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67 \documentclass[conference,pdf,a4paper,10pt,final,twoside,twocolumn]{IEEEtran}
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263 % replacement for subfigure.sty. However, subfig.sty requires and
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267 % caption.sty with its "caption=false" package option. This is will preserve
268 % IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later
269 % (recommended due to many improvements over 1.2) of subfig.sty supports
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281 % *** FLOAT PACKAGES ***
283 %\usepackage{fixltx2e}
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333 % *** Do not adjust lengths that control margins, column widths, etc. ***
334 % *** Do not use packages that alter fonts (such as pslatex). ***
335 % There should be no need to do such things with IEEEtran.cls V1.6 and later.
336 % (Unless specifically asked to do so by the journal or conference you plan
337 % to submit to, of course. )
339 % correct bad hyphenation here
340 \hyphenation{op-tical net-works semi-conduc-tor}
342 % Macro for certain acronyms in small caps. Doesn't work with the
343 % default font, though (it contains no smallcaps it seems).
344 \def\acro#1{{\small{#1}}}
345 \def\VHDL{\acro{VHDL}}
347 \def\CLaSH{{\small{C}}$\lambda$a{\small{SH}}}
349 % Macro for pretty printing haskell snippets. Just monospaced for now, perhaps
350 % we'll get something more complex later on.
351 \def\hs#1{\texttt{#1}}
352 \def\quote#1{``{#1}"}
354 \newenvironment{xlist}[1][\rule{0em}{0em}]{%
356 \settowidth{\labelwidth}{#1:}
357 \setlength{\labelsep}{0.5cm}
358 \setlength{\leftmargin}{\labelwidth}
359 \addtolength{\leftmargin}{\labelsep}
360 \setlength{\rightmargin}{0pt}
361 \setlength{\listparindent}{\parindent}
362 \setlength{\itemsep}{0 ex plus 0.2ex}
363 \renewcommand{\makelabel}[1]{##1:\hfil}
368 \usepackage{paralist}
370 \def\comment#1{{\color[rgb]{1.0,0.0,0.0}{#1}}}
372 \usepackage{cleveref}
373 \crefname{figure}{figure}{figures}
374 \newcommand{\fref}[1]{\cref{#1}}
375 \newcommand{\Fref}[1]{\Cref{#1}}
378 %include polycode.fmt
384 % can use linebreaks \\ within to get better formatting as desired
385 \title{C$\lambda$aSH: Structural Descriptions \\ of Synchronous Hardware using Haskell}
388 % author names and affiliations
389 % use a multiple column layout for up to three different
391 \author{\IEEEauthorblockN{Christiaan P.R. Baaij, Matthijs Kooijman, Jan Kuper, Marco E.T. Gerards, Bert Molenkamp, Sabih H. Gerez}
392 \IEEEauthorblockA{University of Twente, Department of EEMCS\\
393 P.O. Box 217, 7500 AE, Enschede, The Netherlands\\
394 c.p.r.baaij@@utwente.nl, matthijs@@stdin.nl}}
396 % \IEEEauthorblockN{Homer Simpson}
397 % \IEEEauthorblockA{Twentieth Century Fox\\
399 % Email: homer@thesimpsons.com}
401 % \IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
402 % \IEEEauthorblockA{Starfleet Academy\\
403 % San Francisco, California 96678-2391\\
404 % Telephone: (800) 555--1212\\
405 % Fax: (888) 555--1212}}
407 % conference papers do not typically use \thanks and this command
408 % is locked out in conference mode. If really needed, such as for
409 % the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
410 % after \documentclass
412 % for over three affiliations, or if they all won't fit within the width
413 % of the page, use this alternative format:
415 %\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
416 %Homer Simpson\IEEEauthorrefmark{2},
417 %James Kirk\IEEEauthorrefmark{3},
418 %Montgomery Scott\IEEEauthorrefmark{3} and
419 %Eldon Tyrell\IEEEauthorrefmark{4}}
420 %\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
421 %Georgia Institute of Technology,
422 %Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
423 %\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
424 %Email: homer@thesimpsons.com}
425 %\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
426 %Telephone: (800) 555--1212, Fax: (888) 555--1212}
427 %\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}
432 % use for special paper notices
433 %\IEEEspecialpapernotice{(Invited Paper)}
438 % make the title area
444 The abstract goes here.
446 % IEEEtran.cls defaults to using nonbold math in the Abstract.
447 % This preserves the distinction between vectors and scalars. However,
448 % if the conference you are submitting to favors bold math in the abstract,
449 % then you can use LaTeX's standard command \boldmath at the very start
450 % of the abstract to achieve this. Many IEEE journals/conferences frown on
451 % math in the abstract anyway.
458 % For peer review papers, you can put extra information on the cover
460 % \ifCLASSOPTIONpeerreview
461 % \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
464 % For peerreview papers, this IEEEtran command inserts a page break and
465 % creates the second title. It will be ignored for other modes.
466 \IEEEpeerreviewmaketitle
469 \section{Introduction}
470 Hardware description languages has allowed the productivity of hardware
471 engineers to keep pace with the development of chip technology. Standard
472 Hardware description languages, like \VHDL~\cite{VHDL2008} and
473 Verilog~\cite{Verilog}, allowed an engineer to describe circuits using a
474 programming language. These standard languages are very good at describing
475 detailed hardware properties such as timing behavior, but are generally
476 cumbersome in expressing higher-level abstractions. In an attempt to raise the
477 abstraction level of the descriptions, a great number of approaches based on
478 functional languages has been proposed \cite{T-Ruby,Hydra,HML2,Hawk1,Lava,
479 ForSyDe1,Wired,reFLect}. The idea of using functional languages for hardware
480 descriptions started in the early 1980s \cite{Cardelli1981, muFP,DAISY,FHDL},
481 a time which also saw the birth of the currently popular hardware description
482 languages such as \VHDL. The merit of using a functional language to describe
483 hardware comes from the fact that basic combinatorial circuits are equivalent
484 to mathematical functions and that functional languages are very good at
485 describing and composing mathematical functions.
487 In an attempt to decrease the amount of work involved with creating all the
488 required tooling, such as parsers and type-checkers, many functional hardware
489 description languages are embedded as a domain specific language inside the
490 functional language Haskell \cite{Hydra,Hawk1,Lava,ForSyDe1,Wired}. This
491 means that a developer is given a library of Haskell~\cite{Haskell} functions
492 and types that together form the language primitives of the domain specific
493 language. As a result of how the signals are modeled and abstracted, the
494 functions used to describe a circuit also build a large domain-specific
495 datatype (hidden from the designer) which can be further processed by an
496 embedded compiler. This compiler actually runs in the same environment as the
497 description; as a result compile-time and run-time become hard to define, as
498 the embedded compiler is usually compiled by the same Haskell compiler as the
499 circuit description itself.
501 The approach taken in this research is not to make another domain specific
502 language embedded in Haskell, but to use (a subset of) the Haskell language
503 itself for the purpose of describing hardware. By taking this approach, we can
504 capture certain language constructs, such as Haskell's choice elements
505 (if-constructs, case-constructs, pattern matching, etc.), which are not
506 available in the functional hardware description languages that are embedded
507 in Haskell as a domain specific languages. As far as the authors know, such
508 extensive support for choice-elements is new in the domain of functional
509 hardware description language. As the hardware descriptions are plain Haskell
510 functions, these descriptions can be compiled for simulation using using the
511 optimizing Haskell compiler \GHC.
513 Where descriptions in a conventional hardware description language have an
514 explicit clock for the purpose state and synchronicity, the clock is implied
515 in this research. The functions describe the behavior of the hardware between
516 clock cycles, as such, only synchronous systems can be described. Many
517 functional hardware description models signals as a stream of all values over
518 time; state is then modeled as a delay on this stream of values. The approach
519 taken in this research is to make the current state of a circuit part of the
520 input of the function and the updated state part of the output.
522 Like the standard hardware description languages, descriptions made in a
523 functional hardware description language must eventually be converted into a
524 netlist. This research also features a prototype translator called \CLaSH\
525 (pronounced: clash), which converts the Haskell code to equivalently behaving
526 synthesizable \VHDL\ code, ready to be converted to an actual netlist format
527 by an optimizing \VHDL\ synthesis tools.
529 \section{Hardware description in Haskell}
531 \subsection{Function application}
532 The basic syntactic elements of a functional program are functions
533 and function application. These have a single obvious translation to a
534 netlist: every function becomes a component, every function argument is an
535 input port and the result value is of a function is an output port. This
536 output port can have a complex type (such as a tuple), so having just a
537 single output port does not create a limitation. Each function application
538 in turn becomes a component instantiation. Here, the result of each
539 argument expression is assigned to a signal, which is mapped to the
540 corresponding input port. The output port of the function is also mapped
541 to a signal, which is used as the result of the application itself.
543 Since every top level function generates its own component, the
544 hierarchy of function calls is reflected in the final netlist aswell,
545 creating a hierarchical description of the hardware. This separation in
546 different components makes the resulting \VHDL\ output easier to read and
549 As an example we can see the netlist of the |mac| function in
550 \Cref{img:mac-comb}; the |mac| function applies both the |mul| and |add|
551 function to calculate $a * b + c$:
553 mac a b c = add (mul a b) c
556 \centerline{\includegraphics{mac}}
557 \caption{Combinatorial Multiply-Accumulate}
560 The result of using a complex input type can be seen in
561 \cref{img:mac-comb-nocurry} where the |mac| function now uses a single
562 input tuple for the |a|, |b|, and |c| arguments:
564 mac (a, b, c) = add (mul a b) c
567 \centerline{\includegraphics{mac-nocurry}}
568 \caption{Combinatorial Multiply-Accumulate (complex input)}
569 \label{img:mac-comb-nocurry}
573 Although describing components and connections allows describing a
574 lot of hardware designs already, there is an obvious thing missing:
575 choice. We need some way to be able to choose between values based
576 on another value. In Haskell, choice is achieved by \hs{case}
577 expressions, \hs{if} expressions, pattern matching and guards.
579 The easiest of these are of course case expressions (and \hs{if}
580 expressions, which can be very directly translated to \hs{case}
581 expressions). A \hs{case} expression can in turn simply be
582 translated to a conditional assignment in \VHDL, where the
583 conditions use equality comparisons against the constructors in the
584 \hs{case} expressions.
586 A slightly more complex (but very powerful) form of choice is
587 pattern matching. A function can be defined in multiple clauses,
588 where each clause specifies a pattern. When the arguments match the
589 pattern, the corresponding clause will be used.
591 A pattern match (with optional guards) can also be implemented using
592 conditional assignments in \VHDL, where the condition is the logical
593 and of comparison results of each part of the pattern as well as the
596 Contrived example that sums two values when they are equal or
597 non-equal (depending on the predicate given) and returns 0
598 otherwise. This shows three implementations, one using and if
599 expression, one using only case expressions and one using pattern
603 sumif pred a b = if pred == Eq && a == b ||
604 pred == Neq && a != b
608 sumif pred a b = case pred of
612 Neq -> case a != b of
616 sumif Eq a b | a == b = a + b
617 sumif Neq a b | a != b = a + b
622 \centerline{\includegraphics{choice-ifthenelse}}
623 \caption{Choice - \emph{if-then-else}}
628 \centerline{\includegraphics{choice-case}}
629 \caption{Choice - \emph{case-statement / pattern matching}}
634 Translation of two most basic functional concepts has been
635 discussed: function application and choice. Before looking further
636 into less obvious concepts like higher-order expressions and
637 polymorphism, the possible types that can be used in hardware
638 descriptions will be discussed.
640 Some way is needed to translate every value used to its hardware
641 equivalents. In particular, this means a hardware equivalent for
642 every \emph{type} used in a hardware description is needed.
644 The following types are \emph{built-in}, meaning that their hardware
645 translation is fixed into the \CLaSH\ compiler. A designer can also
646 define his own types, which will be translated into hardware types
647 using translation rules that are discussed later on.
649 \subsection{Built-in types}
652 This is the most basic type available. It can have two values:
653 \hs{Low} and \hs{High}. It is mapped directly onto the
654 \texttt{std\_logic} \VHDL\ type.
656 This is a basic logic type. It can have two values: \hs{True}
657 and \hs{False}. It is translated to \texttt{std\_logic} exactly
658 like the \hs{Bit} type (where a value of \hs{True} corresponds
659 to a value of \hs{High}). Supporting the Bool type is
660 particularly useful to support \hs{if ... then ... else ...}
661 expressions, which always have a \hs{Bool} value for the
663 \item[\hs{SizedWord}, \hs{SizedInt}]
664 These are types to represent integers. A \hs{SizedWord} is unsigned,
665 while a \hs{SizedInt} is signed. These types are parametrized by a
666 length type, so you can define an unsigned word of 32 bits wide as
670 type Word32 = SizedWord D32
673 Here, a type synonym \hs{Word32} is defined that is equal to the
674 \hs{SizedWord} type constructor applied to the type \hs{D32}. \hs{D32}
675 is the \emph{type level representation} of the decimal number 32,
676 making the \hs{Word32} type a 32-bit unsigned word. These types are
677 translated to the \VHDL\ \texttt{unsigned} and \texttt{signed}
680 This is a vector type, that can contain elements of any other type and
681 has a fixed length. The \hs{Vector} type constructor takes two type
682 arguments: the length of the vector and the type of the elements
683 contained in it. The state type of an 8 element register bank would
687 type RegisterState = Vector D8 Word32
690 Here, a type synonym \hs{RegisterState} is defined that is equal to
691 the \hs{Vector} type constructor applied to the types \hs{D8} (The
692 type level representation of the decimal number 8) and \hs{Word32}
693 (The 32 bit word type as defined above). In other words, the
694 \hs{RegisterState} type is a vector of 8 32-bit words. A fixed size
695 vector is translated to a \VHDL\ array type.
696 \item[\hs{RangedWord}]
697 This is another type to describe integers, but unlike the previous
698 two it has no specific bit-width, but an upper bound. This means that
699 its range is not limited to powers of two, but can be any number.
700 A \hs{RangedWord} only has an upper bound, its lower bound is
701 implicitly zero. The main purpose of the \hs{RangedWord} type is to be
702 used as an index to a \hs{Vector}.
704 \comment{TODO: Perhaps remove this example?} To define an index for
705 the 8 element vector above, we would do:
708 type RegisterIndex = RangedWord D7
711 Here, a type synonym \hs{RegisterIndex} is defined that is equal to
712 the \hs{RangedWord} type constructor applied to the type \hs{D7}. In
713 other words, this defines an unsigned word with values from
714 0 to 7 (inclusive). This word can be be used to index the
715 8 element vector \hs{RegisterState} above. This type is translated to
716 the \texttt{unsigned} \VHDL type.
719 \subsection{User-defined types}
720 There are three ways to define new types in Haskell: algebraic
721 data-types with the \hs{data} keyword, type synonyms with the \hs{type}
722 keyword and type renamings with the \hs{newtype} keyword. \GHC\
723 offers a few more advanced ways to introduce types (type families,
724 existential typing, {\small{GADT}}s, etc.) which are not standard
725 Haskell. These are not currently supported.
727 Only an algebraic datatype declaration actually introduces a
728 completely new type, for which we provide the \VHDL\ translation
729 below. Type synonyms and renamings only define new names for
730 existing types (where synonyms are completely interchangeable and
731 renamings need explicit conversion). Therefore, these do not need
732 any particular \VHDL\ translation, a synonym or renamed type will
733 just use the same representation as the original type. The
734 distinction between a renaming and a synonym does no longer matter
735 in hardware and can be disregarded in the generated \VHDL.
737 For algebraic types, we can make the following distinction:
740 \item[\bf{Single constructor}]
741 Algebraic datatypes with a single constructor with one or more
742 fields, are essentially a way to pack a few values together in a
743 record-like structure. An example of such a type is the following pair
747 data IntPair = IntPair Int Int
750 Haskell's builtin tuple types are also defined as single
751 constructor algebraic types and are translated according to this
752 rule by the \CLaSH\ compiler. These types are translated to \VHDL\
753 record types, with one field for every field in the constructor.
754 \item[\bf{No fields}]
755 Algebraic datatypes with multiple constructors, but without any
756 fields are essentially a way to get an enumeration-like type
757 containing alternatives. Note that Haskell's \hs{Bool} type is also
758 defined as an enumeration type, but we have a fixed translation for
759 that. These types are translated to \VHDL\ enumerations, with one
760 value for each constructor. This allows references to these
761 constructors to be translated to the corresponding enumeration value.
762 \item[\bf{Multiple constructors with fields}]
763 Algebraic datatypes with multiple constructors, where at least
764 one of these constructors has one or more fields are not
769 A very important concept in hardware it the concept of state. In a
770 stateful design, the outputs depend on the history of the inputs, or the
771 state. State is usually stored in registers, which retain their value
772 during a clock cycle. As we want to describe more than simple
773 combinatorial designs, \CLaSH\ needs an abstraction mechanism for state.
775 An important property in Haskell, and in most other functional languages,
776 is \emph{purity}. A function is said to be \emph{pure} if it satisfies two
779 \item given the same arguments twice, it should return the same value in
781 \item when the function is called, it should not have observable
784 This purity property is important for functional languages, since it
785 enables all kinds of mathematical reasoning that could not be guaranteed
786 correct for impure functions. Pure functions are as such a perfect match
787 for a combinatorial circuit, where the output solely depends on the
788 inputs. When a circuit has state however, it can no longer be simply
789 described by a pure function. Simply removing the purity property is not a
790 valid option, as the language would then lose many of it mathematical
791 properties. In an effort to include the concept of state in pure
792 functions, the current value of the state is made an argument of the
793 function; the updated state becomes part of the result.
795 A simple example is the description of an accumulator circuit:
797 acc :: Word -> State Word -> (State Word, Word)
798 acc inp (State s) = (State s', outp)
803 This approach makes the state of a function very explicit: which variables
804 are part of the state is completely determined by the type signature. This
805 approach to state is well suited to be used in combination with the
806 existing code and language features, such as all the choice constructs, as
807 state values are just normal values.
808 \section{\CLaSH\ prototype}
812 \section{Related work}
813 Many functional hardware description languages have been developed over the
814 years. Early work includes such languages as $\mu$\acro{FP}~\cite{muFP}, an
815 extension of Backus' \acro{FP} language to synchronous streams, designed
816 particularly for describing and reasoning about regular circuits. The
817 Ruby~\cite{Ruby} language uses relations, instead of functions, to describe
818 circuits, and has a particular focus on layout. \acro{HML}~\cite{HML2} is a
819 hardware modeling language based on the strict functional language
820 \acro{ML}, and has support for polymorphic types and higher-order functions.
821 Published work suggests that there is no direct simulation support for
822 \acro{HML}, and that the translation to \VHDL\ is only partial.
824 Like this work, many functional hardware description languages have some sort
825 of foundation in the functional programming language Haskell.
826 Hawk~\cite{Hawk1} uses Haskell to describe system-level executable
827 specifications used to model the behavior of superscalar microprocessors. Hawk
828 specifications can be simulated, but there seems to be no support for
829 automated circuit synthesis. The ForSyDe~\cite{ForSyDe2} system uses Haskell
830 to specify abstract system models, which can (manually) be transformed into an
831 implementation model using semantic preserving transformations. ForSyDe has
832 several simulation and synthesis backends, though synthesis is restricted to
833 the synchronous subset of the ForSyDe language.
835 Lava~\cite{Lava} is a hardware description language that focuses on the
836 structural representation of hardware. Besides support for simulation and
837 circuit synthesis, Lava descriptions can be interfaced with formal method
838 tools for formal verification. Lava descriptions are actually circuit
839 generators when viewed from a synthesis viewpoint, in that the language
840 elements of Haskell, such as choice, can be used to guide the circuit
841 generation. If a developer wants to insert a choice element inside an actual
842 circuit he will have to specify this explicitly as a component. In this
843 respect \CLaSH\ differs from Lava, in that all the choice elements, such as
844 case-statements and pattern matching, are synthesized to choice elements in the
845 eventual circuit. As such, richer control structures can both be specified and
846 synthesized in \CLaSH\ compared to any of the languages mentioned in this
849 The merits of polymorphic typing, combined with higher-order functions, are
850 now also recognized in the `main-stream' hardware description languages,
851 exemplified by the new \VHDL-2008 standard~\cite{VHDL2008}. \VHDL-2008 has
852 support to specify types as generics, thus allowing a developer to describe
853 polymorphic components. Note that those types still require an explicit
854 generic map, whereas type-inference and type-specialization are implicit in
857 % Wired~\cite{Wired},, T-Ruby~\cite{T-Ruby}, Hydra~\cite{Hydra}.
859 % A functional language designed specifically for hardware design is
860 % $re{\mathit{FL}}^{ect}$~\cite{reFLect}, which draws experience from earlier
861 % language called \acro{FL}~\cite{FL} to la
863 % An example of a floating figure using the graphicx package.
864 % Note that \label must occur AFTER (or within) \caption.
865 % For figures, \caption should occur after the \includegraphics.
866 % Note that IEEEtran v1.7 and later has special internal code that
867 % is designed to preserve the operation of \label within \caption
868 % even when the captionsoff option is in effect. However, because
869 % of issues like this, it may be the safest practice to put all your
870 % \label just after \caption rather than within \caption{}.
872 % Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
873 % option should be used if it is desired that the figures are to be
874 % displayed while in draft mode.
878 %\includegraphics[width=2.5in]{myfigure}
879 % where an .eps filename suffix will be assumed under latex,
880 % and a .pdf suffix will be assumed for pdflatex; or what has been declared
881 % via \DeclareGraphicsExtensions.
882 %\caption{Simulation Results}
886 % Note that IEEE typically puts floats only at the top, even when this
887 % results in a large percentage of a column being occupied by floats.
890 % An example of a double column floating figure using two subfigures.
891 % (The subfig.sty package must be loaded for this to work.)
892 % The subfigure \label commands are set within each subfloat command, the
893 % \label for the overall figure must come after \caption.
894 % \hfil must be used as a separator to get equal spacing.
895 % The subfigure.sty package works much the same way, except \subfigure is
896 % used instead of \subfloat.
899 %\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
900 %\label{fig_first_case}}
902 %\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
903 %\label{fig_second_case}}}
904 %\caption{Simulation results}
908 % Note that often IEEE papers with subfigures do not employ subfigure
909 % captions (using the optional argument to \subfloat), but instead will
910 % reference/describe all of them (a), (b), etc., within the main caption.
913 % An example of a floating table. Note that, for IEEE style tables, the
914 % \caption command should come BEFORE the table. Table text will default to
915 % \footnotesize as IEEE normally uses this smaller font for tables.
916 % The \label must come after \caption as always.
919 %% increase table row spacing, adjust to taste
920 %\renewcommand{\arraystretch}{1.3}
921 % if using array.sty, it might be a good idea to tweak the value of
922 % \extrarowheight as needed to properly center the text within the cells
923 %\caption{An Example of a Table}
924 %\label{table_example}
926 %% Some packages, such as MDW tools, offer better commands for making tables
927 %% than the plain LaTeX2e tabular which is used here.
928 %\begin{tabular}{|c||c|}
938 % Note that IEEE does not put floats in the very first column - or typically
939 % anywhere on the first page for that matter. Also, in-text middle ("here")
940 % positioning is not used. Most IEEE journals/conferences use top floats
941 % exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
942 % footnotes above bottom floats. This can be corrected via the \fnbelowfloat
943 % command of the stfloats package.
948 The conclusion goes here.
953 % conference papers do not normally have an appendix
956 % use section* for acknowledgement
957 \section*{Acknowledgment}
960 The authors would like to thank...
966 % trigger a \newpage just before the given reference
967 % number - used to balance the columns on the last page
968 % adjust value as needed - may need to be readjusted if
969 % the document is modified later
970 %\IEEEtriggeratref{8}
971 % The "triggered" command can be changed if desired:
972 %\IEEEtriggercmd{\enlargethispage{-5in}}
976 % can use a bibliography generated by BibTeX as a .bbl file
977 % BibTeX documentation can be easily obtained at:
978 % http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
979 % The IEEEtran BibTeX style support page is at:
980 % http://www.michaelshell.org/tex/ieeetran/bibtex/
981 \bibliographystyle{IEEEtran}
982 % argument is your BibTeX string definitions and bibliography database(s)
983 \bibliography{IEEEabrv,clash.bib}
985 % <OR> manually copy in the resultant .bbl file
986 % set second argument of \begin to the number of references
987 % (used to reserve space for the reference number labels box)
988 % \begin{thebibliography}{1}
990 % \bibitem{IEEEhowto:kopka}
991 % H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
992 % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
994 % \end{thebibliography}
1002 % vim: set ai sw=2 sts=2 expandtab: