the compiler data-structures using a functional-programming approach to reduce memory complexity. The improvements were suggested by running the compiler builds with a performance profiler against the \CFA standard-library source-code and a test suite to find the most underperforming components in the compiler algorithm.
107
108The \CFA team endorses a pragmatic philosophy that focuses on practical implications of language design and implementation rather than theoretical limits. In particular, the compiler is designed to be expressive with respect to code reuse while maintaining type safety, but compromise theoretical soundness in extreme corner cases. However, when these corner cases do appear in actual usage, they need to be thoroughly investigated. A case-by-case analysis is presented for several of these corner cases, some of which point to certain weaknesses in the language design with solutions proposed based on experimental results.
109
110\section{AST restructuring}
111
112\subsection{Memory model with sharing}
113
114A major rework of the AST data-structure in the compiler was completed as the first step of the project. The majority of this work is documented in my prior report documenting the compiler reference-manual~\cite{cfa-cc}. To summarize:
115\begin{itemize}
116\item
117AST nodes (and therefore subtrees) can be shared without copying.
118\item
119Modifications are performed using functional-programming principles, making copies for local changes without affecting the original data shared by other owners. In-place mutations are permitted as a special case when there is no sharing. The logic is implemented by reference counting.
120\item
121Memory allocation and freeing are performed automatically using smart pointers~\cite{smartpointers}.
122\end{itemize}
123
124The resolver algorithm, designed for overload resolution, allows a significant amount of code reused, and hence copying, for the intermediate representations, especially in the following two places:
125\begin{itemize}
126\item
127Function overload candidates are computed by combining the argument candidates bottom-up, with many being a common term. For example, if $n$ overloads of a function @f@ all take an integer for the first parameter but different types for the second, \eg @f( int, int )@, @f( int, double )@, etc., the first term is copied $n$ times for each of the generated candidate expressions. This copying is particularly bad for deep expression trees.
128\item
129In the unification algorithm and candidate elimination step, actual types are obtained by substituting the type parameters by their bindings. Let $n$ be the complexity (\ie number of nodes in representation) of the original type, $m$ be the complexity of the bound type for parameters, and $k$ be the number of occurrences of type parameters in the original type. If every substitution needs to be deep-copied, these copy step takes $O(n+mk)$ time and memory, while using shared nodes it is reduced to $O(n)$ time and $O(k)$ memory.
130\end{itemize}
131One of the worst examples for the old compiler is a long chain of I/O operations:
132\begin{cfa}
133sout | 1 | 2 | 3 | 4 | ...;   // print integer constants
134\end{cfa}
135The pipe operator is overloaded by the \CFA I/O library for every primitive type in the C language, as well as I/O manipulators defined by the library. In total, there are around 50 overloads for the output stream operation. On resolving the $n$-th pipe operator in the sequence, the first term, which is the result of sub-expression containing $n-1$ pipe operators, is reused to resolve every overload. Therefore at least $O(n^2)$ copies of expression nodes are made during resolution, not even counting type unification cost; combined with the two large factors from number of overloads of pipe operators, and that the output stream type'' in \CFA is a trait with 27 assertions (which adds to complexity of the pipe operator's type) this makes compiling a long output sequence extremely slow. In the new AST representation, only $O(n)$ copies are required and the type of the pipe operator is not copied at all.
136Reduction in space complexity is especially important, as preliminary profiling results on the old compiler build showed over half of the time spent in expression resolution is on memory allocations.
137
138Since the compiler codebase is large and the new memory model mostly benefits expression resolution, some of the old data structures are still kept, and a conversion pass happens before and after the general resolve phase. Rewriting every compiler module will take longer, and whether the new model is correct was unknown when this project started, therefore only the resolver is currently implemented with the new data structure.
139
140
141\subsection{Merged resolver calls}
142
143The pre-resolve phase of compilation, inappropriately called validate'' in the compiler source code, has a number of passes that do more than simple syntax and semantic validation; some passes also normalizes the input program. A few of these passes require type information for expressions, and therefore, need to call the resolver before the general resolve phase. There are three notable places where the resolver is invoked:
144\begin{itemize}
145\item
146Generate default constructor, copy constructor and destructor for user-defined @struct@ types.
147\item
148Resolve @with@ statements (the same as in Pascal~\cite{pascal}), which introduces fields of a structure directly into a scope.
149\item
150Resolve @typeof@ expressions (cf. @decltype@ in \CC); note that this step may depend on symbols introduced by @with@ statements.
151\end{itemize}
152
153Since the constructor calls are one of the most expensive to resolve (reason given in~\VRef{s:SpecialFunctionLookup}), this pre-resolve phase was taking a large amount of time even after the resolver was changed to the more efficient new implementation. The problem is that multiple resolutions repeat a significant amount of work. Therefore, to better facilitate the new resolver, every step that requires type information should be integrated as part of the general resolver phase.
154
155A by-product of this work is that reversed dependence between @with@ statement and @typeof@ can now be handled. Previously, the compiler was unable to handle cases such as:
156\begin{cfa}
157struct S { int x; };
158S foo();
159typeof( foo() ) s; // type is S
160with (s) {
161        x; // refers to s.x
162}
163\end{cfa}
164since the type of @s@ is unresolved when handling @with@ expressions because the @with@ pass follows the @typeof@ pass (interchanging passes only interchanges the problem). Instead, the new (and correct) approach is to evaluate @typeof@ expressions when the declaration is first seen during resolution, and it suffices because of the declaration-before-use rule.
165
166
167\subsection{Special function lookup}
168\label{s:SpecialFunctionLookup}
169
170Reducing the number of function looked ups for overload resolution is an effective way to gain performance when there are many overloads but most of them are trivially wrong. In practice, most functions have few (if any) overloads but there are notable exceptions. Most importantly, constructor @?{}@, destructor @^?{}@, and assignment @?=?@ are generated for every user-defined type (@struct@ and @union@ in C), and in a large source file there can be hundreds of them. Furthermore, many calls are generated for initializing variables, passing arguments and copying values. This fact makes them the most overloaded and most called functions.
171
172In an object-oriented programming language, the object-method types are scoped within a class, so a call such as @obj.f()@ only needs to perform lookup in the method table corresponding to the type of @obj@. \CFA on the other hand, does not have methods, and all types are open, \ie new operations can be defined on them without inheritance; at best a \CFA type can be constrained by a translation unit. However, the big 3'' operators have a unique property enforced by the language rules: the first parameter must be a reference to its associated type, which acts as the @this@ parameter in an object-oriented language. Since \CFA does not have class inheritance, the reference type must always match exactly. Therefore, argument-dependent lookup can be implemented for these operators by using a dedicated, fast symbol-table.
173
174The lookup key for the special functions is the mangled type name of the first parameter. To handle generic types, the type parameters are stripped off, and only the base type is matched. Note a constructor (destructor, assignment operator) may not take an arbitrary @this@ argument, \eg @forall( dtype T ) void ?{}( T & )@, thus guaranteeing that if the @this@ type is known, all possible overloads can be found by searching with this given type. In the case where the @this@ argument itself is overloaded, it is resolved first and all possible result types are used for lookup.
175
176Note that for a generated expression, the particular variable for the @this@ argument is fully known, without overloads, so the majority of constructor-call resolutions only need to check for one given object type. Explicit constructor calls and assignment statements sometimes require lookup for multiple types. In the extremely rare case that the @this@-argument type is unbound, all necessary types are guaranteed to be checked, as for the previous lookup without the argument-dependent lookup; fortunately, this complex case almost never happens in practice. An example is found in the library function @new@:
177\begin{cfa}
178forall( dtype T | sized( T ), ttype TT | { void ?{}( T &, TT ); } )
179T * new( TT p ) { return &(*malloc()){ p }; }
180\end{cfa}
181as @malloc@ may return a pointer to any type, depending on context.
182
183Interestingly, this particular declaration actually causes another complicated issue, making the complex checking of every constructor even worse. \VRef[Section]{s:TtypeResolutionInfiniteRecursion} presents a detailed analysis of this problem.
184
185The callable'' operator @?()@ (cf. @operator()@ in \CC) can also be included in this special operator list, as it is usually only on user-defined types, and the restriction that the first argument must be a reference seems reasonable in this case.
186
187
188\subsection{Improvement of function type representation}
189
190Since substituting type parameters with their bound types is one fundamental operation in many parts of resolver algorithm (particularly unification and environment binding), making as few copies of type nodes as possible helps reducing memory complexity. Even with the new memory management model, allocation is still a significant factor of resolver performance. Conceptually, operations on type nodes of the AST should be performed in functional-programming style, treating the data structure as immutable and only copying when necessary. The in-place mutation is a mere optimization that does not change the logic for operations.
191
192However, the model was broken for function types by an inappropriate design. Function types require special treatment due to the existence of assertions that constrain the types it supports. Specifically, it must be possible to distinguish two different kinds of type parameter usage:
193\begin{cfa}
194forall( dtype T ) void foo( T * t ) {
195        forall( dtype U ) void bar( @T@ * t, @U@ * u ) { ... }
196}
197\end{cfa}
198Here, only @U@ is a free parameter in the nested declaration of function @bar@, as @T@ must be bound at the call site when resolving @bar@.
199
200Moreover, the resolution algorithm also has to distinguish type bindings of multiple calls to the same function, \eg:
201\begin{cfa}
202forall( dtype T ) int foo( T x );
203int i = foo( foo( 1.0 ) );
204\end{cfa}
205The inner call has binding (T: double) while the outer call has binding (T: int). Therefore a unique representation for the free parameters is required in each expression. This type binding was previously done by creating a copy of the parameter declarations inside the function type and fixing references afterwards. However, fixing references is an inherently deep operation that does not work well with the functional-programming style, as it forces eager evaluation on the entire syntax tree representing the function type.
206
207The revised approach generates a unique ID value for each function call expression instance and represents an occurrence of a free-parameter type with a pair of generated ID and original parameter declaration, so references are unique and a shallow copy of the function type is possible.
208
209Note that after the change, all declaration nodes in the syntax-tree representation now map one-to-one with the actual declarations in the program, and therefore are guaranteed to be unique. This property can potentially enable more optimizations, and some related ideas are presented at the end of \VRef{s:SharedSub-ExpressionCaseUniqueExpressions}.
210
211
212\subsection{Improvement of pruning steps}
213
214A minor improvement for candidate elimination is to skip the step on the function overloads and only check the results of function application. As function calls are usually by name (versus pointers to functions), the name resolution rule dictates that every function candidate necessarily has a different type; indirect function calls are rare, and when they do appear, there are even fewer cases with multiple interpretations, and these rarely match exactly in argument type. Since function types have a much more complex representation (with multiple parameters and assertions) than data types, checking equality on them also takes longer.
215
216A brief test of this approach shows that the number of function overloads considered in expression resolution increases by an amount of less than 1 percent, while type comparisons in candidate elimination are reduced by more than half. This improvement is consistent over all \CFA source files in the test suite.
217
218
219\subsection{Shared sub-expression case: Unique expressions}
220\label{s:SharedSub-ExpressionCaseUniqueExpressions}
221
222Unique expression denotes an expression evaluated only once to prevent unwanted side effects. It is currently only a compiler artifact, generated for tuple-member expression of the form:
223\begin{cfa}
224struct S { int a; int b; };
225S s;
226s.[a, b]; // tuple member expression, type is [int, int]
227\end{cfa}
228If the aggregate expression is function call, it cannot be evaluated multiple times:
229\begin{cfa}
230S makeS();
231makeS().[a, b]; // this should only generate a unique S
232\end{cfa}
233Before code generation, the above expression is internally represented as
234\begin{cfa}
235[uniqueExpr{makeS()}.a, uniqueExpr{makeS()}.b];
236\end{cfa}
237and the unique expression is expanded to$\footnote{This uses gcc's statement expression syntax, where \lstinline|(\{block\})| evaluates to value of last expression in the block.}$
238\begin{cfa}
239({
240        if ( !_unique_var_evaluated ) {
241                _unique_var_evaluated = true;
242                _unique_var = makeS();
243        }
244        _unique_var;
245})
246\end{cfa}
247at code generation, where @_unique_var@ and @_unique_var_evaluated@ are generated variables whose scope covers all appearances of the same expression.
248The conditional check ensures a single call to @makeS()@ even though there are logically multiple calls because of the tuple field expansion.
249
250Note that although the unique expression is only used for tuple expansion now, it is a generally useful construction, and is seen in other programming languages, such as Scala's @lazy val@~\cite{Scala}; therefore it may be worthwhile to introduce the unique expression to a broader context in \CFA and even make it directly available to programmers.
251
252In the compiler's visitor pattern, however, this creates a problem where multiple paths to a logically unique expression exist, so it may be modified more than once and become ill-formed; some specific intervention is required to ensure unique expressions are only visited once. Furthermore, a unique expression appearing in more than one places is copied on mutation so its representation is no longer unique.
253
254Currently, special cases are required to keep everything synchronized, and the methods are different when mutating the unique expression instance itself or its underlying expression:
255\begin{itemize}
256\item
257When mutating the underlying expression (visit-once guard)
258\begin{cfa}
259void InsertImplicitCalls::previsit( const ast::UniqueExpr * unqExpr ) {
260        @if ( visitedIds.count( unqExpr->id ) ) visit_children = false;@
261        else visitedIds.insert( unqExpr->id );
262}
263\end{cfa}
264\item
265When mutating the unique instance itself, which actually creates copies
266\begin{cfa}
267auto mutExpr = mutate( unqExpr ); // internally calls copy when shared
268@if ( ! unqMap.count( unqExpr->id ) ) {@
269        ...
270} else {
271        mutExpr->expr = unqMap[mutExpr->id]->expr;
272        mutExpr->result = mutExpr->expr->result;
273}
274\end{cfa}
275\end{itemize}
276Such workarounds are difficult to fit into the common visitor pattern, which suggests the memory model may need different kinds of nodes to accurately represent this feature in the AST.
277
278Given that declaration nodes are unique, it is possible for AST nodes to be divided into three different types:
279\begin{itemize}
280\item
281\textbf{Singleton} with only one owner (declarations);
282\item
283\textbf{No-copy} with multiple owners but cannot be copied (unique expression example presented here);
284\item
285\textbf{Copy} by functional-programming style, which assumes immutable data structures that are copied on mutation.
286\end{itemize}
287The boilerplate code can potentially handle these three cases differently.
288
289
290\section{Analysis of resolver algorithm complexity}
291
292The focus of this section is to identify and analyze some realistic cases that cause the resolver algorithm to have an exponential runtime. As previous work has shown~\cite[\S~4.2.1]{Moss19}, the overload resolution problem in \CFA has worst-case exponential complexity; however, only few specific patterns can trigger the exponential complexity in practice. Implementing heuristic-based optimization for those selected cases is helpful to alleviate the problem.
293
294
295\subsection{Unbound return type}
296\label{s:UnboundReturnType}
297
298The interaction of return-type overloading and polymorphic functions creates function calls with unbounded return-type, and is further complicated by the presence of assertions.
299The prime example of a function with unbound return type is the type-safe version of C @malloc@:
300\begin{cfa}
301forall( dtype T | sized( T ) )
302T * malloc( void ) { return (T *)malloc( sizeof(T) ); } // call C malloc
303int * i = malloc();  // type deduced from left-hand size $$$\Rightarrow$$$ no size argument or return cast
304\end{cfa}
305An unbound return-type is problematic in resolver complexity because a single match of a function call with an unbound return type may create multiple candidates. In the worst case, consider a function declared that returns any @otype@ (defined \VPageref{otype}):
306\begin{cfa}
307forall( otype T ) T anyObj( void );
308\end{cfa}
309As the resolver attempts to satisfy the otype constraint on @T@, a call to @anyObj()@ in an expression, without the result type known, creates at least as many candidates as the number of complete types currently in scope; with generic types it becomes even worse, \eg assuming a declaration of a generic @pair@ is available at that point:
310\begin{cfa}
311forall( otype T, otype U ) struct pair { T first; U second; };
312\end{cfa}
313Then an @anyObj()@ call can result in arbitrarily complex types, such as @pair( pair( int, int ), pair( int, int ) )@, and the depth can grow indefinitely until a specified parameter-depth limit, thus creating exponentially many candidates. However, the expected types allowed by parent expressions are practically very few, so most of those interpretations are invalid; if the result type is never bound up to the top level, by the semantic rules it is ambiguous if there is more than one valid binding and resolution fails quickly. It is therefore reasonable to delay resolving assertions on an unbound parameter in a return type; however, with the current cost model, such behavior may further cause irregularities in candidate selection, such that the presence of assertions can change the preferred candidate, even when order of expression costs are supposed to stay the same. A detailed analysis of this issue is presented in \VRef{s:AnalysisTypeSystemCorrectness}.
314
315
316\subsection[ttype resolution infinite recursion]{\lstinline|ttype| resolution infinite recursion}
317\label{s:TtypeResolutionInfiniteRecursion}
318
319@ttype@ (`tuple type'') is a relatively new addition to the language that attempts to provide type-safe variadic argument semantics. Unlike regular @dtype@ parameters, @ttype@ is only valid in a function parameter-list, and may only appear once as the last parameter type. At the call site, a @ttype@ parameter is bound to the tuple type of all remaining function-call arguments.
320
321There are two kinds of idiomatic @ttype@ usage: one is to provide flexible argument forwarding, similar to the variadic template in \CC (\lstinline[language=C++]|template<typename... args>|), as shown below in the implementation of @unique_ptr@
322\begin{cfa}
323forall( dtype T )
324struct unique_ptr {
325        T * data;
326};
327forall( dtype T | sized( T ), @ttype Args@ | { void ?{}( T &, Args ); })
328void ?{}( unique_ptr( T ) & this, Args @args@ ) {
329        this.data = new( @args@ )// forward constructor arguments to dynamic allocator
330}
331\end{cfa}
332The other usage is to implement structural recursion in the first-rest pattern:
333\begin{cfa}
334forall( otype T, @ttype Params@ | { void process( T ); void func( Params ); })
335void func( T arg1, Params p ) {
336        process( arg1 );
337        func( @p@ )// recursive call until base case of one argument
338}
339\end{cfa}
340For the second use case, it is imperative the number of parameters in the recursive call goes down, since the call site must deduce all assertion candidates, and that is only possible if by observation of the argument types (and not their values), the recursion is known to be completed in a finite number of steps.
341
342In recent experiments, however, a flaw in the type-binding rules can lead to the first kind of @ttype@ use case producing an invalid candidate and the resolver enters an infinite loop.
343This bug was discovered in an attempt to raise the assertion recursive-depth limit and one of the library programs took exponentially longer to compile. The cause of the problem is the following set of functions:
344\begin{cfa}
345// unique_ptr  declaration from above
346
347forall( dtype T | sized( T ), ttype Args | { void ?{}( T &, Args ); } ) { // distribute forall clause
348        void ?{}( counter_data( T ) & this, Args args );
349        void ?{}( counter_ptr( T ) & this, Args args );
350        void ?{}( unique_ptr( T ) & this, Args args );
351}
352
353forall( dtype T | sized( T ), ttype TT | { void ?{}( T &, TT ); } )
354T * new( TT p ) { return @&(*malloc()){ p };@ }
355\end{cfa}
356In the expression @(*malloc()){p}@, the type of the object being constructed is unknown, since the return-type information is not immediately available. That causes every constructor to be searched, and while normally a bound @ttype@ cannot be unified with any free parameter, it is possible with another free @ttype@. Therefore, in addition to the correct option provided by the assertion, 3 wrong options are examined, each of which again requires the same assertion, for an unknown base-type @T@ and @ttype@ argument, which becomes an infinite loop until the specified recursion limit and resolution is fails. Moreover, during the recursion steps, the number of candidates grows exponentially, since there are always 3 options at each step.
357
358Unfortunately, @ttype@ to @ttype@ binding is necessary, to allow indirectly calling a function provided in an assertion.
359\begin{cfa}
360forall( dtype T | sized( T ), ttype Args | { @void ?{}( T &, Args );@ })
361void ?{}( unique_ptr( T ) & this, Args args ) { this.data = (T *)@new( args )@; } // constructor call
362\end{cfa}
363Here the constructor assertion is used by the @new( args )@ call to indirectly call the constructor on the allocated storage.
364Therefore, it is hard, perhaps impossible, to solve this problem by tweaking the type binding rules. An assertion caching algorithm can help improve this case by detecting cycles in recursion.
365
366Meanwhile, without a caching algorithm implemented, some changes in the \CFA source code are enough to eliminate this problem, at least in the current codebase. Note that the issue only happens with an overloaded variadic function, which rarely appears in practice, since the idiomatic use cases are for argument forwarding and self-recursion. The only overloaded @ttype@ function so far discovered in all of \CFA standard library is the constructor, and by utilizing the argument-dependent lookup process described in \VRef{s:UnboundReturnType}, adding a cast before the constructor call removes the issue.
367\begin{cfa}
368T * new( TT p ) { return &(*@(T * )@malloc()){ p }; }
369\end{cfa}
370
371
372\subsection{Reused assertions in nested generic type}
373
374The following test of deeply nested, dynamic generic type reveals that locally caching reused assertions is necessary, rather than just a resolver optimization, because recomputing assertions can result in bloated generated code size:
375\begin{cfa}
376struct nil {};
377forall( otype L, otype R )
378struct cons { L l; R r; };
379
380int main() {
381        #if   N==0
382        nil @x@;
383        #elif N==1
384        cons( size_t, nil ) @x@;
385        #elif N==2
386        cons( size_t, cons( size_t, nil ) ) @x@;
387        #elif N==3
388        cons( size_t, cons( size_t, cons( size_t, nil ) ) ) @x@;
389        // similarly for N=4,5,6
390        #endif
391}
392\end{cfa}
393At the declaration of @x@, it is implicitly initialized by generated constructor call, with signature:
394\begin{cfa}
395forall( otype L, otype R ) void ?{}( cons( L, R ) & );
396\end{cfa}
397where the @otype@ constraint contains the 4 assertions:\label{otype}
398\begin{cfa}
399void ?{}( L & ); // default constructor
400void ?{}( L &, L & ); // copy constructor
401void ^?{}( L & ); // destructor
402L & ?=?( L &, L & ); // assignment
403\end{cfa}
404
405\begin{table}[htb]
406\centering
407\caption{Compilation results of nested cons test}
408\label{t:NestedConsTest}
409\begin{tabular}{|r|r|r|}
410\hline
411N       & Assertions resolved   & Binary size (KB) \\
412\hline
4133       & 170           & 70    \\
414\hline
4154       & 682           & 219   \\
416\hline
4175       & 2,730         & 829   \\
418\hline
4196       & 10,922        & 3,261 \\
420\hline
421\end{tabular}
422\end{table}
423
424Now since the right hand side of outermost cons is again a cons, recursive assertions are required. \VRef[Table]{t:NestedConsTest} shows when the compiler does not cache and reuse already resolved assertions, it becomes a problem, as each of these 4 pending assertions again asks for 4 more assertions one level below. Without caching, the number of resolved assertions grows exponentially, which is unnecessary since there are only $n+1$ different types involved. Even worse, this problem causes exponentially many wrapper functions to be generated at the backend, resulting in a huge binary. As the local functions are implemented by emitting executable code on the stack~\cite{gcc-nested-func}, it means that compiled code also has exponential run time. This problem has practical implications, as nested collection types are frequently used in real production code.
425
426\section{Analysis of type system correctness}
427\label{s:AnalysisTypeSystemCorrectness}
428
429In Moss' thesis~\cite[\S~4.1.2,~p.~45]{Moss19}, the author presents the following example:
430\begin{quote}
431The cost model of \CFA precludes a greedy bottom-up resolution pass, as constraints and costs introduced by calls higher in the expression tree can change the interpretation of those lower in the tree, as in the following example:
432\begin{cfa}
433void f( int );
434double g$$$_1$$$( int );
435int g$$$_2$$$( long );
436f( g( 42 ) );
437\end{cfa}
438Considered independently, @g$_1$( 42 )@ is the cheapest interpretation of @g( 42 )@, with cost (0, 0, 0, 0, 0, 0, 0) since the argument type is an exact match. However, in context, an unsafe conversion is required to downcast the return type of @g1@ to an @int@ suitable for @f@, for a total cost of (1, 0, 0, 0, 0, 0, 0) for @f( g1( 42 ) )@. If @g2@ is chosen, on the other hand, there is a safe upcast from the int type of 42 to @long@, but no cast on the return of @g2@, for a total cost of (0, 0, 1, 0, 0, 0, 0) for @f( g2( 42 ) );@ as this is cheaper, @g2@ is chosen. Due to this design, all valid interpretations of subexpressions must in general be propagated to the top ...
439\end{quote}
440The cost model in the thesis sums up all costs in resolving sub-expressions and chooses the global optimal option. However, the current implementation in @cfa-cc@, based on the original Bilson model~\cite[\S~2.2.4,~p.~32]{Bilson03}, does eager resolution and only allows local optimal candidate selections to propagate upwards:
441\begin{quote}
442From the set of candidates whose parameter and argument types have been unified and whose assertions have been satisfied, those whose sub-expression interpretations have the smallest total cost of conversion are selected ... The total cost of conversion for each of these candidates is then calculated based on the implicit conversions and polymorphism involved in adapting the types of the sub-expression interpretations to the formal parameter types.
443\end{quote}
444With this model, the algorithm picks @g1@ in resolving the @f( g( 42 ) )@ call, which is undesirable.
445
446There is further evidence that shows the Bilson model is fundamentally incorrect, following the discussion of unbound return type in \VRef{s:UnboundReturnType}. By the conversion-cost specification, a binding from a polymorphic type-parameter to a concrete type incurs a polymorphic cost of 1. It remains unspecified \emph{when} the type parameters should become bound. When the parameterized types appear in function parameters, they can be deduced from the argument type, and there is no ambiguity. In the unbound return case, however, the binding may happen at any stage in expression resolution, therefore it is impossible to define a unique local conversion cost. Note that type binding happens exactly once per parameter in resolving the entire expression, so the global binding cost is unambiguously 1.
447
448In the current compiler implementation, there is a notable inconsistency in handling this case. For any unbound parameter that does \emph{not} come with an associated assertion, it remains unbound to the parent expression; for those that do, however, they are immediately bound in the assertion resolution step, and concrete result types are used in the parent expressions.
449Consider the following example:
450\begin{cfa}
451forall( dtype T ) T * f( void );
452void h( int * );
453\end{cfa}
454The expression @h( f() )@ eventually has a total cost of 1 from binding (T: int), but in the eager-resolution model, the cost of 1 may occur either at the call to @f@ or at call to @h@, and with the assertion resolution triggering a binding, the local cost of @f()@ is (0 poly, 0 spec) with no assertions, but (1 poly, -1 spec) with an assertion:
455\begin{cfa}
456forall( dtype T | @{ void g( T * ); }@ ) T * f( void );
457void g( int * );
458void h( int * );
459\end{cfa}
460and that contradicts the principle that adding assertions should make expression cost lower. Furthermore, the time at which type binding and assertion resolution happens is an implementation detail of the compiler, not part of the language definition. That means two compliant \CFA compilers, one performing immediate assertion resolution at each step, and one delaying assertion resolution on unbound types, can produce different expression costs and therefore different candidate selection, making the language rule itself partially undefined, and therefore, unsound. By the above reasoning, the updated cost model using global sum of costs should be accepted as the standard. It also allows the compiler to freely choose when to resolve assertions, as the sum of total costs is independent of that choice; more optimizations regarding assertion resolution can also be implemented.
461
462
463\section{Timing results}
464
465For the timing results presented here, the \CFA compiler is built with gcc 9.3.0, and tested on a server machine running Ubuntu 20.04, 64GB RAM and 32-core 2.2 GHz CPU.
466Timing is reported by the @time@ command and an experiment is run using 8 cores, where each core is at 100\% CPU utilization.
467
468On the most recent build, the \CFA standard library ($\approx$1.3 MB of source code) compiles in 4 minutes 47 seconds total processor time (single thread equivalent), with the slowest file taking 13 seconds. The test suite (178 test cases, $\approx$2.2MB of source code) completes within 25 minutes total processor time,
469% PAB: I do not understand this footnote.
470%\footnote{Including a few runtime tests; total time spent in compilation is approximately 21 minutes.}
471with the slowest file taking 23 seconds. In contrast, the library build with the old compiler takes 85 minutes total, 5 minutes for the slowest file. The full test-suite takes too long with old compiler build and is therefore not run, but the slowest test cases take approximately 5 minutes. Overall, the most recent build compared to an old build is consistently faster by a factor of 20.
472
473Additionally, 6 selected \CFA source files with distinct features from the library and test suite are used to illustrate the compiler performance change after each of the implemented optimizations. Test files are from the most recent build and run through the C preprocessor to expand header file, perform macro expansions, but no line number information (@gcc -E -P@).
474\VRef[Table]{t:SelectedFileByCompilerBuild} shows the selected tests:
475\begin{itemize}
476\item
477@lib/fstream@ (112 KB)
478\item
479@lib/mutex@ (166 KB): implementation of concurrency primitive
480\item
481@lib/vector@ (43 KB): container example, similar to \CC vector
482\item
483@lib/stdlib@ (64 KB): type-safe wrapper to @void *@-based C standard library functions
484\item
485@test/io2@ (55 KB): application of I/O library
486\item
488\end{itemize}
489versus \CFA compiler builds picked from the git commit history that implement the optimizations incrementally:
490\begin{itemize}
491\item
492old resolver
493\item
494\#0 is the first working build of the new AST data structure
495\item
496\#1 implements special symbol table and argument-dependent lookup
497\item
498\#2 implements late assertion-satisfaction
499\item
500\#3 implements revised function-type representation
501\item
502\#4 skips pruning on expressions for function types (most recent build)
503\end{itemize}
504Reading left to right for a test shows the benefit of each optimization on the cost of compilation.
505
506\begin{table}[htb]
507\centering
508\caption{Compile time of selected files by compiler build, in seconds}
509\label{t:SelectedFileByCompilerBuild}
510\begin{tabular}{|l|r|r|r|r|r|r|}
511\hline
512Test case               & old   & \#0   & \#1   & \#2   & \#3   & \#4   \\
513\hline
514@lib/fstream@   & 86.4  & 25.2  & 10.8  & 9.5   & 7.8   & 7.1   \\
515\hline
516@lib/mutex@             & 210.4 & 77.4  & 16.7  & 15.1  & 12.6  & 11.7  \\
517\hline
518@lib/vector@    & 17.2  & 8.9   & 3.1   & 2.8   & 2.4   & 2.2   \\
519\hline
520@lib/stdlib@    & 16.6  & 8.3   & 3.2   & 2.9   & 2.6   & 2.4   \\
521\hline
522@test/io2@              & 300.8 & 53.6  & 43.2  & 27.9  & 19.1  & 16.3  \\
523\hline
524@test/thread@   & 210.9 & 73.5  & 17.0  & 15.1  & 12.6  & 11.8  \\
525\hline
526\end{tabular}
527\smallskip
528\newline
529Results are average of 5 runs (3 runs if time exceeds 100 seconds)
530\end{table}
531
532\section{Conclusion}
533
534Over the course of 8 months of active research and development of the \CFA type system and compiler algorithms, performance of the reference \CFA compiler, cfa-cc, has been greatly improved. Now, mid-sized \CFA programs are compiled reasonably fast. Currently, there are ongoing efforts by the \CFA team to augment the standard library and evaluate its runtime performance, and incorporate \CFA with existing software written in C; therefore this project is especially meaningful for these practical purposes.
535
536Accomplishing this work was difficult. Analysis conducted in the project is based significantly on heuristics and practical evidence, as the theoretical bounds and average cases for the expression resolution problem differ. As well, the slowness of the initial compiler made attempts to understand why and where problems exist extremely difficult because both debugging and validation tools (\eg @gdb@, @valgrind@, @pref@) further slowed down compilation time. However, by the end of the project, I had found and fixed several significant problems and new optimizations are easier to introduce and test. The reduction in the development cycle benefits the \CFA team as a whole.
537
538Some potential issues of the language, which happen frequently in practice, have been identified. Due to the time constraint and complex nature of these problems, a handful of them remain unsolved, but some constructive proposals are made. Notably, introducing a local assertion cache in the resolver is a reasonable solution for a few remaining problems, so that should be the focus of future work.
539
540The \CFA team are planning on a public alpha release of the language as the compiler performance, given my recent improvements, is now useable. Other parts of the system, such as the standard library, have made significant gains due to the speed up in the development cycle. Ideally, the remaining problems should be resolved before release, and the solutions will also be integral to drafting a formal specification.
541