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333 % *** Do not adjust lengths that control margins, column widths, etc. ***
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335 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
336 % (Unless specifically asked to do so by the journal or conference you plan
337 % to submit to, of course. )
339 % correct bad hyphenation here
340 \hyphenation{op-tical net-works semi-conduc-tor}
342 % Macro for certain acronyms in small caps. Doesn't work with the
343 % default font, though (it contains no smallcaps it seems).
344 \def\acro#1{{\small{#1}}}
345 \def\VHDL{\acro{VHDL}}
347 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
350 % we'll get something more complex later on.
351 \def\hs#1{\texttt{#1}}
352 \def\quote#1{``{#1}"}
354 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
356 \settowidth{\labelwidth}{#1:}
357 \setlength{\labelsep}{0.5em}
358 \setlength{\leftmargin}{\labelwidth}
359 \addtolength{\leftmargin}{\labelsep}
360 \addtolength{\leftmargin}{\parindent}
361 \setlength{\rightmargin}{0pt}
362 \setlength{\listparindent}{\parindent}
363 \setlength{\itemsep}{0 ex plus 0.2ex}
364 \renewcommand{\makelabel}[1]{##1:\hfil}
369 \usepackage{paralist}
371 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
373 \usepackage{cleveref}
374 \crefname{figure}{figure}{figures}
375 \newcommand{\fref}[1]{\cref{#1}}
376 \newcommand{\Fref}[1]{\Cref{#1}}
378 \usepackage{epstopdf}
380 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
382 %include polycode.fmt
388 % can use linebreaks \\ within to get better formatting as desired
389 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
392 % author names and affiliations
393 % use a multiple column layout for up to three different
395 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
396 \IEEEauthorblockA{Computer Architecture for Embedded Systems (CAES)\\
397 Department of EEMCS, University of Twente\\
398 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
399 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}}
401 % \IEEEauthorblockN{Homer Simpson}
402 % \IEEEauthorblockA{Twentieth Century Fox\\
404 % Email: homer@thesimpsons.com}
406 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
407 % \IEEEauthorblockA{Starfleet Academy\\
408 % San Francisco, California 96678-2391\\
409 % Telephone: (800) 555--1212\\
410 % Fax: (888) 555--1212}}
412 % conference papers do not typically use \thanks and this command
413 % is locked out in conference mode. If really needed, such as for
414 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
415 % after \documentclass
417 % for over three affiliations, or if they all won't fit within the width
418 % of the page, use this alternative format:
420 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
421 %Homer Simpson\IEEEauthorrefmark{2},
422 %James Kirk\IEEEauthorrefmark{3},
423 %Montgomery Scott\IEEEauthorrefmark{3} and
424 %Eldon Tyrell\IEEEauthorrefmark{4}}
425 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
426 %Georgia Institute of Technology,
427 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
428 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
429 %Email: homer@thesimpsons.com}
430 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
431 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
432 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
437 % use for special paper notices
438 %\IEEEspecialpapernotice{(Invited Paper)}
443 % make the title area
449 \CLaSH\ is a functional hardware description language that borrows both its
450 syntax and semantics from the functional programming language Haskell. Circuit
451 descriptions can be translated to synthesizable VHDL using the prototype
452 \CLaSH\ compiler. As the circuit descriptions are made in plain Haskell,
453 simulations can also be compiled by a Haskell compiler.
455 The use of polymorphism and higher-order functions allow a circuit designer to
456 describe more abstract and general specifications than are possible in the
457 traditional hardware description languages.
459 % IEEEtran.cls defaults to using nonbold math in the Abstract.
460 % This preserves the distinction between vectors and scalars. However,
461 % if the conference you are submitting to favors bold math in the abstract,
462 % then you can use LaTeX's standard command \boldmath at the very start
463 % of the abstract to achieve this. Many IEEE journals/conferences frown on
464 % math in the abstract anyway.
471 % For peer review papers, you can put extra information on the cover
473 % \ifCLASSOPTIONpeerreview
474 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
477 % For peerreview papers, this IEEEtran command inserts a page break and
478 % creates the second title. It will be ignored for other modes.
479 \IEEEpeerreviewmaketitle
482 \section{Introduction}
483 Hardware description languages have allowed the productivity of hardware
484 engineers to keep pace with the development of chip technology. Standard
485 Hardware description languages, like \VHDL~\cite{VHDL2008} and
486 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
487 programming language. These standard languages are very good at describing
488 detailed hardware properties such as timing behavior, but are generally
489 cumbersome in expressing higher-level abstractions. In an attempt to raise the
490 abstraction level of the descriptions, a great number of approaches based on
491 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
492 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
493 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
494 a time which also saw the birth of the currently popular hardware description
495 languages such as \VHDL. The merit of using a functional language to describe
496 hardware comes from the fact that combinatorial circuits can be directly
497 modeled as mathematical functions and that functional languages are very good
498 at describing and composing mathematical functions.
500 In an attempt to decrease the amount of work involved with creating all the
501 required tooling, such as parsers and type-checkers, many functional hardware
502 description languages are embedded as a domain specific language inside the
503 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
504 means that a developer is given a library of Haskell~\cite{Haskell} functions
505 and types that together form the language primitives of the domain specific
506 language. As a result of how the signals are modeled and abstracted, the
507 functions used to describe a circuit also build a large domain-specific
508 datatype (hidden from the designer) which can then be processed further by an
509 embedded compiler. This compiler actually runs in the same environment as the
510 description; as a result compile-time and run-time become hard to define, as
511 the embedded compiler is usually compiled by the same Haskell compiler as the
512 circuit description itself.
514 The approach taken in this research is not to make another domain specific
515 language embedded in Haskell, but to use (a subset of) the Haskell language
516 itself for the purpose of describing hardware. By taking this approach, we can
517 capture certain language constructs, such as Haskell's choice elements
518 (if-constructs, case-constructs, pattern matching, etc.), which are not
519 available in the functional hardware description languages that are embedded
520 in Haskell as a domain specific language. As far as the authors know, such
521 extensive support for choice-elements is new in the domain of functional
522 hardware description languages. As the hardware descriptions are plain Haskell
523 functions, these descriptions can be compiled for simulation using an
524 optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC)~\cite{ghc}.
526 Where descriptions in a conventional hardware description language have an
527 explicit clock for the purpose state and synchronicity, the clock is implied
528 in this research. A developer describes the behavior of the hardware between
529 clock cycles. The current abstraction of state and time limits the
530 descriptions to synchronous hardware, there however is room within the
531 language to eventually add a different abstraction mechanism that will allow
532 for the modeling of asynchronous systems. Many functional hardware description
533 model signals as a stream of all values over time; state is then modeled as a
534 delay on this stream of values. The approach taken in this research is to make
535 the current state of a circuit part of the input of the function and the
536 updated state part of the output.
538 Like the standard hardware description languages, descriptions made in a
539 functional hardware description language must eventually be converted into a
540 netlist. This research also features a prototype translator, which has the
541 same name as the language: \CLaSH\footnote{C$\lambda$aSH: CAES Language for
542 Synchronous Hardware} (pronounced: clash). This compiler converts the Haskell
543 code to equivalently behaving synthesizable \VHDL\ code, ready to be converted
544 to an actual netlist format by an (optimizing) \VHDL\ synthesis tool.
546 Besides trivial circuits such as variants of both the FIR filter and the
547 simple CPU shown in \Cref{sec:usecases}, the \CLaSH\ compiler has also been
548 shown to work for non-trivial descriptions. \CLaSH\ has been able to
549 successfully translate the functional description of a streaming reduction
550 circuit~\cite{reductioncircuit} for floating point numbers.
552 \section{Hardware description in Haskell}
554 \subsection{Function application}
555 The basic syntactic elements of a functional program are functions
556 and function application. These have a single obvious translation to a
559 \item every function is translated to a component,
560 \item every function argument is translated to an input port,
561 \item the result value of a function is translated to an output port,
563 \item function applications are translated to component instantiations.
565 The output port can have a complex type (such as a tuple), so having just
566 a single output port does not pose any limitation. The arguments of a
567 function applications are assigned to a signal, which are then mapped to
568 the corresponding input ports of the component. The output port of the
569 function is also mapped to a signal, which is used as the result of the
572 Since every top level function generates its own component, the
573 hierarchy of function calls is reflected in the final netlist,% aswell,
574 creating a hierarchical description of the hardware. This separation in
575 different components makes the resulting \VHDL\ output easier to read and
578 As an example we can see the netlist of the |mac| function in
579 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
580 function to calculate $a * b + c$:
583 mac a b c = add (mul a b) c
587 \centerline{\includegraphics{mac.svg}}
588 \caption{Combinatorial Multiply-Accumulate}
592 The result of using a complex input type can be seen in
593 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
594 input tuple for the |a|, |b|, and |c| arguments:
597 mac (a, b, c) = add (mul a b) c
601 \centerline{\includegraphics{mac-nocurry.svg}}
602 \caption{Combinatorial Multiply-Accumulate (complex input)}
603 \label{img:mac-comb-nocurry}
607 In Haskell, choice can be achieved by a large set of language constructs,
608 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
609 pattern matching, and guards. The easiest of these are the \hs{case}
610 constructs (\hs{if} expressions can be very directly translated to
611 \hs{case} expressions). A \hs{case} construct is translated to a
612 multiplexer, where the control value is linked to the selection port and
613 the output of each case is linked to the corresponding input port on the
615 % A \hs{case} expression can in turn simply be translated to a conditional
616 % assignment in \VHDL, where the conditions use equality comparisons
617 % against the constructors in the \hs{case} expressions.
618 We can see two versions of a contrived example below, the first
619 using a \hs{case} construct and the other using a \hs{if-then-else}
620 constructs, in the code below.
623 sumif pred a b = case pred of
627 Neq -> case a != b of
635 if a == b then a + b else 0
637 if a != b then a + b else 0
641 \centerline{\includegraphics{choice-case.svg}}
642 \caption{Choice - sumif}
646 The example sums two values when they are equal or non-equal (depending on
647 the predicate given) and returns 0 otherwise. Both versions of the example
648 roughly correspond to the same netlist, which is depicted in
651 A slightly more complex (but very powerful) form of choice is pattern
652 matching. A function can be defined in multiple clauses, where each clause
653 specifies a pattern. When the arguments match the pattern, the
654 corresponding clause will be used. Expressions can also contain guards,
655 where the expression is only executed if the guard evaluates to true. Like
656 \hs{if-then-else} constructs, pattern matching and guards have a
657 (straightforward) translation to \hs{case} constructs and can as such be
658 mapped to multiplexers. A third version of the earlier example, using both
659 pattern matching and guards, can be seen below. The version using pattern
660 matching and guards also has roughly the same netlist representation
661 (\Cref{img:choice}) as the earlier two versions of the example.
664 sumif Eq a b | a == b = a + b
666 sumif Neq a b | a != b = a + b
671 % \centerline{\includegraphics{choice-ifthenelse}}
672 % \caption{Choice - \emph{if-then-else}}
677 Haskell is a statically-typed language, meaning that the type of a
678 variable or function is determined at compile-time. Not all of Haskell's
679 typing constructs have a clear translation to hardware, as such this
680 section will only deal with the types that do have a clear correspondence
681 to hardware. The translatable types are divided into two categories:
682 \emph{built-in} types and \emph{user-defined} types. Built-in types are
683 those types for which a direct translation is defined within the \CLaSH\
684 compiler; the term user-defined types should not require any further
685 elaboration. The translatable types are also inferable by the compiler,
686 meaning that a developer does not have to annotate every function with a
689 % Translation of two most basic functional concepts has been
690 % discussed: function application and choice. Before looking further
691 % into less obvious concepts like higher-order expressions and
692 % polymorphism, the possible types that can be used in hardware
693 % descriptions will be discussed.
695 % Some way is needed to translate every value used to its hardware
696 % equivalents. In particular, this means a hardware equivalent for
697 % every \emph{type} used in a hardware description is needed.
699 % The following types are \emph{built-in}, meaning that their hardware
700 % translation is fixed into the \CLaSH\ compiler. A designer can also
701 % define his own types, which will be translated into hardware types
702 % using translation rules that are discussed later on.
704 \subsubsection{Built-in types}
705 The following types have direct translation defined within the \CLaSH\
709 This is the most basic type available. It can have two values:
710 \hs{Low} and \hs{High}.
711 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
713 This is a basic logic type. It can have two values: \hs{True}
715 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
716 % type (where a value of \hs{True} corresponds to a value of
718 Supporting the Bool type is required in order to support the
719 \hs{if-then-else} construct, which requires a \hs{Bool} value for
721 \item[\bf{SizedWord}, \bf{SizedInt}]
722 These are types to represent integers. A \hs{SizedWord} is unsigned,
723 while a \hs{SizedInt} is signed. Both are parametrizable in their
725 % , so you can define an unsigned word of 32 bits wide as follows:
728 % type Word32 = SizedWord D32
731 % Here, a type synonym \hs{Word32} is defined that is equal to the
732 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
733 % \hs{D32} is the \emph{type level representation} of the decimal
734 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
735 % types are translated to the \VHDL\ \texttt{unsigned} and
736 % \texttt{signed} respectively.
738 This is a vector type that can contain elements of any other type and
739 has a fixed length. The \hs{Vector} type constructor takes two type
740 arguments: the length of the vector and the type of the elements
741 contained in it. The short-hand notation used for the vector type in
742 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
743 type, and \hs{n} is the length of the vector.
744 % The state type of an 8 element register bank would then for example
748 % type RegisterState = Vector D8 Word32
751 % Here, a type synonym \hs{RegisterState} is defined that is equal to
752 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
753 % type level representation of the decimal number 8) and \hs{Word32}
754 % (The 32 bit word type as defined above). In other words, the
755 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
756 % vector is translated to a \VHDL\ array type.
758 This is another type to describe integers, but unlike the previous
759 two it has no specific bit-width, but an upper bound. This means that
760 its range is not limited to powers of two, but can be any number.
761 An \hs{Index} only has an upper bound, its lower bound is
762 implicitly zero. The main purpose of the \hs{Index} type is to be
763 used as an index to a \hs{Vector}.
765 % \comment{TODO: Perhaps remove this example?} To define an index for
766 % the 8 element vector above, we would do:
769 % type RegisterIndex = RangedWord D7
772 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
773 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
774 % other words, this defines an unsigned word with values from
775 % 0 to 7 (inclusive). This word can be be used to index the
776 % 8 element vector \hs{RegisterState} above. This type is translated
777 % to the \texttt{unsigned} \VHDL type.
780 \subsubsection{User-defined types}
781 There are three ways to define new types in Haskell: algebraic
782 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
783 keyword and datatype renaming constructs with the \hs{newtype} keyword.
784 \GHC\ offers a few more advanced ways to introduce types (type families,
785 existential typing, {\small{GADT}}s, etc.) which are not standard Haskell.
786 As it is currently unclear how these advanced type constructs correspond
787 with hardware, they are for now unsupported by the \CLaSH\ compiler
789 Only an algebraic datatype declaration actually introduces a
790 completely new type. Type synonyms and renaming constructs only define new
791 names for existing types, where synonyms are completely interchangeable
792 and renaming constructs need explicit conversions. Therefore, these do not
793 need any particular translation, a synonym or renamed type will just use
794 the same representation as the original type. For algebraic types, we can
795 make the following distinctions:
798 \item[\bf{Single constructor}]
799 Algebraic datatypes with a single constructor with one or more
800 fields, are essentially a way to pack a few values together in a
801 record-like structure. Haskell's built-in tuple types are also defined
802 as single constructor algebraic types An example of a single
803 constructor type is the following pair of integers:
805 data IntPair = IntPair Int Int
807 % These types are translated to \VHDL\ record types, with one field
808 % for every field in the constructor.
809 \item[\bf{No fields}]
810 Algebraic datatypes with multiple constructors, but without any
811 fields are essentially a way to get an enumeration-like type
812 containing alternatives. Note that Haskell's \hs{Bool} type is also
813 defined as an enumeration type, but we have a fixed translation for
814 that. An example of such an enum type is the type that represents the
815 colors in a traffic light:
817 data TrafficLight = Red | Orange | Green
819 % These types are translated to \VHDL\ enumerations, with one
820 % value for each constructor. This allows references to these
821 % constructors to be translated to the corresponding enumeration
823 \item[\bf{Multiple constructors with fields}]
824 Algebraic datatypes with multiple constructors, where at least
825 one of these constructors has one or more fields are currently not
829 \subsection{Polymorphism}
830 A powerful construct in most functional languages is polymorphism, it
831 allows a function to handle values of different data types in a uniform
832 way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
833 meaning functions can be written without mention of any specific type and
834 can be used transparently with any number of new types.
836 As an example of a parametric polymorphic function, consider the type of
837 the following \hs{append} function, which appends an element to a vector:
839 append :: [a|n] -> a -> [a|n + 1]
842 This type is parameterized by \hs{a}, which can contain any type at
843 all. This means that \hs{append} can append an element to a vector,
844 regardless of the type of the elements in the list (as long as the type of
845 the value to be added is of the same type as the values in the vector).
846 This kind of polymorphism is extremely useful in hardware designs to make
847 operations work on a vector without knowing exactly what elements are
848 inside, routing signals without knowing exactly what kinds of signals
849 these are, or working with a vector without knowing exactly how long it
850 is. Polymorphism also plays an important role in most higher order
851 functions, as we will see in the next section.
853 Another type of polymorphism is \emph{ad-hoc
854 polymorphism}~\cite{polymorphism}, which refers to polymorphic
855 functions which can be applied to arguments of different types, but which
856 behave differently depending on the type of the argument to which they are
857 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
858 type classes, where a class definition provides the general interface of a
859 function, and class instances define the functionality for the specific
860 types. An example of such a type class is the \hs{Num} class, which
861 contains all of Haskell's numerical operations. A developer can make use
862 of this ad-hoc polymorphism by adding a constraint to a parametrically
863 polymorphic type variable. Such a constraint indicates that the type
864 variable can only be instantiated to a type whose members supports the
865 overloaded functions associated with the type class.
867 As an example we will take a look at type signature of the function
868 \hs{sum}, which sums the values in a vector:
870 sum :: Num a => [a|n] -> a
873 This type is again parameterized by \hs{a}, but it can only contain
874 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
875 we know that the addition (+) operator is defined for that type.
876 \CLaSH's built-in numerical types are also instances of the \hs{Num}
877 class, so we can use the addition operator on \hs{SizedWords} as
878 well as on \hs{SizedInts}.
880 In \CLaSH, parametric polymorphism is completely supported. Any function
881 defined can have any number of unconstrained type parameters. The \CLaSH\
882 compiler will infer the type of every such argument depending on how the
883 function is applied. There is one exception to this: The top level
884 function that is translated, can not have any polymorphic arguments (as
885 they are never applied, so there is no way to find out the actual types
886 for the type parameters).
888 \CLaSH\ does not support user-defined type classes, but does use some
889 of the built-in type classes for its built-in function, such as: \hs{Num}
890 for numerical operations, \hs{Eq} for the equality operators, and
891 \hs{Ord} for the comparison/order operators.
893 \subsection{Higher-order functions \& values}
894 Another powerful abstraction mechanism in functional languages, is
895 the concept of \emph{higher-order functions}, or \emph{functions as
896 a first class value}. This allows a function to be treated as a
897 value and be passed around, even as the argument of another
898 function. The following example should clarify this concept:
901 negVector xs = map not xs
904 The code above defines a function \hs{negVector}, which takes a vector of
905 booleans, and returns a vector where all the values are negated. It
906 achieves this by calling the \hs{map} function, and passing it
907 \emph{another function}, boolean negation, and the vector of booleans,
908 \hs{xs}. The \hs{map} function applies the negation function to all the
909 elements in the vector.
911 The \hs{map} function is called a higher-order function, since it takes
912 another function as an argument. Also note that \hs{map} is again a
913 parametric polymorphic function: It does not pose any constraints on the
914 type of the vector elements, other than that it must be the same type as
915 the input type of the function passed to \hs{map}. The element type of the
916 resulting vector is equal to the return type of the function passed, which
917 need not necessarily be the same as the element type of the input vector.
918 All of these characteristics can readily be inferred from the type
919 signature belonging to \hs{map}:
922 map :: (a -> b) -> [a|n] -> [b|n]
925 So far, only functions have been used as higher-order values. In
926 Haskell, there are two more ways to obtain a function-typed value:
927 partial application and lambda abstraction. Partial application
928 means that a function that takes multiple arguments can be applied
929 to a single argument, and the result will again be a function (but
930 that takes one argument less). As an example, consider the following
931 expression, that adds one to every element of a vector:
937 Here, the expression \hs{(+) 1} is the partial application of the
938 plus operator to the value \hs{1}, which is again a function that
939 adds one to its argument. A lambda expression allows one to introduce an
940 anonymous function in any expression. Consider the following expression,
941 which again adds one to every element of a vector:
947 Finally, higher order arguments are not limited to just built-in
948 functions, but any function defined in \CLaSH\ can have function
949 arguments. This allows the hardware designer to use a powerful
950 abstraction mechanism in his designs and have an optimal amount of
953 \comment{TODO: Describe ALU example (no code)}
956 A very important concept in hardware it the concept of state. In a
957 stateful design, the outputs depend on the history of the inputs, or the
958 state. State is usually stored in registers, which retain their value
959 during a clock cycle. As we want to describe more than simple
960 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
962 An important property in Haskell, and in most other functional languages,
963 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
966 \item given the same arguments twice, it should return the same value in
968 \item when the function is called, it should not have observable
971 % This purity property is important for functional languages, since it
972 % enables all kinds of mathematical reasoning that could not be guaranteed
973 % correct for impure functions.
974 Pure functions are as such a perfect match or a combinatorial circuit,
975 where the output solely depends on the inputs. When a circuit has state
976 however, it can no longer be simply described by a pure function.
977 % Simply removing the purity property is not a valid option, as the
978 % language would then lose many of it mathematical properties.
979 In an effort to include the concept of state in pure
980 functions, the current value of the state is made an argument of the
981 function; the updated state becomes part of the result. In this sense the
982 descriptions made in \CLaSH are the describing the combinatorial parts of
985 A simple example is adding an accumulator register to the earlier
986 multiply-accumulate circuit, of which the resulting netlist can be seen in
987 \Cref{img:mac-state}:
990 macS (State c) a b = (State c', outp)
997 \centerline{\includegraphics{mac-state.svg}}
998 \caption{Stateful Multiply-Accumulate}
999 \label{img:mac-state}
1002 The \hs{State} keyword indicates which arguments are part of the current
1003 state, and what part of the output is part of the updated state. This
1004 aspect will also reflected in the type signature of the function.
1005 Abstracting the state of a circuit in this way makes it very explicit:
1006 which variables are part of the state is completely determined by the
1007 type signature. This approach to state is well suited to be used in
1008 combination with the existing code and language features, such as all the
1009 choice constructs, as state values are just normal values. We can simulate
1010 stateful descriptions using the recursive \hs{run} function:
1013 run f s (i:inps) = o : (run f s' inps)
1018 The \hs{run} function maps a list of inputs over the function that a
1019 developer wants to simulate, passing the state to each new iteration. Each
1020 value in the input list corresponds to exactly one cycle of the (implicit)
1021 clock. The result of the simulation is a list of outputs for every clock
1022 cycle. As both the \hs{run} function and the hardware description are
1023 plain Haskell, the complete simulation can be compiled by an optimizing
1026 \section{\CLaSH\ prototype}
1028 The \CLaSH\ language as presented above can be translated to \VHDL\ using
1029 the prototype \CLaSH\ compiler. This compiler allows experimentation with
1030 the \CLaSH\ language and allows for running \CLaSH\ designs on actual FPGA
1034 \centerline{\includegraphics{compilerpipeline.svg}}
1035 \caption{\CLaSH\ compiler pipeline}
1036 \label{img:compilerpipeline}
1039 The prototype heavily uses \GHC, the Glasgow Haskell Compiler.
1040 \Cref{img:compilerpipeline} shows the \CLaSH\ compiler pipeline. As you can
1041 see, the front-end is completely reused from \GHC, which allows the \CLaSH\
1042 prototype to support most of the Haskell Language. The \GHC\ front-end
1043 produces the program in the \emph{Core} format, which is a very small,
1044 functional, typed language which is relatively easy to process.
1046 The second step in the compilation process is \emph{normalization}. This
1047 step runs a number of \emph{meaning preserving} transformations on the
1048 Core program, to bring it into a \emph{normal form}. This normal form
1049 has a number of restrictions that make the program similar to hardware.
1050 In particular, a program in normal form no longer has any polymorphism
1051 or higher order functions.
1053 The final step is a simple translation to \VHDL.
1056 \label{sec:usecases}
1057 As an example of a common hardware design where the use of higher-order
1058 functions leads to a very natural description is a FIR filter, which is
1059 basically the dot-product of two vectors:
1062 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1065 A FIR filter multiplies fixed constants ($h$) with the current
1066 and a few previous input samples ($x$). Each of these multiplications
1067 are summed, to produce the result at time $t$. The equation of a FIR
1068 filter is indeed equivalent to the equation of the dot-product, which is
1072 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
1075 We can easily and directly implement the equation for the dot-product
1076 using higher-order functions:
1079 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
1082 The \hs{zipWith} function is very similar to the \hs{map} function seen
1083 earlier: It takes a function, two vectors, and then applies the function to
1084 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1085 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
1087 The \hs{foldl1} function takes a function, a single vector, and applies
1088 the function to the first two elements of the vector. It then applies the
1089 function to the result of the first application and the next element from
1090 the vector. This continues until the end of the vector is reached. The
1091 result of the \hs{foldl1} function is the result of the last application.
1092 As you can see, the \hs{zipWith (*)} function is just pairwise
1093 multiplication and the \hs{foldl1 (+)} function is just summation.
1095 Returning to the actual FIR filter, we will slightly change the
1096 equation belong to it, so as to make the translation to code more obvious.
1097 What we will do is change the definition of the vector of input samples.
1098 So, instead of having the input sample received at time
1099 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1100 stores the $ith$ previous sample. This changes the equation to the
1101 following (Note that this is completely equivalent to the original
1102 equation, just with a different definition of $x$ that will better suit
1103 the transformation to code):
1106 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1109 Consider that the vector \hs{hs} contains the FIR coefficients and the
1110 vector \hs{xs} contains the current input sample in front and older
1111 samples behind. The function that shifts the input samples is shown below:
1114 x >> xs = x +> tail xs
1117 Where the \hs{tail} function returns all but the first element of a
1118 vector, and the concatenate operator ($\succ$) adds a new element to the
1119 left of a vector. The complete definition of the FIR filter then becomes:
1122 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1125 The resulting netlist of a 4-taps FIR filter based on the above definition
1126 is depicted in \Cref{img:4tapfir}.
1129 \centerline{\includegraphics{4tapfir.svg}}
1130 \caption{4-taps FIR Filter}
1134 \section{Related work}
1135 Many functional hardware description languages have been developed over the
1136 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1137 extension of Backus' \acro{FP} language to synchronous streams, designed
1138 particularly for describing and reasoning about regular circuits. The
1139 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1140 circuits, and has a particular focus on layout.
1142 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1143 functional language \acro{ML}, and has support for polymorphic types and
1144 higher-order functions. Published work suggests that there is no direct
1145 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1146 be translated to \VHDL\ and that the translated description can than be
1147 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1148 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1149 on the other hand can correctly translate all of the language constructs
1150 mentioned in this paper to a netlist format.
1152 Like this work, many functional hardware description languages have some sort
1153 of foundation in the functional programming language Haskell.
1154 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1155 specifications used to model the behavior of superscalar microprocessors. Hawk
1156 specifications can be simulated, but there seems to be no support for
1157 automated circuit synthesis.
1159 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1160 models, which can (manually) be transformed into an implementation model using
1161 semantic preserving transformations. A designer can model systems using
1162 heterogeneous models of computation, which include continuous time,
1163 synchronous and untimed models of computation. Using so-called domain
1164 interfaces a designer can simulate electronic systems which have both analog
1165 as digital parts. ForSyDe has several backends including simulation and
1166 automated synthesis, though automated synthesis is restricted to the
1167 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1168 support for the automated synthesis of descriptions that contain polymorphism
1169 or higher-order functions.
1171 Lava~\cite{Lava} is a hardware description language that focuses on the
1172 structural representation of hardware. Besides support for simulation and
1173 circuit synthesis, Lava descriptions can be interfaced with formal method
1174 tools for formal verification. Lava descriptions are actually circuit
1175 generators when viewed from a synthesis viewpoint, in that the language
1176 elements of Haskell, such as choice, can be used to guide the circuit
1177 generation. If a developer wants to insert a choice element inside an actual
1178 circuit he will have to explicitly instantiate a multiplexer-like component.
1180 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1181 such as case-statements and pattern matching, are synthesized to choice
1182 elements in the eventual circuit. As such, richer control structures can both
1183 be specified and synthesized in \CLaSH\ compared to any of the languages
1184 mentioned in this section.
1186 The merits of polymorphic typing, combined with higher-order functions, are
1187 now also recognized in the `main-stream' hardware description languages,
1188 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to types, allowing a developer to describe
1189 polymorphic components. Note that those types still require an explicit
1190 generic map, whereas types can be automatically inferred in \CLaSH.
1192 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1194 % A functional language designed specifically for hardware design is
1195 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1196 % language called \acro{FL}~\cite{FL} to la
1198 % An example of a floating figure using the graphicx package.
1199 % Note that \label must occur AFTER (or within) \caption.
1200 % For figures, \caption should occur after the \includegraphics.
1201 % Note that IEEEtran v1.7 and later has special internal code that
1202 % is designed to preserve the operation of \label within \caption
1203 % even when the captionsoff option is in effect. However, because
1204 % of issues like this, it may be the safest practice to put all your
1205 % \label just after \caption rather than within \caption{}.
1207 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1208 % option should be used if it is desired that the figures are to be
1209 % displayed while in draft mode.
1213 %\includegraphics[width=2.5in]{myfigure}
1214 % where an .eps filename suffix will be assumed under latex,
1215 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1216 % via \DeclareGraphicsExtensions.
1217 %\caption{Simulation Results}
1221 % Note that IEEE typically puts floats only at the top, even when this
1222 % results in a large percentage of a column being occupied by floats.
1225 % An example of a double column floating figure using two subfigures.
1226 % (The subfig.sty package must be loaded for this to work.)
1227 % The subfigure \label commands are set within each subfloat command, the
1228 % \label for the overall figure must come after \caption.
1229 % \hfil must be used as a separator to get equal spacing.
1230 % The subfigure.sty package works much the same way, except \subfigure is
1231 % used instead of \subfloat.
1233 %\begin{figure*}[!t]
1234 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1235 %\label{fig_first_case}}
1237 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1238 %\label{fig_second_case}}}
1239 %\caption{Simulation results}
1243 % Note that often IEEE papers with subfigures do not employ subfigure
1244 % captions (using the optional argument to \subfloat), but instead will
1245 % reference/describe all of them (a), (b), etc., within the main caption.
1248 % An example of a floating table. Note that, for IEEE style tables, the
1249 % \caption command should come BEFORE the table. Table text will default to
1250 % \footnotesize as IEEE normally uses this smaller font for tables.
1251 % The \label must come after \caption as always.
1254 %% increase table row spacing, adjust to taste
1255 %\renewcommand{\arraystretch}{1.3}
1256 % if using array.sty, it might be a good idea to tweak the value of
1257 % \extrarowheight as needed to properly center the text within the cells
1258 %\caption{An Example of a Table}
1259 %\label{table_example}
1261 %% Some packages, such as MDW tools, offer better commands for making tables
1262 %% than the plain LaTeX2e tabular which is used here.
1263 %\begin{tabular}{|c||c|}
1273 % Note that IEEE does not put floats in the very first column - or typically
1274 % anywhere on the first page for that matter. Also, in-text middle ("here")
1275 % positioning is not used. Most IEEE journals/conferences use top floats
1276 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1277 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1278 % command of the stfloats package.
1282 \section{Conclusion}
1283 The conclusion goes here.
1288 % conference papers do not normally have an appendix
1291 % use section* for acknowledgement
1292 \section*{Acknowledgment}
1295 The authors would like to thank...
1301 % trigger a \newpage just before the given reference
1302 % number - used to balance the columns on the last page
1303 % adjust value as needed - may need to be readjusted if
1304 % the document is modified later
1305 %\IEEEtriggeratref{8}
1306 % The "triggered" command can be changed if desired:
1307 %\IEEEtriggercmd{\enlargethispage{-5in}}
1309 % references section
1311 % can use a bibliography generated by BibTeX as a .bbl file
1312 % BibTeX documentation can be easily obtained at:
1313 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1314 % The IEEEtran BibTeX style support page is at:
1315 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1316 \bibliographystyle{IEEEtran}
1317 % argument is your BibTeX string definitions and bibliography database(s)
1318 \bibliography{clash}
1320 % <OR> manually copy in the resultant .bbl file
1321 % set second argument of \begin to the number of references
1322 % (used to reserve space for the reference number labels box)
1323 % \begin{thebibliography}{1}
1325 % \bibitem{IEEEhowto:kopka}
1326 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1327 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1329 % \end{thebibliography}
1337 % vim: set ai sw=2 sts=2 expandtab: