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
+ The output port can have a structured type (such as a tuple), so having
+ just a single output port does not pose any limitation. The arguments of a
function application are assigned to signals, which are then mapped to
the corresponding input ports of the component. The output port of the
function is also mapped to a signal, which is used as the result of the
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|
\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:
\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}
+ pattern matching, and guards. The most general of these are the \hs{case}
constructs (\hs{if} expressions can be very directly translated to
\hs{case} expressions). A \hs{case} construct is translated to a
multiplexer, where the control value is linked to the selection port and
% 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.
+ using a \hs{case} construct and the other using an \hs{if-then-else}
+ construct, in the code below. The examples sums two values when they are
+ equal or non-equal (depending on the given predicate, the \hs{pred}
+ variable) and returns 0 otherwise. The \hs{pred} variable has the
+ following, user-defined, enumeration datatype:
\begin{code}
+ data Pred = Equiv | NotEquiv
+ \end{code}
+
+ The naive netlist corresponding to both versions of the example is
+ depicted in \Cref{img:choice}.
+
+ \begin{code}
sumif pred a b = case pred of
- Eq -> case a == b of
- True -> a + b
- False -> 0
- Neq -> case a != b of
- True -> a + b
- False -> 0
+ Equiv -> case a == b of
+ True -> a + b
+ False -> 0
+ NotEquiv -> case a != b of
+ True -> a + b
+ False -> 0
\end{code}
\begin{code}
\caption{Choice - sumif}
\label{img:choice}
\end{figure}
-
- 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}.
- 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
+ where the expression is only executed if the guard evaluates to true, and
+ continues with the next clause if the guard evaluates to false. Like
\hs{if-then-else} constructs, pattern matching and guards have a
(straightforward) translation to \hs{case} constructs and can as such be
mapped to multiplexers. A third version of the earlier example, using both
- pattern matching and guards, can be seen below. The 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
\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
+ therefor only deal with the types that do have a clear correspondence
to hardware. The translatable types are divided into two categories:
\emph{built-in} types and \emph{user-defined} types. Built-in types are
those types for which a direct translation is defined within the \CLaSH\
% 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 direct translations defined within the \CLaSH\
compiler:
\begin{xlist}
\item[\bf{Bit}]
- This is the most basic type available. It can have two values:
- \hs{Low} and \hs{High}.
+ the most basic type available. It can have two values:
+ \hs{Low} or \hs{High}.
% It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
\item[\bf{Bool}]
- This is a basic logic type. It can have two values: \hs{True}
- and \hs{False}.
+ this is a basic logic type. It can have two values: \hs{True}
+ or \hs{False}.
% It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
% type (where a value of \hs{True} corresponds to a value of
% \hs{High}).
\hs{if-then-else} construct, which requires a \hs{Bool} value for
the condition.
\item[\bf{SizedWord}, \bf{SizedInt}]
- These are types to represent integers. A \hs{SizedWord} is unsigned,
+ these are types to represent integers. A \hs{SizedWord} is unsigned,
while a \hs{SizedInt} is signed. Both are parametrizable in their
size.
% , so you can define an unsigned word of 32 bits wide as follows:
% types are translated to the \VHDL\ \texttt{unsigned} and
% \texttt{signed} respectively.
\item[\bf{Vector}]
- This is a vector type that can contain elements of any other type and
+ this is a vector type that can contain elements of any other type and
has a fixed length. The \hs{Vector} type constructor takes two type
arguments: the length of the vector and the type of the elements
contained in it. The short-hand notation used for the vector type in
% \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 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 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}
\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:
+
\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
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 they are never applied and
+ consequently there is no way to determine the actual types for the type
+ parameters.
\CLaSH\ does not support user-defined type classes, but does use some
- of the 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 \& values}
projects / matthijs / master-project / dsd-paper.git / blobdiff