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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
454 \CLaSH\ is a functional hardware description language that borrows both its
455 syntax and semantics from the functional programming language Haskell. Due to
456 the abstraction and generality offered by polymorphism and higher-order
457 functions, a circuit designer can describe circuits in a more natural way than
458 he could in the traditional hardware description languages.
460 Circuit descriptions can be translated to synthesizable VHDL using the
461 prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
462 test input are plain Haskell, complete simulations can be compiled to an
463 executable binary by a Haskell compiler allowing high-speed simulation and
466 Stateful descriptions are supported by explicitly making the current state an
467 argument of the function, and the updated state part of the result. In this
468 sense, the descriptions made in \CLaSH\ are the combinational parts of a mealy
471 % IEEEtran.cls defaults to using nonbold math in the Abstract.
472 % This preserves the distinction between vectors and scalars. However,
473 % if the conference you are submitting to favors bold math in the abstract,
474 % then you can use LaTeX's standard command \boldmath at the very start
475 % of the abstract to achieve this. Many IEEE journals/conferences frown on
476 % math in the abstract anyway.
483 % For peer review papers, you can put extra information on the cover
485 % \ifCLASSOPTIONpeerreview
486 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
489 % For peerreview papers, this IEEEtran command inserts a page break and
490 % creates the second title. It will be ignored for other modes.
491 \IEEEpeerreviewmaketitle
494 \section{Introduction}
495 Hardware description languages have allowed the productivity of hardware
496 engineers to keep pace with the development of chip technology. Standard
497 Hardware description languages, like \VHDL~\cite{VHDL2008} and
498 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
499 programming language. These standard languages are very good at describing
500 detailed hardware properties such as timing behavior, but are generally
501 cumbersome in expressing higher-level abstractions. In an attempt to raise the
502 abstraction level of the descriptions, a great number of approaches based on
503 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
504 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
505 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
506 a time which also saw the birth of the currently popular hardware description
507 languages such as \VHDL. Functional languages are especially suited to
508 describe hardware because combinational circuits can be directly modeled
509 as mathematical functions and that functional languages are very good at
510 describing and composing mathematical functions.
512 In an attempt to decrease the amount of work involved in creating all the
513 required tooling, such as parsers and type-checkers, many functional
514 hardware description languages \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}
515 are embedded as a domain specific language inside the functional
516 language Haskell \cite{Haskell}. This means that a developer is given a
517 library of Haskell functions and types that together form the language
518 primitives of the domain specific language. The primitive functions used
519 to describe a circuit do not actually process any signals, but instead
520 compose a large domain-specific datatype (which is usually hidden from
521 the designer). This datatype is then further processed by an embedded
522 circuit compiler. This circuit compiler actually runs in the same
523 environment as the description; as a result compile-time and run-time
524 become hard to define, as the embedded circuit compiler is usually
525 compiled by the same Haskell compiler as the circuit description itself.
527 The approach taken in this research is not to make another domain specific
528 language embedded in Haskell, but to use (a subset of) the Haskell language
529 itself for the purpose of describing hardware. By taking this approach, we can
530 capture certain language constructs, such as Haskell's choice elements
531 (if-expressions, case-expressions, pattern matching, etc.), which are not
532 available in the functional hardware description languages that are embedded
533 in Haskell as a domain specific language. As far as the authors know, such
534 extensive support for choice-elements is new in the domain of functional
535 hardware description languages. As the hardware descriptions are plain Haskell
536 functions, these descriptions can be compiled to an executable binary
537 for simulation using an optimizing Haskell compiler such as the Glasgow
538 Haskell Compiler (\GHC)~\cite{ghc}.
540 Where descriptions in a conventional hardware description language have an
541 explicit clock for the purpose state and synchronicity, the clock is implied
542 in this research. A developer describes the behavior of the hardware between
543 clock cycles. Many functional hardware description model signals as a stream
544 of all values over time; state is then modeled as a delay on this stream of
545 values. The approach taken in this research is to make the current state of a
546 circuit part of the input of the function and the updated state part of the
547 output. The current abstraction of state and time limits the descriptions to
548 synchronous hardware, there however is room within the language to eventually
549 add a different abstraction mechanism that will allow for the modeling of
550 asynchronous systems.
552 Like the standard hardware description languages, descriptions made in a
553 functional hardware description language must eventually be converted into a
554 netlist. This research also features a prototype translator, which has the
555 same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES}
556 Language for Synchronous Hardware} (pronounced: clash). This compiler converts
557 the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to
558 be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis
561 Besides trivial circuits such as variants of both the \acro{FIR} filter and
562 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
563 also been shown to work for non-trivial descriptions. \CLaSH\ has been able to
564 successfully translate the functional description of a streaming reduction
565 circuit~\cite{reductioncircuit} for floating point numbers.
567 \section{Hardware description in Haskell}
569 \subsection{Function application}
570 The basic syntactic elements of a functional program are functions
571 and function application. These have a single obvious translation to a
574 \item every function is translated to a component,
575 \item every function argument is translated to an input port,
576 \item the result value of a function is translated to an output port,
578 \item function applications are translated to component instantiations.
580 The output port can have a structured type (such as a tuple), so having
581 just a single output port does not pose any limitation. The actual
582 arguments of a function application are assigned to signals, which are
583 then mapped to the corresponding input ports of the component. The output
584 port of the function is also mapped to a signal, which is used as the
585 result of the application itself.
587 Since every top level function generates its own component, the
588 hierarchy of function calls is reflected in the final netlist,% aswell,
589 creating a hierarchical description of the hardware. The separation in
590 different components makes it easier for a developer to understand and
591 possibly hand-optimize the resulting \VHDL\ output of the \CLaSH\
594 As an example we can see the netlist of the |mac| function in
595 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
596 function to calculate $a * b + c$:
599 mac a b c = add (mul a b) c
603 \centerline{\includegraphics{mac.svg}}
604 \caption{Combinatorial Multiply-Accumulate}
608 The result of using a structural input type can be seen in
609 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
610 input tuple for the |a|, |b|, and |c| arguments:
613 mac (a, b, c) = add (mul a b) c
617 \centerline{\includegraphics{mac-nocurry.svg}}
618 \caption{Combinatorial Multiply-Accumulate (complex input)}
619 \label{img:mac-comb-nocurry}
623 In Haskell, choice can be achieved by a large set of syntactic elements,
624 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
625 pattern matching, and guards. The most general of these are the \hs{case}
626 expressions (\hs{if} expressions can be very directly translated to
627 \hs{case} expressions). A \hs{case} expression is translated to a
628 multiplexer, where the control value is fed into a number of
629 comparators and their output is used to compose the selection port
630 of the multiplexer. The result of each alternative is linked to the
631 corresponding input port on the multiplexer.
632 % A \hs{case} expression can in turn simply be translated to a conditional
633 % assignment in \VHDL, where the conditions use equality comparisons
634 % against the constructors in the \hs{case} expressions.
635 We can see two versions of a contrived example below, the first
636 using a \hs{case} expression and the other using an \hs{if-then-else}
637 expression. Both examples sums two values when they are
638 equal or non-equal (depending on the given predicate, the \hs{pred}
639 variable) and returns 0 otherwise. The \hs{pred} variable has the
640 following, user-defined, enumeration datatype:
643 data Pred = Equal | NotEqual
646 The naive netlist corresponding to both versions of the example is
647 depicted in \Cref{img:choice}.
650 sumif pred a b = case pred of
651 Equal -> case a == b of
654 NotEqual -> case a != b of
661 if pred == Equal then
662 if a == b then a + b else 0
664 if a != b then a + b else 0
668 \centerline{\includegraphics{choice-case.svg}}
669 \caption{Choice - sumif}
673 A user-friendly and also very powerful form of choice is pattern
674 matching. A function can be defined in multiple clauses, where each clause
675 corresponds to a pattern. When an argument matches a pattern, the
676 corresponding clause will be used. Expressions can also contain guards,
677 where the expression is only executed if the guard evaluates to true, and
678 continues with the next clause if the guard evaluates to false. Like
679 \hs{if-then-else} expressions, pattern matching and guards have a
680 (straightforward) translation to \hs{case} expressions and can as such be
681 mapped to multiplexers. A third version of the earlier example, using both
682 pattern matching and guards, can be seen below. The guard is the
683 expression that follows the vertical bar (\hs{|}) and precedes the
684 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
687 The version using pattern matching and guards corresponds to the same
688 naive netlist representation (\Cref{img:choice}) as the earlier two
689 versions of the example.
692 sumif Equal a b | a == b = a + b
694 sumif NotEqual a b | a != b = a + b
699 % \centerline{\includegraphics{choice-ifthenelse}}
700 % \caption{Choice - \emph{if-then-else}}
705 Haskell is a statically-typed language, meaning that the type of a
706 variable or function is determined at compile-time. Not all of Haskell's
707 typing constructs have a clear translation to hardware, this section will
708 therefore only deal with the types that do have a clear correspondence
709 to hardware. The translatable types are divided into two categories:
710 \emph{built-in} types and \emph{user-defined} types. Built-in types are
711 those types for which a fixed translation is defined within the \CLaSH\
712 compiler. The \CLaSH\ compiler has generic translation rules to
713 translated the user-defined types described below.
715 The \CLaSH\ compiler is able to infer unspecified types,
716 meaning that a developer does not have to annotate every function with a
717 type signature (even if it is good practice to do so).
719 % Translation of two most basic functional concepts has been
720 % discussed: function application and choice. Before looking further
721 % into less obvious concepts like higher-order expressions and
722 % polymorphism, the possible types that can be used in hardware
723 % descriptions will be discussed.
725 % Some way is needed to translate every value used to its hardware
726 % equivalents. In particular, this means a hardware equivalent for
727 % every \emph{type} used in a hardware description is needed.
729 % The following types are \emph{built-in}, meaning that their hardware
730 % translation is fixed into the \CLaSH\ compiler. A designer can also
731 % define his own types, which will be translated into hardware types
732 % using translation rules that are discussed later on.
734 \subsubsection{Built-in types}
735 The following types have fixed translations defined within the \CLaSH\
739 the most basic type available. It can have two values:
740 \hs{Low} or \hs{High}.
741 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
743 this is a basic logic type. It can have two values: \hs{True}
745 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
746 % type (where a value of \hs{True} corresponds to a value of
748 Supporting the Bool type is required in order to support the
749 \hs{if-then-else} expression, which requires a \hs{Bool} value for
751 \item[\bf{SizedWord}, \bf{SizedInt}]
752 these are types to represent integers. A \hs{SizedWord} is unsigned,
753 while a \hs{SizedInt} is signed. Both are parametrizable in their
755 % , so you can define an unsigned word of 32 bits wide as follows:
758 % type Word32 = SizedWord D32
761 % Here, a type synonym \hs{Word32} is defined that is equal to the
762 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
763 % \hs{D32} is the \emph{type level representation} of the decimal
764 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
765 % types are translated to the \VHDL\ \texttt{unsigned} and
766 % \texttt{signed} respectively.
768 this is a vector type that can contain elements of any other type and
769 has a fixed length. The \hs{Vector} type constructor takes two type
770 arguments: the length of the vector and the type of the elements
771 contained in it. The short-hand notation used for the vector type in
772 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
773 type, and \hs{n} is the length of the vector. Note that this is
774 a notation used in this paper only, vectors are slightly more
775 verbose in real \CLaSH\ descriptions.
776 % The state type of an 8 element register bank would then for example
780 % type RegisterState = Vector D8 Word32
783 % Here, a type synonym \hs{RegisterState} is defined that is equal to
784 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
785 % type level representation of the decimal number 8) and \hs{Word32}
786 % (The 32 bit word type as defined above). In other words, the
787 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
788 % vector is translated to a \VHDL\ array type.
790 this is another type to describe integers, but unlike the previous
791 two it has no specific bit-width, but an upper bound. This means that
792 its range is not limited to powers of two, but can be any number.
793 An \hs{Index} only has an upper bound, its lower bound is
794 implicitly zero. The main purpose of the \hs{Index} type is to be
795 used as an index to a \hs{Vector}.
797 % \comment{TODO: Perhaps remove this example?} To define an index for
798 % the 8 element vector above, we would do:
801 % type RegisterIndex = RangedWord D7
804 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
805 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
806 % other words, this defines an unsigned word with values from
807 % 0 to 7 (inclusive). This word can be be used to index the
808 % 8 element vector \hs{RegisterState} above. This type is translated
809 % to the \texttt{unsigned} \VHDL type.
812 \subsubsection{User-defined types}
813 There are three ways to define new types in Haskell: algebraic
814 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
815 keyword and datatype renaming constructs with the \hs{newtype} keyword.
816 \GHC\ offers a few more advanced ways to introduce types (type families,
817 existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell.
818 As it is currently unclear how these advanced type constructs correspond
819 to hardware, they are for now unsupported by the \CLaSH\ compiler.
821 Only an algebraic datatype declaration actually introduces a
822 completely new type. Type synonyms and type renaming only define new
823 names for existing types, where synonyms are completely interchangeable
824 and type renaming requires explicit conversions. Therefore, these do not
825 need any particular translation, a synonym or renamed type will just use
826 the same representation as the original type. For algebraic types, we can
827 make the following distinctions:
830 \item[\bf{Single constructor}]
831 Algebraic datatypes with a single constructor with one or more
832 fields, are essentially a way to pack a few values together in a
833 record-like structure. Haskell's built-in tuple types are also defined
834 as single constructor algebraic types (but with a bit of
835 syntactic sugar). An example of a single constructor type is the
836 following pair of integers:
838 data IntPair = IntPair Int Int
840 % These types are translated to \VHDL\ record types, with one field
841 % for every field in the constructor.
842 \item[\bf{No fields}]
843 Algebraic datatypes with multiple constructors, but without any
844 fields are essentially a way to get an enumeration-like type
845 containing alternatives. Note that Haskell's \hs{Bool} type is also
846 defined as an enumeration type, but that there is a fixed translation
847 for that type within the \CLaSH\ compiler. An example of such an
848 enumeration type is the type that represents the colors in a traffic
851 data TrafficLight = Red | Orange | Green
853 % These types are translated to \VHDL\ enumerations, with one
854 % value for each constructor. This allows references to these
855 % constructors to be translated to the corresponding enumeration
857 \item[\bf{Multiple constructors with fields}]
858 Algebraic datatypes with multiple constructors, where at least
859 one of these constructors has one or more fields are currently not
863 \subsection{Polymorphism}
864 A powerful feature of most (functional) programming languages is
865 polymorphism, it allows a function to handle values of different data
866 types in a uniform way. Haskell supports \emph{parametric
867 polymorphism}~\cite{polymorphism}, meaning functions can be written
868 without mention of any specific type and can be used transparently with
869 any number of new types.
871 As an example of a parametric polymorphic function, consider the type of
872 the following \hs{append} function, which appends an element to a
873 vector:\footnote{The \hs{::} operator is used to annotate a function
877 append :: [a|n] -> a -> [a|n + 1]
880 This type is parameterized by \hs{a}, which can contain any type at
881 all. This means that \hs{append} can append an element to a vector,
882 regardless of the type of the elements in the list (as long as the type of
883 the value to be added is of the same type as the values in the vector).
884 This kind of polymorphism is extremely useful in hardware designs to make
885 operations work on a vector without knowing exactly what elements are
886 inside, routing signals without knowing exactly what kinds of signals
887 these are, or working with a vector without knowing exactly how long it
888 is. Polymorphism also plays an important role in most higher order
889 functions, as we will see in the next section.
891 Another type of polymorphism is \emph{ad-hoc
892 polymorphism}~\cite{polymorphism}, which refers to polymorphic
893 functions which can be applied to arguments of different types, but which
894 behave differently depending on the type of the argument to which they are
895 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
896 type classes, where a class definition provides the general interface of a
897 function, and class instances define the functionality for the specific
898 types. An example of such a type class is the \hs{Num} class, which
899 contains all of Haskell's numerical operations. A designer can make use
900 of this ad-hoc polymorphism by adding a constraint to a parametrically
901 polymorphic type variable. Such a constraint indicates that the type
902 variable can only be instantiated to a type whose members supports the
903 overloaded functions associated with the type class.
905 As an example we will take a look at type signature of the function
906 \hs{sum}, which sums the values in a vector:
908 sum :: Num a => [a|n] -> a
911 This type is again parameterized by \hs{a}, but it can only contain
912 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
913 we know that the addition (+) operator is defined for that type.
914 \CLaSH's built-in numerical types are also instances of the \hs{Num}
915 class, so we can use the addition operator (and thus the \hs{sum}
916 function) with \hs{SizedWords} as well as with \hs{SizedInts}.
918 In \CLaSH, parametric polymorphism is completely supported. Any function
919 defined can have any number of unconstrained type parameters. The \CLaSH\
920 compiler will infer the type of every such argument depending on how the
921 function is applied. There is however one constraint: the top level
922 function that is being translated can not have any polymorphic arguments.
923 The arguments can not be polymorphic as the function is never applied and
924 consequently there is no way to determine the actual types for the type
927 \CLaSH\ does not support user-defined type classes, but does use some
928 of the standard Haskell type classes for its built-in function, such as:
929 \hs{Num} for numerical operations, \hs{Eq} for the equality operators, and
930 \hs{Ord} for the comparison/order operators.
932 \subsection{Higher-order functions \& values}
933 Another powerful abstraction mechanism in functional languages, is
934 the concept of \emph{higher-order functions}, or \emph{functions as
935 a first class value}. This allows a function to be treated as a
936 value and be passed around, even as the argument of another
937 function. The following example should clarify this concept:
940 negateVector xs = map not xs
943 The code above defines the \hs{negateVector} function, which takes a
944 vector of booleans, \hs{xs}, and returns a vector where all the values are
945 negated. It achieves this by calling the \hs{map} function, and passing it
946 \emph{another function}, boolean negation, and the vector of booleans,
947 \hs{xs}. The \hs{map} function applies the negation function to all the
948 elements in the vector.
950 The \hs{map} function is called a higher-order function, since it takes
951 another function as an argument. Also note that \hs{map} is again a
952 parametric polymorphic function: it does not pose any constraints on the
953 type of the input vector, other than that its elements must have the same
954 type as the first argument of the function passed to \hs{map}. The element
955 type of the resulting vector is equal to the return type of the function
956 passed, which need not necessarily be the same as the element type of the
957 input vector. All of these characteristics can readily be inferred from
958 the type signature belonging to \hs{map}:
961 map :: (a -> b) -> [a|n] -> [b|n]
964 So far, only functions have been used as higher-order values. In
965 Haskell, there are two more ways to obtain a function-typed value:
966 partial application and lambda abstraction. Partial application
967 means that a function that takes multiple arguments can be applied
968 to a single argument, and the result will again be a function (but
969 that takes one argument less). As an example, consider the following
970 expression, that adds one to every element of a vector:
976 Here, the expression \hs{(+ 1)} is the partial application of the
977 plus operator to the value \hs{1}, which is again a function that
978 adds one to its (next) argument. A lambda expression allows one to
979 introduce an anonymous function in any expression. Consider the following
980 expression, which again adds one to every element of a vector:
986 Finally, not only built-in functions can have higher order
987 arguments, but any function defined in \CLaSH can have function
988 arguments. This allows the hardware designer to use a powerful
989 abstraction mechanism in his designs and have an optimal amount of
990 code reuse. The only exception is again the top-level function: if a
991 function-typed argument is not applied with an actual function, no
992 hardware can be generated.
994 % \comment{TODO: Describe ALU example (no code)}
997 A very important concept in hardware is the concept of state. In a
998 stateful design, the outputs depend on the history of the inputs, or the
999 state. State is usually stored in registers, which retain their value
1000 during a clock cycle. As we want to describe more than simple
1001 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1003 An important property in Haskell, and in most other functional languages,
1004 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1007 \item given the same arguments twice, it should return the same value in
1009 \item when the function is called, it should not have observable
1012 % This purity property is important for functional languages, since it
1013 % enables all kinds of mathematical reasoning that could not be guaranteed
1014 % correct for impure functions.
1015 Pure functions are as such a perfect match for combinational circuits,
1016 where the output solely depends on the inputs. When a circuit has state
1017 however, it can no longer be simply described by a pure function.
1018 % Simply removing the purity property is not a valid option, as the
1019 % language would then lose many of it mathematical properties.
1020 In \CLaSH\ we deal with the concept of state in pure functions by making
1021 current value of the state an additional argument of the function and the
1022 updated state part of result. In this sense the descriptions made in
1023 \CLaSH\ are the combinational parts of a mealy machine.
1025 A simple example is adding an accumulator register to the earlier
1026 multiply-accumulate circuit, of which the resulting netlist can be seen in
1027 \Cref{img:mac-state}:
1030 macS (State c) a b = (State c', c')
1036 \centerline{\includegraphics{mac-state.svg}}
1037 \caption{Stateful Multiply-Accumulate}
1038 \label{img:mac-state}
1041 The \hs{State} keyword indicates which arguments are part of the current
1042 state, and what part of the output is part of the updated state. This
1043 aspect will also be reflected in the type signature of the function.
1044 Abstracting the state of a circuit in this way makes it very explicit:
1045 which variables are part of the state is completely determined by the
1046 type signature. This approach to state is well suited to be used in
1047 combination with the existing code and language features, such as all the
1048 choice elements, as state values are just normal values. We can simulate
1049 stateful descriptions using the recursive \hs{run} function:
1052 run f s (i : inps) = o : (run f s' inps)
1057 The \hs{(:)} operator is the list concatenation operator, where the
1058 left-hand side is the head of a list and the right-hand side is the
1059 remainder of the list. The \hs{run} function applies the function the
1060 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1061 first input value, \hs{i}. The result is the first output value, \hs{o},
1062 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1063 is then called with the updated state, \hs{s'}, and the rest of the
1064 inputs, \hs{inps}. It is assumed that there is one input per clock cycle.
1065 Also note how the order of the input, output, and state in the \hs{run}
1066 function corresponds with the order of the input, output and state of the
1067 \hs{macS} function described earlier.
1069 As both the \hs{run} function, the hardware description, and the test
1070 inputs are plain Haskell, the complete simulation can be compiled to an
1071 executable binary by an optimizing Haskell compiler, or executed in an
1072 Haskell interpreter. Both simulation paths are much faster than first
1073 translating the description to \VHDL\ and then running a \VHDL\
1074 simulation, where the executable binary has an additional simulation speed
1075 bonus in case there is a large set of test inputs.
1077 \section{\CLaSH\ compiler}
1078 An important aspect in this research is the creation of the prototype
1079 compiler, which allows us to translate descriptions made in the \CLaSH\
1080 language as described in the previous section to synthesizable \VHDL, allowing
1081 a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1083 The Glasgow Haskell Compiler (\GHC) is an open-source Haskell compiler that
1084 also provides a high level API to most of its internals. The availability of
1085 this high-level API obviated the need to design many of the tedious parts of
1086 the prototype compiler, such as the parser, semantic checker, and especially
1087 the type-checker. The parser, semantic checker, and type-checker together form
1088 the front-end of the prototype compiler pipeline, as depicted in
1089 \Cref{img:compilerpipeline}.
1092 \centerline{\includegraphics{compilerpipeline.svg}}
1093 \caption{\CLaSHtiny\ compiler pipeline}
1094 \label{img:compilerpipeline}
1097 The output of the \GHC\ front-end is the original Haskell description
1098 translated to \emph{Core}~\cite{Sulzmann2007}, which is smaller, typed,
1099 functional language that is relatively easier to process than the larger
1100 Haskell language. A description in \emph{Core} can still contain properties
1101 which have no direct translation to hardware, such as polymorphic types and
1102 function-valued arguments. Such a description needs to be transformed to a
1103 \emph{normal form}, which only contains properties that have a direct
1104 translation. The second stage of the compiler, the \emph{normalization} phase,
1105 exhaustively applies a set of \emph{meaning-preserving} transformations on the
1106 \emph{Core} description until this description is in a \emph{normal form}.
1107 This set of transformations includes transformations typically found in
1108 reduction systems for lambda calculus~\cite{lambdacalculus}, such a
1109 $\beta$-reduction and $\eta$-expansion, but also includes self-defined
1110 transformations that are responsible for the reduction of higher-order
1111 functions to `regular' first-order functions.
1113 The final step in the compiler pipeline is the translation to a \VHDL\
1114 \emph{netlist}, which is a straightforward process due to resemblance of a
1115 normalized description and a set of concurrent signal assignments. We call the
1116 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1117 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1120 \label{sec:usecases}
1121 \subsection{FIR Filter}
1122 As an example of a common hardware design where the use of higher-order
1123 functions leads to a very natural description is a \acro{FIR} filter, which is
1124 basically the dot-product of two vectors:
1127 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1130 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1131 and a few previous input samples ($x$). Each of these multiplications
1132 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1133 filter is indeed equivalent to the equation of the dot-product, which is
1137 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1140 We can easily and directly implement the equation for the dot-product
1141 using higher-order functions:
1144 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1147 The \hs{zipWith} function is very similar to the \hs{map} function seen
1148 earlier: It takes a function, two vectors, and then applies the function to
1149 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1150 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1152 The \hs{foldl1} function takes a binary function, a single vector, and applies
1153 the function to the first two elements of the vector. It then applies the
1154 function to the result of the first application and the next element in the
1155 vector. This continues until the end of the vector is reached. The result of
1156 the \hs{foldl1} function is the result of the last application. It is obvious
1157 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1158 \hs{foldl1 (+)} function is summation.
1160 Returning to the actual \acro{FIR} filter, we will slightly change the
1161 equation describing it, so as to make the translation to code more obvious and
1162 concise. What we do is change the definition of the vector of input samples
1163 and delay the computation by one sample. Instead of having the input sample
1164 received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1165 sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1166 to the following (note that this is completely equivalent to the original
1167 equation, just with a different definition of $x$ that will better suit the
1168 transformation to code):
1171 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1174 The complete definition of the \acro{FIR} filter in code then becomes:
1177 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1180 Where the vector \hs{hs} contains the \acro{FIR} coefficients and the vector
1181 \hs{xs} contains the previous input sample in front and older samples behind.
1182 The code for the shift (\hs{>>}) operator, that adds the new input sample
1183 (\hs{x}) to the list of previous input samples (\hs{xs}) and removes the
1184 oldest sample, is shown below:
1187 x >> xs = x +> init xs
1190 The \hs{init} function returns all but the last element of a vector, and the
1191 concatenate operator (\hs{+>}) adds a new element to the front of a vector.
1192 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1193 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1197 \centerline{\includegraphics{4tapfir.svg}}
1198 \caption{4-taps \acrotiny{FIR} Filter}
1202 \subsection{Higher order CPU}
1203 The following simple CPU is an example of user-defined higher order
1204 functions and pattern matching. The CPU consists of four function units,
1205 of which three have a fixed function and one can perform some less
1208 The CPU contains a number of data sources, represented by the horizontal
1209 lines in figure TODO:REF. These data sources offer the previous outputs
1210 of each function units, along with the single data input the cpu has and
1211 two fixed intialization values.
1213 Each of the function units has both its operands connected to all data
1214 sources, and can be programmed to select any data source for either
1215 operand. In addition, the leftmost function unit has an additional
1216 opcode input to select the operation it performs. Its output is also the
1217 output of the entire cpu.
1219 Looking at the code, the function unit is the most simple. It arranges
1220 the operand selection for the function unit. Note that it does not
1221 define the actual operation that takes place inside the function unit,
1222 but simply accepts the (higher order) argument "op" which is a function
1223 of two arguments that defines the operation.
1226 fu op inputs (addr1, addr2) = regIn
1233 The multiop function defines the operation that takes place in the
1234 leftmost function unit. It is essentially a simple three operation alu
1235 that makes good use of pattern matching and guards in its description.
1236 The \hs{shift} function used here shifts its first operand by the number
1237 of bits indicated in the second operand, the \hs{xor} function produces
1238 the bitwise xor of its operands.
1241 data Opcode = Shift | Xor | Equal
1243 multiop :: Opcode -> Word -> Word -> Word
1244 multiop opc a b = case opc of
1251 The cpu function ties everything together. It applies the \hs{fu}
1252 function four times, to create a different function unit each time. The
1253 first application is interesting, because it does not just pass a
1254 function to \hs{fu}, but a partial application of \hs{multiop}. This
1255 shows how the first funcition unit effectively gets an extra input,
1256 compared to the others.
1258 The vector \hs{inputs} is the set of data sources, which is passed to
1259 each function unit for operand selection. The cpu also receives a vector
1260 of address pairs, which are used by each function unit to select their
1261 operand. The application of the function units to the \hs{inputs} and
1262 \hs{addrs} arguments seems quite repetive and could be rewritten to use
1263 a combination of the \hs{map} and \hs{zipwith} functions instead.
1264 However, the prototype does not currently support working with lists of
1265 functions, so the more explicit version of the code is given instead).
1268 type CpuState = State [Word | 4]
1270 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1271 -> Opcode -> (CpuState, Word)
1272 cpu (State s) input addrs opc = (State s', out)
1274 s' = [ fu (multiop opc) inputs (addrs!0)
1275 , fu add inputs (addrs!1)
1276 , fu sub inputs (addrs!2)
1277 , fu mul inputs (addrs!3)
1279 inputs = 0 +> (1 +> (input +> s))
1283 Of course, this is still a simple example, but it could form the basis
1284 of an actual design, in which the same techniques can be reused.
1286 \section{Related work}
1287 This section describes the features of existing (functional) hardware
1288 description languages and highlights the advantages that this research has
1291 Many functional hardware description languages have been developed over the
1292 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1293 extension of Backus' \acro{FP} language to synchronous streams, designed
1294 particularly for describing and reasoning about regular circuits. The
1295 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1296 circuits, and has a particular focus on layout.
1298 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1299 functional language \acro{ML}, and has support for polymorphic types and
1300 higher-order functions. Published work suggests that there is no direct
1301 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1302 be translated to \VHDL\ and that the translated description can then be
1303 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1304 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1305 on the other hand can correctly translate all of the language constructs
1306 mentioned in this paper to a netlist format.
1308 Like this work, many functional hardware description languages have some sort
1309 of foundation in the functional programming language Haskell.
1310 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1311 specifications used to model the behavior of superscalar microprocessors. Hawk
1312 specifications can be simulated, but there seems to be no support for
1313 automated circuit synthesis.
1315 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1316 models, which can (manually) be transformed into an implementation model using
1317 semantic preserving transformations. A designer can model systems using
1318 heterogeneous models of computation, which include continuous time,
1319 synchronous and untimed models of computation. Using so-called domain
1320 interfaces a designer can simulate electronic systems which have both analog
1321 as digital parts. ForSyDe has several backends including simulation and
1322 automated synthesis, though automated synthesis is restricted to the
1323 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1324 support for the automated synthesis of descriptions that contain polymorphism
1325 or higher-order functions.
1327 Lava~\cite{Lava} is a hardware description language that focuses on the
1328 structural representation of hardware. Besides support for simulation and
1329 circuit synthesis, Lava descriptions can be interfaced with formal method
1330 tools for formal verification. Lava descriptions are actually circuit
1331 generators when viewed from a synthesis viewpoint, in that the language
1332 elements of Haskell, such as choice, can be used to guide the circuit
1333 generation. If a developer wants to insert a choice element inside an actual
1334 circuit he will have to explicitly instantiate a multiplexer-like component.
1336 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1337 such as case-statements and pattern matching, are synthesized to choice
1338 elements in the eventual circuit. As such, richer control structures can both
1339 be specified and synthesized in \CLaSH\ compared to any of the languages
1340 mentioned in this section.
1342 The merits of polymorphic typing, combined with higher-order functions, are
1343 now also recognized in the `main-stream' hardware description languages,
1344 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support
1345 for generics has been extended to types and subprograms, allowing a developer to describe components with polymorphic ports and function-valued arguments. Note that the types and subprograms still require an explicit generic map, whereas types can be automatically inferred, and function-values can be automatically propagated by the \CLaSH\ compiler. There are also no (generally available) \VHDL\ synthesis tools that currently support the \VHDL-2008 standard, and thus the synthesis of polymorphic types and function-valued arguments.
1347 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1349 % A functional language designed specifically for hardware design is
1350 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1351 % language called \acro{FL}~\cite{FL} to la
1353 % An example of a floating figure using the graphicx package.
1354 % Note that \label must occur AFTER (or within) \caption.
1355 % For figures, \caption should occur after the \includegraphics.
1356 % Note that IEEEtran v1.7 and later has special internal code that
1357 % is designed to preserve the operation of \label within \caption
1358 % even when the captionsoff option is in effect. However, because
1359 % of issues like this, it may be the safest practice to put all your
1360 % \label just after \caption rather than within \caption{}.
1362 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1363 % option should be used if it is desired that the figures are to be
1364 % displayed while in draft mode.
1368 %\includegraphics[width=2.5in]{myfigure}
1369 % where an .eps filename suffix will be assumed under latex,
1370 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1371 % via \DeclareGraphicsExtensions.
1372 %\caption{Simulation Results}
1376 % Note that IEEE typically puts floats only at the top, even when this
1377 % results in a large percentage of a column being occupied by floats.
1380 % An example of a double column floating figure using two subfigures.
1381 % (The subfig.sty package must be loaded for this to work.)
1382 % The subfigure \label commands are set within each subfloat command, the
1383 % \label for the overall figure must come after \caption.
1384 % \hfil must be used as a separator to get equal spacing.
1385 % The subfigure.sty package works much the same way, except \subfigure is
1386 % used instead of \subfloat.
1388 %\begin{figure*}[!t]
1389 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1390 %\label{fig_first_case}}
1392 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1393 %\label{fig_second_case}}}
1394 %\caption{Simulation results}
1398 % Note that often IEEE papers with subfigures do not employ subfigure
1399 % captions (using the optional argument to \subfloat), but instead will
1400 % reference/describe all of them (a), (b), etc., within the main caption.
1403 % An example of a floating table. Note that, for IEEE style tables, the
1404 % \caption command should come BEFORE the table. Table text will default to
1405 % \footnotesize as IEEE normally uses this smaller font for tables.
1406 % The \label must come after \caption as always.
1409 %% increase table row spacing, adjust to taste
1410 %\renewcommand{\arraystretch}{1.3}
1411 % if using array.sty, it might be a good idea to tweak the value of
1412 % \extrarowheight as needed to properly center the text within the cells
1413 %\caption{An Example of a Table}
1414 %\label{table_example}
1416 %% Some packages, such as MDW tools, offer better commands for making tables
1417 %% than the plain LaTeX2e tabular which is used here.
1418 %\begin{tabular}{|c||c|}
1428 % Note that IEEE does not put floats in the very first column - or typically
1429 % anywhere on the first page for that matter. Also, in-text middle ("here")
1430 % positioning is not used. Most IEEE journals/conferences use top floats
1431 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1432 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1433 % command of the stfloats package.
1437 \section{Conclusion}
1438 This research demonstrates once more that functional languages are well suited
1439 for hardware descriptions: function applications provide an elegant notation
1440 for component instantiation. Where this research goes beyond the existing
1441 (functional) hardware descriptions languages is the inclusion of various
1442 choice elements, such as patter matching, that are well suited to describe the
1443 conditional assignments in control-oriented hardware. Besides being able to
1444 translate these basic constructs to synthesizable \VHDL, the prototype
1445 compiler can also correctly translate descriptions that contain both
1446 polymorphic types and function-valued arguments.
1448 Where recent functional hardware description languages have mostly opted to
1449 embed themselves in an existing functional language, this research features a
1450 `true' compiler. As a result there is a clear distinction between compile-time
1451 and run-time, which allows a myriad of choice constructs to be part of the
1452 actual circuit description; a feature the embedded hardware description
1453 languages do not offer.
1455 \section{Future Work}
1456 The choice of describing state explicitly as extra arguments and results can
1457 be seen as a mixed blessing. Even though the description that use state are
1458 usually very clear, one finds that dealing with unpacking, passing, receiving
1459 and repacking can become tedious and even error-prone, especially in the case
1460 of sub-states. Removing this boilerplate, or finding a more suitable
1461 abstraction mechanism would make \CLaSH\ easier to use.
1463 The transformations in normalization phase of the prototype compiler were
1464 developed in an ad-hoc manner, which makes the existence of many desirable
1465 properties unclear. Such properties include whether the complete set of
1466 transformations will always lead to a normal form or if the normalization
1467 process always terminates. Though various use cases suggests that these
1468 properties usually hold, they have not been formally proven. A systematic
1469 approach to defining the set of transformations allows one to proof that the
1470 earlier mentioned properties do indeed exist.
1472 % conference papers do not normally have an appendix
1475 % use section* for acknowledgement
1476 % \section*{Acknowledgment}
1478 % The authors would like to thank...
1480 % trigger a \newpage just before the given reference
1481 % number - used to balance the columns on the last page
1482 % adjust value as needed - may need to be readjusted if
1483 % the document is modified later
1484 \IEEEtriggeratref{14}
1485 % The "triggered" command can be changed if desired:
1486 %\IEEEtriggercmd{\enlargethispage{-5in}}
1488 % references section
1490 % can use a bibliography generated by BibTeX as a .bbl file
1491 % BibTeX documentation can be easily obtained at:
1492 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1493 % The IEEEtran BibTeX style support page is at:
1494 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1495 \bibliographystyle{IEEEtran}
1496 % argument is your BibTeX string definitions and bibliography database(s)
1497 \bibliography{clash}
1499 % <OR> manually copy in the resultant .bbl file
1500 % set second argument of \begin to the number of references
1501 % (used to reserve space for the reference number labels box)
1502 % \begin{thebibliography}{1}
1504 % \bibitem{IEEEhowto:kopka}
1505 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1506 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1508 % \end{thebibliography}
1516 % vim: set ai sw=2 sts=2 expandtab: