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44 %%*************************************************************************
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67 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
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263 % replacement for subfigure.sty. However, subfig.sty requires and
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269 % (recommended due to many improvements over 1.2) of subfig.sty supports
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281 % *** FLOAT PACKAGES ***
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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.
612 sumif pred a b = case pred of
616 Neq -> case a != b of
624 if a == b then a + b else 0
626 if a != b then a + b else 0
630 \centerline{\includegraphics{choice-case.svg}}
631 \caption{Choice - sumif}
635 The example sums two values when they are equal or non-equal (depending on
636 the predicate given) and returns 0 otherwise. Both versions of the example
637 roughly correspond to the same netlist, which is depicted in
640 A slightly more complex (but very powerful) form of choice is pattern
641 matching. A function can be defined in multiple clauses, where each clause
642 specifies a pattern. When the arguments match the pattern, the
643 corresponding clause will be used. Expressions can also contain guards,
644 where the expression is only executed if the guard evaluates to true. Like
645 \hs{if-then-else} constructs, pattern matching and guards have a
646 (straightforward) translation to \hs{case} constructs and can as such be
647 mapped to multiplexers. A third version of the earlier example, using both
648 pattern matching and guards, can be seen below. The version using pattern
649 matching and guards also has roughly the same netlist representation
650 (\Cref{img:choice}) as the earlier two versions of the example.
653 sumif Eq a b | a == b = a + b
654 sumif Neq a b | a != b = a + b
659 % \centerline{\includegraphics{choice-ifthenelse}}
660 % \caption{Choice - \emph{if-then-else}}
665 Haskell is a statically-typed language, meaning that the type of a
666 variable or function is determined at compile-time. Not all of Haskell's
667 typing constructs have a clear translation to hardware, as such this
668 section will only deal with the types that do have a clear correspondence
669 to hardware. The translatable types are divided into two categories:
670 \emph{built-in} types and \emph{user-defined} types. Built-in types are
671 those types for which a direct translation is defined within the \CLaSH\
672 compiler; the term user-defined types should not require any further
673 elaboration. The translatable types are also inferable by the compiler,
674 meaning that a developer does not have to annotate every function with a
677 % Translation of two most basic functional concepts has been
678 % discussed: function application and choice. Before looking further
679 % into less obvious concepts like higher-order expressions and
680 % polymorphism, the possible types that can be used in hardware
681 % descriptions will be discussed.
683 % Some way is needed to translate every value used to its hardware
684 % equivalents. In particular, this means a hardware equivalent for
685 % every \emph{type} used in a hardware description is needed.
687 % The following types are \emph{built-in}, meaning that their hardware
688 % translation is fixed into the \CLaSH\ compiler. A designer can also
689 % define his own types, which will be translated into hardware types
690 % using translation rules that are discussed later on.
692 \subsubsection{Built-in types}
693 The following types have direct translation defined within the \CLaSH\
697 This is the most basic type available. It can have two values:
698 \hs{Low} and \hs{High}.
699 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
701 This is a basic logic type. It can have two values: \hs{True}
703 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
704 % type (where a value of \hs{True} corresponds to a value of
706 Supporting the Bool type is required in order to support the
707 \hs{if-then-else} construct, which requires a \hs{Bool} value for
709 \item[\bf{SizedWord}, \bf{SizedInt}]
710 These are types to represent integers. A \hs{SizedWord} is unsigned,
711 while a \hs{SizedInt} is signed. Both are parametrizable in their
713 % , so you can define an unsigned word of 32 bits wide as follows:
716 % type Word32 = SizedWord D32
719 % Here, a type synonym \hs{Word32} is defined that is equal to the
720 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
721 % \hs{D32} is the \emph{type level representation} of the decimal
722 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
723 % types are translated to the \VHDL\ \texttt{unsigned} and
724 % \texttt{signed} respectively.
726 This is a vector type that can contain elements of any other type and
727 has a fixed length. The \hs{Vector} type constructor takes two type
728 arguments: the length of the vector and the type of the elements
729 contained in it. The short-hand notation used for the vector type in
730 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
731 type, and \hs{n} is the length of the vector.
732 % The state type of an 8 element register bank would then for example
736 % type RegisterState = Vector D8 Word32
739 % Here, a type synonym \hs{RegisterState} is defined that is equal to
740 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
741 % type level representation of the decimal number 8) and \hs{Word32}
742 % (The 32 bit word type as defined above). In other words, the
743 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
744 % vector is translated to a \VHDL\ array type.
746 This is another type to describe integers, but unlike the previous
747 two it has no specific bit-width, but an upper bound. This means that
748 its range is not limited to powers of two, but can be any number.
749 An \hs{Index} only has an upper bound, its lower bound is
750 implicitly zero. The main purpose of the \hs{Index} type is to be
751 used as an index to a \hs{Vector}.
753 % \comment{TODO: Perhaps remove this example?} To define an index for
754 % the 8 element vector above, we would do:
757 % type RegisterIndex = RangedWord D7
760 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
761 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
762 % other words, this defines an unsigned word with values from
763 % 0 to 7 (inclusive). This word can be be used to index the
764 % 8 element vector \hs{RegisterState} above. This type is translated
765 % to the \texttt{unsigned} \VHDL type.
768 \subsubsection{User-defined types}
769 There are three ways to define new types in Haskell: algebraic
770 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
771 keyword and datatype renaming constructs with the \hs{newtype} keyword.
772 \GHC\ offers a few more advanced ways to introduce types (type families,
773 existential typing, {\small{GADT}}s, etc.) which are not standard Haskell.
774 As it is currently unclear how these advanced type constructs correspond
775 with hardware, they are for now unsupported by the \CLaSH\ compiler
777 Only an algebraic datatype declaration actually introduces a
778 completely new type. Type synonyms and renaming constructs only define new
779 names for existing types, where synonyms are completely interchangeable
780 and renaming constructs need explicit conversions. Therefore, these do not
781 need any particular translation, a synonym or renamed type will just use
782 the same representation as the original type. For algebraic types, we can
783 make the following distinctions:
786 \item[\bf{Single constructor}]
787 Algebraic datatypes with a single constructor with one or more
788 fields, are essentially a way to pack a few values together in a
789 record-like structure. Haskell's built-in tuple types are also defined
790 as single constructor algebraic types An example of a single
791 constructor type is the following pair of integers:
793 data IntPair = IntPair Int Int
795 % These types are translated to \VHDL\ record types, with one field
796 % for every field in the constructor.
797 \item[\bf{No fields}]
798 Algebraic datatypes with multiple constructors, but without any
799 fields are essentially a way to get an enumeration-like type
800 containing alternatives. Note that Haskell's \hs{Bool} type is also
801 defined as an enumeration type, but we have a fixed translation for
802 that. An example of such an enum type is the type that represents the
803 colors in a traffic light:
805 data TrafficLight = Red | Orange | Green
807 % These types are translated to \VHDL\ enumerations, with one
808 % value for each constructor. This allows references to these
809 % constructors to be translated to the corresponding enumeration
811 \item[\bf{Multiple constructors with fields}]
812 Algebraic datatypes with multiple constructors, where at least
813 one of these constructors has one or more fields are currently not
817 \subsection{Polymorphism}
818 A powerful construct in most functional languages is polymorphism, it
819 allows a function to handle values of different data types in a uniform
820 way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
821 meaning functions can be written without mention of any specific type and
822 can be used transparently with any number of new types.
824 As an example of a parametric polymorphic function, consider the type of
825 the following \hs{append} function, which appends an element to a vector:
827 append :: [a|n] -> a -> [a|n + 1]
830 This type is parameterized by \hs{a}, which can contain any type at
831 all. This means that \hs{append} can append an element to a vector,
832 regardless of the type of the elements in the list (as long as the type of
833 the value to be added is of the same type as the values in the vector).
834 This kind of polymorphism is extremely useful in hardware designs to make
835 operations work on a vector without knowing exactly what elements are
836 inside, routing signals without knowing exactly what kinds of signals
837 these are, or working with a vector without knowing exactly how long it
838 is. Polymorphism also plays an important role in most higher order
839 functions, as we will see in the next section.
841 Another type of polymorphism is \emph{ad-hoc
842 polymorphism}~\cite{polymorphism}, which refers to polymorphic
843 functions which can be applied to arguments of different types, but which
844 behave differently depending on the type of the argument to which they are
845 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
846 type classes, where a class definition provides the general interface of a
847 function, and class instances define the functionality for the specific
848 types. An example of such a type class is the \hs{Num} class, which
849 contains all of Haskell's numerical operations. A developer can make use
850 of this ad-hoc polymorphism by adding a constraint to a parametrically
851 polymorphic type variable. Such a constraint indicates that the type
852 variable can only be instantiated to a type whose members supports the
853 overloaded functions associated with the type class.
855 As an example we will take a look at type signature of the function
856 \hs{sum}, which sums the values in a vector:
858 sum :: Num a => [a|n] -> a
861 This type is again parameterized by \hs{a}, but it can only contain
862 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
863 we know that the addition (+) operator is defined for that type.
864 \CLaSH's built-in numerical types are also instances of the \hs{Num}
865 class, so we can use the addition operator on \hs{SizedWords} as
866 well as on \hs{SizedInts}.
868 In \CLaSH, parametric polymorphism is completely supported. Any function
869 defined can have any number of unconstrained type parameters. The \CLaSH\
870 compiler will infer the type of every such argument depending on how the
871 function is applied. There is one exception to this: The top level
872 function that is translated, can not have any polymorphic arguments (as
873 they are never applied, so there is no way to find out the actual types
874 for the type parameters).
876 \CLaSH\ does not support user-defined type classes, but does use some
877 of the built-in type classes for its built-in function, such as: \hs{Num}
878 for numerical operations, \hs{Eq} for the equality operators, and
879 \hs{Ord} for the comparison/order operators.
881 \subsection{Higher-order functions \& values}
882 Another powerful abstraction mechanism in functional languages, is
883 the concept of \emph{higher-order functions}, or \emph{functions as
884 a first class value}. This allows a function to be treated as a
885 value and be passed around, even as the argument of another
886 function. The following example should clarify this concept:
889 negVector xs = map not xs
892 The code above defines a function \hs{negVector}, which takes a vector of
893 booleans, and returns a vector where all the values are negated. It
894 achieves this by calling the \hs{map} function, and passing it
895 \emph{another function}, boolean negation, and the vector of booleans,
896 \hs{xs}. The \hs{map} function applies the negation function to all the
897 elements in the vector.
899 The \hs{map} function is called a higher-order function, since it takes
900 another function as an argument. Also note that \hs{map} is again a
901 parametric polymorphic function: It does not pose any constraints on the
902 type of the vector elements, other than that it must be the same type as
903 the input type of the function passed to \hs{map}. The element type of the
904 resulting vector is equal to the return type of the function passed, which
905 need not necessarily be the same as the element type of the input vector.
906 All of these characteristics can readily be inferred from the type
907 signature belonging to \hs{map}:
910 map :: (a -> b) -> [a|n] -> [b|n]
913 So far, only functions have been used as higher-order values. In
914 Haskell, there are two more ways to obtain a function-typed value:
915 partial application and lambda abstraction. Partial application
916 means that a function that takes multiple arguments can be applied
917 to a single argument, and the result will again be a function (but
918 that takes one argument less). As an example, consider the following
919 expression, that adds one to every element of a vector:
925 Here, the expression \hs{(+) 1} is the partial application of the
926 plus operator to the value \hs{1}, which is again a function that
927 adds one to its argument. A lambda expression allows one to introduce an
928 anonymous function in any expression. Consider the following expression,
929 which again adds one to every element of a vector:
935 Finally, higher order arguments are not limited to just built-in
936 functions, but any function defined in \CLaSH\ can have function
937 arguments. This allows the hardware designer to use a powerful
938 abstraction mechanism in his designs and have an optimal amount of
941 \comment{TODO: Describe ALU example (no code)}
944 A very important concept in hardware it the concept of state. In a
945 stateful design, the outputs depend on the history of the inputs, or the
946 state. State is usually stored in registers, which retain their value
947 during a clock cycle. As we want to describe more than simple
948 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
950 An important property in Haskell, and in most other functional languages,
951 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
954 \item given the same arguments twice, it should return the same value in
956 \item when the function is called, it should not have observable
959 % This purity property is important for functional languages, since it
960 % enables all kinds of mathematical reasoning that could not be guaranteed
961 % correct for impure functions.
962 Pure functions are as such a perfect match or a combinatorial circuit,
963 where the output solely depends on the inputs. When a circuit has state
964 however, it can no longer be simply described by a pure function.
965 % Simply removing the purity property is not a valid option, as the
966 % language would then lose many of it mathematical properties.
967 In an effort to include the concept of state in pure
968 functions, the current value of the state is made an argument of the
969 function; the updated state becomes part of the result. In this sense the
970 descriptions made in \CLaSH are the describing the combinatorial parts of
973 A simple example is adding an accumulator register to the earlier
974 multiply-accumulate circuit, of which the resulting netlist can be seen in
975 \Cref{img:mac-state}:
978 macS (State c) a b = (State c', outp)
985 \centerline{\includegraphics{mac-state.svg}}
986 \caption{Stateful Multiply-Accumulate}
987 \label{img:mac-state}
990 The \hs{State} keyword indicates which arguments are part of the current
991 state, and what part of the output is part of the updated state. This
992 aspect will also reflected in the type signature of the function.
993 Abstracting the state of a circuit in this way makes it very explicit:
994 which variables are part of the state is completely determined by the
995 type signature. This approach to state is well suited to be used in
996 combination with the existing code and language features, such as all the
997 choice constructs, as state values are just normal values. We can simulate
998 stateful descriptions using the recursive \hs{run} function:
1001 run f s (i:inps) = o : (run f s' inps)
1006 The \hs{run} function maps a list of inputs over the function that a
1007 developer wants to simulate, passing the state to each new iteration. Each
1008 value in the input list corresponds to exactly one cycle of the (implicit)
1009 clock. The result of the simulation is a list of outputs for every clock
1010 cycle. As both the \hs{run} function and the hardware description are
1011 plain hardware, the complete simulation can be compiled by an optimizing
1014 \section{\CLaSH\ prototype}
1016 The \CLaSH\ language as presented above can be translated to \VHDL\ using
1017 the prototype \CLaSH\ compiler. This compiler allows experimentation with
1018 the \CLaSH\ language and allows for running \CLaSH\ designs on actual FPGA
1022 \centerline{\includegraphics{compilerpipeline.svg}}
1023 \caption{\CLaSH\ compiler pipeline}
1024 \label{img:compilerpipeline}
1027 The prototype heavily uses \GHC, the Glasgow Haskell Compiler.
1028 \Cref{img:compilerpipeline} shows the \CLaSH\ compiler pipeline. As you can
1029 see, the front-end is completely reused from \GHC, which allows the \CLaSH\
1030 prototype to support most of the Haskell Language. The \GHC\ front-end
1031 produces the program in the \emph{Core} format, which is a very small,
1032 functional, typed language which is relatively easy to process.
1034 The second step in the compilation process is \emph{normalization}. This
1035 step runs a number of \emph{meaning preserving} transformations on the
1036 Core program, to bring it into a \emph{normal form}. This normal form
1037 has a number of restrictions that make the program similar to hardware.
1038 In particular, a program in normal form no longer has any polymorphism
1039 or higher order functions.
1041 The final step is a simple translation to \VHDL.
1044 As an example of a common hardware design where the use of higher-order
1045 functions leads to a very natural description is a FIR filter, which is
1046 basically the dot-product of two vectors:
1049 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1052 A FIR filter multiplies fixed constants ($h$) with the current
1053 and a few previous input samples ($x$). Each of these multiplications
1054 are summed, to produce the result at time $t$. The equation of a FIR
1055 filter is indeed equivalent to the equation of the dot-product, which is
1059 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
1062 We can easily and directly implement the equation for the dot-product
1063 using higher-order functions:
1066 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
1069 The \hs{zipWith} function is very similar to the \hs{map} function seen
1070 earlier: It takes a function, two vectors, and then applies the function to
1071 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1072 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
1074 The \hs{foldl1} function takes a function, a single vector, and applies
1075 the function to the first two elements of the vector. It then applies the
1076 function to the result of the first application and the next element from
1077 the vector. This continues until the end of the vector is reached. The
1078 result of the \hs{foldl1} function is the result of the last application.
1079 As you can see, the \hs{zipWith (*)} function is just pairwise
1080 multiplication and the \hs{foldl1 (+)} function is just summation.
1082 Returning to the actual FIR filter, we will slightly change the
1083 equation belong to it, so as to make the translation to code more obvious.
1084 What we will do is change the definition of the vector of input samples.
1085 So, instead of having the input sample received at time
1086 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1087 stores the $ith$ previous sample. This changes the equation to the
1088 following (Note that this is completely equivalent to the original
1089 equation, just with a different definition of $x$ that will better suit
1090 the transformation to code):
1093 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1096 Consider that the vector \hs{hs} contains the FIR coefficients and the
1097 vector \hs{xs} contains the current input sample in front and older
1098 samples behind. The function that shifts the input samples is shown below:
1101 x >> xs = x +> tail xs
1104 Where the \hs{tail} function returns all but the first element of a
1105 vector, and the concatenate operator ($\succ$) adds a new element to the
1106 left of a vector. The complete definition of the FIR filter then becomes:
1109 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1112 The resulting netlist of a 4-taps FIR filter based on the above definition
1113 is depicted in \Cref{img:4tapfir}.
1116 \centerline{\includegraphics{4tapfir.svg}}
1117 \caption{4-taps FIR Filter}
1121 \section{Related work}
1122 Many functional hardware description languages have been developed over the
1123 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1124 extension of Backus' \acro{FP} language to synchronous streams, designed
1125 particularly for describing and reasoning about regular circuits. The
1126 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1127 circuits, and has a particular focus on layout.
1129 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1130 functional language \acro{ML}, and has support for polymorphic types and
1131 higher-order functions. Published work suggests that there is no direct
1132 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1133 be translated to \VHDL\ and that the translated description can than be
1134 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1135 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1136 on the other hand can correctly translate all of the language constructs
1137 mentioned in this paper to a netlist format.
1139 Like this work, many functional hardware description languages have some sort
1140 of foundation in the functional programming language Haskell.
1141 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1142 specifications used to model the behavior of superscalar microprocessors. Hawk
1143 specifications can be simulated, but there seems to be no support for
1144 automated circuit synthesis.
1146 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1147 models, which can (manually) be transformed into an implementation model using
1148 semantic preserving transformations. A designer can model systems using
1149 heterogeneous models of computation, which include continuous time,
1150 synchronous and untimed models of computation. Using so-called domain
1151 interfaces a designer can simulate electronic systems which have both analog
1152 as digital parts. ForSyDe has several simulation and synthesis backends,
1153 though synthesis is restricted to the synchronous subset of the ForSyDe
1154 language. Unlike \CLaSH\ there is no support for the automated synthesis of descriptions that contain polymorphism or higher-order functions.
1156 Lava~\cite{Lava} is a hardware description language that focuses on the
1157 structural representation of hardware. Besides support for simulation and
1158 circuit synthesis, Lava descriptions can be interfaced with formal method
1159 tools for formal verification. Lava descriptions are actually circuit
1160 generators when viewed from a synthesis viewpoint, in that the language
1161 elements of Haskell, such as choice, can be used to guide the circuit
1162 generation. If a developer wants to insert a choice element inside an actual
1163 circuit he will have to explicitly instantiate a multiplexer-like component.
1165 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1166 such as case-statements and pattern matching, are synthesized to choice
1167 elements in the eventual circuit. As such, richer control structures can both
1168 be specified and synthesized in \CLaSH\ compared to any of the languages
1169 mentioned in this section.
1171 The merits of polymorphic typing, combined with higher-order functions, are
1172 now also recognized in the `main-stream' hardware description languages,
1173 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to types, allowing a developer to describe
1174 polymorphic components. Note that those types still require an explicit
1175 generic map, whereas types can be automatically inferred in \CLaSH.
1177 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1179 % A functional language designed specifically for hardware design is
1180 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1181 % language called \acro{FL}~\cite{FL} to la
1183 % An example of a floating figure using the graphicx package.
1184 % Note that \label must occur AFTER (or within) \caption.
1185 % For figures, \caption should occur after the \includegraphics.
1186 % Note that IEEEtran v1.7 and later has special internal code that
1187 % is designed to preserve the operation of \label within \caption
1188 % even when the captionsoff option is in effect. However, because
1189 % of issues like this, it may be the safest practice to put all your
1190 % \label just after \caption rather than within \caption{}.
1192 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1193 % option should be used if it is desired that the figures are to be
1194 % displayed while in draft mode.
1198 %\includegraphics[width=2.5in]{myfigure}
1199 % where an .eps filename suffix will be assumed under latex,
1200 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1201 % via \DeclareGraphicsExtensions.
1202 %\caption{Simulation Results}
1206 % Note that IEEE typically puts floats only at the top, even when this
1207 % results in a large percentage of a column being occupied by floats.
1210 % An example of a double column floating figure using two subfigures.
1211 % (The subfig.sty package must be loaded for this to work.)
1212 % The subfigure \label commands are set within each subfloat command, the
1213 % \label for the overall figure must come after \caption.
1214 % \hfil must be used as a separator to get equal spacing.
1215 % The subfigure.sty package works much the same way, except \subfigure is
1216 % used instead of \subfloat.
1218 %\begin{figure*}[!t]
1219 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1220 %\label{fig_first_case}}
1222 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1223 %\label{fig_second_case}}}
1224 %\caption{Simulation results}
1228 % Note that often IEEE papers with subfigures do not employ subfigure
1229 % captions (using the optional argument to \subfloat), but instead will
1230 % reference/describe all of them (a), (b), etc., within the main caption.
1233 % An example of a floating table. Note that, for IEEE style tables, the
1234 % \caption command should come BEFORE the table. Table text will default to
1235 % \footnotesize as IEEE normally uses this smaller font for tables.
1236 % The \label must come after \caption as always.
1239 %% increase table row spacing, adjust to taste
1240 %\renewcommand{\arraystretch}{1.3}
1241 % if using array.sty, it might be a good idea to tweak the value of
1242 % \extrarowheight as needed to properly center the text within the cells
1243 %\caption{An Example of a Table}
1244 %\label{table_example}
1246 %% Some packages, such as MDW tools, offer better commands for making tables
1247 %% than the plain LaTeX2e tabular which is used here.
1248 %\begin{tabular}{|c||c|}
1258 % Note that IEEE does not put floats in the very first column - or typically
1259 % anywhere on the first page for that matter. Also, in-text middle ("here")
1260 % positioning is not used. Most IEEE journals/conferences use top floats
1261 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1262 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1263 % command of the stfloats package.
1267 \section{Conclusion}
1268 The conclusion goes here.
1273 % conference papers do not normally have an appendix
1276 % use section* for acknowledgement
1277 \section*{Acknowledgment}
1280 The authors would like to thank...
1286 % trigger a \newpage just before the given reference
1287 % number - used to balance the columns on the last page
1288 % adjust value as needed - may need to be readjusted if
1289 % the document is modified later
1290 %\IEEEtriggeratref{8}
1291 % The "triggered" command can be changed if desired:
1292 %\IEEEtriggercmd{\enlargethispage{-5in}}
1294 % references section
1296 % can use a bibliography generated by BibTeX as a .bbl file
1297 % BibTeX documentation can be easily obtained at:
1298 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1299 % The IEEEtran BibTeX style support page is at:
1300 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1301 \bibliographystyle{IEEEtran}
1302 % argument is your BibTeX string definitions and bibliography database(s)
1303 \bibliography{IEEEabrv,clash.bib}
1305 % <OR> manually copy in the resultant .bbl file
1306 % set second argument of \begin to the number of references
1307 % (used to reserve space for the reference number labels box)
1308 % \begin{thebibliography}{1}
1310 % \bibitem{IEEEhowto:kopka}
1311 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1312 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1314 % \end{thebibliography}
1322 % vim: set ai sw=2 sts=2 expandtab: