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% *** CITATION PACKAGES ***
%
\usepackage{cite}
\usepackage{xcolor}
\def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
+\usepackage{cleveref}
+\crefname{figure}{figure}{figures}
+\newcommand{\fref}[1]{\cref{#1}}
+\newcommand{\Fref}[1]{\Cref{#1}}
+
+
%include polycode.fmt
%include clash.fmt
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 tools.
+by an optimizing \VHDL\ synthesis tool.
\section{Hardware description in Haskell}
\subsection{Function application}
The basic syntactic elements of a functional program are functions
- and function application. These have a single obvious \VHDL\
- translation: each top level function becomes a hardware component,
- where each argument is an input port and the result value is the
- (single) output port. This output port can have a complex type (such
- as a tuple), so having just a single output port does not create a
- limitation.
-
- Each function application in turn becomes a component instantiation.
- Here, the result of each argument expression is assigned to a
- signal, which is mapped to the corresponding input port. The output
- port of the function is also mapped to a signal, which is used as
- the result of the application itself.
+ and function application. These have a single obvious translation to a
+ netlist: every function becomes a component, every function argument is an
+ input port and the result value is of a function is an output port. This
+ output port can have a complex type (such as a tuple), so having just a
+ single output port does not create a limitation. Each function application
+ in turn becomes a component instantiation. Here, the result of each
+ argument expression is assigned to a signal, which is mapped to the
+ corresponding input port. The output port of the function is also mapped
+ to a signal, which is used as the result of the application itself.
Since every top level function generates its own component, the
- hierarchy of function calls is reflected in the final \VHDL\
- output as well, creating a hierarchical \VHDL\ description of the
- hardware. This separation in different components makes the
- resulting \VHDL\ output easier to read and debug.
-
- Example that defines the \texttt{mac} function by applying the
- \texttt{add} and \texttt{mul} functions to calculate $a * b + c$:
-
-\begin{code}
-mac a b c = add (mul a b) c
-\end{code}
-
-\begin{figure}
-\centerline{\includegraphics{mac}}
-\caption{Combinatorial Multiply-Accumulate (curried)}
-\label{img:mac-comb}
-\end{figure}
-
-\begin{figure}
-\centerline{\includegraphics{mac-nocurry}}
-\caption{Combinatorial Multiply-Accumulate (uncurried)}
-\label{img:mac-comb-nocurry}
-\end{figure}
-
- \subsection{Choices}
- Although describing components and connections allows describing a
- lot of hardware designs already, there is an obvious thing missing:
- choice. We need some way to be able to choose between values based
- on another value. In Haskell, choice is achieved by \hs{case}
- expressions, \hs{if} expressions, pattern matching and guards.
-
- The easiest of these are of course case expressions (and \hs{if}
- expressions, which can be very directly translated to \hs{case}
- expressions). A \hs{case} expression can in turn simply be
- translated to a conditional assignment in \VHDL, where the
- conditions use equality comparisons against the constructors in the
- \hs{case} expressions.
-
- A slightly more complex (but 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 corresponding clause will be used.
-
- A pattern match (with optional guards) can also be implemented using
- conditional assignments in \VHDL, where the condition is the logical
- and of comparison results of each part of the pattern as well as the
- guard.
-
- Contrived example that sums two values when they are equal or
- non-equal (depending on the predicate given) and returns 0
- otherwise. This shows three implementations, one using and if
- expression, one using only case expressions and one using pattern
- matching and guards.
-
+ 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.
+
+ 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|
+ function to calculate $a * b + c$:
+
+ \begin{code}
+ mac a b c = add (mul a b) c
+ \end{code}
+
+ \begin{figure}
+ \centerline{\includegraphics{mac}}
+ \caption{Combinatorial Multiply-Accumulate}
+ \label{img:mac-comb}
+ \end{figure}
+
+ The result of using a complex 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:
+
+ \begin{code}
+ mac (a, b, c) = add (mul a b) c
+ \end{code}
+
+ \begin{figure}
+ \centerline{\includegraphics{mac-nocurry}}
+ \caption{Combinatorial Multiply-Accumulate (complex input)}
+ \label{img:mac-comb-nocurry}
+ \end{figure}
+
+ \subsection{Choice}
+ In Haskell, choice can be achieved by a large set of language constructs,
+ consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
+ pattern matching, and guards. The easiest of these are the \hs{case}
+ constructs (and \hs{if} expressions, which can be very directly translated
+ to \hs{case} expressions). A \hs{case} expression can in turn simply be
+ translated to a conditional assignment in \VHDL, where the conditions use
+ equality comparisons against the constructors in the \hs{case}
+ expressions. We can see two versions of a contrived example, the first
+ using a \hs{case} construct and the other using a \hs{if-then-else}
+ constructs, in the code below. The example sums two values when they are
+ equal or non-equal (depending on the predicate given) and returns 0
+ otherwise.
+
\begin{code}
- sumif pred a b = if pred == Eq && a == b ||
- pred == Neq && a != b
- then a + b
- else 0
-
sumif pred a b = case pred of
Eq -> case a == b of
True -> a + b
Neq -> case a != b of
True -> a + b
False -> 0
+ \end{code}
+
+ \begin{code}
+ sumif pred a b =
+ if pred == Eq then
+ if a == b then a + b else 0
+ else
+ if a != b then a + b else 0
+ \end{code}
+ Both versions of the example correspond to the same netlist, which is
+ depicted in \Cref{img:choice}
+
+ \begin{figure}
+ \centerline{\includegraphics{choice-case}}
+ \caption{Choice - sumif}
+ \label{img:choice}
+ \end{figure}
+
+ A slightly more complex (but 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
+ corresponding clause will be used. Expressions can also contain guards,
+ where the expression is only executed if the guard evaluates to true. A
+ pattern match (with optional guards) can be to a conditional assignments
+ in \VHDL, where the conditions are an equality test of the argument and
+ one of the patterns (combined with the guard if was present). A third
+ version of the earlier example, using both pattern matching and guards,
+ can be seen below:
+
+ \begin{code}
sumif Eq a b | a == b = a + b
sumif Neq a b | a != b = a + b
sumif _ _ _ = 0
\end{code}
+
+ The version using pattern matching and guards has the same netlist
+ representation (\Cref{img:choice}) as the earlier two versions of the
+ example.
- \comment{TODO: Pretty picture}
+ % \begin{figure}
+ % \centerline{\includegraphics{choice-ifthenelse}}
+ % \caption{Choice - \emph{if-then-else}}
+ % \label{img:choice}
+ % \end{figure}
\subsection{Types}
Translation of two most basic functional concepts has been
In \CLaSH, unconstrained polymorphism is completely supported. Any
function defined can have any number of unconstrained type
- parameters. The \CLaSH compiler will infer the type of every such
+ parameters. The \CLaSH\ compiler will infer the type of every such
argument depending on how the function is applied. There is one
exception to this: The top level function that is translated, can
not have any polymorphic arguments (since it is never applied, so
there is no way to find out the actual types for the type
parameters).
- \CLaSH does not support user-defined type classes, but does use some
+ \CLaSH\ does not support user-defined type classes, but does use some
of the builtin ones for its builtin functions (like \hs{Num} and
\hs{Eq}).
\end{code}
Finally, higher order arguments are not limited to just builtin
- functions, but any function defined in \CLaSH can have function
+ functions, 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.
projects / matthijs / master-project / dsd-paper.git / blobdiff