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337 % (Unless specifically asked to do so by the journal or conference you plan
338 % to submit to, of course. )
340 % correct bad hyphenation here
341 \hyphenation{op-tical net-works semi-conduc-tor}
343 % Macro for certain acronyms in small caps. Doesn't work with the
344 % default font, though (it contains no smallcaps it seems).
345 \def\acro#1{{\small{#1}}}
346 \def\acrotiny#1{{\scriptsize{#1}}}
347 \def\VHDL{\acro{VHDL}}
349 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
350 \def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}}
352 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
353 % we'll get something more complex later on.
354 \def\hs#1{\texttt{#1}}
355 \def\quote#1{``{#1}"}
357 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
359 \settowidth{\labelwidth}{#1:}
360 \setlength{\labelsep}{0.5em}
361 \setlength{\leftmargin}{\labelwidth}
362 \addtolength{\leftmargin}{\labelsep}
363 \addtolength{\leftmargin}{\parindent}
364 \setlength{\rightmargin}{0pt}
365 \setlength{\listparindent}{\parindent}
366 \setlength{\itemsep}{0 ex plus 0.2ex}
367 \renewcommand{\makelabel}[1]{##1:\hfil}
372 \usepackage{paralist}
374 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
376 \usepackage{cleveref}
377 \crefname{figure}{figure}{figures}
378 \newcommand{\fref}[1]{\cref{#1}}
379 \newcommand{\Fref}[1]{\Cref{#1}}
381 \usepackage{epstopdf}
383 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
385 %include polycode.fmt
391 % can use linebreaks \\ within to get better formatting as desired
392 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
395 % author names and affiliations
396 % use a multiple column layout for up to three different
398 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
399 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
400 Department of EEMCS, University of Twente\\
401 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
402 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}
403 \thanks{Supported through the FP7 project: S(o)OS (248465)}
406 % \IEEEauthorblockN{Homer Simpson}
407 % \IEEEauthorblockA{Twentieth Century Fox\\
409 % Email: homer@thesimpsons.com}
411 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
412 % \IEEEauthorblockA{Starfleet Academy\\
413 % San Francisco, California 96678-2391\\
414 % Telephone: (800) 555--1212\\
415 % Fax: (888) 555--1212}}
417 % conference papers do not typically use \thanks and this command
418 % is locked out in conference mode. If really needed, such as for
419 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
420 % after \documentclass
422 % for over three affiliations, or if they all won't fit within the width
423 % of the page, use this alternative format:
425 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
426 %Homer Simpson\IEEEauthorrefmark{2},
427 %James Kirk\IEEEauthorrefmark{3},
428 %Montgomery Scott\IEEEauthorrefmark{3} and
429 %Eldon Tyrell\IEEEauthorrefmark{4}}
430 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
431 %Georgia Institute of Technology,
432 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
433 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
434 %Email: homer@thesimpsons.com}
435 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
436 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
437 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
442 % use for special paper notices
443 %\IEEEspecialpapernotice{(Invited Paper)}
448 % make the title area
453 \CLaSH\ is a functional hardware description language that borrows both its
454 syntax and semantics from the functional programming language Haskell. Due to
455 the abstraction and generality offered by polymorphism and higher-order
456 functions, a circuit designer can describe circuits in a more natural way than
457 he could in the traditional hardware description languages.
459 Circuit descriptions can be translated to synthesizable VHDL using the
460 prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
461 test input are also valid Haskell, complete simulations can be compiled to an
462 executable binary by a Haskell compiler allowing high-speed simulation and
465 Stateful descriptions are supported by explicitly making the current state an
466 argument of the function, and the updated state part of the result. In this
467 sense, the descriptions made in \CLaSH\ are the combinational parts of a mealy
470 % IEEEtran.cls defaults to using nonbold math in the Abstract.
471 % This preserves the distinction between vectors and scalars. However,
472 % if the conference you are submitting to favors bold math in the abstract,
473 % then you can use LaTeX's standard command \boldmath at the very start
474 % of the abstract to achieve this. Many IEEE journals/conferences frown on
475 % math in the abstract anyway.
482 % For peer review papers, you can put extra information on the cover
484 % \ifCLASSOPTIONpeerreview
485 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
488 % For peerreview papers, this IEEEtran command inserts a page break and
489 % creates the second title. It will be ignored for other modes.
490 \IEEEpeerreviewmaketitle
492 \section{Introduction}
493 Hardware description languages have allowed the productivity of hardware
494 engineers to keep pace with the development of chip technology. Standard
495 Hardware description languages, like \VHDL~\cite{VHDL2008} and
496 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
497 programming language. These standard languages are very good at describing
498 detailed hardware properties such as timing behavior, but are generally
499 cumbersome in expressing higher-level abstractions. In an attempt to raise the
500 abstraction level of the descriptions, a great number of approaches based on
501 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
502 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
503 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
504 a time which also saw the birth of the currently popular hardware description
505 languages such as \VHDL. Functional languages are especially suited to
506 describe hardware because combinational circuits can be directly modeled
507 as mathematical functions. Furthermore, functional languages are very good at
508 describing and composing mathematical functions.
510 In an attempt to decrease the amount of work involved in creating all the
511 required tooling, such as parsers and type-checkers, many functional
512 hardware description languages \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}
513 are embedded as a domain specific language inside the functional
514 language Haskell \cite{Haskell}. This means that a developer is given a
515 library of Haskell functions and types that together form the language
516 primitives of the domain specific language. The primitive functions used
517 to describe a circuit do not actually process any signals, but instead
518 compose a large domain-specific datatype (which is usually hidden from
519 the designer). This datatype is then further processed by an embedded
520 circuit compiler. This circuit compiler actually runs in the same
521 environment as the description; as a result compile-time and run-time
522 become hard to define, as the embedded circuit compiler is usually
523 compiled by the same Haskell compiler as the circuit description itself.
525 The approach taken in this research is not to make another domain specific
526 language embedded in Haskell, but to use (a subset of) the Haskell language
527 \emph{itself} for the purpose of describing hardware. By taking this approach,
528 we can capture certain language constructs, such as Haskell's choice elements
529 (if-expressions, case-expressions, pattern matching, etc.), which are not
530 available in the functional hardware description languages that are embedded
531 in Haskell as a domain specific language. As far as the authors know, such
532 extensive support for choice-elements is new in the domain of functional
533 hardware description languages. As the hardware descriptions are plain Haskell
534 functions, these descriptions can be compiled to an executable binary
535 for simulation using an optimizing Haskell compiler such as the Glasgow
536 Haskell Compiler (\GHC)~\cite{ghc}.
538 Where descriptions in a conventional hardware description language have an
539 explicit clock for the purposes state and synchronicity, in the research
540 presented in this paper the clock is implied. A developer describes the
541 behavior of the hardware between clock cycles. Many functional hardware
542 description model signals as a stream of all values over time; state is then
543 modeled as a delay on this stream of values. The approach taken in this
544 research is to make the current state of a circuit part of the input of the
545 function and the updated state part of the output. The current abstraction of
546 state and time limits the descriptions to synchronous hardware, there however
547 is room within the language to eventually add a different abstraction
548 mechanism that will allow for the modeling of asynchronous systems.
550 Like the standard hardware description languages, descriptions made in a
551 functional hardware description language must eventually be converted into a
552 netlist. This research also features a prototype translator, which has the
553 same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES}
554 Language for Synchronous Hardware} (pronounced: clash). This compiler converts
555 the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to
556 be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis
559 Besides trivial circuits such as variants of both the \acro{FIR} filter and
560 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
561 also been shown to work for non-trivial descriptions. \CLaSH\ has been able to
562 successfully translate the functional description of a streaming reduction
563 circuit~\cite{reductioncircuit} for floating point numbers.
565 \section{Hardware description in Haskell}
567 \subsection{Function application}
568 Two basic syntactic elements of a functional program are functions
569 and function application. These have a single obvious translation to a
572 \item every function is translated to a component,
573 \item every function argument is translated to an input port,
574 \item the result value of a function is translated to an output port,
576 \item function applications are translated to component instantiations.
578 The result value can have a composite type (such as a tuple), so having
579 just a single result value does not pose any limitation. The actual
580 arguments of a function application are assigned to signals, which are
581 then mapped to the corresponding input ports of the component. The output
582 port of the function is also mapped to a signal, which is used as the
583 result of the application itself. Since every top level function generates
584 its own component, the hierarchy of function calls is reflected in the
585 final netlist, creating a hierarchical description of the hardware.
586 % The separation in different components makes it easier for a developer
587 % to understand and possibly hand-optimize the resulting \VHDL\ output of
588 % the \CLaSH\ compiler.
590 The short example demonstrated below gives an indication of the level of
591 conciseness that can be achieved with functional hardware description
592 languages when compared with the more traditional hardware description
593 languages. The example is a combinational multiply-accumulate circuit that
594 works for \emph{any} word length (this type of polymorphism will be
595 further elaborated in \Cref{sec:polymorhpism}). The corresponding netlist
596 is depicted in \Cref{img:mac-comb}.
599 mac a b c = add (mul a b) c
603 \centerline{\includegraphics{mac.svg}}
604 \caption{Combinatorial Multiply-Accumulate}
608 The use of a composite result value is demonstrated in the next example,
609 where the multiply-accumulate circuit not only returns the accumulation
610 result, but also the intermediate multiplication result. Its corresponding
611 netlist can be see in \Cref{img:mac-comb-composite}.
614 mac a b c = (z, add z c)
620 \centerline{\includegraphics{mac-nocurry.svg}}
621 \caption{Combinatorial Multiply-Accumulate (composite output)}
622 \label{img:mac-comb-composite}
626 In Haskell, choice can be achieved by a large set of syntactic elements,
627 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
628 pattern matching, and guards. The most general of these are the \hs{case}
629 expressions (\hs{if} expressions can be very directly translated to
630 \hs{case} expressions). A \hs{case} expression is translated to a
631 multiplexer, where the control value is fed into a number of
632 comparators and their output is used to compose the selection port
633 of the multiplexer. The result of each alternative is linked to the
634 corresponding input port on the multiplexer.
635 % A \hs{case} expression can in turn simply be translated to a conditional
636 % assignment in \VHDL, where the conditions use equality comparisons
637 % against the constructors in the \hs{case} expressions.
638 We can see two versions of a contrived example below, the first
639 using a \hs{case} expression and the other using an \hs{if-then-else}
640 expression. Both examples sums two values when they are
641 equal or non-equal (depending on the given predicate, the \hs{pred}
642 variable) and returns 0 otherwise. The \hs{pred} variable has the
643 following, user-defined, enumeration datatype:
646 data Pred = Equal | NotEqual
649 The naive netlist corresponding to both versions of the example is
650 depicted in \Cref{img:choice}. Note that the \hs{pred} variable is only
651 compared to the \hs{Equal} value, as an inequality immediately implies
652 that the \hs{pred} variable has a \hs{NotEqual} value.
655 sumif pred a b = case pred of
656 Equal -> case a == b of
659 NotEqual -> case a != b of
666 if pred == Equal then
667 if a == b then a + b else 0
669 if a != b then a + b else 0
673 \centerline{\includegraphics{choice-case.svg}}
674 \caption{Choice - sumif}
678 A user-friendly and also very powerful form of choice that is not found in
679 the traditional hardware description languages is pattern matching. A
680 function can be defined in multiple clauses, where each clause corresponds
681 to a pattern. When an argument matches a pattern, the corresponding clause
682 will be used. Expressions can also contain guards, where the expression is
683 only executed if the guard evaluates to true, and continues with the next
684 clause if the guard evaluates to false. Like \hs{if-then-else}
685 expressions, pattern matching and guards have a (straightforward)
686 translation to \hs{case} expressions and can as such be mapped to
687 multiplexers. A third version of the earlier example, using both pattern
688 matching and guards, can be seen below. The guard is the expression that
689 follows the vertical bar (\hs{|}) and precedes the assignment operator
690 (\hs{=}). The \hs{otherwise} guards always evaluate to \hs{true}.
692 The version using pattern matching and guards corresponds to the same
693 naive netlist representation (\Cref{img:choice}) as the earlier two
694 versions of the example.
697 sumif Equal a b | a == b = a + b
699 sumif NotEqual a b | a != b = a + b
704 % \centerline{\includegraphics{choice-ifthenelse}}
705 % \caption{Choice - \emph{if-then-else}}
710 Haskell is a statically-typed language, meaning that the type of a
711 variable or function is determined at compile-time. Not all of Haskell's
712 typing constructs have a clear translation to hardware, this section will
713 therefore only deal with the types that do have a clear correspondence
714 to hardware. The translatable types are divided into two categories:
715 \emph{built-in} types and \emph{user-defined} types. Built-in types are
716 those types for which a fixed translation is defined within the \CLaSH\
717 compiler. The \CLaSH\ compiler has generic translation rules to
718 translated the user-defined types described below.
720 The \CLaSH\ compiler is able to infer unspecified types,
721 meaning that a developer does not have to annotate every function with a
722 type signature (even if it is good practice to do so).
724 % Translation of two most basic functional concepts has been
725 % discussed: function application and choice. Before looking further
726 % into less obvious concepts like higher-order expressions and
727 % polymorphism, the possible types that can be used in hardware
728 % descriptions will be discussed.
730 % Some way is needed to translate every value used to its hardware
731 % equivalents. In particular, this means a hardware equivalent for
732 % every \emph{type} used in a hardware description is needed.
734 % The following types are \emph{built-in}, meaning that their hardware
735 % translation is fixed into the \CLaSH\ compiler. A designer can also
736 % define his own types, which will be translated into hardware types
737 % using translation rules that are discussed later on.
739 \subsubsection{Built-in types}
740 The following types have fixed translations defined within the \CLaSH\
744 the most basic type available. It can have two values:
745 \hs{Low} or \hs{High}.
746 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
748 this is a basic logic type. It can have two values: \hs{True}
750 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
751 % type (where a value of \hs{True} corresponds to a value of
753 Supporting the Bool type is required in order to support the
754 \hs{if-then-else} expression, which requires a \hs{Bool} value for
756 \item[\bf{SizedWord}, \bf{SizedInt}]
757 these are types to represent integers. A \hs{SizedWord} is unsigned,
758 while a \hs{SizedInt} is signed. Both are parametrizable in their
760 % , so you can define an unsigned word of 32 bits wide as follows:
763 % type Word32 = SizedWord D32
766 % Here, a type synonym \hs{Word32} is defined that is equal to the
767 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
768 % \hs{D32} is the \emph{type level representation} of the decimal
769 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
770 % types are translated to the \VHDL\ \texttt{unsigned} and
771 % \texttt{signed} respectively.
773 this is a vector type that can contain elements of any other type and
774 has a fixed length. The \hs{Vector} type constructor takes two type
775 arguments: the length of the vector and the type of the elements
776 contained in it. The short-hand notation used for the vector type in
777 the rest of paper is: \hs{[a|n]}, here \hs{a} is the element
778 type, and \hs{n} is the length of the vector. Note that this is
779 a notation used in this paper only, vectors are slightly more
780 verbose in real \CLaSH\ descriptions.
781 % The state type of an 8 element register bank would then for example
785 % type RegisterState = Vector D8 Word32
788 % Here, a type synonym \hs{RegisterState} is defined that is equal to
789 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
790 % type level representation of the decimal number 8) and \hs{Word32}
791 % (The 32 bit word type as defined above). In other words, the
792 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
793 % vector is translated to a \VHDL\ array type.
795 this is another type to describe integers, but unlike the previous
796 two it has no specific bit-width, but an upper bound. This means that
797 its range is not limited to powers of two, but can be any number.
798 An \hs{Index} only has an upper bound, its lower bound is
799 implicitly zero. The main purpose of the \hs{Index} type is to be
800 used as an index to a \hs{Vector}.
802 % \comment{TODO: Perhaps remove this example?} To define an index for
803 % the 8 element vector above, we would do:
806 % type RegisterIndex = RangedWord D7
809 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
810 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
811 % other words, this defines an unsigned word with values from
812 % 0 to 7 (inclusive). This word can be be used to index the
813 % 8 element vector \hs{RegisterState} above. This type is translated
814 % to the \texttt{unsigned} \VHDL type.
817 \subsubsection{User-defined types}
818 There are three ways to define new types in Haskell: algebraic
819 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
820 keyword and datatype renaming constructs with the \hs{newtype} keyword.
821 \GHC\ offers a few more advanced ways to introduce types (type families,
822 existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell.
823 As it is currently unclear how these advanced type constructs correspond
824 to hardware, they are for now unsupported by the \CLaSH\ compiler.
826 Only an algebraic datatype declaration actually introduces a
827 completely new type. Type synonyms and type renaming only define new
828 names for existing types, where synonyms are completely interchangeable
829 and type renaming requires explicit conversions. Therefore, these do not
830 need any particular translation, a synonym or renamed type will just use
831 the same representation as the original type.
833 For algebraic types, we can make the following distinctions:
835 \item[\bf{Single constructor}]
836 Algebraic datatypes with a single constructor with one or more
837 fields, are essentially a way to pack a few values together in a
838 record-like structure. Haskell's built-in tuple types are also defined
839 as single constructor algebraic types (but with a bit of
840 syntactic sugar). An example of a single constructor type is the
841 following pair of integers:
843 data IntPair = IntPair Int Int
845 % These types are translated to \VHDL\ record types, with one field
846 % for every field in the constructor.
847 \item[\bf{No fields}]
848 Algebraic datatypes with multiple constructors, but without any
849 fields are essentially a way to get an enumeration-like type
850 containing alternatives. Note that Haskell's \hs{Bool} type is also
851 defined as an enumeration type, but that there is a fixed translation
852 for that type within the \CLaSH\ compiler. An example of such an
853 enumeration type is the type that represents the colors in a traffic
856 data TrafficLight = Red | Orange | Green
858 % These types are translated to \VHDL\ enumerations, with one
859 % value for each constructor. This allows references to these
860 % constructors to be translated to the corresponding enumeration
862 \item[\bf{Multiple constructors with fields}]
863 Algebraic datatypes with multiple constructors, where at least
864 one of these constructors has one or more fields are currently not
868 \subsection{Polymorphism}\label{sec:polymorhpism}
869 A powerful feature of most (functional) programming languages is
870 polymorphism, it allows a function to handle values of different data
871 types in a uniform way. Haskell supports \emph{parametric
872 polymorphism}~\cite{polymorphism}, meaning functions can be written
873 without mention of any specific type and can be used transparently with
874 any number of new types.
876 As an example of a parametric polymorphic function, consider the type of
877 the following \hs{append} function, which appends an element to a
878 vector:\footnote{The \hs{::} operator is used to annotate a function
882 append :: [a|n] -> a -> [a|n + 1]
885 This type is parameterized by \hs{a}, which can contain any type at
886 all. This means that \hs{append} can append an element to a vector,
887 regardless of the type of the elements in the list (as long as the type of
888 the value to be added is of the same type as the values in the vector).
889 This kind of polymorphism is extremely useful in hardware designs to make
890 operations work on a vector without knowing exactly what elements are
891 inside, routing signals without knowing exactly what kinds of signals
892 these are, or working with a vector without knowing exactly how long it
893 is. Polymorphism also plays an important role in most higher order
894 functions, as we will see in the next section.
896 Another type of polymorphism is \emph{ad-hoc
897 polymorphism}~\cite{polymorphism}, which refers to polymorphic
898 functions which can be applied to arguments of different types, but which
899 behave differently depending on the type of the argument to which they are
900 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
901 type classes, where a class definition provides the general interface of a
902 function, and class instances define the functionality for the specific
903 types. An example of such a type class is the \hs{Num} class, which
904 contains all of Haskell's numerical operations. A designer can make use
905 of this ad-hoc polymorphism by adding a constraint to a parametrically
906 polymorphic type variable. Such a constraint indicates that the type
907 variable can only be instantiated to a type whose members supports the
908 overloaded functions associated with the type class.
910 As an example we will take a look at type signature of the function
911 \hs{sum}, which sums the values in a vector:
913 sum :: Num a => [a|n] -> a
916 This type is again parameterized by \hs{a}, but it can only contain
917 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
918 we know that the addition (+) operator is defined for that type.
919 \CLaSH's built-in numerical types are also instances of the \hs{Num}
920 class, so we can use the addition operator (and thus the \hs{sum}
921 function) with \hs{SizedWords} as well as with \hs{SizedInts}.
923 In \CLaSH, parametric polymorphism is completely supported. Any function
924 defined can have any number of unconstrained type parameters. The \CLaSH\
925 compiler will infer the type of every such argument depending on how the
926 function is applied. There is however one constraint: the top level
927 function that is being translated can not have any polymorphic arguments.
928 The arguments can not be polymorphic as the function is never applied and
929 consequently there is no way to determine the actual types for the type
932 \CLaSH\ does \emph{currently} not support\emph{ user-defined} type
933 classes, but does use some of the standard Haskell type classes for its
934 built-in function, such as: \hs{Num} for numerical operations, \hs{Eq} for
935 the equality operators, and \hs{Ord} for the comparison/order operators.
937 \subsection{Higher-order functions \& values}
938 Another powerful abstraction mechanism in functional languages, is
939 the concept of \emph{higher-order functions}, or \emph{functions as
940 a first class value}. This allows a function to be treated as a
941 value and be passed around, even as the argument of another
942 function. The following example should clarify this concept:
944 %format not = "\mathit{not}"
946 negateVector xs = map not xs
949 The code above defines the \hs{negateVector} function, which takes a
950 vector of booleans, \hs{xs}, and returns a vector where all the values are
951 negated. It achieves this by calling the \hs{map} function, and passing it
952 \emph{another function}, boolean negation, and the vector of booleans,
953 \hs{xs}. The \hs{map} function applies the negation function to all the
954 elements in the vector.
956 The \hs{map} function is called a higher-order function, since it takes
957 another function as an argument. Also note that \hs{map} is again a
958 parametric polymorphic function: it does not pose any constraints on the
959 type of the input vector, other than that its elements must have the same
960 type as the first argument of the function passed to \hs{map}. The element
961 type of the resulting vector is equal to the return type of the function
962 passed, which need not necessarily be the same as the element type of the
963 input vector. All of these characteristics can readily be inferred from
964 the type signature belonging to \hs{map}:
967 map :: (a -> b) -> [a|n] -> [b|n]
970 So far, only functions have been used as higher-order values. In
971 Haskell, there are two more ways to obtain a function-typed value:
972 partial application and lambda abstraction. Partial application
973 means that a function that takes multiple arguments can be applied
974 to a single argument, and the result will again be a function (but
975 that takes one argument less). As an example, consider the following
976 expression, that adds one to every element of a vector:
982 Here, the expression \hs{(add 1)} is the partial application of the
983 addition function to the value \hs{1}, which is again a function that
984 adds one to its (next) argument. A lambda expression allows one to
985 introduce an anonymous function in any expression. Consider the following
986 expression, which again adds one to every element of a vector:
992 Finally, not only built-in functions can have higher order
993 arguments, but any function defined in \CLaSH can have function
994 arguments. This allows the hardware designer to use a powerful
995 abstraction mechanism in his designs and have an optimal amount of
996 code reuse. The only exception is again the top-level function: if a
997 function-typed argument is not applied with an actual function, no
998 hardware can be generated.
1000 % \comment{TODO: Describe ALU example (no code)}
1003 A very important concept in hardware is the concept of state. In a
1004 stateful design, the outputs depend on the history of the inputs, or the
1005 state. State is usually stored in registers, which retain their value
1006 during a clock cycle. As we want to describe more than simple
1007 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1009 An important property in Haskell, and in most other functional languages,
1010 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1013 \item given the same arguments twice, it should return the same value in
1015 \item that the function has no observable side-effects.
1017 % This purity property is important for functional languages, since it
1018 % enables all kinds of mathematical reasoning that could not be guaranteed
1019 % correct for impure functions.
1020 Pure functions are as such a perfect match for combinational circuits,
1021 where the output solely depends on the inputs. When a circuit has state
1022 however, it can no longer be simply described by a pure function.
1023 % Simply removing the purity property is not a valid option, as the
1024 % language would then lose many of it mathematical properties.
1025 In \CLaSH\ we deal with the concept of state in pure functions by making
1026 current value of the state an additional argument of the function and the
1027 updated state part of result. In this sense the descriptions made in
1028 \CLaSH\ are the combinational parts of a mealy machine.
1030 A simple example is adding an accumulator register to the earlier
1031 multiply-accumulate circuit, of which the resulting netlist can be seen in
1032 \Cref{img:mac-state}:
1035 macS (State c) a b = (State c', c')
1041 \centerline{\includegraphics{mac-state.svg}}
1042 \caption{Stateful Multiply-Accumulate}
1043 \label{img:mac-state}
1046 Note that the \hs{macS} function returns bot the new state and the value
1047 of the output port. The \hs{State} keyword indicates which arguments are
1048 part of the current state, and what part of the output is part of the
1049 updated state. This aspect will also be reflected in the type signature of
1050 the function. Abstracting the state of a circuit in this way makes it very
1051 explicit: which variables are part of the state is completely determined
1052 by the type signature. This approach to state is well suited to be used in
1053 combination with the existing code and language features, such as all the
1054 choice elements, as state values are just normal values. We can simulate
1055 stateful descriptions using the recursive \hs{run} function:
1058 run f s (i : inps) = o : (run f s' inps)
1063 The \hs{(:)} operator is the list concatenation operator, where the
1064 left-hand side is the head of a list and the right-hand side is the
1065 remainder of the list. The \hs{run} function applies the function the
1066 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1067 first input value, \hs{i}. The result is the first output value, \hs{o},
1068 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1069 is then called with the updated state, \hs{s'}, and the rest of the
1070 inputs, \hs{inps}. For the time being, and in the context of this paper,
1071 It is assumed that there is one input per clock cycle.
1072 Also note how the order of the input, output, and state in the \hs{run}
1073 function corresponds with the order of the input, output and state of the
1074 \hs{macS} function described earlier.
1076 As the \hs{run} function, the hardware description, and the test
1077 inputs are also valid Haskell, the complete simulation can be compiled to
1078 an executable binary by an optimizing Haskell compiler, or executed in an
1079 Haskell interpreter. Both simulation paths are much faster than first
1080 translating the description to \VHDL\ and then running a \VHDL\
1083 \section{The \CLaSH\ compiler}
1084 An important aspect in this research is the creation of the prototype
1085 compiler, which allows us to translate descriptions made in the \CLaSH\
1086 language as described in the previous section to synthesizable \VHDL, allowing
1087 a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1089 The Glasgow Haskell Compiler (\GHC) is an open-source Haskell compiler that
1090 also provides a high level API to most of its internals. The availability of
1091 this high-level API obviated the need to design many of the tedious parts of
1092 the prototype compiler, such as the parser, semantic checker, and especially
1093 the type-checker. These parts together form the front-end of the prototype compiler pipeline, as seen in \Cref{img:compilerpipeline}.
1096 \centerline{\includegraphics{compilerpipeline.svg}}
1097 \caption{\CLaSHtiny\ compiler pipeline}
1098 \label{img:compilerpipeline}
1101 The output of the \GHC\ front-end consists of the translation of the original Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller, typed, functional language. This \emph{Core} language is relatively easy to process compared to the larger Haskell language. A description in \emph{Core} can still contain elements 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 elements that have a direct 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 reduction systems and lambda calculus~\cite{lambdacalculus}, such as $\beta$-reduction and $\eta$-expansion. It also includes self-defined transformations that are responsible for the reduction of higher-order functions to `regular' first-order functions.
1103 The final step in the compiler pipeline is the translation to a \VHDL\
1104 \emph{netlist}, which is a straightforward process due to resemblance of a
1105 normalized description and a set of concurrent signal assignments. We call the
1106 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1107 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1110 \label{sec:usecases}
1111 \subsection{FIR Filter}
1112 As an example of a common hardware design where the use of higher-order
1113 functions leads to a very natural description is a \acro{FIR} filter, which is
1114 basically the dot-product of two vectors:
1117 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1120 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1121 and a few previous input samples ($x$). Each of these multiplications
1122 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1123 filter is indeed equivalent to the equation of the dot-product, which is
1127 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1130 We can easily and directly implement the equation for the dot-product
1131 using higher-order functions:
1134 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1137 The \hs{zipWith} function is very similar to the \hs{map} function seen
1138 earlier: It takes a function, two vectors, and then applies the function to
1139 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1140 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1142 The \hs{foldl1} function takes a binary function, a single vector, and applies
1143 the function to the first two elements of the vector. It then applies the
1144 function to the result of the first application and the next element in the
1145 vector. This continues until the end of the vector is reached. The result of
1146 the \hs{foldl1} function is the result of the last application. It is obvious
1147 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1148 \hs{foldl1 (+)} function is summation.
1149 % Returning to the actual \acro{FIR} filter, we will slightly change the
1150 % equation describing it, so as to make the translation to code more obvious and
1151 % concise. What we do is change the definition of the vector of input samples
1152 % and delay the computation by one sample. Instead of having the input sample
1153 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1154 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1155 % to the following (note that this is completely equivalent to the original
1156 % equation, just with a different definition of $x$ that will better suit the
1157 % transformation to code):
1160 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1162 The complete definition of the \acro{FIR} filter in code then becomes:
1165 fir (State (xs,hs)) x =
1166 (State (x >> xs,hs), (x +> xs) *+* hs)
1169 Where the vector \hs{xs} contains the previous input samples, the vector \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input sample. The concatenate operator (\hs{+>}) creates a new vector by placing the current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). 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:
1172 x >> xs = x +> init xs
1175 Where the \hs{init} function returns all but the last element of a vector.
1176 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1177 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1181 \centerline{\includegraphics{4tapfir.svg}}
1182 \caption{4-taps \acrotiny{FIR} Filter}
1186 \subsection{Higher-order CPU}
1187 The following simple CPU is an example of user-defined higher order
1188 functions and pattern matching. The CPU consists of four function units,
1189 of which three have a fixed function and one can perform some less
1192 The CPU contains a number of data sources, represented by the horizontal
1193 lines in figure TODO:REF. These data sources offer the previous outputs
1194 of each function units, along with the single data input the cpu has and
1195 two fixed intialization values.
1197 Each of the function units has both its operands connected to all data
1198 sources, and can be programmed to select any data source for either
1199 operand. In addition, the leftmost function unit has an additional
1200 opcode input to select the operation it performs. Its output is also the
1201 output of the entire cpu.
1203 Looking at the code, the function unit is the most simple. It arranges
1204 the operand selection for the function unit. Note that it does not
1205 define the actual operation that takes place inside the function unit,
1206 but simply accepts the (higher order) argument \hs{op} which is a function
1207 of two arguments that defines the operation.
1210 fu op inputs (addr1, addr2) = regIn
1217 The multiop function defines the operation that takes place in the
1218 leftmost function unit. It is essentially a simple three operation alu
1219 that makes good use of pattern matching and guards in its description.
1220 The \hs{shift} function used here shifts its first operand by the number
1221 of bits indicated in the second operand, the \hs{xor} function produces
1222 the bitwise xor of its operands.
1225 data Opcode = Shift | Xor | Equal
1227 multiop :: Opcode -> Word -> Word -> Word
1228 multiop opc a b = case opc of
1235 The cpu function ties everything together. It applies the \hs{fu}
1236 function four times, to create a different function unit each time. The
1237 first application is interesting, because it does not just pass a
1238 function to \hs{fu}, but a partial application of \hs{multiop}. This
1239 shows how the first funcition unit effectively gets an extra input,
1240 compared to the others.
1242 The vector \hs{inputs} is the set of data sources, which is passed to
1243 each function unit for operand selection. The cpu also receives a vector
1244 of address pairs, which are used by each function unit to select their
1245 operand. The application of the function units to the \hs{inputs} and
1246 \hs{addrs} arguments seems quite repetive and could be rewritten to use
1247 a combination of the \hs{map} and \hs{zipwith} functions instead.
1248 However, the prototype does not currently support working with lists of
1249 functions, so the more explicit version of the code is given instead).
1252 type CpuState = State [Word | 4]
1254 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1255 -> Opcode -> (CpuState, Word)
1256 cpu (State s) input addrs opc = (State s', out)
1258 s' = [ fu (multiop opc) inputs (addrs!0)
1259 , fu add inputs (addrs!1)
1260 , fu sub inputs (addrs!2)
1261 , fu mul inputs (addrs!3)
1263 inputs = 0 +> (1 +> (input +> s))
1267 Of course, this is still a simple example, but it could form the basis
1268 of an actual design, in which the same techniques can be reused.
1270 \section{Related work}
1271 This section describes the features of existing (functional) hardware
1272 description languages and highlights the advantages that this research has
1275 Many functional hardware description languages have been developed over the
1276 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1277 extension of Backus' \acro{FP} language to synchronous streams, designed
1278 particularly for describing and reasoning about regular circuits. The
1279 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1280 circuits, and has a particular focus on layout.
1282 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1283 functional language \acro{ML}, and has support for polymorphic types and
1284 higher-order functions. Published work suggests that there is no direct
1285 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1286 be translated to \VHDL\ and that the translated description can then be
1287 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1288 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1289 on the other hand can correctly translate all of the language constructs
1290 mentioned in this paper to a netlist format.
1292 Like the work presented in this paper, 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
1293 specifications used to model the behavior of superscalar microprocessors. Hawk
1294 specifications can be simulated; to the best knowledge of the authors there is however no support for automated circuit synthesis.
1296 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1297 models, which can (manually) be transformed into an implementation model using
1298 semantic preserving transformations. A designer can model systems using
1299 heterogeneous models of computation, which include continuous time,
1300 synchronous and untimed models of computation. Using so-called domain
1301 interfaces a designer can simulate electronic systems which have both analog
1302 as digital parts. ForSyDe has several backends including simulation and
1303 automated synthesis, though automated synthesis is restricted to the
1304 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1305 support for the automated synthesis of descriptions that contain polymorphism
1306 or higher-order functions.
1308 Lava~\cite{Lava} is a hardware description language that focuses on the
1309 structural representation of hardware. Besides support for simulation and
1310 circuit synthesis, Lava descriptions can be interfaced with formal method
1311 tools for formal verification. Lava descriptions are actually circuit
1312 generators when viewed from a synthesis viewpoint, in that the language
1313 elements of Haskell, such as choice, can be used to guide the circuit
1314 generation. If a developer wants to insert a choice element inside an actual
1315 circuit he will have to explicitly instantiate a multiplexer-like component.
1316 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1317 such as case-statements and pattern matching, are synthesized to choice
1318 elements in the eventual circuit. As such, richer control structures can both
1319 be specified and synthesized in \CLaSH\ compared to any of the embedded
1320 languages such as Hawk, ForSyDe and Lava.
1322 The merits of polymorphic typing, combined with higher-order functions, are
1323 now also recognized in the `main-stream' hardware description languages,
1324 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support
1325 for generics has been extended to types and subprograms, allowing a developer
1326 to describe components with polymorphic ports and function-valued arguments.
1327 Note that the types and subprograms still require an explicit generic map,
1328 whereas types can be automatically inferred, and function-values can be
1329 automatically propagated by the \CLaSH\ compiler. There are also no (generally
1330 available) \VHDL\ synthesis tools that currently support the \VHDL-2008
1331 standard, and thus the synthesis of polymorphic types and function-valued
1334 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1336 % A functional language designed specifically for hardware design is
1337 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1338 % language called \acro{FL}~\cite{FL} to la
1340 % An example of a floating figure using the graphicx package.
1341 % Note that \label must occur AFTER (or within) \caption.
1342 % For figures, \caption should occur after the \includegraphics.
1343 % Note that IEEEtran v1.7 and later has special internal code that
1344 % is designed to preserve the operation of \label within \caption
1345 % even when the captionsoff option is in effect. However, because
1346 % of issues like this, it may be the safest practice to put all your
1347 % \label just after \caption rather than within \caption{}.
1349 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1350 % option should be used if it is desired that the figures are to be
1351 % displayed while in draft mode.
1355 %\includegraphics[width=2.5in]{myfigure}
1356 % where an .eps filename suffix will be assumed under latex,
1357 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1358 % via \DeclareGraphicsExtensions.
1359 %\caption{Simulation Results}
1363 % Note that IEEE typically puts floats only at the top, even when this
1364 % results in a large percentage of a column being occupied by floats.
1367 % An example of a double column floating figure using two subfigures.
1368 % (The subfig.sty package must be loaded for this to work.)
1369 % The subfigure \label commands are set within each subfloat command, the
1370 % \label for the overall figure must come after \caption.
1371 % \hfil must be used as a separator to get equal spacing.
1372 % The subfigure.sty package works much the same way, except \subfigure is
1373 % used instead of \subfloat.
1375 %\begin{figure*}[!t]
1376 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1377 %\label{fig_first_case}}
1379 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1380 %\label{fig_second_case}}}
1381 %\caption{Simulation results}
1385 % Note that often IEEE papers with subfigures do not employ subfigure
1386 % captions (using the optional argument to \subfloat), but instead will
1387 % reference/describe all of them (a), (b), etc., within the main caption.
1390 % An example of a floating table. Note that, for IEEE style tables, the
1391 % \caption command should come BEFORE the table. Table text will default to
1392 % \footnotesize as IEEE normally uses this smaller font for tables.
1393 % The \label must come after \caption as always.
1396 %% increase table row spacing, adjust to taste
1397 %\renewcommand{\arraystretch}{1.3}
1398 % if using array.sty, it might be a good idea to tweak the value of
1399 % \extrarowheight as needed to properly center the text within the cells
1400 %\caption{An Example of a Table}
1401 %\label{table_example}
1403 %% Some packages, such as MDW tools, offer better commands for making tables
1404 %% than the plain LaTeX2e tabular which is used here.
1405 %\begin{tabular}{|c||c|}
1415 % Note that IEEE does not put floats in the very first column - or typically
1416 % anywhere on the first page for that matter. Also, in-text middle ("here")
1417 % positioning is not used. Most IEEE journals/conferences use top floats
1418 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1419 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1420 % command of the stfloats package.
1424 \section{Conclusion}
1425 This research demonstrates once more that functional languages are well suited
1426 for hardware descriptions: function applications provide an elegant notation
1427 for component instantiation. Where this research goes beyond the existing
1428 (functional) hardware descriptions languages is the inclusion of various
1429 choice elements, such as patter matching, that are well suited to describe the
1430 conditional assignments in control-oriented hardware. Besides being able to
1431 translate these basic constructs to synthesizable \VHDL, the prototype
1432 compiler can also correctly translate descriptions that contain both
1433 polymorphic types and function-valued arguments.
1435 Where recent functional hardware description languages have mostly opted to
1436 embed themselves in an existing functional language, this research features a
1437 `true' compiler. As a result there is a clear distinction between compile-time
1438 and run-time, which allows a myriad of choice constructs to be part of the
1439 actual circuit description; a feature the embedded hardware description
1440 languages do not offer.
1442 \section{Future Work}
1443 The choice of describing state explicitly as extra arguments and results can
1444 be seen as a mixed blessing. Even though the description that use state are
1445 usually very clear, one finds that dealing with unpacking, passing, receiving
1446 and repacking can become tedious and even error-prone, especially in the case
1447 of sub-states. Removing this boilerplate, or finding a more suitable
1448 abstraction mechanism would make \CLaSH\ easier to use.
1450 The transformations in normalization phase of the prototype compiler were
1451 developed in an ad-hoc manner, which makes the existence of many desirable
1452 properties unclear. Such properties include whether the complete set of
1453 transformations will always lead to a normal form or if the normalization
1454 process always terminates. Though various use cases suggests that these
1455 properties usually hold, they have not been formally proven. A systematic
1456 approach to defining the set of transformations allows one to proof that the
1457 earlier mentioned properties do indeed exist.
1459 % conference papers do not normally have an appendix
1462 % use section* for acknowledgement
1463 % \section*{Acknowledgment}
1465 % The authors would like to thank...
1467 % trigger a \newpage just before the given reference
1468 % number - used to balance the columns on the last page
1469 % adjust value as needed - may need to be readjusted if
1470 % the document is modified later
1471 % \IEEEtriggeratref{14}
1472 % The "triggered" command can be changed if desired:
1473 %\IEEEtriggercmd{\enlargethispage{-5in}}
1475 % references section
1477 % can use a bibliography generated by BibTeX as a .bbl file
1478 % BibTeX documentation can be easily obtained at:
1479 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1480 % The IEEEtran BibTeX style support page is at:
1481 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1482 \bibliographystyle{IEEEtran}
1483 % argument is your BibTeX string definitions and bibliography database(s)
1484 \bibliography{clash}
1486 % <OR> manually copy in the resultant .bbl file
1487 % set second argument of \begin to the number of references
1488 % (used to reserve space for the reference number labels box)
1489 % \begin{thebibliography}{1}
1491 % \bibitem{IEEEhowto:kopka}
1492 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1493 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1495 % \end{thebibliography}
1503 % vim: set ai sw=2 sts=2 expandtab: