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Added benchmark results to generic chapter of thesis

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1\chapter{Generic Types}
2\label{generic-chap}
3
4A significant shortcoming in standard C is the lack of reusable type-safe abstractions for generic data structures and algorithms.
5Broadly speaking, there are three approaches to implement abstract data structures in C.
6One approach is to write bespoke data structures for each context in which they are needed.
7While this approach is flexible and supports integration with the C type checker and tooling, it is also tedious and error prone, especially for more complex data structures.
8A second approach is to use !void*!-based polymorphism, \eg{} the C standard library functions !bsearch! and !qsort!, which allow for the reuse of common functionality.
9However, basing all polymorphism on !void*! eliminates the type checker's ability to ensure that argument types are properly matched, often requiring a number of extra function parameters, pointer indirection, and dynamic allocation that is otherwise not needed.
10A third approach to generic code is to use preprocessor macros, which does allow the generated code to be both generic and type checked, but errors in such code may be difficult to locate and debug.
11Furthermore, writing and using preprocessor macros is unnatural and inflexible.
12Figure~\ref{bespoke-generic-fig} demonstrates the bespoke approach for a simple linked list with !insert! and !head! operations, while Figure~\ref{void-generic-fig} and Figure~\ref{macro-generic-fig} show the same example using !void*!- and !#define!-based polymorphism, respectively.
13
14\begin{figure}
15        \begin{cfa}
16                struct int_list { int value; struct int_list* next; };
17
18                void int_list_insert( struct int_list** ls, int x ) {
19                        struct int_list* node = malloc(sizeof(struct int_list));
20                        node->value = x; node->next = *ls;
21                        *ls = node;
22                }
23
24                int int_list_head( const struct int_list* ls ) { return ls->value; }
25
26                $\C[\textwidth]{// all code must be duplicated for every generic instantiation}$
27
28                struct string_list { const char* value; struct string_list* next; };
29
30                void string_list_insert( struct string_list** ls, const char* x ) {
31                        struct string_list* node = malloc(sizeof(struct string_list));
32                        node->value = x; node->next = *ls;
33                        *ls = node;
34                }
35
36                const char* string_list_head( const struct string_list* ls )
37                        { return ls->value; }
38
39                $\C[\textwidth]{// use is efficient and idiomatic}$
40
41                int main() {
42                        struct int_list* il = NULL;
43                        int_list_insert( &il, 42 );
44                        printf("%d\n", int_list_head(il));
45                       
46                        struct string_list* sl = NULL;
47                        string_list_insert( &sl, "hello" );
48                        printf("%s\n", string_list_head(sl));
49                }
50        \end{cfa}
51
52        \caption{Bespoke code for linked list implementation.} \label{bespoke-generic-fig}
53\end{figure}
54
55\begin{figure}
56        \begin{cfa}
57                // single code implementation
58
59                struct list { void* value; struct list* next; };
60
61                $\C[\textwidth]{// internal memory management requires helper functions}$
62
63                void list_insert( struct list** ls, void* x, void* (*copy)(void*) ) {
64                        struct list* node = malloc(sizeof(struct list));
65                        node->value = copy(x); node->next = *ls;
66                        *ls = node;
67                }
68
69                void* list_head( const struct list* ls ) { return ls->value; }
70
71                $\C[\textwidth]{// helpers duplicated per type}$
72
73                void* int_copy(void* x) {
74                        int* n = malloc(sizeof(int));
75                        *n = *(int*)x;
76                        return n;
77                }
78
79                void* string_copy(void* x) { return strdup((const char*)x); }
80
81                int main() {
82                        struct list* il = NULL;
83                        int i = 42;
84                        list_insert( &il, &i, int_copy );
85                        printf("%d\n", *(int*)list_head(il));  $\C[2in]{// unsafe type cast}$
86                       
87                        struct list* sl = NULL;
88                        list_insert( &sl, "hello", string_copy );
89                        printf("%s\n", (char*)list_head(sl));  $\C[2in]{// unsafe type cast}$
90                }
91        \end{cfa}
92
93        \caption{\lstinline{void*}-polymorphic code for linked list implementation.} \label{void-generic-fig}
94\end{figure}
95
96\begin{figure}
97        \begin{cfa}
98                $\C[\textwidth]{// code is nested in macros}$
99
100                #define list(N) N ## _list
101
102                #define list_insert(N) N ## _list_insert
103
104                #define list_head(N) N ## _list_head
105
106                #define define_list(N, T) $\C[0.25in]{ \textbackslash }$
107                        struct list(N) { T value; struct list(N)* next; }; $\C[0.25in]{ \textbackslash }$
108                        $\C[0.25in]{ \textbackslash }$
109                        void list_insert(N)( struct list(N)** ls, T x ) { $\C[0.25in]{ \textbackslash }$
110                                struct list(N)* node = malloc(sizeof(struct list(N))); $\C[0.25in]{ \textbackslash }$
111                                node->value = x; node->next = *ls; $\C[0.25in]{ \textbackslash }$
112                                *ls = node; $\C[0.25in]{ \textbackslash }$
113                        } $\C[0.25in]{ \textbackslash }$
114                        $\C[0.25in]{ \textbackslash }$
115                        T list_head(N)( const struct list(N)* ls ) { return ls->value; }
116
117                define_list(int, int); $\C[3in]{// defines int\_list}$
118                define_list(string, const char*); $\C[3in]{// defines string\_list}$
119
120                $\C[\textwidth]{// use is efficient, but syntactically idiosyncratic}$
121
122                int main() {
123                        struct list(int)* il = NULL; $\C[3in]{// does not match compiler-visible name}$
124                        list_insert(int)( &il, 42 );
125                        printf("%d\n", list_head(int)(il));
126                       
127                        struct list(string)* sl = NULL;
128                        list_insert(string)( &sl, "hello" );
129                        printf("%s\n", list_head(string)(sl));
130                }
131        \end{cfa}
132
133        \caption{Macros for generic linked list implementation.} \label{macro-generic-fig}
134\end{figure}
135
136\CC{}, Java, and other languages use \emph{generic types} to produce type-safe abstract data types.
137Design and implementation of generic types for \CFA{} is the first major contribution of this thesis, a summary of which is published in \cite{Moss18} and from which this chapter is closely based.
138\CFA{} generic types integrate efficiently and naturally with the existing polymorphic functions in \CFA{}, while retaining backward compatibility with C in layout and support for separate compilation.
139A generic type can be declared in \CFA{} by placing a !forall! specifier on a !struct! or !union! declaration, and instantiated using a parenthesized list of types after the generic name.
140An example comparable to the C polymorphism examples in Figures~\ref{bespoke-generic-fig}, \ref{void-generic-fig}, and \ref{macro-generic-fig} can be seen in Figure~\ref{cfa-generic-fig} \TODO{test this code}.
141
142\begin{figure}
143        \begin{cfa}
144                forall(otype T) struct list { T value; list(T)* next; };
145
146                $\C[\textwidth]{// single polymorphic implementation of each function}$
147                $\C[\textwidth]{// overloading reduces need for namespace prefixes}$
148
149                forall(otype T) void insert( list(T)** ls, T x ) {
150                        list(T)* node = alloc();  $\C{// type-inferring alloc}$
151                        (*node){ x, *ls }$\C{// concise constructor syntax}$
152                        *ls = node;
153                }
154
155                forall(otype T) T head( const list(T)* ls ) { return ls->value; }
156
157                $\C[\textwidth]{// use is clear and efficient}$
158
159                int main() {
160                        list(int)* il = 0;
161                        insert( &il, 42 );  $\C{// inferred polymorphic T}$
162                        printf("%d\n", head(il));
163                       
164                        list(const char*)* sl = 0;
165                        insert( &sl, "hello" );
166                        printf("%s\n", head(sl));
167                }
168        \end{cfa}
169
170        \caption{\CFA{} generic linked list implementation.} \label{cfa-generic-fig}
171\end{figure}
172
173\section{Design}
174
175Though a number of languages have some implementation of generic types, backward compatibility with both C and existing \CFA{} polymorphism presented some unique design constraints for this project.
176The guiding principle was to maintain an unsurprising language model for C programmers without compromising runtime efficiency.
177A key insight for this design was that C already possesses a handful of built-in generic types (\emph{compound types} in the language of the standard\cit{}), notably pointer (!T*!) and array (!T[]!), and that user-definable generics should act similarly.
178
179\subsection{Related Work}
180
181One approach to the design of generic types is that taken by \CC{} templates\cite{C++}.
182The template approach is closely related to the macro-expansion approach to C polymorphism demonstrated in Figure~\ref{macro-generic-fig}, but where the macro-expansion syntax has been given first-class language support.
183Template expansion has the benefit of generating code with near-optimal runtime efficiency, as distinct optimizations can be applied for each instantiation of the template.
184On the other hand, template expansion can also lead to significant code bloat, exponential in the worst case\cit{}, and the costs of increased instruction cache pressure at runtime and wasted developer time when compiling cannot be discounted.
185The most significant restriction of the \CC{} template model is that it breaks separate compilation and C's translation-unit-based encapsulation mechanisms.
186Because a \CC{} template is not actually code, but rather a sort of ``recipe'' to generate code, template code must be visible at its call site to be used.
187Furthermore, \CC{} template code cannot be type-checked without instantiating it, a time consuming process with no hope of improvement until \CC{} concepts\cite{C++Concepts} are standardized in \CCtwenty{}.
188C code, by contrast, only needs a !struct! or function declaration to call that function or use (by-pointer) values of that type, a desirable property to maintain for \CFA{}.
189
190Java\cite{Java8} has another prominent implementation for generic types, introduced in Java~5 and based on a significantly different approach than \CC{}.
191The Java approach has much more in common with the !void*!-polymorphism shown in Figure~\ref{void-generic-fig}; since in Java nearly all data is stored by reference, the Java approach to polymorphic data is to store pointers to arbitrary data and insert type-checked implicit casts at compile-time.
192This process of \emph{type erasure} has the benefit of allowing a single instantiation of polymorphic code, but relies heavily on Java's object model and garbage collector.
193To use this model, a more C-like language such as \CFA{} would be required to dynamically allocate internal storage for variables, track their lifetime, and properly clean them up afterward.
194
195Cyclone\cite{Grossman06} is another language extending C, and also provides capabilities for polymorphic functions and existential types, similar to \CFA{}'s !forall! functions and generic types.
196Cyclone existential types can include function pointers in a construct similar to a virtual function table, but these pointers must be explicitly initialized at some point in the code, which is tedious and error-prone compared to \CFA{}'s implicit assertion satisfaction.
197Furthermore, Cyclone's polymorphic functions and types are restricted to abstraction over types with the same layout and calling convention as !void*!, \ie{} only pointer types and !int!.
198In the \CFA{} terminology discussed in Section~\ref{generic-impl-sec}, all Cyclone polymorphism must be dtype-static.
199While the Cyclone polymorphism design provides the efficiency benefits discussed in Section~\ref{dtype-static-sec} for dtype-static polymorphism, it is more restrictive than the more general model of \CFA{}.
200
201Many other languages include some form of generic types.
202As a brief survey, ML\cite{ML} was the first language to support parameteric polymorphism, but unlike \CFA{} does not support the use of assertions and traits to constrain type arguments.
203Haskell\cite{Haskell10} combines ML-style polymorphism with the notion of type classes, similar to \CFA{} traits, but requiring an explicit association with their implementing types, unlike \CFA{}.
204Objective-C\cite{obj-c-book} is an extension to C which has had some industrial success; however, it did not support type-checked generics until recently\cite{xcode7}, and it's garbage-collected, message-passing object-oriented model is a radical departure from C.
205Go\cite{Go}, and Rust\cite{Rust} are modern compiled languages with abstraction features similar to \CFA{} traits, \emph{interfaces} in Go and \emph{traits} in Rust.
206Go has implicit interface implementation and uses a ``fat pointer'' construct to pass polymorphic objects to functions, similar in principle to \CFA{}'s implicit forall paramters.
207Go does not, however, allow user code to define generic types, restricting Go programmers to the small set of generic types defined by the compiler.
208Rust has powerful abstractions for generic programming, including explicit implemenation of traits and options for both separately-compiled virtual dispatch and template-instantiated static dispatch in functions.
209On the other hand, the safety guarantees of Rust's \emph{lifetime} abstraction and borrow checker impose a distinctly idiosyncratic programming style and steep learning curve; \CFA{}, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
210
211\subsection{\CFA{} Generics}
212
213The generic types design in \CFA{} draws inspiration from both \CC{} and Java generics, capturing the better aspects of each.
214Like \CC{} template types, generic !struct!s and !union!s in \CFA{} have macro-expanded storage layouts, but, like Java generics, \CFA{} generic types can be used with separately-compiled polymorphic functions without requiring either the type or function definition to be visible to the other.
215The fact that the storage layout of any instantiation of a \CFA{} generic type is identical to that of the monomorphic type produced by simple macro replacement of the generic type parameters is important to provide consistent and predictable runtime performance, and to not impose any undue abstraction penalty on generic code.
216As an example, consider the following generic type and function \TODO{test this}:
217
218\begin{cfa}
219forall( otype R, otype S ) struct pair { R first; S second; };
220
221pair(const char*, int) with_len( const char* s ) {
222        return (pair(const char*), int){ s, strlen(s) };
223}
224\end{cfa}
225
226In this example, !with_len! is defined at the same scope as !pair!, but it could be called from any context that can see the definition of !pair! and a declaration of !with_len!.
227If its return type was !pair(const char*, int)*!, callers of !with_len! would only need the declaration !forall(otype R, otype S) struct pair! to call it, in accordance with the usual C rules for opaque types.
228
229!with_len! is itself a monomorphic function, returning a type that is structurally identical to !struct { const char* first; int second; }!, and as such could be called from C given an appropriate redeclaration and demangling flags.
230However, the definition of !with_len! depends on a polymorphic function call to the !pair! constructor, which only needs to be written once (in this case, implicitly by the compiler according to the usual \CFA{} constructor generation\cite{Moss18}) and can be re-used for a wide variety of !pair! instantiations.
231Since the parameters to this polymorphic constructor call are all statically known, compiler inlining can eliminate any runtime overhead of this polymorphic call.
232
233\CFA{} deliberately does not support \CC{}-style partial specializations of generic types.
234A particularly infamous example in the \CC{} standard library is !vector<bool>!, which is represented as a bitstring rather than the array representation of the other !vector! instantiations.
235Complications from this inconsistency (chiefly the fact that a single bit is not addressable, unlike an array element) make the \CC{} !vector! unpleasant to use in generic contexts due to the break in its public interface.
236Rather than attempting to plug leaks in the template specialization abstraction with a detailed method interface, \CFA{} takes the more principled position that two types with an unrelated data layout are in fact unrelated types, and should be handled with different code.
237Of course, to the degree that distinct types are similar enough to share an interface, the \CFA{} !trait! system allows one to be defined, and objects of types implementing that !trait! to be operated on in the same polymorphic functions.
238
239Since \CFA{} polymorphic functions can operate over polymorphic generic types, functions over such types can be partially or completely specialized using the usual overload selection rules.
240As an example, the !with_len! function above could be an optimization of the following more general function:
241
242\begin{cfa}
243forall(otype T, otype I | { I len(T); })
244pair(T, I) with_len( T s ) {
245        return (pair(T,I)){ s, len(s) };
246}
247\end{cfa}
248
249\CFA{} generic types also support the type constraints from !forall! functions.
250For example, the following declaration of a sorted set type ensures that the set key implements equality and relational comparison:
251
252\begin{cfa}
253forall(otype Key | { int ?==?(Key, Key); int ?<?(Key, Key); }) struct sorted_set;
254\end{cfa}
255
256These constraints are implemented by applying equivalent constraints to the compiler-generated constructors for this type.
257
258\section{Implementation} \label{generic-impl-sec}
259
260The ability to use generic types in polymorphic contexts means that the \CFA{} implementation in \CFACC{} must support a mechanism for accessing fields of generic types dynamically at runtime.
261While \CFACC{} could in principle use this same mechanism for accessing fields of all generic types, such an approach would throw away compiler knowledge of static types and impose an unnecessary runtime cost, limiting the utility of the generic type design.
262Instead, my design for generic type support in \CFACC{} distinguishes between \emph{concrete} generic types that have a fixed memory layout regardless of type parameters and \emph{dynamic} generic types that may vary in memory layout depending on their type parameters.
263A \emph{dtype-static} type has polymorphic parameters but is still concrete.
264Polymorphic pointers are an example of dtype-static types; given some type variable !T!, T is a polymorphic type, but !T*! has a fixed size and can therefore be represented by a !void*! in code generation.
265In particular, generic types where all parameters are un-!sized! (\ie{} they do not conform to the built-in !sized! trait because the compiler does not know their size and alignment) are always concrete, as there is no possibility for their layout to vary based on type parameters of unknown size and alignment.
266More precisely, a type is concrete if and only if all of its !sized! type parameters are concrete, and a concrete type is dtype-static if any of its type parameters are (possibly recursively) polymorphic.
267To illustrate, the following code using the !pair! type from above \TODO{test this} has each use of !pair! commented with its class:
268
269\begin{cfa}
270//dynamic, layout varies based on T
271forall(otype T) T value( pair(const char*, T) p ) { return p.second; }
272
273// dtype-static, F* and T* are concrete but recursively polymorphic
274forall(dtype F, otype T) T value( pair(F*, T*) ) { return *p.second; }
275
276pair(const char*, int) p = {"magic", 42}; $\C[2.5in]{// concrete}$
277int i = value(p);
278pair(void*, int*) q = {0, &p.second}; $\C[2.5in]{// concrete}$
279i = value(q);
280double d = 1.0;
281pair(double*, double*) r = {&d, &d}; $\C[2.5in]{// concrete}$
282d = value(r);
283\end{cfa}
284
285\subsection{Concrete Generic Types}
286
287The \CFACC{} translator template expands concrete generic types into new structure types, affording maximal inlining.
288To enable interoperation among equivalent instantiations of a generic type, \CFACC{} saves the set of instantiations currently in scope and reuses the generated structure declarations where appropriate.
289In particular, tuple types are implemented as a single compiler-generated generic type definition per tuple arity, and can be instantiated and reused according to the usual rules for generic types.
290A function declaration that accepts or returns a concrete generic type produces a declaration for the instantiated structure in the same scope, which all callers may reuse.
291As an example, the concrete instantiation for !pair(const char*, int)! is\footnote{This omits the field name mangling performed by \CFACC{} for overloading purposes.\label{mangle-foot}}
292
293\begin{cfa}
294struct _pair_conc0 { const char * first; int second; };
295\end{cfa}
296
297A concrete generic type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
298In the example above, the !pair(F*, T*)! parameter to !value! is such a type; its expansion is below\footref{mangle-foot}, and it is used as the type of the variables !q! and !r! as well, with casts for member access where appropriate.
299
300\begin{cfa}
301struct _pair_conc1 { void* first; void* second; };
302\end{cfa}
303
304\subsection{Dynamic Generic Types}
305
306In addition to this efficient implementation of concrete generic types, \CFA{} also offers flexibility with powerful support for dynamic generic types.
307In the pre-existing compiler design, !otype! (and all !sized!) type parameters come with implicit size and alignment parameters provided by the caller.
308The design for generic types presented here adds an \emph{offset array} containing structure-member offsets for dynamic generic !struct! types.
309A dynamic generic !union! needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
310Access to members of a dynamic structure is provided at runtime via base displacement addressing the structure pointer and the member offset (similar to the !offsetof! macro), moving a compile-time offset calculation to runtime.
311
312the offset arrays are statically generated where possible.
313If a dynamic generic type is passed or returned by value from a polymorphic function, \CFACC{} can safely assume that the generic type is complete (\ie{} has a known layout) at any call site, and the offset array is passed from the caller; if the generic type is concrete at the call site, the elements of this offset array can even be statically generated using the C !offsetof! macro.
314As an example, the body of the second !value! function above is implemented as
315
316\begin{cfa}
317_assign_T( _retval, p + _offsetof_pair[1] ); $\C[2in]{// return *p.second}$
318\end{cfa}
319
320Here, !_assign_T! is passed in as an implicit parameter from !otype T! and takes two !T*! (!void*! in the generated code), a destination and a source, and !_retval! is the pointer to a caller-allocated buffer for the return value, the usual \CFA{} method to handle dynamically-sized return types.
321!_offsetof_pair! is the offset array passed into !value!; this array is generated at the call site as
322
323\begin{cfa}
324size_t _offsetof_pair[] = {offsetof(_pair_conc0, first),  offsetof(_pair_conc0, second)};
325\end{cfa}
326
327\subsubsection{Layout Functions}
328
329In some cases, the offset arrays cannot be statically generated.
330For instance, modularity is generally provided in C by including an opaque forward declaration of a structure and associated accessor and mutator functions in a header file, with the actual implementations in a separately-compiled \texttt{.c} file.
331\CFA{} supports this pattern for generic types, implying that the caller of a polymorphic function may not know the actual layout or size of a dynamic generic type and only holds it by pointer.
332\CFACC{} automatically generates \emph{layout functions} for cases where the size, alignment, and offset array of a generic struct cannot be passed into a function from that functions's caller.
333These layout functions take as arguments pointers to size and alignment variables and a caller-allocated array of member offsets, as well as the size and alignment of all !sized! parameters to the generic structure.
334Un!sized! parameters not passed because they are forbidden from being used in a context that affects layout by C's usual rules about incomplete types.
335Similarly, the layout function can only safely be called from a context where the generic type definition is visible, because otherwise the caller will not know how large to allocate the array of member offsets.
336
337The C standard does not specify a memory layout for structs, but the POSIX ABI for x86\cit{} does; this memory layout is common for C implementations, but is a platform-specific issue for porting \CFA{}.
338This algorithm, sketched below in pseudo-\CFA{}, is a straightforward mapping of consecutive fields into the first properly-aligned offset in the !struct! layout; layout functions for !union! types omit the offset array and simply calculate the maximum size and alignment over all union variants.
339Since \CFACC{} generates a distinct layout function for each type, constant-folding and loop unrolling are applied.
340
341\begin{cfa}
342forall(dtype T1, dtype T2, ... | sized(T1) | sized(T2) | ...)
343void layout(size_t* size, size_t* align, size_t* offsets) {
344        // initialize values
345        *size = 0; *align = 1;
346        // set up members
347        for ( int i = 0; i < n_fields; ++i ) {
348                // pad to alignment
349                size_t off_align = *size % alignof(field[i]);
350                if ( off_align != 0 ) { *size += alignof(field[i]) - off_align; }
351                // mark member, increase size, and fix alignment
352                offsets[i] = *size;
353                *size += sizeof(field[i]);
354                if ( *align < alignof(field[i]) ) { *align = alignof(field[i]); }
355        }
356        // final padding to alignment
357        size_t off_align = *size % *align;
358        if ( off_align != 0 ) { *size += *align - off_align; }
359}
360\end{cfa}
361
362Results of layout function calls are cached so that they are only computed once per type per function.
363Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature, an important implemenation-hiding constraint of the design.
364For instance, a function that strips duplicate values from an unsorted !list(T)! likely has a reference to the list as its only explicit parameter, but uses some sort of !set(T)! internally to test for duplicate values.
365This function could acquire the layout for !set(T)! by calling its layout function, providing as an argument the layout of !T! implicitly passed into that function.
366
367Whether a type is concrete, dtype-static, or dynamic is decided solely on the basis of the type arguments and !forall! clause type paramters.
368This design allows opaque forward declarations of generic types, \eg{} !forall(otype T) struct Box;! like in C, all uses of $Box(T)$ can be separately compiled, and callers from other translation units know the proper calling conventions to use.
369In an alternate design where the definition of a structure type is included in deciding whether a generic type is dynamic or concrete, some further types may be recognized as dtype-static --- \eg{} !Box! could be defined with a body !{ T* p; }!, and would thus not depend on !T! for its layout.
370However, the existence of an !otype! parameter !T! means that !Box! \emph{could} depend on !T! for its layout if this definition is not visible, and we judged preserving separate compilation (and the associated C compatibility) in the implemented design to be an acceptable trade-off.
371
372\subsection{Applications of Dtype-static Types} \label{dtype-static-sec}
373
374The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
375The most important such pattern is using !forall(dtype T) T*! as a type-checked replacement for !void*!, \eg{} creating a lexicographic comparison function for pairs of pointers.
376
377\begin{cfa}
378forall(dtype T)
379int lexcmp( pair(T*, T*)* a, pair(T*, T*)* b, int (*cmp)(T*, T*) ) {
380        int c = cmp( a->first, b->first );
381        return c ? c : cmp( a->second, b->second );
382}
383\end{cfa}
384
385Since !pair(T*, T*)! is a concrete type, there are no implicit parameters passed to !lexcmp!; hence, the generated code is identical to a function written in standard C using !void*!, yet the \CFA{} version is type-checked to ensure members of both pairs and arguments to the comparison function match in type.
386
387Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag structures}.
388Sometimes, information is only used for type checking and can be omitted at runtime.
389In the example below, !scalar! is a dtype-static type; hence, all uses have a single structure definition containing !unsigned long! and can share the same implementations of common functions like !?+?!.
390These implementations may even be separately compiled, unlike \CC{} template functions.
391However, the \CFA{} type checker ensures matching types are used by all calls to !?+?!, preventing nonsensical computations like adding a length to a volume.
392
393\begin{cfa}
394forall(dtype Unit) struct scalar { unsigned long value; };
395struct metres {};
396struct litres {};
397
398forall(dtype U) scalar(U) ?+?(scalar(U) a, scalar(U) b) {
399        return (scalar(U)){ a.value + b.value };
400}
401
402scalar(metres) half_marathon = { 21098 };
403scalar(litres) pool = { 2500000 };
404scalar(metres) marathon = half_marathon + half_marathon;
405`marathon + pool;` $\C[4in]{// compiler ERROR, mismatched types}$
406\end{cfa}
407
408\section{Performance Experiments} \label{generic-performance-sec}
409
410To validate the practicality of this generic type design I have conducted microbenchmark-based tests against a number of comparable code designs in C and \CC{}, first published in \cite{Moss18}.
411Since all these languages are compiled with the same compiler backend and share a subset essentially comprising standard C, maximal-performance benchmarks should show little runtime variance, differing only in length and clarity of source code.
412A more illustrative comparison measures the costs of idiomatic usage of each language's features.
413The code below shows the \CFA{} benchmark tests for a generic stack based on a singly-linked list; the test suite is equivalent for the other other languages.
414The experiment uses element types !int! and !pair(short, char)! and pushes $N = 40M$ elements on a generic stack, copies the stack, clears one of the stacks, and finds the maximum value in the other stack.
415
416\begin{cfa}
417int main() {
418        int max = 0, val = 42;
419        stack( int ) si, ti;
420
421        REPEAT_TIMED( "push_int", N, push( si, val ); )
422        TIMED( "copy_int", ti{ si }; )
423        TIMED( "clear_int", clear( si ); )
424        REPEAT_TIMED( "pop_int", N, int x = pop( ti ); if ( x > max ) max = x; )
425
426        pair( short, char ) max = { 0h, '\0' }, val = { 42h, 'a' };
427        stack( pair( short, char ) ) sp, tp;
428
429        REPEAT_TIMED( "push_pair", N, push( sp, val ); )
430        TIMED( "copy_pair", tp{ sp }; )
431        TIMED( "clear_pair", clear( sp ); )
432        REPEAT_TIMED( "pop_pair", N, pair(short, char) x = pop( tp );
433                if ( x > max ) max = x; )
434}
435\end{cfa}
436
437The four versions of the benchmark implemented are C with !void*!-based polymorphism, \CFA{} with parameteric polymorphism, \CC{} with templates, and \CC{} using only class inheritance for polymorphism, denoted \CCV{}.
438The \CCV{} variant illustrates an alternative object-oriented idiom where all objects inherit from a base !object! class, mimicking a Java-like interface; in particular, runtime checks are necessary to safely downcast objects.
439The most notable difference among the implementations is the memory layout of generic types: \CFA{} and \CC{} inline the stack and pair elements into corresponding list and pair nodes, while C and \CCV{} lack such capability and, instead, must store generic objects via pointers to separately allocated objects.
440Note that the C benchmark uses unchecked casts as C has no runtime mechanism to perform such checks, whereas \CFA{} and \CC{} provide type safety statically.
441
442Figure~\ref{generic-eval-fig} and Table~\ref{generic-eval-table} show the results of running the described benchmark.
443The graph plots the median of five consecutive runs of each program, with an initial warm-up run omitted.
444All code is compiled at \texttt{-O2} by gcc or g++ 6.4.0, with all \CC{} code compiled as \CCfourteen{}.
445The benchmarks are run on an Ubuntu 16.04 workstation with 16 GB of RAM and a 6-core AMD FX-6300 CPU with 3.5 GHz maximum clock frequency.
446I conjecture that these results scale across most uses of generic types, given the constant underlying polymorphism implementation.
447
448\begin{figure}
449\centering
450\input{generic-timing}
451\caption{Benchmark timing results (smaller is better)} \label{generic-eval-fig}
452\end{figure}
453
454\begin{table}
455\caption{Properties of benchmark code} \label{generic-eval-table}
456\centering
457\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
458\begin{tabular}{lrrrr}
459                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\
460maximum memory usage (MB)                       & 10\,001       & 2\,502        & 2\,503        & 11\,253               \\
461source code size (lines)                        & 201           & 191           & 125           & 294                   \\
462redundant type annotations (lines)      & 27            & 0                     & 2                     & 16                    \\
463binary size (KB)                                        & 14            & 257           & 14            & 37                    \\
464\end{tabular}
465\end{table}
466
467The C and \CCV{} variants are generally the slowest and have the largest memory footprint, due to their less-efficient memory layout and the pointer indirection necessary to implement generic types in those languages; this inefficiency is exacerbated by the second level of generic types in the pair benchmarks.
468By contrast, the \CFA{} and \CC{} variants run in roughly equivalent time for both the integer and pair because of the equivalent storage layout, with the inlined libraries (\ie{} no separate compilation) and greater maturity of the \CC{} compiler contributing to its lead.
469\CCV{} is slower than C largely due to the cost of runtime type checking of downcasts (implemented with !dynamic_cast!); the outlier for \CFA{}, pop !pair!, results from the complexity of the generated-C polymorphic code.
470The gcc compiler is unable to optimize some dead code and condense nested calls; a compiler designed for \CFA{} could more easily perform these optimizations.
471Finally, the binary size for \CFA{} is larger because of static linking with \CFA{} libraries.
472
473\CFA{} is also competitive in terms of source code size, measured as a proxy for programmer effort.
474The line counts in Table~\ref{generic-eval-table} include implementations of !pair! and !stack! types for all four languages for purposes of direct comparison, although it should be noted that \CFA{} and \CC{} have prewritten data structures in their standard libraries that programmers would generally use instead.
475Use of these standard library types has minimal impact on the performance benchmarks, but shrinks the \CFA{} and \CC{} code to 39 and 42 lines, respectively.
476The difference between the \CFA{} and \CC{} line counts is primarily declaration duplication to implement separate compilation; a header-only \CFA{} library is similar in length to the \CC{} version.
477On the other hand, due to the language shortcomings mentioned at the beginning of the chapter, C does not have a generic collections library in its standard distribution, resulting in frequent reimplementation of such collection types by C programmers.
478\CCV{} does not use the \CC{} standard template library by construction, and, in fact, includes the definition of !object! and wrapper classes for !char!, !short!, and !int! in its line count, which inflates this count somewhat, as an actual object-oriented language would include these in the standard library.
479I justify the given line count by noting that many object-oriented languages do not allow implementing new interfaces on library types without subclassing or wrapper types, which may be similarly verbose.
480
481Line count is a fairly rough measure of code complexity; another important factor is how much type information the programmer must specify manually, especially where that information is not type-checked.
482Such unchecked type information produces a heavier documentation burden and increased potential for runtime bugs and is much less common in \CFA{} than C, with its manually specified function pointer arguments and format codes, or \CCV{}, with its extensive use of un-type-checked downcasts, \eg{} !object! to !integer! when popping a stack.
483To quantify this manual typing, the ``redundant type annotations'' line in Table~\ref{generic-eval-table} counts the number of lines on which the known type of a variable is respecified, either as a format specifier, explicit downcast, type-specific function, or by name in a !sizeof!, !struct! literal, or !new! expression.
484The \CC{} benchmark uses two redundant type annotations to create new stack nodes, whereas the C and \CCV{} benchmarks have several such annotations spread throughout their code.
485The \CFA{} benchmark is able to eliminate \emph{all} redundant type annotations through use of the return-type polymorphic !alloc! function in the \CFA{} standard library.
486
487\section{Future Work}
488
489The generic types design presented here is already sufficiently expressive to implement a variety of useful library types.
490However, some other features based on this design could further improve \CFA{}.
491
492The most pressing addition is the ability to have non-type generic parameters.
493C already supports fixed-length array types, \eg{} !int[10]!; these types are essentially generic types with unsigned integer parameters, and allowing \CFA{} users the capability to build similar types is a requested feature.
494More exotically, the ability to have these non-type parameters depend on dynamic runtime values rather than static compile-time constants opens up interesting opportunities for type-checking problematic code patterns.
495For example, if a collection iterator was parameterized over the pointer to the collection it was drawn from, then a sufficiently powerful static analysis pass could ensure that that iterator was only used for that collection, eliminating one source of hard-to-find bugs.
496
497The implementation mechanisms behind this generic types design can also be used to add new features to \CFA{}.
498One such potential feature would be to add \emph{field assertions} to the existing function and variable assertions on polymorphic type variables.
499Implementation of these field assertions would be based on the same code that supports member access by dynamic offset calculation for dynamic generic types.
500Simulating field access can already be done more flexibly in \CFA{} by declaring a trait containing an accessor function to be called from polymorphic code, but these accessor functions impose some overhead both to write and call, and directly providing field access via an implicit offset parameter would be both more concise and more efficient.
501Of course, there are language design trade-offs to such an approach, notably that providing the two similar features of field and function assertions would impose a burden of choice on programmers writing traits, with field assertions more efficient, but function assertions more general; given this open design question we have deferred a decision on field assertions until we have more experience using \CFA{}.
502If field assertions are included in the language, a natural extension would be to provide a structural inheritance mechanism for every !struct! type that simply turns the list of !struct! fields into a list of field assertions, allowing monomorphic functions over that type to be generalized to polymorphic functions over other similar types with added or reordered fields.
503\CFA{} could also support a packed or otherwise size-optimized representation for generic types based on a similar mechanism --- the layout function would need to be re-written, but nothing in the use of the offset arrays implies that the field offsets need be monotonically increasing.
504
505With respect to the broader \CFA{} polymorphism design, the experimental results in Section~\ref{generic-performance-sec} demonstrate that though the runtime impact of \CFA{}'s dynamic virtual dispatch is low, it is not as low as the static dispatch of \CC{} template inlining.
506However, rather than subject all \CFA{} users to the compile-time costs of ubiquitous template expansion, we are considering more targeted mechanisms for performance-sensitive code.
507Two promising approaches are are an !inline! annotation at polymorphic function call sites to create a template specialization of the function (provided the code is visible) or placing a different !inline! annotation on polymorphic function definitions to instantiate a specialized version of the function for some set of types.
508These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code bloat.
509In general, the \CFA{} team believes that separate compilation works well with loaded hardware caches by producing smaller code, which may offset the benefit of larger inlined code.
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