% 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}
+\author{\IEEEauthorblockN{Matthijs Kooijman, Christiaan P.R. Baaij, 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}
+matthijs@@stdin.nl, c.p.r.baaij@@utwente.nl, j.kuper@@utwente.nl}
% \thanks{Supported through the FP7 project: S(o)OS (248465)}
}
% \and
executable binary by a Haskell compiler allowing high-speed simulation and
analysis.
-Stateful descriptions are supported by explicitly making the current state an
-argument of the function, and the updated state part of the result. In this
-sense, \CLaSH\ descriptions are the combinational parts of a mealy machine.
+% \CLaSH\ supports stateful descriptions by explicitly making the current
+% state an argument of the function, and the updated state part of the result.
+% This makes \CLaSH\ descriptions in essence the combinational parts of a
+% mealy machine.
\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 (\acrop{HDL}) have allowed the productivity of
hardware engineers to keep pace with the development of chip technology.
-Standard \acrop{HDL}, like \VHDL~\cite{VHDL2008} and Verilog~\cite{Verilog},
-allowed an engineer to describe circuits using a `programming' language. These
-standard languages are very good at describing detailed hardware properties
-such as timing behavior, but are generally cumbersome in expressing
-higher-level abstractions. 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,FHDL,T-Ruby,Hydra,HML2,Hawk1,
-Lava,ForSyDe1,Wired,reFLect}. The idea of using functional languages for
-hardware descriptions started in the early 1980s \cite{Cardelli1981,muFP,
-DAISY,FHDL}, a time which also saw the birth of the currently popular hardware
-description languages such as \VHDL. Functional languages are especially well
-suited to describe hardware because combinational circuits can be directly
-modeled as mathematical functions. Furthermore, functional languages are very
-good at describing and composing mathematical functions.
+Traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
+Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
+`programming' language. These standard languages are very good at describing
+detailed hardware properties such as timing behavior, but are generally
+cumbersome in expressing higher-level abstractions. 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,Wired,ForSyDe1,reFLect}. The idea of using
+functional languages for hardware descriptions started in the early 1980s
+\cite{Cardelli1981,muFP,DAISY}, a time which also saw the birth of the
+currently popular hardware description languages, 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
+mathematical functions.
In an attempt to decrease the amount of work involved in creating all the
required tooling, such as parsers and type-checkers, many functional
-\acrop{HDL} \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired} are embedded as a domain
-specific language (\acro{DSL}) inside the functional language Haskell
+\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, but instead compose a large domain-specific datatype
-(which is usually hidden from the designer). This datatype is then further
-processed by an embedded circuit compiler. This circuit 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 circuit compiler is usually
-compiled by the same Haskell compiler as the circuit description itself.
-Though the embedded language approach still allows for the support of
-polymorphism and higher-order functions, it impossible to capture Haskell's
-choice elements within a circuit description.
+process any signals, they instead compose a large domain-specific datatype
+(which is usually hidden from the designer). This datatype is then further
+processed by an embedded circuit compiler which can perform for example
+simulation or synthesis. As Haskell's choice elements (\hs{if}-expressions,
+\hs{case}-expressions, etc.) are evaluated at the time the domain-specific
+datatype is being build, they are no longer visible to the embedded compiler
+that processes the datatype. Consequently, it is impossible the 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 language
+elements.
The approach taken in this research is not to make another \acro{DSL} embedded
in Haskell, but to use (a subset of) the Haskell language \emph{itself} for
-the purpose of describing hardware. By taking this approach, we \emph{can}
-capture certain language constructs, such as Haskell's choice elements
-(\hs{if}-expressions, \hs{case}-expressions, pattern matching, etc.), within
-circuit descriptions. To the best knowledge of the authors, supporting
-polymorphism, higher-order functions and such an extensive array of
-choice-elements is new in the domain of functional \acrop{HDL}.
+the purpose of describing hardware. By taking this approach, this research
+\emph{can} capture certain language constructs, such as Haskell's choice
+elements, within circuit descriptions. To the best knowledge of the authors,
+supporting polymorphism, higher-order functions and such an extensive array of
+choice-elements is new in the domain of (functional) \acrop{HDL}.
% As the hardware descriptions are plain Haskell
% functions, these descriptions can be compiled to an executable binary
% for simulation using an optimizing Haskell compiler such as the Glasgow
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. 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 is however room within the
-language to eventually add a different abstraction mechanism that will allow
-for the modeling of asynchronous systems.
+state an additional input and the updated state a part of the output of a
+function. 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.
Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
must eventually be converted into a netlist. This research also features a
point numbers.
\section{Hardware description in Haskell}
+The following section describes the basic language elements of \CLaSH\ and the
+extensiveness of the support of these elements within the \CLaSH\ compiler. In
+various subsections, the relation between the language elements and their
+eventual netlist representation is also highlighted.
\subsection{Function application}
Two basic syntactic elements of a functional program are functions
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.
+ 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.
\begin{figure}
\centerline{\includegraphics{mac.svg}}
- \caption{Combinatorial Multiply-Accumulate}
+ \caption{Combinational Multiply-Accumulate}
\label{img:mac-comb}
+ \vspace{-1.5em}
\end{figure}
The use of a composite result value is demonstrated in the next example
(\ref{lst:code2}), where the multiply-accumulate circuit not only returns
the accumulation result, but also the intermediate multiplication result.
- Its corresponding netlist can be see in \Cref{img:mac-comb-composite}.
+ Its corresponding netlist can be seen in \Cref{img:mac-comb-composite}.
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\begin{figure}
\centerline{\includegraphics{mac-nocurry.svg}}
- \caption{Combinatorial Multiply-Accumulate (composite output)}
+ \caption{Combinational Multiply-Accumulate (composite output)}
\label{img:mac-comb-composite}
+ \vspace{-1.5em}
\end{figure}
\subsection{Choice}
In Haskell, choice can be achieved by a large set of syntactic elements,
consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
pattern matching, and guards. The most general of these are the \hs{case}
- expressions (\hs{if} expressions can be very directly translated to
- \hs{case} expressions). A \hs{case} expression is translated to a
- multiplexer, where the control value is fed into a number of
- comparators and their output is used to compose the selection port
- of the multiplexer. The result of each alternative is linked to the
- corresponding input port on the multiplexer.
+ expressions (\hs{if} expressions can be directly translated to
+ \hs{case} expressions). When transforming a \CLaSH\ description to a
+ netlist, a \hs{case} expression is translated to a multiplexer. The
+ control value of the \hs{case} expression is fed into a number of
+ comparators and their combined output forms the selection port of the
+ multiplexer. The result of each alternative in the \hs{case} expression is
+ linked to the corresponding input port of 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
- (\ref{lst:code3}) using a \hs{case} expression, and the other
- (\ref{lst:code4}) using an \hs{if-then-else} expression . Both 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:
+ Two versions of a contrived example are displayed below, the first
+ (\ref{lst:code3}) using a \hs{case} expression and the second
+ (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
+ sum two values when they are equal or non-equal (depending on the given
+ predicate, the \hs{pred} variable) and return 0 otherwise. The \hs{pred}
+ variable is of the following, user-defined, enumeration datatype:
\begin{code}
data Pred = Equal | NotEqual
The naive netlist corresponding to both versions of the example is
depicted in \Cref{img:choice}. Note that the \hs{pred} variable is only
- compared to the \hs{Equal} value, as an inequality immediately implies
- that the \hs{pred} variable has a \hs{NotEqual} value.
+ compared to \hs{Equal}, as an inequality immediately implies that
+ \hs{pred} is \hs{NotEqual}.
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
\end{minipage}
\begin{figure}
+ \vspace{1em}
\centerline{\includegraphics{choice-case.svg}}
\caption{Choice - sumif}
\label{img:choice}
+ \vspace{-1.5em}
\end{figure}
A user-friendly and also very powerful form of choice that is not found in
expressions, pattern matching and guards have a (straightforward)
translation to \hs{case} expressions and can as such be mapped to
multiplexers. A third version (\ref{lst:code5}) 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
+ 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}.
\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
- translated the user-defined types described below.
+ translate the user-defined types, which are described later on.
- The \CLaSH\ compiler is able to infer unspecified types,
+ 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 (even if it is good practice to do so).
+ type signature. % (even if it is good practice to do so).
+ Given that the top-level entity of a circuit design is annotated with
+ concrete/monomorphic types, the \CLaSH\ compiler can specialize
+ polymorphic functions to functions with concrete types.
% Translation of two most basic functional concepts has been
% discussed: function application and choice. Before looking further
Supporting the Bool type is required in order to support the
\hs{if-then-else} expression, 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,
- while a \hs{SizedInt} is signed. Both are parametrizable in their
- size.
+ \item[\bf{Signed}, \bf{Unsigned}]
+ these are types to represent integers and both are parametrizable in
+ their size. The overflow behavior of the numeric operators defined for
+ these types is \emph{wrap-around}.
% , so you can define an unsigned word of 32 bits wide as follows:
% \begin{code}
% \texttt{signed} respectively.
\item[\bf{Vector}]
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
+ has a static length. The \hs{Vector} type constructor takes two type
arguments: the length of the vector and the type of the elements
contained in it. The short-hand notation used for the vector type in
- the rest of paper is: \hs{[a|n]}, here \hs{a} is the element
+ the rest of paper is: \hs{[a|n]}, where \hs{a} is the element
type, and \hs{n} is the length of the vector. Note that this is
a notation used in this paper only, vectors are slightly more
verbose in real \CLaSH\ descriptions.
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.
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}.
+ implicitly zero. If a value of this type exceeds either bounds, an
+ error will be thrown at simulation-time. The main purpose of the
+ \hs{Index} type is to be used as an index into a \hs{Vector}.
% \comment{TODO: Perhaps remove this example?} To define an index for
% the 8 element vector above, we would do:
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 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.
+ % \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. 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.
+ and a type renaming requires an explicit conversion. Type synonyms and
+ type renaming 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}
fields, are essentially a way to pack a few values together in a
record-like structure. Haskell's built-in tuple types are also defined
as single constructor algebraic types (but with a bit of
- syntactic sugar). An example of a single constructor type is the
- following pair of integers:
+ 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}
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:
+ 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:
\begin{code}
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}, 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 (and thus the \hs{sum}
- function) with \hs{SizedWords} as well as with \hs{SizedInts}.
-
- 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 the function is never applied and
- consequently there is no way to determine the actual types for the type
- parameters.
-
- \CLaSH\ does \emph{currently} not support\emph{ user-defined} type
- classes, but does use some 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.
+ the compiler knows 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 (and thus the \hs{sum}
+ % function) with \hs{Signed} as well as with \hs{Unsigned}.
+
+ \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. Any
+ function defined can have any number of unconstrained type parameters. A
+ developer can also specify his own type classes and corresponding
+ instances. The \CLaSH\ compiler will infer the type of every polymorphic
+ 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 of the top-level can not be
+ polymorphic as the function is never applied and consequently there is no
+ way to determine the actual types for the type parameters.
+
+ With regard to the built-in types, it should be noted that members of
+ some of the standard Haskell type classes are supported as built-in
+ functions. These include: the numerial operators of \hs{Num}, the equality
+ operators of \hs{Eq}, and the comparison/order operators of \hs{Ord}.
\subsection{Higher-order functions \& values}
Another powerful abstraction mechanism in functional languages, is
- the concept of \emph{higher-order functions}, or \emph{functions as
- a first class value}. This allows a function to be treated as a
+ the concept of \emph{functions as a first class value}, also called
+ \emph{higher-order functions}. This allows a function to be treated as a
value and be passed around, even as the argument of another
function. The following example should clarify this concept:
\end{example}
\end{minipage}
- Finally, not only built-in functions can have higher order
- arguments, but any function defined in \CLaSH can have function
- arguments. This allows the hardware designer to use a powerful
- abstraction mechanism in his designs and have an optimal amount of
- 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.
+ 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 use a
+ powerful amount of 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)}
% Simply removing the purity property is not a valid option, as the
% language would then lose many of it mathematical properties.
In \CLaSH\ we deal with the concept of state in pure functions by making
- current value of the state an additional argument of the function and the
+ the current state an additional argument of the function, and the
updated state part of result. In this sense the descriptions made in
\CLaSH\ are the combinational parts of a mealy machine.
\centerline{\includegraphics{mac-state.svg}}
\caption{Stateful Multiply-Accumulate}
\label{img:mac-state}
+ \vspace{-1.5em}
\end{figure}
- Note that the \hs{macS} function returns bot the new state and the value
+ Note that the \hs{macS} function returns both the new state and the value
of the output port. 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 be reflected in the type signature of
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.
- Also note how the order of the input, output, and state in the \hs{run}
- function corresponds with the order of the input, output and state of the
- \hs{macS} function described earlier.
+ it is assumed that there is one input per clock cycle. Also note how the
+ order of the input, output, and state in the \hs{run} function corresponds
+ with the order of the input, output and state of the \hs{macS} function
+ described earlier.
As the \hs{run} function, the hardware description, and the test
inputs are also valid Haskell, the complete simulation can be compiled to
\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\
-language as described in the previous section to synthesizable \VHDL, allowing
-a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
+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) is an open-source Haskell compiler that
-also provides a high level API to most of its internals. The availability of
-this high-level API obviated the need to design many of the tedious parts of
-the prototype compiler, such as the parser, semantic checker, and especially
-the type-checker. These parts together form the front-end of the prototype compiler pipeline, as seen in \Cref{img:compilerpipeline}.
+The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
+compiler that also provides a high level API to most of its internals. The
+availability of this high-level 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
+\Cref{img:compilerpipeline}.
\begin{figure}
\centerline{\includegraphics{compilerpipeline.svg}}
\caption{\CLaSHtiny\ compiler pipeline}
\label{img:compilerpipeline}
+\vspace{-1.5em}
\end{figure}
-The output of the \GHC\ front-end consists of the translation of the original Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller, typed, functional language. This \emph{Core} language is relatively easy to 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' first-order functions.
+The output of the \GHC\ front-end consists of the translation of the original
+Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller,
+typed, functional language. This \emph{Core} language is relatively easy to
+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'
+first-order functions, and specializing polymorphic types to concrete types.
The final step in the compiler pipeline is the translation to a \VHDL\
\emph{netlist}, which is a straightforward process due to resemblance of a
\end{example}
\end{minipage}
-Where the vector \hs{xs} contains the previous input samples, the vector \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input sample. The concatenate operator (\hs{+>}) creates a new vector by placing the current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x}) to the list of previous input samples (\hs{xs}) and removes the oldest sample, is shown below:
+Where the vector \hs{xs} contains the previous input samples, the vector
+\hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
+sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
+current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
+code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x})
+to the list of previous input samples (\hs{xs}) and removes the oldest sample,
+is shown below:
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
their operand. The application of the function units to the \hs{inputs} and
\hs{addrs} arguments seems quite repetitive and could be rewritten to use
a combination of the \hs{map} and \hs{zipwith} functions instead.
-However, the prototype compiler does not currently support working with lists of functions, so a more explicit version of the code is given instead.
+However, the prototype compiler does not currently support working with lists
+of functions, so a more explicit version of the code is given instead.
\hspace{-1.7em}
\begin{minipage}{0.93\linewidth}
description languages and highlights the advantages that this research has
over existing work.
-Many functional hardware description languages have been developed over the
-years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
-extension of Backus' \acro{FP} language to synchronous streams, designed
-particularly for describing and reasoning about regular circuits. The
-Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
-circuits, and has a particular focus on layout.
-
-\begin{figure}
-\centerline{\includegraphics{highordcpu.svg}}
-\caption{CPU with higher-order Function Units}
-\label{img:highordcpu}
-\end{figure}
+% Many functional hardware description languages have been developed over the
+% years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
+% extension of Backus' \acro{FP} language to synchronous streams, designed
+% particularly for describing and reasoning about regular circuits. The
+% Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
+% circuits, and has a particular focus on layout.
\acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
functional language \acro{ML}, and has support for polymorphic types and
higher-order functions. Published work suggests that there is no direct
simulation support for \acro{HML}, but that a description in \acro{HML} has to
be translated to \VHDL\ and that the translated description can then 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.
+simulated in a \VHDL\ simulator. Certain aspects of HML, such as higher-order
+functions are however not supported by the \VHDL\ translator~\cite{HML3}. The
+\CLaSH\ compiler on the other hand can correctly translate all of the language
+constructs mentioned in this paper. % to a netlist format.
+
+\begin{figure}
+\centerline{\includegraphics{highordcpu.svg}}
+\caption{CPU with higher-order Function Units}
+\label{img:highordcpu}
+\vspace{-1.5em}
+\end{figure}
-Like the work presented in this paper, 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; to the best knowledge of the authors there is however no support for automated circuit synthesis.
+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} uses Haskell to describe
+system-level executable specifications used to model the behavior of
+superscalar microprocessors. 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, 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
-circuit synthesis, Lava descriptions can be interfaced with formal method
-tools for formal verification. Lava descriptions are actually circuit
-generators when viewed from a synthesis viewpoint, in that the language
-elements of Haskell, such as choice, can be used to guide the circuit
-generation. If a developer wants to insert a choice element inside an actual
-circuit he will have to 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 embedded
-languages such as Hawk, ForSyDe and Lava.
-
-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 support
-for generics has been extended to types and subprograms, allowing a developer
-to describe components with polymorphic ports and function-valued arguments.
-Note that the types and subprograms still require an explicit generic map,
-whereas types can be automatically inferred, and function-values can be
-automatically propagated by the \CLaSH\ compiler. There are also no (generally
-available) \VHDL\ synthesis tools that currently support the \VHDL-2008
-standard, and thus the synthesis of polymorphic types and function-valued
-arguments.
+models. 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.
+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 function have to be wrapped in processes and
+processes have to be wrapped in systems, combined with the explicit
+instantiations of components, also makes ForSyDe more verbose than \CLaSH.
+
+Lava~\cite{Lava} is a hardware description language, embedded in Haskell, and
+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 are hence 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
+structures based on these atomic transactions. Bluespec, like \CLaSH, supports
+polymorphic typing and function-valued arguments. Bluespec's syntax and
+language features \emph{had} their basis in Haskell. However, in order to
+appeal to the users of the traditional \acrop{HDL}, Bluespec has adapted
+imperative features and a syntax that resembles Verilog. As a result, Bluespec
+is (unnecessarily) verbose when compared to \CLaSH.
+
+The merits of polymorphic typing and function-valued arguments are now also
+recognized in the traditional \acrop{HDL}, exemplified by the new \VHDL-2008
+standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to
+types and subprograms, allowing a designer to describe components with
+polymorphic ports and function-valued arguments. Note that the types and
+subprograms still require an explicit generic map, whereas types can be
+automatically inferred, and function-values can be automatically propagated
+by the \CLaSH\ compiler. There are also no (generally available) \VHDL\
+synthesis tools that currently support the \VHDL-2008 standard.
% Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
%
for hardware descriptions: function applications provide an elegant notation
for component instantiation. Where this research goes beyond the existing
(functional) hardware descriptions languages is the inclusion of various
-choice elements, such as patter matching, that are well suited to describe the
-conditional assignments in control-oriented hardware. Besides being able to
-translate these basic constructs to synthesizable \VHDL, the prototype
+choice elements, such as pattern matching, that 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 function-valued arguments.
projects / matthijs / master-project / dsd-paper.git / blobdiff