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
+Besides trivial circuits such as variants of both the \acro{FIR} filter and
+the simple \acro{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.
\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 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.
+ 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,
\end{figure}
\subsection{Choice}
- In Haskell, choice can be achieved by a large set of syntacic elements,
+ 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
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,
+ The \CLaSH\ compiler is able to infer unspecified types,
meaning that a developer does not have to annotate every function with a
- type signature (though it is good practice to do so anyway).
+ type signature (even if it is good practice to do so).
% Translation of two most basic functional concepts has been
% discussed: function application and choice. Before looking further
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. Note that this is
a notation used in this paper only, vectors are slightly more
- elaborate in real \CLaSH programs.
+ verbose in real \CLaSH\ descriptions.
% The state type of an 8 element register bank would then for example
% be:
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 that there is a fixed translation for
- that type within the \CLaSH\ compiler. An example of such an
+ 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}
As an example of a parametric polymorphic function, consider the type of
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}
+ with its type.}
\begin{code}
append :: [a|n] -> a -> [a|n + 1]
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 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
- signature belonging to \hs{map}:
+ 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 signature belonging to \hs{map}:
\begin{code}
map :: (a -> b) -> [a|n] -> [b|n]
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 (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:
+ 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
% 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,
+ Pure functions are as such a perfect match for combinational circuits,
where the output solely depends on the inputs. When a circuit has state
however, it can no longer be simply described by a pure function.
% Simply removing the purity property is not a valid option, as the
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.
+ \CLaSH\ are the combinational 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
bonus in case there is a large set of test inputs.
\section{\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}.
+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}.
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
The output of the \GHC\ front-end is the original Haskell description
translated to \emph{Core}~\cite{Sulzmann2007}, which is smaller, typed,
-functional language that is relatively easier to process than the larger Haskell
-language. A description in \emph{Core} can still contain properties which have
-no direct translation to hardware, such as polymorphic types and
+functional language that is relatively easier to process than the larger
+Haskell language. A description in \emph{Core} can still contain properties
+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 properties that have a direct
-translation. The second stage of the compiler, the \emph{normalization} phase
+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
\VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
\section{Use cases}
-
-\subsection{FIR Filter}
\label{sec:usecases}
+\subsection{FIR Filter}
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
+functions leads to a very natural description is a \acro{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
+A \acro{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
+are summed, to produce the result at time $t$. The equation of a \acro{FIR}
filter is indeed equivalent to the equation of the dot-product, which is
shown below:
that the \hs{zipWith (*)} function is pairwise multiplication and that the
\hs{foldl1 (+)} function is summation.
-Returning to the actual FIR filter, we will slightly change the equation
-describing it, so as to make the translation to code more obvious and concise.
-What we do is change the definition of the vector of input samples and delay
-the computation by one sample. Instead of having the input sample received at
-time $t$ stored in $x_t$, $x_0$ now always stores the newest 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):
+Returning to the actual \acro{FIR} filter, we will slightly change the
+equation describing it, so as to make the translation to code more obvious and
+concise. What we do is change the definition of the vector of input samples
+and delay the computation by one sample. Instead of having the input sample
+received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
+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}
-The complete definition of the FIR filter in code then becomes:
+The complete definition of the \acro{FIR} filter in code then becomes:
\begin{code}
fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
\end{code}
-Where the vector \hs{hs} contains the FIR coefficients and the vector \hs{xs}
-contains the latest input sample in front and older samples behind. 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{hs} contains the \acro{FIR} coefficients and the vector
+\hs{xs} contains the previous input sample in front and older samples behind.
+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:
\begin{code}
x >> xs = x +> init xs
\end{code}
The \hs{init} function returns all but the last element of a vector, and the
-concatenate operator ($\succ$) adds a new element to the front of a vector. The
-resulting netlist of a 4-taps FIR filter, created by specializing the vectors of the above definition to a length of 4, is depicted in \Cref{img:4tapfir}.
+concatenate operator (\hs{+>}) adds a new element to the front of a vector.
+The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
+the vectors of the \acro{FIR} code to a length of 4, is depicted in
+\Cref{img:4tapfir}.
\begin{figure}
\centerline{\includegraphics{4tapfir.svg}}
\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)
+fu op inputs (addr1, addr2) = regIn
where
- in1 = inputs!addr1
- in2 = inputs!addr2
- out' = op in1 in2
+ in1 = inputs!addr1
+ in2 = inputs!addr2
+ regIn = 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)
+cpu :: Word -> [(Index 6, Index 6) | 4]
+ -> State [Word | 4] -> (State [Word | 4], 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
+ fuss' = [ fu const inputs (addrs!0) (fuss!0)
+ , fu (+) inputs (addrs!1) (fuss!1)
+ , fu (-) inputs (addrs!2) (fuss!2)
+ , fu (*) inputs (addrs!3) (fuss!3)
+ ]
+ inputs = 0 +> (1 +> (input +> fuss))
+ out = head fuss
\end{code}
\section{Related work}
+This section describes the features of existing (functional) hardware
+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
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
+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
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, allowing a developer to describe
-polymorphic components. Note that those types still require an explicit
-generic map, whereas types can be automatically inferred in \CLaSH.
+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.
% Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
%
% use section* for acknowledgement
-\section*{Acknowledgment}
-
-
-The authors would like to thank...
-
-
-
-
+% \section*{Acknowledgment}
+%
+% The authors would like to thank...
% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
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