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333 % *** Do not adjust lengths that control margins, column widths, etc. ***
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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\acrotiny#1{{\scriptsize{#1}}}
346 \def\VHDL{\acro{VHDL}}
348 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 \def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}}
351 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
352 % we'll get something more complex later on.
353 \def\hs#1{\texttt{#1}}
354 \def\quote#1{``{#1}"}
356 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
358 \settowidth{\labelwidth}{#1:}
359 \setlength{\labelsep}{0.5em}
360 \setlength{\leftmargin}{\labelwidth}
361 \addtolength{\leftmargin}{\labelsep}
362 \addtolength{\leftmargin}{\parindent}
363 \setlength{\rightmargin}{0pt}
364 \setlength{\listparindent}{\parindent}
365 \setlength{\itemsep}{0 ex plus 0.2ex}
366 \renewcommand{\makelabel}[1]{##1:\hfil}
371 \usepackage{paralist}
373 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
375 \usepackage{cleveref}
376 \crefname{figure}{figure}{figures}
377 \newcommand{\fref}[1]{\cref{#1}}
378 \newcommand{\Fref}[1]{\Cref{#1}}
380 \usepackage{epstopdf}
382 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
384 %include polycode.fmt
390 % can use linebreaks \\ within to get better formatting as desired
391 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
394 % author names and affiliations
395 % use a multiple column layout for up to three different
397 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
398 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
399 Department of EEMCS, University of Twente\\
400 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
401 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl, j.kuper@@utwente.nl}}
403 % \IEEEauthorblockN{Homer Simpson}
404 % \IEEEauthorblockA{Twentieth Century Fox\\
406 % Email: homer@thesimpsons.com}
408 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
409 % \IEEEauthorblockA{Starfleet Academy\\
410 % San Francisco, California 96678-2391\\
411 % Telephone: (800) 555--1212\\
412 % Fax: (888) 555--1212}}
414 % conference papers do not typically use \thanks and this command
415 % is locked out in conference mode. If really needed, such as for
416 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
417 % after \documentclass
419 % for over three affiliations, or if they all won't fit within the width
420 % of the page, use this alternative format:
422 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
423 %Homer Simpson\IEEEauthorrefmark{2},
424 %James Kirk\IEEEauthorrefmark{3},
425 %Montgomery Scott\IEEEauthorrefmark{3} and
426 %Eldon Tyrell\IEEEauthorrefmark{4}}
427 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
428 %Georgia Institute of Technology,
429 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
430 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
431 %Email: homer@thesimpsons.com}
432 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
433 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
434 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
439 % use for special paper notices
440 %\IEEEspecialpapernotice{(Invited Paper)}
445 % make the title area
451 \CLaSH\ is a functional hardware description language that borrows both its
452 syntax and semantics from the functional programming language Haskell. Circuit
453 descriptions can be translated to synthesizable VHDL using the prototype
454 \CLaSH\ compiler. As the circuit descriptions are made in plain Haskell,
455 simulations can also be compiled by a Haskell compiler.
457 The use of polymorphism and higher-order functions allow a circuit designer to
458 describe more abstract and general specifications than are possible in the
459 traditional hardware description languages.
461 % IEEEtran.cls defaults to using nonbold math in the Abstract.
462 % This preserves the distinction between vectors and scalars. However,
463 % if the conference you are submitting to favors bold math in the abstract,
464 % then you can use LaTeX's standard command \boldmath at the very start
465 % of the abstract to achieve this. Many IEEE journals/conferences frown on
466 % math in the abstract anyway.
473 % For peer review papers, you can put extra information on the cover
475 % \ifCLASSOPTIONpeerreview
476 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
479 % For peerreview papers, this IEEEtran command inserts a page break and
480 % creates the second title. It will be ignored for other modes.
481 \IEEEpeerreviewmaketitle
484 \section{Introduction}
485 Hardware description languages have allowed the productivity of hardware
486 engineers to keep pace with the development of chip technology. Standard
487 Hardware description languages, like \VHDL~\cite{VHDL2008} and
488 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
489 programming language. These standard languages are very good at describing
490 detailed hardware properties such as timing behavior, but are generally
491 cumbersome in expressing higher-level abstractions. In an attempt to raise the
492 abstraction level of the descriptions, a great number of approaches based on
493 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
494 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
495 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
496 a time which also saw the birth of the currently popular hardware description
497 languages such as \VHDL. The merit of using a functional language to describe
498 hardware comes from the fact that combinatorial circuits can be directly
499 modeled as mathematical functions and that functional languages are very good
500 at describing and composing mathematical functions.
502 In an attempt to decrease the amount of work involved with creating all the
503 required tooling, such as parsers and type-checkers, many functional hardware
504 description languages are embedded as a domain specific language inside the
505 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
506 means that a developer is given a library of Haskell~\cite{Haskell} functions
507 and types that together form the language primitives of the domain specific
508 language. As a result of how the signals are modeled and abstracted, the
509 functions used to describe a circuit also build a large domain-specific
510 datatype (hidden from the designer) which can then be processed further by an
511 embedded compiler. This compiler actually runs in the same environment as the
512 description; as a result compile-time and run-time become hard to define, as
513 the embedded compiler is usually compiled by the same Haskell compiler as the
514 circuit description itself.
516 The approach taken in this research is not to make another domain specific
517 language embedded in Haskell, but to use (a subset of) the Haskell language
518 itself for the purpose of describing hardware. By taking this approach, we can
519 capture certain language constructs, such as Haskell's choice elements
520 (if-constructs, case-constructs, pattern matching, etc.), which are not
521 available in the functional hardware description languages that are embedded
522 in Haskell as a domain specific language. As far as the authors know, such
523 extensive support for choice-elements is new in the domain of functional
524 hardware description languages. As the hardware descriptions are plain Haskell
525 functions, these descriptions can be compiled for simulation using an
526 optimizing Haskell compiler such as the Glasgow Haskell Compiler (\GHC)~\cite{ghc}.
528 Where descriptions in a conventional hardware description language have an
529 explicit clock for the purpose state and synchronicity, the clock is implied
530 in this research. A developer describes the behavior of the hardware between
531 clock cycles. Many functional hardware description model signals as a stream
532 of all values over time; state is then modeled as a delay on this stream of
533 values. The approach taken in this research is to make the current state of a
534 circuit part of the input of the function and the updated state part of the
535 output. The current abstraction of state and time limits the descriptions to
536 synchronous hardware, there however is room within the language to eventually
537 add a different abstraction mechanism that will allow for the modeling of
538 asynchronous systems.
540 Like the standard hardware description languages, descriptions made in a
541 functional hardware description language must eventually be converted into a
542 netlist. This research also features a prototype translator, which has the
543 same name as the language: \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES}
544 Language for Synchronous Hardware} (pronounced: clash). This compiler converts
545 the Haskell code to equivalently behaving synthesizable \VHDL\ code, ready to
546 be converted to an actual netlist format by an (optimizing) \VHDL\ synthesis
549 Besides trivial circuits such as variants of both the FIR filter and the
550 simple CPU shown in \Cref{sec:usecases}, the \CLaSH\ compiler has also been
551 shown to work for non-trivial descriptions. \CLaSH\ has been able to
552 successfully translate the functional description of a streaming reduction
553 circuit~\cite{reductioncircuit} for floating point numbers.
555 \section{Hardware description in Haskell}
557 \subsection{Function application}
558 The basic syntactic elements of a functional program are functions
559 and function application. These have a single obvious translation to a
562 \item every function is translated to a component,
563 \item every function argument is translated to an input port,
564 \item the result value of a function is translated to an output port,
566 \item function applications are translated to component instantiations.
568 The output port can have a complex type (such as a tuple), so having just
569 a single output port does not pose any limitation. The arguments of a
570 function application are assigned to signals, which are then mapped to
571 the corresponding input ports of the component. The output port of the
572 function is also mapped to a signal, which is used as the result of the
575 Since every top level function generates its own component, the
576 hierarchy of function calls is reflected in the final netlist,% aswell,
577 creating a hierarchical description of the hardware. This separation in
578 different components makes the resulting \VHDL\ output easier to read and
581 As an example we can see the netlist of the |mac| function in
582 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
583 function to calculate $a * b + c$:
586 mac a b c = add (mul a b) c
590 \centerline{\includegraphics{mac.svg}}
591 \caption{Combinatorial Multiply-Accumulate}
595 The result of using a complex input type can be seen in
596 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
597 input tuple for the |a|, |b|, and |c| arguments:
600 mac (a, b, c) = add (mul a b) c
604 \centerline{\includegraphics{mac-nocurry.svg}}
605 \caption{Combinatorial Multiply-Accumulate (complex input)}
606 \label{img:mac-comb-nocurry}
610 In Haskell, choice can be achieved by a large set of language constructs,
611 consisting of: \hs{case} constructs, \hs{if-then-else} constructs,
612 pattern matching, and guards. The easiest of these are the \hs{case}
613 constructs (\hs{if} expressions can be very directly translated to
614 \hs{case} expressions). A \hs{case} construct is translated to a
615 multiplexer, where the control value is linked to the selection port and
616 the output of each case is linked to the corresponding input port on the
618 % A \hs{case} expression can in turn simply be translated to a conditional
619 % assignment in \VHDL, where the conditions use equality comparisons
620 % against the constructors in the \hs{case} expressions.
621 We can see two versions of a contrived example below, the first
622 using a \hs{case} construct and the other using a \hs{if-then-else}
623 constructs, in the code below.
626 sumif pred a b = case pred of
630 Neq -> case a != b of
638 if a == b then a + b else 0
640 if a != b then a + b else 0
644 \centerline{\includegraphics{choice-case.svg}}
645 \caption{Choice - sumif}
649 The example sums two values when they are equal or non-equal (depending on
650 the predicate given) and returns 0 otherwise. Both versions of the example
651 roughly correspond to the same netlist, which is depicted in
654 A slightly more complex (but very powerful) form of choice is pattern
655 matching. A function can be defined in multiple clauses, where each clause
656 specifies a pattern. When the arguments match the pattern, the
657 corresponding clause will be used. Expressions can also contain guards,
658 where the expression is only executed if the guard evaluates to true. Like
659 \hs{if-then-else} constructs, pattern matching and guards have a
660 (straightforward) translation to \hs{case} constructs and can as such be
661 mapped to multiplexers. A third version of the earlier example, using both
662 pattern matching and guards, can be seen below. The version using pattern
663 matching and guards also has roughly the same netlist representation
664 (\Cref{img:choice}) as the earlier two versions of the example.
667 sumif Eq a b | a == b = a + b
669 sumif Neq a b | a != b = a + b
674 % \centerline{\includegraphics{choice-ifthenelse}}
675 % \caption{Choice - \emph{if-then-else}}
680 Haskell is a statically-typed language, meaning that the type of a
681 variable or function is determined at compile-time. Not all of Haskell's
682 typing constructs have a clear translation to hardware, as such this
683 section will only deal with the types that do have a clear correspondence
684 to hardware. The translatable types are divided into two categories:
685 \emph{built-in} types and \emph{user-defined} types. Built-in types are
686 those types for which a direct translation is defined within the \CLaSH\
687 compiler; the term user-defined types should not require any further
688 elaboration. The translatable types are also inferable by the compiler,
689 meaning that a developer does not have to annotate every function with a
692 % Translation of two most basic functional concepts has been
693 % discussed: function application and choice. Before looking further
694 % into less obvious concepts like higher-order expressions and
695 % polymorphism, the possible types that can be used in hardware
696 % descriptions will be discussed.
698 % Some way is needed to translate every value used to its hardware
699 % equivalents. In particular, this means a hardware equivalent for
700 % every \emph{type} used in a hardware description is needed.
702 % The following types are \emph{built-in}, meaning that their hardware
703 % translation is fixed into the \CLaSH\ compiler. A designer can also
704 % define his own types, which will be translated into hardware types
705 % using translation rules that are discussed later on.
707 \subsubsection{Built-in types}
708 The following types have direct translation defined within the \CLaSH\
712 This is the most basic type available. It can have two values:
713 \hs{Low} and \hs{High}.
714 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
716 This is a basic logic type. It can have two values: \hs{True}
718 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
719 % type (where a value of \hs{True} corresponds to a value of
721 Supporting the Bool type is required in order to support the
722 \hs{if-then-else} construct, which requires a \hs{Bool} value for
724 \item[\bf{SizedWord}, \bf{SizedInt}]
725 These are types to represent integers. A \hs{SizedWord} is unsigned,
726 while a \hs{SizedInt} is signed. Both are parametrizable in their
728 % , so you can define an unsigned word of 32 bits wide as follows:
731 % type Word32 = SizedWord D32
734 % Here, a type synonym \hs{Word32} is defined that is equal to the
735 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
736 % \hs{D32} is the \emph{type level representation} of the decimal
737 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
738 % types are translated to the \VHDL\ \texttt{unsigned} and
739 % \texttt{signed} respectively.
741 This is a vector type that can contain elements of any other type and
742 has a fixed length. The \hs{Vector} type constructor takes two type
743 arguments: the length of the vector and the type of the elements
744 contained in it. The short-hand notation used for the vector type in
745 the rest of paper is: \hs{[a|n]}. Where the \hs{a} is the element
746 type, and \hs{n} is the length of the vector.
747 % The state type of an 8 element register bank would then for example
751 % type RegisterState = Vector D8 Word32
754 % Here, a type synonym \hs{RegisterState} is defined that is equal to
755 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
756 % type level representation of the decimal number 8) and \hs{Word32}
757 % (The 32 bit word type as defined above). In other words, the
758 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
759 % vector is translated to a \VHDL\ array type.
761 This is another type to describe integers, but unlike the previous
762 two it has no specific bit-width, but an upper bound. This means that
763 its range is not limited to powers of two, but can be any number.
764 An \hs{Index} only has an upper bound, its lower bound is
765 implicitly zero. The main purpose of the \hs{Index} type is to be
766 used as an index to a \hs{Vector}.
768 % \comment{TODO: Perhaps remove this example?} To define an index for
769 % the 8 element vector above, we would do:
772 % type RegisterIndex = RangedWord D7
775 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
776 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
777 % other words, this defines an unsigned word with values from
778 % 0 to 7 (inclusive). This word can be be used to index the
779 % 8 element vector \hs{RegisterState} above. This type is translated
780 % to the \texttt{unsigned} \VHDL type.
783 \subsubsection{User-defined types}
784 There are three ways to define new types in Haskell: algebraic
785 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
786 keyword and datatype renaming constructs with the \hs{newtype} keyword.
787 \GHC\ offers a few more advanced ways to introduce types (type families,
788 existential typing, {\small{GADT}}s, etc.) which are not standard Haskell.
789 As it is currently unclear how these advanced type constructs correspond
790 with hardware, they are for now unsupported by the \CLaSH\ compiler
792 Only an algebraic datatype declaration actually introduces a
793 completely new type. Type synonyms and renaming constructs only define new
794 names for existing types, where synonyms are completely interchangeable
795 and renaming constructs need explicit conversions. Therefore, these do not
796 need any particular translation, a synonym or renamed type will just use
797 the same representation as the original type. For algebraic types, we can
798 make the following distinctions:
801 \item[\bf{Single constructor}]
802 Algebraic datatypes with a single constructor with one or more
803 fields, are essentially a way to pack a few values together in a
804 record-like structure. Haskell's built-in tuple types are also defined
805 as single constructor algebraic types An example of a single
806 constructor type is the following pair of integers:
808 data IntPair = IntPair Int Int
810 % These types are translated to \VHDL\ record types, with one field
811 % for every field in the constructor.
812 \item[\bf{No fields}]
813 Algebraic datatypes with multiple constructors, but without any
814 fields are essentially a way to get an enumeration-like type
815 containing alternatives. Note that Haskell's \hs{Bool} type is also
816 defined as an enumeration type, but we have a fixed translation for
817 that. An example of such an enum type is the type that represents the
818 colors in a traffic light:
820 data TrafficLight = Red | Orange | Green
822 % These types are translated to \VHDL\ enumerations, with one
823 % value for each constructor. This allows references to these
824 % constructors to be translated to the corresponding enumeration
826 \item[\bf{Multiple constructors with fields}]
827 Algebraic datatypes with multiple constructors, where at least
828 one of these constructors has one or more fields are currently not
832 \subsection{Polymorphism}
833 A powerful construct in most functional languages is polymorphism, it
834 allows a function to handle values of different data types in a uniform
835 way. Haskell supports \emph{parametric polymorphism}~\cite{polymorphism},
836 meaning functions can be written without mention of any specific type and
837 can be used transparently with any number of new types.
839 As an example of a parametric polymorphic function, consider the type of
840 the following \hs{append} function, which appends an element to a vector:
842 append :: [a|n] -> a -> [a|n + 1]
845 This type is parameterized by \hs{a}, which can contain any type at
846 all. This means that \hs{append} can append an element to a vector,
847 regardless of the type of the elements in the list (as long as the type of
848 the value to be added is of the same type as the values in the vector).
849 This kind of polymorphism is extremely useful in hardware designs to make
850 operations work on a vector without knowing exactly what elements are
851 inside, routing signals without knowing exactly what kinds of signals
852 these are, or working with a vector without knowing exactly how long it
853 is. Polymorphism also plays an important role in most higher order
854 functions, as we will see in the next section.
856 Another type of polymorphism is \emph{ad-hoc
857 polymorphism}~\cite{polymorphism}, which refers to polymorphic
858 functions which can be applied to arguments of different types, but which
859 behave differently depending on the type of the argument to which they are
860 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
861 type classes, where a class definition provides the general interface of a
862 function, and class instances define the functionality for the specific
863 types. An example of such a type class is the \hs{Num} class, which
864 contains all of Haskell's numerical operations. A developer can make use
865 of this ad-hoc polymorphism by adding a constraint to a parametrically
866 polymorphic type variable. Such a constraint indicates that the type
867 variable can only be instantiated to a type whose members supports the
868 overloaded functions associated with the type class.
870 As an example we will take a look at type signature of the function
871 \hs{sum}, which sums the values in a vector:
873 sum :: Num a => [a|n] -> a
876 This type is again parameterized by \hs{a}, but it can only contain
877 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
878 we know that the addition (+) operator is defined for that type.
879 \CLaSH's built-in numerical types are also instances of the \hs{Num}
880 class, so we can use the addition operator on \hs{SizedWords} as
881 well as on \hs{SizedInts}.
883 In \CLaSH, parametric polymorphism is completely supported. Any function
884 defined can have any number of unconstrained type parameters. The \CLaSH\
885 compiler will infer the type of every such argument depending on how the
886 function is applied. There is one exception to this: The top level
887 function that is translated, can not have any polymorphic arguments (as
888 they are never applied, so there is no way to find out the actual types
889 for the type parameters).
891 \CLaSH\ does not support user-defined type classes, but does use some
892 of the built-in type classes for its built-in function, such as: \hs{Num}
893 for numerical operations, \hs{Eq} for the equality operators, and
894 \hs{Ord} for the comparison/order operators.
896 \subsection{Higher-order functions \& values}
897 Another powerful abstraction mechanism in functional languages, is
898 the concept of \emph{higher-order functions}, or \emph{functions as
899 a first class value}. This allows a function to be treated as a
900 value and be passed around, even as the argument of another
901 function. The following example should clarify this concept:
904 negVector xs = map not xs
907 The code above defines a function \hs{negVector}, which takes a vector of
908 booleans, and returns a vector where all the values are negated. It
909 achieves this by calling the \hs{map} function, and passing it
910 \emph{another function}, boolean negation, and the vector of booleans,
911 \hs{xs}. The \hs{map} function applies the negation function to all the
912 elements in the vector.
914 The \hs{map} function is called a higher-order function, since it takes
915 another function as an argument. Also note that \hs{map} is again a
916 parametric polymorphic function: It does not pose any constraints on the
917 type of the vector elements, other than that it must be the same type as
918 the input type of the function passed to \hs{map}. The element type of the
919 resulting vector is equal to the return type of the function passed, which
920 need not necessarily be the same as the element type of the input vector.
921 All of these characteristics can readily be inferred from the type
922 signature belonging to \hs{map}:
925 map :: (a -> b) -> [a|n] -> [b|n]
928 So far, only functions have been used as higher-order values. In
929 Haskell, there are two more ways to obtain a function-typed value:
930 partial application and lambda abstraction. Partial application
931 means that a function that takes multiple arguments can be applied
932 to a single argument, and the result will again be a function (but
933 that takes one argument less). As an example, consider the following
934 expression, that adds one to every element of a vector:
940 Here, the expression \hs{(+) 1} is the partial application of the
941 plus operator to the value \hs{1}, which is again a function that
942 adds one to its argument. A lambda expression allows one to introduce an
943 anonymous function in any expression. Consider the following expression,
944 which again adds one to every element of a vector:
950 Finally, higher order arguments are not limited to just built-in
951 functions, but any function defined in \CLaSH\ can have function
952 arguments. This allows the hardware designer to use a powerful
953 abstraction mechanism in his designs and have an optimal amount of
956 \comment{TODO: Describe ALU example (no code)}
959 A very important concept in hardware it the concept of state. In a
960 stateful design, the outputs depend on the history of the inputs, or the
961 state. State is usually stored in registers, which retain their value
962 during a clock cycle. As we want to describe more than simple
963 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
965 An important property in Haskell, and in most other functional languages,
966 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
969 \item given the same arguments twice, it should return the same value in
971 \item when the function is called, it should not have observable
974 % This purity property is important for functional languages, since it
975 % enables all kinds of mathematical reasoning that could not be guaranteed
976 % correct for impure functions.
977 Pure functions are as such a perfect match or a combinatorial circuit,
978 where the output solely depends on the inputs. When a circuit has state
979 however, it can no longer be simply described by a pure function.
980 % Simply removing the purity property is not a valid option, as the
981 % language would then lose many of it mathematical properties.
982 In an effort to include the concept of state in pure
983 functions, the current value of the state is made an argument of the
984 function; the updated state becomes part of the result. In this sense the
985 descriptions made in \CLaSH are the describing the combinatorial parts of
988 A simple example is adding an accumulator register to the earlier
989 multiply-accumulate circuit, of which the resulting netlist can be seen in
990 \Cref{img:mac-state}:
993 macS (State c) a b = (State c', outp)
1000 \centerline{\includegraphics{mac-state.svg}}
1001 \caption{Stateful Multiply-Accumulate}
1002 \label{img:mac-state}
1005 The \hs{State} keyword indicates which arguments are part of the current
1006 state, and what part of the output is part of the updated state. This
1007 aspect will also reflected in the type signature of the function.
1008 Abstracting the state of a circuit in this way makes it very explicit:
1009 which variables are part of the state is completely determined by the
1010 type signature. This approach to state is well suited to be used in
1011 combination with the existing code and language features, such as all the
1012 choice constructs, as state values are just normal values. We can simulate
1013 stateful descriptions using the recursive \hs{run} function:
1016 run f s (i:inps) = o : (run f s' inps)
1021 The \hs{run} function maps a list of inputs over the function that a
1022 developer wants to simulate, passing the state to each new iteration. Each
1023 value in the input list corresponds to exactly one cycle of the (implicit)
1024 clock. The result of the simulation is a list of outputs for every clock
1025 cycle. As both the \hs{run} function and the hardware description are
1026 plain Haskell, the complete simulation can be compiled by an optimizing
1029 \section{\CLaSH\ prototype}
1031 The \CLaSH\ language as presented above can be translated to \VHDL\ using
1032 the prototype \CLaSH\ compiler. This compiler allows experimentation with
1033 the \CLaSH\ language and allows for running \CLaSH\ designs on actual FPGA
1037 \centerline{\includegraphics{compilerpipeline.svg}}
1038 \caption{\CLaSHtiny\ compiler pipeline}
1039 \label{img:compilerpipeline}
1042 The prototype heavily uses \GHC, the Glasgow Haskell Compiler.
1043 \Cref{img:compilerpipeline} shows the \CLaSH\ compiler pipeline. As you can
1044 see, the front-end is completely reused from \GHC, which allows the \CLaSH\
1045 prototype to support most of the Haskell Language. The \GHC\ front-end
1046 produces the program in the \emph{Core} format, which is a very small,
1047 functional, typed language which is relatively easy to process.
1049 The second step in the compilation process is \emph{normalization}. This
1050 step runs a number of \emph{meaning preserving} transformations on the
1051 Core program, to bring it into a \emph{normal form}. This normal form
1052 has a number of restrictions that make the program similar to hardware.
1053 In particular, a program in normal form no longer has any polymorphism
1054 or higher order functions.
1056 The final step is a simple translation to \VHDL.
1059 \label{sec:usecases}
1060 As an example of a common hardware design where the use of higher-order
1061 functions leads to a very natural description is a FIR filter, which is
1062 basically the dot-product of two vectors:
1065 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1068 A FIR filter multiplies fixed constants ($h$) with the current
1069 and a few previous input samples ($x$). Each of these multiplications
1070 are summed, to produce the result at time $t$. The equation of a FIR
1071 filter is indeed equivalent to the equation of the dot-product, which is
1075 \mathbf{x}\bullet\mathbf{y} = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot y_i }
1078 We can easily and directly implement the equation for the dot-product
1079 using higher-order functions:
1082 xs *+* ys = foldl1 (+) (zipWith (*) xs hs)
1085 The \hs{zipWith} function is very similar to the \hs{map} function seen
1086 earlier: It takes a function, two vectors, and then applies the function to
1087 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1088 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]} $\equiv$ \hs{[3,8]}).
1090 The \hs{foldl1} function takes a function, a single vector, and applies
1091 the function to the first two elements of the vector. It then applies the
1092 function to the result of the first application and the next element from
1093 the vector. This continues until the end of the vector is reached. The
1094 result of the \hs{foldl1} function is the result of the last application.
1095 As you can see, the \hs{zipWith (*)} function is just pairwise
1096 multiplication and the \hs{foldl1 (+)} function is just summation.
1098 Returning to the actual FIR filter, we will slightly change the
1099 equation belong to it, so as to make the translation to code more obvious.
1100 What we will do is change the definition of the vector of input samples.
1101 So, instead of having the input sample received at time
1102 $t$ stored in $x_t$, $x_0$ now always stores the current sample, and $x_i$
1103 stores the $ith$ previous sample. This changes the equation to the
1104 following (Note that this is completely equivalent to the original
1105 equation, just with a different definition of $x$ that will better suit
1106 the transformation to code):
1109 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1112 Consider that the vector \hs{hs} contains the FIR coefficients and the
1113 vector \hs{xs} contains the current input sample in front and older
1114 samples behind. The function that shifts the input samples is shown below:
1117 x >> xs = x +> tail xs
1120 Where the \hs{tail} function returns all but the first element of a
1121 vector, and the concatenate operator ($\succ$) adds a new element to the
1122 left of a vector. The complete definition of the FIR filter then becomes:
1125 fir (State (xs,hs)) x = (State (x >> xs,hs), xs *+* hs)
1128 The resulting netlist of a 4-taps FIR filter based on the above definition
1129 is depicted in \Cref{img:4tapfir}.
1132 \centerline{\includegraphics{4tapfir.svg}}
1133 \caption{4-taps \acrotiny{FIR} Filter}
1137 \section{Related work}
1138 Many functional hardware description languages have been developed over the
1139 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1140 extension of Backus' \acro{FP} language to synchronous streams, designed
1141 particularly for describing and reasoning about regular circuits. The
1142 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1143 circuits, and has a particular focus on layout.
1145 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1146 functional language \acro{ML}, and has support for polymorphic types and
1147 higher-order functions. Published work suggests that there is no direct
1148 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1149 be translated to \VHDL\ and that the translated description can than be
1150 simulated in a \VHDL\ simulator. Also not all of the mentioned language
1151 features of \acro{HML} could be translated to hardware. The \CLaSH\ compiler
1152 on the other hand can correctly translate all of the language constructs
1153 mentioned in this paper to a netlist format.
1155 Like this work, many functional hardware description languages have some sort
1156 of foundation in the functional programming language Haskell.
1157 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
1158 specifications used to model the behavior of superscalar microprocessors. Hawk
1159 specifications can be simulated, but there seems to be no support for
1160 automated circuit synthesis.
1162 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1163 models, which can (manually) be transformed into an implementation model using
1164 semantic preserving transformations. A designer can model systems using
1165 heterogeneous models of computation, which include continuous time,
1166 synchronous and untimed models of computation. Using so-called domain
1167 interfaces a designer can simulate electronic systems which have both analog
1168 as digital parts. ForSyDe has several backends including simulation and
1169 automated synthesis, though automated synthesis is restricted to the
1170 synchronous model of computation within ForSyDe. Unlike \CLaSH\ there is no
1171 support for the automated synthesis of descriptions that contain polymorphism
1172 or higher-order functions.
1174 Lava~\cite{Lava} is a hardware description language that focuses on the
1175 structural representation of hardware. Besides support for simulation and
1176 circuit synthesis, Lava descriptions can be interfaced with formal method
1177 tools for formal verification. Lava descriptions are actually circuit
1178 generators when viewed from a synthesis viewpoint, in that the language
1179 elements of Haskell, such as choice, can be used to guide the circuit
1180 generation. If a developer wants to insert a choice element inside an actual
1181 circuit he will have to explicitly instantiate a multiplexer-like component.
1183 In this respect \CLaSH\ differs from Lava, in that all the choice elements,
1184 such as case-statements and pattern matching, are synthesized to choice
1185 elements in the eventual circuit. As such, richer control structures can both
1186 be specified and synthesized in \CLaSH\ compared to any of the languages
1187 mentioned in this section.
1189 The merits of polymorphic typing, combined with higher-order functions, are
1190 now also recognized in the `main-stream' hardware description languages,
1191 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to types, allowing a developer to describe
1192 polymorphic components. Note that those types still require an explicit
1193 generic map, whereas types can be automatically inferred in \CLaSH.
1195 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1197 % A functional language designed specifically for hardware design is
1198 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1199 % language called \acro{FL}~\cite{FL} to la
1201 % An example of a floating figure using the graphicx package.
1202 % Note that \label must occur AFTER (or within) \caption.
1203 % For figures, \caption should occur after the \includegraphics.
1204 % Note that IEEEtran v1.7 and later has special internal code that
1205 % is designed to preserve the operation of \label within \caption
1206 % even when the captionsoff option is in effect. However, because
1207 % of issues like this, it may be the safest practice to put all your
1208 % \label just after \caption rather than within \caption{}.
1210 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1211 % option should be used if it is desired that the figures are to be
1212 % displayed while in draft mode.
1216 %\includegraphics[width=2.5in]{myfigure}
1217 % where an .eps filename suffix will be assumed under latex,
1218 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1219 % via \DeclareGraphicsExtensions.
1220 %\caption{Simulation Results}
1224 % Note that IEEE typically puts floats only at the top, even when this
1225 % results in a large percentage of a column being occupied by floats.
1228 % An example of a double column floating figure using two subfigures.
1229 % (The subfig.sty package must be loaded for this to work.)
1230 % The subfigure \label commands are set within each subfloat command, the
1231 % \label for the overall figure must come after \caption.
1232 % \hfil must be used as a separator to get equal spacing.
1233 % The subfigure.sty package works much the same way, except \subfigure is
1234 % used instead of \subfloat.
1236 %\begin{figure*}[!t]
1237 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1238 %\label{fig_first_case}}
1240 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1241 %\label{fig_second_case}}}
1242 %\caption{Simulation results}
1246 % Note that often IEEE papers with subfigures do not employ subfigure
1247 % captions (using the optional argument to \subfloat), but instead will
1248 % reference/describe all of them (a), (b), etc., within the main caption.
1251 % An example of a floating table. Note that, for IEEE style tables, the
1252 % \caption command should come BEFORE the table. Table text will default to
1253 % \footnotesize as IEEE normally uses this smaller font for tables.
1254 % The \label must come after \caption as always.
1257 %% increase table row spacing, adjust to taste
1258 %\renewcommand{\arraystretch}{1.3}
1259 % if using array.sty, it might be a good idea to tweak the value of
1260 % \extrarowheight as needed to properly center the text within the cells
1261 %\caption{An Example of a Table}
1262 %\label{table_example}
1264 %% Some packages, such as MDW tools, offer better commands for making tables
1265 %% than the plain LaTeX2e tabular which is used here.
1266 %\begin{tabular}{|c||c|}
1276 % Note that IEEE does not put floats in the very first column - or typically
1277 % anywhere on the first page for that matter. Also, in-text middle ("here")
1278 % positioning is not used. Most IEEE journals/conferences use top floats
1279 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1280 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1281 % command of the stfloats package.
1285 \section{Conclusion}
1286 The conclusion goes here.
1291 % conference papers do not normally have an appendix
1294 % use section* for acknowledgement
1295 \section*{Acknowledgment}
1298 The authors would like to thank...
1304 % trigger a \newpage just before the given reference
1305 % number - used to balance the columns on the last page
1306 % adjust value as needed - may need to be readjusted if
1307 % the document is modified later
1308 %\IEEEtriggeratref{8}
1309 % The "triggered" command can be changed if desired:
1310 %\IEEEtriggercmd{\enlargethispage{-5in}}
1312 % references section
1314 % can use a bibliography generated by BibTeX as a .bbl file
1315 % BibTeX documentation can be easily obtained at:
1316 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1317 % The IEEEtran BibTeX style support page is at:
1318 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1319 \bibliographystyle{IEEEtran}
1320 % argument is your BibTeX string definitions and bibliography database(s)
1321 \bibliography{clash}
1323 % <OR> manually copy in the resultant .bbl file
1324 % set second argument of \begin to the number of references
1325 % (used to reserve space for the reference number labels box)
1326 % \begin{thebibliography}{1}
1328 % \bibitem{IEEEhowto:kopka}
1329 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1330 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1332 % \end{thebibliography}
1340 % vim: set ai sw=2 sts=2 expandtab: