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67 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
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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}}
379 %include polycode.fmt
385 % can use linebreaks \\ within to get better formatting as desired
386 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
389 % author names and affiliations
390 % use a multiple column layout for up to three different
392 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
393 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
394 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
395 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}}
397 % \IEEEauthorblockN{Homer Simpson}
398 % \IEEEauthorblockA{Twentieth Century Fox\\
400 % Email: homer@thesimpsons.com}
402 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
403 % \IEEEauthorblockA{Starfleet Academy\\
404 % San Francisco, California 96678-2391\\
405 % Telephone: (800) 555--1212\\
406 % Fax: (888) 555--1212}}
408 % conference papers do not typically use \thanks and this command
409 % is locked out in conference mode. If really needed, such as for
410 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
411 % after \documentclass
413 % for over three affiliations, or if they all won't fit within the width
414 % of the page, use this alternative format:
416 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
417 %Homer Simpson\IEEEauthorrefmark{2},
418 %James Kirk\IEEEauthorrefmark{3},
419 %Montgomery Scott\IEEEauthorrefmark{3} and
420 %Eldon Tyrell\IEEEauthorrefmark{4}}
421 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
422 %Georgia Institute of Technology,
423 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
424 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
425 %Email: homer@thesimpsons.com}
426 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
427 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
428 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
433 % use for special paper notices
434 %\IEEEspecialpapernotice{(Invited Paper)}
439 % make the title area
445 The abstract goes here.
447 % IEEEtran.cls defaults to using nonbold math in the Abstract.
448 % This preserves the distinction between vectors and scalars. However,
449 % if the conference you are submitting to favors bold math in the abstract,
450 % then you can use LaTeX's standard command \boldmath at the very start
451 % of the abstract to achieve this. Many IEEE journals/conferences frown on
452 % math in the abstract anyway.
459 % For peer review papers, you can put extra information on the cover
461 % \ifCLASSOPTIONpeerreview
462 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
465 % For peerreview papers, this IEEEtran command inserts a page break and
466 % creates the second title. It will be ignored for other modes.
467 \IEEEpeerreviewmaketitle
470 \section{Introduction}
471 Hardware description languages has allowed the productivity of hardware
472 engineers to keep pace with the development of chip technology. Standard
473 Hardware description languages, like \VHDL~\cite{VHDL2008} and
474 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
475 programming language. These standard languages are very good at describing
476 detailed hardware properties such as timing behavior, but are generally
477 cumbersome in expressing higher-level abstractions. In an attempt to raise the
478 abstraction level of the descriptions, a great number of approaches based on
479 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
480 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
481 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
482 a time which also saw the birth of the currently popular hardware description
483 languages such as \VHDL. The merit of using a functional language to describe
484 hardware comes from the fact that combinatorial circuits can be directly
485 modeled as mathematical functions and that functional languages are very good
486 at describing and composing mathematical functions.
488 In an attempt to decrease the amount of work involved with creating all the
489 required tooling, such as parsers and type-checkers, many functional hardware
490 description languages are embedded as a domain specific language inside the
491 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
492 means that a developer is given a library of Haskell~\cite{Haskell} functions
493 and types that together form the language primitives of the domain specific
494 language. As a result of how the signals are modeled and abstracted, the
495 functions used to describe a circuit also build a large domain-specific
496 datatype (hidden from the designer) which can be further processed by an
497 embedded compiler. This compiler actually runs in the same environment as the
498 description; as a result compile-time and run-time become hard to define, as
499 the embedded compiler is usually compiled by the same Haskell compiler as the
500 circuit description itself.
502 The approach taken in this research is not to make another domain specific
503 language embedded in Haskell, but to use (a subset of) the Haskell language
504 itself for the purpose of describing hardware. By taking this approach, we can
505 capture certain language constructs, such as Haskell's choice elements
506 (if-constructs, case-constructs, pattern matching, etc.), which are not
507 available in the functional hardware description languages that are embedded
508 in Haskell as a domain specific languages. As far as the authors know, such
509 extensive support for choice-elements is new in the domain of functional
510 hardware description languages. As the hardware descriptions are plain Haskell
511 functions, these descriptions can be compiled for simulation using an
512 optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC).
514 Where descriptions in a conventional hardware description language have an
515 explicit clock for the purpose state and synchronicity, the clock is implied
516 in this research. A developer describes the behavior of the hardware between
517 clock cycles, as such, only synchronous systems can be described. Many
518 functional hardware description model signals as a stream of all values over
519 time; state is then modeled as a delay on this stream of values. The approach
520 taken in this research is to make the current state of a circuit part of the
521 input of the function and the updated state part of the output.
523 Like the standard hardware description languages, descriptions made in a
524 functional hardware description language must eventually be converted into a
525 netlist. This research also features a prototype translator called \CLaSH\
526 (pronounced: clash), which converts the Haskell code to equivalently behaving
527 synthesizable \VHDL\ code, ready to be converted to an actual netlist format
528 by an (optimizing) \VHDL\ synthesis tool.
530 \section{Hardware description in Haskell}
532 \subsection{Function application}
533 The basic syntactic elements of a functional program are functions
534 and function application. These have a single obvious translation to a
537 \item every function is translated to a component,
538 \item every function argument is translated to an input port,
539 \item the result value of a function is translated to an output port,
541 \item function applications are translated to component instantiations.
543 The output port can have a complex type (such as a tuple), so having just
544 a single output port does not pose any limitation. The arguments of a
545 function applications are assigned to a signal, which are then mapped to
546 the corresponding input ports of the component. The output port of the
547 function is also mapped to a signal, which is used as the result of the
550 Since every top level function generates its own component, the
551 hierarchy of function calls is reflected in the final netlist,% aswell,
552 creating a hierarchical description of the hardware. This separation in
553 different components makes the resulting \VHDL\ output easier to read and
556 As an example we can see the netlist of the |mac| function in
557 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
558 function to calculate $a * b + c$:
561 mac a b c = add (mul a b) c
565 \centerline{\includegraphics{mac}}
566 \caption{Combinatorial Multiply-Accumulate}
570 The result of using a complex input type can be seen in
571 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
572 input tuple for the |a|, |b|, and |c| arguments:
575 mac (a, b, c) = add (mul a b) c
579 \centerline{\includegraphics{mac-nocurry}}
580 \caption{Combinatorial Multiply-Accumulate (complex input)}
581 \label{img:mac-comb-nocurry}
585 In Haskell, choice can be achieved by a large set of language constructs,
586 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
587 pattern matching, and guards. The easiest of these are the \hs{case}
588 constructs (\hs{if} expressions can be very directly translated to
589 \hs{case} expressions). A \hs{case} construct is translated to a
590 multiplexer, where the control value is linked to the selection port and
591 the output of each case is linked to the corresponding input port on the
593 % A \hs{case} expression can in turn simply be translated to a conditional
594 % assignment in \VHDL, where the conditions use equality comparisons
595 % against the constructors in the \hs{case} expressions.
596 We can see two versions of a contrived example below, the first
597 using a \hs{case} construct and the other using a \hs{if-then-else}
598 constructs, in the code below. The example sums two values when they are
599 equal or non-equal (depending on the predicate given) and returns 0
600 otherwise. Both versions of the example roughly correspond to the same
601 netlist, which is depicted in \Cref{img:choice}.
604 sumif pred a b = case pred of
608 Neq -> case a != b of
616 if a == b then a + b else 0
618 if a != b then a + b else 0
622 \centerline{\includegraphics{choice-case}}
623 \caption{Choice - sumif}
627 A slightly more complex (but very powerful) form of choice is pattern
628 matching. A function can be defined in multiple clauses, where each clause
629 specifies a pattern. When the arguments match the pattern, the
630 corresponding clause will be used. Expressions can also contain guards,
631 where the expression is only executed if the guard evaluates to true. Like
632 \hs{if-then-else} constructs, pattern matching and guards have a
633 (straightforward) translation to \hs{case} constructs and can as such be
634 mapped to multiplexers. A third version of the earlier example, using both
635 pattern matching and guards, can be seen below. The version using pattern
636 matching and guards also has roughly the same netlist representation
637 (\Cref{img:choice}) as the earlier two versions of the example.
640 sumif Eq a b | a == b = a + b
641 sumif Neq a b | a != b = a + b
646 % \centerline{\includegraphics{choice-ifthenelse}}
647 % \caption{Choice - \emph{if-then-else}}
652 Haskell is a statically-typed language, meaning that the type of a
653 variable or function is determined at compile-time. Not all of Haskell's
654 typing constructs have a clear translation to hardware, as such this
655 section will only deal with the types that do have a clear correspondence
656 to hardware. The translatable types are divided into two categories:
657 \emph{built-in} types and \emph{user-defined} types. Built-in types are
658 those types for which a direct translation is defined within the \CLaSH\
659 compiler; the term user-defined types should not require any further
660 elaboration. The translatable types are also inferable by the compiler,
661 meaning that a developer does not have to annotate every function with a
664 % Translation of two most basic functional concepts has been
665 % discussed: function application and choice. Before looking further
666 % into less obvious concepts like higher-order expressions and
667 % polymorphism, the possible types that can be used in hardware
668 % descriptions will be discussed.
670 % Some way is needed to translate every value used to its hardware
671 % equivalents. In particular, this means a hardware equivalent for
672 % every \emph{type} used in a hardware description is needed.
674 % The following types are \emph{built-in}, meaning that their hardware
675 % translation is fixed into the \CLaSH\ compiler. A designer can also
676 % define his own types, which will be translated into hardware types
677 % using translation rules that are discussed later on.
679 \subsubsection{Built-in types}
680 The following types have direct translation defined within the \CLaSH\
684 This is the most basic type available. It can have two values:
685 \hs{Low} and \hs{High}.
686 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
688 This is a basic logic type. It can have two values: \hs{True}
690 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
691 % type (where a value of \hs{True} corresponds to a value of
693 Supporting the Bool type is required in order to support the
694 \hs{if-then-else} construct, which requires a \hs{Bool} value for
696 \item[\bf{SizedWord}, \bf{SizedInt}]
697 These are types to represent integers. A \hs{SizedWord} is unsigned,
698 while a \hs{SizedInt} is signed. Both are parametrizable in their
700 % , so you can define an unsigned word of 32 bits wide as follows:
703 % type Word32 = SizedWord D32
706 % Here, a type synonym \hs{Word32} is defined that is equal to the
707 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
708 % \hs{D32} is the \emph{type level representation} of the decimal
709 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
710 % types are translated to the \VHDL\ \texttt{unsigned} and
711 % \texttt{signed} respectively.
713 This is a vector type that can contain elements of any other type and
714 has a fixed length. The \hs{Vector} type constructor takes two type
715 arguments: the length of the vector and the type of the elements
716 contained in it. The short-hand notation used for the vector type in
717 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
718 type, and \hs{n} is the length of the vector.
719 % The state type of an 8 element register bank would then for example
723 % type RegisterState = Vector D8 Word32
726 % Here, a type synonym \hs{RegisterState} is defined that is equal to
727 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
728 % type level representation of the decimal number 8) and \hs{Word32}
729 % (The 32 bit word type as defined above). In other words, the
730 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
731 % vector is translated to a \VHDL\ array type.
733 This is another type to describe integers, but unlike the previous
734 two it has no specific bit-width, but an upper bound. This means that
735 its range is not limited to powers of two, but can be any number.
736 An \hs{Index} only has an upper bound, its lower bound is
737 implicitly zero. The main purpose of the \hs{Index} type is to be
738 used as an index to a \hs{Vector}.
740 % \comment{TODO: Perhaps remove this example?} To define an index for
741 % the 8 element vector above, we would do:
744 % type RegisterIndex = RangedWord D7
747 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
748 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
749 % other words, this defines an unsigned word with values from
750 % 0 to 7 (inclusive). This word can be be used to index the
751 % 8 element vector \hs{RegisterState} above. This type is translated
752 % to the \texttt{unsigned} \VHDL type.
755 \subsubsection{User-defined types}
756 There are three ways to define new types in Haskell: algebraic
757 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
758 keyword and datatype renaming constructs with the \hs{newtype} keyword.
759 \GHC\ offers a few more advanced ways to introduce types (type families,
760 existential typing, {\small{GADT}}s, etc.) which are not standard Haskell.
761 As it is currently unclear how these advanced type constructs correspond
762 with hardware, they are for now unsupported by the \CLaSH\ compiler
764 Only an algebraic datatype declaration actually introduces a
765 completely new type. Type synonyms and renaming constructs only define new
766 names for existing types, where synonyms are completely interchangeable
767 and renaming constructs need explicit conversions. Therefore, these do not
768 need any particular translation, a synonym or renamed type will just use
769 the same representation as the original type. For algebraic types, we can
770 make the following distinctions:
773 \item[\bf{Single constructor}]
774 Algebraic datatypes with a single constructor with one or more
775 fields, are essentially a way to pack a few values together in a
776 record-like structure. Haskell's built-in tuple types are also defined
777 as single constructor algebraic types An example of a single
778 constructor type is the following pair of integers:
780 data IntPair = IntPair Int Int
782 % These types are translated to \VHDL\ record types, with one field
783 % for every field in the constructor.
784 \item[\bf{No fields}]
785 Algebraic datatypes with multiple constructors, but without any
786 fields are essentially a way to get an enumeration-like type
787 containing alternatives. Note that Haskell's \hs{Bool} type is also
788 defined as an enumeration type, but we have a fixed translation for
789 that. An example of such an enum type is the type that represents the
790 colors in a traffic light:
792 data TrafficLight = Red | Orange | Green
794 % These types are translated to \VHDL\ enumerations, with one
795 % value for each constructor. This allows references to these
796 % constructors to be translated to the corresponding enumeration
798 \item[\bf{Multiple constructors with fields}]
799 Algebraic datatypes with multiple constructors, where at least
800 one of these constructors has one or more fields are not
804 \subsection{Polymorphism}
805 A powerful construct in most functional languages is polymorphism, it
806 allows a function to handle values of different data types in a uniform
807 way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
808 meaning functions can be written without mention of any specific type and
809 can be used transparently with any number of new types.
811 As an example of a parametric polymorphic function, consider the type of
812 the following \hs{append} function, which appends an element to a vector:
814 append :: [a|n] -> a -> [a|n + 1]
817 This type is parameterized by \hs{a}, which can contain any type at
818 all. This means that \hs{append} can append an element to a vector,
819 regardless of the type of the elements in the list (as long as the type of
820 the value to be added is of the same type as the values in the vector).
821 This kind of polymorphism is extremely useful in hardware designs to make
822 operations work on a vector without knowing exactly what elements are
823 inside, routing signals without knowing exactly what kinds of signals
824 these are, or working with a vector without knowing exactly how long it
825 is. Polymorphism also plays an important role in most higher order
826 functions, as we will see in the next section.
828 Another type of polymorphism is \emph{ad-hoc
829 polymorphism}~\cite{polymorphism}, which refers to polymorphic
830 functions which can be applied to arguments of different types, but which
831 behave differently depending on the type of the argument to which they are
832 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
833 type classes, where a class definition provides the general interface of a
834 function, and class instances define the functionality for the specific
835 types. An example of such a type class is the \hs{Num} class, which
836 contains all of Haskell's numerical operations. A developer can make use
837 of this ad-hoc polymorphism by adding a constraint to a parametrically
838 polymorphic type variable. Such a constraint indicates that the type
839 variable can only be instantiated to a type whose members supports the
840 overloaded functions associated with the type class.
842 As an example we will take a look at type signature of the function
843 \hs{sum}, which sums the values in a vector:
845 sum :: Num a => [a|n] -> a
848 This type is again parameterized by \hs{a}, but it can only contain
849 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
850 we know that the addition (+) operator is defined for that type.
851 \CLaSH's built-in numerical types are also instances of the \hs{Num}
852 class, so we can use the addition operator on \hs{SizedWords} as
853 well as on \hs{SizedInts}.
855 In \CLaSH, parametric polymorphism is completely supported. Any function
856 defined can have any number of unconstrained type parameters. The \CLaSH\
857 compiler will infer the type of every such argument depending on how the
858 function is applied. There is one exception to this: The top level
859 function that is translated, can not have any polymorphic arguments (as
860 they are never applied, so there is no way to find out the actual types
861 for the type parameters).
863 \CLaSH\ does not support user-defined type classes, but does use some
864 of the built-in type classes for its built-in function, such as: \hs{Num}
865 for numerical operations, \hs{Eq} for the equality operators, and
866 \hs{Ord} for the comparison/order operators.
868 \subsection{Higher-order functions \& values}
869 Another powerful abstraction mechanism in functional languages, is
870 the concept of \emph{higher-order functions}, or \emph{functions as
871 a first class value}. This allows a function to be treated as a
872 value and be passed around, even as the argument of another
873 function. The following example should clarify this concept:
876 negVector xs = map not xs
879 The code above defines a function \hs{negVector}, which takes a vector of
880 booleans, and returns a vector where all the values are negated. It
881 achieves this by calling the \hs{map} function, and passing it
882 \emph{another function}, boolean negation, and the vector of booleans,
883 \hs{xs}. The \hs{map} function applies the negation function to all the
884 elements in the vector.
886 The \hs{map} function is called a higher-order function, since it takes
887 another function as an argument. Also note that \hs{map} is again a
888 parametric polymorphic function: It does not pose any constraints on the
889 type of the vector elements, other than that it must be the same type as
890 the input type of the function passed to \hs{map}. The element type of the
891 resulting vector is equal to the return type of the function passed, which
892 need not necessarily be the same as the element type of the input vector.
893 All of these characteristics can readily be inferred from the type
894 signature belonging to \hs{map}:
897 map :: (a -> b) -> [a|n] -> [b|n]
900 As an example of a common hardware design where the use of higher-order
901 functions leads to a very natural description is a FIR filter, which is
902 basically the dot-product of two vectors:
905 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
908 A FIR filter multiplies fixed constants ($h$) with the current
909 and a few previous input samples ($x$). Each of these multiplications
910 are summed, to produce the result at time $t$. The equation of the FIR
911 filter is indeed equivalent to the equation of the dot-product, which is
915 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
918 We can easily and directly implement the equation for the dot-product
919 using higher-order functions:
922 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
925 The \hs{zipWith} function is very similar to the \hs{map} function: It
926 takes a function, two vectors, and then applies the function to each of
927 the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*) [1,
928 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
930 The \hs{foldl1} function takes a function, a single vector, and applies
931 the function to the first two elements of the vector. It then applies the
932 function to the result of the first application and the next element from
933 the vector. This continues until the end of the vector is reached. The
934 result of the \hs{foldl1} function is the result of the last application.
935 As you can see, the \hs{zipWith (*)} function is just pairwise
936 multiplication and the \hs{foldl1 (+)} function is just summation.
938 So far, only functions have been used as higher-order values. In
939 Haskell, there are two more ways to obtain a function-typed value:
940 partial application and lambda abstraction. Partial application
941 means that a function that takes multiple arguments can be applied
942 to a single argument, and the result will again be a function (but
943 that takes one argument less). As an example, consider the following
944 expression, that adds one to every element of a vector:
950 Here, the expression \hs{(+) 1} is the partial application of the
951 plus operator to the value \hs{1}, which is again a function that
952 adds one to its argument. A lambda expression allows one to introduce an
953 anonymous function in any expression. Consider the following expression,
954 which again adds one to every element of a vector:
960 Finally, higher order arguments are not limited to just built-in
961 functions, but any function defined in \CLaSH\ can have function
962 arguments. This allows the hardware designer to use a powerful
963 abstraction mechanism in his designs and have an optimal amount of
966 \comment{TODO: Describe ALU example (no code)}
969 A very important concept in hardware it the concept of state. In a
970 stateful design, the outputs depend on the history of the inputs, or the
971 state. State is usually stored in registers, which retain their value
972 during a clock cycle. As we want to describe more than simple
973 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
975 An important property in Haskell, and in most other functional languages,
976 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
979 \item given the same arguments twice, it should return the same value in
981 \item when the function is called, it should not have observable
984 % This purity property is important for functional languages, since it
985 % enables all kinds of mathematical reasoning that could not be guaranteed
986 % correct for impure functions.
987 Pure functions are as such a perfect match or a combinatorial circuit,
988 where the output solely depends on the inputs. When a circuit has state
989 however, it can no longer be simply described by a pure function.
990 % Simply removing the purity property is not a valid option, as the
991 % language would then lose many of it mathematical properties.
992 In an effort to include the concept of state in pure
993 functions, the current value of the state is made an argument of the
994 function; the updated state becomes part of the result. In this sense the
995 descriptions made in \CLaSH are the describing the combinatorial parts of
998 A simple example is adding an accumulator register to the earlier
999 multiply-accumulate circuit, of which the resulting netlist can be seen in
1000 \Cref{img:mac-state}:
1003 macS (State c) a b = (State c', outp)
1010 \centerline{\includegraphics{mac-state}}
1011 \caption{Stateful Multiply-Accumulate}
1012 \label{img:mac-state}
1015 The \hs{State} keyword indicates which arguments are part of the current
1016 state, and what part of the output is part of the updated state. This
1017 aspect will also reflected in the type signature of the function.
1018 Abstracting the state of a circuit in this way makes it very explicit:
1019 which variables are part of the state is completely determined by the
1020 type signature. This approach to state is well suited to be used in
1021 combination with the existing code and language features, such as all the
1022 choice constructs, as state values are just normal values.
1024 Returning to the example of the FIR filter, we will slightly change the
1025 equation belong to it, so as to make the translation to code more obvious.
1026 What we will do is change the definition of the vector of input samples.
1027 So, instead of having the input sample received at time
1028 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1029 stores the $ith$ previous sample. This changes the equation to the
1030 following (Note that this is completely equivalent to the original
1031 equation, just with a different definition of $x$ that will better suit
1032 the the transformation to code):
1035 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1038 Consider that the vector \hs{hs} contains the FIR coefficients and the
1039 vector \hs{xs} contains the current input sample in front and older
1040 samples behind. The function that does this shifting of the input samples
1044 x >> xs = x +> tail xs
1047 Where the \hs{tail} functions returns all but the first element of a
1048 vector, and the concatenate operator ($\succ$) adds the new element to the
1049 left of a vector. The complete definition of the FIR filter then becomes:
1052 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1055 The resulting netlist of a 4-taps FIR filter based on the above definition
1056 is depicted in \Cref{img:4tapfir}.
1059 \centerline{\includegraphics{4tapfir}}
1060 \caption{4-taps FIR Filter}
1064 \section{\CLaSH\ prototype}
1068 \section{Related work}
1069 Many functional hardware description languages have been developed over the
1070 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1071 extension of Backus' \acro{FP} language to synchronous streams, designed
1072 particularly for describing and reasoning about regular circuits. The
1073 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1074 circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a
1075 hardware modeling language based on the strict functional language
1076 \acro{ML}, and has support for polymorphic types and higher-order functions.
1077 Published work suggests that there is no direct simulation support for
1078 \acro{HML}, and that the translation to \VHDL\ is only partial.
1080 Like this work, many functional hardware description languages have some sort
1081 of foundation in the functional programming language Haskell.
1082 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1083 specifications used to model the behavior of superscalar microprocessors. Hawk
1084 specifications can be simulated, but there seems to be no support for
1085 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
1086 to specify abstract system models, which can (manually) be transformed into an
1087 implementation model using semantic preserving transformations. ForSyDe has
1088 several simulation and synthesis backends, though synthesis is restricted to
1089 the synchronous subset of the ForSyDe language.
1091 Lava~\cite{Lava} is a hardware description language that focuses on the
1092 structural representation of hardware. Besides support for simulation and
1093 circuit synthesis, Lava descriptions can be interfaced with formal method
1094 tools for formal verification. Lava descriptions are actually circuit
1095 generators when viewed from a synthesis viewpoint, in that the language
1096 elements of Haskell, such as choice, can be used to guide the circuit
1097 generation. If a developer wants to insert a choice element inside an actual
1098 circuit he will have to specify this explicitly as a component. In this
1099 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
1100 case-statements and pattern matching, are synthesized to choice elements in the
1101 eventual circuit. As such, richer control structures can both be specified and
1102 synthesized in \CLaSH\ compared to any of the languages mentioned in this
1105 The merits of polymorphic typing, combined with higher-order functions, are
1106 now also recognized in the `main-stream' hardware description languages,
1107 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
1108 support to specify types as generics, thus allowing a developer to describe
1109 polymorphic components. Note that those types still require an explicit
1110 generic map, whereas type-inference and type-specialization are implicit in
1113 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1115 % A functional language designed specifically for hardware design is
1116 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1117 % language called \acro{FL}~\cite{FL} to la
1119 % An example of a floating figure using the graphicx package.
1120 % Note that \label must occur AFTER (or within) \caption.
1121 % For figures, \caption should occur after the \includegraphics.
1122 % Note that IEEEtran v1.7 and later has special internal code that
1123 % is designed to preserve the operation of \label within \caption
1124 % even when the captionsoff option is in effect. However, because
1125 % of issues like this, it may be the safest practice to put all your
1126 % \label just after \caption rather than within \caption{}.
1128 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1129 % option should be used if it is desired that the figures are to be
1130 % displayed while in draft mode.
1134 %\includegraphics[width=2.5in]{myfigure}
1135 % where an .eps filename suffix will be assumed under latex,
1136 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1137 % via \DeclareGraphicsExtensions.
1138 %\caption{Simulation Results}
1142 % Note that IEEE typically puts floats only at the top, even when this
1143 % results in a large percentage of a column being occupied by floats.
1146 % An example of a double column floating figure using two subfigures.
1147 % (The subfig.sty package must be loaded for this to work.)
1148 % The subfigure \label commands are set within each subfloat command, the
1149 % \label for the overall figure must come after \caption.
1150 % \hfil must be used as a separator to get equal spacing.
1151 % The subfigure.sty package works much the same way, except \subfigure is
1152 % used instead of \subfloat.
1154 %\begin{figure*}[!t]
1155 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1156 %\label{fig_first_case}}
1158 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1159 %\label{fig_second_case}}}
1160 %\caption{Simulation results}
1164 % Note that often IEEE papers with subfigures do not employ subfigure
1165 % captions (using the optional argument to \subfloat), but instead will
1166 % reference/describe all of them (a), (b), etc., within the main caption.
1169 % An example of a floating table. Note that, for IEEE style tables, the
1170 % \caption command should come BEFORE the table. Table text will default to
1171 % \footnotesize as IEEE normally uses this smaller font for tables.
1172 % The \label must come after \caption as always.
1175 %% increase table row spacing, adjust to taste
1176 %\renewcommand{\arraystretch}{1.3}
1177 % if using array.sty, it might be a good idea to tweak the value of
1178 % \extrarowheight as needed to properly center the text within the cells
1179 %\caption{An Example of a Table}
1180 %\label{table_example}
1182 %% Some packages, such as MDW tools, offer better commands for making tables
1183 %% than the plain LaTeX2e tabular which is used here.
1184 %\begin{tabular}{|c||c|}
1194 % Note that IEEE does not put floats in the very first column - or typically
1195 % anywhere on the first page for that matter. Also, in-text middle ("here")
1196 % positioning is not used. Most IEEE journals/conferences use top floats
1197 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1198 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1199 % command of the stfloats package.
1203 \section{Conclusion}
1204 The conclusion goes here.
1209 % conference papers do not normally have an appendix
1212 % use section* for acknowledgement
1213 \section*{Acknowledgment}
1216 The authors would like to thank...
1222 % trigger a \newpage just before the given reference
1223 % number - used to balance the columns on the last page
1224 % adjust value as needed - may need to be readjusted if
1225 % the document is modified later
1226 %\IEEEtriggeratref{8}
1227 % The "triggered" command can be changed if desired:
1228 %\IEEEtriggercmd{\enlargethispage{-5in}}
1230 % references section
1232 % can use a bibliography generated by BibTeX as a .bbl file
1233 % BibTeX documentation can be easily obtained at:
1234 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1235 % The IEEEtran BibTeX style support page is at:
1236 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1237 \bibliographystyle{IEEEtran}
1238 % argument is your BibTeX string definitions and bibliography database(s)
1239 \bibliography{IEEEabrv,clash.bib}
1241 % <OR> manually copy in the resultant .bbl file
1242 % set second argument of \begin to the number of references
1243 % (used to reserve space for the reference number labels box)
1244 % \begin{thebibliography}{1}
1246 % \bibitem{IEEEhowto:kopka}
1247 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1248 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1250 % \end{thebibliography}
1258 % vim: set ai sw=2 sts=2 expandtab: