7 %% http://www.michaelshell.org/
8 %% for current contact information.
10 %% This is a skeleton file demonstrating the use of IEEEtran.cls
11 %% (requires IEEEtran.cls version 1.7 or later) with an IEEE conference paper.
14 %% http://www.michaelshell.org/tex/ieeetran/
15 %% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
17 %% http://www.ieee.org/
19 %%*************************************************************************
21 %% This code is offered as-is without any warranty either expressed or
22 %% implied; without even the implied warranty of MERCHANTABILITY or
23 %% FITNESS FOR A PARTICULAR PURPOSE!
24 %% User assumes all risk.
25 %% In no event shall IEEE or any contributor to this code be liable for
26 %% any damages or losses, including, but not limited to, incidental,
27 %% consequential, or any other damages, resulting from the use or misuse
28 %% of any information contained here.
30 %% All comments are the opinions of their respective authors and are not
31 %% necessarily endorsed by the IEEE.
33 %% This work is distributed under the LaTeX Project Public License (LPPL)
34 %% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
35 %% distributed and modified. A copy of the LPPL, version 1.3, is included
36 %% in the base LaTeX documentation of all distributions of LaTeX released
37 %% 2003/12/01 or later.
38 %% Retain all contribution notices and credits.
39 %% ** Modified files should be clearly indicated as such, including **
40 %% ** renaming them and changing author support contact information. **
42 %% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
43 %% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
44 %%*************************************************************************
46 % *** Authors should verify (and, if needed, correct) their LaTeX system ***
47 % *** with the testflow diagnostic prior to trusting their LaTeX platform ***
48 % *** with production work. IEEE's font choices can trigger bugs that do ***
49 % *** not appear when using other class files. ***
50 % The testflow support page is at:
51 % http://www.michaelshell.org/tex/testflow/
55 % Note that the a4paper option is mainly intended so that authors in
56 % countries using A4 can easily print to A4 and see how their papers will
57 % look in print - the typesetting of the document will not typically be
58 % affected with changes in paper size (but the bottom and side margins will).
59 % Use the testflow package mentioned above to verify correct handling of
60 % both paper sizes by the user's LaTeX system.
62 % Also note that the "draftcls" or "draftclsnofoot", not "draft", option
63 % should be used if it is desired that the figures are to be displayed in
67 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
68 \IEEEoverridecommandlockouts
69 % Add the compsoc option for Computer Society conferences.
71 % If IEEEtran.cls has not been installed into the LaTeX system files,
72 % manually specify the path to it like:
73 % \documentclass[conference]{../sty/IEEEtran}
75 % Some very useful LaTeX packages include:
76 % (uncomment the ones you want to load)
78 % *** MISC UTILITY PACKAGES ***
81 % Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
82 % compilation based on whether the output is pdf or dvi.
89 % The latest version of ifpdf.sty can be obtained from:
90 % http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
91 % Also, note that IEEEtran.cls V1.7 and later provides a builtin
92 % \ifCLASSINFOpdf conditional that works the same way.
93 % When switching from latex to pdflatex and vice-versa, the compiler may
94 % have to be run twice to clear warning/error messages.
98 % *** CITATION PACKAGES ***
101 % cite.sty was written by Donald Arseneau
102 % V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
103 % \cite{} output to follow that of IEEE. Loading the cite package will
104 % result in citation numbers being automatically sorted and properly
105 % "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
106 % cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
107 % \cite will automatically add leading space, if needed. Use cite.sty's
108 % noadjust option (cite.sty V3.8 and later) if you want to turn this off.
109 % cite.sty is already installed on most LaTeX systems. Be sure and use
110 % version 4.0 (2003-05-27) and later if using hyperref.sty. cite.sty does
111 % not currently provide for hyperlinked citations.
112 % The latest version can be obtained at:
113 % http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
114 % The documentation is contained in the cite.sty file itself.
121 % *** GRAPHICS RELATED PACKAGES ***
124 \usepackage[pdftex]{graphicx}
125 % declare the path(s) where your graphic files are
126 % \graphicspath{{../pdf/}{../jpeg/}}
127 % and their extensions so you won't have to specify these with
128 % every instance of \includegraphics
129 % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
131 % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
132 % will default to the driver specified in the system graphics.cfg if no
133 % driver is specified.
134 % \usepackage[dvips]{graphicx}
135 % declare the path(s) where your graphic files are
136 % \graphicspath{{../eps/}}
137 % and their extensions so you won't have to specify these with
138 % every instance of \includegraphics
139 % \DeclareGraphicsExtensions{.eps}
141 % graphicx was written by David Carlisle and Sebastian Rahtz. It is
142 % required if you want graphics, photos, etc. graphicx.sty is already
143 % installed on most LaTeX systems. The latest version and documentation can
145 % http://www.ctan.org/tex-archive/macros/latex/required/graphics/
146 % Another good source of documentation is "Using Imported Graphics in
147 % LaTeX2e" by Keith Reckdahl which can be found as epslatex.ps or
148 % epslatex.pdf at: http://www.ctan.org/tex-archive/info/
150 % latex, and pdflatex in dvi mode, support graphics in encapsulated
151 % postscript (.eps) format. pdflatex in pdf mode supports graphics
152 % in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
153 % that all non-photo figures use a vector format (.eps, .pdf, .mps) and
154 % not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
155 % which can result in "jaggedy"/blurry rendering of lines and letters as
156 % well as large increases in file sizes.
158 % You can find documentation about the pdfTeX application at:
159 % http://www.tug.org/applications/pdftex
165 % *** MATH PACKAGES ***
167 %\usepackage[cmex10]{amsmath}
168 % A popular package from the American Mathematical Society that provides
169 % many useful and powerful commands for dealing with mathematics. If using
170 % it, be sure to load this package with the cmex10 option to ensure that
171 % only type 1 fonts will utilized at all point sizes. Without this option,
172 % it is possible that some math symbols, particularly those within
173 % footnotes, will be rendered in bitmap form which will result in a
174 % document that can not be IEEE Xplore compliant!
176 % Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
177 % thus preventing page breaks from occurring within multiline equations. Use:
178 %\interdisplaylinepenalty=2500
179 % after loading amsmath to restore such page breaks as IEEEtran.cls normally
180 % does. amsmath.sty is already installed on most LaTeX systems. The latest
181 % version and documentation can be obtained at:
182 % http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/
188 % *** SPECIALIZED LIST PACKAGES ***
190 %\usepackage{algorithmic}
191 % algorithmic.sty was written by Peter Williams and Rogerio Brito.
192 % This package provides an algorithmic environment fo describing algorithms.
193 % You can use the algorithmic environment in-text or within a figure
194 % environment to provide for a floating algorithm. Do NOT use the algorithm
195 % floating environment provided by algorithm.sty (by the same authors) or
196 % algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
197 % algorithm float types and packages that provide these will not provide
198 % correct IEEE style captions. The latest version and documentation of
199 % algorithmic.sty can be obtained at:
200 % http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
201 % There is also a support site at:
202 % http://algorithms.berlios.de/index.html
203 % Also of interest may be the (relatively newer and more customizable)
204 % algorithmicx.sty package by Szasz Janos:
205 % http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/
210 % *** ALIGNMENT PACKAGES ***
213 % Frank Mittelbach's and David Carlisle's array.sty patches and improves
214 % the standard LaTeX2e array and tabular environments to provide better
215 % appearance and additional user controls. As the default LaTeX2e table
216 % generation code is lacking to the point of almost being broken with
217 % respect to the quality of the end results, all users are strongly
218 % advised to use an enhanced (at the very least that provided by array.sty)
219 % set of table tools. array.sty is already installed on most systems. The
220 % latest version and documentation can be obtained at:
221 % http://www.ctan.org/tex-archive/macros/latex/required/tools/
224 %\usepackage{mdwmath}
226 % Also highly recommended is Mark Wooding's extremely powerful MDW tools,
227 % especially mdwmath.sty and mdwtab.sty which are used to format equations
228 % and tables, respectively. The MDWtools set is already installed on most
229 % LaTeX systems. The lastest version and documentation is available at:
230 % http://www.ctan.org/tex-archive/macros/latex/contrib/mdwtools/
233 % IEEEtran contains the IEEEeqnarray family of commands that can be used to
234 % generate multiline equations as well as matrices, tables, etc., of high
238 %\usepackage{eqparbox}
239 % Also of notable interest is Scott Pakin's eqparbox package for creating
240 % (automatically sized) equal width boxes - aka "natural width parboxes".
242 % http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/
248 % *** SUBFIGURE PACKAGES ***
249 %\usepackage[tight,footnotesize]{subfigure}
250 % subfigure.sty was written by Steven Douglas Cochran. This package makes it
251 % easy to put subfigures in your figures. e.g., "Figure 1a and 1b". For IEEE
252 % work, it is a good idea to load it with the tight package option to reduce
253 % the amount of white space around the subfigures. subfigure.sty is already
254 % installed on most LaTeX systems. The latest version and documentation can
256 % http://www.ctan.org/tex-archive/obsolete/macros/latex/contrib/subfigure/
257 % subfigure.sty has been superceeded by subfig.sty.
261 %\usepackage[caption=false]{caption}
262 %\usepackage[font=footnotesize]{subfig}
263 % subfig.sty, also written by Steven Douglas Cochran, is the modern
264 % replacement for subfigure.sty. However, subfig.sty requires and
265 % automatically loads Axel Sommerfeldt's caption.sty which will override
266 % IEEEtran.cls handling of captions and this will result in nonIEEE style
267 % figure/table captions. To prevent this problem, be sure and preload
268 % caption.sty with its "caption=false" package option. This is will preserve
269 % IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
270 % (recommended due to many improvements over 1.2) of subfig.sty supports
271 % the caption=false option directly:
272 %\usepackage[caption=false,font=footnotesize]{subfig}
274 % The latest version and documentation can be obtained at:
275 % http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/
276 % The latest version and documentation of caption.sty can be obtained at:
277 % http://www.ctan.org/tex-archive/macros/latex/contrib/caption/
282 % *** FLOAT PACKAGES ***
284 %\usepackage{fixltx2e}
285 % fixltx2e, the successor to the earlier fix2col.sty, was written by
286 % Frank Mittelbach and David Carlisle. This package corrects a few problems
287 % in the LaTeX2e kernel, the most notable of which is that in current
288 % LaTeX2e releases, the ordering of single and double column floats is not
289 % guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
290 % single column figure to be placed prior to an earlier double column
291 % figure. The latest version and documentation can be found at:
292 % http://www.ctan.org/tex-archive/macros/latex/base/
296 %\usepackage{stfloats}
297 % stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
298 % the ability to do double column floats at the bottom of the page as well
299 % as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
300 % LaTeX2e). It also provides a command:
302 % to enable the placement of footnotes below bottom floats (the standard
303 % LaTeX2e kernel puts them above bottom floats). This is an invasive package
304 % which rewrites many portions of the LaTeX2e float routines. It may not work
305 % with other packages that modify the LaTeX2e float routines. The latest
306 % version and documentation can be obtained at:
307 % http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
308 % Documentation is contained in the stfloats.sty comments as well as in the
309 % presfull.pdf file. Do not use the stfloats baselinefloat ability as IEEE
310 % does not allow \baselineskip to stretch. Authors submitting work to the
311 % IEEE should note that IEEE rarely uses double column equations and
312 % that authors should try to avoid such use. Do not be tempted to use the
313 % cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does
314 % not format its papers in such ways.
320 % *** PDF, URL AND HYPERLINK PACKAGES ***
323 % url.sty was written by Donald Arseneau. It provides better support for
324 % handling and breaking URLs. url.sty is already installed on most LaTeX
325 % systems. The latest version can be obtained at:
326 % http://www.ctan.org/tex-archive/macros/latex/contrib/misc/
327 % Read the url.sty source comments for usage information. Basically,
334 % *** Do not adjust lengths that control margins, column widths, etc. ***
335 % *** Do not use packages that alter fonts (such as pslatex). ***
336 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
337 % (Unless specifically asked to do so by the journal or conference you plan
338 % to submit to, of course. )
340 % correct bad hyphenation here
341 \hyphenation{op-tical net-works semi-conduc-tor}
343 % Macro for certain acronyms in small caps. Doesn't work with the
344 % default font, though (it contains no smallcaps it seems).
345 \def\acro#1{{\small{#1}}}
346 \def\acrop#1{\acro{#1}s}
347 \def\acrotiny#1{{\scriptsize{#1}}}
348 \def\VHDL{\acro{VHDL}}
350 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
351 \def\CLaSHtiny{{\scriptsize{C}}$\lambda$a{\scriptsize{SH}}}
353 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
354 % we'll get something more complex later on.
355 \def\hs#1{\texttt{#1}}
356 \def\quote#1{``{#1}"}
358 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
360 \settowidth{\labelwidth}{#1:}
361 \setlength{\labelsep}{0.5em}
362 \setlength{\leftmargin}{\labelwidth}
363 \addtolength{\leftmargin}{\labelsep}
364 \addtolength{\leftmargin}{\parindent}
365 \setlength{\rightmargin}{0pt}
366 \setlength{\listparindent}{\parindent}
367 \setlength{\itemsep}{0 ex plus 0.2ex}
368 \renewcommand{\makelabel}[1]{##1:\hfil}
373 \usepackage{paralist}
375 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
377 \usepackage{cleveref}
378 \crefname{figure}{figure}{figures}
379 \newcommand{\fref}[1]{\cref{#1}}
380 \newcommand{\Fref}[1]{\Cref{#1}}
382 \usepackage{epstopdf}
384 \epstopdfDeclareGraphicsRule{.svg}{pdf}{.pdf}{rsvg-convert --format=pdf < #1 > \noexpand\OutputFile}
386 %include polycode.fmt
389 \newcounter{Codecount}
390 \setcounter{Codecount}{0}
392 \newenvironment{example}
394 \refstepcounter{equation}
405 % can use linebreaks \\ within to get better formatting as desired
406 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
409 % author names and affiliations
410 % use a multiple column layout for up to three different
412 \author{\IEEEauthorblockN{Matthijs Kooijman, Christiaan P.R. Baaij, Jan Kuper, Marco E.T. Gerards}%, Bert Molenkamp, Sabih H. Gerez}
413 \IEEEauthorblockA{%Computer Architecture for Embedded Systems (CAES)\\
414 Department of EEMCS, University of Twente\\
415 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
416 matthijs@@stdin.nl, c.p.r.baaij@@utwente.nl, j.kuper@@utwente.nl}
417 % \thanks{Supported through the FP7 project: S(o)OS (248465)}
420 % \IEEEauthorblockN{Homer Simpson}
421 % \IEEEauthorblockA{Twentieth Century Fox\\
423 % Email: homer@thesimpsons.com}
425 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
426 % \IEEEauthorblockA{Starfleet Academy\\
427 % San Francisco, California 96678-2391\\
428 % Telephone: (800) 555--1212\\
429 % Fax: (888) 555--1212}}
431 % conference papers do not typically use \thanks and this command
432 % is locked out in conference mode. If really needed, such as for
433 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
434 % after \documentclass
436 % for over three affiliations, or if they all won't fit within the width
437 % of the page, use this alternative format:
439 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
440 %Homer Simpson\IEEEauthorrefmark{2},
441 %James Kirk\IEEEauthorrefmark{3},
442 %Montgomery Scott\IEEEauthorrefmark{3} and
443 %Eldon Tyrell\IEEEauthorrefmark{4}}
444 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
445 %Georgia Institute of Technology,
446 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
447 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
448 %Email: homer@thesimpsons.com}
449 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
450 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
451 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
456 % use for special paper notices
457 %\IEEEspecialpapernotice{(Invited Paper)}
462 % make the title area
467 \CLaSH\ is a functional hardware description language that borrows both its
468 syntax and semantics from the functional programming language Haskell.
469 Polymorphism and higher-order functions provide a level of abstraction and
470 generality that allow a circuit designer to describe circuits in a more
471 natural way than possible in a traditional hardware description language.
473 Circuit descriptions can be translated to synthesizable VHDL using the
474 prototype \CLaSH\ compiler. As the circuit descriptions, simulation code, and
475 test input are also valid Haskell, complete simulations can be compiled as an
476 executable binary by a Haskell compiler allowing high-speed simulation and
479 % \CLaSH\ supports stateful descriptions by explicitly making the current
480 % state an argument of the function, and the updated state part of the result.
481 % This makes \CLaSH\ descriptions in essence the combinational parts of a
484 % IEEEtran.cls defaults to using nonbold math in the Abstract.
485 % This preserves the distinction between vectors and scalars. However,
486 % if the conference you are submitting to favors bold math in the abstract,
487 % then you can use LaTeX's standard command \boldmath at the very start
488 % of the abstract to achieve this. Many IEEE journals/conferences frown on
489 % math in the abstract anyway.
496 % For peer review papers, you can put extra information on the cover
498 % \ifCLASSOPTIONpeerreview
499 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
502 % For peerreview papers, this IEEEtran command inserts a page break and
503 % creates the second title. It will be ignored for other modes.
504 \IEEEpeerreviewmaketitle
506 \section{Introduction}
507 Hardware description languages (\acrop{HDL}) have allowed the productivity of
508 hardware engineers to keep pace with the development of chip technology.
509 Traditional \acrop{HDL}, like \VHDL~\cite{VHDL2008} and
510 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
511 `programming' language. These standard languages are very good at describing
512 detailed hardware properties such as timing behavior, but are generally
513 cumbersome in expressing higher-level abstractions. In an attempt to raise the
514 abstraction level of the descriptions, a great number of approaches based on
515 functional languages has been proposed \cite{Cardelli1981,muFP,DAISY,
516 T-Ruby,HML2,Hydra,Hawk1,Lava,Wired,ForSyDe1,reFLect}. The idea of using
517 functional languages for hardware descriptions started in the early 1980s
518 \cite{Cardelli1981,muFP,DAISY}, a time which also saw the birth of the
519 currently popular \acrop{HDL}, such as \VHDL. Functional
520 languages are especially well suited to describe hardware because
521 combinational circuits can be directly modeled as mathematical functions and
522 functional languages are very good at describing and composing these
525 In an attempt to decrease the amount of work involved in creating all the
526 required tooling, such as parsers and type-checkers, many functional
527 \acrop{HDL} \cite{Hydra,Hawk1,Lava,Wired} are embedded as a domain
528 specific language (\acro{DSL}) within the functional language Haskell
529 \cite{Haskell}. This means that a developer is given a library of Haskell
530 functions and types that together form the language primitives of the
531 \acro{DSL}. The primitive functions used to describe a circuit do not actually
532 process any signals, they instead compose a large domain-specific datatype
533 (which is usually hidden from the designer). This datatype is then further
534 processed by an embedded circuit compiler which can perform for example
535 simulation or synthesis. As Haskell's choice elements (\hs{if}-expressions,
536 \hs{case}-expressions, etc.) are evaluated at the time the domain-specific
537 datatype is being build, they are no longer visible to the embedded compiler
538 that processes the datatype. Consequently, it is impossible to capture
539 Haskell's choice elements within a circuit description when taking the
540 embedded language approach. This does not mean that circuits specified in an
541 embedded language can not contain choice, just that choice elements only
542 exists as functions, e.g. a multiplexer function, and not as language
545 The approach taken in this research is not to make another \acro{DSL} embedded
546 in Haskell, but to use (a subset of) the Haskell language \emph{itself} for
547 the purpose of describing hardware. By taking this approach, this research
548 \emph{can} capture certain language constructs, such as Haskell's choice
549 elements, within circuit descriptions. To the best knowledge of the authors,
550 supporting polymorphism, higher-order functions and such an extensive array of
551 choice-elements, combined with a very concise way of specifying circuits is
552 new in the domain of (functional) \acrop{HDL}.
553 % As the hardware descriptions are plain Haskell
554 % functions, these descriptions can be compiled to an executable binary
555 % for simulation using an optimizing Haskell compiler such as the Glasgow
556 % Haskell Compiler (\GHC)~\cite{ghc}.
558 Where descriptions in a conventional \acro{HDL} have an explicit clock for the
559 purposes state and synchronicity, the clock is implied in the context of the
560 research presented in this paper. A circuit designer describes the behavior of
561 the hardware between clock cycles. Many functional \acrop{HDL} model signals
562 as a stream of all values over time; state is then modeled as a delay on this
563 stream of values. The approach taken in this research is to make the current
564 state an additional input and the updated state a part of the output of a
565 function. This abstraction of state and time limits the descriptions to
566 synchronous hardware, there is however room within the language to eventually
567 add a different abstraction mechanism that will allow for the modeling of
568 asynchronous systems.
570 Like the traditional \acrop{HDL}, descriptions made in a functional \acro{HDL}
571 must eventually be converted into a netlist. This research also features a
572 prototype translator, which has the same name as the language:
573 \CLaSH\footnote{\CLaSHtiny: \acrotiny{CAES} Language for Synchronous Hardware}
574 (pronounced: clash). This compiler converts the Haskell code to equivalently
575 behaving synthesizable \VHDL\ code, ready to be converted to an actual netlist
576 format by an (optimizing) \VHDL\ synthesis tool.
578 Besides trivial circuits such as variants of both the \acro{FIR} filter and
579 the simple \acro{CPU} shown in \Cref{sec:usecases}, the \CLaSH\ compiler has
580 also been able to successfully translate non-trivial functional descriptions
581 such as a streaming reduction circuit~\cite{reductioncircuit} for floating
584 \section{Hardware description in Haskell}
585 The following section describes the basic language elements of \CLaSH\ and the
586 extensiveness of the support of these elements within the \CLaSH\ compiler. In
587 various subsections, the relation between the language elements and their
588 eventual netlist representation is also highlighted.
590 \subsection{Function application}
591 Two basic syntactic elements of a functional program are functions
592 and function application. These have a single obvious translation to a
595 \item every function is translated to a component,
596 \item every function argument is translated to an input port,
597 \item the result value of a function is translated to an output port,
599 \item function applications are translated to component instantiations.
601 The result value can have a composite type (such as a tuple), so having
602 just a single result value does not pose any limitation. The actual
603 arguments of a function application are assigned to signals, which are
604 then mapped to the corresponding input ports of the component. The output
605 port of the function is also mapped to a signal, which is used as the
606 result of the application itself. Since every top level function generates
607 its own component, the hierarchy of function calls is reflected in the
608 final netlist. %, creating a hierarchical description of the hardware.
609 % The separation in different components makes it easier for a developer
610 % to understand and possibly hand-optimize the resulting \VHDL\ output of
611 % the \CLaSH\ compiler.
613 The short example (\ref{lst:code1}) demonstrated below gives an indication
614 of the level of conciseness that can be achieved with functional hardware
615 description languages when compared with the more traditional hardware
616 description languages. The example is a combinational multiply-accumulate
617 circuit that works for \emph{any} word length (this type of polymorphism
618 will be further elaborated in \Cref{sec:polymorhpism}). The corresponding
619 netlist is depicted in \Cref{img:mac-comb}.
622 \begin{minipage}{0.93\linewidth}
624 mac a b c = add (mul a b) c
627 \begin{minipage}{0.07\linewidth}
634 \centerline{\includegraphics{mac.svg}}
635 \caption{Combinational Multiply-Accumulate}
640 The use of a composite result value is demonstrated in the next example
641 (\ref{lst:code2}), where the multiply-accumulate circuit not only returns
642 the accumulation result, but also the intermediate multiplication result.
643 Its corresponding netlist can be seen in \Cref{img:mac-comb-composite}.
646 \begin{minipage}{0.93\linewidth}
648 mac a b c = (z, add z c)
653 \begin{minipage}{0.07\linewidth}
660 \centerline{\includegraphics{mac-nocurry.svg}}
661 \caption{Combinational Multiply-Accumulate (composite output)}
662 \label{img:mac-comb-composite}
667 In Haskell, choice can be achieved by a large set of syntactic elements,
668 consisting of: \hs{case} expressions, \hs{if-then-else} expressions,
669 pattern matching, and guards. The most general of these are the \hs{case}
670 expressions (\hs{if} expressions can be directly translated to
671 \hs{case} expressions). When transforming a \CLaSH\ description to a
672 netlist, a \hs{case} expression is translated to a multiplexer. The
673 control value of the \hs{case} expression is fed into a number of
674 comparators and their combined output forms the selection port of the
675 multiplexer. The result of each alternative in the \hs{case} expression is
676 linked to the corresponding input port of the multiplexer.
677 % A \hs{case} expression can in turn simply be translated to a conditional
678 % assignment in \VHDL, where the conditions use equality comparisons
679 % against the constructors in the \hs{case} expressions.
680 Two versions of a contrived example are displayed below, the first
681 (\ref{lst:code3}) using a \hs{case} expression and the second
682 (\ref{lst:code4}) using an \hs{if-then-else} expression. Both examples
683 sum two values when they are equal or non-equal (depending on the given
684 predicate, the \hs{pred} variable) and return 0 otherwise. The \hs{pred}
685 variable is of the following, user-defined, enumeration datatype:
688 data Pred = Equal | NotEqual
691 The naive netlist corresponding to both versions of the example is
692 depicted in \Cref{img:choice}. Note that the \hs{pred} variable is only
693 compared to \hs{Equal}, as an inequality immediately implies that
694 \hs{pred} is \hs{NotEqual}.
697 \begin{minipage}{0.93\linewidth}
699 sumif pred a b = case pred of
700 Equal -> case a == b of
703 NotEqual -> case a != b of
708 \begin{minipage}{0.07\linewidth}
715 \begin{minipage}{0.93\linewidth}
718 if pred == Equal then
719 if a == b then a + b else 0
721 if a != b then a + b else 0
724 \begin{minipage}{0.07\linewidth}
732 \centerline{\includegraphics{choice-case.svg}}
733 \caption{Choice - sumif}
738 A user-friendly and also very powerful form of choice that is not found in
739 the traditional hardware description languages is pattern matching. A
740 function can be defined in multiple clauses, where each clause corresponds
741 to a pattern. When an argument matches a pattern, the corresponding clause
742 will be used. Expressions can also contain guards, where the expression is
743 only executed if the guard evaluates to true, and continues with the next
744 clause if the guard evaluates to false. Like \hs{if-then-else}
745 expressions, pattern matching and guards have a (straightforward)
746 translation to \hs{case} expressions and can as such be mapped to
747 multiplexers. A third version (\ref{lst:code5}) of the earlier example,
748 now using both pattern matching and guards, can be seen below. The guard
749 is the expression that follows the vertical bar (\hs{|}) and precedes the
750 assignment operator (\hs{=}). The \hs{otherwise} guards always evaluate to
753 The version using pattern matching and guards corresponds to the same
754 naive netlist representation (\Cref{img:choice}) as the earlier two
755 versions of the example.
758 \begin{minipage}{0.93\linewidth}
760 sumif Equal a b | a == b = a + b
762 sumif NotEqual a b | a != b = a + b
766 \begin{minipage}{0.07\linewidth}
773 % \centerline{\includegraphics{choice-ifthenelse}}
774 % \caption{Choice - \emph{if-then-else}}
779 Haskell is a statically-typed language, meaning that the type of a
780 variable or function is determined at compile-time. Not all of Haskell's
781 typing constructs have a clear translation to hardware, this section will
782 therefore only deal with the types that do have a clear correspondence
783 to hardware. The translatable types are divided into two categories:
784 \emph{built-in} types and \emph{user-defined} types. Built-in types are
785 those types for which a fixed translation is defined within the \CLaSH\
786 compiler. The \CLaSH\ compiler has generic translation rules to
787 translate the user-defined types, which are described later on.
789 The \CLaSH\ compiler is able to infer unspecified (polymorphic) types,
790 meaning that a developer does not have to annotate every function with a
791 type signature. % (even if it is good practice to do so).
792 Given that the top-level entity of a circuit design is annotated with
793 concrete/monomorphic types, the \CLaSH\ compiler can specialize
794 polymorphic functions to functions with concrete types.
796 % Translation of two most basic functional concepts has been
797 % discussed: function application and choice. Before looking further
798 % into less obvious concepts like higher-order expressions and
799 % polymorphism, the possible types that can be used in hardware
800 % descriptions will be discussed.
802 % Some way is needed to translate every value used to its hardware
803 % equivalents. In particular, this means a hardware equivalent for
804 % every \emph{type} used in a hardware description is needed.
806 % The following types are \emph{built-in}, meaning that their hardware
807 % translation is fixed into the \CLaSH\ compiler. A designer can also
808 % define his own types, which will be translated into hardware types
809 % using translation rules that are discussed later on.
811 \subsubsection{Built-in types}
812 The following types have fixed translations defined within the \CLaSH\
816 the most basic type available. It can have two values:
817 \hs{Low} or \hs{High}.
818 % It is mapped directly onto the \texttt{std\_logic} \VHDL\ type.
820 this is a basic logic type. It can have two values: \hs{True}
822 % It is translated to \texttt{std\_logic} exactly like the \hs{Bit}
823 % type (where a value of \hs{True} corresponds to a value of
825 Supporting the Bool type is required in order to support the
826 \hs{if-then-else} expression, which requires a \hs{Bool} value for
828 \item[\bf{Signed}, \bf{Unsigned}]
829 these are types to represent integers and both are parametrizable in
830 their size. The overflow behavior of the numeric operators defined for
831 these types is \emph{wrap-around}.
832 % , so you can define an unsigned word of 32 bits wide as follows:
835 % type Word32 = SizedWord D32
838 % Here, a type synonym \hs{Word32} is defined that is equal to the
839 % \hs{SizedWord} type constructor applied to the type \hs{D32}.
840 % \hs{D32} is the \emph{type level representation} of the decimal
841 % number 32, making the \hs{Word32} type a 32-bit unsigned word. These
842 % types are translated to the \VHDL\ \texttt{unsigned} and
843 % \texttt{signed} respectively.
845 this is a vector type that can contain elements of any other type and
846 has a static length. The \hs{Vector} type constructor takes two type
847 arguments: the length of the vector and the type of the elements
848 contained in it. The short-hand notation used for the vector type in
849 the rest of paper is: \hs{[a|n]}, where \hs{a} is the element
850 type, and \hs{n} is the length of the vector. Note that this is
851 a notation used in this paper only, vectors are slightly more
852 verbose in real \CLaSH\ descriptions.
853 % The state type of an 8 element register bank would then for example
857 % type RegisterState = Vector D8 Word32
860 % Here, a type synonym \hs{RegisterState} is defined that is equal to
861 % the \hs{Vector} type constructor applied to the types \hs{D8} (The
862 % type level representation of the decimal number 8) and \hs{Word32}
863 % (The 32 bit word type as defined above). In other words, the
864 % \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
865 % vector is translated to a \VHDL\ array type.
867 this is another type to describe integers, but unlike the previous
868 two it has no specific bit-width, but an upper bound. This means that
869 its range is not limited to powers of two, but can be any number.
870 An \hs{Index} only has an upper bound, its lower bound is
871 implicitly zero. If a value of this type exceeds either bounds, an
872 error will be thrown at simulation-time. The main purpose of the
873 \hs{Index} type is to be used as an index into a \hs{Vector}.
875 % \comment{TODO: Perhaps remove this example?} To define an index for
876 % the 8 element vector above, we would do:
879 % type RegisterIndex = RangedWord D7
882 % Here, a type synonym \hs{RegisterIndex} is defined that is equal to
883 % the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
884 % other words, this defines an unsigned word with values from
885 % 0 to 7 (inclusive). This word can be be used to index the
886 % 8 element vector \hs{RegisterState} above. This type is translated
887 % to the \texttt{unsigned} \VHDL type.
890 \subsubsection{User-defined types}
891 There are three ways to define new types in Haskell: algebraic
892 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
893 keyword and datatype renaming constructs with the \hs{newtype} keyword.
894 % \GHC\ offers a few more advanced ways to introduce types (type families,
895 % existential typing, {\acro{GADT}}s, etc.) which are not standard
896 % Haskell. As it is currently unclear how these advanced type constructs
897 % correspond to hardware, they are for now unsupported by the \CLaSH\
900 Only an algebraic datatype declaration actually introduces a
901 completely new type. Type synonyms and type renaming only define new
902 names for existing types, where synonyms are completely interchangeable
903 and a type renaming requires an explicit conversion. Type synonyms and
904 type renaming do not need any particular translation, a synonym or
905 renamed type will just use the same representation as the original type.
907 For algebraic types, we can make the following distinctions:
909 \item[\bf{Single constructor}]
910 Algebraic datatypes with a single constructor with one or more
911 fields, are essentially a way to pack a few values together in a
912 record-like structure. Haskell's built-in tuple types are also defined
913 as single constructor algebraic types (but with a bit of
914 syntactic sugar). An example of a single constructor type with
915 multiple fields is the following pair of integers:
917 data IntPair = IntPair Int Int
919 % These types are translated to \VHDL\ record types, with one field
920 % for every field in the constructor.
921 \item[\bf{No fields}]
922 Algebraic datatypes with multiple constructors, but without any
923 fields are essentially a way to get an enumeration-like type
924 containing alternatives. Note that Haskell's \hs{Bool} type is also
925 defined as an enumeration type, but that there is a fixed translation
926 for that type within the \CLaSH\ compiler. An example of such an
927 enumeration type is the type that represents the colors in a traffic
930 data TrafficLight = Red | Orange | Green
932 % These types are translated to \VHDL\ enumerations, with one
933 % value for each constructor. This allows references to these
934 % constructors to be translated to the corresponding enumeration
936 \item[\bf{Multiple constructors with fields}]
937 Algebraic datatypes with multiple constructors, where at least
938 one of these constructors has one or more fields are currently not
942 \subsection{Polymorphism}\label{sec:polymorhpism}
943 A powerful feature of most (functional) programming languages is
944 polymorphism, it allows a function to handle values of different data
945 types in a uniform way. Haskell supports \emph{parametric
946 polymorphism}~\cite{polymorphism}, meaning functions can be written
947 without mention of any specific type and can be used transparently with
948 any number of new types.
950 As an example of a parametric polymorphic function, consider the type of
951 the following \hs{append} function, which appends an element to a
952 vector:\footnote{The \hs{::} operator is used to annotate a function
956 append :: [a|n] -> a -> [a|n + 1]
959 This type is parameterized by \hs{a}, which can contain any type at
960 all. This means that \hs{append} can append an element to a vector,
961 regardless of the type of the elements in the list (as long as the type of
962 the value to be added is of the same type as the values in the vector).
963 This kind of polymorphism is extremely useful in hardware designs to make
964 operations work on a vector without knowing exactly what elements are
965 inside, routing signals without knowing exactly what kinds of signals
966 these are, or working with a vector without knowing exactly how long it
967 is. Polymorphism also plays an important role in most higher order
968 functions, as we will see in the next section.
970 Another type of polymorphism is \emph{ad-hoc
971 polymorphism}~\cite{polymorphism}, which refers to polymorphic
972 functions which can be applied to arguments of different types, but which
973 behave differently depending on the type of the argument to which they are
974 applied. In Haskell, ad-hoc polymorphism is achieved through the use of
975 type classes, where a class definition provides the general interface of a
976 function, and class instances define the functionality for the specific
977 types. An example of such a type class is the \hs{Num} class, which
978 contains all of Haskell's numerical operations. A designer can make use
979 of this ad-hoc polymorphism by adding a constraint to a parametrically
980 polymorphic type variable. Such a constraint indicates that the type
981 variable can only be instantiated to a type whose members supports the
982 overloaded functions associated with the type class.
984 An example of a type signature that includes such a constraint if the
985 signature of the \hs{sum} function, which sums the values in a vector:
987 sum :: Num a => [a|n] -> a
990 This type is again parameterized by \hs{a}, but it can only contain
991 types that are \emph{instances} of the \emph{type class} \hs{Num}, so that
992 the compiler knows that the addition (+) operator is defined for that
994 % \CLaSH's built-in numerical types are also instances of the \hs{Num}
996 % so we can use the addition operator (and thus the \hs{sum}
997 % function) with \hs{Signed} as well as with \hs{Unsigned}.
999 \CLaSH\ supports both parametric polymorphism and ad-hoc polymorphism. Any
1000 function defined can have any number of unconstrained type parameters. A
1001 developer can also specify his own type classes and corresponding
1002 instances. The \CLaSH\ compiler will infer the type of every polymorphic
1003 argument depending on how the function is applied. There is however one
1004 constraint: the top level function that is being translated can not have
1005 any polymorphic arguments. The arguments of the top-level can not be
1006 polymorphic as the function is never applied and consequently there is no
1007 way to determine the actual types for the type parameters.
1009 With regard to the built-in types, it should be noted that members of
1010 some of the standard Haskell type classes are supported as built-in
1011 functions. These include: the numerial operators of \hs{Num}, the equality
1012 operators of \hs{Eq}, and the comparison/order operators of \hs{Ord}.
1014 \subsection{Higher-order functions \& values}
1015 Another powerful abstraction mechanism in functional languages, is
1016 the concept of \emph{functions as a first class value}, also called
1017 \emph{higher-order functions}. This allows a function to be treated as a
1018 value and be passed around, even as the argument of another
1019 function. The following example should clarify this concept:
1022 \begin{minipage}{0.93\linewidth}
1023 %format not = "\mathit{not}"
1025 negateVector xs = map not xs
1028 \begin{minipage}{0.07\linewidth}
1034 The code above defines the \hs{negateVector} function, which takes a
1035 vector of booleans, \hs{xs}, and returns a vector where all the values are
1036 negated. It achieves this by calling the \hs{map} function, and passing it
1037 \emph{another function}, boolean negation, and the vector of booleans,
1038 \hs{xs}. The \hs{map} function applies the negation function to all the
1039 elements in the vector.
1041 The \hs{map} function is called a higher-order function, since it takes
1042 another function as an argument. Also note that \hs{map} is again a
1043 parametric polymorphic function: it does not pose any constraints on the
1044 type of the input vector, other than that its elements must have the same
1045 type as the first argument of the function passed to \hs{map}. The element
1046 type of the resulting vector is equal to the return type of the function
1047 passed, which need not necessarily be the same as the element type of the
1048 input vector. All of these characteristics can readily be inferred from
1049 the type signature belonging to \hs{map}:
1052 map :: (a -> b) -> [a|n] -> [b|n]
1055 So far, only functions have been used as higher-order values. In
1056 Haskell, there are two more ways to obtain a function-typed value:
1057 partial application and lambda abstraction. Partial application
1058 means that a function that takes multiple arguments can be applied
1059 to a single argument, and the result will again be a function (but
1060 that takes one argument less). As an example, consider the following
1061 expression, that adds one to every element of a vector:
1064 \begin{minipage}{0.93\linewidth}
1069 \begin{minipage}{0.07\linewidth}
1075 Here, the expression \hs{(add 1)} is the partial application of the
1076 addition function to the value \hs{1}, which is again a function that
1077 adds one to its (next) argument. A lambda expression allows one to
1078 introduce an anonymous function in any expression. Consider the following
1079 expression, which again adds one to every element of a vector:
1082 \begin{minipage}{0.93\linewidth}
1084 map (\x -> x + 1) xs
1087 \begin{minipage}{0.07\linewidth}
1093 Finally, not only built-in functions can have higher order arguments (such
1094 as the \hs{map} function), but any function defined in \CLaSH\ may have
1095 functions as arguments. This allows the circuit designer to use a
1096 powerful amount of code reuse. The only exception is again the top-level
1097 function: if a function-typed argument is not applied with an actual
1098 function, no hardware can be generated.
1100 % \comment{TODO: Describe ALU example (no code)}
1103 A very important concept in hardware is the concept of state. In a
1104 stateful design, the outputs depend on the history of the inputs, or the
1105 state. State is usually stored in registers, which retain their value
1106 during a clock cycle. As we want to describe more than simple
1107 combinational designs, \CLaSH\ needs an abstraction mechanism for state.
1109 An important property in Haskell, and in most other functional languages,
1110 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
1113 \item given the same arguments twice, it should return the same value in
1115 \item that the function has no observable side-effects.
1117 % This purity property is important for functional languages, since it
1118 % enables all kinds of mathematical reasoning that could not be guaranteed
1119 % correct for impure functions.
1120 Pure functions are as such a perfect match for combinational circuits,
1121 where the output solely depends on the inputs. When a circuit has state
1122 however, it can no longer be simply described by a pure function.
1123 % Simply removing the purity property is not a valid option, as the
1124 % language would then lose many of it mathematical properties.
1125 In \CLaSH\ we deal with the concept of state in pure functions by making
1126 the current state an additional argument of the function, and the
1127 updated state part of result. In this sense the descriptions made in
1128 \CLaSH\ are the combinational parts of a mealy machine.
1130 A simple example is adding an accumulator register to the earlier
1131 multiply-accumulate circuit, of which the resulting netlist can be seen in
1132 \Cref{img:mac-state}:
1135 \begin{minipage}{0.93\linewidth}
1137 macS (State c) a b = (State c', c')
1142 \begin{minipage}{0.07\linewidth}
1149 \centerline{\includegraphics{mac-state.svg}}
1150 \caption{Stateful Multiply-Accumulate}
1151 \label{img:mac-state}
1155 Note that the \hs{macS} function returns both the new state and the value
1156 of the output port. The \hs{State} keyword indicates which arguments are
1157 part of the current state, and what part of the output is part of the
1158 updated state. This aspect will also be reflected in the type signature of
1159 the function. Abstracting the state of a circuit in this way makes it very
1160 explicit: which variables are part of the state is completely determined
1161 by the type signature. This approach to state is well suited to be used in
1162 combination with the existing code and language features, such as all the
1163 choice elements, as state values are just normal values. We can simulate
1164 stateful descriptions using the recursive \hs{run} function:
1167 \begin{minipage}{0.93\linewidth}
1169 run f s (i : inps) = o : (run f s' inps)
1174 \begin{minipage}{0.07\linewidth}
1180 The \hs{(:)} operator is the list concatenation operator, where the
1181 left-hand side is the head of a list and the right-hand side is the
1182 remainder of the list. The \hs{run} function applies the function the
1183 developer wants to simulate, \hs{f}, to the current state, \hs{s}, and the
1184 first input value, \hs{i}. The result is the first output value, \hs{o},
1185 and the updated state \hs{s'}. The next iteration of the \hs{run} function
1186 is then called with the updated state, \hs{s'}, and the rest of the
1187 inputs, \hs{inps}. For the time being, and in the context of this paper,
1188 it is assumed that there is one input per clock cycle. Also note how the
1189 order of the input, output, and state in the \hs{run} function corresponds
1190 with the order of the input, output and state of the \hs{macS} function
1193 As the \hs{run} function, the hardware description, and the test
1194 inputs are also valid Haskell, the complete simulation can be compiled to
1195 an executable binary by an optimizing Haskell compiler, or executed in an
1196 Haskell interpreter. Both simulation paths are much faster than first
1197 translating the description to \VHDL\ and then running a \VHDL\
1200 \section{The \CLaSH\ compiler}
1201 An important aspect in this research is the creation of the prototype
1202 compiler, which allows us to translate descriptions made in the \CLaSH\
1203 language as described in the previous section to synthesizable \VHDL.
1204 % , allowing a designer to actually run a \CLaSH\ design on an \acro{FPGA}.
1206 The Glasgow Haskell Compiler (\GHC)~\cite{ghc} is an open-source Haskell
1207 compiler that also provides a high level API to most of its internals. The
1208 availability of this high-level API obviated the need to design many of the
1209 tedious parts of the prototype compiler, such as the parser, semantics
1210 checker, and especially the type-checker. These parts together form the
1211 front-end of the prototype compiler pipeline, as seen in
1212 \Cref{img:compilerpipeline}.
1215 \centerline{\includegraphics{compilerpipeline.svg}}
1216 \caption{\CLaSHtiny\ compiler pipeline}
1217 \label{img:compilerpipeline}
1221 The output of the \GHC\ front-end consists of the translation of the original
1222 Haskell description in \emph{Core}~\cite{Sulzmann2007}, which is a smaller,
1223 typed, functional language. This \emph{Core} language is relatively easy to
1224 process compared to the larger Haskell language. A description in \emph{Core}
1225 can still contain elements which have no direct translation to hardware, such
1226 as polymorphic types and function-valued arguments. Such a description needs
1227 to be transformed to a \emph{normal form}, which only contains elements that
1228 have a direct translation. The second stage of the compiler, the
1229 \emph{normalization} phase, exhaustively applies a set of
1230 \emph{meaning-preserving} transformations on the \emph{Core} description until
1231 this description is in a \emph{normal form}. This set of transformations
1232 includes transformations typically found in reduction systems and lambda
1233 calculus~\cite{lambdacalculus}, such as $\beta$-reduction and
1234 $\eta$-expansion. It also includes self-defined transformations that are
1235 responsible for the reduction of higher-order functions to `regular'
1236 first-order functions, and specializing polymorphic types to concrete types.
1238 The final step in the compiler pipeline is the translation to a \VHDL\
1239 \emph{netlist}, which is a straightforward process due to resemblance of a
1240 normalized description and a set of concurrent signal assignments. We call the
1241 end-product of the \CLaSH\ compiler a \VHDL\ \emph{netlist} as the resulting
1242 \VHDL\ resembles an actual netlist description and not idiomatic \VHDL.
1245 \label{sec:usecases}
1246 \subsection{FIR Filter}
1247 As an example of a common hardware design where the use of higher-order
1248 functions leads to a very natural description is a \acro{FIR} filter, which is
1249 basically the dot-product of two vectors:
1252 y_t = \sum\nolimits_{i = 0}^{n - 1} {x_{t - i} \cdot h_i }
1255 A \acro{FIR} filter multiplies fixed constants ($h$) with the current
1256 and a few previous input samples ($x$). Each of these multiplications
1257 are summed, to produce the result at time $t$. The equation of a \acro{FIR}
1258 filter is indeed equivalent to the equation of the dot-product, which is
1262 \mathbf{a}\bullet\mathbf{b} = \sum\nolimits_{i = 0}^{n - 1} {a_i \cdot b_i }
1265 We can easily and directly implement the equation for the dot-product
1266 using higher-order functions:
1269 \begin{minipage}{0.93\linewidth}
1271 as *+* bs = foldl1 (+) (zipWith (*) as bs)
1274 \begin{minipage}{0.07\linewidth}
1280 The \hs{zipWith} function is very similar to the \hs{map} function seen
1281 earlier: It takes a function, two vectors, and then applies the function to
1282 each of the elements in the two vectors pairwise (\emph{e.g.}, \hs{zipWith (*)
1283 [1, 2] [3, 4]} becomes \hs{[1 * 3, 2 * 4]}).
1285 The \hs{foldl1} function takes a binary function, a single vector, and applies
1286 the function to the first two elements of the vector. It then applies the
1287 function to the result of the first application and the next element in the
1288 vector. This continues until the end of the vector is reached. The result of
1289 the \hs{foldl1} function is the result of the last application. It is obvious
1290 that the \hs{zipWith (*)} function is pairwise multiplication and that the
1291 \hs{foldl1 (+)} function is summation.
1292 % Returning to the actual \acro{FIR} filter, we will slightly change the
1293 % equation describing it, so as to make the translation to code more obvious and
1294 % concise. What we do is change the definition of the vector of input samples
1295 % and delay the computation by one sample. Instead of having the input sample
1296 % received at time $t$ stored in $x_t$, $x_0$ now always stores the newest
1297 % sample, and $x_i$ stores the $ith$ previous sample. This changes the equation
1298 % to the following (note that this is completely equivalent to the original
1299 % equation, just with a different definition of $x$ that will better suit the
1300 % transformation to code):
1303 % y_t = \sum\nolimits_{i = 0}^{n - 1} {x_i \cdot h_i }
1305 The complete definition of the \acro{FIR} filter in code then becomes:
1308 \begin{minipage}{0.93\linewidth}
1310 fir (State (xs,hs)) x =
1311 (State (x >> xs,hs), (x +> xs) *+* hs)
1314 \begin{minipage}{0.07\linewidth}
1320 Where the vector \hs{xs} contains the previous input samples, the vector
1321 \hs{hs} contains the \acro{FIR} coefficients, and \hs{x} is the current input
1322 sample. The concatenate operator (\hs{+>}) creates a new vector by placing the
1323 current sample (\hs{x}) in front of the previous samples vector (\hs{xs}). The
1324 code for the shift (\hs{>>}) operator, that adds the new input sample (\hs{x})
1325 to the list of previous input samples (\hs{xs}) and removes the oldest sample,
1329 \begin{minipage}{0.93\linewidth}
1331 x >> xs = x +> init xs
1334 \begin{minipage}{0.07\linewidth}
1340 Where the \hs{init} function returns all but the last element of a vector.
1341 The resulting netlist of a 4-taps \acro{FIR} filter, created by specializing
1342 the vectors of the \acro{FIR} code to a length of 4, is depicted in
1346 \centerline{\includegraphics{4tapfir.svg}}
1347 \caption{4-taps \acrotiny{FIR} Filter}
1352 \subsection{Higher-order CPU}
1353 The following simple \acro{CPU} is an example of user-defined higher order
1354 functions and pattern matching. The \acro{CPU} consists of four function
1355 units, of which three have a fixed function and one can perform certain less
1358 The \acro{CPU} contains a number of data sources, represented by the
1359 horizontal wires in \Cref{img:highordcpu}. These data sources offer the
1360 previous outputs of each function units, along with the single data input the
1361 \acro{CPU} has and two fixed initialization values.
1363 Each of the function units has both its operands connected to all data
1364 sources, and can be programmed to select any data source for either
1365 operand. In addition, the leftmost function unit has an additional
1366 opcode input to select the operation it performs. The output of the rightmost
1367 function unit is also the output of the entire \acro{CPU}.
1369 Looking at the code, the function unit (\hs{fu}) is the most simple. It
1370 arranges the operand selection for the function unit. Note that it does not
1371 define the actual operation that takes place inside the function unit,
1372 but simply accepts the (higher-order) argument \hs{op} which is a function
1373 of two arguments that defines the operation.
1376 \begin{minipage}{0.93\linewidth}
1378 fu op inputs (addr1, addr2) = regIn
1385 \begin{minipage}{0.07\linewidth}
1391 The \hs{multiop} function defines the operation that takes place in the
1392 leftmost function unit. It is essentially a simple three operation \acro{ALU}
1393 that makes good use of pattern matching and guards in its description.
1394 The \hs{shift} function used here shifts its first operand by the number
1395 of bits indicated in the second operand, the \hs{xor} function produces
1396 the bitwise xor of its operands.
1399 \begin{minipage}{0.93\linewidth}
1401 data Opcode = Shift | Xor | Equal
1403 multiop :: Opcode -> Word -> Word -> Word
1404 multiop Shift a b = shift a b
1405 multiop Xor a b = xor a b
1406 multiop Equal a b | a == b = 1
1410 \begin{minipage}{0.07\linewidth}
1416 The \acro{CPU} function ties everything together. It applies the \hs{fu}
1417 function four times, to create a different function unit each time. The
1418 first application is interesting, because it does not just pass a
1419 function to \hs{fu}, but a partial application of \hs{multiop}. This
1420 shows how the first function unit effectively gets an extra input,
1421 compared to the others.
1423 The vector \hs{inputs} is the set of data sources, which is passed to
1424 each function unit as a set of possible operants. The \acro{CPU} also receives
1425 a vector of address pairs, which are used by each function unit to select
1426 their operand. The application of the function units to the \hs{inputs} and
1427 \hs{addrs} arguments seems quite repetitive and could be rewritten to use
1428 a combination of the \hs{map} and \hs{zipwith} functions instead.
1429 However, the prototype compiler does not currently support working with lists
1430 of functions, so a more explicit version of the code is given instead.
1433 \begin{minipage}{0.93\linewidth}
1435 type CpuState = State [Word | 4]
1437 cpu :: CpuState -> Word -> [(Index 6, Index 6) | 4]
1438 -> Opcode -> (CpuState, Word)
1439 cpu (State s) input addrs opc = (State s', out)
1441 s' = [ fu (multiop opc) inputs (addrs!0)
1442 , fu add inputs (addrs!1)
1443 , fu sub inputs (addrs!2)
1444 , fu mul inputs (addrs!3)
1446 inputs = 0 +> (1 +> (input +> s))
1450 \begin{minipage}{0.07\linewidth}
1456 This is still a simple example, but it could form the basis
1457 of an actual design, in which the same techniques can be reused.
1459 \section{Related work}
1460 This section describes the features of existing (functional) hardware
1461 description languages and highlights the advantages that this research has
1464 % Many functional hardware description languages have been developed over the
1465 % years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
1466 % extension of Backus' \acro{FP} language to synchronous streams, designed
1467 % particularly for describing and reasoning about regular circuits. The
1468 % Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
1469 % circuits, and has a particular focus on layout.
1471 \acro{HML}~\cite{HML2} is a hardware modeling language based on the strict
1472 functional language \acro{ML}, and has support for polymorphic types and
1473 higher-order functions. Published work suggests that there is no direct
1474 simulation support for \acro{HML}, but that a description in \acro{HML} has to
1475 be translated to \VHDL\ and that the translated description can then be
1476 simulated in a \VHDL\ simulator. Certain aspects of HML, such as higher-order
1477 functions are however not supported by the \VHDL\ translator~\cite{HML3}. The
1478 \CLaSH\ compiler on the other hand can correctly translate all of the language
1479 constructs mentioned in this paper. % to a netlist format.
1482 \centerline{\includegraphics{highordcpu.svg}}
1483 \caption{CPU with higher-order Function Units}
1484 \label{img:highordcpu}
1488 Like the research presented in this paper, many functional hardware
1489 description languages have some sort of foundation in the functional
1490 programming language Haskell. Hawk~\cite{Hawk1} uses Haskell to describe
1491 system-level executable specifications used to model the behavior of
1492 superscalar microprocessors. Hawk specifications can be simulated; to the best
1493 knowledge of the authors there is however no support for automated circuit
1496 The ForSyDe~\cite{ForSyDe2} system uses Haskell to specify abstract system
1497 models. A designer can model systems using heterogeneous models of
1498 computation, which include continuous time, synchronous and untimed models of
1499 computation. Using so-called domain interfaces a designer can simulate
1500 electronic systems which have both analog as digital parts. ForSyDe has
1501 several backends including simulation and automated synthesis, though
1502 automated synthesis is restricted to the synchronous model of computation.
1503 Though ForSyDe offers higher-order functions and polymorphism, ForSyDe's
1504 choice elements are limited to \hs{if} and \hs{case} expressions. ForSyDe's
1505 explicit conversions, where function have to be wrapped in processes and
1506 processes have to be wrapped in systems, combined with the explicit
1507 instantiations of components, also makes ForSyDe more verbose than \CLaSH.
1509 Lava~\cite{Lava} is a hardware description language, embedded in Haskell, and
1510 focuses on the structural representation of hardware. Like \CLaSH, Lava has
1511 support for polymorphic types and higher-order functions. Besides support for
1512 simulation and circuit synthesis, Lava descriptions can be interfaced with
1513 formal method tools for formal verification. As discussed in the introduction,
1514 taking the embedded language approach does not allow for Haskell's choice
1515 elements to be captured within the circuit descriptions. In this respect
1516 \CLaSH\ differs from Lava, in that all of Haskell's choice elements, such as
1517 \hs{case}-expressions and pattern matching, are synthesized to choice elements
1518 in the eventual circuit. Consequently, descriptions containing rich control
1519 structures can be specified in a more user-friendly way in \CLaSH\ than possible within Lava, and are hence less error-prone.
1521 Bluespec~\cite{Bluespec} is a high-level synthesis language that features
1522 guarded atomic transactions and allows for the automated derivation of control
1523 structures based on these atomic transactions. Bluespec, like \CLaSH, supports
1524 polymorphic typing and function-valued arguments. Bluespec's syntax and
1525 language features \emph{had} their basis in Haskell. However, in order to
1526 appeal to the users of the traditional \acrop{HDL}, Bluespec has adapted
1527 imperative features and a syntax that resembles Verilog. As a result, Bluespec
1528 is (unnecessarily) verbose when compared to \CLaSH.
1530 The merits of polymorphic typing and function-valued arguments are now also
1531 recognized in the traditional \acrop{HDL}, exemplified by the new \VHDL-2008
1532 standard~\cite{VHDL2008}. \VHDL-2008 support for generics has been extended to
1533 types and subprograms, allowing a designer to describe components with
1534 polymorphic ports and function-valued arguments. Note that the types and
1535 subprograms still require an explicit generic map, whereas types can be
1536 automatically inferred, and function-values can be automatically propagated
1537 by the \CLaSH\ compiler. There are also no (generally available) \VHDL\
1538 synthesis tools that currently support the \VHDL-2008 standard.
1540 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
1542 % A functional language designed specifically for hardware design is
1543 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
1544 % language called \acro{FL}~\cite{FL} to la
1546 % An example of a floating figure using the graphicx package.
1547 % Note that \label must occur AFTER (or within) \caption.
1548 % For figures, \caption should occur after the \includegraphics.
1549 % Note that IEEEtran v1.7 and later has special internal code that
1550 % is designed to preserve the operation of \label within \caption
1551 % even when the captionsoff option is in effect. However, because
1552 % of issues like this, it may be the safest practice to put all your
1553 % \label just after \caption rather than within \caption{}.
1555 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
1556 % option should be used if it is desired that the figures are to be
1557 % displayed while in draft mode.
1561 %\includegraphics[width=2.5in]{myfigure}
1562 % where an .eps filename suffix will be assumed under latex,
1563 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
1564 % via \DeclareGraphicsExtensions.
1565 %\caption{Simulation Results}
1569 % Note that IEEE typically puts floats only at the top, even when this
1570 % results in a large percentage of a column being occupied by floats.
1573 % An example of a double column floating figure using two subfigures.
1574 % (The subfig.sty package must be loaded for this to work.)
1575 % The subfigure \label commands are set within each subfloat command, the
1576 % \label for the overall figure must come after \caption.
1577 % \hfil must be used as a separator to get equal spacing.
1578 % The subfigure.sty package works much the same way, except \subfigure is
1579 % used instead of \subfloat.
1581 %\begin{figure*}[!t]
1582 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
1583 %\label{fig_first_case}}
1585 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
1586 %\label{fig_second_case}}}
1587 %\caption{Simulation results}
1591 % Note that often IEEE papers with subfigures do not employ subfigure
1592 % captions (using the optional argument to \subfloat), but instead will
1593 % reference/describe all of them (a), (b), etc., within the main caption.
1596 % An example of a floating table. Note that, for IEEE style tables, the
1597 % \caption command should come BEFORE the table. Table text will default to
1598 % \footnotesize as IEEE normally uses this smaller font for tables.
1599 % The \label must come after \caption as always.
1602 %% increase table row spacing, adjust to taste
1603 %\renewcommand{\arraystretch}{1.3}
1604 % if using array.sty, it might be a good idea to tweak the value of
1605 % \extrarowheight as needed to properly center the text within the cells
1606 %\caption{An Example of a Table}
1607 %\label{table_example}
1609 %% Some packages, such as MDW tools, offer better commands for making tables
1610 %% than the plain LaTeX2e tabular which is used here.
1611 %\begin{tabular}{|c||c|}
1621 % Note that IEEE does not put floats in the very first column - or typically
1622 % anywhere on the first page for that matter. Also, in-text middle ("here")
1623 % positioning is not used. Most IEEE journals/conferences use top floats
1624 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
1625 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
1626 % command of the stfloats package.
1630 \section{Conclusion}
1631 This research demonstrates once more that functional languages are well suited
1632 for hardware descriptions: function applications provide an elegant notation
1633 for component instantiation. Where this research goes beyond the existing
1634 (functional) hardware descriptions languages is the inclusion of various
1635 choice elements, such as pattern matching, that are well suited to describe
1636 the conditional assignments in control-oriented circuits. Besides being able
1637 to translate these basic constructs to synthesizable \VHDL, the prototype
1638 compiler can also correctly translate descriptions that contain both
1639 polymorphic types and function-valued arguments.
1641 Where recent functional hardware description languages have mostly opted to
1642 embed themselves in an existing functional language, this research features a
1643 `true' compiler. As a result there is a clear distinction between compile-time
1644 and run-time, which allows a myriad of choice constructs to be part of the
1645 actual circuit description; a feature the embedded hardware description
1646 languages do not offer.
1648 \section{Future Work}
1649 The choice of describing state explicitly as extra arguments and results can
1650 be seen as a mixed blessing. Even though the description that use state are
1651 usually very clear, one finds that dealing with unpacking, passing, receiving
1652 and repacking can become tedious and even error-prone, especially in the case
1653 of sub-states. Removing this boilerplate, or finding a more suitable
1654 abstraction mechanism would make \CLaSH\ easier to use.
1656 The transformations in normalization phase of the prototype compiler were
1657 developed in an ad-hoc manner, which makes the existence of many desirable
1658 properties unclear. Such properties include whether the complete set of
1659 transformations will always lead to a normal form or if the normalization
1660 process always terminates. Though various use cases suggests that these
1661 properties usually hold, they have not been formally proven. A systematic
1662 approach to defining the set of transformations allows one to proof that the
1663 earlier mentioned properties do indeed exist.
1665 % conference papers do not normally have an appendix
1668 % use section* for acknowledgement
1669 % \section*{Acknowledgment}
1671 % The authors would like to thank...
1673 % trigger a \newpage just before the given reference
1674 % number - used to balance the columns on the last page
1675 % adjust value as needed - may need to be readjusted if
1676 % the document is modified later
1677 % \IEEEtriggeratref{14}
1678 % The "triggered" command can be changed if desired:
1679 %\IEEEtriggercmd{\enlargethispage{-5in}}
1681 % references section
1683 % can use a bibliography generated by BibTeX as a .bbl file
1684 % BibTeX documentation can be easily obtained at:
1685 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
1686 % The IEEEtran BibTeX style support page is at:
1687 % http://www.michaelshell.org/tex/ieeetran/bibtex/
1688 \bibliographystyle{IEEEtran}
1689 % argument is your BibTeX string definitions and bibliography database(s)
1690 \bibliography{clash}
1692 % <OR> manually copy in the resultant .bbl file
1693 % set second argument of \begin to the number of references
1694 % (used to reserve space for the reference number labels box)
1695 % \begin{thebibliography}{1}
1697 % \bibitem{IEEEhowto:kopka}
1698 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
1699 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1701 % \end{thebibliography}
1709 % vim: set ai sw=2 sts=2 expandtab: