% 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{%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}
-\thanks{Supported through the FP7 project: S(o)OS (248465)}
+% \author{\IEEEauthorblockN{Christiaan Baaij, Matthijs Kooijman, Jan Kuper, Arjan Boeijink, Marco 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}
+% \thanks{Supported through the FP7 project: S(o)OS (248465)}
+% }
+
+\author{\IEEEauthorblockN{Blind Review}%, Bert Molenkamp, Sabih H. Gerez}
+\IEEEauthorblockA{
+\\
+\\
+\\
+\\
}
+\thanks{Supported through: ``Hidden for blind review''}
+}
+
% \and
% \IEEEauthorblockN{Homer Simpson}
% \IEEEauthorblockA{Twentieth Century Fox\\
\begin{abstract}
%\boldmath
-\CLaSH\ is a functional hardware description language that borrows both its
-syntax and semantics from the functional programming language Haskell.
-Polymorphism and higher-order functions provide a level of abstraction and
-generality that allow a circuit designer to describe circuits in a more
-natural way than possible in a traditional hardware description language.
+\CLaSH\ is a functional hardware description language that borrows both its syntax and semantics from the functional programming language Haskell. Polymorphism and higher-order functions provide a level of abstraction and generality that allow a circuit designer to describe circuits in a more natural way than possible with the language elements found in the traditional hardware description languages.
-Circuit descriptions can be translated to synthesizable VHDL using the
-prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
-test input are also valid Haskell, complete simulations can be done by a
-Haskell compiler allowing high-speed simulation and analysis.
+Circuit descriptions can be translated to synthesizable \VHDL\ using the prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and test input are also valid Haskell, complete simulations can be done by a Haskell compiler or interpreter, allowing high-speed simulation and analysis.
% \CLaSH\ supports stateful descriptions by explicitly making the current
% state an argument of the function, and the updated state part of the result.
properties such as timing behavior, they are generally cumbersome in
expressing the higher-level abstractions needed for today's large and complex
circuit designs. In an attempt to raise the abstraction level of the
-descriptions, a great number of approaches based on functional languages has
-been proposed \cite{Cardelli1981,muFP,DAISY,T-Ruby,HML2,Hydra,Hawk1,Lava,
+descriptions, a great number of approaches based on functional languages have
+been proposed \cite{Cardelli1981,muFP,DAISY,FHDL,T-Ruby,HML2,Hydra,Hawk1,Lava,
Wired,ForSyDe1,reFLect}. The idea of using functional languages for hardware
-descriptions started in the early 1980s \cite{Cardelli1981,muFP,DAISY}, a
+descriptions started in the early 1980s \cite{Cardelli1981,muFP,DAISY,FHDL}, a
time which also saw the birth of the currently popular \acrop{HDL}, such as
\VHDL. Functional languages are especially well suited to describe hardware
because combinational circuits can be directly modeled as mathematical
functions and functional languages are very good at describing and composing
these functions.
-In an attempt to ease the prototyping process of the language, such as
-creating all the required tooling like parsers and type-checkers, many
-functional \acrop{HDL} \cite{Hydra,Hawk1,Lava,Wired} are embedded as a domain
-specific language (\acro{DSL}) within the functional language Haskell
-\cite{Haskell}. This means that a developer is given a library of Haskell
-functions and types that together form the language primitives of the
-\acro{DSL}. The primitive functions used to describe a circuit do not actually
-process any signals, they instead compose a large domain-specific graph
-(which is usually hidden from the designer). This graph is then further
+In an attempt to reduce the effort involved with prototyping a new
+language, such as creating all the required tooling like parsers and
+type-checkers, many functional \acrop{HDL} \cite{Hydra,Hawk1,Lava,Wired} are
+embedded as a domain specific language (\acro{DSL}) within the functional
+language Haskell \cite{Haskell}. This means that a developer is given a
+library of Haskell functions and types that together form the language
+primitives of the \acro{DSL}. The primitive functions used to describe a
+circuit do not actually process any signals, they instead compose a large
+graph (which is usually hidden from the designer). This graph is then further
processed by an embedded circuit compiler which can perform e.g. simulation or
synthesis. As Haskell's choice elements (\hs{case}-expressions,
-pattern-matching, etc.) are evaluated at the time the domain-specific graph is
-being build, they are no longer visible to the embedded compiler that
-processes the datatype. Consequently, it is impossible to capture Haskell's
-choice elements within a circuit description when taking the embedded language
-approach. This does not mean that circuits specified in an embedded language
-can not contain choice, just that choice elements only exists as functions,
-e.g. a multiplexer function, and not as syntactic elements of the language
-itself.
-
-The approach taken in this research is to use (a subset of) the Haskell
-language \emph{itself} for the purpose of describing hardware. By taking this
-approach, this research \emph{can} capture certain language constructs, like
-all of Haskell's choice elements, within circuit descriptions. The more
-advanced features of Haskell, such as polymorphic typing and higher-order
-functions, are also supported.
+pattern-matching, etc.) are evaluated at the time the graph is being build,
+they are no longer visible to the embedded compiler that processes the graph.
+Consequently, it is impossible to capture Haskell's choice elements within a
+circuit description when taking the embedded language approach. This does not
+mean that circuits specified in an embedded language can not contain choice,
+just that choice elements only exist as functions, e.g. a multiplexer
+function, and not as syntactic elements of the language itself.
+
+This research uses (a subset of) the Haskell language \emph{itself} for the
+purpose of describing hardware. As a result, certain language constructs, like
+all of Haskell's choice elements, \emph{can} now be captured within circuit
+descriptions. Advanced features of Haskell, such as polymorphic typing and
+higher-order functions, are also supported.
% supporting polymorphism, higher-order functions and such an extensive array
% of choice-elements, combined with a very concise way of specifying circuits
Where descriptions in a conventional \acro{HDL} have an explicit clock for the
purposes state and synchronicity, the clock is implicit for the descriptions
and research presented in this paper. A circuit designer describes the
-behavior of the hardware between clock cycles. Many functional \acrop{HDL}
-model signals as a stream of all values over time; state is then modeled as a
-delay on this stream of values. Descriptions presented in this research make
-the current state an additional input and the updated state a part of their
-output. This abstraction of state and time limits the descriptions to
-synchronous hardware, there is however room within the language to eventually
-add a different abstraction mechanism that will allow for the modeling of
-asynchronous systems.
-
-Likewise as with the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL} must eventually be converted into a netlist. This research also features a prototype compiler, which has the same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware, where \acrotiny{CAES} is the acronyom of our chair.} (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.
+behavior of the hardware between clock cycles, as a transition from the
+current state to the next. Many functional \acrop{HDL} model signals as a
+stream of values over time; state is then modeled as a delay on this stream of
+values. Descriptions presented in this research make the current state an
+additional input and the updated state a part of their output. This
+abstraction of state and time limits the descriptions to synchronous hardware.
+However, work is in progress to add an abstraction mechanism that allows the
+modeling of asynchronous and multi-clock systems.
+
+Likewise as with the traditional \acrop{HDL}, descriptions made in a
+functional \acro{HDL} must eventually be converted into a netlist. This
+research also features a prototype compiler, which has the same name as the
+language: \CLaSH\footnote{\CLaSHtiny:
+% \acrotiny{CAES} Language for Synchronous Hardware.
+``Hidden for blind review'' 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.
To the best knowledge of the authors, \CLaSH\ is the only (functional)
\acro{HDL} that allows circuit specification to be written in a very concise
way and at the same time support such advanced features as polymorphic typing,
user-defined higher-order functions and pattern matching.
+\newpage
+\noindent The next section will describe the language elements of \CLaSH, and
+\Cref{sec:compiler} gives a high-level overview of the \CLaSH\ compiler.
+\Cref{sec:usecases} discusses two use-cases, a \acro{FIR} filter, and a
+higher-order \acro{CPU} design. The related work section
+(\Cref{sec:relatedwork}) is placed towards the end, as the features of \CLaSH\
+should be presented before comparing \CLaSH\ to existing (functional)
+\acrop{HDL}. Conclusions are presented in \Cref{sec:conclusion}, and future
+work is discussed in \Cref{sec:futurework}.
+
\section{Hardware description in Haskell}
This section describes the basic language elements of \CLaSH\ and the support
of these elements within the \CLaSH\ compiler. In various subsections, the
and
\item function applications are translated to component instantiations.
\end{inparaenum}
- The result value can have a composite type (such as a tuple), so having
- just a single result value does not pose any limitation. The actual
- 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. %, creating a hierarchical description of the hardware.
+ The result value can have a composite type (such as a tuple), so the fact
+ that a function has just a single result value does not pose any
+ limitation. The actual 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
+ function generates its own component, the hierarchy of function calls is
+ reflected in the final netlist.
+ %, 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.
The short example below (\ref{code:mac}) gives a demonstration of
- the conciseness that can be achieved with \CLaSH\ when compared with
+ the conciseness that can be achieved with \CLaSH\ when compared to
other (more traditional) \acrop{HDL}. The example is a combinational
multiply-accumulate circuit that works for \emph{any} word length (this
type of polymorphism will be further elaborated in
\end{figure}
The use of a composite result value is demonstrated in the next example
- (\ref{code:mac-composite}), where the multiply-accumulate circuit not only
- returns the accumulation result, but also the intermediate multiplication
+ (\ref{code:mac-composite}), where the multiply-accumulate circuit returns
+ not only the accumulation result, but also the intermediate multiplication
result (see \Cref{img:mac-comb-composite}, where the double arrow suggests
the composite output).
\vspace{-1.5em}
\begin{figure}
- \vspace{1em}
\centerline{\includegraphics{mac-nocurry.svg}}
\caption{Combinational Multiply-Accumulate (composite output)}
\label{img:mac-comb-composite}
\centerline{\includegraphics{counter.svg}}
\caption{Counter netlist}
\label{img:counter}
- \vspace{-2em}
+ \vspace{-1.5em}
\end{figure}
- A user-friendly and also very powerful form of choice that is not found in
- the traditional hardware description languages is pattern matching. A
- function can be defined in multiple clauses, where each clause 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, and continues with the next
- clause if the guard evaluates to false. Like \hs{if-then-else}
- expressions, pattern matching and guards have a (straightforward)
- translation to \hs{case} expressions and can as such be mapped to
- multiplexers. A second version (\ref{code:counter2}) of the earlier
- example, now 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}.
+ A \emph{user-friendly} and also powerful form of choice that is not found
+ in the traditional \acrop{HDL} is pattern matching. A function can be
+ defined in multiple clauses, where each clause 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, and continues with the next clause if the
+ guard evaluates to false. Like \hs{if-then-else} expressions, pattern
+ matching and guards have a (straightforward) translation to \hs{case}
+ expressions and can as such be mapped to multiplexers. A second version
+ (\ref{code:counter2}) of the earlier example, now 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 second version corresponds to the same naive netlist representation
(\Cref{img:counter}) as the earlier example.
\subsection{Types}
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 therefor only deals with the types that do have a clear
+ Haskell's typing constructs have a clear translation to hardware,
+ therefore this section only deals 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 fixed translation is defined within the
\CLaSH\ compiler. The \CLaSH\ compiler has generic translation rules to
translate the user-defined types, which are described later on.
- The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
- meaning that a developer does not have to annotate every function with a
- type signature. Given that the top-level entity of a circuit design is
- annotated with specific types, the \CLaSH\ compiler can specialize
- polymorphic functions to functions with specific types.
+ Type annotations (entities in \VHDL) are optional, since the \CLaSH\
+ compiler can derive them when the top-level function \emph{is} annotated
+ with its type.
% Translation of two most basic functional concepts has been
% discussed: function application and choice. Before looking further
datatypes with a single constructor with one or more fields allow
values to be packed together in a record-like structure. Haskell's
built-in tuple types are also defined as single constructor algebraic
- types (using a bit of syntactic sugar). An example of a single
- constructor type with multiple fields is the following pair of
- integers:
+ types (using some syntactic sugar). An example of a single constructor
+ type with multiple fields is the following pair of integers:
\begin{code}
data IntPair = IntPair Int Int
\end{code}
% These types are translated to \VHDL\ record types, with one field
% for every field in the constructor.
\item[\bf{Multiple constructors, No fields}]
- datatypes with multiple constructors, but without any
- fields are essentially enumeration types.
+ datatypes with multiple constructors, but without any fields are
+ enumeration types.
% Note that Haskell's \hs{Bool} type is also defined as an enumeration
% type, but that there is a fixed translation for that type within the
% \CLaSH\ compiler.
A powerful feature of some programming languages is polymorphism, it
allows a function to handle values of different data types in a uniform
way. Haskell supports \emph{parametric polymorphism}, meaning that
- functions can be written without mentioning specific types, and they can
- be used for arbitrary types.
+ functions can be written without mentioning specific types, and that those
+ functions can be used for arbitrary types.
As an example of a parametric polymorphic function, consider the type of
- the following \hs{first} function, which returns the first element of a
+ the \hs{first} function, which returns the first element of a
tuple:\footnote{The \hs{::} operator is used to annotate a function
with its type.}
\end{code}
This type is parameterized in \hs{a} and \hs{b}, which can both
- represent any type at all, as long as that type is supported by the
- \CLaSH\ compiler. This means that \hs{first} works for any tuple,
- regardless of what elements it contains. This kind of polymorphism is
- extremely useful in hardware designs, for example when routing signals
- without knowing their exact type, or specifying vector operations that
- work on vectors of any length and element type. Polymorphism also plays an
- important role in most higher order functions, as will be shown in the
- next section.
+ represent any type that is supported by the \CLaSH\ compiler. This means
+ that \hs{first} works for any tuple, regardless of what elements it
+ contains. This kind of polymorphism is extremely useful in hardware
+ designs, for example when routing signals without knowing their exact
+ type, or specifying vector operations that work on vectors of any length
+ and element type. Polymorphism also plays an important role in most higher
+ order functions, as will be shown in the next section.
% Another type of polymorphism is \emph{ad-hoc
% polymorphism}~\cite{polymorphism}, which refers to polymorphic
% associated with the type class.
Another type of polymorphism is \emph{ad-hoc polymorphism}, which refers
- to function that can be applied to arguments of a limited set to types.
+ to functions that can be applied to arguments of a limited set to types.
Furthermore, how such functions work may depend on the type of their
- arguments. For example, addition only works for numeric types, and it
- works differently for e.g. integers and complex numbers.
+ arguments. For instance, multiplication only works for numeric types, and
+ it works differently for e.g. integers and complex numbers.
In Haskell, ad-hoc polymorphism is achieved through the use of \emph{type
classes}, where a class definition provides the general interface of a
By prefixing a type signature with class constraints, the constrained type
parameters are forced to belong to that type class. For example, the
arguments of the \hs{add} function must belong to the \hs{Num} type class
- because the \hs{add} function adds them with the (+) operator:
+ because the \hs{add} function adds them with the (\hs{+}) operator:
+ \hspace{-1.7em}
+ \begin{minipage}{0.93\linewidth}
\begin{code}
add :: Num a => a -> a -> a
add a b = a + b
\end{code}
+ \end{minipage}
+ \begin{minipage}{0.07\linewidth}
+ \begin{example}
+ \label{code:add}
+ \end{example}
+ \end{minipage}
% An example of a type signature that includes such a constraint if the
% signature of the \hs{sum} function, which sums the values in a vector:
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 be inferred from the type
- signature belonging to \hs{map}:
+ signature of \hs{map}:
\begin{code}
map :: (a -> b) -> [a|n] -> [b|n]
\end{example}
\end{minipage}
- Finally, not only built-in functions can have higher order arguments (such
+ Finally, not only built-in functions can have higher-order arguments (such
as the \hs{map} function), but any function defined in \CLaSH\ may have
functions as arguments. This allows the circuit designer to apply a
large amount of code reuse. The only exception is again the top-level
\end{example}
\end{minipage}
- The the \hs{crossbar} function selects those values from \hs{inputs} that
+ The \hs{crossbar} function selects those values from \hs{inputs} that
are indicated by the indexes in the vector \hs{selects}. The crossbar is
polymorphic in the width of the input (defined by the length of
\hs{inputs}), the width of the output (defined by the length of
\subsection{State}
In a stateful design, the outputs depend on the history of the inputs, or
the state. State is usually stored in registers, which retain their value
- during a clock cycle. As \CLaSH\ has to be able to describe more than
- plain combinational designs, there is a need for an abstraction mechanism
- for state.
+ during a clock cycle.
+ % As \CLaSH\ has to be able to describe more than plain combinational
+ % designs, there is a need for an abstraction mechanism for state.
An important property in Haskell, and in many other functional languages,
is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
% 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 combinational circuits,
- where the output solely depends on the inputs. When a circuit has state
- however, it can no longer be described by a pure function.
+ Pure functions are a perfect match for combinational circuits, where the
+ output solely depends on the inputs. When a circuit has state however, it
+ can no longer be 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.
\CLaSH\ deals with the concept of state by making the current state an
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\begin{code}
- macS (State c) a b = (State c', c')
+ macS (State c) (a, b) = (State c', c')
where
c' = mac a b c
\end{code}
first input value, \hs{i}. The result is the first output value, \hs{o},
and the updated state \hs{s'}. The next iteration of the \hs{run} function
is then called with the updated state, \hs{s'}, and the rest of the
- inputs, \hs{inps}. For the time being, and in the context of this paper,
- it is assumed that there is one input per clock cycle. Note that the order
- of \hs{s',o,s,i} in the where clause of the \hs{run} functions corresponds
- with the order of the input, output and state of the \hs{macS} function
- described earlier. Thus, in Haskell the expression \hs{run macS 0 inputs}
- simulates \hs{macS} on \hs{inputs} starting with the value \hs{0}
-
+ inputs, \hs{inps}. In the context of this paper, it is assumed that there
+ is one input per clock cycle. Note that the order of \hs{s',o,s,i} in the
+ \hs{where} clause of the \hs{run} functions corresponds with the order of
+ the input, output and state of the \hs{macS} function
+ (\ref{code:macstate}). Thus, the expression below (\ref{code:runmacs})
+ simulates \hs{macS} on \hs{inputpairs} starting with the value \hs{0}:
+
+ \hspace{-1.7em}
+ \begin{minipage}{0.93\linewidth}
+ \begin{code}
+ run macS 0 inputpairs
+ \end{code}
+ \end{minipage}
+ \begin{minipage}{0.07\linewidth}
+ \begin{example}
+ \label{code:runmacs}
+ \end{example}
+ \end{minipage}
+
\begin{figure}
\centerline{\includegraphics{mac-state.svg}}
\caption{Stateful Multiply-Accumulate}
\end{figure}
The complete simulation can be compiled to an executable binary by a
- Haskell compiler, or executed in an Haskell interpreter. Both
+ Haskell compiler, or executed in a Haskell interpreter. Both
simulation paths require less effort from a circuit designer than first
translating the description to \VHDL\ and then running a \VHDL\
simulation; it is also very likely that both simulation paths are much
faster.
\section{The \CLaSH\ compiler}
-An important aspect in this research is the creation of the prototype
-compiler, which allows us to translate descriptions made in the \CLaSH\
+\label{sec:compiler}
+The prototype \CLaSH\ compiler translates descriptions made in the \CLaSH\
language as described in the previous section to synthesizable \VHDL.
% , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
-The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
+The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open source Haskell
compiler that also provides a high level \acro{API} to most of its internals.
-The availability of this high-level \acro{API} obviated the need to design
-many of the tedious parts of the prototype compiler, such as the parser,
-semantics checker, and especially the type-checker. These parts together form
-the front-end of the prototype compiler pipeline, as seen in
+Furthermore, it provides several parts of the prototype compiler for free,
+such as the parser, the semantics checker, and the type checker. These parts
+together form the front-end of the prototype compiler pipeline, as seen in
\Cref{img:compilerpipeline}.
\begin{figure}
process compared to the larger Haskell language. A description in \emph{Core}
can still contain elements which have no direct translation to hardware, such
as polymorphic types and function-valued arguments. Such a description needs
-to be transformed to a \emph{normal form}, which only contains elements that
-have a direct translation. The second stage of the compiler, the
-\emph{normalization} phase, exhaustively applies a set of
-\emph{meaning-preserving} transformations on the \emph{Core} description until
-this description is in a \emph{normal form}. This set of transformations
-includes transformations typically found in reduction systems and lambda
-calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
-$\eta$-expansion. It also includes self-defined transformations that are
-responsible for the reduction of higher-order functions to `regular'
+to be transformed to a \emph{normal form}, which corresponds directly to
+hardware. The second stage of the compiler, the \emph{normalization} phase,
+exhaustively applies a set of \emph{meaning-preserving} transformations on the
+\emph{Core} description until this description is in a \emph{normal form}.
+This set of transformations includes transformations typically found in
+reduction systems and lambda calculus~\cite{lambdacalculus}, such as
+$\beta$-reduction and $\eta$-expansion. It also includes transformations that
+are responsible for the specialization of higher-order functions to `regular'
first-order functions, and specializing polymorphic types to concrete types.
The final step in the compiler pipeline is the translation to a \VHDL\
normalized description and a set of concurrent signal assignments. The
end-product of the \CLaSH\ compiler is called a \VHDL\ \emph{netlist} as the
result resembles an actual netlist description, and the fact that it is \VHDL\
-is only an implementation detail; e.g., the output could have been Verilog.
+is only an implementation detail; e.g., the output could have been Verilog or
+even \acro{EDIF}.
\section{Use cases}
\label{sec:usecases}
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\begin{code}
-as *+* bs = fold (+) (zipWith (*) as bs)
+as *+* bs = fold (+) (zip{-"\!\!\!"-}With (*) as bs)
\end{code}
\end{minipage}
\begin{minipage}{0.07\linewidth}
\end{example}
\end{minipage}
-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]}).
+The \hs{zip{-"\!\!\!"-}With} 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{zip{-"\!\!\!"-}With (*) [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
The \hs{fold} function takes a binary 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 in the
vector. This continues until the end of the vector is reached. The result of
the \hs{fold} function is the result of the last application. It is obvious
-that the \hs{zipWith (*)} function is pairwise multiplication and that the
-\hs{fold (+)} function is summation.
+that the \hs{zip{-"\!\!\!\!"-}With (*)} function is pairwise multiplication
+and that the \hs{fold (+)} function is summation.
% Returning to the actual \acro{FIR} filter, we will slightly change the
% equation describing it, so as to make the translation to code more obvious and
% concise. What we do is change the definition of the vector of input samples
\subsection{Higher-order CPU}
%format fun x = "\textit{fu}_" x
-In this section discusses a somewhat more serious example in which
-user-defined higher-order function, partial application, lambda expressions,
-and pattern matching are exploited. The example concerns a \acro{CPU} which
-consists of four function unites \hs{fun 0,{-"\ldots"-},fun 3} (see
+This section discusses a somewhat more elaborate example in which user-defined
+higher-order function, partial application, lambda expressions, and pattern
+matching are exploited. The example concerns a \acro{CPU} which consists of
+four function units, \hs{fun 0,{-"\ldots"-},fun 3}, (see
\Cref{img:highordcpu}) that each perform some binary operation.
\begin{figure}
\vspace{-1.5em}
\end{figure}
-Every function unit has seven data inputs (of type \hs{Word}), and two address
-inputs (of type \hs{Index 6}) which indicate which data inputs have to be
-chosen as arguments for the the binary operation that the unit performs. These
-data inputs consists of one external input \hs{x}, two fixed initialization
-values (0 and 1), and the previous outputs of the four function units. The
-output of the \acro{CPU} as a whole is the previous output of \hs{fun 3}.
+Every function unit has seven data inputs (of type \hs{Signed 16}), and two
+address inputs (of type \hs{Index 6}). The latter two addresses indicate
+which of the seven data inputs are to be used as operands for the binary
+operation the function unit performs.
-The function units \hs{fun 1, fun 2, fun 3} can perform a fixed binary
-operation, whereas \hs{fun 0} has an additional input for an opcode to choose
-a binary operation out of a few possibilities.
+These seven data inputs consist of one external input \hs{x}, two fixed
+initialization values (0 and 1), and the previous outputs of the four function
+units. The output of the \acro{CPU} as a whole is the previous output of
+\hs{fun 3}.
-Each function unit outputs its result into a register, i.e., the state of the
-\acro{CPU}. This can can e.g. be defined as follows:
+Function units \hs{fun 1}, \hs{fun 2}, and \hs{fun 3} can perform a fixed
+binary operation, whereas \hs{fun 0} has an additional input for an opcode to
+choose a binary operation out of a few possibilities. Each function unit
+outputs its result into a register, i.e., the state of the \acro{CPU}. This
+state can e.g. be defined as follows:
\begin{code}
-type CpuState = State [Word | 4]
+type CpuState = State [Signed 16 | 4]
\end{code}
-Every function unit can now be defined by the following higher-order function
+Every function unit can now be defined by the following higher-order function,
\hs{fu}, which takes three arguments: the operation \hs{op} that the function
-unit performs, the seven \hs{inputs}, and the pair \hs{(a1,a2)} of two
-addresses:
+unit should perform, the seven \hs{inputs}, and the address pair
+\hs{({-"a_0"-},{-"a_1"-})}. It selects two inputs, based on the
+addresses, and applies the given operation to them, returning the
+result:
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\begin{code}
-fu op inputs (a1, a2) = regIn
- where
- arg1 = inputs!a1
- arg2 = inputs!a2
- regIn = op arg1 arg2
+fu op inputs ({-"a_0"-}, {-"a_1"-}) =
+ op (inputs!{-"a_0"-}) (inputs!{-"a_1"-})
\end{code}
\end{minipage}
\begin{minipage}{0.07\linewidth}
\end{example}
\end{minipage}
-Using partial application we now define:
+\noindent Using partial application we now define:
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\end{example}
\end{minipage}
-In order to define \hs{fun 0} we first define the type \hs{Opcode} for the
-opcode and the function \hs{multiop} that chooses a specific operation given
-the opcode. We assume that the functions \hs{shifts} (which shifts its first
-operand by the number of bits indicate in the second operand), \hs{xor} (for
-the bitwise \hs{xor}), and (==) (for equality) already exits.
+In order to define \hs{fun 0}, the \hs{Opcode} type and the \hs{multiop}
+function that chooses a specific operation given the opcode, are defined
+first. It is assumed that the binary functions \hs{shift} (where \hs{shift a
+b} shifts \hs{a} by the number of bits indicated by \hs{b}) and \hs{xor} (for
+the bitwise \hs{xor}) exist.
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\end{minipage}
Note that the result of \hs{multiop} is a binary function; this is supported
-by \CLaSH. We can now define \hs{fun 0} as a function which takes an opcode as
-additional argument:
+by \CLaSH. The complete definition of \hs{fun 0}, which takes an opcode as
+additional argument, is:
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\end{example}
\end{minipage}
-Now we come to the definition \hs{cpu} of the full \acro{CPU}. Its type is:
+\noindent Now comes the definition of the full \acro{CPU}. Its type is:
\begin{code}
cpu :: CpuState
- -> (Word, Opcode, [(Index 6, Index 6) | 4])
- -> (CpuState, Word)
+ -> (Signed 16, Opcode, [(Index 6, Index 6) | 4])
+ -> (CpuState, Signed 16)
\end{code}
-Note that this type fits the requirements of the function \hs{run}. The
-definition of the \hs{cpu} now is:
+\noindent Note that this type fits the requirements of the \hs{run}
+function (meaning it can be simulated and synthesized). The actual
+definition of the \hs{cpu} function is:
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\end{example}
\end{minipage}
-While this is still a simple (and maybe not very useful) design, it
+Due to space restrictions, \Cref{img:highordcpu} does not show the
+internals of each function unit, but note that e.g. \hs{multiop} is a
+subcomponent of \hs{fun 0}.
+
+While the \acro{CPU} has a simple (and maybe not very useful) design, it
illustrates some possibilities that \CLaSH\ offers and suggests how to write
actual designs.
% design, in which the same techniques can be reused.
\section{Related work}
+\label{sec:relatedwork}
This section describes the features of existing (functional) hardware
-description languages and highlights the advantages that this research has
+description languages and highlights the advantages that \CLaSH\ has
over existing work.
% Many functional hardware description languages have been developed over the
correctly translate all of its language constructs.
Like the research presented in this paper, many functional hardware
-description languages have some sort of foundation in the functional
-programming language Haskell. Hawk~\cite{Hawk1} is a hardware modeling
-language embedded in Haskell and has sequential environments that make it
-easier to specify stateful computation (by using the \acro{ST} monad). Hawk
-specifications can be simulated; to the best knowledge of the authors there is
-however no support for automated circuit synthesis.
+description languages have a foundation in the functional programming language
+Haskell. Hawk~\cite{Hawk1} is a hardware modeling language embedded in Haskell
+and has sequential environments that make it easier to specify stateful
+computation (by using the \acro{ST} monad). Hawk specifications can be
+simulated; to the best knowledge of the authors there is however no support
+for automated circuit synthesis.
The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
models. A designer can model systems using heterogeneous models of
electronic systems which have both analog and digital parts. ForSyDe has
several backends including simulation and automated synthesis, though
automated synthesis is restricted to the synchronous model of computation.
-Though ForSyDe offers higher-order functions and polymorphism, ForSyDe's
-choice elements are limited to \hs{if} and \hs{case} expressions. ForSyDe's
-explicit conversions, where functions have to be wrapped in processes and
-processes have to be wrapped in systems, combined with the explicit
-instantiations of components, also makes ForSyDe far more verbose than \CLaSH.
-
-Lava~\cite{Lava,kansaslava} is a hardware description language embedded in
-Haskell which focuses on the structural representation of hardware. Like
-\CLaSH, Lava has support for polymorphic types and higher-order functions.
-Besides support for simulation and circuit synthesis, Lava descriptions can be
-interfaced with formal method tools for formal verification. As discussed in
-the introduction, taking the embedded language approach does not allow for
-Haskell's choice elements to be captured within the circuit descriptions. In
-this respect \CLaSH\ differs from Lava, in that all of Haskell's choice
-elements, such as \hs{case}-expressions and pattern matching, are synthesized
-to choice elements in the eventual circuit. Consequently, descriptions
-containing rich control structures can be specified in a more user-friendly
-way in \CLaSH\ than possible within Lava, and hence are less error-prone.
+Although ForSyDe offers higher-order functions and polymorphism, ForSyDe's
+choice elements are limited to \hs{if-then-else} and \hs{case} expressions.
+ForSyDe's explicit conversions, where functions have to be wrapped in
+processes and processes have to be wrapped in systems, combined with the
+explicit instantiations of components, also makes ForSyDe far more verbose
+than \CLaSH.
+
+Lava~\cite{Lava,kansaslava} is a \acro{HDL} embedded in Haskell which focuses
+on the structural representation of hardware. Like \CLaSH, Lava has support
+for polymorphic types and higher-order functions. Besides support for
+simulation and circuit synthesis, Lava descriptions can be interfaced with
+formal method tools for formal verification. As discussed in the introduction,
+taking the embedded language approach does not allow for Haskell's choice
+elements to be captured within the circuit descriptions. In this respect
+\CLaSH\ differs from Lava, in that all of Haskell's choice elements, such as
+\hs{case}-expressions and pattern matching, are synthesized to choice elements
+in the eventual circuit. Consequently, descriptions containing rich control
+structures can be specified in a more user-friendly way in \CLaSH\ than
+possible within Lava, and hence are less error-prone.
Bluespec~\cite{Bluespec} is a high-level synthesis language that features
guarded atomic transactions and allows for the automated derivation of control
\section{Conclusion}
+\label{sec:conclusion}
This research demonstrates once more that functional languages are well suited
for hardware descriptions: function applications provide an elegant notation
for component instantiation. While circuit descriptions made in \CLaSH\ are
very concise when compared to other (traditional) \acrop{HDL}, their intended
functionality remains clear. \CLaSH\ goes beyond the existing (functional)
-hardware descriptions languages by including advanced choice elements, such as
-pattern matching and guards, which are well suited to describe the conditional
-assignments in control-oriented circuits. Besides being able to translate
-these basic constructs to synthesizable \VHDL, the prototype compiler can also
-correctly translate descriptions that contain both polymorphic types and
-user-defined higher-order functions.
+\acrop{HDL} by including advanced choice elements, such as pattern matching
+and guards, which are well suited to describe the conditional assignments in
+control-oriented circuits. Besides being able to translate these basic
+constructs to synthesizable \VHDL, the prototype compiler can also translate
+descriptions that contain both polymorphic types and user-defined higher-order
+functions.
% Where recent functional hardware description languages have mostly opted to
% embed themselves in an existing functional language, this research features
Besides simple circuits such as variants of both the \acro{FIR} filter and
the higher-order \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler
has also been able to translate non-trivial functional descriptions such as a
-streaming reduction circuit~\cite{reductioncircuit} for floating point
-numbers.
+streaming reduction circuit~\cite{blindreview} %~\cite{reductioncircuit}
+for floating point numbers.
\section{Future Work}
-The choice of describing state explicitly as and extra argument and result can
+\label{sec:futurework}
+The choice of describing state explicitly as an extra argument and result can
be seen as a mixed blessing. Even though descriptions that use state are
usually very clear, distributing and collecting substate can become tedious
and even error-prone. Automating the required distribution and collection, or
developed in an ad-hoc manner, which makes the existence of many desirable
properties unclear. Such properties include whether the complete set of
transformations will always lead to a normal form or whether the normalization
-process always terminates. Though extensive use of the compiler suggests that
-these properties usually hold, they have not been formally proven. A
+process always terminates. Although extensive use of the compiler suggests
+that these properties usually hold, they have not been formally proven. A
systematic approach to defining the set of transformations allows one to proof
that the earlier mentioned properties do indeed hold.
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