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336 % (Unless specifically asked to do so by the journal or conference you plan
337 % to submit to, of course. )
339 % correct bad hyphenation here
340 \hyphenation{op-tical net-works semi-conduc-tor}
342 % Macro for certain acronyms in small caps. Doesn't work with the
343 % default font, though (it contains no smallcaps it seems).
344 \def\acro#1{{\small{#1}}}
345 \def\acrotiny#1{{\scriptsize{#1}}}
346 \def\VHDL{\acro{VHDL}}
348 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 \def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}}
351 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
352 % we'll get something more complex later on.
353 \def\hs#1{\texttt{#1}}
354 \def\quote#1{``{#1}"}
356 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
358 \settowidth{\labelwidth}{#1:}
359 \setlength{\labelsep}{0.5em}
360 \setlength{\leftmargin}{\labelwidth}
361 \addtolength{\leftmargin}{\labelsep}
362 \addtolength{\leftmargin}{\parindent}
363 \setlength{\rightmargin}{0pt}
364 \setlength{\listparindent}{\parindent}
365 \setlength{\itemsep}{0 ex plus 0.2ex}
366 \renewcommand{\makelabel}[1]{##1:\hfil}
371 \usepackage{paralist}
373 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
375 \usepackage{cleveref}
376 \crefname{figure}{figure}{figures}
377 \newcommand{\fref}[1]{\cref{#1}}
378 \newcommand{\Fref}[1]{\Cref{#1}}
380 \usepackage{epstopdf}
382 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
384 %include polycode.fmt
390 % can use linebreaks \\ within to get better formatting as desired
391 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
394 % author names and affiliations
395 % use a multiple column layout for up to three different
397 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
398 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
399 Department of EEMCS, University of Twente\\
400 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
401 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}}
403 % \IEEEauthorblockN{Homer Simpson}
404 % \IEEEauthorblockA{Twentieth Century Fox\\
406 % Email: homer@thesimpsons.com}
408 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
409 % \IEEEauthorblockA{Starfleet Academy\\
410 % San Francisco, California 96678-2391\\
411 % Telephone: (800) 555--1212\\
412 % Fax: (888) 555--1212}}
414 % conference papers do not typically use \thanks and this command
415 % is locked out in conference mode. If really needed, such as for
416 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
417 % after \documentclass
419 % for over three affiliations, or if they all won't fit within the width
420 % of the page, use this alternative format:
422 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
423 %Homer Simpson\IEEEauthorrefmark{2},
424 %James Kirk\IEEEauthorrefmark{3},
425 %Montgomery Scott\IEEEauthorrefmark{3} and
426 %Eldon Tyrell\IEEEauthorrefmark{4}}
427 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
428 %Georgia Institute of Technology,
429 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
430 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
431 %Email: homer@thesimpsons.com}
432 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
433 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
434 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
439 % use for special paper notices
440 %\IEEEspecialpapernotice{(Invited Paper)}
445 % make the title area
451 \CLaSH\ is a functional hardware description language that borrows both its
452 syntax and semantics from the functional programming language Haskell. Circuit
453 descriptions can be translated to synthesizable VHDL using the prototype
454 \CLaSH\ compiler. As the circuit descriptions are made in plain Haskell,
455 simulations can also be compiled by a Haskell compiler.
457 The use of polymorphism and higher-order functions allow a circuit designer to
458 describe more abstract and general specifications than are possible in the
459 traditional hardware description languages.
461 % IEEEtran.cls defaults to using nonbold math in the Abstract.
462 % This preserves the distinction between vectors and scalars. However,
463 % if the conference you are submitting to favors bold math in the abstract,
464 % then you can use LaTeX's standard command \boldmath at the very start
465 % of the abstract to achieve this. Many IEEE journals/conferences frown on
466 % math in the abstract anyway.
473 % For peer review papers, you can put extra information on the cover
475 % \ifCLASSOPTIONpeerreview
476 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
479 % For peerreview papers, this IEEEtran command inserts a page break and
480 % creates the second title. It will be ignored for other modes.
481 \IEEEpeerreviewmaketitle
484 \section{Introduction}
485 Hardware description languages have allowed the productivity of hardware
486 engineers to keep pace with the development of chip technology. Standard
487 Hardware description languages, like \VHDL~\cite{VHDL2008} and
488 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
489 programming language. These standard languages are very good at describing
490 detailed hardware properties such as timing behavior, but are generally
491 cumbersome in expressing higher-level abstractions. In an attempt to raise the
492 abstraction level of the descriptions, a great number of approaches based on
493 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
494 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
495 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
496 a time which also saw the birth of the currently popular hardware description
497 languages such as \VHDL. The merit of using a functional language to describe
498 hardware comes from the fact that combinatorial circuits can be directly
499 modeled as mathematical functions and that functional languages are very good
500 at describing and composing mathematical functions.
502 In an attempt to decrease the amount of work involved with creating all the
503 required tooling, such as parsers and type-checkers, many functional hardware
504 description languages are embedded as a domain specific language inside the
505 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
506 means that a developer is given a library of Haskell~\cite{Haskell} functions
507 and types that together form the language primitives of the domain specific
508 language. As a result of how the signals are modeled and abstracted, the
509 functions used to describe a circuit also build a large domain-specific
510 datatype (hidden from the designer) which can then be processed further by an
511 embedded compiler. This compiler actually runs in the same environment as the
512 description; as a result compile-time and run-time become hard to define, as
513 the embedded compiler is usually compiled by the same Haskell compiler as the
514 circuit description itself.
516 The approach taken in this research is not to make another domain specific
517 language embedded in Haskell, but to use (a subset of) the Haskell language
518 itself for the purpose of describing hardware. By taking this approach, we can
519 capture certain language constructs, such as Haskell's choice elements
520 (if-constructs, case-constructs, pattern matching, etc.), which are not
521 available in the functional hardware description languages that are embedded
522 in Haskell as a domain specific language. As far as the authors know, such
523 extensive support for choice-elements is new in the domain of functional
524 hardware description languages. As the hardware descriptions are plain Haskell
525 functions, these descriptions can be compiled for simulation using an
526 optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC)~\cite{ghc}.
528 Where descriptions in a conventional hardware description language have an
529 explicit clock for the purpose state and synchronicity, the clock is implied
530 in this research. A developer describes the behavior of the hardware between
531 clock cycles. Many functional hardware description model signals as a stream
532 of all values over time; state is then modeled as a delay on this stream of
533 values. The approach taken in this research is to make the current state of a
534 circuit part of the input of the function and the updated state part of the
535 output. The current abstraction of state and time limits the descriptions to
536 synchronous hardware, there however is room within the language to eventually
537 add a different abstraction mechanism that will allow for the modeling of
538 asynchronous systems.
540 Like the standard hardware description languages, descriptions made in a
541 functional hardware description language must eventually be converted into a
542 netlist. This research also features a prototype translator, which has the
543 same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES}
544 Language for Synchronous Hardware} (pronounced: clash). This compiler converts
545 the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to
546 be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis
549 Besides trivial circuits such as variants of both the FIR filter and the
550 simple CPU shown in \Cref{sec:usecases}, the \CLaSH\ compiler has also been
551 shown to work for non-trivial descriptions. \CLaSH\ has been able to
552 successfully translate the functional description of a streaming reduction
553 circuit~\cite{reductioncircuit} for floating point numbers.
555 \section{Hardware description in Haskell}
557 \subsection{Function application}
558 The basic syntactic elements of a functional program are functions
559 and function application. These have a single obvious translation to a
562 \item every function is translated to a component,
563 \item every function argument is translated to an input port,
564 \item the result value of a function is translated to an output port,
566 \item function applications are translated to component instantiations.
568 The output port can have a structured type (such as a tuple), so having
569 just a single output port does not pose any limitation. The arguments of a
570 function application are assigned to signals, which are then mapped to
571 the corresponding input ports of the component. The output port of the
572 function is also mapped to a signal, which is used as the result of the
575 Since every top level function generates its own component, the
576 hierarchy of function calls is reflected in the final netlist,% aswell,
577 creating a hierarchical description of the hardware. The separation in
578 different components makes it easier for a developer to understand and
579 possibly hand-optimize the resulting \VHDL\ output of the \CLaSH\
582 As an example we can see the netlist of the |mac| function in
583 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
584 function to calculate $a * b + c$:
587 mac a b c = add (mul a b) c
591 \centerline{\includegraphics{mac.svg}}
592 \caption{Combinatorial Multiply-Accumulate}
596 The result of using a structural input type can be seen in
597 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
598 input tuple for the |a|, |b|, and |c| arguments:
601 mac (a, b, c) = add (mul a b) c
605 \centerline{\includegraphics{mac-nocurry.svg}}
606 \caption{Combinatorial Multiply-Accumulate (complex input)}
607 \label{img:mac-comb-nocurry}
611 In Haskell, choice can be achieved by a large set of language constructs,
612 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
613 pattern matching, and guards. The most general of these are the \hs{case}
614 constructs (\hs{if} expressions can be very directly translated to
615 \hs{case} expressions). A \hs{case} construct is translated to a
616 multiplexer, where the control value is linked to the selection port and
617 the output of each case is linked to the corresponding input port on the
619 % A \hs{case} expression can in turn simply be translated to a conditional
620 % assignment in \VHDL, where the conditions use equality comparisons
621 % against the constructors in the \hs{case} expressions.
622 We can see two versions of a contrived example below, the first
623 using a \hs{case} construct and the other using an \hs{if-then-else}
624 construct, in the code below. The examples sums two values when they are
625 equal or non-equal (depending on the given predicate, the \hs{pred}
626 variable) and returns 0 otherwise. The \hs{pred} variable has the
627 following, user-defined, enumeration datatype:
630 data Pred = Equiv | NotEquiv
633 The naive netlist corresponding to both versions of the example is
634 depicted in \Cref{img:choice}.
637 sumif pred a b = case pred of
638 Equiv -> case a == b of
641 NotEquiv -> case a != b of
648 if pred == Equiv then
649 if a == b then a + b else 0
651 if a != b then a + b else 0
655 \centerline{\includegraphics{choice-case.svg}}
656 \caption{Choice - sumif}
660 A user-friendly and also very powerful form of choice is pattern
661 matching. A function can be defined in multiple clauses, where each clause
662 corresponds to a pattern. When an argument matches a pattern, the
663 corresponding clause will be used. Expressions can also contain guards,
664 where the expression is only executed if the guard evaluates to true, and
665 continues with the next clause if the guard evaluates to false. Like
666 \hs{if-then-else} constructs, pattern matching and guards have a
667 (straightforward) translation to \hs{case} constructs and can as such be
668 mapped to multiplexers. A third version of the earlier example, using both
669 pattern matching and guards, can be seen below. The guard is the
670 expression that follows the vertical bar (\hs{|}) and precedes the
671 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
674 The version using pattern matching and guards corresponds to the same
675 naive netlist representation (\Cref{img:choice}) as the earlier two
676 versions of the example.
679 sumif Equiv a b | a == b = a + b
681 sumif NotEquiv a b | a != b = a + b
686 % \centerline{\includegraphics{choice-ifthenelse}}
687 % \caption{Choice - \emph{if-then-else}}
692 Haskell is a statically-typed language, meaning that the type of a
693 variable or function is determined at compile-time. Not all of Haskell's
694 typing constructs have a clear translation to hardware, this section will
695 therefor only deal with the types that do have a clear correspondence
696 to hardware. The translatable types are divided into two categories:
697 \emph{built-in} types and \emph{user-defined} types. Built-in types are
698 those types for which a direct translation is defined within the \CLaSH\
699 compiler; the term user-defined types should not require any further
700 elaboration. The translatable types are also inferable by the compiler,
701 meaning that a developer does not have to annotate every function with a
704 % Translation of two most basic functional concepts has been
705 % discussed: function application and choice. Before looking further
706 % into less obvious concepts like higher-order expressions and
707 % polymorphism, the possible types that can be used in hardware
708 % descriptions will be discussed.
710 % Some way is needed to translate every value used to its hardware
711 % equivalents. In particular, this means a hardware equivalent for
712 % every \emph{type} used in a hardware description is needed.
714 % The following types are \emph{built-in}, meaning that their hardware
715 % translation is fixed into the \CLaSH\ compiler. A designer can also
716 % define his own types, which will be translated into hardware types
717 % using translation rules that are discussed later on.
719 \subsubsection{Built-in types}
720 The following types have direct translations defined within the \CLaSH\
724 the most basic type available. It can have two values:
725 \hs{Low} or \hs{High}.
726 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
728 this is a basic logic type. It can have two values: \hs{True}
730 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
731 % type (where a value of \hs{True} corresponds to a value of
733 Supporting the Bool type is required in order to support the
734 \hs{if-then-else} construct, which requires a \hs{Bool} value for
736 \item[\bf{SizedWord}, \bf{SizedInt}]
737 these are types to represent integers. A \hs{SizedWord} is unsigned,
738 while a \hs{SizedInt} is signed. Both are parametrizable in their
740 % , so you can define an unsigned word of 32 bits wide as follows:
743 % type Word32 = SizedWord D32
746 % Here, a type synonym \hs{Word32} is defined that is equal to the
747 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
748 % \hs{D32} is the \emph{type level representation} of the decimal
749 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
750 % types are translated to the \VHDL\ \texttt{unsigned} and
751 % \texttt{signed} respectively.
753 this is a vector type that can contain elements of any other type and
754 has a fixed length. The \hs{Vector} type constructor takes two type
755 arguments: the length of the vector and the type of the elements
756 contained in it. The short-hand notation used for the vector type in
757 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
758 type, and \hs{n} is the length of the vector.
759 % The state type of an 8 element register bank would then for example
763 % type RegisterState = Vector D8 Word32
766 % Here, a type synonym \hs{RegisterState} is defined that is equal to
767 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
768 % type level representation of the decimal number 8) and \hs{Word32}
769 % (The 32 bit word type as defined above). In other words, the
770 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
771 % vector is translated to a \VHDL\ array type.
773 this is another type to describe integers, but unlike the previous
774 two it has no specific bit-width, but an upper bound. This means that
775 its range is not limited to powers of two, but can be any number.
776 An \hs{Index} only has an upper bound, its lower bound is
777 implicitly zero. The main purpose of the \hs{Index} type is to be
778 used as an index to a \hs{Vector}.
780 % \comment{TODO: Perhaps remove this example?} To define an index for
781 % the 8 element vector above, we would do:
784 % type RegisterIndex = RangedWord D7
787 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
788 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
789 % other words, this defines an unsigned word with values from
790 % 0 to 7 (inclusive). This word can be be used to index the
791 % 8 element vector \hs{RegisterState} above. This type is translated
792 % to the \texttt{unsigned} \VHDL type.
795 \subsubsection{User-defined types}
796 There are three ways to define new types in Haskell: algebraic
797 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
798 keyword and datatype renaming constructs with the \hs{newtype} keyword.
799 \GHC\ offers a few more advanced ways to introduce types (type families,
800 existential typing, {\acro{GADT}}s, etc.) which are not standard Haskell.
801 As it is currently unclear how these advanced type constructs correspond
802 to hardware, they are for now unsupported by the \CLaSH\ compiler.
804 Only an algebraic datatype declaration actually introduces a
805 completely new type. Type synonyms and type renaming only define new
806 names for existing types, where synonyms are completely interchangeable
807 and type renaming requires explicit conversions. Therefore, these do not
808 need any particular translation, a synonym or renamed type will just use
809 the same representation as the original type. For algebraic types, we can
810 make the following distinctions:
813 \item[\bf{Single constructor}]
814 Algebraic datatypes with a single constructor with one or more
815 fields, are essentially a way to pack a few values together in a
816 record-like structure. Haskell's built-in tuple types are also defined
817 as single constructor algebraic types An example of a single
818 constructor type is the following pair of integers:
820 data IntPair = IntPair Int Int
822 % These types are translated to \VHDL\ record types, with one field
823 % for every field in the constructor.
824 \item[\bf{No fields}]
825 Algebraic datatypes with multiple constructors, but without any
826 fields are essentially a way to get an enumeration-like type
827 containing alternatives. Note that Haskell's \hs{Bool} type is also
828 defined as an enumeration type, but that there a fixed translation for
829 that type within the \CLaSH\ compiler. An example of such an
830 enumeration type is the type that represents the colors in a traffic
833 data TrafficLight = Red | Orange | Green
835 % These types are translated to \VHDL\ enumerations, with one
836 % value for each constructor. This allows references to these
837 % constructors to be translated to the corresponding enumeration
839 \item[\bf{Multiple constructors with fields}]
840 Algebraic datatypes with multiple constructors, where at least
841 one of these constructors has one or more fields are currently not
845 \subsection{Polymorphism}
846 A powerful feature of most (functional) programming languages is
847 polymorphism, it allows a function to handle values of different data
848 types in a uniform way. Haskell supports \emph{parametric
849 polymorphism}~\cite{polymorphism}, meaning functions can be written
850 without mention of any specific type and can be used transparently with
851 any number of new types.
853 As an example of a parametric polymorphic function, consider the type of
854 the following \hs{append} function, which appends an element to a vector:
857 append :: [a|n] -> a -> [a|n + 1]
860 This type is parameterized by \hs{a}, which can contain any type at
861 all. This means that \hs{append} can append an element to a vector,
862 regardless of the type of the elements in the list (as long as the type of
863 the value to be added is of the same type as the values in the vector).
864 This kind of polymorphism is extremely useful in hardware designs to make
865 operations work on a vector without knowing exactly what elements are
866 inside, routing signals without knowing exactly what kinds of signals
867 these are, or working with a vector without knowing exactly how long it
868 is. Polymorphism also plays an important role in most higher order
869 functions, as we will see in the next section.
871 Another type of polymorphism is \emph{ad-hoc
872 polymorphism}~\cite{polymorphism}, which refers to polymorphic
873 functions which can be applied to arguments of different types, but which
874 behave differently depending on the type of the argument to which they are
875 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
876 type classes, where a class definition provides the general interface of a
877 function, and class instances define the functionality for the specific
878 types. An example of such a type class is the \hs{Num} class, which
879 contains all of Haskell's numerical operations. A designer can make use
880 of this ad-hoc polymorphism by adding a constraint to a parametrically
881 polymorphic type variable. Such a constraint indicates that the type
882 variable can only be instantiated to a type whose members supports the
883 overloaded functions associated with the type class.
885 As an example we will take a look at type signature of the function
886 \hs{sum}, which sums the values in a vector:
888 sum :: Num a => [a|n] -> a
891 This type is again parameterized by \hs{a}, but it can only contain
892 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
893 we know that the addition (+) operator is defined for that type.
894 \CLaSH's built-in numerical types are also instances of the \hs{Num}
895 class, so we can use the addition operator on \hs{SizedWords} as
896 well as on \hs{SizedInts}.
898 In \CLaSH, parametric polymorphism is completely supported. Any function
899 defined can have any number of unconstrained type parameters. The \CLaSH\
900 compiler will infer the type of every such argument depending on how the
901 function is applied. There is however one constraint: the top level
902 function that is being translated can not have any polymorphic arguments.
903 The arguments can not be polymorphic as they are never applied and
904 consequently there is no way to determine the actual types for the type
907 \CLaSH\ does not support user-defined type classes, but does use some
908 of the standard Haskell type classes for its built-in function, such as:
909 \hs{Num} for numerical operations, \hs{Eq} for the equality operators, and
910 \hs{Ord} for the comparison/order operators.
912 \subsection{Higher-order functions \& values}
913 Another powerful abstraction mechanism in functional languages, is
914 the concept of \emph{higher-order functions}, or \emph{functions as
915 a first class value}. This allows a function to be treated as a
916 value and be passed around, even as the argument of another
917 function. The following example should clarify this concept:
920 negateVector xs = map not xs
923 The code above defines the \hs{negateVector} function, which takes a
924 vector of booleans, \hs{xs}, and returns a vector where all the values are
925 negated. It achieves this by calling the \hs{map} function, and passing it
926 \emph{another function}, boolean negation, and the vector of booleans,
927 \hs{xs}. The \hs{map} function applies the negation function to all the
928 elements in the vector.
930 The \hs{map} function is called a higher-order function, since it takes
931 another function as an argument. Also note that \hs{map} is again a
932 parametric polymorphic function: it does not pose any constraints on the
933 type of the vector elements, other than that it must be the same type as
934 the input type of the function passed to \hs{map}. The element type of the
935 resulting vector is equal to the return type of the function passed, which
936 need not necessarily be the same as the element type of the input vector.
937 All of these characteristics can readily be inferred from the type
938 signature belonging to \hs{map}:
941 map :: (a -> b) -> [a|n] -> [b|n]
944 So far, only functions have been used as higher-order values. In
945 Haskell, there are two more ways to obtain a function-typed value:
946 partial application and lambda abstraction. Partial application
947 means that a function that takes multiple arguments can be applied
948 to a single argument, and the result will again be a function (but
949 that takes one argument less). As an example, consider the following
950 expression, that adds one to every element of a vector:
956 Here, the expression \hs{(+) 1} is the partial application of the
957 plus operator to the value \hs{1}, which is again a function that
958 adds one to its argument. A lambda expression allows one to introduce an
959 anonymous function in any expression. Consider the following expression,
960 which again adds one to every element of a vector:
966 Finally, higher order arguments are not limited to just built-in
967 functions, but any function defined by a developer can have function
968 arguments. This allows the hardware designer to use a powerful
969 abstraction mechanism in his designs and have an optimal amount of
970 code reuse. The only exception is again the top-level function: if a
971 function-typed argument is not applied with an actual function, no
972 hardware can be generated.
974 % \comment{TODO: Describe ALU example (no code)}
977 A very important concept in hardware is the concept of state. In a
978 stateful design, the outputs depend on the history of the inputs, or the
979 state. State is usually stored in registers, which retain their value
980 during a clock cycle. As we want to describe more than simple
981 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
983 An important property in Haskell, and in most other functional languages,
984 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
987 \item given the same arguments twice, it should return the same value in
989 \item when the function is called, it should not have observable
992 % This purity property is important for functional languages, since it
993 % enables all kinds of mathematical reasoning that could not be guaranteed
994 % correct for impure functions.
995 Pure functions are as such a perfect match for combinatorial circuits,
996 where the output solely depends on the inputs. When a circuit has state
997 however, it can no longer be simply described by a pure function.
998 % Simply removing the purity property is not a valid option, as the
999 % language would then lose many of it mathematical properties.
1000 In \CLaSH\ we deal with the concept of state in pure functions by making
1001 current value of the state an additional argument of the function and the
1002 updated state part of result. In this sense the descriptions made in
1003 \CLaSH\ are the combinatorial parts of a mealy machine.
1005 A simple example is adding an accumulator register to the earlier
1006 multiply-accumulate circuit, of which the resulting netlist can be seen in
1007 \Cref{img:mac-state}:
1010 macS (State c) a b = (State c', c')
1016 \centerline{\includegraphics{mac-state.svg}}
1017 \caption{Stateful Multiply-Accumulate}
1018 \label{img:mac-state}
1021 The \hs{State} keyword indicates which arguments are part of the current
1022 state, and what part of the output is part of the updated state. This
1023 aspect will also be reflected in the type signature of the function.
1024 Abstracting the state of a circuit in this way makes it very explicit:
1025 which variables are part of the state is completely determined by the
1026 type signature. This approach to state is well suited to be used in
1027 combination with the existing code and language features, such as all the
1028 choice constructs, as state values are just normal values. We can simulate
1029 stateful descriptions using the recursive \hs{run} function:
1032 run f s (i : inps) = o : (run f s' inps)
1037 The \hs{(:)} operator is the list concatenation operator, where the
1038 left-hand side is the head of a list and the right-hand side is the
1039 remainder of the list. The \hs{run} function applies the function the
1040 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1041 first input value, \hs{i}. The result is the first output value, \hs{o},
1042 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1043 is then called with the updated state, \hs{s'}, and the rest of the
1044 inputs, \hs{inps}. Each value in the input list corresponds to exactly one
1045 cycle of the (implicit) clock.
1047 As both the \hs{run} function, the hardware description, and the test
1048 inputs are plain Haskell, the complete simulation can be compiled to an
1049 executable binary by an optimizing Haskell compiler, or executed in an
1050 Haskell interpreter. Both simulation paths are much faster than first
1051 translating the description to \VHDL\ and then running a \VHDL\
1052 simulation, where the executable binary has an additional simulation speed
1053 bonus in case there is a large set of test inputs.
1055 \section{\CLaSH\ prototype}
1057 The \CLaSH\ language as presented above can be translated to \VHDL\ using
1058 the prototype \CLaSH\ compiler. This compiler allows experimentation with
1059 the \CLaSH\ language and allows for running \CLaSH\ designs on actual FPGA
1063 \centerline{\includegraphics{compilerpipeline.svg}}
1064 \caption{\CLaSHtiny\ compiler pipeline}
1065 \label{img:compilerpipeline}
1068 The prototype heavily uses \GHC, the Glasgow Haskell Compiler.
1069 \Cref{img:compilerpipeline} shows the \CLaSH\ compiler pipeline. As you can
1070 see, the front-end is completely reused from \GHC, which allows the \CLaSH\
1071 prototype to support most of the Haskell Language. The \GHC\ front-end
1072 produces the program in the \emph{Core} format, which is a very small,
1073 functional, typed language which is relatively easy to process.
1075 The second step in the compilation process is \emph{normalization}. This
1076 step runs a number of \emph{meaning preserving} transformations on the
1077 Core program, to bring it into a \emph{normal form}. This normal form
1078 has a number of restrictions that make the program similar to hardware.
1079 In particular, a program in normal form no longer has any polymorphism
1080 or higher order functions.
1082 The final step is a simple translation to \VHDL.
1085 \label{sec:usecases}
1086 As an example of a common hardware design where the use of higher-order
1087 functions leads to a very natural description is a FIR filter, which is
1088 basically the dot-product of two vectors:
1091 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1094 A FIR filter multiplies fixed constants ($h$) with the current
1095 and a few previous input samples ($x$). Each of these multiplications
1096 are summed, to produce the result at time $t$. The equation of a FIR
1097 filter is indeed equivalent to the equation of the dot-product, which is
1101 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
1104 We can easily and directly implement the equation for the dot-product
1105 using higher-order functions:
1108 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
1111 The \hs{zipWith} function is very similar to the \hs{map} function seen
1112 earlier: It takes a function, two vectors, and then applies the function to
1113 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1114 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
1116 The \hs{foldl1} function takes a function, a single vector, and applies
1117 the function to the first two elements of the vector. It then applies the
1118 function to the result of the first application and the next element from
1119 the vector. This continues until the end of the vector is reached. The
1120 result of the \hs{foldl1} function is the result of the last application.
1121 As you can see, the \hs{zipWith (*)} function is just pairwise
1122 multiplication and the \hs{foldl1 (+)} function is just summation.
1124 Returning to the actual FIR filter, we will slightly change the
1125 equation belong to it, so as to make the translation to code more obvious.
1126 What we will do is change the definition of the vector of input samples.
1127 So, instead of having the input sample received at time
1128 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1129 stores the $ith$ previous sample. This changes the equation to the
1130 following (Note that this is completely equivalent to the original
1131 equation, just with a different definition of $x$ that will better suit
1132 the transformation to code):
1135 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1138 Consider that the vector \hs{hs} contains the FIR coefficients and the
1139 vector \hs{xs} contains the current input sample in front and older
1140 samples behind. The function that shifts the input samples is shown below:
1143 x >> xs = x +> tail xs
1146 Where the \hs{tail} function returns all but the first element of a
1147 vector, and the concatenate operator ($\succ$) adds a new element to the
1148 left of a vector. The complete definition of the FIR filter then becomes:
1151 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1154 The resulting netlist of a 4-taps FIR filter based on the above definition
1155 is depicted in \Cref{img:4tapfir}.
1158 \centerline{\includegraphics{4tapfir.svg}}
1159 \caption{4-taps \acrotiny{FIR} Filter}
1164 \subsection{Higher order CPU}
1168 type FuState = State Word
1171 -> (RangedWord n, RangedWord n)
1174 fu op inputs (addr1, addr2) (State out) =
1183 type CpuState = State [FuState]:4
1185 -> [(RangedWord 7, RangedWord 7)]:4
1188 cpu input addrs (State fuss) =
1191 fures = [ fu const inputs!0 fuss!0
1192 , fu (+) inputs!1 fuss!1
1193 , fu (-) inputs!2 fuss!2
1194 , fu (*) inputs!3 fuss!3
1196 (fuss', outputs) = unzip fures
1197 inputs = 0 +> 1 +> input +> outputs
1201 \section{Related work}
1202 Many functional hardware description languages have been developed over the
1203 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1204 extension of Backus' \acro{FP} language to synchronous streams, designed
1205 particularly for describing and reasoning about regular circuits. The
1206 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1207 circuits, and has a particular focus on layout.
1209 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1210 functional language \acro{ML}, and has support for polymorphic types and
1211 higher-order functions. Published work suggests that there is no direct
1212 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1213 be translated to \VHDL\ and that the translated description can than be
1214 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1215 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1216 on the other hand can correctly translate all of the language constructs
1217 mentioned in this paper to a netlist format.
1219 Like this work, many functional hardware description languages have some sort
1220 of foundation in the functional programming language Haskell.
1221 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1222 specifications used to model the behavior of superscalar microprocessors. Hawk
1223 specifications can be simulated, but there seems to be no support for
1224 automated circuit synthesis.
1226 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1227 models, which can (manually) be transformed into an implementation model using
1228 semantic preserving transformations. A designer can model systems using
1229 heterogeneous models of computation, which include continuous time,
1230 synchronous and untimed models of computation. Using so-called domain
1231 interfaces a designer can simulate electronic systems which have both analog
1232 as digital parts. ForSyDe has several backends including simulation and
1233 automated synthesis, though automated synthesis is restricted to the
1234 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1235 support for the automated synthesis of descriptions that contain polymorphism
1236 or higher-order functions.
1238 Lava~\cite{Lava} is a hardware description language that focuses on the
1239 structural representation of hardware. Besides support for simulation and
1240 circuit synthesis, Lava descriptions can be interfaced with formal method
1241 tools for formal verification. Lava descriptions are actually circuit
1242 generators when viewed from a synthesis viewpoint, in that the language
1243 elements of Haskell, such as choice, can be used to guide the circuit
1244 generation. If a developer wants to insert a choice element inside an actual
1245 circuit he will have to explicitly instantiate a multiplexer-like component.
1247 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1248 such as case-statements and pattern matching, are synthesized to choice
1249 elements in the eventual circuit. As such, richer control structures can both
1250 be specified and synthesized in \CLaSH\ compared to any of the languages
1251 mentioned in this section.
1253 The merits of polymorphic typing, combined with higher-order functions, are
1254 now also recognized in the `main-stream' hardware description languages,
1255 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to types, allowing a developer to describe
1256 polymorphic components. Note that those types still require an explicit
1257 generic map, whereas types can be automatically inferred in \CLaSH.
1259 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1261 % A functional language designed specifically for hardware design is
1262 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1263 % language called \acro{FL}~\cite{FL} to la
1265 % An example of a floating figure using the graphicx package.
1266 % Note that \label must occur AFTER (or within) \caption.
1267 % For figures, \caption should occur after the \includegraphics.
1268 % Note that IEEEtran v1.7 and later has special internal code that
1269 % is designed to preserve the operation of \label within \caption
1270 % even when the captionsoff option is in effect. However, because
1271 % of issues like this, it may be the safest practice to put all your
1272 % \label just after \caption rather than within \caption{}.
1274 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1275 % option should be used if it is desired that the figures are to be
1276 % displayed while in draft mode.
1280 %\includegraphics[width=2.5in]{myfigure}
1281 % where an .eps filename suffix will be assumed under latex,
1282 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1283 % via \DeclareGraphicsExtensions.
1284 %\caption{Simulation Results}
1288 % Note that IEEE typically puts floats only at the top, even when this
1289 % results in a large percentage of a column being occupied by floats.
1292 % An example of a double column floating figure using two subfigures.
1293 % (The subfig.sty package must be loaded for this to work.)
1294 % The subfigure \label commands are set within each subfloat command, the
1295 % \label for the overall figure must come after \caption.
1296 % \hfil must be used as a separator to get equal spacing.
1297 % The subfigure.sty package works much the same way, except \subfigure is
1298 % used instead of \subfloat.
1300 %\begin{figure*}[!t]
1301 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1302 %\label{fig_first_case}}
1304 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1305 %\label{fig_second_case}}}
1306 %\caption{Simulation results}
1310 % Note that often IEEE papers with subfigures do not employ subfigure
1311 % captions (using the optional argument to \subfloat), but instead will
1312 % reference/describe all of them (a), (b), etc., within the main caption.
1315 % An example of a floating table. Note that, for IEEE style tables, the
1316 % \caption command should come BEFORE the table. Table text will default to
1317 % \footnotesize as IEEE normally uses this smaller font for tables.
1318 % The \label must come after \caption as always.
1321 %% increase table row spacing, adjust to taste
1322 %\renewcommand{\arraystretch}{1.3}
1323 % if using array.sty, it might be a good idea to tweak the value of
1324 % \extrarowheight as needed to properly center the text within the cells
1325 %\caption{An Example of a Table}
1326 %\label{table_example}
1328 %% Some packages, such as MDW tools, offer better commands for making tables
1329 %% than the plain LaTeX2e tabular which is used here.
1330 %\begin{tabular}{|c||c|}
1340 % Note that IEEE does not put floats in the very first column - or typically
1341 % anywhere on the first page for that matter. Also, in-text middle ("here")
1342 % positioning is not used. Most IEEE journals/conferences use top floats
1343 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1344 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1345 % command of the stfloats package.
1349 \section{Conclusion}
1350 The conclusion goes here.
1355 % conference papers do not normally have an appendix
1358 % use section* for acknowledgement
1359 \section*{Acknowledgment}
1362 The authors would like to thank...
1368 % trigger a \newpage just before the given reference
1369 % number - used to balance the columns on the last page
1370 % adjust value as needed - may need to be readjusted if
1371 % the document is modified later
1372 %\IEEEtriggeratref{8}
1373 % The "triggered" command can be changed if desired:
1374 %\IEEEtriggercmd{\enlargethispage{-5in}}
1376 % references section
1378 % can use a bibliography generated by BibTeX as a .bbl file
1379 % BibTeX documentation can be easily obtained at:
1380 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1381 % The IEEEtran BibTeX style support page is at:
1382 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1383 \bibliographystyle{IEEEtran}
1384 % argument is your BibTeX string definitions and bibliography database(s)
1385 \bibliography{clash}
1387 % <OR> manually copy in the resultant .bbl file
1388 % set second argument of \begin to the number of references
1389 % (used to reserve space for the reference number labels box)
1390 % \begin{thebibliography}{1}
1392 % \bibitem{IEEEhowto:kopka}
1393 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1394 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1396 % \end{thebibliography}
1404 % vim: set ai sw=2 sts=2 expandtab: