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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 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. Circuit
456 descriptions can be translated to synthesizable VHDL using the prototype
457 \CLaSH\ compiler. As the circuit descriptions are made in plain Haskell,
458 simulations can also be compiled by a Haskell compiler.
460 The use of polymorphism and higher-order functions allow a circuit designer to
461 describe more abstract and general specifications than are possible in the
462 traditional hardware description languages.
464 % IEEEtran.cls defaults to using nonbold math in the Abstract.
465 % This preserves the distinction between vectors and scalars. However,
466 % if the conference you are submitting to favors bold math in the abstract,
467 % then you can use LaTeX's standard command \boldmath at the very start
468 % of the abstract to achieve this. Many IEEE journals/conferences frown on
469 % math in the abstract anyway.
476 % For peer review papers, you can put extra information on the cover
478 % \ifCLASSOPTIONpeerreview
479 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
482 % For peerreview papers, this IEEEtran command inserts a page break and
483 % creates the second title. It will be ignored for other modes.
484 \IEEEpeerreviewmaketitle
487 \section{Introduction}
488 Hardware description languages have allowed the productivity of hardware
489 engineers to keep pace with the development of chip technology. Standard
490 Hardware description languages, like \VHDL~\cite{VHDL2008} and
491 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
492 programming language. These standard languages are very good at describing
493 detailed hardware properties such as timing behavior, but are generally
494 cumbersome in expressing higher-level abstractions. In an attempt to raise the
495 abstraction level of the descriptions, a great number of approaches based on
496 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
497 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
498 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
499 a time which also saw the birth of the currently popular hardware description
500 languages such as \VHDL. Functional languages are especially suited to
501 describe hardware because combinational circuits can be directly modeled
502 as mathematical functions and that functional languages are very good at
503 describing and composing mathematical functions.
505 In an attempt to decrease the amount of work involved in creating all the
506 required tooling, such as parsers and type-checkers, many functional
507 hardware description languages \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}
508 are embedded as a domain specific language inside the functional
509 language Haskell \cite{Haskell}. This means that a developer is given a
510 library of Haskell functions and types that together form the language
511 primitives of the domain specific language. The primitive functions used
512 to describe a circuit do not actually process any signals, but instead
513 compose a large domain-specific datatype (which is usually hidden from
514 the designer). This datatype is then further processed by an embedded
515 circuit compiler. This circuit compiler actually runs in the same
516 environment as the description; as a result compile-time and run-time
517 become hard to define, as the embedded circuit compiler is usually
518 compiled by the same Haskell compiler as the circuit description itself.
520 The approach taken in this research is not to make another domain specific
521 language embedded in Haskell, but to use (a subset of) the Haskell language
522 itself for the purpose of describing hardware. By taking this approach, we can
523 capture certain language constructs, such as Haskell's choice elements
524 (if-expressions, case-expressions, pattern matching, etc.), which are not
525 available in the functional hardware description languages that are embedded
526 in Haskell as a domain specific language. As far as the authors know, such
527 extensive support for choice-elements is new in the domain of functional
528 hardware description languages. As the hardware descriptions are plain Haskell
529 functions, these descriptions can be compiled to an executable binary
530 for simulation using an optimizing Haskell compiler such as the Glasgow
531 Haskell Compiler (\GHC)~\cite{ghc}.
533 Where descriptions in a conventional hardware description language have an
534 explicit clock for the purpose state and synchronicity, the clock is implied
535 in this research. A developer describes the behavior of the hardware between
536 clock cycles. Many functional hardware description model signals as a stream
537 of all values over time; state is then modeled as a delay on this stream of
538 values. The approach taken in this research is to make the current state of a
539 circuit part of the input of the function and the updated state part of the
540 output. The current abstraction of state and time limits the descriptions to
541 synchronous hardware, there however is room within the language to eventually
542 add a different abstraction mechanism that will allow for the modeling of
543 asynchronous systems.
545 Like the standard hardware description languages, descriptions made in a
546 functional hardware description language must eventually be converted into a
547 netlist. This research also features a prototype translator, which has the
548 same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES}
549 Language for Synchronous Hardware} (pronounced: clash). This compiler converts
550 the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to
551 be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis
554 Besides trivial circuits such as variants of both the \acro{FIR} filter and
555 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
556 also been shown to work for non-trivial descriptions. \CLaSH\ has been able to
557 successfully translate the functional description of a streaming reduction
558 circuit~\cite{reductioncircuit} for floating point numbers.
560 \section{Hardware description in Haskell}
562 \subsection{Function application}
563 The basic syntactic elements of a functional program are functions
564 and function application. These have a single obvious translation to a
567 \item every function is translated to a component,
568 \item every function argument is translated to an input port,
569 \item the result value of a function is translated to an output port,
571 \item function applications are translated to component instantiations.
573 The output port can have a structured type (such as a tuple), so having
574 just a single output port does not pose any limitation. The actual
575 arguments of a function application are assigned to signals, which are
576 then mapped to the corresponding input ports of the component. The output
577 port of the function is also mapped to a signal, which is used as the
578 result of the application itself.
580 Since every top level function generates its own component, the
581 hierarchy of function calls is reflected in the final netlist,% aswell,
582 creating a hierarchical description of the hardware. The separation in
583 different components makes it easier for a developer to understand and
584 possibly hand-optimize the resulting \VHDL\ output of the \CLaSH\
587 As an example we can see the netlist of the |mac| function in
588 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
589 function to calculate $a * b + c$:
592 mac a b c = add (mul a b) c
596 \centerline{\includegraphics{mac.svg}}
597 \caption{Combinatorial Multiply-Accumulate}
601 The result of using a structural input type can be seen in
602 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
603 input tuple for the |a|, |b|, and |c| arguments:
606 mac (a, b, c) = add (mul a b) c
610 \centerline{\includegraphics{mac-nocurry.svg}}
611 \caption{Combinatorial Multiply-Accumulate (complex input)}
612 \label{img:mac-comb-nocurry}
616 In Haskell, choice can be achieved by a large set of syntactic elements,
617 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
618 pattern matching, and guards. The most general of these are the \hs{case}
619 expressions (\hs{if} expressions can be very directly translated to
620 \hs{case} expressions). A \hs{case} expression is translated to a
621 multiplexer, where the control value is fed into a number of
622 comparators and their output is used to compose the selection port
623 of the multiplexer. The result of each alternative is linked to the
624 corresponding input port on the multiplexer.
625 % A \hs{case} expression can in turn simply be translated to a conditional
626 % assignment in \VHDL, where the conditions use equality comparisons
627 % against the constructors in the \hs{case} expressions.
628 We can see two versions of a contrived example below, the first
629 using a \hs{case} expression and the other using an \hs{if-then-else}
630 expression. Both examples sums two values when they are
631 equal or non-equal (depending on the given predicate, the \hs{pred}
632 variable) and returns 0 otherwise. The \hs{pred} variable has the
633 following, user-defined, enumeration datatype:
636 data Pred = Equal | NotEqual
639 The naive netlist corresponding to both versions of the example is
640 depicted in \Cref{img:choice}.
643 sumif pred a b = case pred of
644 Equal -> case a == b of
647 NotEqual -> case a != b of
654 if pred == Equal then
655 if a == b then a + b else 0
657 if a != b then a + b else 0
661 \centerline{\includegraphics{choice-case.svg}}
662 \caption{Choice - sumif}
666 A user-friendly and also very powerful form of choice is pattern
667 matching. A function can be defined in multiple clauses, where each clause
668 corresponds to a pattern. When an argument matches a pattern, the
669 corresponding clause will be used. Expressions can also contain guards,
670 where the expression is only executed if the guard evaluates to true, and
671 continues with the next clause if the guard evaluates to false. Like
672 \hs{if-then-else} expressions, pattern matching and guards have a
673 (straightforward) translation to \hs{case} expressions and can as such be
674 mapped to multiplexers. A third version of the earlier example, using both
675 pattern matching and guards, can be seen below. The guard is the
676 expression that follows the vertical bar (\hs{|}) and precedes the
677 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
680 The version using pattern matching and guards corresponds to the same
681 naive netlist representation (\Cref{img:choice}) as the earlier two
682 versions of the example.
685 sumif Equal a b | a == b = a + b
687 sumif NotEqual a b | a != b = a + b
692 % \centerline{\includegraphics{choice-ifthenelse}}
693 % \caption{Choice - \emph{if-then-else}}
698 Haskell is a statically-typed language, meaning that the type of a
699 variable or function is determined at compile-time. Not all of Haskell's
700 typing constructs have a clear translation to hardware, this section will
701 therefore only deal with the types that do have a clear correspondence
702 to hardware. The translatable types are divided into two categories:
703 \emph{built-in} types and \emph{user-defined} types. Built-in types are
704 those types for which a fixed translation is defined within the \CLaSH\
705 compiler. The \CLaSH\ compiler has generic translation rules to
706 translated the user-defined types described below.
708 The \CLaSH\ compiler is able to infer unspecified types,
709 meaning that a developer does not have to annotate every function with a
710 type signature (even if it is good practice to do so).
712 % Translation of two most basic functional concepts has been
713 % discussed: function application and choice. Before looking further
714 % into less obvious concepts like higher-order expressions and
715 % polymorphism, the possible types that can be used in hardware
716 % descriptions will be discussed.
718 % Some way is needed to translate every value used to its hardware
719 % equivalents. In particular, this means a hardware equivalent for
720 % every \emph{type} used in a hardware description is needed.
722 % The following types are \emph{built-in}, meaning that their hardware
723 % translation is fixed into the \CLaSH\ compiler. A designer can also
724 % define his own types, which will be translated into hardware types
725 % using translation rules that are discussed later on.
727 \subsubsection{Built-in types}
728 The following types have fixed translations defined within the \CLaSH\
732 the most basic type available. It can have two values:
733 \hs{Low} or \hs{High}.
734 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
736 this is a basic logic type. It can have two values: \hs{True}
738 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
739 % type (where a value of \hs{True} corresponds to a value of
741 Supporting the Bool type is required in order to support the
742 \hs{if-then-else} expression, which requires a \hs{Bool} value for
744 \item[\bf{SizedWord}, \bf{SizedInt}]
745 these are types to represent integers. A \hs{SizedWord} is unsigned,
746 while a \hs{SizedInt} is signed. Both are parametrizable in their
748 % , so you can define an unsigned word of 32 bits wide as follows:
751 % type Word32 = SizedWord D32
754 % Here, a type synonym \hs{Word32} is defined that is equal to the
755 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
756 % \hs{D32} is the \emph{type level representation} of the decimal
757 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
758 % types are translated to the \VHDL\ \texttt{unsigned} and
759 % \texttt{signed} respectively.
761 this is a vector type that can contain elements of any other type and
762 has a fixed length. The \hs{Vector} type constructor takes two type
763 arguments: the length of the vector and the type of the elements
764 contained in it. The short-hand notation used for the vector type in
765 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
766 type, and \hs{n} is the length of the vector. Note that this is
767 a notation used in this paper only, vectors are slightly more
768 verbose in real \CLaSH\ descriptions.
769 % The state type of an 8 element register bank would then for example
773 % type RegisterState = Vector D8 Word32
776 % Here, a type synonym \hs{RegisterState} is defined that is equal to
777 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
778 % type level representation of the decimal number 8) and \hs{Word32}
779 % (The 32 bit word type as defined above). In other words, the
780 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
781 % vector is translated to a \VHDL\ array type.
783 this is another type to describe integers, but unlike the previous
784 two it has no specific bit-width, but an upper bound. This means that
785 its range is not limited to powers of two, but can be any number.
786 An \hs{Index} only has an upper bound, its lower bound is
787 implicitly zero. The main purpose of the \hs{Index} type is to be
788 used as an index to a \hs{Vector}.
790 % \comment{TODO: Perhaps remove this example?} To define an index for
791 % the 8 element vector above, we would do:
794 % type RegisterIndex = RangedWord D7
797 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
798 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
799 % other words, this defines an unsigned word with values from
800 % 0 to 7 (inclusive). This word can be be used to index the
801 % 8 element vector \hs{RegisterState} above. This type is translated
802 % to the \texttt{unsigned} \VHDL type.
805 \subsubsection{User-defined types}
806 There are three ways to define new types in Haskell: algebraic
807 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
808 keyword and datatype renaming constructs with the \hs{newtype} keyword.
809 \GHC\ offers a few more advanced ways to introduce types (type families,
810 existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell.
811 As it is currently unclear how these advanced type constructs correspond
812 to hardware, they are for now unsupported by the \CLaSH\ compiler.
814 Only an algebraic datatype declaration actually introduces a
815 completely new type. Type synonyms and type renaming only define new
816 names for existing types, where synonyms are completely interchangeable
817 and type renaming requires explicit conversions. Therefore, these do not
818 need any particular translation, a synonym or renamed type will just use
819 the same representation as the original type. For algebraic types, we can
820 make the following distinctions:
823 \item[\bf{Single constructor}]
824 Algebraic datatypes with a single constructor with one or more
825 fields, are essentially a way to pack a few values together in a
826 record-like structure. Haskell's built-in tuple types are also defined
827 as single constructor algebraic types (but with a bit of
828 syntactic sugar). An example of a single constructor type is the
829 following pair of integers:
831 data IntPair = IntPair Int Int
833 % These types are translated to \VHDL\ record types, with one field
834 % for every field in the constructor.
835 \item[\bf{No fields}]
836 Algebraic datatypes with multiple constructors, but without any
837 fields are essentially a way to get an enumeration-like type
838 containing alternatives. Note that Haskell's \hs{Bool} type is also
839 defined as an enumeration type, but that there is a fixed translation
840 for that type within the \CLaSH\ compiler. An example of such an
841 enumeration type is the type that represents the colors in a traffic
844 data TrafficLight = Red | Orange | Green
846 % These types are translated to \VHDL\ enumerations, with one
847 % value for each constructor. This allows references to these
848 % constructors to be translated to the corresponding enumeration
850 \item[\bf{Multiple constructors with fields}]
851 Algebraic datatypes with multiple constructors, where at least
852 one of these constructors has one or more fields are currently not
856 \subsection{Polymorphism}
857 A powerful feature of most (functional) programming languages is
858 polymorphism, it allows a function to handle values of different data
859 types in a uniform way. Haskell supports \emph{parametric
860 polymorphism}~\cite{polymorphism}, meaning functions can be written
861 without mention of any specific type and can be used transparently with
862 any number of new types.
864 As an example of a parametric polymorphic function, consider the type of
865 the following \hs{append} function, which appends an element to a
866 vector:\footnote{The \hs{::} operator is used to annotate a function
870 append :: [a|n] -> a -> [a|n + 1]
873 This type is parameterized by \hs{a}, which can contain any type at
874 all. This means that \hs{append} can append an element to a vector,
875 regardless of the type of the elements in the list (as long as the type of
876 the value to be added is of the same type as the values in the vector).
877 This kind of polymorphism is extremely useful in hardware designs to make
878 operations work on a vector without knowing exactly what elements are
879 inside, routing signals without knowing exactly what kinds of signals
880 these are, or working with a vector without knowing exactly how long it
881 is. Polymorphism also plays an important role in most higher order
882 functions, as we will see in the next section.
884 Another type of polymorphism is \emph{ad-hoc
885 polymorphism}~\cite{polymorphism}, which refers to polymorphic
886 functions which can be applied to arguments of different types, but which
887 behave differently depending on the type of the argument to which they are
888 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
889 type classes, where a class definition provides the general interface of a
890 function, and class instances define the functionality for the specific
891 types. An example of such a type class is the \hs{Num} class, which
892 contains all of Haskell's numerical operations. A designer can make use
893 of this ad-hoc polymorphism by adding a constraint to a parametrically
894 polymorphic type variable. Such a constraint indicates that the type
895 variable can only be instantiated to a type whose members supports the
896 overloaded functions associated with the type class.
898 As an example we will take a look at type signature of the function
899 \hs{sum}, which sums the values in a vector:
901 sum :: Num a => [a|n] -> a
904 This type is again parameterized by \hs{a}, but it can only contain
905 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
906 we know that the addition (+) operator is defined for that type.
907 \CLaSH's built-in numerical types are also instances of the \hs{Num}
908 class, so we can use the addition operator (and thus the \hs{sum}
909 function) with \hs{SizedWords} as well as with \hs{SizedInts}.
911 In \CLaSH, parametric polymorphism is completely supported. Any function
912 defined can have any number of unconstrained type parameters. The \CLaSH\
913 compiler will infer the type of every such argument depending on how the
914 function is applied. There is however one constraint: the top level
915 function that is being translated can not have any polymorphic arguments.
916 The arguments can not be polymorphic as the function is never applied and
917 consequently there is no way to determine the actual types for the type
920 \CLaSH\ does not support user-defined type classes, but does use some
921 of the standard Haskell type classes for its built-in function, such as:
922 \hs{Num} for numerical operations, \hs{Eq} for the equality operators, and
923 \hs{Ord} for the comparison/order operators.
925 \subsection{Higher-order functions \& values}
926 Another powerful abstraction mechanism in functional languages, is
927 the concept of \emph{higher-order functions}, or \emph{functions as
928 a first class value}. This allows a function to be treated as a
929 value and be passed around, even as the argument of another
930 function. The following example should clarify this concept:
933 negateVector xs = map not xs
936 The code above defines the \hs{negateVector} function, which takes a
937 vector of booleans, \hs{xs}, and returns a vector where all the values are
938 negated. It achieves this by calling the \hs{map} function, and passing it
939 \emph{another function}, boolean negation, and the vector of booleans,
940 \hs{xs}. The \hs{map} function applies the negation function to all the
941 elements in the vector.
943 The \hs{map} function is called a higher-order function, since it takes
944 another function as an argument. Also note that \hs{map} is again a
945 parametric polymorphic function: it does not pose any constraints on the
946 type of the input vector, other than that its elements must have the same
947 type as the first argument of the function passed to \hs{map}. The element
948 type of the resulting vector is equal to the return type of the function
949 passed, which need not necessarily be the same as the element type of the
950 input vector. All of these characteristics can readily be inferred from
951 the type signature belonging to \hs{map}:
954 map :: (a -> b) -> [a|n] -> [b|n]
957 So far, only functions have been used as higher-order values. In
958 Haskell, there are two more ways to obtain a function-typed value:
959 partial application and lambda abstraction. Partial application
960 means that a function that takes multiple arguments can be applied
961 to a single argument, and the result will again be a function (but
962 that takes one argument less). As an example, consider the following
963 expression, that adds one to every element of a vector:
969 Here, the expression \hs{(+ 1)} is the partial application of the
970 plus operator to the value \hs{1}, which is again a function that
971 adds one to its (next) argument. A lambda expression allows one to
972 introduce an anonymous function in any expression. Consider the following
973 expression, which again adds one to every element of a vector:
979 Finally, not only built-in functions can have higher order
980 arguments, but any function defined in \CLaSH can have function
981 arguments. This allows the hardware designer to use a powerful
982 abstraction mechanism in his designs and have an optimal amount of
983 code reuse. The only exception is again the top-level function: if a
984 function-typed argument is not applied with an actual function, no
985 hardware can be generated.
987 % \comment{TODO: Describe ALU example (no code)}
990 A very important concept in hardware is the concept of state. In a
991 stateful design, the outputs depend on the history of the inputs, or the
992 state. State is usually stored in registers, which retain their value
993 during a clock cycle. As we want to describe more than simple
994 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
996 An important property in Haskell, and in most other functional languages,
997 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1000 \item given the same arguments twice, it should return the same value in
1002 \item when the function is called, it should not have observable
1005 % This purity property is important for functional languages, since it
1006 % enables all kinds of mathematical reasoning that could not be guaranteed
1007 % correct for impure functions.
1008 Pure functions are as such a perfect match for combinational circuits,
1009 where the output solely depends on the inputs. When a circuit has state
1010 however, it can no longer be simply described by a pure function.
1011 % Simply removing the purity property is not a valid option, as the
1012 % language would then lose many of it mathematical properties.
1013 In \CLaSH\ we deal with the concept of state in pure functions by making
1014 current value of the state an additional argument of the function and the
1015 updated state part of result. In this sense the descriptions made in
1016 \CLaSH\ are the combinational parts of a mealy machine.
1018 A simple example is adding an accumulator register to the earlier
1019 multiply-accumulate circuit, of which the resulting netlist can be seen in
1020 \Cref{img:mac-state}:
1023 macS (State c) a b = (State c', c')
1029 \centerline{\includegraphics{mac-state.svg}}
1030 \caption{Stateful Multiply-Accumulate}
1031 \label{img:mac-state}
1034 The \hs{State} keyword indicates which arguments are part of the current
1035 state, and what part of the output is part of the updated state. This
1036 aspect will also be reflected in the type signature of the function.
1037 Abstracting the state of a circuit in this way makes it very explicit:
1038 which variables are part of the state is completely determined by the
1039 type signature. This approach to state is well suited to be used in
1040 combination with the existing code and language features, such as all the
1041 choice elements, as state values are just normal values. We can simulate
1042 stateful descriptions using the recursive \hs{run} function:
1045 run f s (i : inps) = o : (run f s' inps)
1050 The \hs{(:)} operator is the list concatenation operator, where the
1051 left-hand side is the head of a list and the right-hand side is the
1052 remainder of the list. The \hs{run} function applies the function the
1053 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1054 first input value, \hs{i}. The result is the first output value, \hs{o},
1055 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1056 is then called with the updated state, \hs{s'}, and the rest of the
1057 inputs, \hs{inps}. It is assumed that there is one input per clock cycle.
1058 Also note how the order of the input, output, and state in the \hs{run}
1059 function corresponds with the order of the input, output and state of the
1060 \hs{macS} function described earlier.
1062 As both the \hs{run} function, the hardware description, and the test
1063 inputs are plain Haskell, the complete simulation can be compiled to an
1064 executable binary by an optimizing Haskell compiler, or executed in an
1065 Haskell interpreter. Both simulation paths are much faster than first
1066 translating the description to \VHDL\ and then running a \VHDL\
1067 simulation, where the executable binary has an additional simulation speed
1068 bonus in case there is a large set of test inputs.
1070 \section{\CLaSH\ compiler}
1071 An important aspect in this research is the creation of the prototype
1072 compiler, which allows us to translate descriptions made in the \CLaSH\
1073 language as described in the previous section to synthesizable \VHDL, allowing
1074 a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1076 The Glasgow Haskell Compiler (\GHC) is an open-source Haskell compiler that
1077 also provides a high level API to most of its internals. The availability of
1078 this high-level API obviated the need to design many of the tedious parts of
1079 the prototype compiler, such as the parser, semantic checker, and especially
1080 the type-checker. The parser, semantic checker, and type-checker together form
1081 the front-end of the prototype compiler pipeline, as depicted in
1082 \Cref{img:compilerpipeline}.
1085 \centerline{\includegraphics{compilerpipeline.svg}}
1086 \caption{\CLaSHtiny\ compiler pipeline}
1087 \label{img:compilerpipeline}
1090 The output of the \GHC\ front-end is the original Haskell description
1091 translated to \emph{Core}~\cite{Sulzmann2007}, which is smaller, typed,
1092 functional language that is relatively easier to process than the larger
1093 Haskell language. A description in \emph{Core} can still contain properties
1094 which have no direct translation to hardware, such as polymorphic types and
1095 function-valued arguments. Such a description needs to be transformed to a
1096 \emph{normal form}, which only contains properties that have a direct
1097 translation. The second stage of the compiler, the \emph{normalization} phase,
1098 exhaustively applies a set of \emph{meaning-preserving} transformations on the
1099 \emph{Core} description until this description is in a \emph{normal form}.
1100 This set of transformations includes transformations typically found in
1101 reduction systems for lambda calculus~\cite{lambdacalculus}, such a
1102 $\beta$-reduction and $\eta$-expansion, but also includes self-defined
1103 transformations that are responsible for the reduction of higher-order
1104 functions to `regular' first-order functions.
1106 The final step in the compiler pipeline is the translation to a \VHDL\
1107 \emph{netlist}, which is a straightforward process due to resemblance of a
1108 normalized description and a set of concurrent signal assignments. We call the
1109 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1110 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1113 \label{sec:usecases}
1114 \subsection{FIR Filter}
1115 As an example of a common hardware design where the use of higher-order
1116 functions leads to a very natural description is a \acro{FIR} filter, which is
1117 basically the dot-product of two vectors:
1120 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1123 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1124 and a few previous input samples ($x$). Each of these multiplications
1125 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1126 filter is indeed equivalent to the equation of the dot-product, which is
1130 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1133 We can easily and directly implement the equation for the dot-product
1134 using higher-order functions:
1137 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1140 The \hs{zipWith} function is very similar to the \hs{map} function seen
1141 earlier: It takes a function, two vectors, and then applies the function to
1142 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1143 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1145 The \hs{foldl1} function takes a binary function, a single vector, and applies
1146 the function to the first two elements of the vector. It then applies the
1147 function to the result of the first application and the next element in the
1148 vector. This continues until the end of the vector is reached. The result of
1149 the \hs{foldl1} function is the result of the last application. It is obvious
1150 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1151 \hs{foldl1 (+)} function is summation.
1153 Returning to the actual \acro{FIR} filter, we will slightly change the
1154 equation describing it, so as to make the translation to code more obvious and
1155 concise. What we do is change the definition of the vector of input samples
1156 and delay the computation by one sample. Instead of having the input sample
1157 received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1158 sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1159 to the following (note that this is completely equivalent to the original
1160 equation, just with a different definition of $x$ that will better suit the
1161 transformation to code):
1164 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1167 The complete definition of the \acro{FIR} filter in code then becomes:
1170 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1173 Where the vector \hs{hs} contains the \acro{FIR} coefficients and the vector
1174 \hs{xs} contains the previous input sample in front and older samples behind.
1175 The code for the shift (\hs{>>}) operator, that adds the new input sample
1176 (\hs{x}) to the list of previous input samples (\hs{xs}) and removes the
1177 oldest sample, is shown below:
1180 x >> xs = x +> init xs
1183 The \hs{init} function returns all but the last element of a vector, and the
1184 concatenate operator (\hs{+>}) adds a new element to the front of a vector.
1185 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1186 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1190 \centerline{\includegraphics{4tapfir.svg}}
1191 \caption{4-taps \acrotiny{FIR} Filter}
1195 \subsection{Higher order CPU}
1198 fu op inputs (addr1, addr2) = regIn
1206 cpu :: Word -> [(Index 6, Index 6) | 4]
1207 -> State [Word | 4] -> (State [Word | 4], Word)
1208 cpu input addrs (State fuss) = (State fuss', out)
1210 fuss' = [ fu const inputs (addrs!0) (fuss!0)
1211 , fu (+) inputs (addrs!1) (fuss!1)
1212 , fu (-) inputs (addrs!2) (fuss!2)
1213 , fu (*) inputs (addrs!3) (fuss!3)
1215 inputs = 0 +> (1 +> (input +> fuss))
1219 \section{Related work}
1220 This section describes the features of existing (functional) hardware
1221 description languages and highlights the advantages that this research has
1224 Many functional hardware description languages have been developed over the
1225 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1226 extension of Backus' \acro{FP} language to synchronous streams, designed
1227 particularly for describing and reasoning about regular circuits. The
1228 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1229 circuits, and has a particular focus on layout.
1231 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1232 functional language \acro{ML}, and has support for polymorphic types and
1233 higher-order functions. Published work suggests that there is no direct
1234 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1235 be translated to \VHDL\ and that the translated description can then be
1236 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1237 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1238 on the other hand can correctly translate all of the language constructs
1239 mentioned in this paper to a netlist format.
1241 Like this work, many functional hardware description languages have some sort
1242 of foundation in the functional programming language Haskell.
1243 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1244 specifications used to model the behavior of superscalar microprocessors. Hawk
1245 specifications can be simulated, but there seems to be no support for
1246 automated circuit synthesis.
1248 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1249 models, which can (manually) be transformed into an implementation model using
1250 semantic preserving transformations. A designer can model systems using
1251 heterogeneous models of computation, which include continuous time,
1252 synchronous and untimed models of computation. Using so-called domain
1253 interfaces a designer can simulate electronic systems which have both analog
1254 as digital parts. ForSyDe has several backends including simulation and
1255 automated synthesis, though automated synthesis is restricted to the
1256 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1257 support for the automated synthesis of descriptions that contain polymorphism
1258 or higher-order functions.
1260 Lava~\cite{Lava} is a hardware description language that focuses on the
1261 structural representation of hardware. Besides support for simulation and
1262 circuit synthesis, Lava descriptions can be interfaced with formal method
1263 tools for formal verification. Lava descriptions are actually circuit
1264 generators when viewed from a synthesis viewpoint, in that the language
1265 elements of Haskell, such as choice, can be used to guide the circuit
1266 generation. If a developer wants to insert a choice element inside an actual
1267 circuit he will have to explicitly instantiate a multiplexer-like component.
1269 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1270 such as case-statements and pattern matching, are synthesized to choice
1271 elements in the eventual circuit. As such, richer control structures can both
1272 be specified and synthesized in \CLaSH\ compared to any of the languages
1273 mentioned in this section.
1275 The merits of polymorphic typing, combined with higher-order functions, are
1276 now also recognized in the `main-stream' hardware description languages,
1277 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support
1278 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.
1280 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1282 % A functional language designed specifically for hardware design is
1283 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1284 % language called \acro{FL}~\cite{FL} to la
1286 % An example of a floating figure using the graphicx package.
1287 % Note that \label must occur AFTER (or within) \caption.
1288 % For figures, \caption should occur after the \includegraphics.
1289 % Note that IEEEtran v1.7 and later has special internal code that
1290 % is designed to preserve the operation of \label within \caption
1291 % even when the captionsoff option is in effect. However, because
1292 % of issues like this, it may be the safest practice to put all your
1293 % \label just after \caption rather than within \caption{}.
1295 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1296 % option should be used if it is desired that the figures are to be
1297 % displayed while in draft mode.
1301 %\includegraphics[width=2.5in]{myfigure}
1302 % where an .eps filename suffix will be assumed under latex,
1303 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1304 % via \DeclareGraphicsExtensions.
1305 %\caption{Simulation Results}
1309 % Note that IEEE typically puts floats only at the top, even when this
1310 % results in a large percentage of a column being occupied by floats.
1313 % An example of a double column floating figure using two subfigures.
1314 % (The subfig.sty package must be loaded for this to work.)
1315 % The subfigure \label commands are set within each subfloat command, the
1316 % \label for the overall figure must come after \caption.
1317 % \hfil must be used as a separator to get equal spacing.
1318 % The subfigure.sty package works much the same way, except \subfigure is
1319 % used instead of \subfloat.
1321 %\begin{figure*}[!t]
1322 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1323 %\label{fig_first_case}}
1325 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1326 %\label{fig_second_case}}}
1327 %\caption{Simulation results}
1331 % Note that often IEEE papers with subfigures do not employ subfigure
1332 % captions (using the optional argument to \subfloat), but instead will
1333 % reference/describe all of them (a), (b), etc., within the main caption.
1336 % An example of a floating table. Note that, for IEEE style tables, the
1337 % \caption command should come BEFORE the table. Table text will default to
1338 % \footnotesize as IEEE normally uses this smaller font for tables.
1339 % The \label must come after \caption as always.
1342 %% increase table row spacing, adjust to taste
1343 %\renewcommand{\arraystretch}{1.3}
1344 % if using array.sty, it might be a good idea to tweak the value of
1345 % \extrarowheight as needed to properly center the text within the cells
1346 %\caption{An Example of a Table}
1347 %\label{table_example}
1349 %% Some packages, such as MDW tools, offer better commands for making tables
1350 %% than the plain LaTeX2e tabular which is used here.
1351 %\begin{tabular}{|c||c|}
1361 % Note that IEEE does not put floats in the very first column - or typically
1362 % anywhere on the first page for that matter. Also, in-text middle ("here")
1363 % positioning is not used. Most IEEE journals/conferences use top floats
1364 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1365 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1366 % command of the stfloats package.
1370 \section{Conclusion}
1371 The conclusion goes here.
1376 % conference papers do not normally have an appendix
1379 % use section* for acknowledgement
1380 % \section*{Acknowledgment}
1382 % The authors would like to thank...
1384 % trigger a \newpage just before the given reference
1385 % number - used to balance the columns on the last page
1386 % adjust value as needed - may need to be readjusted if
1387 % the document is modified later
1388 %\IEEEtriggeratref{8}
1389 % The "triggered" command can be changed if desired:
1390 %\IEEEtriggercmd{\enlargethispage{-5in}}
1392 % references section
1394 % can use a bibliography generated by BibTeX as a .bbl file
1395 % BibTeX documentation can be easily obtained at:
1396 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1397 % The IEEEtran BibTeX style support page is at:
1398 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1399 \bibliographystyle{IEEEtran}
1400 % argument is your BibTeX string definitions and bibliography database(s)
1401 \bibliography{clash}
1403 % <OR> manually copy in the resultant .bbl file
1404 % set second argument of \begin to the number of references
1405 % (used to reserve space for the reference number labels box)
1406 % \begin{thebibliography}{1}
1408 % \bibitem{IEEEhowto:kopka}
1409 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1410 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1412 % \end{thebibliography}
1420 % vim: set ai sw=2 sts=2 expandtab: