% 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.
\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
ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
a time which also saw the birth of the currently popular hardware description
-languages such as \VHDL. The merit of using a functional language to describe
-hardware comes from the fact that 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
-description languages are embedded as a domain specific language inside the
-functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
-means that a developer is given a library of Haskell~\cite{Haskell} functions
-and types that together form the language primitives of the domain specific
-language. As a result of how the signals are modeled and abstracted, the
-functions used to describe a circuit also build a large domain-specific
-datatype (hidden from the designer) which can be further processed by an
-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
-circuit description itself.
+languages such as \VHDL. Functional languages are especially suited to
+describe hardware because combinational 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 in creating all the
+required tooling, such as parsers and type-checkers, many functional
+hardware description languages \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}
+are embedded as a domain specific language inside 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 domain specific language. 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.
The approach taken in this research is not to make another domain specific
language embedded in Haskell, but to use (a subset of) the Haskell language
itself for the purpose of describing hardware. By taking this approach, we can
capture certain language constructs, such as Haskell's choice elements
-(if-constructs, case-constructs, pattern matching, etc.), which are not
+(if-expressions, case-expressions, 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 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).
+functions, these descriptions can be compiled to an executable binary
+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. A developer describes the behavior of the hardware between
-clock cycles, as such, only synchronous systems can be described. 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.
+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}
and
\item function applications are translated to component instantiations.
\end{inparaenum}
- The output port can have a complex type (such as a tuple), so having just
- a single output port does not pose any limitation. The arguments of a
- function applications are assigned to a signal, which are then mapped to
+ 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 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,% aswell,
- creating a hierarchical description of the hardware. This separation in
- different components makes the resulting \VHDL\ output easier to read and
- debug.
+ 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 (\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.
+ In Haskell, choice can be achieved by a large set of syntacic 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.
% 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 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. Both versions of the example roughly correspond to the same
- netlist, which is depicted in \Cref{img:choice}.
+ using a \hs{case} expression and the other 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:
\begin{code}
+ data Pred = Equal | NotEqual
+ \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
+ Equal -> case a == b of
+ True -> a + b
+ False -> 0
+ NotEqual -> case a != b of
+ True -> a + b
+ False -> 0
\end{code}
\begin{code}
sumif pred a b =
- if pred == Eq then
+ if pred == Equal then
if a == b then a + b else 0
else
if a != b then a + b else 0
\end{code}
\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. Like
- \hs{if-then-else} constructs, pattern matching and guards have a
- (straightforward) translation to \hs{case} constructs and can as such be
+ 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 third version of the earlier example, using both
- pattern matching and guards, can be seen below. The version using pattern
- matching and guards also has roughly the same netlist representation
- (\Cref{img:choice}) as the earlier two versions of the example.
+ 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 Equal a b | a == b = a + b
+ | otherwise = 0
+ sumif NotEqual a b | a != b = a + b
+ | otherwise = 0
\end{code}
% \begin{figure}
\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, as such this
- section will only deal with the types that do have a clear correspondence
+ typing constructs have a clear translation to hardware, this section will
+ therefore 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,
+ 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.
+
+ The \CLaSH compiler is able to infer unspecified types,
meaning that a developer does not have to annotate every function with a
- type signature.
+ type signature (though it is good practice to do so anyway).
% 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 translation defined within the \CLaSH\
+ The following types have fixed 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}).
Supporting the Bool type is required in order to support the
- \hs{if-then-else} construct, which requires a \hs{Bool} value for
+ \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,
+ 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. 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.
+ 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
+ elaborate in real \CLaSH programs.
% The state type of an 8 element register bank would then for example
% be:
% \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
% vector is translated to a \VHDL\ array type.
\item[\bf{Index}]
- This is another type to describe integers, but unlike the previous
+ 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.
An \hs{Index} only has an upper bound, its lower bound is
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, {\small{GADT}}s, etc.) which are not standard Haskell.
+ existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell.
As it is currently unclear how these advanced type constructs correspond
- with hardware, they are for now unsupported by the \CLaSH\ compiler
+ 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 renaming constructs only define new
+ completely new type. Type synonyms and type renaming only define new
names for existing types, where synonyms are completely interchangeable
- and renaming constructs need explicit conversions. Therefore, these do not
+ 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:
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. 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:
+ 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:
\begin{code}
data IntPair = IntPair Int Int
\end{code}
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. An example of such an enum type is the type that represents the
- colors in a traffic light:
+ defined as an enumeration type, but that there is 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}
% 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{Polymorphism}
- A powerful construct in most functional languages is polymorphism, it
- allows a function to handle values of different data types in a uniform
- way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
- meaning functions can be written without mention of any specific type and
- can be used transparently with any number of new types.
+ 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 parametric polymorphic function, consider the type of
- the following \hs{append} function, which appends an element to a vector:
+ the following \hs{append} function, which appends an element to a
+ vector:\footnote{The \hs{::} operator is used to annotate a function
+ with its type in \CLaSH}
+
\begin{code}
append :: [a|n] -> a -> [a|n + 1]
\end{code}
type classes, where a class definition provides the general interface of a
function, and class instances define the functionality for the specific
types. An example of such a type class is the \hs{Num} class, which
- contains all of Haskell's numerical operations. A developer can make use
+ 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
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 \hs{SizedInts}.
+ 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 one exception to this: The top level
- function that is translated, can not have any polymorphic arguments (as
- they are never applied, so there is no way to find out the actual types
- for the type parameters).
+ 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 not support user-defined type classes, but does use some
- of the built-in type classes for its built-in function, such as: \hs{Num}
- for numerical operations, \hs{Eq} for the equality operators, and
+ 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 functions}
+ \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
function. The following example should clarify this concept:
\begin{code}
- negVector xs = map not xs
+ negateVector xs = map not xs
\end{code}
- The code above defines a function \hs{negVector}, which takes a vector of
- booleans, and returns a vector where all the values are negated. It
- achieves this by calling the \hs{map} function, and passing it
+ 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
+ parametric polymorphic function: it does not pose any constraints on the
+ type of the input vector, other than that its elements must have the same type as
+ the first argument 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
\begin{code}
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 {-"$\ldots$"-} = 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 (next) 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, 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.
+ 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
+ A very important concept in hardware is the concept of 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 we want to describe more than simple
- combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
+ combinational designs, \CLaSH\ needs an abstraction mechanism for state.
An important property in Haskell, and in most other functional languages,
is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
\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
- functions, the current value of the state is made an argument of the
- function; the updated state becomes part of the result. A simple example
- is adding an accumulator register to the earlier multiply-accumulate
- circuit, of which the resulting netlist can be seen in
+ % 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 combinaionial circuits,
+ 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 \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
+ updated state part of result. In this sense the descriptions made in
+ \CLaSH\ are the combinaionial 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 a b (State c) = (State c', outp)
+ macS (State c) a b = (State c', c')
where
- outp = mac a b c
- c' = outp
+ c' = mac a b c
\end{code}
\begin{figure}
- \centerline{\includegraphics{mac-state}}
+ \centerline{\includegraphics{mac-state.svg}}
\caption{Stateful Multiply-Accumulate}
\label{img:mac-state}
\end{figure}
- This approach makes the state of a circuit 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{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 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 elements, as state values are just normal values. We can simulate
+ stateful descriptions using the recursive \hs{run} function:
+
+ \begin{code}
+ run f s (i : inps) = o : (run f s' inps)
+ where
+ (s', o) = f s i
+ \end{code}
+
+ The \hs{(:)} operator is the list concatenation operator, where the
+ left-hand side is the head of a list and the right-hand side is the
+ remainder of the list. The \hs{run} function applies the function the
+ developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
+ 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}. Each value in the input list corresponds to exactly one
+ cycle of the (implicit) clock.
+
+ As both the \hs{run} function, the hardware description, and the test
+ inputs are plain Haskell, the complete simulation can be compiled to an
+ executable binary by an optimizing Haskell compiler, or executed in an
+ Haskell interpreter. Both simulation paths are much faster than first
+ translating the description to \VHDL\ and then running a \VHDL\
+ simulation, where the executable binary has an additional simulation speed
+ bonus in case there is a large set of test inputs.
+
\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,
+typed, functional 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{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
+\end{equation}
+
+We can easily and directly implement the equation for the dot-product
+using higher-order functions:
+
+\begin{code}
+as *+* bs = foldl1 (+) (zipWith (*) as bs)
+\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 pairwise
+multiplication and the \hs{foldl1 (+)} function is 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
+front 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}
+
+
+\subsection{Higher order CPU}
+
+
+\begin{code}
+type FuState = State Word
+fu :: (a -> a -> a)
+ -> [a]:n
+ -> (RangedWord n, RangedWord n)
+ -> FuState
+ -> (FuState, a)
+fu op inputs (addr1, addr2) (State out) =
+ (State out', out)
+ where
+ in1 = inputs!addr1
+ in2 = inputs!addr2
+ out' = op in1 in2
+\end{code}
+
+\begin{code}
+type CpuState = State [FuState]:4
+cpu :: Word
+ -> [(RangedWord 7, RangedWord 7)]:4
+ -> CpuState
+ -> (CpuState, Word)
+cpu input addrs (State fuss) =
+ (State fuss', out)
+ where
+ fures = [ fu const inputs!0 fuss!0
+ , fu (+) inputs!1 fuss!1
+ , fu (-) inputs!2 fuss!2
+ , fu (*) inputs!3 fuss!3
+ ]
+ (fuss', outputs) = unzip fures
+ inputs = 0 +> 1 +> input +> outputs
+ out = head outputs
+\end{code}
\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}.
%
% http://www.michaelshell.org/tex/ieeetran/bibtex/
\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
-\bibliography{IEEEabrv,clash.bib}
+\bibliography{clash}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
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