% 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.
\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}
\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
% 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
\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,
\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
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
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
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|
\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:
\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}
\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}
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}}
% \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
% 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}).
\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:
% 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:
% (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
\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.
+ defined as an enumeration type, but that there a fixed translation for
+ that type within the \CLaSH\ compiler. An example of such an
+ enumeration 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.
+ \subsection{Polymorphism}
+ A powerful feature of most (functional) programming 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 polymorphic function, consider the following
- \hs{append} function's type:
+ As an example of a parametric polymorphic function, consider the type of
+ the following \hs{append} function, which appends an element to a vector:
- \comment{TODO: Use vectors instead of lists?}
-
\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 designer 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 however one constraint: the top level
+ function that is being translated can not have any polymorphic arguments.
+ The arguments can not be polymorphic as they are never applied and
+ consequently there is no way to determine 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 standard Haskell 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
+ negateVector 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}:
+ The code above defines the \hs{negateVector} function, which takes a
+ vector of booleans, \hs{xs}, 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}
- map :: (a -> b) -> [a] -> [b]
+ map :: (a -> b) -> [a|n] -> [b|n]
\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.
-
- \begin{code}
- fir ... = foldl1 (+) (zipwith (*) xs hs)
- \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
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
- functions, but any function defined in \CLaSH\ can have function
+ Finally, higher order arguments are not limited to just built-in
+ functions, but any function defined by a developer can have function
arguments. This allows the hardware designer to use a powerful
abstraction mechanism in his designs and have an optimal amount of
- code reuse.
+ code reuse. The only exception is again the top-level function: if a
+ function-typed argument is not applied with an actual function, no
+ hardware can be generated.
- \comment{TODO: Describe ALU example (no code)}
+ % \comment{TODO: Describe ALU example (no code)}
\subsection{State}
A very important concept in hardware it the concept of state. In a
\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}:
+
+ \begin{code}
+ macS (State c) a b = (State c', outp)
+ where
+ outp = mac a b c
+ c' = outp
+ \end{code}
+
+ \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:
- 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)
+ run f s (i:inps) = o : (run f s' inps)
where
- outp = s + inp
- s' = outp
+ (s', o) = f s i
\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.
+
+ 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
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
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}.
%
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\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
-\bibliography{IEEEabrv,clash.bib}
+\bibliography{clash}
%
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