X-Git-Url: https://git.stderr.nl/gitweb?p=matthijs%2Fmaster-project%2Fdsd-paper.git;a=blobdiff_plain;f=c%CE%BBash.lhs;h=886376648304d8550742b94de4148a53399dcbcd;hp=07a49f494c3d15b4043b4618effce1d65789eaaf;hb=d8b9a02732239603a440bf060bdbe6db0522b981;hpb=4d3702134fe4193bcd4d0bcf88287d2b5bbde476 diff --git "a/c\316\273ash.lhs" "b/c\316\273ash.lhs" index 07a49f4..8863766 100644 --- "a/c\316\273ash.lhs" +++ "b/c\316\273ash.lhs" @@ -342,9 +342,11 @@ % Macro for certain acronyms in small caps. Doesn't work with the % default font, though (it contains no smallcaps it seems). \def\acro#1{{\small{#1}}} +\def\acrotiny#1{{\scriptsize{#1}}} \def\VHDL{\acro{VHDL}} \def\GHC{\acro{GHC}} \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}} +\def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}} % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps % we'll get something more complex later on. @@ -354,9 +356,10 @@ \newenvironment{xlist}[1][\rule{0em}{0em}]{% \begin{list}{}{% \settowidth{\labelwidth}{#1:} - \setlength{\labelsep}{0.5cm} + \setlength{\labelsep}{0.5em} \setlength{\leftmargin}{\labelwidth} \addtolength{\leftmargin}{\labelsep} + \addtolength{\leftmargin}{\parindent} \setlength{\rightmargin}{0pt} \setlength{\listparindent}{\parindent} \setlength{\itemsep}{0 ex plus 0.2ex} @@ -374,6 +377,9 @@ \newcommand{\fref}[1]{\cref{#1}} \newcommand{\Fref}[1]{\Cref{#1}} +\usepackage{epstopdf} + +\epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile} %include polycode.fmt %include clash.fmt @@ -388,8 +394,9 @@ % author names and affiliations % use a multiple column layout for up to three different % affiliations -\author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez} -\IEEEauthorblockA{University of Twente, Department of EEMCS\\ +\author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez} +\IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\ +Department of EEMCS, University of Twente\\ P.O. Box 217, 7500 AE, Enschede, The Netherlands\\ c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}} % \and @@ -441,7 +448,15 @@ c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}} \begin{abstract} %\boldmath -The abstract goes here. +\CLaSH\ is a functional hardware description language that borrows both its +syntax and semantics from the functional programming language Haskell. Circuit +descriptions can be translated to synthesizable VHDL using the prototype +\CLaSH\ compiler. As the circuit descriptions are made in plain Haskell, +simulations can also be compiled by a Haskell compiler. + +The use of polymorphism and higher-order functions allow a circuit designer to +describe more abstract and general specifications than are possible in the +traditional hardware description languages. \end{abstract} % IEEEtran.cls defaults to using nonbold math in the Abstract. % This preserves the distinction between vectors and scalars. However, @@ -467,7 +482,7 @@ The abstract goes here. \section{Introduction} -Hardware description languages has allowed the productivity of hardware +Hardware description languages have allowed the productivity of hardware engineers to keep pace with the development of chip technology. Standard Hardware description languages, like \VHDL~\cite{VHDL2008} and Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a @@ -480,9 +495,9 @@ ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL}, a time which also saw the birth of the currently popular hardware description languages such as \VHDL. The merit of using a functional language to describe -hardware comes from the fact that basic combinatorial circuits are equivalent -to mathematical functions and that functional languages are very good at -describing and composing mathematical functions. +hardware comes from the fact that combinatorial circuits can be directly +modeled as mathematical functions and that functional languages are very good +at describing and composing mathematical functions. In an attempt to decrease the amount of work involved with creating all the required tooling, such as parsers and type-checkers, many functional hardware @@ -492,7 +507,7 @@ means that a developer is given a library of Haskell~\cite{Haskell} functions and types that together form the language primitives of the domain specific language. As a result of how the signals are modeled and abstracted, the functions used to describe a circuit also build a large domain-specific -datatype (hidden from the designer) which can be further processed by an +datatype (hidden from the designer) which can then be processed further by an embedded compiler. This compiler actually runs in the same environment as the description; as a result compile-time and run-time become hard to define, as the embedded compiler is usually compiled by the same Haskell compiler as the @@ -504,47 +519,65 @@ itself for the purpose of describing hardware. By taking this approach, we can capture certain language constructs, such as Haskell's choice elements (if-constructs, case-constructs, pattern matching, etc.), which are not available in the functional hardware description languages that are embedded -in Haskell as a domain specific languages. As far as the authors know, such +in Haskell as a domain specific language. As far as the authors know, such extensive support for choice-elements is new in the domain of functional -hardware description language. As the hardware descriptions are plain Haskell -functions, these descriptions can be compiled for simulation using using the -optimizing Haskell compiler \GHC. +hardware description languages. As the hardware descriptions are plain Haskell +functions, these descriptions can be compiled for simulation using an +optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC)~\cite{ghc}. Where descriptions in a conventional hardware description language have an explicit clock for the purpose state and synchronicity, the clock is implied -in this research. The functions describe the behavior of the hardware between -clock cycles, as such, only synchronous systems can be described. Many -functional hardware description models signals as a stream of all values over -time; state is then modeled as a delay on this stream of values. The approach -taken in this research is to make the current state of a circuit part of the -input of the function and the updated state part of the output. +in this research. A developer describes the behavior of the hardware between +clock cycles. Many functional hardware description model signals as a stream +of all values over time; state is then modeled as a delay on this stream of +values. The approach taken in this research is to make the current state of a +circuit part of the input of the function and the updated state part of the +output. The current abstraction of state and time limits the descriptions to +synchronous hardware, there however is room within the language to eventually +add a different abstraction mechanism that will allow for the modeling of +asynchronous systems. Like the standard hardware description languages, descriptions made in a functional hardware description language must eventually be converted into a -netlist. This research also features a prototype translator called \CLaSH\ -(pronounced: clash), which converts the Haskell code to equivalently behaving -synthesizable \VHDL\ code, ready to be converted to an actual netlist format -by an optimizing \VHDL\ synthesis tool. +netlist. This research also features a prototype translator, which has the +same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} +Language for Synchronous Hardware} (pronounced: clash). This compiler converts +the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to +be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis +tool. + +Besides trivial circuits such as variants of both the FIR filter and the +simple CPU shown in \Cref{sec:usecases}, the \CLaSH\ compiler has also been +shown to work for non-trivial descriptions. \CLaSH\ has been able to +successfully translate the functional description of a streaming reduction +circuit~\cite{reductioncircuit} for floating point numbers. \section{Hardware description in Haskell} \subsection{Function application} The basic syntactic elements of a functional program are functions and function application. These have a single obvious translation to a - netlist: every function becomes a component, every function argument is an - input port and the result value is of a function is an output port. This - output port can have a complex type (such as a tuple), so having just a - single output port does not create a limitation. Each function application - in turn becomes a component instantiation. Here, the result of each - argument expression is assigned to a signal, which is mapped to the - corresponding input port. The output port of the function is also mapped - to a signal, which is used as the result of the application itself. + netlist format: + \begin{inparaenum} + \item every function is translated to a component, + \item every function argument is translated to an input port, + \item the result value of a function is translated to an output port, + and + \item function applications are translated to component instantiations. + \end{inparaenum} + The output port can have a structured type (such as a tuple), so having + just a single output port does not pose any limitation. The arguments of a + function application are assigned to signals, which are then mapped to + the corresponding input ports of the component. The output port of the + function is also mapped to a signal, which is used as the result of the + application itself. Since every top level function generates its own component, the - hierarchy of function calls is reflected in the final netlist aswell, - creating a hierarchical description of the hardware. This separation in - different components makes the resulting \VHDL\ output easier to read and - debug. + hierarchy of function calls is reflected in the final netlist,% aswell, + creating a hierarchical description of the hardware. The separation in + different components makes it easier for a developer to understand and + possibly hand-optimize the resulting \VHDL\ output of the \CLaSH\ + compiler. As an example we can see the netlist of the |mac| function in \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add| @@ -555,12 +588,12 @@ by an optimizing \VHDL\ synthesis tool. \end{code} \begin{figure} - \centerline{\includegraphics{mac}} + \centerline{\includegraphics{mac.svg}} \caption{Combinatorial Multiply-Accumulate} \label{img:mac-comb} \end{figure} - The result of using a complex input type can be seen in + The result of using a structural input type can be seen in \cref{img:mac-comb-nocurry} where the |mac| function now uses a single input tuple for the |a|, |b|, and |c| arguments: @@ -569,7 +602,7 @@ by an optimizing \VHDL\ synthesis tool. \end{code} \begin{figure} - \centerline{\includegraphics{mac-nocurry}} + \centerline{\includegraphics{mac-nocurry.svg}} \caption{Combinatorial Multiply-Accumulate (complex input)} \label{img:mac-comb-nocurry} \end{figure} @@ -577,25 +610,37 @@ by an optimizing \VHDL\ synthesis tool. \subsection{Choice} In Haskell, choice can be achieved by a large set of language constructs, consisting of: \hs{case} constructs, \hs{if-then-else} constructs, - pattern matching, and guards. The easiest of these are the \hs{case} - constructs (and \hs{if} expressions, which can be very directly translated - to \hs{case} expressions). A \hs{case} expression can in turn simply be - translated to a conditional assignment in \VHDL, where the conditions use - equality comparisons against the constructors in the \hs{case} - expressions. We can see two versions of a contrived example, the first - using a \hs{case} construct and the other using a \hs{if-then-else} - constructs, in the code below. The example sums two values when they are - equal or non-equal (depending on the predicate given) and returns 0 - otherwise. + pattern matching, and guards. The most general of these are the \hs{case} + constructs (\hs{if} expressions can be very directly translated to + \hs{case} expressions). A \hs{case} construct is translated to a + multiplexer, where the control value is linked to the selection port and + the output of each case is linked to the corresponding input port on the + multiplexer. + % A \hs{case} expression can in turn simply be translated to a conditional + % assignment in \VHDL, where the conditions use equality comparisons + % against the constructors in the \hs{case} expressions. + We can see two versions of a contrived example below, the first + using a \hs{case} construct and the other using an \hs{if-then-else} + construct, in the code below. The examples sums two values when they are + equal or non-equal (depending on the given predicate, the \hs{pred} + variable) and returns 0 otherwise. The \hs{pred} variable has the + following, user-defined, enumeration datatype: \begin{code} + data Pred = Equiv | NotEquiv + \end{code} + + The naive netlist corresponding to both versions of the example is + depicted in \Cref{img:choice}. + + \begin{code} sumif pred a b = case pred of - Eq -> case a == b of - True -> a + b - False -> 0 - Neq -> case a != b of - True -> a + b - False -> 0 + Equiv -> case a == b of + True -> a + b + False -> 0 + NotEquiv -> case a != b of + True -> a + b + False -> 0 \end{code} \begin{code} @@ -606,35 +651,36 @@ by an optimizing \VHDL\ synthesis tool. if a != b then a + b else 0 \end{code} - Both versions of the example correspond to the same netlist, which is - depicted in \Cref{img:choice}. - \begin{figure} - \centerline{\includegraphics{choice-case}} + \centerline{\includegraphics{choice-case.svg}} \caption{Choice - sumif} \label{img:choice} \end{figure} - A slightly more complex (but very powerful) form of choice is pattern + A user-friendly and also very powerful form of choice is pattern matching. A function can be defined in multiple clauses, where each clause - specifies a pattern. When the arguments match the pattern, the + corresponds to a pattern. When an argument matches a pattern, the corresponding clause will be used. Expressions can also contain guards, - where the expression is only executed if the guard evaluates to true. A - pattern match (with optional guards) can be to a conditional assignments - in \VHDL, where the conditions are an equality test of the argument and - one of the patterns (combined with the guard if was present). A third - version of the earlier example, using both pattern matching and guards, - can be seen below: + where the expression is only executed if the guard evaluates to true, and + continues with the next clause if the guard evaluates to false. Like + \hs{if-then-else} constructs, pattern matching and guards have a + (straightforward) translation to \hs{case} constructs and can as such be + mapped to multiplexers. A third version of the earlier example, using both + pattern matching and guards, can be seen below. The guard is the + expression that follows the vertical bar (\hs{|}) and precedes the + assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to + \hs{true}. + + The version using pattern matching and guards corresponds to the same + naive netlist representation (\Cref{img:choice}) as the earlier two + versions of the example. \begin{code} - sumif Eq a b | a == b = a + b - sumif Neq a b | a != b = a + b - sumif _ _ _ = 0 + sumif Eq a b | a == b = a + b + | otherwise = 0 + sumif Neq a b | a != b = a + b + | otherwise = 0 \end{code} - - The version using pattern matching and guards has the same netlist - representation (\Cref{img:choice}) as the earlier two versions of the - example. % \begin{figure} % \centerline{\includegraphics{choice-ifthenelse}} @@ -643,14 +689,17 @@ by an optimizing \VHDL\ synthesis tool. % \end{figure} \subsection{Types} - Haskell is a strongly-typed language, meaning that the type of a variable - or function is determined at compile-time. Not all of Haskell's typing - constructs have a clear translation to hardware, as such this section will - only deal with the types that do have a clear correspondence to hardware. - The translatable types are divided into two categories: \emph{built-in} - types and \emph{user-defined} types. Built-in types are those types for - which a direct translation is defined within the \CLaSH\ compiler; the - term user-defined types should not require any further elaboration. + Haskell is a statically-typed language, meaning that the type of a + variable or function is determined at compile-time. Not all of Haskell's + typing constructs have a clear translation to hardware, this section will + therefor only deal with the types that do have a clear correspondence + to hardware. The translatable types are divided into two categories: + \emph{built-in} types and \emph{user-defined} types. Built-in types are + those types for which a direct translation is defined within the \CLaSH\ + compiler; the term user-defined types should not require any further + elaboration. The translatable types are also inferable by the compiler, + meaning that a developer does not have to annotate every function with a + type signature. % Translation of two most basic functional concepts has been % discussed: function application and choice. Before looking further @@ -668,14 +717,16 @@ by an optimizing \VHDL\ synthesis tool. % using translation rules that are discussed later on. \subsubsection{Built-in types} + The following types have direct translations defined within the \CLaSH\ + compiler: \begin{xlist} \item[\bf{Bit}] - This is the most basic type available. It can have two values: - \hs{Low} and \hs{High}. + the most basic type available. It can have two values: + \hs{Low} or \hs{High}. % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type. \item[\bf{Bool}] - This is a basic logic type. It can have two values: \hs{True} - and \hs{False}. + this is a basic logic type. It can have two values: \hs{True} + or \hs{False}. % It is translated to \texttt{std\_logic} exactly like the \hs{Bit} % type (where a value of \hs{True} corresponds to a value of % \hs{High}). @@ -683,7 +734,7 @@ by an optimizing \VHDL\ synthesis tool. \hs{if-then-else} construct, which requires a \hs{Bool} value for the condition. \item[\bf{SizedWord}, \bf{SizedInt}] - These are types to represent integers. A \hs{SizedWord} is unsigned, + these are types to represent integers. A \hs{SizedWord} is unsigned, while a \hs{SizedInt} is signed. Both are parametrizable in their size. % , so you can define an unsigned word of 32 bits wide as follows: @@ -699,10 +750,12 @@ by an optimizing \VHDL\ synthesis tool. % types are translated to the \VHDL\ \texttt{unsigned} and % \texttt{signed} respectively. \item[\bf{Vector}] - This is a vector type that can contain elements of any other type and + this is a vector type that can contain elements of any other type and has a fixed length. The \hs{Vector} type constructor takes two type arguments: the length of the vector and the type of the elements - contained in it. + contained in it. The short-hand notation used for the vector type in + the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element + type, and \hs{n} is the length of the vector. % The state type of an 8 element register bank would then for example % be: @@ -716,12 +769,12 @@ by an optimizing \VHDL\ synthesis tool. % (The 32 bit word type as defined above). In other words, the % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size % vector is translated to a \VHDL\ array type. - \item[\bf{RangedWord}] - This is another type to describe integers, but unlike the previous + \item[\bf{Index}] + this is another type to describe integers, but unlike the previous two it has no specific bit-width, but an upper bound. This means that its range is not limited to powers of two, but can be any number. - A \hs{RangedWord} only has an upper bound, its lower bound is - implicitly zero. The main purpose of the \hs{RangedWord} type is to be + An \hs{Index} only has an upper bound, its lower bound is + implicitly zero. The main purpose of the \hs{Index} type is to be used as an index to a \hs{Vector}. % \comment{TODO: Perhaps remove this example?} To define an index for @@ -742,194 +795,149 @@ by an optimizing \VHDL\ synthesis tool. \subsubsection{User-defined types} There are three ways to define new types in Haskell: algebraic data-types with the \hs{data} keyword, type synonyms with the \hs{type} - keyword and datatype renamings with the \hs{newtype} keyword. \GHC\ - offers a few more advanced ways to introduce types (type families, - existential typing, {\small{GADT}}s, etc.) which are not standard - Haskell. These are not currently supported. + keyword and datatype renaming constructs with the \hs{newtype} keyword. + \GHC\ offers a few more advanced ways to introduce types (type families, + existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell. + As it is currently unclear how these advanced type constructs correspond + to hardware, they are for now unsupported by the \CLaSH\ compiler. Only an algebraic datatype declaration actually introduces a - completely new type, for which we provide the \VHDL\ translation - below. Type synonyms and renamings only define new names for - existing types, where synonyms are completely interchangeable and - renamings need explicit conversion. Therefore, these do not need - any particular \VHDL\ translation, a synonym or renamed type will - just use the same representation as the original type. The - distinction between a renaming and a synonym does no longer matter - in hardware and can be disregarded in the generated \VHDL. For algebraic - types, we can make the following distinction: + completely new type. Type synonyms and type renaming only define new + names for existing types, where synonyms are completely interchangeable + and type renaming requires explicit conversions. Therefore, these do not + need any particular translation, a synonym or renamed type will just use + the same representation as the original type. For algebraic types, we can + make the following distinctions: \begin{xlist} \item[\bf{Single constructor}] Algebraic datatypes with a single constructor with one or more fields, are essentially a way to pack a few values together in a - record-like structure. An example of such a type is the following pair - of integers: - + record-like structure. Haskell's built-in tuple types are also defined + as single constructor algebraic types An example of a single + constructor type is the following pair of integers: \begin{code} data IntPair = IntPair Int Int \end{code} - - Haskell's builtin tuple types are also defined as single - constructor algebraic types and are translated according to this - rule by the \CLaSH\ compiler. These types are translated to \VHDL\ - record types, with one field for every field in the constructor. + % These types are translated to \VHDL\ record types, with one field + % for every field in the constructor. \item[\bf{No fields}] Algebraic datatypes with multiple constructors, but without any fields are essentially a way to get an enumeration-like type containing alternatives. Note that Haskell's \hs{Bool} type is also defined as an enumeration type, but we have a fixed translation for - that. These types are translated to \VHDL\ enumerations, with one - value for each constructor. This allows references to these - constructors to be translated to the corresponding enumeration value. + that. An example of such an enum type is the type that represents the + colors in a traffic light: + \begin{code} + data TrafficLight = Red | Orange | Green + \end{code} + % These types are translated to \VHDL\ enumerations, with one + % value for each constructor. This allows references to these + % constructors to be translated to the corresponding enumeration + % value. \item[\bf{Multiple constructors with fields}] Algebraic datatypes with multiple constructors, where at least - one of these constructors has one or more fields are not - currently supported. + one of these constructors has one or more fields are currently not + supported. \end{xlist} - \subsection{Polymorphic functions} - A powerful construct in most functional language is polymorphism. - This means the arguments of a function (and consequentially, values - within the function as well) do not need to have a fixed type. - Haskell supports \emph{parametric polymorphism}, meaning a - function's type can be parameterized with another type. - - As an example of a polymorphic function, consider the following - \hs{append} function's type: - - \comment{TODO: Use vectors instead of lists?} + \subsection{Polymorphism} + A powerful construct in most functional languages is polymorphism, it + allows a function to handle values of different data types in a uniform + way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism}, + meaning functions can be written without mention of any specific type and + can be used transparently with any number of new types. + As an example of a parametric polymorphic function, consider the type of + the following \hs{append} function, which appends an element to a vector: \begin{code} - append :: [a] -> a -> [a] + append :: [a|n] -> a -> [a|n + 1] \end{code} This type is parameterized by \hs{a}, which can contain any type at - all. This means that append can append an element to a list, - regardless of the type of the elements in the list (but the element - added must match the elements in the list, since there is only one - \hs{a}). - - This kind of polymorphism is extremely useful in hardware designs to - make operations work on a vector without knowing exactly what elements - are inside, routing signals without knowing exactly what kinds of - signals these are, or working with a vector without knowing exactly - how long it is. Polymorphism also plays an important role in most - higher order functions, as we will see in the next section. - - The previous example showed unconstrained polymorphism \comment{(TODO: How - is this really called?)}: \hs{a} can have \emph{any} type. - Furthermore,Haskell supports limiting the types of a type parameter to - specific class of types. An example of such a type class is the - \hs{Num} class, which contains all of Haskell's numerical types. - - Now, take the addition operator, which has the following type: - + all. This means that \hs{append} can append an element to a vector, + regardless of the type of the elements in the list (as long as the type of + the value to be added is of the same type as the values in the vector). + This kind of polymorphism is extremely useful in hardware designs to make + operations work on a vector without knowing exactly what elements are + inside, routing signals without knowing exactly what kinds of signals + these are, or working with a vector without knowing exactly how long it + is. Polymorphism also plays an important role in most higher order + functions, as we will see in the next section. + + Another type of polymorphism is \emph{ad-hoc + polymorphism}~\cite{polymorphism}, which refers to polymorphic + functions which can be applied to arguments of different types, but which + behave differently depending on the type of the argument to which they are + applied. In Haskell, ad-hoc polymorphism is achieved through the use of + type classes, where a class definition provides the general interface of a + function, and class instances define the functionality for the specific + types. An example of such a type class is the \hs{Num} class, which + contains all of Haskell's numerical operations. A developer can make use + of this ad-hoc polymorphism by adding a constraint to a parametrically + polymorphic type variable. Such a constraint indicates that the type + variable can only be instantiated to a type whose members supports the + overloaded functions associated with the type class. + + As an example we will take a look at type signature of the function + \hs{sum}, which sums the values in a vector: \begin{code} - (+) :: Num a => a -> a -> a + sum :: Num a => [a|n] -> a \end{code} This type is again parameterized by \hs{a}, but it can only contain - types that are \emph{instances} of the \emph{type class} \hs{Num}. - Our numerical built-in types are also instances of the \hs{Num} + types that are \emph{instances} of the \emph{type class} \hs{Num}, so that + we know that the addition (+) operator is defined for that type. + \CLaSH's built-in numerical types are also instances of the \hs{Num} class, so we can use the addition operator on \hs{SizedWords} as - well as on {SizedInts}. + well as on \hs{SizedInts}. - In \CLaSH, unconstrained polymorphism is completely supported. Any - function defined can have any number of unconstrained type - parameters. The \CLaSH\ compiler will infer the type of every such - argument depending on how the function is applied. There is one - exception to this: The top level function that is translated, can - not have any polymorphic arguments (since it is never applied, so - there is no way to find out the actual types for the type - parameters). + In \CLaSH, parametric polymorphism is completely supported. Any function + defined can have any number of unconstrained type parameters. The \CLaSH\ + compiler will infer the type of every such argument depending on how the + function is applied. There is one exception to this: The top level + function that is translated, can not have any polymorphic arguments (as + they are never applied, so there is no way to find out the actual types + for the type parameters). \CLaSH\ does not support user-defined type classes, but does use some - of the builtin ones for its builtin functions (like \hs{Num} and - \hs{Eq}). + of the built-in type classes for its built-in function, such as: \hs{Num} + for numerical operations, \hs{Eq} for the equality operators, and + \hs{Ord} for the comparison/order operators. - \subsection{Higher order} + \subsection{Higher-order functions \& values} Another powerful abstraction mechanism in functional languages, is - the concept of \emph{higher order functions}, or \emph{functions as + the concept of \emph{higher-order functions}, or \emph{functions as a first class value}. This allows a function to be treated as a value and be passed around, even as the argument of another - function. Let's clarify that with an example: + function. The following example should clarify this concept: \begin{code} - notList xs = map not xs - \end{code} - - This defines a function \hs{notList}, with a single list of booleans - \hs{xs} as an argument, which simply negates all of the booleans in - the list. To do this, it uses the function \hs{map}, which takes - \emph{another function} as its first argument and applies that other - function to each element in the list, returning again a list of the - results. - - As you can see, the \hs{map} function is a higher order function, - since it takes another function as an argument. Also note that - \hs{map} is again a polymorphic function: It does not pose any - constraints on the type of elements in the list passed, other than - that it must be the same as the type of the argument the passed - function accepts. The type of elements in the resulting list is of - course equal to the return type of the function passed (which need - not be the same as the type of elements in the input list). Both of - these can be readily seen from the type of \hs{map}: - - \begin{code} - map :: (a -> b) -> [a] -> [b] + negVector xs = map not xs \end{code} - - As an example from a common hardware design, let's look at the - equation of a FIR filter. - - \begin{equation} - y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i } - \end{equation} - A FIR filter multiplies fixed constants ($h$) with the current and - a few previous input samples ($x$). Each of these multiplications - are summed, to produce the result at time $t$. - - This is easily and directly implemented using higher order - functions. Consider that the vector \hs{hs} contains the FIR - coefficients and the vector \hs{xs} contains the current input sample - in front and older samples behind. How \hs{xs} gets its value will be - show in the next section about state. + The code above defines a function \hs{negVector}, which takes a vector of + booleans, and returns a vector where all the values are negated. It + achieves this by calling the \hs{map} function, and passing it + \emph{another function}, boolean negation, and the vector of booleans, + \hs{xs}. The \hs{map} function applies the negation function to all the + elements in the vector. + + The \hs{map} function is called a higher-order function, since it takes + another function as an argument. Also note that \hs{map} is again a + parametric polymorphic function: It does not pose any constraints on the + type of the vector elements, other than that it must be the same type as + the input type of the function passed to \hs{map}. The element type of the + resulting vector is equal to the return type of the function passed, which + need not necessarily be the same as the element type of the input vector. + All of these characteristics can readily be inferred from the type + signature belonging to \hs{map}: \begin{code} - fir ... = foldl1 (+) (zipwith (*) xs hs) + map :: (a -> b) -> [a|n] -> [b|n] \end{code} - Here, the \hs{zipwith} function is very similar to the \hs{map} - function: It takes a function two lists and then applies the - function to each of the elements of the two lists pairwise - (\emph{e.g.}, \hs{zipwith (+) [1, 2] [3, 4]} becomes - \hs{[1 + 3, 2 + 4]}. - - The \hs{foldl1} function takes a function and a single list and applies the - function to the first two elements of the list. It then applies to - function to the result of the first application and the next element - from the list. This continues until the end of the list is reached. - The result of the \hs{foldl1} function is the result of the last - application. - - As you can see, the \hs{zipwith (*)} function is just pairwise - multiplication and the \hs{foldl1 (+)} function is just summation. - - To make the correspondence between the code and the equation even - more obvious, we turn the list of input samples in the equation - around. So, instead of having the the input sample received at time - $t$ in $x_t$, $x_0$ now always stores the current sample, and $x_i$ - stores the $ith$ previous sample. This changes the equation to the - following (Note that this is completely equivalent to the original - equation, just with a different definition of $x$ that better suits - the \hs{x} from the code): - - \begin{equation} - y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i } - \end{equation} - - So far, only functions have been used as higher order values. In + So far, only functions have been used as higher-order values. In Haskell, there are two more ways to obtain a function-typed value: partial application and lambda abstraction. Partial application means that a function that takes multiple arguments can be applied @@ -943,17 +951,15 @@ by an optimizing \VHDL\ synthesis tool. Here, the expression \hs{(+) 1} is the partial application of the plus operator to the value \hs{1}, which is again a function that - adds one to its argument. - - A labmda expression allows one to introduce an anonymous function - in any expression. Consider the following expression, which again - adds one to every element of a list: + adds one to its argument. A lambda expression allows one to introduce an + anonymous function in any expression. Consider the following expression, + which again adds one to every element of a vector: \begin{code} map (\x -> x + 1) xs \end{code} - Finally, higher order arguments are not limited to just builtin + Finally, higher order arguments are not limited to just built-in functions, but any function defined in \CLaSH\ can have function arguments. This allows the hardware designer to use a powerful abstraction mechanism in his designs and have an optimal amount of @@ -977,33 +983,168 @@ by an optimizing \VHDL\ synthesis tool. \item when the function is called, it should not have observable side-effects. \end{inparaenum} - This purity property is important for functional languages, since it - enables all kinds of mathematical reasoning that could not be guaranteed - correct for impure functions. Pure functions are as such a perfect match - for a combinatorial circuit, where the output solely depends on the - inputs. When a circuit has state however, it can no longer be simply - described by a pure function. Simply removing the purity property is not a - valid option, as the language would then lose many of it mathematical - properties. In an effort to include the concept of state in pure + % This purity property is important for functional languages, since it + % enables all kinds of mathematical reasoning that could not be guaranteed + % correct for impure functions. + Pure functions are as such a perfect match or a combinatorial circuit, + where the output solely depends on the inputs. When a circuit has state + however, it can no longer be simply described by a pure function. + % Simply removing the purity property is not a valid option, as the + % language would then lose many of it mathematical properties. + In an effort to include the concept of state in pure functions, the current value of the state is made an argument of the - function; the updated state becomes part of the result. + function; the updated state becomes part of the result. In this sense the + descriptions made in \CLaSH are the describing the combinatorial parts of + a mealy machine. + + A simple example is adding an accumulator register to the earlier + multiply-accumulate circuit, of which the resulting netlist can be seen in + \Cref{img:mac-state}: - A simple example is the description of an accumulator circuit: \begin{code} - acc :: Word -> State Word -> (State Word, Word) - acc inp (State s) = (State s', outp) + macS (State c) a b = (State c', outp) where - outp = s + inp - s' = outp + outp = mac a b c + c' = outp \end{code} - This approach makes the state of a function very explicit: which variables - are part of the state is completely determined by the type signature. This - approach to state is well suited to be used in combination with the - existing code and language features, such as all the choice constructs, as - state values are just normal values. + + \begin{figure} + \centerline{\includegraphics{mac-state.svg}} + \caption{Stateful Multiply-Accumulate} + \label{img:mac-state} + \end{figure} + + The \hs{State} keyword indicates which arguments are part of the current + state, and what part of the output is part of the updated state. This + aspect will also reflected in the type signature of the function. + Abstracting the state of a circuit in this way makes it very explicit: + which variables are part of the state is completely determined by the + type signature. This approach to state is well suited to be used in + combination with the existing code and language features, such as all the + choice constructs, as state values are just normal values. We can simulate + stateful descriptions using the recursive \hs{run} function: + + \begin{code} + run f s (i:inps) = o : (run f s' inps) + where + (s', o) = f s i + \end{code} + + The \hs{run} function maps a list of inputs over the function that a + developer wants to simulate, passing the state to each new iteration. Each + value in the input list corresponds to exactly one cycle of the (implicit) + clock. The result of the simulation is a list of outputs for every clock + cycle. As both the \hs{run} function and the hardware description are + plain Haskell, the complete simulation can be compiled by an optimizing + Haskell compiler. + \section{\CLaSH\ prototype} -foo\par bar +The \CLaSH\ language as presented above can be translated to \VHDL\ using +the prototype \CLaSH\ compiler. This compiler allows experimentation with +the \CLaSH\ language and allows for running \CLaSH\ designs on actual FPGA +hardware. + +\begin{figure} +\centerline{\includegraphics{compilerpipeline.svg}} +\caption{\CLaSHtiny\ compiler pipeline} +\label{img:compilerpipeline} +\end{figure} + +The prototype heavily uses \GHC, the Glasgow Haskell Compiler. +\Cref{img:compilerpipeline} shows the \CLaSH\ compiler pipeline. As you can +see, the front-end is completely reused from \GHC, which allows the \CLaSH\ +prototype to support most of the Haskell Language. The \GHC\ front-end +produces the program in the \emph{Core} format, which is a very small, +functional, typed language which is relatively easy to process. + +The second step in the compilation process is \emph{normalization}. This +step runs a number of \emph{meaning preserving} transformations on the +Core program, to bring it into a \emph{normal form}. This normal form +has a number of restrictions that make the program similar to hardware. +In particular, a program in normal form no longer has any polymorphism +or higher order functions. + +The final step is a simple translation to \VHDL. + +\section{Use cases} +\label{sec:usecases} +As an example of a common hardware design where the use of higher-order +functions leads to a very natural description is a FIR filter, which is +basically the dot-product of two vectors: + +\begin{equation} +y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i } +\end{equation} + +A FIR filter multiplies fixed constants ($h$) with the current +and a few previous input samples ($x$). Each of these multiplications +are summed, to produce the result at time $t$. The equation of a FIR +filter is indeed equivalent to the equation of the dot-product, which is +shown below: + +\begin{equation} +\mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i } +\end{equation} + +We can easily and directly implement the equation for the dot-product +using higher-order functions: + +\begin{code} +xs *+* ys = foldl1 (+) (zipWith (*) xs hs) +\end{code} + +The \hs{zipWith} function is very similar to the \hs{map} function seen +earlier: It takes a function, two vectors, and then applies the function to +each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*) +[1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}). + +The \hs{foldl1} function takes a function, a single vector, and applies +the function to the first two elements of the vector. It then applies the +function to the result of the first application and the next element from +the vector. This continues until the end of the vector is reached. The +result of the \hs{foldl1} function is the result of the last application. +As you can see, the \hs{zipWith (*)} function is just pairwise +multiplication and the \hs{foldl1 (+)} function is just summation. + +Returning to the actual FIR filter, we will slightly change the +equation belong to it, so as to make the translation to code more obvious. +What we will do is change the definition of the vector of input samples. +So, instead of having the input sample received at time +$t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$ +stores the $ith$ previous sample. This changes the equation to the +following (Note that this is completely equivalent to the original +equation, just with a different definition of $x$ that will better suit +the transformation to code): + +\begin{equation} +y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i } +\end{equation} + +Consider that the vector \hs{hs} contains the FIR coefficients and the +vector \hs{xs} contains the current input sample in front and older +samples behind. The function that shifts the input samples is shown below: + +\begin{code} +x >> xs = x +> tail xs +\end{code} + +Where the \hs{tail} function returns all but the first element of a +vector, and the concatenate operator ($\succ$) adds a new element to the +left of a vector. The complete definition of the FIR filter then becomes: + +\begin{code} +fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs) +\end{code} + +The resulting netlist of a 4-taps FIR filter based on the above definition +is depicted in \Cref{img:4tapfir}. + +\begin{figure} +\centerline{\includegraphics{4tapfir.svg}} +\caption{4-taps \acrotiny{FIR} Filter} +\label{img:4tapfir} +\end{figure} \section{Related work} Many functional hardware description languages have been developed over the @@ -1011,22 +1152,36 @@ years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an extension of Backus' \acro{FP} language to synchronous streams, designed particularly for describing and reasoning about regular circuits. The Ruby~\cite{Ruby} language uses relations, instead of functions, to describe -circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a -hardware modeling language based on the strict functional language -\acro{ML}, and has support for polymorphic types and higher-order functions. -Published work suggests that there is no direct simulation support for -\acro{HML}, and that the translation to \VHDL\ is only partial. +circuits, and has a particular focus on layout. + +\acro{HML}~\cite{HML2} is a hardware modeling language based on the strict +functional language \acro{ML}, and has support for polymorphic types and +higher-order functions. Published work suggests that there is no direct +simulation support for \acro{HML}, but that a description in \acro{HML} has to +be translated to \VHDL\ and that the translated description can than be +simulated in a \VHDL\ simulator. Also not all of the mentioned language +features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler +on the other hand can correctly translate all of the language constructs +mentioned in this paper to a netlist format. Like this work, many functional hardware description languages have some sort of foundation in the functional programming language Haskell. Hawk~\cite{Hawk1} uses Haskell to describe system-level executable specifications used to model the behavior of superscalar microprocessors. Hawk specifications can be simulated, but there seems to be no support for -automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell -to specify abstract system models, which can (manually) be transformed into an -implementation model using semantic preserving transformations. ForSyDe has -several simulation and synthesis backends, though synthesis is restricted to -the synchronous subset of the ForSyDe language. +automated circuit synthesis. + +The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system +models, which can (manually) be transformed into an implementation model using +semantic preserving transformations. A designer can model systems using +heterogeneous models of computation, which include continuous time, +synchronous and untimed models of computation. Using so-called domain +interfaces a designer can simulate electronic systems which have both analog +as digital parts. ForSyDe has several backends including simulation and +automated synthesis, though automated synthesis is restricted to the +synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no +support for the automated synthesis of descriptions that contain polymorphism +or higher-order functions. Lava~\cite{Lava} is a hardware description language that focuses on the structural representation of hardware. Besides support for simulation and @@ -1035,20 +1190,19 @@ tools for formal verification. Lava descriptions are actually circuit generators when viewed from a synthesis viewpoint, in that the language elements of Haskell, such as choice, can be used to guide the circuit generation. If a developer wants to insert a choice element inside an actual -circuit he will have to specify this explicitly as a component. In this -respect \CLaSH\ differs from Lava, in that all the choice elements, such as -case-statements and pattern matching, are synthesized to choice elements in the -eventual circuit. As such, richer control structures can both be specified and -synthesized in \CLaSH\ compared to any of the languages mentioned in this -section. +circuit he will have to explicitly instantiate a multiplexer-like component. + +In this respect \CLaSH\ differs from Lava, in that all the choice elements, +such as case-statements and pattern matching, are synthesized to choice +elements in the eventual circuit. As such, richer control structures can both +be specified and synthesized in \CLaSH\ compared to any of the languages +mentioned in this section. The merits of polymorphic typing, combined with higher-order functions, are now also recognized in the `main-stream' hardware description languages, -exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has -support to specify types as generics, thus allowing a developer to describe +exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to types, allowing a developer to describe polymorphic components. Note that those types still require an explicit -generic map, whereas type-inference and type-specialization are implicit in -\CLaSH. +generic map, whereas types can be automatically inferred in \CLaSH. % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}. % @@ -1176,7 +1330,7 @@ The authors would like to thank... % http://www.michaelshell.org/tex/ieeetran/bibtex/ \bibliographystyle{IEEEtran} % argument is your BibTeX string definitions and bibliography database(s) -\bibliography{IEEEabrv,clash.bib} +\bibliography{clash} % % manually copy in the resultant .bbl file % set second argument of \begin to the number of references