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44 %%*************************************************************************
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67 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
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262 % subfig.sty, also written by Steven Douglas Cochran, is the modern
263 % replacement for subfigure.sty. However, subfig.sty requires and
264 % automatically loads Axel Sommerfeldt's caption.sty which will override
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268 % IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
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281 % *** FLOAT PACKAGES ***
283 %\usepackage{fixltx2e}
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326 % Read the url.sty source comments for usage information. Basically,
333 % *** Do not adjust lengths that control margins, column widths, etc. ***
334 % *** Do not use packages that alter fonts (such as pslatex). ***
335 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
336 % (Unless specifically asked to do so by the journal or conference you plan
337 % to submit to, of course. )
339 % correct bad hyphenation here
340 \hyphenation{op-tical net-works semi-conduc-tor}
342 % Macro for certain acronyms in small caps. Doesn't work with the
343 % default font, though (it contains no smallcaps it seems).
344 \def\acro#1{{\small{#1}}}
345 \def\VHDL{\acro{VHDL}}
347 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
350 % we'll get something more complex later on.
351 \def\hs#1{\texttt{#1}}
352 \def\quote#1{``{#1}"}
354 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
356 \settowidth{\labelwidth}{#1:}
357 \setlength{\labelsep}{0.5em}
358 \setlength{\leftmargin}{\labelwidth}
359 \addtolength{\leftmargin}{\labelsep}
360 \addtolength{\leftmargin}{\parindent}
361 \setlength{\rightmargin}{0pt}
362 \setlength{\listparindent}{\parindent}
363 \setlength{\itemsep}{0 ex plus 0.2ex}
364 \renewcommand{\makelabel}[1]{##1:\hfil}
369 \usepackage{paralist}
371 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
373 \usepackage{cleveref}
374 \crefname{figure}{figure}{figures}
375 \newcommand{\fref}[1]{\cref{#1}}
376 \newcommand{\Fref}[1]{\Cref{#1}}
378 \usepackage{epstopdf}
380 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
382 %include polycode.fmt
388 % can use linebreaks \\ within to get better formatting as desired
389 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
392 % author names and affiliations
393 % use a multiple column layout for up to three different
395 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
396 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
397 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
398 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}}
400 % \IEEEauthorblockN{Homer Simpson}
401 % \IEEEauthorblockA{Twentieth Century Fox\\
403 % Email: homer@thesimpsons.com}
405 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
406 % \IEEEauthorblockA{Starfleet Academy\\
407 % San Francisco, California 96678-2391\\
408 % Telephone: (800) 555--1212\\
409 % Fax: (888) 555--1212}}
411 % conference papers do not typically use \thanks and this command
412 % is locked out in conference mode. If really needed, such as for
413 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
414 % after \documentclass
416 % for over three affiliations, or if they all won't fit within the width
417 % of the page, use this alternative format:
419 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
420 %Homer Simpson\IEEEauthorrefmark{2},
421 %James Kirk\IEEEauthorrefmark{3},
422 %Montgomery Scott\IEEEauthorrefmark{3} and
423 %Eldon Tyrell\IEEEauthorrefmark{4}}
424 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
425 %Georgia Institute of Technology,
426 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
427 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
428 %Email: homer@thesimpsons.com}
429 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
430 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
431 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
436 % use for special paper notices
437 %\IEEEspecialpapernotice{(Invited Paper)}
442 % make the title area
448 \CLaSH\ is a functional hardware description language that borrows both its
449 syntax and semantics from the functional programming language Haskell. Circuit
450 descriptions can be translated to synthesizable VHDL using the prototype
451 \CLaSH\ compiler. As the circuit descriptions are made in plain Haskell,
452 simulations can also be compiled by a Haskell compiler.
454 The use of polymorphism and higher-order functions allow a circuit designer to
455 describe more abstract and general specifications than are possible in the
456 traditional hardware description languages.
458 % IEEEtran.cls defaults to using nonbold math in the Abstract.
459 % This preserves the distinction between vectors and scalars. However,
460 % if the conference you are submitting to favors bold math in the abstract,
461 % then you can use LaTeX's standard command \boldmath at the very start
462 % of the abstract to achieve this. Many IEEE journals/conferences frown on
463 % math in the abstract anyway.
470 % For peer review papers, you can put extra information on the cover
472 % \ifCLASSOPTIONpeerreview
473 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
476 % For peerreview papers, this IEEEtran command inserts a page break and
477 % creates the second title. It will be ignored for other modes.
478 \IEEEpeerreviewmaketitle
481 \section{Introduction}
482 Hardware description languages has allowed the productivity of hardware
483 engineers to keep pace with the development of chip technology. Standard
484 Hardware description languages, like \VHDL~\cite{VHDL2008} and
485 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
486 programming language. These standard languages are very good at describing
487 detailed hardware properties such as timing behavior, but are generally
488 cumbersome in expressing higher-level abstractions. In an attempt to raise the
489 abstraction level of the descriptions, a great number of approaches based on
490 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
491 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
492 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
493 a time which also saw the birth of the currently popular hardware description
494 languages such as \VHDL. The merit of using a functional language to describe
495 hardware comes from the fact that combinatorial circuits can be directly
496 modeled as mathematical functions and that functional languages are very good
497 at describing and composing mathematical functions.
499 In an attempt to decrease the amount of work involved with creating all the
500 required tooling, such as parsers and type-checkers, many functional hardware
501 description languages are embedded as a domain specific language inside the
502 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
503 means that a developer is given a library of Haskell~\cite{Haskell} functions
504 and types that together form the language primitives of the domain specific
505 language. As a result of how the signals are modeled and abstracted, the
506 functions used to describe a circuit also build a large domain-specific
507 datatype (hidden from the designer) which can be further processed by an
508 embedded compiler. This compiler actually runs in the same environment as the
509 description; as a result compile-time and run-time become hard to define, as
510 the embedded compiler is usually compiled by the same Haskell compiler as the
511 circuit description itself.
513 The approach taken in this research is not to make another domain specific
514 language embedded in Haskell, but to use (a subset of) the Haskell language
515 itself for the purpose of describing hardware. By taking this approach, we can
516 capture certain language constructs, such as Haskell's choice elements
517 (if-constructs, case-constructs, pattern matching, etc.), which are not
518 available in the functional hardware description languages that are embedded
519 in Haskell as a domain specific languages. As far as the authors know, such
520 extensive support for choice-elements is new in the domain of functional
521 hardware description languages. As the hardware descriptions are plain Haskell
522 functions, these descriptions can be compiled for simulation using an
523 optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC)~\cite{ghc}.
525 Where descriptions in a conventional hardware description language have an
526 explicit clock for the purpose state and synchronicity, the clock is implied
527 in this research. A developer describes the behavior of the hardware between
528 clock cycles, as such, only synchronous systems can be described. Many
529 functional hardware description model signals as a stream of all values over
530 time; state is then modeled as a delay on this stream of values. The approach
531 taken in this research is to make the current state of a circuit part of the
532 input of the function and the updated state part of the output.
534 Like the standard hardware description languages, descriptions made in a
535 functional hardware description language must eventually be converted into a
536 netlist. This research also features a prototype translator called \CLaSH\
537 (pronounced: clash), which converts the Haskell code to equivalently behaving
538 synthesizable \VHDL\ code, ready to be converted to an actual netlist format
539 by an (optimizing) \VHDL\ synthesis tool.
541 \section{Hardware description in Haskell}
543 \subsection{Function application}
544 The basic syntactic elements of a functional program are functions
545 and function application. These have a single obvious translation to a
548 \item every function is translated to a component,
549 \item every function argument is translated to an input port,
550 \item the result value of a function is translated to an output port,
552 \item function applications are translated to component instantiations.
554 The output port can have a complex type (such as a tuple), so having just
555 a single output port does not pose any limitation. The arguments of a
556 function applications are assigned to a signal, which are then mapped to
557 the corresponding input ports of the component. The output port of the
558 function is also mapped to a signal, which is used as the result of the
561 Since every top level function generates its own component, the
562 hierarchy of function calls is reflected in the final netlist,% aswell,
563 creating a hierarchical description of the hardware. This separation in
564 different components makes the resulting \VHDL\ output easier to read and
567 As an example we can see the netlist of the |mac| function in
568 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
569 function to calculate $a * b + c$:
572 mac a b c = add (mul a b) c
576 \centerline{\includegraphics{mac.svg}}
577 \caption{Combinatorial Multiply-Accumulate}
581 The result of using a complex input type can be seen in
582 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
583 input tuple for the |a|, |b|, and |c| arguments:
586 mac (a, b, c) = add (mul a b) c
590 \centerline{\includegraphics{mac-nocurry.svg}}
591 \caption{Combinatorial Multiply-Accumulate (complex input)}
592 \label{img:mac-comb-nocurry}
596 In Haskell, choice can be achieved by a large set of language constructs,
597 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
598 pattern matching, and guards. The easiest of these are the \hs{case}
599 constructs (\hs{if} expressions can be very directly translated to
600 \hs{case} expressions). A \hs{case} construct is translated to a
601 multiplexer, where the control value is linked to the selection port and
602 the output of each case is linked to the corresponding input port on the
604 % A \hs{case} expression can in turn simply be translated to a conditional
605 % assignment in \VHDL, where the conditions use equality comparisons
606 % against the constructors in the \hs{case} expressions.
607 We can see two versions of a contrived example below, the first
608 using a \hs{case} construct and the other using a \hs{if-then-else}
609 constructs, in the code below. The example sums two values when they are
610 equal or non-equal (depending on the predicate given) and returns 0
611 otherwise. Both versions of the example roughly correspond to the same
612 netlist, which is depicted in \Cref{img:choice}.
615 sumif pred a b = case pred of
619 Neq -> case a != b of
627 if a == b then a + b else 0
629 if a != b then a + b else 0
633 \centerline{\includegraphics{choice-case.svg}}
634 \caption{Choice - sumif}
638 A slightly more complex (but very powerful) form of choice is pattern
639 matching. A function can be defined in multiple clauses, where each clause
640 specifies a pattern. When the arguments match the pattern, the
641 corresponding clause will be used. Expressions can also contain guards,
642 where the expression is only executed if the guard evaluates to true. Like
643 \hs{if-then-else} constructs, pattern matching and guards have a
644 (straightforward) translation to \hs{case} constructs and can as such be
645 mapped to multiplexers. A third version of the earlier example, using both
646 pattern matching and guards, can be seen below. The version using pattern
647 matching and guards also has roughly the same netlist representation
648 (\Cref{img:choice}) as the earlier two versions of the example.
651 sumif Eq a b | a == b = a + b
652 sumif Neq a b | a != b = a + b
657 % \centerline{\includegraphics{choice-ifthenelse}}
658 % \caption{Choice - \emph{if-then-else}}
663 Haskell is a statically-typed language, meaning that the type of a
664 variable or function is determined at compile-time. Not all of Haskell's
665 typing constructs have a clear translation to hardware, as such this
666 section will only deal with the types that do have a clear correspondence
667 to hardware. The translatable types are divided into two categories:
668 \emph{built-in} types and \emph{user-defined} types. Built-in types are
669 those types for which a direct translation is defined within the \CLaSH\
670 compiler; the term user-defined types should not require any further
671 elaboration. The translatable types are also inferable by the compiler,
672 meaning that a developer does not have to annotate every function with a
675 % Translation of two most basic functional concepts has been
676 % discussed: function application and choice. Before looking further
677 % into less obvious concepts like higher-order expressions and
678 % polymorphism, the possible types that can be used in hardware
679 % descriptions will be discussed.
681 % Some way is needed to translate every value used to its hardware
682 % equivalents. In particular, this means a hardware equivalent for
683 % every \emph{type} used in a hardware description is needed.
685 % The following types are \emph{built-in}, meaning that their hardware
686 % translation is fixed into the \CLaSH\ compiler. A designer can also
687 % define his own types, which will be translated into hardware types
688 % using translation rules that are discussed later on.
690 \subsubsection{Built-in types}
691 The following types have direct translation defined within the \CLaSH\
695 This is the most basic type available. It can have two values:
696 \hs{Low} and \hs{High}.
697 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
699 This is a basic logic type. It can have two values: \hs{True}
701 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
702 % type (where a value of \hs{True} corresponds to a value of
704 Supporting the Bool type is required in order to support the
705 \hs{if-then-else} construct, which requires a \hs{Bool} value for
707 \item[\bf{SizedWord}, \bf{SizedInt}]
708 These are types to represent integers. A \hs{SizedWord} is unsigned,
709 while a \hs{SizedInt} is signed. Both are parametrizable in their
711 % , so you can define an unsigned word of 32 bits wide as follows:
714 % type Word32 = SizedWord D32
717 % Here, a type synonym \hs{Word32} is defined that is equal to the
718 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
719 % \hs{D32} is the \emph{type level representation} of the decimal
720 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
721 % types are translated to the \VHDL\ \texttt{unsigned} and
722 % \texttt{signed} respectively.
724 This is a vector type that can contain elements of any other type and
725 has a fixed length. The \hs{Vector} type constructor takes two type
726 arguments: the length of the vector and the type of the elements
727 contained in it. The short-hand notation used for the vector type in
728 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
729 type, and \hs{n} is the length of the vector.
730 % The state type of an 8 element register bank would then for example
734 % type RegisterState = Vector D8 Word32
737 % Here, a type synonym \hs{RegisterState} is defined that is equal to
738 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
739 % type level representation of the decimal number 8) and \hs{Word32}
740 % (The 32 bit word type as defined above). In other words, the
741 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
742 % vector is translated to a \VHDL\ array type.
744 This is another type to describe integers, but unlike the previous
745 two it has no specific bit-width, but an upper bound. This means that
746 its range is not limited to powers of two, but can be any number.
747 An \hs{Index} only has an upper bound, its lower bound is
748 implicitly zero. The main purpose of the \hs{Index} type is to be
749 used as an index to a \hs{Vector}.
751 % \comment{TODO: Perhaps remove this example?} To define an index for
752 % the 8 element vector above, we would do:
755 % type RegisterIndex = RangedWord D7
758 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
759 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
760 % other words, this defines an unsigned word with values from
761 % 0 to 7 (inclusive). This word can be be used to index the
762 % 8 element vector \hs{RegisterState} above. This type is translated
763 % to the \texttt{unsigned} \VHDL type.
766 \subsubsection{User-defined types}
767 There are three ways to define new types in Haskell: algebraic
768 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
769 keyword and datatype renaming constructs with the \hs{newtype} keyword.
770 \GHC\ offers a few more advanced ways to introduce types (type families,
771 existential typing, {\small{GADT}}s, etc.) which are not standard Haskell.
772 As it is currently unclear how these advanced type constructs correspond
773 with hardware, they are for now unsupported by the \CLaSH\ compiler
775 Only an algebraic datatype declaration actually introduces a
776 completely new type. Type synonyms and renaming constructs only define new
777 names for existing types, where synonyms are completely interchangeable
778 and renaming constructs need explicit conversions. Therefore, these do not
779 need any particular translation, a synonym or renamed type will just use
780 the same representation as the original type. For algebraic types, we can
781 make the following distinctions:
784 \item[\bf{Single constructor}]
785 Algebraic datatypes with a single constructor with one or more
786 fields, are essentially a way to pack a few values together in a
787 record-like structure. Haskell's built-in tuple types are also defined
788 as single constructor algebraic types An example of a single
789 constructor type is the following pair of integers:
791 data IntPair = IntPair Int Int
793 % These types are translated to \VHDL\ record types, with one field
794 % for every field in the constructor.
795 \item[\bf{No fields}]
796 Algebraic datatypes with multiple constructors, but without any
797 fields are essentially a way to get an enumeration-like type
798 containing alternatives. Note that Haskell's \hs{Bool} type is also
799 defined as an enumeration type, but we have a fixed translation for
800 that. An example of such an enum type is the type that represents the
801 colors in a traffic light:
803 data TrafficLight = Red | Orange | Green
805 % These types are translated to \VHDL\ enumerations, with one
806 % value for each constructor. This allows references to these
807 % constructors to be translated to the corresponding enumeration
809 \item[\bf{Multiple constructors with fields}]
810 Algebraic datatypes with multiple constructors, where at least
811 one of these constructors has one or more fields are not
815 \subsection{Polymorphism}
816 A powerful construct in most functional languages is polymorphism, it
817 allows a function to handle values of different data types in a uniform
818 way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
819 meaning functions can be written without mention of any specific type and
820 can be used transparently with any number of new types.
822 As an example of a parametric polymorphic function, consider the type of
823 the following \hs{append} function, which appends an element to a vector:
825 append :: [a|n] -> a -> [a|n + 1]
828 This type is parameterized by \hs{a}, which can contain any type at
829 all. This means that \hs{append} can append an element to a vector,
830 regardless of the type of the elements in the list (as long as the type of
831 the value to be added is of the same type as the values in the vector).
832 This kind of polymorphism is extremely useful in hardware designs to make
833 operations work on a vector without knowing exactly what elements are
834 inside, routing signals without knowing exactly what kinds of signals
835 these are, or working with a vector without knowing exactly how long it
836 is. Polymorphism also plays an important role in most higher order
837 functions, as we will see in the next section.
839 Another type of polymorphism is \emph{ad-hoc
840 polymorphism}~\cite{polymorphism}, which refers to polymorphic
841 functions which can be applied to arguments of different types, but which
842 behave differently depending on the type of the argument to which they are
843 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
844 type classes, where a class definition provides the general interface of a
845 function, and class instances define the functionality for the specific
846 types. An example of such a type class is the \hs{Num} class, which
847 contains all of Haskell's numerical operations. A developer can make use
848 of this ad-hoc polymorphism by adding a constraint to a parametrically
849 polymorphic type variable. Such a constraint indicates that the type
850 variable can only be instantiated to a type whose members supports the
851 overloaded functions associated with the type class.
853 As an example we will take a look at type signature of the function
854 \hs{sum}, which sums the values in a vector:
856 sum :: Num a => [a|n] -> a
859 This type is again parameterized by \hs{a}, but it can only contain
860 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
861 we know that the addition (+) operator is defined for that type.
862 \CLaSH's built-in numerical types are also instances of the \hs{Num}
863 class, so we can use the addition operator on \hs{SizedWords} as
864 well as on \hs{SizedInts}.
866 In \CLaSH, parametric polymorphism is completely supported. Any function
867 defined can have any number of unconstrained type parameters. The \CLaSH\
868 compiler will infer the type of every such argument depending on how the
869 function is applied. There is one exception to this: The top level
870 function that is translated, can not have any polymorphic arguments (as
871 they are never applied, so there is no way to find out the actual types
872 for the type parameters).
874 \CLaSH\ does not support user-defined type classes, but does use some
875 of the built-in type classes for its built-in function, such as: \hs{Num}
876 for numerical operations, \hs{Eq} for the equality operators, and
877 \hs{Ord} for the comparison/order operators.
879 \subsection{Higher-order functions \& values}
880 Another powerful abstraction mechanism in functional languages, is
881 the concept of \emph{higher-order functions}, or \emph{functions as
882 a first class value}. This allows a function to be treated as a
883 value and be passed around, even as the argument of another
884 function. The following example should clarify this concept:
887 negVector xs = map not xs
890 The code above defines a function \hs{negVector}, which takes a vector of
891 booleans, and returns a vector where all the values are negated. It
892 achieves this by calling the \hs{map} function, and passing it
893 \emph{another function}, boolean negation, and the vector of booleans,
894 \hs{xs}. The \hs{map} function applies the negation function to all the
895 elements in the vector.
897 The \hs{map} function is called a higher-order function, since it takes
898 another function as an argument. Also note that \hs{map} is again a
899 parametric polymorphic function: It does not pose any constraints on the
900 type of the vector elements, other than that it must be the same type as
901 the input type of the function passed to \hs{map}. The element type of the
902 resulting vector is equal to the return type of the function passed, which
903 need not necessarily be the same as the element type of the input vector.
904 All of these characteristics can readily be inferred from the type
905 signature belonging to \hs{map}:
908 map :: (a -> b) -> [a|n] -> [b|n]
911 So far, only functions have been used as higher-order values. In
912 Haskell, there are two more ways to obtain a function-typed value:
913 partial application and lambda abstraction. Partial application
914 means that a function that takes multiple arguments can be applied
915 to a single argument, and the result will again be a function (but
916 that takes one argument less). As an example, consider the following
917 expression, that adds one to every element of a vector:
923 Here, the expression \hs{(+) 1} is the partial application of the
924 plus operator to the value \hs{1}, which is again a function that
925 adds one to its argument. A lambda expression allows one to introduce an
926 anonymous function in any expression. Consider the following expression,
927 which again adds one to every element of a vector:
933 Finally, higher order arguments are not limited to just built-in
934 functions, but any function defined in \CLaSH\ can have function
935 arguments. This allows the hardware designer to use a powerful
936 abstraction mechanism in his designs and have an optimal amount of
939 \comment{TODO: Describe ALU example (no code)}
942 A very important concept in hardware it the concept of state. In a
943 stateful design, the outputs depend on the history of the inputs, or the
944 state. State is usually stored in registers, which retain their value
945 during a clock cycle. As we want to describe more than simple
946 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
948 An important property in Haskell, and in most other functional languages,
949 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
952 \item given the same arguments twice, it should return the same value in
954 \item when the function is called, it should not have observable
957 % This purity property is important for functional languages, since it
958 % enables all kinds of mathematical reasoning that could not be guaranteed
959 % correct for impure functions.
960 Pure functions are as such a perfect match or a combinatorial circuit,
961 where the output solely depends on the inputs. When a circuit has state
962 however, it can no longer be simply described by a pure function.
963 % Simply removing the purity property is not a valid option, as the
964 % language would then lose many of it mathematical properties.
965 In an effort to include the concept of state in pure
966 functions, the current value of the state is made an argument of the
967 function; the updated state becomes part of the result. In this sense the
968 descriptions made in \CLaSH are the describing the combinatorial parts of
971 A simple example is adding an accumulator register to the earlier
972 multiply-accumulate circuit, of which the resulting netlist can be seen in
973 \Cref{img:mac-state}:
976 macS (State c) a b = (State c', outp)
983 \centerline{\includegraphics{mac-state.svg}}
984 \caption{Stateful Multiply-Accumulate}
985 \label{img:mac-state}
988 The \hs{State} keyword indicates which arguments are part of the current
989 state, and what part of the output is part of the updated state. This
990 aspect will also reflected in the type signature of the function.
991 Abstracting the state of a circuit in this way makes it very explicit:
992 which variables are part of the state is completely determined by the
993 type signature. This approach to state is well suited to be used in
994 combination with the existing code and language features, such as all the
995 choice constructs, as state values are just normal values. We can simulate
996 stateful descriptions using the recursive \hs{run} function:
999 run f s (i:inps) = o : (run f s' inps)
1004 The \hs{run} function maps a list of inputs over the function that a
1005 developer wants to simulate, passing the state to each new iteration. Each
1006 value in the input list corresponds to exactly one cycle of the (implicit)
1007 clock. The result of the simulation is a list of outputs for every clock
1008 cycle. As both the \hs{run} function and the hardware description are
1009 plain hardware, the complete simulation can be compiled by an optimizing
1012 \section{\CLaSH\ prototype}
1017 As an example of a common hardware design where the use of higher-order
1018 functions leads to a very natural description is a FIR filter, which is
1019 basically the dot-product of two vectors:
1022 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1025 A FIR filter multiplies fixed constants ($h$) with the current
1026 and a few previous input samples ($x$). Each of these multiplications
1027 are summed, to produce the result at time $t$. The equation of a FIR
1028 filter is indeed equivalent to the equation of the dot-product, which is
1032 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
1035 We can easily and directly implement the equation for the dot-product
1036 using higher-order functions:
1039 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
1042 The \hs{zipWith} function is very similar to the \hs{map} function seen
1043 earlier: It takes a function, two vectors, and then applies the function to
1044 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1045 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
1047 The \hs{foldl1} function takes a function, a single vector, and applies
1048 the function to the first two elements of the vector. It then applies the
1049 function to the result of the first application and the next element from
1050 the vector. This continues until the end of the vector is reached. The
1051 result of the \hs{foldl1} function is the result of the last application.
1052 As you can see, the \hs{zipWith (*)} function is just pairwise
1053 multiplication and the \hs{foldl1 (+)} function is just summation.
1055 Returning to the actual FIR filter, we will slightly change the
1056 equation belong to it, so as to make the translation to code more obvious.
1057 What we will do is change the definition of the vector of input samples.
1058 So, instead of having the input sample received at time
1059 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1060 stores the $ith$ previous sample. This changes the equation to the
1061 following (Note that this is completely equivalent to the original
1062 equation, just with a different definition of $x$ that will better suit
1063 the transformation to code):
1066 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1069 Consider that the vector \hs{hs} contains the FIR coefficients and the
1070 vector \hs{xs} contains the current input sample in front and older
1071 samples behind. The function that shifts the input samples is shown below:
1074 x >> xs = x +> tail xs
1077 Where the \hs{tail} function returns all but the first element of a
1078 vector, and the concatenate operator ($\succ$) adds a new element to the
1079 left of a vector. The complete definition of the FIR filter then becomes:
1082 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1085 The resulting netlist of a 4-taps FIR filter based on the above definition
1086 is depicted in \Cref{img:4tapfir}.
1089 \centerline{\includegraphics{4tapfir.svg}}
1090 \caption{4-taps FIR Filter}
1094 \section{Related work}
1095 Many functional hardware description languages have been developed over the
1096 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1097 extension of Backus' \acro{FP} language to synchronous streams, designed
1098 particularly for describing and reasoning about regular circuits. The
1099 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1100 circuits, and has a particular focus on layout.
1102 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1103 functional language \acro{ML}, and has support for polymorphic types and
1104 higher-order functions. Published work suggests that there is no direct
1105 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1106 be translated to \VHDL\ and that the translated description can than be
1107 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1108 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1109 on the other hand can correctly translate all of the language constructs
1110 mentioned in this paper to a netlist format.
1112 Like this work, many functional hardware description languages have some sort
1113 of foundation in the functional programming language Haskell.
1114 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1115 specifications used to model the behavior of superscalar microprocessors. Hawk
1116 specifications can be simulated, but there seems to be no support for
1117 automated circuit synthesis.
1119 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1120 models, which can (manually) be transformed into an implementation model using
1121 semantic preserving transformations. A designer can model systems using
1122 heterogeneous models of computation, which include continuous time,
1123 synchronous and untimed models of computation. Using so-called domain
1124 interfaces a designer can simulate electronic systems which have both analog
1125 as digital parts. ForSyDe has several simulation and synthesis backends,
1126 though synthesis is restricted to the synchronous subset of the ForSyDe
1127 language. Unlike \CLaSH\ there is no support for the automated synthesis of description that contain polymorphism or higher-order functions.
1129 Lava~\cite{Lava} is a hardware description language that focuses on the
1130 structural representation of hardware. Besides support for simulation and
1131 circuit synthesis, Lava descriptions can be interfaced with formal method
1132 tools for formal verification. Lava descriptions are actually circuit
1133 generators when viewed from a synthesis viewpoint, in that the language
1134 elements of Haskell, such as choice, can be used to guide the circuit
1135 generation. If a developer wants to insert a choice element inside an actual
1136 circuit he will have to specify this explicitly as a component.
1138 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1139 such as case-statements and pattern matching, are synthesized to choice
1140 elements in the eventual circuit. As such, richer control structures can both
1141 be specified and synthesized in \CLaSH\ compared to any of the languages
1142 mentioned in this section.
1144 The merits of polymorphic typing, combined with higher-order functions, are
1145 now also recognized in the `main-stream' hardware description languages,
1146 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
1147 support to specify types as generics, thus allowing a developer to describe
1148 polymorphic components. Note that those types still require an explicit
1149 generic map, whereas type-inference and type-specialization are implicit in
1152 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1154 % A functional language designed specifically for hardware design is
1155 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1156 % language called \acro{FL}~\cite{FL} to la
1158 % An example of a floating figure using the graphicx package.
1159 % Note that \label must occur AFTER (or within) \caption.
1160 % For figures, \caption should occur after the \includegraphics.
1161 % Note that IEEEtran v1.7 and later has special internal code that
1162 % is designed to preserve the operation of \label within \caption
1163 % even when the captionsoff option is in effect. However, because
1164 % of issues like this, it may be the safest practice to put all your
1165 % \label just after \caption rather than within \caption{}.
1167 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1168 % option should be used if it is desired that the figures are to be
1169 % displayed while in draft mode.
1173 %\includegraphics[width=2.5in]{myfigure}
1174 % where an .eps filename suffix will be assumed under latex,
1175 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1176 % via \DeclareGraphicsExtensions.
1177 %\caption{Simulation Results}
1181 % Note that IEEE typically puts floats only at the top, even when this
1182 % results in a large percentage of a column being occupied by floats.
1185 % An example of a double column floating figure using two subfigures.
1186 % (The subfig.sty package must be loaded for this to work.)
1187 % The subfigure \label commands are set within each subfloat command, the
1188 % \label for the overall figure must come after \caption.
1189 % \hfil must be used as a separator to get equal spacing.
1190 % The subfigure.sty package works much the same way, except \subfigure is
1191 % used instead of \subfloat.
1193 %\begin{figure*}[!t]
1194 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1195 %\label{fig_first_case}}
1197 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1198 %\label{fig_second_case}}}
1199 %\caption{Simulation results}
1203 % Note that often IEEE papers with subfigures do not employ subfigure
1204 % captions (using the optional argument to \subfloat), but instead will
1205 % reference/describe all of them (a), (b), etc., within the main caption.
1208 % An example of a floating table. Note that, for IEEE style tables, the
1209 % \caption command should come BEFORE the table. Table text will default to
1210 % \footnotesize as IEEE normally uses this smaller font for tables.
1211 % The \label must come after \caption as always.
1214 %% increase table row spacing, adjust to taste
1215 %\renewcommand{\arraystretch}{1.3}
1216 % if using array.sty, it might be a good idea to tweak the value of
1217 % \extrarowheight as needed to properly center the text within the cells
1218 %\caption{An Example of a Table}
1219 %\label{table_example}
1221 %% Some packages, such as MDW tools, offer better commands for making tables
1222 %% than the plain LaTeX2e tabular which is used here.
1223 %\begin{tabular}{|c||c|}
1233 % Note that IEEE does not put floats in the very first column - or typically
1234 % anywhere on the first page for that matter. Also, in-text middle ("here")
1235 % positioning is not used. Most IEEE journals/conferences use top floats
1236 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1237 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1238 % command of the stfloats package.
1242 \section{Conclusion}
1243 The conclusion goes here.
1248 % conference papers do not normally have an appendix
1251 % use section* for acknowledgement
1252 \section*{Acknowledgment}
1255 The authors would like to thank...
1261 % trigger a \newpage just before the given reference
1262 % number - used to balance the columns on the last page
1263 % adjust value as needed - may need to be readjusted if
1264 % the document is modified later
1265 %\IEEEtriggeratref{8}
1266 % The "triggered" command can be changed if desired:
1267 %\IEEEtriggercmd{\enlargethispage{-5in}}
1269 % references section
1271 % can use a bibliography generated by BibTeX as a .bbl file
1272 % BibTeX documentation can be easily obtained at:
1273 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1274 % The IEEEtran BibTeX style support page is at:
1275 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1276 \bibliographystyle{IEEEtran}
1277 % argument is your BibTeX string definitions and bibliography database(s)
1278 \bibliography{IEEEabrv,clash.bib}
1280 % <OR> manually copy in the resultant .bbl file
1281 % set second argument of \begin to the number of references
1282 % (used to reserve space for the reference number labels box)
1283 % \begin{thebibliography}{1}
1285 % \bibitem{IEEEhowto:kopka}
1286 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1287 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1289 % \end{thebibliography}
1297 % vim: set ai sw=2 sts=2 expandtab: