% Help on BibTeX bib files: http://nwalsh.com/tex/texhelp/bibtx-4.html

% compiler avec l'option -min-crossrefs=100 pour eviter la factorisation

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  Mode{on}
  Collation{mixed}
  SortTypeOrder{pattern,key,name}
  NameOrder{ascending}
  Key{{author,editor},\year{year,note}}
  KeyOrder{descending,nulls first}
  Pattern{author+editor: "doron"}
  PatternOrder{first}
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@String{AcmToms = {ACM Transactions on Mathematical Software}}

@inproceedings{Bruel2006,
        author={C. Bruel},
        title={If-conversion {SSA} framework for partially predicated {VLIW} architectures},
        booktitle={Digest of the 4th Workshop on Optimizations for DSP and Embedded Systems (Manhattan, New York, NY)},
        year= 2006,
        month={March},
        url= "{http://www.ece.vill.edu/~deepu/odes/odes-5_digest.pdf}"
}

@article{BenoitDDD2004,
        author          = "B. de Dinechin",
        title           = "From Machine Scheduling to {VLIW} Instruction Scheduling",
        journal         = "ST Journal of Research",
        volume          = "1",
        number          = "2",
        year            = "2004",
        month           = "September",
        OPTnote            = "{http://cri.ensmp.fr/classement/2003}"
}


@Article{MonMez90,
  author =       {P. Montuschi and P.~M. Mezzalama},
  title =        {Survey of square rooting algorithms},
  journal =      {Computers and Digital Techniques, IEE Proceedings E.},
  year =         {1990},
  OPTkey =       {},
  volume =       {137},
  number =       {1},
  pages =        {31-40},
  OPTmonth =     {},
  OPTnote =      {},
  OPTannote =    {}
}



@InProceedings{MarksteinDSP2008,
  author =	{Peter Markstein},
  title =	{The New IEEE-754 Standard for Floating Point Arithmetic},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  year =	{2008},
  noeditor =	{Annie Cuyt and Walter Kr{\"a}mer and Wolfram Luther and Peter Markstein},
  number =	{08021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1448},
  annote =	{Keywords: Floating point arithmetic, standards}
}



@inproceedings{Ahrendt96,
author = {T.~Ahrendt},
title = {Fast High-Precision Computation of Complex Square Roots},
booktitle = {Proceedings of ISSAC'96 (Zurich, Switzerland)},
year = 1996,
}

@inproceedings{ABCW97,
    author={M. G. Arnold and T. A. Bailey and J. R. Cowles and M. D. Winkel},
    title={Arithmetic Co-Transformations in the Real and Complex Logarithmic Number
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    booktitle={Proceedings of the 13th {IEEE} Symposium on Computer Arithmetic (Asilomar,
        California)},
    year= 1997,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={190--199}
}

@article{ABCW98,
    author={M. G. Arnold and T. A. Bailey and J. R. Cowles and M. D. Winkel},
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    pages={777--786},
    number= 7
}

@article{Monniaux2008,
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    year= {2008},
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    note = {A preliminary version is available at \url{http://hal.archives-ouvertes.fr/hal-00128124}}
}

@inproceedings{ABVHZ95,
    author={E.~Antelo and J.~D.~Bruguera and J.~Villalba and J.~H.~Hidalgo and E.~Zapata},
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    key={ABVHZ95}
}

@inproceedings{ABVZ95,
    author={E.~Antelo and J.~D.~Bruguera and J.~Villalba and E.~Zapata},
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@inproceedings{Cornea2007,
    author={M.~Cornea and C.~Anderson and J.~Harrison and P.~T.~P.~Tang and E.~Schneider and C.~Tsen},
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    year= 2007,
    month= jun,
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}

@Article{CoHaAn+09,
  author = 	 {M.~Cornea and J.~Harrison and C.~Anderson and P.~T.~P.~Tang 
                  and E.~Schneider and E.~Gvozdev},
  title = 	 {A Software Implementation of the {IEEE 754R} Decimal 
                  Floating-Point Arithmetic Using the Binary Encoding Format},
  journal = 	 {{IEEE} Transactions on Computers},
  year = 	 {2009},
  OPTkey = 	 {},
  volume = 	 {58},
  number = 	 {2},
  pages = 	 {148--162},
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@inproceedings{PatilEtAl2007,
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    year= 2007,
    month= jun,
    publisher={IEEE Computer Society Conference Publishing Services},
    editor={P.~Kornerup and J.-M.~Muller},
    pages={29--37},
    location={Montpellier, France}
}


@inproceedings{Fousse2007a,
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    month= jun,
    publisher={IEEE Computer Society Conference Publishing Services},
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    pages={150--160},
    key={Cornea2007},
    location={Montpellier, France}
}

@unpublished{Fousse2007b,
    author={L.~Fousse},
    title={Accurate Multiple-Precision Gauss-Legendre Quadrature},
    note={Transparencies of the talk given at the 18th IEEE Symposium on Computer Arithmetic (ARITH-18) for~\cite{Fousse2007a}}
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@unpublished{Bernstein2001,
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@unpublished{May2008,
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@inproceedings{Erle2007,
    author = {Erle, M. A. and Schulte, M. J. and  Hickmann, B. J.},
    title={Decimal Floating-Point Multiplication via Carry-Save Addition},
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    month= jun,
    publisher={IEEE Computer Society Conference Publishing Services},
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    key={Cornea2007},
    location={Montpellier, France}
}

@article{ACGSST86,
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@BOOK{BrentZimmermann09,
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@BOOK{Minkowski1905,
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@BOOK{AH83,
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@BOOK{Aspray1990,
        AUTHOR             = {W.~Aspray and A.~G.~Bromley and M.~Campbell-Kelly and P.~E.~Ceruzzi and M.~R.~Williams},
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        TITLE              = {Computing Before Computers},
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@ARTICLE{AM00,
        AUTHOR             = {Alefeld, G. and Mayer, G.},
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}

@article{BaiBorBorPlo97,
    author={D.~H.~Bailey and J.~M.~Borwein and P.~B. Borwein and S.~Plouffe},
    title={The Quest for Pi},
    journal={Mathematical Intelligencer},
    volume={19},
    year={1997},
    pages={50--57},
    number={1},
    key={BaiBorBorPlo97}
}

@article{BaillyThiran99,
    author={B.~Le~Bailly and J.~P.~Thiran},
    title={Computing Complex Polynomial Chebyshev Approximants on the Unit Circle by
        the Real Remez Algorithm},
    journal={SIAM Journal on Numerical Analysis},
    volume={36},
    year={1999},
    pages={1858-1877},
    number={6},
    key={BaillyThiran99}
}



@phdthesis{Vazquez-thesis,
    author={V\'azquez, A.},
    title={High-Performance Decimal Floating-Point Units},
    school={Universidade de Santiago de Compostela},
    year= 2009
}

@phdthesis{Baj93b,
    author={J.~C. Bajard},
    title={Evaluation de fonctions dans des syst{\`e}mes redondants d'{\'e}criture des nombres},
    school={{{\'E}cole Normale Sup{\'e}rieure de Lyon, Universit{\'e} Claude Bernard}},
    year= 1993,
    month= feb,
    keywords={on-line arithmetic,polynomial approximations,redundant number systems}
}

@proceedings{BajFrouMul99,
    editor={J.C. Bajard and C. Frougny and J.M. Muller},
    title={Special Issue ``Real Numbers and Computers'' of Theoretical Computer Science},
    year= 1999,
    month= jan
}

@book{BajMul2004,
    author={J.-C.~Bajard and J.-M.~Muller (coordinators)},
    title={Calcul et Arithm{\'e}tique des Ordinateurs},
    publisher={Herm{\`e}s Science Publishing},
    year={2004},
    series={{IC} 2}
}

@INBOOK{BR98,
        AUTHOR             = {Bajard, J.-C.  and Revol, N.},
        CHAPTER            = {Arithm\'etique multipr\'ecision},
        PAGES              = {93--116},
        PUBLISHER          = {ed. by M. Daumas, J.-M. Muller,Masson},
        TITLE              = {Qualit\'e des calculs sur ordinateur},
        YEAR               = {1998}
}

@book{Bak75,
    author={G.~A. Baker},
    title={Essentials of Pad{\'e} Approximants},
    publisher={Academic Press, New York, NY},
    year= 1975,
    keywords={rational approximations}
}

@article{Bak76,
    author={P.~W. Baker},
    title={Suggestion for a fast binary sine/cosine generator},
    journal={{IEEE} Transactions on Computers},
    volume={C-25},
    year= 1976,
    month= nov,
    number= 11,
    keywords={cordic,elementary functions,trigonometric functions}
}

@article{Baker92,
    author={H.~G.~Baker},
    title={Less complex elementary functions},
    journal={ACM SIGPLAN Notices},
    volume={27},
    year={1992},
    pages={15--16},
    number={11},
    issn={0362-1340},
    doi={http://doi.acm.org/10.1145/141018.141022},
    publisher={ACM Press},
    address={New York, NY}
}

@book{BakGra96,
    author={G.~A. Baker},
    title={Pad{\'e} Approximants},
    publisher={Cambridge University Press, New York, NY},
    year= 1996,
    series={Encyclopedia of Mathematics and its Applications},
    keywords={rational approximations},
    number= 59
}

@article{Ban74,
    author={D.~K. Banerji},
    title={A novel implementation method for addition and subtraction in residue number
        systems},
    journal={{IEEE} Transactions on Computers},
    volume={C-23},
    year= 1974,
    pages={106-108},
    month= jan,
    number= 1,
    keywords={residue number systems}
}

@article{Barrio2003,
    author={R. Barrio},
    title={A Unified Rounding Error Bound for Polynomial Evaluation},
    journal={Advances in Computational Mathematics},
    volume={19},
    year={2003},
    pages={385--400},
    number={4},
    issn={1019-7168}
}

@inproceedings{BB88,
    author={M. Bennani and M.~C. Brunet},
    title={PRECISE: simulation of round-off error propagation model},
    booktitle={Proceedings of the 12th World IMACS Congress},
    year= 1988,
    month= jul,
    location={Paris, France},
    keywords={accuracy control,floating-point arithmetic,perturbation methods}
}

@article{BBM84,
    author={C.~M.~Black and R.~P.~Burton and T.~H.~Miller},
    title={The Need for an Industry Standard of Accuracy for Elementary-Function Programs},
    journal={{ACM} Transactions on Mathematical Software},
    volume={10},
    year={1984},
    pages={361--366},
    month= dec,
    number={4},
    key={BBM84}
}

@inproceedings{BC87,
    author={M.~C. Brunet and F. Chatelin},
    title={A probabilistic round-off error propagation model, application to the eigenvalue
        problem},
    booktitle={Reliable Numerical Software},
    year= 1987,
    publisher={Oxford University Press, London},
    note={Available at \url{http://www.boutell.com/fracster-src/doubledouble/doubledouble.html}},
    editor={M.~G.~Cox and S.~Hammarling},
    keywords={accuracy control,floating-point arithmetic,perturbation methods}
}

@article{BCH86,
    author={P. Beame and S. Cook and H. Hoover},
    title={Log depth circuits for division and related problems},
    journal={SIAM Journal on Computing},
    volume= 15,
    year= 1986,
    pages={994-1003},
    keywords={complexity theory,division,residue number systems}
}

@book{BCKKMMPR97,
    author={J.C.~Bajard and H.~Comon and C.~Kenyon and D.~Krob and M.~Morvan and J.M.~Muller
        and A.~Petit and Y.~Robert},
    title={Exercices d'algorithmique},
    publisher={International Thomson Publishing},
    year= 1997,
    key={BCKKMMPR97}
}

@article{BDKM94,
    author={J.~C. Bajard and J. Duprat and S. Kla and J.~M. Muller},
    title={Some operators for on-line radix 2 computations},
    journal={Journal of Parallel and Distributed Computing},
    volume= 22,
    year= 1994,
    pages={336-345},
    month= aug,
    number= 2,
    keywords={addition,multiplication,on-line arithmetic,redundant number systems}
}

@inproceedings{BDM96,
    author={J.~C.~Bajard and L.~S.~Didier and J.~M.~Muller},
    title={A New Euclidean Division Algorithm for Residue Number Systems},
    booktitle={Proceedings of ASAP'96},
    year= 1996,
    month= aug,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    key={BDM96},
    location={Chicago, IL}
}

@article{BDM98,
    author={J.C.~Bajard and L.S.~Didier and J.M.~Muller},
    title={A New Euclidean Division Algorithm for Residue Number Systems},
    journal={Journal of VLSI Signal Processing},
    volume= 19,
    year= 1998,
    pages={167--178},
    number= 2,
    key={BDM98}
}

@inproceedings{BeaBurLefLim99,
    author={A. Beaumont-Smith and N. Burgess and D. Lefrere and C.C. Lim},
    title={Reduced Latency {IEEE} Floating-Point Standard Adder Architecture},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic (Adelaide,
        Australia)},
    year= 1999,
    month= apr,
    publisher={IEEE Computer Society Press},
    editor={Koren and Kornerup},
    pages={35--42}
}

@article{BekHuiNow2000,
    author={M. Bekooij and J. Huisken and K. Nowak},
    title={Numerical Accuracy of Fast Fourier Transforms with {CORDIC} Arithmetic},
    journal={Journal of VLSI Signal Processing Systems},
    volume= 25,
    year= 2000,
    pages={187--193},
    month= jun,
    number= 2
}

@inproceedings{Ber2004,
    author={C.~Bertin and N.~Brisebarre and B.~Dupont de Dinechin and C.-P.~Jeannerod
        and C.~Monat and J.-M.~Muller and S.-K.~Raina and A.~Tisserand},
    title={A Floating-Point Library for Integer Processors},
    booktitle={Proc. of {SPIE} $49$th Annual Meeting International Symposium on Optical
        Science and Technology, Denver},
    year={2004},
    month= aug,
    publisher={{SPIE}}
}

@techreport{Ber97,
    author={V.~Berth{\'e}},
    title={Three distance theorems and combinatorics on words},
    institution={Institut de Math{\'e}matiques de Luminy, Marseille, France},
    year= 1997,
    key={Ber97}
}

@article{BerrutMittel2004,
    author={J.-P. Berrut and H.D. Mittelmann},
    title={Adaptive Point Shifts in Rational Approximation with Optimized Denominator},
    journal={Journal of Computational and Applied Mathematics},
    volume={164--165},
    year={2004},
    pages={81--92},
    key={BerrutMittel2004}
}

@article{BeuMul2004,
    author={J.-L.~Beuchat and J.-M.~Muller},
    title={Modulo $m$ Multiplication-Addition: Algorithms and {FPGA} Implementation},
    journal={Electronic Letters},
    volume={40},
    year={2004},
    pages={654-655},
    number={11}
}

@article{Benford1938,
    author = {F.~Benford},
    title = {The law of anomalous numbers},
    journal = {Proceedings of the American Philosophical Society},
    volume = {78},
    number = {4},
    pages = {551--572},
    year = {1938}
}

@inproceedings{BEW89,
    author={R.~H. Brackert and M.~D. Ercegovac and A.~N. Willson},
    title={Design of an On-line Multiply-Add Module for Recursive Digital Filters.},
    booktitle={Proceedings of the 9th IEEE Symposium on Computer Arithmetic},
    year= 1989,
    month={sep},
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={M. D. Ercegovac and E. Swartzlander},
    pages={34-41},
    location={Santa Monica, CA},
    keywords={multiplication,on-line arithmetic}
}

@inproceedings{BF91,
    author={W. Ferguson and T. Brightman},
    title={Accurate and monotone approximations of some transcendental functions},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={237-244},
    location={Grenoble, France},
    keywords={elementary functions}
}

@proceedings{BFMV96,
    editor={J.C.~Bajard and C.~Frougny and J.M.~Muller and G.~Villard},
    title={Special issue ``Real Numbers and Computers'' of Theoretical Computer Science},
    year= 1996,
    month= aug,
    volume= 162,
    key={BFMV96}
}

@inproceedings{BG91,
    author={R. Boskovic and D. Gamberger},
    title={New approach to integer division in residue number systems},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={84-91},
    location={Grenoble, France},
    keywords={division,residue number systems}
}

@book{BGHN99,
    author={A. Bultheel and P. Gonzales-Vera and E. Hendriksen and O. Njastad},
    title={Orthogonal Rational Functions},
    publisher={Cambridge University Press, New York, NY},
    year={1999},
    volume={5},
    series={Cambridge Monographs on Applied and Computational Mathematics},
    key={BGHN99}
}

@inproceedings{BGMS92,
    author={J.~C. Bajard and A. Guyot and J.~M. Muller and A. Skaf},
    title={On-line approximation of real functions using polynomials},
    booktitle={International conference on Micro-electronics, Monastir-92},
    year= 1992,
    keywords={elementary functions,on-line arithmetic,polynomial approximations}
}

@inproceedings{BGMS93,
    author={J.~C. Bajard and A. Guyot and J.~M. Muller and A. Skaf},
    title={Design of a {VLSI} circuit for on-line evaluation of several elementary
        functions using their Taylor Expansion},
    booktitle={International Conference on Application-Specific Array Processors (ASAP93),
        Venice, Italy},
    year= 1993,
    keywords={elementary functions,on-line arithmetic,polynomial approximations}
}

@inproceedings{BGMS93a,
    author={J.~C. Bajard and A. Guyot and J.~M. Muller and A. Skaf},
    title={A {VLSI} circuit for on-line polynomial computing: application to exponential,
        trigonometric and hyperbolic functions},
    booktitle={VLSI93, Grenoble},
    year= 1993,
    month= sep,
    keywords={elementary functions,on-line arithmetic,polynomial approximations}
}

@techreport{BGN46,
    author={A. Burks and H.~H. Goldstine and J. Von Neumann},
    title={Preliminary discussion of the logic design of an electronic computing instrument},
    institution={Institute for advanced study, princeton},
    year= 1946,
    note={reprinted in C.~G. Bell, Computer structures, readings and examples, Mc
        Graw-Hill, New York, 1971},
    keywords={addition}
}

@inproceedings{BGVHZ2004,
    author={G.~Bandera and M.~Gonzalez and J.~Villalba and J.~Hormigo and E. L. Zapata},
    title={Evaluation of Elementary Functions Using Multimedia Features},
    abstract={Most of current computers include multimedia features. In this paper, we
        use these extensions to compute elementary functions based on polynomial
        approximations. Hence, we present several alternatives taking advantage
        of the new attributes on multimedia processors, such as VLIW and SIMD architectures.
        Our algorithms support the polynomial evaluation in two different ways:
        the first one is only based in addition/shift operations; while the second
        uses MAC instructions. Both approximations are analyzed and tailored to
        subword parallelism units of the new processors. Potential instruction-level
        and machine-level parallelism are fully exploited through concurrent use
        of all functional units. A combined approximation using MAC units and addition
        and shifts is also presented as a third approximation. Two new instructions
        are also presented here to improve the execution of some of our algorithms.},
    booktitle={Proceedings of the 18th International Parallel and Distributed Processing
        Symposium (IPDPS'04)},
    year={2004},
    month= apr,
    publisher={{IEEE} Computer Society Press, Los Alamitos, CA},
    key={BGVHZ2004},
    location={Santa Fe, New Mexico}
}

@article{BHH91,
    author={X. Hu and G. Harber and S.~C. Bass},
    title={Expanding the range of the CORDIC algorithm},
    journal={{IEEE} Transactions on Computers},
    volume= 40,
    year= 1991,
    pages={13-21},
    month= jan,
    number= 1,
    keywords={cordic}
}

@techreport{BHLT2002,
    author={D.~H.~Bailey and Y.~Hida and X.~S.~Li and B.~Thompson},
    title={{ARPREC}: an Arbitrary Precision Computation Package},
    institution={Lawrence Berkeley National Laboratory},
    year={2002},
    key={BHLT2002},
    note={Available at \url{http://crd.lbl.gov/~dhbailey/dhbpapers/arprec.pdf}}
}

@article{BHM89,
    author={V. Milutinovic and M. Bettinger and W. Helbig},
    title={Multiplier/shifter design tradeoffs in a 32-bit microprocessor},
    journal={{IEEE} Transactions on Computers},
    volume= 38,
    year= 1989,
    pages={874-880},
    keywords={multiplication}
}

@article{BHV83,
    author={N. Bandeira and J.~A. Howard and K. Vaccaro},
    title={A two's complement array multiplier using true values of the operands},
    journal={{IEEE} Transactions on Computers},
    volume={C-32},
    year= 1983,
    pages={745-747},
    keywords={multiplication}
}

@article{BHW92,
    author={M.~A. Hasan and M. Wang and V.~K. Bharvaga},
    title={Modular construction of low complexity parallel multipliers for a class
        of finite fields $GF(2^m)$},
    journal={{IEEE} Transactions on Computers},
    volume= 41,
    year= 1992,
    pages={962-971},
    month= aug,
    number= 8,
    keywords={finite fields}
}

@article{BinDemKahMar2002,
    author={D.~Bindel and J.~Demmel and W.~Kahan and O.~Marques},
    title={On computing Givens rotations reliably and efficiently},
    journal={{ACM} Transactions on Mathematical Software},
    volume={28},
    year={2002},
    pages={206--238},
    number={2},
    key={BinDemKahMar2002}
}

@inproceedings{BJJM93,
    author={M.~O. Benouamer and P. Jaillon and D. Michelucci and J.~M. Moreau},
    title={A lazy exact arithmetic},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={242-249},
    location={Windsor, Canada},
    keywords={compilation,exact arithmetic,Lazy arithmetic}
}

@article{BJM83,
    author={M.~A. Bayoumi and G.~A. Jullien and W.~C. Miller},
    title={An area-time efficient NMOS adder},
    journal={Integration},
    volume= 1,
    year= 1983,
    pages={317-334},
    keywords={addition},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{BJMW93,
    author={S.~S. Bizzan and G.~A. Jullien and N.~M. Wigley and W.~C. Miller},
    title={Integer mapping architectures for the polynomial ring engine},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={44-51},
    location={Windsor, Canada},
    keywords={residue number systems}
}

@INBOOK{Brent76,
        AUTHOR             = {Brent, R.P.},
        CHAPTER            = {{The Complexity of Multiple-Precision Arithmetic}},
        PUBLISHER          = {ed. by R.S. Anderssen and R.P. Brent, U. of Queensland Press},
        TITLE              = {The Complexity of Computation Problem Solving},
        NOTE               = {Available at \url{http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pd/rpb032.pdf}.},
        YEAR               = {1976}
}

@ARTICLE{Brent76b,
        AUTHOR             = {Brent, R. P.},
        JOURNAL            = {J.ACM},
        NUMBER             = {2},
        PAGES              = {242--251},
        TITLE              = {{Fast Multiple-Precision Evaluation for Elementary Functions}},
        VOLUME             = {23},
        YEAR               = {1976},
        NOTE               = {Available at \url{http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pd/rpb034a.pdf}.}
}

@article{BK81,
    author={R.~P. Brent and H.~T. Kung},
    title={The area-time complexity of binary multiplication},
    journal={Journal of the ACM},
    volume= 28,
    year= 1981,
    month= jul,
    number= 3,
    keywords={multiplication}
}

@article{BK82,
    author={R.~P. Brent and H.~T. Kung},
    title={A regular layout for parallel adders},
    journal={{IEEE} Transactions on Computers},
    volume={C-31},
    year= 1982,
    pages={260-264},
    month= mar,
    number= 3,
    keywords={addition},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{BK83,
    author={D.~K. Banerji and S. Kaushik},
    title={Representation and Processing of Fractions in a Residue System},
    booktitle={Proceedings of the 6th IEEE Symposium on Computer Arithmetic},
    year= 1983,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Aarhus, Denmark},
    keywords={residue number systems}
}

@inproceedings{BK85,
    author={R.~P. Brent and H.~T. Kung},
    title={A systolic algorithm for integer GCD computation},
    booktitle={Proceedings of the 7th IEEE Symposium on Computer Arithmetic},
    year= 1985,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={118-125},
    location={Urbana, IL},
    keywords={GCD}
}

@inproceedings{BK90,
    author={D.~K{\"o}nig and J.~F.~B{\"o}hme},
    title={Optimizing the {CORDIC} Algorithm for Processors with Pipeline Architectures},
    booktitle={Signal Processing {V}: Theories and Applications},
    year= 1990,
    publisher={Elsevier Science, Amsterdam},
    editor={L.~Torres and E.~Masgrau and M.~A.~Lagunas},
    key={BK90}
}

@inproceedings{BKM93,
    author={J.~C. Bajard and S. Kla and J.~M. Muller},
    title={{BKM}: A New Hardware Algorithm for Complex Elementary Functions},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    location={Windsor, Canada},
    keywords={cordic,elementary functions,redundant number systems}
}

@article{BKM94,
    author={J.~C. Bajard and S. Kla and J.~M. Muller},
    title={{BKM}: A New Hardware Algorithm for Complex Elementary Functions},
    journal={{IEEE} Transactions on Computers},
    volume= 43,
    year= 1994,
    pages={955-963},
    month= aug,
    number= 8,
    keywords={cordic,elementary functions,shift-and-add algorithms}
}

@techreport{BKM94a,
    author={G.~Bohlender and W.~Kr{\"a}mer and W.~L.~Miranker},
    title={Grading of Basic Arithmetical Operations and Functions},
    institution={IBM Research Division, T.~J. Watson Research Center},
    year= 1994,
    number={RC 19593 (86059)},
    key={BKM94a}
}

@book{BKMR93,
    author={L. Boug{\'e} and C. Kenyon and J.~M. Muller and Y. Robert},
    title={Algorithmique, Exercices corrig{\'e}s},
    publisher={Ellipses, Paris},
    year= 1993,
    keywords={Miscellaneous}
}

@inproceedings{BKMW91,
    author={G. Bohlender and W. Walter and P. Kornerup and D.~W. Matula},
    title={Semantics for exact floating point operations},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={22-26},
    location={Grenoble, France},
    keywords={accuracy control,exact arithmetic,floating-point arithmetic}
}

@article{Bla74,
    author={P.~E. Blankship},
    title={Comments on ``A two's complement parallel array multiplication algorithm''},
    journal={{IEEE} Transactions on Computers},
    volume={C-23},
    year= 1974,
    pages= 1327,
    keywords={multiplication},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 1, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@phdthesis{Bli89,
    author={B.~E. Bliss},
    title={Instrumentation of fortran programs for automatic roundoff error analysis
        and performance evaluation},
    school={University of Illinois at Urbana-Champaign},
    year= 1989,
    month= oct,
    keywords={accuracy control,floating-point arithmetic}
}

@inproceedings{BluPaa99,
    author={Thomas Blum and Christof Paar},
    title={Montgomery Modular Exponentiation on Reconfigurable Hardware},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic (Adelaide,
        Australia)},
    year= 1999,
    month= apr,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={Koren and Kornerup},
    pages={70--77}
}

@inproceedings{BM92a,
    author={J.~C. Bajard and J.~M. Muller},
    title={A New {VLSI} Architecture for Fast On-line Evaluation of Power Series},
    booktitle={International Conference on Signal Processing Application \& Technology,
        Boston-92},
    year= 1992,
    keywords={elementary functions,on-line arithmetic,polynomial approximations}
}

@inproceedings{BM92b,
    author={J.~C. Bajard and J.~M. Muller},
    title={Calcul en-ligne : parall{\'e}lisme {\`a} grain ultra fin pour une arithm{\'e}tique rapide},
    booktitle={Actes des Premi{\`e}res Journ{\'e}es de Math{\'e}matiques Appliqu{\'e}es, 1992 Rabat, Marocco},
    year= 1992,
    keywords={elementary functions,on-line arithmetic,polynomial approximations}
}

@inproceedings{BM93,
    author={W.~S. Briggs and D.~W. Matula},
    title={A 17 x 69 bit multiply and add unit with redundant binary feedback and single
        cycle latency},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={163-171},
    location={Windsor, Canada},
    keywords={multiplication,redundant number systems}
}

@proceedings{BMMM95,
    editor={J.~C. Bajard and D. Michelucci and J.~M. Moreau and J.~M. Muller},
    title={Real Numbers and Computers --- Les Nombres r{\'e}els et l'Ordinateur},
    year= 1995,
    location={Saint-Etienne, France},
    keywords={accuracy control,algebraic functions,bit-serial arithmetic,continued fractions,elementary
        functions,exact arithmetic,exponential,interval arithmetic,number systems,on-line
        arithmetic,p-adic arithmetic,perturbation methods,rational approximations,rational
        arithmetic,trigonometric functions}
}

@proceedings{BMMMa95,
    editor={J.~C. Bajard and D. Michelucci and J.~M. Moreau and J.~M. Muller},
    title={Special issue "Real Numbers and Computers" of Journal for Universal Computer
        Science (JUCS)},
    publisher={Springer Verlag},
    year= 1995,
    month= jul,
    keywords={accuracy control,algebraic functions,bit-serial arithmetic,continued fractions,elementary
        functions,exact arithmetic,exponential,interval arithmetic,number systems,on-line
        arithmetic,p-adic arithmetic,perturbation methods,rational approximations,rational
        arithmetic,trigonometric functions}
}

@inproceedings{BO85,
    author={V.~G. Oklobdzija and E.~R. Barnes},
    title={Some optimal shemes for ALU implementation in VLSI technology},
    booktitle={Proceedings of the 7th IEEE Symposium on Computer Arithmetic},
    year= 1985,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={2-8},
    location={Urbana, IL},
    keywords={addition},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{Boh90,
    author={G.~Bohlender},
    title={What do we need beyond {IEEE} arithmetic},
    booktitle={Computer Arithmetic and Self-Validating Numerical Methods},
    year= 1990,
    editor={Academic Press, New York},
    key={Boh90}
}

@inproceedings{Bol06,
  author    = {S. Boldo},
  title     = {Pitfalls of a Full Floating-Point Proof: example on the
               Formal Proof of the {V}eltkamp/{D}ekker Algorithms.},
  booktitle = {Proceedings of the 3rd International Joint Conference on
               Automated Reasoning},
  location  = {Seattle, WA},
  year      = {2006},
  pages     = {52--66},
  editor    = {U.~Furbach and N.~Shankar},
  series    = {Lecture Notes in Computer Science},
  volume    = {4130}
}

@techreport{Boldo2001,
author = {S.~Boldo and M.~Daumas and C.~Moreau-Finot and L.~Th{\'e}ry},
title = {Computer Validated Proofs of a Toolset for Adaptable Arithmetic},
institution = {{\'E}cole Normale Sup{\'e}rieure de Lyon},
year = {2001},
note = {Available at \url{http://arxiv.org/pdf/cs.MS/0107025}}
}


@inproceedings{BolDau03a,
    author={S. Boldo and M. Daumas},
    title={Representable correcting terms for possibly underflowing floating point
        operations},
    booktitle={Proceedings of the 16th Symposium on Computer Arithmetic},
    year= 2003,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={Bajard, J.-C. and Schulte, M.},
    pages={79-86},
    location={Santiago de Compostela, Spain},
    url={http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau03a.pdf}
}

@inproceedings{BolDauThe03,
    author={S. Boldo and M. Daumas and L. Th{\'e}ry},
    title={Formal Proofs and Computations in Finite Precision Arithmetic},
    booktitle={Proceedings of the 11th Symposium on the Integration of Symbolic Computation
        and Mechanized Reasoning},
    year={2003},
    editor={T.~Hardin and R.~Rioboo},
    location={Roma, Italy},
    url={http://ftp.lip6.fr/lip6/reports/2003/lip6.2003.010.pdf}
}

@inproceedings{BoldoFilliatre2007,
    author={S.~Boldo and J.-C.~Filliatre},
    title={Formal Verification of Floating-Point Programs},
    booktitle={Proceedings of the 18th IEEE Symposium on Computer Arithmetic},
    year={2007},
    publisher={IEEE Computer Society Press},
    editor={P.~Kornerup and J;-M.~Muller}
}

@inproceedings{BoldoMuller2005,
    author={S.~Boldo and J.-M.~Muller},
    title={Some functions computable with a fused-MAC},
    booktitle={Proceedings of the 17th {IEEE} Symposium on Computer Arithmetic (ARITH-17)},
    year={2005},
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    key={BoldoMuller2005},
    location={Cape Cod, MA}
}


@inproceedings{BrugueraLang2005:arith,
    author={J.~D. Bruguera and T. Lang},
    title={Floating-point Fused Multiply-Add: Reduced Latency for Floating-Point Addition},
    booktitle={Proceedings of the 17th {IEEE} Symposium on Computer Arithmetic (ARITH-17)},
    year={2005},
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Cape Cod, MA}
}

@article{BolMel08,
  author    = {S. Boldo and G. Melquiond},
  title     = {Emulation of {FMA} and correctly rounded sums: proved algorithms using rounding to odd},
  journal   = {{IEEE} Transactions on Computers},
   year      = {2008},
  volume     = {57},
  number    = {4},
pages = {462--471},
  month       = apr
}

@techreport{BolMul2004,
    author={S.~Boldo and J.-M.~Muller},
    title={Some Functions Computable with a Fused Mac},
    institution={INRIA},
    year={2004},
    month= oct,
    type={Research Report},
    number={5320},
    key={BolMul2004},
    note={available at \url{www.inria.fr}, submitted to the 17th {IEEE} Symposium
        on Computer Arithmetic}
}




@inproceedings{BolMun06,
  author    = {S. Boldo and C. Mu{\~n}oz},
  title     = {Provably faithful evaluation of polynomials},
  booktitle = {Proceedings of the 2006 ACM Symposium on Applied Computing},
  year      = {2006},
  pages     = {1328--1332},
  location  = {Dijon, France},
  publisher = {ACM Press},
  address   = {New York, NY},
}

@article{Boo51,
    author={A.~D. Booth},
    title={A signed binary multiplication technique},
    journal={Quarterly Journal of Mechanics and Applied Mathematics},
    volume= 4,
    year= 1951,
    pages={236-240},
    number= 2,
    keywords={multiplication},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 1, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@article{BorBor84,
    author={J.~M. Borwein and P.~B. Borwein},
    title={The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions},
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    pages={351--366},
    month= jul ,
    number= 3
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@article{BorBor88,
    author={J.~M. Borwein and P.~B. Borwein},
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    key={BorBor88}
}

@book{BorErd95,
    author={P. Borwein and T. Erd{\'e}lyi},
    title={Polynomials and Polynomial Inequalities},
    publisher={Springer-Verlag, New York, NY},
    year={1995},
    series={Graduate Texts in Mathematics, Vol. 161}
}

@book{BorweinBailey2004,
    author={J.~Borwein and D.~H.~Bailey},
    title={Mathematics by Experiment: Plausible Reasoning in the $21$st Century},
    publisher={A.~K. Peters},
    year={2004},
    address={Natick, MA},
    key={BorweinBailey2004},
    isbn={1-56881-211-6}
}

@article{Boute92,
    author={R.~T. Boute},
    title={The Euclidean definition of the functions div and mod},
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}

@inproceedings{BPPT87,
    author={B.~K. Bose and D.~A. Patterson and L. Pei and G.~S. Taylor},
    title={Fast multiply and divide for a VLSI floating-point unit},
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    year= 1987,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Como, Italy},
    keywords={division,floating-point arithmetic,multiplication},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@article{BPV83,
    author={G.~M. Baudet and F. Preparata and J.~E. Vuillemin},
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    year= 1983,
    pages={684-688},
    keywords={convolution}
}

@article{BR69,
    author={W.~S.~Brown and P.~L.~Richman},
    title={The Choice of Base},
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    pages={560--561},
    month= oct,
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    key={BR69}
}

@book{Bra63,
    author={E.~L. Braun},
    title={Digital computer design},
    publisher={Academic Press, New York, NY},
    year= 1963,
    keywords={multiplication}
}

@article{Bra88,
    author={K.~Braune},
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    year= 1988,
    pages={159--184},
    key={Bra88}
}

@article{Bre70,
    author={R.~P. Brent},
    title={On the addition of binary numbers},
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    year= 1970,
    month= aug,
    number= 8,
    keywords={addition}
}

@article{Bre73,
    author={R.~P. Brent},
    title={On the precision attainable with various floating point number systems},
    journal={{IEEE} Transactions on Computers},
    volume={C-22},
    year= 1973,
    pages={601-607},
    month= jun,
    number= 6,
    keywords={accuracy control,floating-point arithmetic}
}

@inproceedings{Bre75,
    author={R.~P. Brent},
    title={Multiple precision zero-finding methods and the complexity of elementary
        function evaluation},
    booktitle={Analytic Computational Complexity},
    year= 1975,
    publisher={Academic Press, New York, NY},
    editor={J.~F. Traub},
    keywords={elementary functions}
}

@article{Bre76,
    author={R.~P. Brent},
    title={Fast multiple precision evaluation of elementary functions},
    journal={Journal of the ACM},
    volume= 23,
    year= 1976,
    pages={242-251},
    keywords={elementary functions}
}

@article{Bre78,
    author={R.~P. Brent},
    title={A {FORTRAN} Multiple-Precision Arithmetic Package},
    journal = AcmToms,
    volume={4},
    year={1978},
    pages={57--70},
    number={1},
    issn={0098-3500},
    doi={http://doi.acm.org/10.1145/355769.355775},
    publisher={ACM Press}
}

@article{Bre78a,
    author={R.~P. Brent},
    title={ALGORITHM 524, MP, A Fortran Multiple-Precision Arithmetic Package},
    journal = AcmToms,
    volume={4},
    year={1978},
    pages={71--81},
    number={1},
    issn={0098-3500},
    publisher={ACM Press}
}

@inproceedings{Brent1980,
    author={R.~P.~Brent},
    title={Unrestricted Algorithms for Elementary and Special Functions},
    booktitle={Information Processing 80},
    year={1980},
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    editor={S.~H.~Lavington},
    pages={613--619},
    key={Brent1980}
}

@inproceedings{Bri82,
    author={E.~F. Brickel},
    title={A Fast Modular Multiplication Algorithm with Applications to Two Key Cryptography},
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    year= 1982,
    publisher={Plenum Press},
    keywords={cryptography,multiplication,residue number systems,RSA}
}

@inproceedings{Bri89,
    author={E.~F. Brickel},
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    year= 1989,
    publisher={Springer-Verlag},
    editor={G.~Brassard},
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}

@article{BriDefKorMulRev2005,
    author={N.~Brisebarre and D.~Defour and P.~Kornerup and J.-M.~Muller and N.~Revol},
    title={A New Range Reduction Algorithm},
    journal={{IEEE} Transactions on Computers},
    volume={54},
    year={2005},
    pages={331--339},
    month= mar,
    number={3},
    key={BriDefKorMulRev2005}
}



@inproceedings{BriMul2004,
    author={N.~Brisebarre and J.-M.~Muller},
    title={Functions Approximable by E-Fractions},
    booktitle={Proc. $38$th {IEEE} Conference on Signals, Systems and Computers},
    year={2004},
    month= nov,
    publisher={{IEEE}}
}

@article{BriMulRai2004,
    author={N.~Brisebarre and J.-M.~Muller and S.-K.~Raina},
    title={Accelerating Correctly Rounded Floating-Point Division when the Divisor
        is Known in Advance},
    journal={{IEEE} Transactions on Computers},
    volume={53},
    year={2004},
    pages={1069--1072},
    month= aug,
    number={8},
    key={BriMulRai2004}
}

@inproceedings{BriMulTis2004,
    author={N.~Brisebarre and J.-M.~Muller and A.~Tisserand},
    title={Sparse-Coefficient Polynomial Approximations for Hardware Implementations},
    booktitle={Proc. $38$th {IEEE} Conference on Signals, Systems and Computers},
    year={2004},
    month= nov,
    publisher={{IEEE}}
}

@techreport{BriMulTis2004a,
    author={N.~Brisebarre and J.-M.~Muller and A.~Tisserand},
    title={Computing Machine-Efficient Polynomial Approximations},
    institution={{LIP} Laboratory},
    year={2004},
    type={Draft},
    address={\url{http://perso.ens-lyon.fr/jean-michel.muller/bmt-toms.ps}}
}


@article{BrisebarreMuller2008,
    author={N.~Brisebarre and J.-M.~Muller},
    title={Correctly rounded multiplication by arbitrary precision constants},
    journal={{IEEE} Transactions on Computers},
    year={2008},
    month= feb,
    volume = {57},
    number={2},
    pages = {165--174},
    doi={10.1109/TC.2007.70813}
}

@article{BrisebarreMuller2007,
    author={N. Brisebarre and J.-M. Muller},
    title={Correct Rounding of Algebraic Functions},
    abstract={We explicit the link between the computer arithmetic problem of providing
        correctly rounded algebraic functions and some diophantine approximation
        issues. This allows to get bounds on the accuracy with which intermediate
        calculations must be performed to correctly round these functions.},
    journal={Theoretical Informatics and Applications},
    volume = {41},
    pages = {71--83},
    month = {Jan--March},
    year={2007}
}

@article{BrisebarreMullerTisserand2006,
    author={N. Brisebarre and J.-M. Muller and A. Tisserand},
    title={Computing machine-efficient polynomial approximations},
    abstract={Polynomial approximations are almost always used when implementing functions
        on a computing system. In most cases, the polynomial that best approximates
        (for a given distance and in a given interval) a function has coefficients
        that are not exactly representable with a finite number of bits. And yet,
        the polynomial approximations that are actually implemented do have coefficients
        that are represented with a finite---and sometimes small---number of bits.
        This is due to the finiteness of the floating-point representations (for
        software implementations), and to the need to have small, hence fast and/or
        inexpensive, multipliers (for hardware implementations). We then have to
        consider polynomial approximations for which the degree-i coefficient has
        at most mi fractional bits; in other words, it is a rational number with
        denominator $2^{mi}$. We provide a general and efficient method for finding
        the best polynomial approximation under this constraint. Moreover, our
        method also applies if some other constraints (such as requiring some coefficients
        to be equal to some predefined constants or minimizing relative error instead
        of absolute error) are required.},
    journal = AcmToms,
    volume={32},
    year={2006},
    pages={236--256},
    month= jun,
    number={2},
    doi={http://doi.acm.org/10.1145/1141885.1141890}
}

@inproceedings{BrisebarreChevillard2007,
 author = {N. Brisebarre and S. Chevillard},
 title = {Efficient polynomial {$L^\infty$} approximations},
 booktitle = {ARITH '07: Proceedings of the 18th IEEE Symposium on Computer Arithmetic},
 year = {2007},
 isbn = {0-7695-2854-6},
 pages = {169--176},
 doi = {http://dx.doi.org/10.1109/ARITH.2007.17},
 publisher = {IEEE Computer Society},
 address = {Washington, DC},
 }

 @inproceedings{BrisebarreHanrot2007,
 author = {N. Brisebarre and G. Hanrot},
 title = {Floating-point {$L^2$} -approximations to functions},
 booktitle = {ARITH '07: Proceedings of the 18th IEEE Symposium on Computer Arithmetic},
 year = {2007},
 isbn = {0-7695-2854-6},
 pages = {177--186},
 doi = {http://dx.doi.org/10.1109/ARITH.2007.38},
 publisher = {IEEE Computer Society},
 address = {Washington, DC},
 }

 @inproceedings{HaLeStZi07,
 author = {G. Hanrot and V. Lef\`evre and D. Stehl\'e and P. Zimmermann},
 title = {Worst Cases of a Periodic Function for Large Arguments},
 booktitle = {ARITH '07: Proceedings of the 18th IEEE Symposium on Computer Arithmetic},
 year = {2007},
 pages = {133--140},
 publisher = {IEEE Computer Society},
 address = {Washington, DC},
 }



@article{LLL82,
author =       {Lenstra, A.~K. and Lenstra, Jr., H.~W. and Lov{\'a}sz, L.},
title =        {Factoring polynomials with rational coefficients},
journal =      {Mathematische Annalen},
volume =       261,
year =         1982,
pages =        {515--534}
}



@inproceedings{Elkies2000,
author= {Elkies, N.~D.},
title={Rational points near curves and small nonzero $|x^3-y^2|$ via lattice
reduction},
booktitle={Proceedings of the 4th {A}lgorithmic {N}umber {T}heory
{S}ymposium ({ANTS IV})},
publisher= {Springer-Verlag, Berlin},
editor    = {Wieb Bosma},
series= {Lecture Notes in Computer Science},
year= 2000,
pages= {33--63},
volume =1838}


@unpublished{Gonnet2002,
author = {Gonnet, G.},
title = {A note on finding difficult values to evaluate numerically},
note = {Available
at \url{http://www.inf.ethz.ch/personal/gonnet/FPAccuracy/NastyValues.ps}},
year = 2002}



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    number= 4,
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    year= 1989
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    number= 24,
    keywords={FPGA}
}

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}

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    institution={DEC paris Research Laboratory},
    year= 1991,
    keywords={multiplication}
}

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}

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}

@inproceedings{BZ85,
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}

@article{BZ87,
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    year= 1987,
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    key={BZ87},
    keywords={on-line arithmetic}
}

@article{Cajori1911,
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    key={Can91}
}

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    editor={Quinton and Robert},
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    key={Can92}
}

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@article{Cauchy1840,
    author={A.~Cauchy},
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    title={A 2.5ns, 40mW, 4x4 GaAs multiplier in two's complement mode},
    journal={IEEE journal of solid-state circuits},
    volume={SC-22},
    year= 1987,
    pages={409-414},
    keywords={multiplication}
}

@inproceedings{Del87a,
    author={J.~M.~Delosme},
    title={A Processor for Two-Dimensional Symmetric Eigenvalue and Singular Value
        Arrays},
    booktitle={Twenty-First Asilomar Conference on Circuits, Systems, and Computers},
    year= 1987,
    month= nov,
    pages={217--221},
    key={Del87a}
}

@article{Del92,
    author={J.~M. Delosme},
    title={Bit-Level Systolic Algorithms for Real Symmetric and Hermitian Eigenvalue
        Problems},
    journal={Journal of VLSI Signal Processing},
    volume= 4,
    year= 1992,
    pages={69--88}
}

@article{Des74,
    author={A.~M. Despain},
    title={Fourier transform computers using {CORDIC} iterations},
    journal={{IEEE} Transactions on Computers},
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    year= 1974,
    month= may,
    number= 5,
    keywords={cordic,FFT}
}

@inproceedings{DetDin2004,
    author={Detrey, J. and de Dinechin, F.},
    title={Second Order Function Approximation Using a Single Multiplication on {FPGA}s},
    booktitle={14th Intl Conference on Field-Programmable Logic and Applications},
    year= 2004,
    month= aug,
    publisher={LNCS 3203},
    pages={221-230},
    location={Antwerp, Belgium}
}

@article{DeunBultheel2004,
    author={J. Van Deun and A. Bultheel},
    title={An Interpolation Algorithm for Orthogonal Rational Functions},
    journal={Journal of Computational and Applied Mathematics},
    volume={164--165},
    year={2004},
    pages={749--762},
    key={DeunBultheel2004}
}

@inproceedings{DFMY91,
    author={J. Duprat and M. Fiallos and J.~M. Muller and H.~J. Yeh},
    title={Delays of on-line floating-point operators in borrow-save representation},
    booktitle={IFIP Workshop on algorithms and parallel VLSI architectures},
    year= 1991,
    month= jun,
    location={Bonas, France},
    keywords={floating-point arithmetic,on-line arithmetic},
    edition={North Holland}
}

@inproceedings{DH91,
    author={J.~M. Delosme and S.~F. Hsiao},
    title={The {CORDIC} Householder algorithm},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={256-263},
    location={Grenoble, France},
    keywords={cordic}
}

@article{DH92,
    author={S.~Dao-Trong and K.~Helwig},
    title={A Single-Chip {IBM} System/390 Floating-Point processor in CMOS},
    journal={IBM Journal of Research and Development},
    volume= 36,
    year= 1992,
    pages={733--748},
    month= jul,
    number= 4,
    key={DH92},
    keywords={floating-point}
}

@inproceedings{DH93,
    author={G.~H. Hekstra and E.~F.~A. Deprettere},
    title={Floating-point {CORDIC}},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={130-137},
    location={Windsor, Canada},
    keywords={cordic}
}

@article{DH95,
    author={S.~F. Hsiao and J.~M. Delosme},
    title={Householder {CORDIC} algorithms},
    journal={{IEEE} Transactions on Computers},
    volume= 44,
    year= 1995,
    pages={990--1000},
    month= aug,
    number= 8,
    keywords={cordic},
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic}
}

@inproceedings{DHK91,
    author={J. Duprat and Y. Herreros and S. Kla},
    title={New {r}edundant {R}epresentations of {C}omplex {N}umbers and {V}ectors},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={2-9},
    location={Grenoble, France},
    keywords={number systems,redundant number systems}
}

@article{DHLMRZ2004,
    author={D.~Defour and G.~Hanrot and V.~Lef{\`e}vre and J.-M.~Muller and N.~Revol and
        P.~Zimmermann},
    title={Proposal for a Standardization of Mathematical Function Implementation in
        Floating-Point Arithmetic},
    journal={Numerical Algorithms},
    volume={37},
    year={2004},
    pages={367--375},
    number={1--4},
    key={DHLMRZ2004}
}


@article{HanZim2004,
  author    = {G. Hanrot and
               P. Zimmermann},
  title     = {A long note on {M}ulders' short product},
  journal   = {J. Symb. Comput.},
  volume    = {37},
  number    = {3},
  year      = {2004},
  pages     = {391-401}
}

@article{Mulders2000,
  author    = {T. Mulders},
  title     = {On Short Multiplications and Divisions},
  journal   = {Appl. Algebra Eng. Commun. Comput.},
  volume    = {11},
  number    = {1},
  year      = {2000},
  pages     = {69-88}
}

@inproceedings{DHM89,
    author={J. Duprat and Y. Herreros and J.~M. Muller},
    title={Some Results about on-line computation of functions.},
    booktitle={Proceedings of the 9th IEEE Symposium on Computer Arithmetic},
    year= 1989,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={M.~D. Ercegovac and E~E. Swartzlander},
    pages={112-118},
    location={Santa Monica, CA},
    keywords={addition,division,multiplication,on-line arithmetic,redundant number systems}
}

@article{Dicker00,
    author={S.R.~Dicker et~al},
    title={Cbm observations with the Jodrell Bank - iac interferometer at 33 Ghz},
    journal={Mon. Not. R. Astron. Soc.},
    volume={00},
    year={2000},
    pages={1--12},
    key={Dicker00}
}

@article{DidierRico2004,
    author={L.S.~Didier and F.~Rico},
    title={High Radix BKM Algorithm},
    journal={Numerical Algorithms},
    volume={37},
    year={2004},
    pages={113--125},
    number={1--4},
    key={DidierRico2004}
}

@article{DimJulMil2000,
    author={V.S. Dimitrov and G.A. Jullien and W.C. Miller},
    title={Complexity and Fast Algorithms for Multiexponentiations},
    journal={{IEEE} Transactions on Computers},
    volume= 49,
    year= 2000,
    pages={141--147},
    month= feb,
    number= 2
}

@article{DimJulMil99,
    author={V.S. Dimitrov and G. Jullien and W.C. Miller},
    title={Theory and Applications of the Double-Base Number System},
    journal={{IEEE} Transactions on Computers},
    volume= 48,
    year= 1999,
    pages={1098--1106},
    month= oct,
    number= 10
}

@techreport{DinDefLau2004Inria,
    author={de~Dinechin, F. and D. Defour and C. Q. Lauter},
    title={Fast correct rounding of elementary functions in double precision using
        double-extended arithmetic},
    institution={INRIA},
    year= 2004,
    month= mar,
    type={Research report},
    number={5137},
    note={Submitted to TOMS.},
    anote={Available at \url{www.inria.fr/rrrt/rr-5137.html}}
}

@article{DinechinLauterMuller2007,
    author={F. de Dinechin and C. Q. Lauter and J.-M. Muller},
    title={Fast and Correctly Rounded Logarithms in Double-Precision},
    abstract={This article is a case study in the implementation of a portable, proven
        and efficient correctly rounded elementary function in double-precision.
        We describe the methodology used to achieve these goals in the CRLIBM library.
        There are two novel aspects to this approach. The first is the proof framework,
        and in general the techniques used to balance performance and provability.
        The second is the introduction of processor-specific optimization to get
        performance equivalent to the best current mathematical libraries, while
        trying to minimize the proof work. The implementation of the natural logarithm
        is detailed to illustrate these questions. },
    journal={Theoretical Informatics and Applications},
    volume = {41},
    pages = {85--102},
    year={2007}
}

@article{DinechinTisserand2005,
    author={F.~de~Dinechin and A.~Tisserand},
    title={Multipartite Table Methods},
    journal={{IEEE} Transactions on Computers},
    volume={54},
    year={2005},
    pages={319--330},
    month= mar,
    number={3},
    key={DinechinTisserand2005}
}

@InProceedings{YuEtAl2006,
  author = 	 {X. Y. Yu  and Y.-H. Chan and  Curran, B. and   Schwarz, E.  and Kelly, M. and   Fleischer, B.},
  title = 	 {A 5{GH}z+ 128-bit Binary Floating-Point Adder for the {POWER6} Processor},
  booktitle = {European Solid-State Circuits Conference},
  pages = 	 {166-169},
  year = 	 2006}

@inproceedings{DinechinPascaCret2008:FPT,
  author    =  {de Dinechin, F. and B. Pasca and  O. Cre\c{t} and  R.  Tudoran},
  title     =   {An {FPGA}-specific Approach
  to Floating-Point Accumulation and Sum-of-Products},
  booktitle = {Field-Programmable Technologies},
  PUBLISHER =	 {IEEE},
  year      =    {2008}
  }

@techreport{DinGas2004,
    author={F.~de~Dinechin and N.~Gast},
    title={Towards the Post-Ultimate libm},
    institution={LIP},
    year={2004},
    type={Research Report},
    address={{\'E}cole normale sup{\'e}rieure de Lyon},
    number={2004-47},
    key={DinGas2004},
    note={Available at \url{http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-47.pdf}}
}

@inproceedings{DinTis2001,
    author={F.~de~Dinechin and A.~Tisserand},
    title={Some Improvements on Multipartite Table Methods},
    crossref = {Arith15},
    pages={128--135},
    key={DinTis2001},
}

@InProceedings{DinMcInSchm2006:ICAP,
  author = 	 {de Dinechin, F. and McIntosh, E. and Schmidt, F.},
  title = 	 {Massive Tracking on Heterogeneous Platforms},
  booktitle =	 {9th International Computational
Accelerator Physics Conference (ICAP)},
  month =	 oct,
  year =	 2006
}

@article{Dio85,
    author={P.~W. Diodato},
    title={The design of an IEEE standard math accelerator unit},
    journal={IEEE journal of solid-state circuits},
    volume={SC-20},
    year= 1985,
    pages={993-997},
    keywords={floating-point arithmetic}
}

@article{DIP93,
    author={G. Dimauro and S. Impedovo and G. Pirlo},
    title={A new technique for fast number comparison in the residue number system},
    journal={{IEEE} Transactions on Computers},
    volume= 42,
    year= 1993,
    pages={608-612},
    month= may,
    number= 5,
    keywords={residue number systems}
}

@inproceedings{DKMR2001,
    author={D. Defour and P. Kornerup and J.-M. Muller and N. Revol},
    title={A New Range Reduction Algorithm},
    booktitle={Thirty-Fifth Asilomar Conference on Signals, Systems, and Computers},
    year={2001},
    volume = 2,
    pages = {1656--1660},
    month= nov,
    key={DKMR2001},
    location={Pacific Grove, CA}
}

@inproceedings{DL91,
    author={E.~F. Deprettere and A.~J. de Lange},
    title={Design and implementation of a floating-point quasi-systolic general purpose
        {CORDIC} rotator for high-rate parallel data and signal processing},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={272-281},
    location={Grenoble, France},
    keywords={cordic}
}

@article{DL91a,
    author={G.~I. Davida and B. Litow},
    title={Fast Parallel Arithmetic Via Modular Representation},
    journal={SIAM Journal on Computing},
    volume= 20,
    year= 1991,
    pages={756-765},
    month= aug,
    number= 4,
    keywords={division,residue number systems}
}

@inproceedings{DL93,
    author={J.~W. Demmel and X. Li},
    title={Faster numerical algorithms via exception handling},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={234-241},
    location={Windsor, Canada},
    keywords={compilation,Lazy arithmetic}
}

@article{DL94,
    author={J.~W. Demmel and X. Li},
    title={Faster Numerical Algorithms via Exception Handling},
    journal={{IEEE} Transactions on Computers},
    volume= 43,
    year= 1994,
    pages={983-992},
    month= aug,
    number= 8,
    keywords={floating-point arithmetic}
}

@article{DM88,
    author={J. Duprat and J.-M. Muller},
    title={Hardwired Polynomial Evaluation},
    journal={Journal of Parallel and Distributed Computing},
    volume={Special Issue on Parallelism in Computer Arithmetic},
    year= 1988,
    number= 5,
    keywords={polynomial approximations}
}

@inproceedings{DM90,
    author={J. Duprat and J.-M. Muller},
    title={Fast {VLSI} Implementation of {CORDIC} using redundancy},
    booktitle={IFIP Workshop on Algorithms and Parallel {VLSI} Architectures},
    year= 1990,
    month= jun,
    location={Pont-a-Mousson, France},
    keywords={{CORDIC},redundant number systems}
}

@article{DM91,
    author={J. Duprat and J.-M. Muller},
    title={Ecrire les nombres autrement pour calculer plus vite.},
    journal={Technique et Science Informatique},
    volume= 10,
    year= 1991,
    number= 3,
    keywords={redundant number systems}
}

@article{DM93,
    author={J. Duprat and J.-M. Muller},
    title={The {CORDIC} Algorithm: {N}ew results for fast {VLSI} implementation.},
    journal={{IEEE} Transactions on Computers},
    volume= 42,
    year= 1993,
    pages={168-178},
    month= feb,
    number= 2,
    keywords={cordic,on-line arithmetic,redundant number systems}
}

@inproceedings{DM93a,
    author={M. Daumas and D.~W. Matula},
    title={Design of a fast validated dot product operation},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={62-69},
    location={Windsor, Canada},
    keywords={dot product}
}

@inproceedings{DM93b,
    author={M. Daumas and D.~W. Matula},
    title={Rounding of floating-point intervals},
    booktitle={Proceedings of SCAN-93},
    year= 1993,
    month= jun,
    key={DM93b},
    location={Wien, Austria}
}

@article{DM94,
    author={D. Das~Sarma and D.~W. Matula},
    title={Measuring the Accuracy of {ROM} Reciprocal Tables},
    journal={{IEEE} Transactions on Computers},
    volume= 43,
    year= 1994,
    pages={932-940},
    month= aug,
    number= 8,
    keywords={division}
}

@article{DM96,
    author={H. Dawid and H. Meyr},
    title={The Differential {CORDIC} Algorithm: Constant Scale Factor Redundant Implementation
        without Correcting Iterations},
    journal={{IEEE} Transactions on Computers},
    volume= 45,
    year= 1996,
    pages={307--318},
    month= mar,
    number= 3,
    key={DM96},
    keywords={CORDIC}
}

@book{DM97,
    author={J.C.~Bajard and O.~Beaumont and J.M.~Chesneaux and M.~Daumas and J.~Erhel
        and D.~Michelucci and J.-M.~Muller and B.~Philippe and N.~Revol and J.L.~Roch
        and J.~Vignes},
    title={Qualit{\'e} des calculs sur Ordinateur},
    publisher={Masson, Paris},
    year= 1997,
    key={DM97},
    note={Coordinated by M.~Daumas and J.-M.~Muller}
}

@article{DMM94,
    author={M.~Daumas and C.~Mazenc and J.-M.~Muller},
    title={Towards a User Transparent Interval Arithmetic},
    journal={Interval Computations},
    volume= 4,
    year= 1994,
    pages={46--63},
    key={DMM94}
}

@inproceedings{DMMM94,
    author={M. Daumas and C. Mazenc and X. Merrheim and J.-M. Muller},
    title={Fast and Accurate Range Reduction for Computation of the Elementary Functions},
    booktitle={Proceedings of the 14th IMACS World Congress on Computational and Applied
        Mathematics},
    year= 1994,
    pages={1196-1198},
    organization={IMACS, Piscataway, NJ},
    location={Atlanta, GA},
    keywords={elementary functions}
}

@article{DMMM95,
    author={M. Daumas and C. Mazenc and X. Merrheim and J.-M. Muller},
    title={Modular Range Reduction: A New Algorithm for Fast and Accurate Computation
        of the Elementary Functions},
    journal={Journal of Universal Computer Science},
    volume= 1,
    year= 1995,
    pages={162-175},
    month= mar,
    number= 3,
    keywords={accuracy control,elementary functions,floating-point arithmetic}
}

@inproceedings{DMT96,
    author={M.~Daumas and J.-M.~Muller and A.~Tisserand},
    title={Theoretical support for standardized elementary functions},
    booktitle={Proceedings of CESA'96 (IMACS Multiconference Computational Engineering
        in Systems Applications)},
    year= 1996,
    month= jul,
    key={DMT96},
    location={Lille, France}
}

@inproceedings{DMT97,
    author={M.~Daumas and J.-M.~Muller and A.~Tisserand},
    title={Very High Radix On-line Arithmetic for Accurate Computations},
    booktitle={15-th IMACS World Congress on Scientific Computation, Modelling and Applied
        Mathematics},
    year= 1997,
    month= aug,
    key={DMT97},
    location={Berlin, Germany}
}

@inproceedings{DMV94,
    author={M. Daumas and J.-M. Muller and J. Vuillemin},
    title={Implementing on-line arithmetic on {PAM}},
    booktitle={4th International Workshop on Field-Programmable Logic and Applications},
    year= 1994,
    month= sep,
    location={Prague}
}

@article{Dor88,
    author={R.~W. Doran},
    title={Variants of an improved carry-lookahead adder},
    journal={{IEEE} Transactions on Computers},
    volume={C-37},
    year= 1988,
    pages={1110-1113},
    keywords={addition}
}

@inproceedings{DPS93,
    author={L. Dadda and V. Piuri and R. Stefanelli},
    title={Multi-parallel convolvers},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={70-77},
    location={Windsor, Canada},
    keywords={convolution}
}

@article{DS88,
    author={P.~B. Denyer and S.~G. Smith},
    title={Advanced Serial-Data Computation},
    journal={Journal of Parallel and distributed Computing},
    volume={Special Issue on Parallelism in Computer Arithmetic},
    year= 1988,
    number= 5
}

@inproceedings{DT85,
    author={F.~J. Taylor and W. Dirr},
    title={A new residue to decimal converter},
    booktitle={Proceedings of the IEEE},
    year= 1985,
    pages={378-380},
    volume= 73 ,
    keywords={residue number systems}
}

@article{Dun76,
    author={C.~B.~Dunham},
    title={Rational Approximation with a Vanishing Weight Function and with a Fixed
        Value at Zero},
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    volume= 30,
    year= 1976,
    pages={45--47},
    month= jan,
    number= 133,
    key={Dun76}
}

@article{Dun82,
    author={C.~B.~Dunham},
    title={Choice of Basis for {Chebyshev} Approximation},
    journal = AcmToms,
    volume= 8,
    year= 1982,
    pages={21--25},
    number= 1,
    key={Dun82}
}

@article{Dun87,
    author={C.~B.~Dunham},
    title={Provably monotone approximations, {I}},
    journal={SIGNUM Newsletter},
    volume= 22,
    year= 1987,
    pages={6--11},
    month= apr,
    key={Dun87}
}

@article{Dun87a,
    author={C.~B.~Dunham},
    title={Provably monotone approximations, {II}},
    journal={SIGNUM Newsletter},
    volume= 22,
    year= 1987,
    pages={30--31},
    month= jul,
    key={Dun87a}
}

@article{Dun90,
    author={C.~B.~Dunham},
    title={Feasibility of ``Perfect'' Function Evaluation},
    journal={SIGNUM Newsletter},
    volume= 25,
    year= 1990,
    pages={25--26},
    month= oct,
    number= 4,
    key={Dun90}
}

@article{Dun90a,
    author={C.~B.~Dunham},
    title={Fitting approximations to the {K}uki-{C}ody-{W}aite form},
    journal={International Journal of Computer Mathematics},
    volume= 31,
    year= 1990,
    pages={263--265},
    key={Dun90a}
}

@techreport{Dun94,
    author={C.~B.~Dunham},
    title={Provably Monotone Approximations, {IV}},
    institution={Dept. of Computer Science, The University of Western Ontario, London, Canada},
    year= 1994,
    number= 422,
    key={Dun94}
}

@article{Dunham03,
    author={Charles B. Dunham},
    title={Approximation with Taylor Matching at the Origin.},
    journal={Int. J. Comput. Math.},
    volume={80},
    year={2003},
    pages={1019-1024},
    number={8},
    ee={http://taylorandfrancis.metapress.com/openurl.asp?genre=article{\&}issn=0020-7160{\&}volume=80{\&}issue=8{\&}spage=1019},
    bibsource={DBLP, http://dblp.uni-trier.de}
}

@article{DVV90,
    author={T. Denayer and A. Vandemeulebroecke and E. Vanzieleghem},
    title={A New Carry-Free Division Algorithm and its Application to a Single-Chip
        1024-b RSA Processor},
    journal={IEEE Journal of Solid-State Circuits},
    volume= 25,
    year= 1990,
    number= 3,
    keywords={cryptography,division,RSA}
}

@article{Edelman1997,
 author = {A. Edelman},
 title = {The Mathematics of the {P}entium Division Bug},
 journal = {SIAM Rev.},
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 year = {1997},
 issn = {0036-1445},
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 publisher = {Society for Industrial and Applied Mathematics},
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 }

@inproceedings{EG83,
    author={M.~D. Ercegovac and A.~L. Grnarov},
    title={On-Line Multiplicative Normalization},
    booktitle={Proceedings of the 6th IEEE Symposium on Computer Arithmetic},
    year= 1983,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={151-155},
    location={Aarhus, Denmark},
    keywords={on-line arithmetic}
}

@inproceedings{EKR93,
    author={D. Eisig and J. Rotstain and I. Koren},
    title={The design of a 64-bit integer multiplier/divider unit},
    booktitle={Proceedings of the 11th Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={171-178},
    location={Windsor, Canada},
    keywords={division,multiplication}
}

@article{El83,
    author={S.~W. Ellacott},
    title={On the {F}aber Transform and Efficient Numerical Rational Approximation},
    journal={SIAM Journal of Numerical Analysis},
    volume= 20,
    year= 1983,
    pages={989--1000},
    month= oct,
    number= 5,
    key={El83}
}

@inproceedings{EL85,
    author={M.~D. Ercegovac and T. Lang},
    title={A division algorithm with prediction of quotient digits},
    booktitle={Proceedings of the 7th IEEE Symposium on Computer Arithmetic},
    year= 1985,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Urbana, IL},
    keywords={division}
}

@article{EL87,
    author={M.~D. Ercegovac and T. Lang},
    title={On-the-fly conversion of redundant into conventional representations},
    journal={{IEEE} Transactions on Computers},
    volume={C-36},
    year= 1987,
    month= jul,
    number= 7,
    keywords={division,multiplication,on-line arithmetic,redundant number systems},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{EL87a,
    author={M.~D. Ercegovac and T. Lang},
    title={On-line scheme for computing rotation factors},
    booktitle={Proceedings of the 8th IEEE Symposium on Computer Arithmetic},
    year= 1987,
    month= may ,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={196-203},
    location={Como, Italy},
    keywords={cordic,on-line arithmetic}
}

@inproceedings{EL87b,
    author={M.~D. Ercegovac and T. Lang},
    title={Radix-4 multiplication without carry-propagate addition},
    booktitle={IEEE International Conference on Computer Design},
    year= 1987,
    month= oct,
    pages={654-658},
    location={Rye Brook, NY},
    keywords={multiplication}
}

@inproceedings{EL87c,
    author={M.~D. Ercegovac and T. Lang},
    title={Fast cosine/sine implementation using on-line {CORDIC}},
    booktitle={Twenty-First Asilomar Conference on Signals, Systems, and Computers},
    year= 1987,
    key={EL87c}
}

@article{EL88,
    author={M.~D. Ercegovac and T. Lang},
    title={On-Line Scheme for Computing Rotation Factors},
    journal={Journal of Parallel and Distributed Computing},
    volume={Special Issue on Parallelism in Computer Arithmetic},
    year= 1988,
    number= 5,
    keywords={on-line arithmetic},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{EL88a,
    author={M.~D. Ercegovac and T. lang},
    title={On-line arithmetic: a design methodology and applications in digital signal
        processing},
    booktitle={{VLSI} Signal Processing III},
    year= 1988,
    pages={252-263},
    keywords={on-line arithmetic},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{EL89,
    author={M.~D. Ercegovac and T. Lang},
    title={Radix-4 square root without initial PLA},
    booktitle={Proceedings of the 9th IEEE Symposium on Computer Arithmetic},
    year= 1989,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={162-168},
    location={Santa Monica, CA},
    keywords={square root}
}

@article{EL90,
    author={M.~D. Ercegovac and T. Lang},
    title={Fast multiplication without carry-propagate addition},
    journal={{IEEE} Transactions on Computers},
    volume= 39,
    year= 1990,
    pages={1385-1390},
    month= nov,
    number= 11,
    keywords={multiplication}
}

@article{EL90a,
    author={M.~D. Ercegovac and T. Lang},
    title={Redundant and On-line {CORDIC}: Application to Matrix Triangularization
        and {SVD}},
    journal={{IEEE} Transactions on Computers},
    volume= 39,
    year= 1990,
    pages={725-740},
    month= jun,
    number= 6,
    keywords={cordic}
}

@article{EL92,
    author={M.~D. Ercegovac and T. Lang},
    title={On-the-fly rounding},
    journal={{IEEE} Transactions on Computers},
    volume= 41,
    year= 1992,
    pages={1497-1503},
    month= dec,
    number= 12,
    keywords={on-line arithmetic,rounding}
}

@inproceedings{EL92a,
    author={M.~E. Louie and M.~D. Ercegovac},
    title={Mapping Division Algorithms to Field Programmable Gate Arrays},
    booktitle={Twenty-Sixth Asilomar Conference on Signals, Systems, and Computers},
    year= 1992,
    month = oct,
    pages = {371-375},
    volume = 1,
    keywords={division,FPGA}
}

@inproceedings{EL93,
    author={M.~E. Louie and M.~D. Ercegovac},
    title={On digit-recurrence division implementation for field programmable gate
        arrays},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={202-209},
    location={Windsor, Canada},
    keywords={division,FPGA}
}

@inproceedings{EL93a,
    author={M.~E. Louie and M.~D. Ercegovac},
    title={A Digit-Recurrence Square Root Implementation for Field Programmable Gate
        Arrays},
    booktitle={IEEE Workshop on FPGAs for Custom Computing Machines},
    year= 1993,
    month= apr,
    keywords={bit-serial arithmetic,FPGA,on-line arithmetic,square root}
}

@book{EL94,
    author={M.~D.~Ercegovac and T.~Lang},
    title={Division and Square Root: Digit-Recurrence Algorithms and Implementations},
    publisher={Kluwer Academic Publishers, Boston, MA},
    year= 1994,
    keywords={division, square root},
    key={EL94}
}

@inproceedings{ELM93,
    author={M.~D. Ercegovac and T. Lang and P. Montuschi},
    title={Very high radix division with selection by rounding and prescaling},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={112-119},
    location={Windsor, Canada},
    keywords={division}
}

@article{ELM94,
    author={M.~D. Ercegovac and T. Lang and P.~Montuschi},
    title={Very-High Radix Division with Prescaling and Selection by Rounding},
    journal={{IEEE} Transactions on Computers},
    volume= 43,
    year= 1994,
    pages={909-918},
    month= aug,
    number= 8,
    keywords={division}
}

@techreport{ELMT97,
    author={M. D.~Ercegovac and T.~Lang and J.-M.~Muller and A.~Tisserand},
    title={Reciprocation, Square root, Inverse Square Root, and some Elementary Functions
        using Small Multipliers},
    institution={LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon},
    year= 1997,
    month= nov,
    number={RR97-47},
    key={ELMT97},
    note={available at ftp://ftp.lip.ens-lyon.fr/pub/Rapports/RR/RR97/RR97-47.ps.Z}
}

@techreport{EM97,
    author={M. D. Ercegovac and J.-M. Muller},
    title={Fast Evaluation of Functions at Regularly-Spaced Points},
    institution={LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon},
    year= 1997,
    month= nov,
    number={RR97-46},
    key={EM97},
    note={available at ftp://ftp.lip.ens-lyon.fr/pub/Rapports/RR/RR97/RR97-46.ps.Z}
}

@inproceedings{EMT95,
    author={M.~D.~Ercegovac and J.~M.~Muller and A.~Tisserand},
    title={{FPGA} Implementation of Polynomial Evaluation Algorithms},
    booktitle={SPIE Photonics East'95 Conference Proceedings},
    year= 1995,
    key={EMT95},
    location={Philadelphia, PA}
}

@inproceedings{EN93,
    author={D. Etiemble and K. Navi},
    title={Algorithms and multi-valued circuits for the multioperand addition in the
        binary stored-carry number system},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={194-201},
    location={Windsor, Canada},
    keywords={addition,redundant number systems}
}

@article{EO82,
    author={V.~G. Oklobdzija and M.~D. Ercegovac},
    title={An on-line square root algorithm},
    journal={{IEEE} Transactions on Computers},
    volume={C-31},
    year= 1982,
    pages={70-75},
    keywords={on-line arithmetic,square root}
}

@article{Erc73,
    author={M.~D. Ercegovac},
    title={Radix 16 evaluation of certain elementary functions},
    journal={{IEEE} Transactions on Computers},
    volume={C-22},
    year= 1973,
    month= jun,
    number= 6,
    keywords={elementary functions,shift-and-add algorithms},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 1, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@phdthesis{Erc75,
    author={M.~D. Ercegovac},
    title={A general method for evaluation of functions and computation in a digital
        computer},
    school={Dept. of Computer Science, University of Illinois, Urbana-Champaign, IL},
    year= 1975,
    keywords={elementary functions}
}

@article{Erc77,
    author={M.~D. Ercegovac},
    title={A General Hardware-Oriented Method for Evaluation of Functions and Computations
        in a Digital Computer},
    journal={{IEEE} Transactions on Computers},
    volume={C-26},
    year= 1977,
    pages={667-680},
    number= 7,
    keywords={elementary functions}
}

@inproceedings{Erc78,
    author={M.~D. Ercegovac},
    title={An on-line square rooting algorithm},
    booktitle={fourth IEEE Symposium on Computer Arithmetic},
    year= 1978,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    keywords={on-line arithmetic,square root}
}

@inproceedings{Erc83,
    author={M.~D. Ercegovac},
    title={A higher-radix division with simple selection of quotient digits},
    booktitle={Proceedings of the 6th IEEE Symposium on Computer Arithmetic},
    year= 1983,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={94-98},
    location={Aarhus, Denmark},
    keywords={division}
}

@inproceedings{Erc84,
    author={M.~D. Ercegovac},
    title={On-line Arithmetic: {A}n Overview.},
    booktitle={SPIE, Real Time Signal Processing VII},
    year= 1984,
    publisher={SPIE-The International Society for Optical Engeneering, Bellingham, WA},
    pages={86--93},
    keywords={on-line arithmetic}
}

@inproceedings{Erc91,
    author={M.~D. Ercegovac},
    title={On-Line Arithmetic For Recurrence Problems},
    booktitle={Advanced Signal Processing Algorithms, Architectures, and implementations
        II},
    year= 1991,
    publisher={SPIE-The International Society for Optical Engeneering},
    keywords={on-line arithmetic}
}

@inproceedings{ErcegovacMuller2006,
    author={M. Ercegovac and J.-M. Muller},
    title={Arithmetic Processor for Solving Tri-Diagonal Systems of Linear Equations},
    booktitle={proc. 40th Conference on Signals, Systems and Computers},
    year={2006},
    month= nov,
    address={Pacific Grove, CA}
}

@article{ErcImbMatMulWei2000,
    author={M. D. Ercegovac and L. Imbert and D. Matula and J.-M. Muller and G. Wei},
    title={Improving Goldschmidt Division, Square Root and Square Root Reciprocal},
    journal={{IEEE} Transactions on Computers},
    volume= 49,
    year= 2000,
    month= jul,
    number= 7
}

@MastersThesis{Goldschmidt1964,
  author =       "R. E. Goldschmidt",
  title =        "Applications of division by convergence",
  type =         "Master's Thesis",
  school =       "Dept. of Electrical Engineering, Massachusetts
                 Institute of Technology",
  address =      "Cambridge, MA",
  month =        jun,
  year =         "1964",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@book{ErcLan2004,
    author={M.~D.~Ercegovac and T.~Lang},
    title={Digital Arithmetic},
    publisher={Morgan Kaufmann Publishers, San Francisco, CA},
    year={2004},
    key={ErcLan2002},
    isbn={1-55860-798-6}
}

@article{ErcLanMulTis2000,
    author={M. Ercegovac and T. Lang and J.-M. Muller and A. Tisserand},
    title={Reciprocation, Square Root, Inverse Square Root and Some Elementary Functions
        Unsing Small Multipliers},
    journal={{IEEE} Transactions on Computers},
    volume= 49,
    year= 2000,
    month= jul,
    number= 7
}

@inproceedings{ErcLanMulTis98,
    author={M. Ercegovac and T. Lang and J.-M. Muller and A. Tisserand},
    title={Reciprocation, Square Root, Inverse Square Root and Some Elementary Functions
        Using Small Multipliers},
    booktitle={{SPIE's} International Symposium on Optical Science, Engineering, and Instrumentation},
    year= 1998,
    month= jul,
    address={San Diego, CA}
}

@inproceedings{ErcMul2003,
    author={M.~D. Ercegovac and J.-M. Muller},
    title={Complex Division with Prescaling of the Operands},
    booktitle={14th IEEE Conference on Application-Specific Systems,
        Architectures and Processors},
    year={2003},
    month= jun,
    publisher={IEEE Computer Society},
    noeditor={E. Deprettere and S. Bhattacharyya and J. Cavallaro and A. Darte},
    pages={304--314},
    key={ErcMul2003}
}


@Article{ErcMul2007:complexsqrt,
  author = 		  {M.~D. Ercegovac and J.-M. Muller},
  title = 		  {Complex Square Root with Operand Prescaling},
  journal = 	  {Journal of {VLSI} Signal Processing},
  year = 		  2007,
  volume = 	  49,
  number = 	  1,
  pages = 	  {19--30}}

@inproceedings{ErcMul2004,
    author={M.~D.~Ercegovac and J.-M.~Muller},
    title={Complex Square Root with Operand Prescaling},
    booktitle={Proc. $15$th {IEEE} International Conference on Application-Specific Systems,
        Architectures and Processors, Galveston, Texas},
    year={2004},
    month= sep,
    publisher={{IEEE} Computer Society Press, Los Alamitos, CA}
}

@inproceedings{ErcMul98,
    author={M. Ercegovac and J.-M. Muller},
    title={Fast Evaluation of Functions at Regularly-Spaced Points},
    booktitle={{SPIE's} Internationa Symposium on Optical Science, Engineering, and Instrumentation},
    year= 1998,
    month= jul
}

@phdthesis{Erh92,
    author={J.~Erhel},
    title={Vitesse et pr{\'e}cision en calcul scientifique},
    school={Universit{\'e} Rennes 1},
    year= 1992,
    type={Habilitation {\`a} Diriger des Recherches},
    key={Erh92}
}

@inproceedings{Est60,
    author={G. Estrin},
    title={Organization of computer systems~-- the fixed plus variable structure computer},
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    year= 1960,
    pages={33-40}
}

@inproceedings{ET75,
    author={K.~S. Trivedi and M.~D. Ercegovac},
    title={On-line algorithms for division and multiplication},
    booktitle={3rd IEEE Symposium on Computer Arithmetic},
    year= 1975,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={161-167},
    location={Dallas, TX},
    keywords={division,multiplication,on-line arithmetic}
}

@article{ET77,
    author={M.~D. Ercegovac and K.~S. Trivedi},
    title={On-line algorithms for division and multiplication},
    journal={{IEEE} Transactions on Computers},
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    year= 1977,
    pages={681-687},
    number= 7,
    keywords={division,multiplication,on-line arithmetic},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{ET87,
    author={M. D. Ercegovac and P. K. G. Tu},
    title={A radix-4 on-line division algorithm.},
    booktitle={Proceedings of the 8th IEEE Symposium on Computer Arithmetic},
    year= 1987,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Como, Italy},
    keywords={division,on-line arithmetic}
}

@inproceedings{ET89,
    author={M. D. Ercegovac and P. K. G. Tu},
    title={Design of On-line Division Unit.},
    booktitle={Proceedings of the 9th IEEE Symposium on Computer Arithmetic},
    year= 1989,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={M. D. Ercegovac and E.~E. Swartzlander},
    pages={42-49},
    location={Santa Monica, CA},
    keywords={division,on-line arithmetic}
}

@inproceedings{ET91,
    author={M.~D. Ercegovac and P.~K.~G. Tu},
    title={Application of on-line arithmetic algorithms to the {SVD} computation: preliminary
        results},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
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    location={Grenoble, France},
    keywords={on-line arithmetic}
}

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@article{EveSei2000,
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    pages={225--232}
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@article{EW83,
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    year= 1983,
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}

@inproceedings{Fan87,
    author={J. Fandrianto},
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    keywords={division,square root}
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}

@inproceedings{FB91,
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@inproceedings{FeaMat2001,
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    key={FeaMat2001},
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@unpublished{Fer97,
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@MISC{FS,
        AUTHOR             = {Figueiredo, L.H. and Stolfi, J.},
        HOWPUBLISHED       = {\url{http://www.ic.unicamp.br/~stolfi/EXPORT/projects/affine-arith/}.},
        TITLE              = {{Affine Arithmetic}}
}

@article{Fik67,
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@book{Fik68,
    author={C.~T. Fike},
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    year= 1968,
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    keywords={elementary functions}
}

@article{Fly70,
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}

@book{FlyObe2001,
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}

@techreport{FM90,
    author={P. Francois and J.-M. Muller},
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        de Lyon, France},
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    type={Research report 90-03},
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}

@inproceedings{FM91,
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}

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    keywords={cordic,elementary functions,shift-and-add algorithms}
}

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}

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}

@inproceedings{IO79,
    author={M.~J. Irwin and R.~M. Owens},
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    year= 1983,
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    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{IO83b,
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    year= 1983,
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    keywords={on-line arithmetic}
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@article{IO87,
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    keywords={on-line arithmetic}
}

@inproceedings{IO89,
    author={M.~J. Irwin and R.~M. Owens},
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}

@inproceedings{IorMat99,
    author={C. Iordache and D. W. Matula},
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@inproceedings{IorTan03,
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}

@phdthesis{Irw77,
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    title={An arithmetic unit for on-line computation},
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        61801},
    year= 1977,
    keywords={on-line arithmetic}
}

@inproceedings{Irw78,
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        Computer Society Press, Los Alamitos, CA, 1990}
}

@Book{ISO9899-1999,
        AUTHOR       = {{International Organization for Standardization}},
        TITLE           = {Programming Languages -- {C}},
        ADDRESS         = {Geneva, Switzerland},
        noPAGES           = {538},
        MONTH           = dec,
publisher = {ISO/IEC Standard 9899:1999},
        YEAR            = {1999}
}

@Book{ISO-TR24732,
author = {{International Organization for Standardization}},
       TITLE           = {Extension for the programming language {C} to support decimal floating-point arithmetic},
publisher={ISO/IEC Draft Standard 24732--N1312},
       MONTH           = may,
       YEAR            = {2008}
}

@Book{IEC-float-99,
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publisher = {International Electrotechnical Commission},
edition = {2nd},
year = {1989}
}

@book{Fortran2003,
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@Book{IEEE754-2008,
   author = {{{IEEE}~Computer~Society}},
   title = {{IEEE} Standard for Floating-Point Arithmetic},
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}



@book{IEEE85,
    author={{American National Standards Institute and Institute of Electrical and Electronic
        Engineers}},
    oldtitle={{IEEE} Standard for Binary Floating-Point Arithmetic,
        {ANSI}/{IEEE} Standard 754--1985},
    title={{IEEE} Standard for Binary Floating-Point Arithmetic},
    publisher={{ANSI}/{IEEE} Standard 754--1985},
    noaddress={New York},
    year= 1985,
    key={IEEE85}
}

@book{IEEE87,
    author={{American National Standards Institute and Institute of Electrical and Electronic
        Engineers}},
    title={{IEEE} Standard for Radix Independent Floating-Point Arithmetic},
    publisher={{ANSI}/{IEEE} Standard 854--1987},
    noaddress={New York},
    year= 1987,
    key={IEEE87}
}

@Book{ISO10967-1-1994,
        AUTHOR          = {{International Organization for Standardization}},
        TITLE           = {Information technology --- Language independent arithmetic --- Part 1: Integer and floating point arithmetic},
        PUBLISHER       = {ISO/IEC standard 10967-1},
        YEAR            = {1994}
}

@Book{ISO10967-2-2001,
        AUTHOR          = {{International Organization for Standardization}},
        TITLE           = {Information technology --- Language independent arithmetic --- Part 2: Elementary numerical functions},
        PUBLISHER       = {ISO/IEC  standard 10967-2},
        YEAR            = {2001}
}

@Book{ISO10967-3-2006,
        AUTHOR          = {{International Organization for Standardization}},
        TITLE           = {Information technology --- Language independent arithmetic --- Part 3: Complex integer and floating point arithmetic and complex elementary numerical functions},
        PUBLISHER       = {ISO/IEC standard  10967-3},
        YEAR            = {2006}
}



@inproceedings{ITY95,
    author={M.~Ito, N.~Takagi and S.~Yajima},
    title={Efficient Initial Approximation and Fast Converging Methods for Division
        and Square Root},
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    month= jul,
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    key={ITY95},
    location={Bath, UK},
    keywords={division, square root}
}

@article{IZ2005,
    author={A.~Iserles and A.~Zanna},
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}

@article{JB:ieeevlsi-5-2,
    author={Yong-Jin Jeong and Wayne P. Burleson},
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    year={1997},
    pages={211--217},
    month= jun,
    number={2}
}

@INPROCEEDINGS{JeKnMoRe07,
author = {C.-P.~Jeannerod and H. Knochel and C. Monat and G. Revy},
title = {Faster floating-point square root for integer processors},
booktitle = {IEEE Symposium on Industrial Embedded Systems (SIES'07)},
year = {2007},
isbn = {1-4244-0840-7}
}

@TechReport{JeKnMoRe08,
 author = {C.-P.~Jeannerod and H. Knochel and C. Monat and G. Revy},
  title = 	 {Computing floating-point square roots via bivariate polynomial evaluation},
  institution =  {LIP},
  year = 	 {2008},
  OPTkey = 	 {},
  OPTtype = 	 {},
  number = 	 {RR2008-38},
  OPTaddress = 	 {},
  month = 	 {October},
  OPTnote = 	 {},
  OPTannote = 	 {}
}

@inproceedings{JeKnMoReVi08,
  author = {C.-P.~Jeannerod and H. Knochel and C. Monat and G. Revy and G. Villard},
  title = {A new binary floating-point division algorithm 
           and its software implementation on the {ST231} processor},
  month = {June},
  year = {2009},
  booktitle={Proceedings of the 19th {IEEE} Symposium on Computer Arithmetic (ARITH-19)},
  address = {Portland, OR}
}

@inproceedings{Jeb93,
    author={T. Jebelan},
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    month= jun,
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    pages={180-185},
    location={Windsor, Canada},
    keywords={GCD}
}

@article{Jen83,
    author={W.~K. Jenkins},
    title={The design of error checkers for self-checking residue number arithmetic},
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    year= 1983,
    pages={388-396},
    keywords={residue number systems}
}

@article{JessaniOlson1996,
     author = {R.~M. Jessani and C.~H. Olson},
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     number = {5},
     pages = {559--566},
     year = {1996}
}

@ARTICLE{Jezequel04,
        AUTHOR = {J\'ez\'equel, F.},
        TITLE = {{Dynamical control of converging sequences computation}},
        JOURNAL = {Applied Numerical Mathematics},
        VOLUME = 50,
        PAGES = {147--164},
        YEAR = 2004
}

@inproceedings{JK93,
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    month= jun,
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    pages={228-233},
    location={Windsor, Canada},
    keywords={floating-point arithmetic,multiplication,rounding}
}

@inproceedings{JL95,
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    key={JL95},
    location={Bath, UK}
}

@article{JM84,
    author={I.~R. Mactaggart and M.~A. Jack},
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    year= 1984,
    pages={368-373},
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@inproceedings{JMRW91,
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    keywords={residue number systems}
}

@inproceedings{JMS93,
    author={W.~K. Jenkins and B.~A. Schnaufer and A.~J. Mansen},
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@inproceedings{Joh83,
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@misc{Jones2004,
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@article{JoyYen2000,
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    month= jul,
    number= 7
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@article{Jul80,
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% VL: Le mot est bien "Pracniques" (contraction de "practical techniques"),
% apparemment inventé par l'ACM et voulant dire "practical techniques of
% value to software engineering practitioners". Cf
%   http://www1.elsevier.com/homepage/sac/isco/pdf/glass.pdf
@article{Kahan1965,
 author = {W. Kahan},
 title = {Pracniques: further remarks on reducing truncation errors},
 journal = {Commun. ACM},
 volume = {8},
 number = {1},
 year = {1965},
 issn = {0001-0782},
 pages = {40},
 doi = {http://doi.acm.org/10.1145/363707.363723},
 publisher = {ACM Press},
 address = {New York, NY},
 }

@unpublished{Kah04,
    author={W.~Kahan},
    title={A Logarithm Too Clever by Half},
    note={Available at \url{http://http.cs.berkeley.edu/~wkahan/LOG10HAF.TXT}},
    year= 2004,
    key={Kah04},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@unpublished{Kah04a,
    author={W.~Kahan},
    title={On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic},
    note={Available at \url{http://http.cs.berkeley.edu/~wkahan/Qdrtcs.pdf}},
    year= 2004,
    key={Kah04a},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@unpublished{Kah04b,
    author={W.~Kahan},
    title={How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?},
    note={Available at \url{http://http.cs.berkeley.edu/~wkahan/Mindless.pdf}},
    year= 2004,
    key={Kah04b},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@unpublished{Kah06,
    author={W.~ Kahan},
    title={Private communication},
    note={Unpublished},
    year={2006},
    month= jun,
    key={Kah06}
}

@unpublished{Kah83,
    author={W.~Kahan},
    title={Minimizing q*m-n. {T}ext accessible electronically at \url{http://http.cs.berkeley.edu/~wkahan/}},
    note={At the beginning of the file "nearpi.c"},
    year= 1983,
    key={Kah83},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@unpublished{Kah88,
    author={W.~Kahan},
    title={Computer System Support for Scientific and Engineering Computation},
    note={Lecture notes, available at \url{http://www.validlab.com/fp-1988/lectures/}},
    year={1988},
    key={Kah88},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@inproceedings{Kah89,
    author={W. Kahan},
    title={Paradoxes in Concepts of Accuracy.},
    booktitle={Lecture notes from Joint Seminar on Issues and Directions in Scientific
        Computations, U.C. Berkeley},
    year= 1989,
    key={Kah89}
}

@unpublished{Kah96,
    author={W.~Kahan},
    title={Lecture Notes on the Status of {IEEE}-754},
    note={PDF file accessible  at \url{http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF}},
    year= 1996,
    key={Kah96},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@unpublished{Kah96a,
    author={W.~Kahan},
    title={What can you learn about floating-point arithmetic in one hour?},
    note={Postscript version accessible electronically at \url{http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps}},
    year= 1996,
    key={Kah96a},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@unpublished{Kahan1996,
    author={W.~Kahan},
    title={A test for correctly rounded SQRT},
    note={Postscript version accessible electronically at \url{http://www.cs.berkeley.edu/~wkahan/SQRTest.ps}},
    year= 1996,
    key={Kahan1996},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@article{Kah98,
    author={W.~Kahan},
    title={{IEEE} 754: An interview with {William} {Kahan}},
    journal={Computer},
    volume={31},
    year={1998},
    pages={114--115},
    month= mar,
    number={3},
    key={Kah98}
}

@inproceedings{Kahan1987,
    author={W.~Kahan},
    title={Branch Cuts for Complex Elementary Functions},
    booktitle={The State of the Art in Numerical Analysis},
    year= 1987,
    publisher={Clarendon Press, Oxford},
    editor={A. Iserles and M. J. D. Powell},
    pages={165--211}
}

@TECHREPORT{Kahan99,
        AUTHOR             = {Kahan, W.},
        INSTITUTION        = {Computer Science, UC Berkeley},
        NOTE               = {Available at \url{http://http.cs.berkeley.edu/~wkahan/improber.ps}},
        TITLE              = {{The improbability of probabilistic error analyses for numerical computations}},
        TYPE               = {Slides},
        YEAR               = {1999}
}

@TECHREPORT{Kahan1981,
        AUTHOR             = {Kahan, W.},
        INSTITUTION        = {Computer Science, UC Berkeley},
        NOTE               = {Available at \url{http://www.cs.berkeley.edu/~wkahan/ieee754status/why-ieee.pdf}},
        TITLE              = {Why do we Need a Floating-Point Standard?},
        YEAR               = {1981}
}

@unpublished{KahDar1998,
    author={W.~Kahan and J.~Darcy},
    title={How {Java}'s Floating-Point Hurts Everyone Everywhere},
    note={Available at \url{http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf}},
    year= 1998,
    key={DahDar1998},
    institution={Elect. Engineering and Computer Science, Univ. of California at Berkeley}
}

@article{KahanZuras2005,
    author={W.~Kahan and D.~Zuras},
    title={An Open Question to Developers of Numerical Software},
    journal={IEEE Computer},
    volume= 38,
    year= 2005,
    pages={91--94},
    month= may,
    number= 5
}

@article{Kal83,
    author={R. Kallman},
    title={A faster 8-bit carry circuit},
    journal={{IEEE} Transactions on Computers},
    volume={C-32},
    year= 1983,
    pages={1209-1211},
    keywords={addition}
}

@inproceedings{Kan91,
    author={V. Kantabutra},
    title={Designing optimum carry-skip adders},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={146-155},
    location={Grenoble, France},
    keywords={addition}
}

@article{Kan96,
    author={V. Kantabutra},
    title={On Hardware for Computing Exponential and Trigonometric Functions},
    journal={{IEEE} Transactions on Computers},
    volume= 45,
    year= 1996,
    pages={328--339},
    month= mar,
    number= 3,
    key={Kan96},
    keywords={CORDIC}
}

@article{Kar84,
    author={A.~H. Karp},
    title={Exponential and Logarithm by sequential Squaring},
    journal={IEEE Transaction on Computers},
    volume={C-33},
    year= 1984,
    number= 5,
    keywords={exponential,logarithm}
}

@article{Kar85,
    author={R.~Karpinsky},
    title={{PARANOIA}: a Floating-Point Benchmark},
    journal={BYTE},
    volume= 10,
    year= 1985,
    number= 2,
    key={Kar85}
}

@article{KaratsubaOfman1962,
    author={A.~Karatsuba and Y.~Ofman},
    title={Multiplication of Many-Digital Numbers by Automatic Computers},
    journal={Doklady Akad. Nauk SSSR},
    volume={145},
    year={1962},
    pages={293--294},
    key={KaratsubaOfman1962},
    note={Translation in Physics-Doklady 7, 595--596, 1963}
}

@article{KarpMarkstein1997,
    author={Alan H. Karp and Peter Markstein},
    title={High-Precision Division and Square Root},
    abstract={We present division and square root algorithms for calculation with more
        bits than are handled by the floating-point hardware. These algorithms
        avoid the need to multiply two high-precision numbers, speeding up the
        last iteration by as much as a factor of 10. We also show how to produce
        the floating-point number closest to the exact result with relatively few
        additional operations.},
    journal = AcmToms,
    volume={23},
    year={1997},
    pages={561--589},
    month= dec,
    number={4},
    keywords={algorithms, performance, division, quad precision, square root.},
    issn={0001-0782},
    coden={CACMA2},
    url={http://doi.acm.org/10.1145/279232.279237; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/},
    accepted={June 1997},
    subject={G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics
        of Computing]: Mathematical Software.}
}

@inproceedings{Kau83,
    author={S. Kaushik},
    title={Sign Detection in Non-Redundant Residue Number System with Reduced Information},
    booktitle={Proceedings of the 6th Symposium on Computer Architecture},
    year= 1983,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    keywords={residue number systems}
}

@article{Kaw88,
    author={S. Kawahito and others},
    title={A 32x32-bit multiplier using multiple-valued MOS current-mode circuits},
    journal={IEEE journal of solid-state circuits},
    volume={SC-23},
    year= 1988,
    pages={124-132},
    keywords={multiplication}
}

@BOOK{Kearfott96,
        AUTHOR             = {Kearfott, R.~B.},
        PUBLISHER          = {Kluwer, Dordrecht},
        TITLE              = {Rigorous global search: continuous problems},
        YEAR               = {1996}
}

@article{KC93,
    author={K.~Kota and J.~R.~Cavallaro},
    title={Numerical Accuracy and Hardware Tradeoffs for {CORDIC} Arithmetic for Special-Purpose
        Processors},
    journal={{IEEE} Transactions on Computers},
    volume= 42,
    year= 1993,
    pages={769--779},
    month= jul,
    number= 7,
    key={KC93}
}

@article{Ker89,
    author={J. Kernhoff and others},
    title={High-speed CMOS adder and multiplier modules for digital signal processing
        in a semicustom environment},
    journal={IEEE journal of solid-state circuits},
    volume= 24,
    year= 1989,
    pages={570-575},
    keywords={addition,multiplication}
}

@article{KGR72,
    author={C.~V. Ramamoorthy and J.~R. Goodman and K.~H. Kim},
    title={Some properties of iterative square-rooting methods using high-speed multiplication},
    journal={{IEEE} Transactions on Computers},
    volume={C-21},
    year= 1972,
    pages={837-847},
    keywords={elementary functions,Newton iteration,square root},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 1, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@article{KH:el-26-13,
    author={C. K. Ko{\c{c}} and C. Y. Hung},
    title={Carry-save adders for computing the product AB modulo N},
    journal={Electronics Letters},
    volume={26},
    year={1990},
    pages={899--900},
    month= jun,
    number={13}
}

@article{KH:el-26-6,
    author={C. K. Ko{\c{c}} and C. Y. Hung},
    title={Multi-operand modulo addition using carry save adders},
    journal={Electronics Letters},
    volume={26},
    year={1990},
    pages={361--363},
    month= mar,
    number={6}
}

@article{Oklobodzija93,
    author={Villeger, D. and Oklobdzija, V.~G.},
    title={Evaluation of {B}ooth encoding techniques for parallel multiplier implementation},
    journal={Electronics Letters},
    volume={29},
    year={1993},
    pages={2016--2017},
    month= nov,
    number={23}
}

@book{Khinchin97,
    author={A. Ya. Khinchin},
    title={Continued Fractions},
    publisher={Dover, New York},
    year={1997},
    key={Khinchin97}
}

@article{KK88,
    author={R. Kirchner and U. Kulisch},
    title={Accurate Arithmetic for Vector Processors},
    journal={Journal of Parallel and distributed Computing},
    volume={Special Issue on Parallelism in Computer Arithmetic},
    year= 1988,
    number= 5,
    keywords={accuracy control}
}

@inproceedings{KKDTMHV98,
    author={F. Kaess and R. Kanan and M. Declercq and A. Tisserand and J.M. Muller and
        B. Hochet and J.M. Vincent},
    title={A Fast Encoding Architecture for High-Speed Flash Analog-to-Digital Converters},
    booktitle={Second International Workshop on Design and Diagnosis of Electronic Circuits
        and Systems},
    year= 1998,
    month= sep,
    location={Szczyrk, Poland}
}

@inproceedings{KKDTMHV98a,
    author={F. Kaess and R. Kanan and M. Declercq and A. Tisserand and J.M. Muller and
        B. Hochet and J.M. Vincent},
    title={Improving High-Speed Flash Analog-to-Digital Converters Accuracy Using Sum
        Encoding},
    booktitle={{SCAN'98}},
    year= 1998,
    month= sep,
    location={Budapest, Hungary}
}

@phdthesis{Kla93,
    author={S. Kla},
    title={Calcul parall{\`e}le et en ligne des fonctions arithm{\'e}tiques},
    school={{\'E}cole Normale Sup{\'e}rieure de Lyon},
    year= 1993,
    month= feb,
    address={46 All{\'e}e d'Italie, 69364 Lyon Cedex 07, France},
    keywords={elementary functions,exponential,logarithm,number systems,rational approximations,redundant
        number systems,square root}
}

@article{KLPS93,
    author={T.~H. Kuo and H.~C. Lin and R.~C. Potter and D. Schupe},
    title={Multiple-valued counter},
    journal={{IEEE} Transactions on Computers},
    volume= 42,
    year= 1993,
    pages={106-109},
    month= jan,
    number= 1,
    keywords={addition}
}

@book{KM81,
    author={U.~W. Kulisch and W.~L. Miranker},
    title={Computer arithmetic in theory and practice},
    publisher={Academic Press, New York, NY},
    year= 1981,
    keywords={accuracy control,floating-point arithmetic,interval arithmetic}
}

@article{KM81a,
    author={I. Koren and Y. Maliniak},
    title={On classes of positive, negative and imaginary radix number systems},
    journal={{IEEE} Transactions on Computers},
    volume={C-30},
    year= 1981,
    pages={312-317},
    keywords={number systems}
}

@inproceedings{KM83,
    author={P. Kornerup and D.~W. Matula},
    title={An Order Preserving Finite Binary Encoding of the Rationals},
    booktitle={Proceedings of the 6th IEEE Symposium on Computer Arithmetic},
    year= 1983,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    pages={201-209},
    location={Aarhus, Denmark}
}

@article{KM83a,
    author={P. Kornerup and D.~W. Matula},
    title={Finite-precision rational arithmetic: an arithmetic unit},
    journal={{IEEE} Transactions on Computers},
    volume={C-32},
    year= 1983,
    pages={378-388},
    keywords={rational arithmetic}
}

@inproceedings{KM85,
    author={P. Kornerup and D.~W. Matula},
    title={Finite precision lexicographic continued fraction number systems},
    booktitle={Proceedings of the 7th IEEE Symposium on Computer Arithmetic},
    year= 1985,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Urbana, IL},
    keywords={continued fractions,number systems,rational arithmetic},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@article{KM86,
    author={U.~W. Kulisch and W.~L. Miranker},
    title={The arithmetic of the digital computer: a new approach},
    journal={SIAM Rev.},
    volume= 28,
    year= 1986,
    pages={1-40},
    keywords={accuracy control,floating-point arithmetic,interval arithmetic}
}

@article{KM88,
    author={P. Kornerup and D.~W. Matula},
    title={An On-Line Arithmetic Unit for Bit-Pipelined Rational Arithmetic},
    journal={Journal of Parallel and distributed Computing},
    volume={Special Issue on Parallelism in Computer Arithmetic},
    year= 1988,
    number= 5,
    keywords={number systems,on-line arithmetic,rational arithmetic}
}

@inproceedings{KM89,
    author={P. Kornerup and D. W. Matula},
    title={Exploiting Redundancy in Bit-Pipelined Rational Arithmetic},
    booktitle={Proceedings of the 9th IEEE Symposium on Computer Arithmetic},
    year= 1989,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={M. D. Ercegovac and E.~E. Swartzlander},
    pages={119-126},
    location={Santa Monica, CA},
    keywords={number systems,rational arithmetic}
}

@inproceedings{KMMM91,
    author={S. Kla and C. Mazenc and X. Merrheim and J.~M. Muller},
    title={New Algorithms For On-Line Computation of Elementary Functions},
    booktitle={Advanced Signal Proceeing Algorithms, Architectures, and implementations
        II},
    year= 1991,
    publisher={SPIE-The International Society for Optical Engeneering},
    keywords={elementary functions,exponential,on-line arithmetic,redundant number systems,shift-and-add
        algorithms,trigonometric functions}
}

@article{KNEVK2000,
    author={L. Kalampoukas and D. Nikolos and C. Efstathiou and H. Vergos and J. Kalamatianos},
    title={High-Speed Parallel-Prefix Modulo $2^n-1$ Adders},
    journal={{IEEE} Transactions on Computers},
    volume= 49,
    year= 2000,
    pages={673--680},
    month= jul,
    number= 7
}

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    author={A. Knofel},
    title={Fast hardware units for the computation of accurate dot products},
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    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={70-74},
    location={Grenoble, France},
    keywords={accuracy control,floating-point arithmetic,interval arithmetic}
}

@inproceedings{Knowles99,
    author={Simon Knowles},
    title={A Family of Adders},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic (Adelaide,
        Australia)},
    year= 1999,
    month= apr,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={Koren and Kornerup},
    pages={30--34}
}

@book{Knu73,
    author={D. Knuth},
    title={The Art of Computer Programming},
    publisher={Addison Wesley, Reading, MA},
    year= 1973,
    volume= 2
}

@book{Knu98,
    author={D. Knuth},
    title={The Art of Computer Programming},
    publisher={Addison-Wesley, Reading, MA},
    year= 1998,
    edition = {3rd},
    volume= 2
}

@article{Knuth62,
    author={D.~E. Knuth},
    title={Evaluation of polynomials by computer},
    journal={Commun. ACM},
    volume={5},
    year={1962},
    pages={595--599},
    number={12},
    issn={0001-0782},
    doi={http://doi.acm.org/10.1145/355580.369074},
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}

@inproceedings{KO91,
    author={P. Kornerup and O. Orup},
    title={A high-radix hardware algorithm for calculating the exponential $M^{E}$
        Modulo N},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={52-56},
    location={Grenoble, France},
    keywords={exponential,multiplication,residue number systems}
}

@book{Ko96,
    author={Ker-I Ko},
    title={Complexity Theory of Real Functions},
    publisher={Birkh{\"a}user},
    year= 1991,
    series={Progress in Theoretical Computer Science},
    key={Ko96}
}

@article{KolLeeDep2000,
    author={K.J. Van der Kolk and J.A. Lee and E.F.A. Deprettere},
    title={A Floating-Point Vectoring Algorithm Based on Fast Rotations},
    journal={Journal of VLSI Signal Processing Systems},
    volume= 25,
    year= 2000,
    pages={125--140},
    month= jun,
    number= 2
}

@book{Kor93,
    author={I. Koren},
    title={Computer Arithmetic Algorithms},
    publisher={Prentice-Hall, Englewood Cliffs, NJ},
    year= 1993,
    keywords={accuracy control,addition,cordic,division,elementary functions,exponential,floating-point
        arithmetic,logarithm,multiplication,number systems,redundant number systems,residue
        number systems,shift-and-add algorithms,square root,survey on computer
        arithmetic,trigonometric functions}
}

@inproceedings{Kor93a,
    author={P. Kornerup},
    title={High-radix modular multiplication for cryptosystems},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={277-283},
    location={Windsor, Canada},
    keywords={cryptography,multiplication,RSA}
}

@article{Kor94,
    author={P. Kornerup},
    title={A Systolic, Linar-Array Multiplier for a Class of Right-Shift Algorithms},
    journal={{IEEE} Transactions on Computers},
    volume= 43,
    year= 1994,
    pages={892-898},
    month= aug,
    number= 8,
    keywords={multiplication}
}

@inproceedings{Kor99,
    author={Peter Kornerup},
    title={Necessary and Sufficient Conditions for Parallel, Constant Time Conversion
        and Addition},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic (Adelaide,
        Australia)},
    year= 1999,
    month= apr,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={Koren and Kornerup},
    pages={152--156}
}

@proceedings{KorBajFrouMul2003,
    editor={Peter Kornerup and Jean-Claude Bajard and Christiane Frougny and Jean-Michel
        Muller},
    title={Special issue ``Real Numbers and Computers'' of Theoretical Computer Science},
    year={2003},
    month= jan,
    volume={291},
    key={KorBajFrouMul2003},
    number={2}
}

@inproceedings{KorMul2003,
    author={P. Kornerup and J.-M. Muller},
    title={Choosing Starting Values for {Newton}-{Raphson} Computation of 
           Reciprocals, Square-Roots and Square-Root Reciprocals},
    booktitle={Proceedings of RNC5},
    year={2003},
    month= sep,
    editor={M. Daumas and N. Revol},
    key={KorMul2003},
    location={Lyon, France}
}

@techreport{KorMul2004,
    author={P.~Kornerup and J.-M.~Muller},
    title={RN-Codings of Numbers: definition and some properties},
    institution={LIP, ENS-Lyon},
    year={2004},
    number={2004-44},
    key={KorMul2004}
}

@article{KorMull2004a,
    author={P.~Kornerup and J.-M.~Muller},
    title={Choosing Starting Values for Certain {Newton}-{Raphson} Iterations},
    journal={Theoretical Computer Science (to appear)},
    year={2004}
}

@article{KornerupMuller2006,
    author={P.~Kornerup and J.-M.~Muller},
    title={Choosing Starting Values for certain {N}ewton--{R}aphson Iterations},
    abstract={We aim at finding the best possible seed values when computing $a^{1/p}$
        using the Newton-Raphson iteration in a given interval. A natural choice
        of the seed value would be the one that best approximates the expected
        result. It turns out that in most cases, the best seed value can be quite
        far from this natural choice. When we evaluate a monotone function f(a)
        in the interval [amin, amax], by building the sequence xn defined by the
        Newton-Raphson iteration, the natural choice consists in choosing x0 equal
        to the arithmetic mean of the endpoint values. This minimizes the maximum
        possible distance between x0 and f(a). And yet, if we perform n iterations,
        what matters is to minimize the maximum possible distance between xn and
        f(a). In several examples, the value of the best starting point varies
        rather significantly with the number of iterations.},
    journal={Theoretical Computer Science},
    volume={351},
    year={2006},
    pages={101-110},
    month= feb,
    number={1}
}

@article{KornerupMuller2006a,
    author={Peter Kornerup and Jean-Michel Muller},
    title={Leading Guard Digits in Finite-Precision Redundant Representations},
    abstract={Redundant number representations are generally used to allow constant time
        additions, based on the fact that only bounded carry-ripples take place.
        But, carries may ripple out into positions which may not be needed to represent
        the final value of the result and, thus, a certain amount of leading guard
        digits are needed to correctly determine the result. Also, when cancellation
        during subtractions occurs, there may be nonzero digits in positions not
        needed to represent the result of the calculation. It is shown here that,
        for normal redundant digit sets with radix greater than two, a single guard
        digit is sufficient to determine the value of such an arbitrary length
        prefix of leading nonzero digits. This is also the case for the unsigned
        carry-save representation, whereas two guard digits are sufficient, and
        may be necessary, for additions in the binary signed-digit and 2's complement
        carry-save representations. Thus, only the guard digits need to be retained
        during sequences of additions and subtractions. At suitable points, the
        guard digits may then be converted into a single digit, representing the
        complete prefix.},
    journal={{IEEE} Transactions on Computers},
    volume={55},
    year={2006},
    pages={541--548},
    month= may,
    number={5},
    doi={http://dx.doi.org/10.1109/TC.2006.79}
}

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    author={D.~K. Kostopoulos},
    title={An algorithm for the computation of binary logarithms},
    journal={{IEEE} Transactions on Computers},
    volume= 40,
    year= 1991,
    pages={1267-1271},
    month= nov,
    number= 11,
    keywords={logarithm}
}

@article{Kot87,
    author={S. Kotani and others},
    title={Feasibility of an ultra-high-speed Josephson multiplier},
    journal={IEEE journal of solid-state circuits},
    volume={SC-22},
    year= 1987,
    pages={98-103},
    keywords={multiplication}
}

@article{KPS77,
    author={D.~J. Kuck and D.~S. Parker and A.~H. Sameh},
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    year= 1977,
    pages={643-650},
    keywords={floating-point arithmetic,rounding},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 1, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

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    author={N.~G. Kingsbury and P.~J.~W. Rayner},
    title={Digital filtering using logarithmic arithmetic},
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    pages={56-58},
    keywords={logarithm,logarithmic number system},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 1, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@article{Kra88,
    author={W.~Kr{\"a}mer},
    title={Inverse Standard Functions for Real and Complex Point and Interval Arguments
        with Dynamic Accuracy},
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    volume= 6,
    year= 1988,
    pages={185--212},
    key={Kra88}
}

@ARTICLE{KR06,
        AUTHOR             = {Kreinovich, V. and Rump, S.},
        TITLE              = {Towards Optimal Use of Multi-Precision Arithmetic: A Remark},
        JOURNAL             = {Reliable Computing},
        VOLUME             = 12,
        PAGES              = {365--369},
        NOTE               = {Available from \url{http://www.ti3.tu-harburg.de/publications/rump/KreiRu06.pdf}},
        YEAR               = {2006}
}

@BOOK{KLRK97,
        AUTHOR             = {Kreinovich, V. and Lakeyev, A. and Rohn, J. and Kahl, P.},
        PUBLISHER          = {Dordrecht},
        TITLE              = {{Computational Complexity and Feasibility of Data Processing and Interval Computations}},
        YEAR               = {1997}
}


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    title={On range transformation techniques for division},
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    number= 3,
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    volume= 51,
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    pages={106-109},
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@inproceedings{KS:assp2001,
    author={Sungwook Kim and Gerald E. Sobelman},
    title={Digit-Serial Modular Multiplication Using Skew-Tolerant Domino {CMOS}},
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        Signal Processing},
    year={2001},
    publisher= IEEECS,
    pages={1173--1176},
    volume={2}
}

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    author={L. Kuhnel and H. Schmeck},
    title={A closer look at {VLSI} multiplication},
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    pages={345-359},
    keywords={multiplication}
}

@inproceedings{KT93,
    author={B.~J. Kirsh and P.~R. Turner},
    title={Adaptive beamforming using RNS arithmetic},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={36-43},
    location={Windsor, Canada},
    keywords={residue number systems}
}

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    author={L. Kuhnel},
    title={Optimal purely systolic addition},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={172-179},
    location={Grenoble, France},
    keywords={addition}
}

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    author={U.~W. Kulisch},
    title={An axiomatic approach to rounded computations},
    journal={Numerische Mathematik},
    volume= 19,
    year= 1971,
    pages={1--17},
    keywords={accuracy control,floating-point arithmetic,interval arithmetic,rounding}
}

@article{Kul77,
    author={U.~W. Kulisch},
    title={Mathematical foundation of computer arithmetic},
    journal={{IEEE} Transactions on Computers},
    volume={C-26},
    year= 1977,
    pages={610--621},
    month= jul,
    number= 7,
    keywords={accuracy control,floating-point arithmetic,interval arithmetic}
}

@article{Kumar1997,
    author = {A. Kumar},
    title = {The {HP PA-8000 RISC CPU}},
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    volume = {17},
    number = {2},
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    month = {March/April},
    year = {1997}
}

@article{KUY84,
    author={M. Uya and K. Kaneko and J. Yasui},
    title={A CMOS floating-point multiplier},
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    pages={697-702},
    month= oct,
    number= 5,
    keywords={floating-point arithmetic,multiplication},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@article{KwaChoSwa2000,
    author={Jae-Hyuck Kwak and Jae Hun Choi and Earl E. Swartzlander},
    title={High-Speed {CORDIC} Based on an Overlapped Architecture and a Novel $\sigma$-Prediction
        Method},
    journal={Journal of VLSI Signal Processing Systems},
    volume= 25,
    year= 2000,
    pages={167--178},
    month= jun,
    number= 2
}

@article{KZ90,
    author={I.~Koren and O.~Zinaty},
    title={Evaluating Elementary Functions in a Numerical Coprocessor Based on Rational
        Approximations},
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    volume= 39,
    year= 1990,
    pages={1030--1037},
    month= aug,
    number= 8,
    key={KZ90}
}

@article{LA2000,
    author={T.~Lang and E.~Antelo},
    title={CORDIC-Based Computation of ArcCos and $\sqrt{1 - t^2}$},
    journal={J. VLSI Signal Process. Syst.},
    volume={25},
    year={2000},
    pages={19--38},
    number={1},
    issn={0922-5773},
    publisher={Kluwer Academic Publishers},
    address={Hingham, MA}
}

@techreport{LA96,
    author={T.~Lang and E.~Antelo},
    title={{CORDIC}-based computation of arccos and arcsin},
    institution={Dept. Eletronica y Computation, Univ. of Santiago de Compostela, Spain},
    year= 1996,
    key={LA96}
}

@inproceedings{LA97,
    author={T.~Lang and E.~Antelo},
    title={{CORDIC}-based computation of arccos and arcsin},
    booktitle={ASAP'97, The {IEEE} International Conference on Application-Specific Systems,
        Architectures and Processors},
    year={1997},
    month= jul,
    publisher={{IEEE} Computer Society Press, Los Alamitos, CA},
    key={LA97}
}

@book{Lai92,
    author={X. Lai},
    title={On the design and Security of Blocks Ciphers},
    publisher={Hartung-Gorre Verlag Konstanz},
    year={1992},
    series={ETH Series in Information Processing},
    key={Lai92}
}

@article{LamLan86,
    author={R.O.~Lamaire and J.H.~Lang},
    title={Performance of Digital Linear Regulators which use Logarithmic Arithmetic},
    journal={IEEE Transactions on Automatic Control},
    volume={AC-31},
    year= 1986,
    pages={394--400},
    month= may,
    number= 5,
    key={LamLan86}
}

@article{Lan87,
    author={E. Lange},
    title={Implementation and test of the ACRITH facility in a system /370},
    journal={{IEEE} Transactions on Computers},
    volume={C-36},
    year= 1987,
    pages={1088-1096},
    keywords={accuracy control,interval arithmetic}
}

@article{LanAnt2000,
    author={T. Lang and E. Antelo},
    title={{CORDIC}-Based Computation of {ArcCos} and $\sqrt{1-t^2}$},
    journal={Journal of VLSI Signal Processing},
    volume= 25,
    year= 2000,
    pages={19--38}
}

@inproceedings{ErleEtal2002,
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@ARTICLE{BLAS02,
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    year= 1981,
    month= jun,
    address={Grenoble},
    number= 259,
    keywords={multiplication}
}

@phdthesis{Luk83,
    author={W.~K. Luk},
    title={Impl{\'e}mentation r{\'e}cursive de multiplicateurs optimaux},
    school={Universit{\'e} de Paris-Sud Orsay},
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}

@inproceedings{LV83,
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@inproceedings{Mac86,
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@book{Map91,
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}

@article{Mar90,
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}

@phdthesis{Mas84,
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    title={L'it{\'e}ration de {Newton}: convergence et chaos},
    school={Universit{\'e} Joseph Fourier de Grenoble},
    year= 1984,
    address={Institut IMAG, Genoble, France},
    keywords={Newton iteration}
}

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}

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@phdthesis{Maz93,
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}

@book{MC80,
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}

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    pages={210-226},
    keywords={elementary functions,shift-and-add algorithms}
}

@phdthesis{Melquiond2006,
    author={G.~Melquiond},
    title={De l'arithm{\'e}tique d'intervalles {\`a} la certification de programmes},
    school={{{\'E}cole Normale Sup{\'e}rieure de Lyon}},
    year= 2006,
    month= nov,
    note={Available at \url{http://www.ens-lyon.fr/LIP/Pub/PhD2006.php}}
}

@phdthesis{Raina2006,
    author={S.-K.~Raina},
    title={{FLIP}: a Floating-point Library for Integer Processors},
    school={{{\'E}cole Normale Sup{\'e}rieure de Lyon}},
    year= 2006,
    month= sep,
    note={Available at \url{http://www.ens-lyon.fr/LIP/Pub/PhD2006.php}}
}

@inproceedings{Mel08b,
  author    = {G. Melquiond},
  title     = {Proving bounds on real-valued functions with computations},
  booktitle = {Proceedings of the 4th International Joint Conference on Automated Reasoning},
  editor    = {A. Armando and P. Baumgartner and G. Dowek},
  address   = {Sydney, Australia},
  year      = {2008},
  volume    = {5195},
  pages     = {2--17},
  series    = {Lecture Notes in Artificial Intelligence}
}

@ARTICLE{MP07,
        AUTHOR = {Melquiond, G. and Pion, S.},
        TITLE = {{Formally Certified Floating-Point Filters for Homogeneous Geometric Predicates}},
        JOURNAL = {Theoretical Informatics and Applications},
        VOLUME = {41},
        NUMBER = {1},
        PAGES = {57-69},
        YEAR = 2007
}

@article{OdlyzkoRiele1985,
    author = {A.~M.~Odlyzko and H.~J.~J.~te~Riele},
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    year = {1985}
}


@inproceedings{KotnikRiele2006,
    author = {T.~Kotnik and H.~J.~J.~te~Riele},
    title = {The {M}ertens Conjecture Revisited},
    booktitle = {Algorithmic Number Theory},
    series = {Lecture Notes in Computer Science},
    volume = {4076/2006},
    pages = {156-167},
    year = {2006}
}

@phdthesis{Pion1999,
    author={S. Pion},
    title={De la {G}\'eom\'etrie {A}lgorithmique au {C}alcul {G}\'eom\'etrique},
    school={Universit{\'e} de Nice Sophia-Antipolis, France},
    year= 1999,
    month= nov,
    note = {In French}
}

@phdthesis{Men94,
    author={V. M{\'e}nissier},
    title={Arithm{\'e}tique Exacte},
    school={Universit{\'e} Pierre et Marie Curie, Paris},
    year= 1994,
    month= dec,
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}

@phdthesis{Mencer2000,
    author={Oskar Mencer},
    title={Rational Arithmetic Units in Computer Systems},
    school={Stanford University},
    year= 2000
}

@article{MenSemMorDel2000,
    author={Oskar Mencer and Luc Semeria and Martin Morf and Jean-Marc Delosme},
    title={Application of Reconfigurable {CORDIC} Architectures},
    journal={Journal of VLSI Signal Processing},
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    month= mar
}

@phdthesis{Mer94,
    author={X.~Merrheim},
    title={Bases discr{\`e}tes et calcul des fonctions {\'e}l{\'e}mentaires par mat{\'e}riel (in {F}rench)},
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    year= 1994,
    month= feb,
    key={Mer94}
}

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@article{MetGou95,
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    pages={53--65}
}

@article{MHR90,
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@article{MicMor97,
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    month= sep,
    number= 9
}

@inproceedings{MMF07,
    author={Michelucci, D. and Moreau, J.-M. and Foufou, S.},
    title={{Robustness and Randomness}},
    booktitle={Reliable Implementation of Real Numbers Algorithms: Theory and Practice},
    year= 2007,
    publisher={Springer-Verlag, Berlin},
    editor={P. Hertling and C. Hoffmann and W. Luther and N. Revol},
    pages={???},
    series={Lecture Notes in Computer Science},
    volume= {???}
}

@article{MigMulPey2000,
    author={A. Mignotte and J.M. Muller and O. Peyran},
    title={Synthesis for Mixed Arithmetic},
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    volume= 5,
    year= 2000,
    month= feb,
    number= 1
}

@article{MK71,
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    journal={{IEEE} Transactions on Computers},
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    year= 1971,
    month= feb,
    number= 2,
    keywords={multiplication}
}

@inproceedings{MK95,
    author={A.~Munk-Nielsen and P.~Kornerup},
    title={MSB-first Digit-Serial Arithmetic},
    booktitle={Real Numbers and Computers (Saint Etienne, France)},
    year= 1995,
    editor={Bajard and Michelucci and Moreau and Muller},
    key={MK95}
}

@article{MM73,
    author={J.~D. Marasa and D.~W. Matula},
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    year= 1973,
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    month= jun,
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}

@inproceedings{MM94,
    author={A. Mignotte and J.~M. Muller},
    title={Overview of Synthesis and Arithmetic},
    booktitle={IFIP Workshop on Logic and Architecture Synthesis},
    year= 1994,
    month= dec,
    location={Grenoble, France}
}

@techreport{MM96,
    author={A. Munk-Nielsen and J.~M. Muller},
    title={On-line Algorithms for Computing Exponentials},
    institution={Laboratoire LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon},
    year= 1996,
    type={Research Report},
    key={MM96}
}

@article{MMM93,
    author={C. Mazenc and X. Merrheim and J.~M. Muller},
    title={Computing functions $cos^{-1}$ and $sin^{-1}$ using {CORDIC}},
    journal={{IEEE} Transactions on Computers},
    volume= 42,
    year= 1993,
    pages={118-122},
    month= jan,
    number= 1,
    keywords={cordic}
}

@inbook{MMP95,
    author={A. Mignotte and J.~M. Muller and O. Peyran},
    title={The influence of modern computer arithmetic on synthesis},
    year= 1995,
    publisher={Chapman et Hall},
    booktitle={Novel approaches in logic and architectural synthesis}
}

@inproceedings{MMP96,
    author={A.~Mignotte and J.~M.~Muller and O.~Peyran},
    title={Mixed Arithmetics: Introduction and Design Structure},
    booktitle={MPCS'96 (Second International Conference on Masssively Parallel Computing
        Systems)},
    year= 1996,
    month= may,
    key={MMP96},
    location={Ischia, Italy}
}

@inproceedings{MMP96a,
    author={A.~Mignotte and J.~M.~Muller and O.~Peyran},
    title={A Model for Using Redundant Number Systems in Special-Purpose Architectures},
    booktitle={Proceedings of CESA'96 (IMACS Multiconference Computational Engineering
        in Systems Applications)},
    year= 1996,
    month= jul,
    key={MMP96a},
    location={Lille, France}
}

@inproceedings{MMP96b,
    author={A.~Mignotte and J.M.~Muller and O.~Peyran},
    title={Am{\'e}lioration des Calculs par l'Arithm{\'e}tique Mixte},
    booktitle={4{\`e}me Symposium Architectures Nouvelles de Machines},
    year= 1996,
    month= feb,
    key={MMP96b}
}

@inproceedings{MMS74,
    author={G.~W. McIver and R.~W. Miller and T.~G. O'Shaughnessy},
    title={A monolithic 16x16 digital multiplier},
    booktitle={IEEE International Solid-State circuits conference digest of technical papers},
    year= 1974,
    pages={231-233},
    keywords={multiplication},
    note={Reprinted in E.~E. Swartzlander, {\em Computer Arithmetic\/}, Vol. 2, IEEE
        Computer Society Press, Los Alamitos, CA, 1990}
}

@inproceedings{MMY93,
    author={X. Merrheim and J.~M. Muller and H.~J. Yeh},
    title={Fast evaluation of polynomials and inverses of polynomials},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={186-192},
    location={Windsor, Canada},
    keywords={polynomial evaluation}
}

@inproceedings{MN96,
    author={A. Munk-Nielsen and J.~M. Muller},
    title={On-Line Operators for Complex Arithmetics},
    booktitle={MPCS'96 (Second International Conference on Masssively Parallel Computing
        Systems)},
    year= 1996,
    month= may,
    key={MN96},
    location={Ischia, Italy}
}

@inproceedings{MN96a,
    author={A.~Munk-Nielsen and J.~M.~Muller},
    title={On-line Algorithms for Computing Exponentials and Logarithms},
    booktitle={Proceedings of Europar'96, Lecture Notes in Computer Science 1124},
    year= 1996,
    month= aug,
    publisher={Springer-Verlag, Berlin},
    key={MN96a},
    location={Lyon, France}
}

@inproceedings{MN96b,
    author={A. Munk-Nielsen and J.~M. Muller},
    title={Borrow-Save Adders for Real and Complex Number Systems},
    booktitle={Real Numbers and computers~2},
    year= 1996,
    month= apr,
    key={MN96b},
    location={Marseille, France}
}

@article{Moller1965,
    author={O. M\o{}ller},
    title={Quasi Double-Precision in Floating-Point Addition},
    journal={BIT},
    volume={5},
    year={1965},
    pages={37--50},
    key={Moller1965}
}
@article{Moller1965b,
    author={O. M\o{}ller},
    title={Note on Quasi Double-Precision},
    journal={BIT},
    volume={5},
    year={1965},
    pages={251--255}
}


@article{Mon85,
    author={P.~Montgomery},
    title={Modular Multiplication Without Trial Division},
    journal={Mathematics of Computation},
    volume={44},
    year={1985},
    pages={519--521},
    number={170},
    key={Mon85}
}

@article{Per02,
    author={C.~Percival},
    title={Rapid multiplication modulo the sum and difference of
                  highly composite numbers},
    journal={Mathematics of Computation},
    volume={72},
    year={2002},
    pages={387--395}
}



@article{BrePerZim07,
    author={R.~P.~Brent and C.~Percival and P.~Zimmermann},
    title={Error Bounds on Complex Floating-Point Multiplication},
    journal={Mathematics of Computation},
    volume={76},
    year={2007},
    pages={1469--1481}
}


@article{MonLan2001,
    author={P. Montuschi and T. Lang},
    title={Boosting Very-High Radix Division with Prescaling and Selection by Rounding},
    journal={{IEEE} Transactions on Computers},
    volume={50},
    year={2005},
    pages={13--27},
    month={jan},
    number={1},
    key={MonLan2001}
}

@inproceedings{MonLan99,
    author={Paolo Montuschi and Tomas Lang},
    title={Boosting Very-High Radix Division with Prescaling and Selection by Rounding},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic (Adelaide,
        Australia)},
    year= 1999,
    month= apr,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={Koren and Kornerup},
    pages={52--59}
}

@article{Montgomery2005,
    author={P.~Montgomery},
    title={Five, Six, and Seven-Term {K}aratsuba-Like Formulae},
    journal={{IEEE} Transactions on Computers},
    volume={54},
    year={2005},
    pages={362--369},
    month= mar,
    number={3},
    key={Montgomery2005}
}

@book{Moo63,
    author={R.~E. Moore},
    title={Interval Analysis},
    publisher={Prentice-Hall, Englewood Cliffs, NJ},
    year= 1963,
    keywords={accuracy control,interval arithmetic}
}
@BOOK{Moore79,
        AUTHOR             = {Moore, R.~E. and Bierbaum, F.},
        PUBLISHER          = {SIAM Studies in Applied Mathematics, Philadelphia, PA},
        TITLE              = {Methods and applications of interval analysis},
        YEAR               = {1979}
}


@article{MooLynKau98,
  author    = {J. S. Moore and T. Lynch and M. Kaufmann},
  title     = {A Mechanically Checked Proof of the Correctness of the
               Kernel of the {AMD5K86} Floating Point Division Algorithm},
  journal   = {IEEE Transactions on Computers},
  volume    = {47},
  number    = {9},
  pages     = {913--926},
  month     = sep,
  year      = {1998}
}

@phdthesis{Mor90,
    author={F. Morain},
    title={Courbes elliptiques et tests de primalit{\'e}},
    school={Universit{\'e} Claude Bernard},
    year= 1990,
    month= sep,
    address={Lyon, France},
    keywords={prime numbers}
}

@article{Mos97,
    author={David Mosberger},
    title={Linux and the Alpha, How to Make your Application Fly, Part 2},
    journal={Linux Journal},
    volume={1997},
    year={1997},
    key={Mos97}
}

@article{MP89,
    author={K.~K. Primlani and J.~L. Meador},
    title={A nonredundant radix-4 serial multiplier},
    journal={IEEE journal of solid-state circuits},
    volume= 24,
    year= 1989,
    pages={1729-1736},
    keywords={bit-serial arithmetic,multiplication}
}

@inproceedings{MP91,
    author={S.~N. Parikh and D.~W. Matula},
    title={A redundant binary euclidean GCD algorithm},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={220-225},
    location={Grenoble, France},
    keywords={GCD}
}

@unpublished{dpe,
    author={P. P{\'e}lissier and P. Zimmermann},
    title={The {DPE} Library},
    note={Available at \url{http://www.loria.fr/~zimmerma/free/dpe-1.4.tar.gz}}
}

@article{magma,
author     = {Bosma, W. and Cannon, J. and Playoust, C.},
title      = {The {Magma} algebra system. {I. The} user language.},
journal = {Journal of Symbolic Computation},
pages = {235--265},
year = 1997,
volume = 24,
number = {3--4}}




@article{MPPZ88,
    author={D.J. Magenheimer and L. Peters and K.W. Pettis and D. Zuras},
    title={Integer Multiplication and Division on the {HP} Precision Architecture},
    journal={{IEEE} Transactions on Computers},
    volume={37},
    year={1988},
    pages={980--990},
    month= aug,
    number={8},
    key={MPPZ88}
}

@inproceedings{MPS91,
    author={M. Mehta and V. Parmar and E.~E. Swartzlander},
    title={High-speed multiplier design using multi-input counter and compressor circuits},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={43-50},
    location={Grenoble, France},
    keywords={multiplication}
}

@inproceedings{MRR91,
    author={M. Muller and C. Rub and W. Rulling},
    title={Exact accumulation of floating-point numbers},
    booktitle={Proceedings of the 10th IEEE Symposium on Computer Arithmetic},
    year= 1991,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P. Kornerup and D.~W. Matula},
    pages={64-69},
    location={Grenoble, France},
    keywords={accuracy control,exact arithmetic,floating-point arithmetic}
}

@article{MS83,
    author={A. Sakurai and S. Muroga},
    title={Parallel binary adders with a minimum number of connections},
    journal={{IEEE} Transactions on Computers},
    volume={C-32},
    year= 1983,
    pages={969-976},
    keywords={addition}
}

@inproceedings{MS88,
    author={J.~M. Muller and F. Siebert-Roch},
    title={{VLSI} manipulation of polynomials},
    booktitle={Computer algebra and parallelism},
    year= 1988,
    publisher={Academic Press, New York},
    editor={J. Della Dora and J. Fitch}
}

@inproceedings{MS93,
    author={D.~Das Sarma and D.~W. Matula},
    title={Measuring the accuracy of {ROM} reciprocal tables},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={95-102},
    location={Windsor, Canada}
}

@inproceedings{MST93,
    author={J.~D. Mellot and J.~C. Smith and F.~J. Taylor},
    title={The Gauss machine: a Galois-enhanced quadratic residue number system systolic
        array},
    booktitle={Proceedings of the 11th IEEE Symposium on Computer Arithmetic},
    year= 1993,
    month= jun,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={E.~E. Swartzlander and M.~J.~Irwin and J.~Jullien},
    pages={156-162},
    location={Windsor, Canada},
    keywords={finite fields,residue number systems}
}

@inproceedings{MST95,
    author={J.-M. Muller and O. Scherbyna and A. Tisserand},
    title={Semi-Logarithmic Number Systems},
    booktitle={Proceedings of the 12th IEEE Symposium on Computer Arithmetic},
    year= 1995,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    location={Bath, UK}
}

@article{MST98,
    author={J.-M.~Muller and A.~Scherbyna and A.~Tisserand},
    title={Semi-Logarithmic Number Systems},
    journal={{IEEE} Transactions on Computers},
    volume= 47,
    year= 1998,
    month= feb,
    number= 2,
    key={MST98}
}

@article{MT88,
    author={J.-M. Muller and D. Trystram},
    title={Architectures pour le calcul de la transform{\'e}e de Fourier discr{\`e}te},
    journal={Traitement du Signal},
    volume= 5,
    year= 1988,
    number= 6,
    keywords={FFT}
}

@inproceedings{MT88a,
    author={J.-M. Muller and D. Trystram},
    title={Perfect Shuffle {VLSI} implementation: applications to sorting and {FFT}
        computation},
    booktitle={CONPAR88},
    year= 1988,
    month= sep,
    location={Manchester,UK},
    keywords={FFT,on-line arithmetic}
}

@inproceedings{MT88b,
    author={J.-M. Muller and D. Trystram},
    title={A {VLSI} architecture for the discrete Fourier transform},
    booktitle={Parallel Processing, Proceedings of the IFIP WG 10.3 Working Conference
        on Parallel Processing},
    year= 1988,
    month= apr,
    publisher={North-Holland},
    editor={M. Cosnard, M.~H. Barton and M. Vanneschi},
    location={Pisa, Italy},
    keywords={FFT,on-line arithmetic}
}

@inproceedings{MT95,
    author={J.-M. Muller and A. Tisserand},
    title={Towards exact rounding of the elementary functions},
    booktitle={Scientific Computing and Validated Numerics ({P}roceedings of {SCAN'95})},
    year= 1996,
    publisher={Akademie Verlag},
    editor={Alefeld and Frommer and Lang},
    key={MT95},
    location={Wuppertal, Germany}
}

@inproceedings{MTV97,
    author={J.-M.~Muller and A.~Tisserand and J.M.~Vincent},
    title={Asynchronous sub-logarithmic adders},
    booktitle={Proceedings of the 1997 IEEE Pacific Rim Conference on Communication, Computers
        and Signal Processing (PACRIM97)},
    year= 1997,
    month= aug,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={A.~Bhargava},
    key={MTV97}
}

@inproceedings{Mul03,
    author={J.-M.~Muller},
    title={``Partially Rounded'' Small-Order Approximations for Accurate, Hardware-Oriented,
        Table-Based Methods},
    booktitle={Proceedings of the 16th {IEEE} Symposium on Computer Arithmetic ({ARITH}16)},
    year={2003},
    month= jun,
    publisher={{IEEE} Computer Society Press, Los Alamitos, CA},
    editor={Bajard and Schulte},
    pages={114--121},
    key={Mul03},
    location={Santiago de Compostela, Spain}
}

@article{Mul2000,
    author={J.-M. Muller},
    title={Vers Des Primitives Propres En Arithm{\'e}tique Des Ordinateurs},
    journal={Technique et Science Informatiques},
    volume= 19 ,
    year= 2000,
    month= jan
}

@article{Mul85,
    author={J.-M. Muller},
    title={Discrete basis and Computation of elementary functions},
    journal={{IEEE} Transactions on Computers},
    volume={C-34},
    year= 1985,
    month= sep,
    number= 9,
    keywords={cordic,elementary functions,shift-and-add algorithms}
}

@phdthesis{Mul85a,
    author={J.-M. Muller},
    title={M{\'e}thodologies de calcul des fonctions {\'e}l{\'e}mentaires (in {F}rench)},
    school={Institut National Polytechnique de Grenoble, France},
    year= 1985,
    month= sep,
    keywords={cordic,elementary functions,exponential,floating-point arithmetic,logarithm,shift-and-add
        algorithms,square root,trigonometric functions}
}

@article{Mul86,
    author={J.-M. Muller},
    title={Une m{\'e}thodologie du calcul hardware des fonctions {\'e}l{\'e}mentaires (in {F}rench)},
    journal={M2AN},
    volume= 20,
    year= 1986,
    pages={667-695},
    month= dec,
    number= 4,
    key={Mul86},
    keywords={elementary functions,shift-and-add algorithms}
}

@book{Mul89,
    author={J.-M. Muller},
    title={Arithm{\'e}tique des Ordinateurs},
    publisher={Masson, Paris},
    year= 1989,
    note = {In French},
    keywords={accuracy control,addition,cordic,division,elementary functions,exponential,floating-point
        arithmetic,interval arithmetic,logarithm,multiplication,number systems,on-line
        arithmetic,polynomial approximations,rational approximations,redundant
        number systems,residue number systems,shift-and-add algorithms,square root,survey
        on computer arithmetic,trigonometric functions}
}

@inproceedings{Mul91a,
    author={J.-M. Muller},
    title={On-line computations: a survey and some new results},
    booktitle={IFIP Workshop on algorithms and parallel {VLSI} architectures},
    year= 1991,
    month= jun,
    location={Bonas, France},
    keywords={on-line arithmetic},
    edition={North Holland}
}

@article{Mul94,
    author={J.-M. Muller},
    title={Some characterizations of functions computable in on-line arithmetic},
    journal={{IEEE} Transactions on Computers},
    volume= 43,
    year= 1994,
    month= jun,
    number= 6,
    key={Mul94},
    keywords={on-line arithmetic}
}

@inproceedings{Mul94a,
    author={J.-M. Muller},
    title={Exotic Systems for Representing Numbers},
    booktitle={4th DGCI},
    year= 1994,
    month= sep,
    key={Mul94a},
    location={Grenoble, France},
    keywords={survey on computer arithmetic}
}

@article{Mul95,
    author={J.-M. Muller},
    title={Ordinateurs en Qu{\^e}te d'Arithm{\'e}tique},
    journal={La Recherche},
    year= 1995,
    month= jul,
    keywords={survey on computer arithmetic}
}

@article{Mul95a,
    author={J.-M. Muller},
    title={Algorithmes de division pour microprocesseurs: illustration {\`a} l'aide du
        ``bug'' du Pentium},
    journal={Technique et Science Informatiques},
    volume= 14,
    year= 1995,
    month= oct,
    number= 8,
    key={Mul95a}
}

@book{Mul97,
    author={J.-M.~Muller},
    title={Elementary Functions, Algorithms and Implementation},
    publisher={Birkhauser, Boston},
    year= 1997,
    key={Mul97},
    issn_isbn={ISBN 0-8176-3990-X}
}

@inproceedings{Mul98,
    author={J.-M. Muller},
    title={Table Methods for Evaluating Functions: A Survey},
    booktitle={{SCAN'98}},
    year= 1998,
    month= sep,
    location={Budapest, Hungary}
}

@article{Mul99,
    author={J.-M. Muller},
    title={A Few Results on Table-Based Methods},
    journal={Reliable Computing},
    volume= 5,
    year= 1999,
    pages={279--288},
    month= aug,
    number= 3 ,
    key={Mul99}
}

@techreport{Muller2005,
    author={J.-M.~Muller},
    title={On the definition of ulp$(x)$},
    institution={{LIP} Laboratory, ENS Lyon},
    year={2005},
    address={\url{ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2005/RR2005-09.pdf}},
    number={2005-09}
}

@book{Muller2006,
    author={J.-M. Muller},
    title={Elementary Functions, Algorithms and Implementation},
    year={2006},
    edition={2nd},
    publisher={Birkh{\"a}user Boston, MA},
    isbn={0-8176-4372-9 }
}

@inproceedings{Muller2006a,
    author={J.-M. Muller},
    title={Generating Functions at Compile-Time},
    booktitle={proc. 40th Conference on Signals, Systems and Computers},
    year={2006},
    month= nov,
    address={Pacific Grove, CA}
}

@techreport{MulNicRob2003,
    author={J.-M. Muller and J.-L. Nicolas and X. Roblot},
    title={Nombres de Solutions dans une Binade de l'Equation $a^2+b^2 = c^2+c$},
    institution={LIP},
    year={2003},
    address={LIP, ENS Lyon},
    number={2003-45}
}

@article{MulNicRob2004,
    author={J.-M.~Muller and J.-L.~Nicolas and X.~Roblot},
    title={Nombre de Solutions dans une Binade de l'Equation $a^2+b^2=c^2+c$ (in {F}rench)},
    journal={l'Enseignement Math{\'e}matique},
    volume={50},
    year={2004},
    pages={147--182}
}

@article{MY91,
    author={P.~Midy and Y.~Yakovlev},
    title={Computing some elementary functions of a complex variable},
    journal={Mathematics and Computers in Simulation},
    volume= 33,
    year= 1991,
    pages={33--49},
    key={MY91}
}

@article{MZ86,
    author={D. Zuras and W.~H. McAllister},
    title={Balanced delays trees and combinatorial division in {VLSI}},
    journal={IEEE journal of solid-state circuits},
    volume={SC-21},
    year= 1986,
    pages={814-819},
    keywords={division}
}

@article{Nak86,
    author={S. Nakamura},
    title={Algorithms for iterative array multiplication},
    journal={{IEEE} Transactions on Computers},
    volume={C-35},
    year= 1986,
    month= aug,
    number= 8,
    keywords={multiplication}
}

@article{Nak88,
    author={Y. Nakayama and others},
    title={A GaAs 16x16 bit parallel multiplier},
    journal={IEEE journal of solid-state circuits},
    volume={SC-18},
    year= 1983,
    pages={599-603},
    keywords={multiplication}
}

@article{Nak89,
    author={T. Nakayama and others},
    title={A 6.7-Mflops floating-point coprocessor with vector/matrix instructions},
    journal={IEEE journal of solid-state circuits},
    volume= 24,
    year= 1989,
    pages={1324-1330},
    keywords={floating-point arithmetic}
}

@inproceedings{NanLan99,
    author={Alberto Nanarelli and Tomas Lang},
    title={Low-Power Division: Comparison Among Implementations of Radix 4, 8 and 16},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic (Adelaide,
        Australia)},
    year= 1999,
    month= apr,
    publisher={Computer Society Press, Los Alamitos, CA},
    editor={Koren and Kornerup},
    pages={60--67}
}

@article{Nav83,
    author={R. Nave},
    title={Implementation of Transcendental Functions on a Numerics Processor},
    journal={Microprocessing and Microprogramming},
    volume= 11,
    year= 1983,
    pages={221--225},
    key={Nav83}
}

@Article{Neumaier:1985:IPR,
  author =       "A. Neumaier",
  title =        "Inner Product Rounding Error Analysis in the Presence
                 of Underflow",
  journal =      "Computing",
  volume =       "34",
  pages =        "365--373",
  year =         "1985",
}

@BOOK{Neumaier90,
        AUTHOR             = {Neumaier, A.},
        PUBLISHER          = {Cambridge University Press, Cambridge, UK},
        TITLE              = {Interval methods for systems of equations},
        YEAR               = {1990}
}

@article{NB92,
    author={K.~C.~Ng and K.~H.~Bierman},
    title={Getting the Right Answer for the Trigonometric Functions},
    journal={SunProgrammer},
    year={Spring 1992},
    key={NB92}
}

@TechReport{SunInterval2002,
  title = 	 {Interval Arithmetic in High Performance Technical Computing},
  author =  {{Sun Microsystems}},
  year = 	 2002,
  NOmonth =	 sep,
  key =		 {Sun}
}


@book{Newton1664,
    author={I.~Newton},
    title={Methodus Fluxionem et Serierum Infinitarum},
    year={1664--1671},
    key={Newton1664}
}

@phdthesis{Nie97,
    author={Asger Munk Nielsen},
    title={Number Systems and Digit Serial Arithmetic},
    school={Dept. of Mathematics and Computer Science, Odense University, Denmark},
    year= 1997
}

@article{NieMatLyuEve2000,
    author={A.M. Nielsen and D.W. Matula and C.N. Lyu and G. Even},
    title={An {IEEE} Compliant Floating-Point Adder That Conforms with the Pipelined
        Packet-Forwarding Paradigm},
    journal={{IEEE} Transactions on Computers},
    volume= 49,
    year= 2000,
    pages={33--47},
    month= jan,
    number= 1
}

@ARTICLE{Nie03,
        AUTHOR             = {Nievergelt, Y.},
        JOURNAL            = AcmToms,
        NUMBER             = {1},
        PAGES              = {27--48},
        TITLE              = {Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit},
        VOLUME             = {29},
        YEAR               = {2003}
}

@article{NNW87,
    author={K. Washio and K. Nakazato and T. Nakamura},
    title={2.7 ns 8x8-bit parallel array multiplier using sidewall base contact structure},
    journal={IEEE journal of solid-state circuits},
    volume={SC-22},
    year= 1987,
    pages={613-614},
    keywords={multiplication}
}

@article{Nol86,
    author={T. Noll and others},
    title={A pipelined 330-MHz multiplier},
    journal={IEEE journal of solid-state circuits},
    volume={SC-21},
    year= 1986,
    pages={411-416}
}

@article{NP87,
    author={C. Neaderhouser Purdy and G.~B. Purdy},
    title={Integer division in linear time with bounded fan-in},
    journal={{IEEE} Transactions on Computers},
    volume={C-36},
    year= 1987,
    pages={640-644},
    keywords={division}
}

@article{NW95,
    author={Y.~V. Nesterenko and M.~Waldschmidt},
    title={On the approximation of the values of exponential function and logarithm
        by algebraic numbers (in {R}ussian)},
    journal={Mat. Zapiski},
    volume= 2,
    year= 1996,
    pages={23--42},
    key={NW95},
    note = {Available in English at \url{http://www.math.jussieu.fr/~miw/articles/ps/Nesterenko.ps}}
}



@inproceedings{OABVZ95,
    author={R.~R.~Osoroi and E.~Antelo and J.~D.~Bruguera and J.~Villalba and E.~Zapata},
    title={Digit On-line Large Radix {CORDIC} Rotator},
    booktitle={Proceedings of ASAP-95 (Strasbourg, France)},
    year= 1995,
    month= jul,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={P.~Cappello and C.~Mongenet and G.~R.~Perrin and P.~Quinton and Y.~Robert},
    pages={246--257},
    key={OABVZ95}
}

@phdthesis{Obe96,
    author={S.~F.~Oberman},
    title={Design issues in high performance floating point arithmetic units},
    school={Dept. of Electrical Engineering, Stanford University, Palo Alto, CA},
    year= 1996,
    month= nov,
    key={Obe96}
}

@inproceedings{Obe99,
    author={S. F. Oberman},
    title={Floating Point Division and Square Root Algorithms and 
           Implementation in the {AMD-K7} Microprocessor},
    booktitle={Proceedings of the 14th {IEEE} Symposium on Computer Arithmetic 
               (Adelaide, Australia)},
    year= 1999,
    month= apr,
    publisher={IEEE Computer Society Press, Los Alamitos, CA},
    editor={I.~Koren and P.~Kornerup},
    pages={106--115}
}

@inproceedings{OBPV2003,
    author={S.~Berna \¨Ors and Lejla Batina and B.~Preneel and J.~Vanderwalle},
    title={Hardware Implementation of a Montgomery Modular Multiplier in a Systolic
        Array},
    booktitle={Proceedings of the 17th International Parallel and Distributed Processing
        Symposium},
    year={2003},
    publisher={IEEE Computer Society},
    key={OBPV2003}
}

@inproceedings{OF96,
    author={S.~Oberman and M.~J.~Flynn},
    title={Implementing Division and Other Floating-Point Operations: A System Perspective},
    booktitle={Scientific Computing and Validated Numerics (Proceedings of SCAN'95)},
    year= 1996,
    publisher={Akademie Verlag, Berlin},
    editor={Alefeld and Frommer and Lang},
    pages={18--24},
    key={OF96},
    chapter={Implementing Division and Other Floating-Point Operations: A System Perspective}
}

@techreport{OF96a,
    author={S.~F.~Oberman and M.~J.~Flynn},
    title={Fast {IEEE} Rounding for Division by Functional Iteration},
    institution={Computer Systems Laboratory, Dept. on Electrical Engineering and Computer
        Science Stanford University},
    year= 1996,
    month= jul,
    number={CSL-TR-96-700},
    key={OF96a}
}

@article{OF97,
    author={S.~F.~Oberman and M.~J.~Flynn},
    title={Design Issues in Division and Other Floating-Point Operations},
    journal={{IEEE} Transactions on Computers},
    volume= 46,
    year= 1997,
    pages={154--161},
    month= feb,
    number= 2,
    key={OF97},
    keywords={division}
}

@article{OF97a,
    author={S.~F. Oberman and M.~J. Flynn},
    title={Division Algorithms and Implementations},
    journal={{IEEE} Transactions on Computers},
    volume={46},
    year={1997},
    pages={833--854},
    number={8}
}

@Article{Anderson:1999:DAF,
  author =       "I. J. Anderson",
  title =        "A Distillation Algorithm for Floating-Point
                 Summation",
  journal =      "SIAM Journal on Scientific Computing",
  volume =       "20",
  number =       "5",
  pages =        "1797--1806",
  year =         "1999",
}



@article{RuOgOi07I,
author = {S. M. Rump and T. Ogita and S. Oishi},
collaboration = {},
title = {Accurate Floating-Point Summation Part {I}: Faithful Rounding},
publisher = {SIAM},
year = {2008},
journal = {SIAM Journal on Scientific Computing},
volume = {31},
number = {1},
pages = {189-224},
keywords = {maximally accurate summation; faithful rounding; error-free transformation; distillation; high accuracy; extended and mixed precision basic linear algebra subprograms; XBLAS; error analysis},
url = {http://link.aip.org/link/?SCE/31/189/1},
doi = {10.1137/050645671}
}


@Article{RuOgOi07II,
  author = 	 {S. M. Rump and T. Ogita and S. Oishi},
  title = 	 {Accurate Floating-point Summation Part {II}: Sign, {K}-fold Faithful
                 and Rounding to Nearest},
  journal = 	 {SIAM Journal on Scientific Computing},
  year = 	 {2005--2008},
  OPTkey = 	 {},
  OPTvolume = 	 {},
  OPTnumber = 	 {},
  OPTpages = 	 {},
  OPTmonth = 	 {},
  note = 	 {Submitted for publication}
}

@TechReport{OgRuOi05,
  author = 	 {T. Ogita and S. M. Rump and S. Oishi},
  title = 	 {Verified solutions of linear systems without directed rounding},
  institution =  {Advanced Research Institute for Science and Engineering, Waseda University, Tokyo, Japan},
  year = 	 {2005},
  number = 	 {2005-04}
}

@inproceedings{ORO04,
    author={Ogita, T. and Rump, S. and Oishi, S.},
    title={{Accurate Sum and Dot Product with Applications}},
    booktitle={Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei},
    year= 2004,
    pages = {152--155}
}

@article{ogita-rump-accurate,
 author = {T. Ogita and S. M. Rump and Oishi, S. },
 title = {Accurate Sum and Dot Product},
 journal = {SIAM Journal on Scientific Computing},
 volume = {26},
 number = {6},
 year = {2005},
 issn = {1064-8275},
 pages = {1955--1988},
 doi = {http://dx.doi.org/10.1137/030601818},
 publisher = {SIAM},
 noaddress = {Philadelphia, PA},
 }


@TECHREPORT{ROO05,
        AUTHOR             = {Rump, S. and Ogita, T. and Oishi, S.},
        INSTITUTION        = {Technical Report 05.1, Faculty of Information and Communication Science, Hamburg University of Technology},
        NOTE               = {Available at \url{http://www.ti3.tu-harburg.de/paper/rump/RuOgOi06.pdf}.},
        TITLE              = {{Accurate Floating-Point Summation}},
        TYPE               = {Preprint},
        YEAR               = {2005}
}

@TECHREPORT{ABCDHT2008,
        AUTHOR             = {Amedro, B. and Bodnartchouck, V. and Caromel, D. and Delbé, C. and Huet, F. and Taboada, G. L.},
        INSTITUTION        = {Technical Report 0353, INRIA},
        NOTE               = {Available at \url{http://hal.inria.fr/inria-00312039/en}.},
        TITLE              = {Current State of {J}ava for {HP}},
        TYPE               = {Preprint},
        YEAR               = {2008}
}

@inproceedings{Rump1988,
      author = {S.~M.~Rump},
      title = {Algorithms for Verified Inclusion},
      booktitle = {Reliability in Computing, Perspectives in Computing},
      editor = {R. Moore},
      pages = {109--126},
      publisher = {Academic Press, New York},
      year = {1988}
}

@inproceedings{Olv87,
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@TECHREPORT{Parker99,
        AUTHOR             = {Parker, D.S.},
        INSTITUTION        = {Technical Report CSD-970014, UCLA Computer Science Department},
        NOTE               = {Available at \url{http://www.cs.ucla.edu/~stott/mca/}.},
        TITLE              = {{Monte Carlo Arithmetic: a framework for the statistical analysis of roundoff error}},
        TYPE               = {Technical Report},
        YEAR               = {1999}
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year = 1969
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@book{Kulisch2002:book,
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@book{Kulisch2008:book,
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@TechReport{Lefevre1999b,
  AUTHOR =	 {V. Lef\`evre},
  TITLE =	 {Multiplication by an Integer Constant},
  ADDRESS =	 {Lyon, France},
  INSTITUTION =	 {Laboratoire de l'Informatique du Parall\'elisme},
  NUMBER =	 {RR1999-06},
  YEAR =	 {1999},
  KEYWORDS =	 {multiplication,addition chains},
  ABSTRACT-URL = {http://www.ens-lyon.fr/LIP/research_reports.us.html},
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}
@InProceedings{DinLef2000:enregle,
        AUTHOR          = {de~Dinechin, F.  and V. Lef\`evre},
        TITLE           = {Constant Multipliers for {FPGA}s},
        longBOOKTITLE       = {2nd Intl Workshop on Engineering of Reconfigurable Hardware/Software Objects ({ENREGLE}), Parallel and Distributed Processing Techniques and Applications},
        BOOKTITLE       = {Parallel and Distributed Processing Techniques and Applications},
        LOCATION         = {Las Vegas, NV},
  Pages = {167-173},
        noMONTH           = jun,
        YEAR            = 2000,
        aNOTE            = {Also available as LIP research report 2000-18},
  nourl = {http://perso.ens-lyon.fr/florent.de.dinechin/recherche/publis/2000-ENREGLE.pdf}
}
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  year =         2007,
  location =      {Montpellier, France},
  longPUBLISHER =	 {IEEE Computer Society Press},
  PUBLISHER =	 {IEEE},
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  month =        jun,
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@InProceedings{DeHon2007:Arith,
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  year =         2007,
  location =      {Montpellier, France},
  longPUBLISHER =	 {IEEE Computer Society Press},
  pages = {205-213},
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@InProceedings{DetDin2007:FPL,
  author =       {Detrey, J. and de~Dinechin, F.},
  title =        {FLOATING-POINT TRIGONOMETRIC FUNCTIONS FOR {FPGAs}},
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  year =         2007,
  month =        aug,
  location =      {Amsterdam, Netherlands}
}


@article{DetDin2007:JMM,
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@InProceedings{DetDin2005:asap,
  author =       {Detrey, J. and de~Dinechin, F.},
  title =        {Table-based polynomials for fast hardware function
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  longbooktitle =    {16th Intl Conference on
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@InProceedings{DetDinPuj2007:Arith,
  author = {J. Detrey and de~Dinechin, F.  and Pujol, X.},
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  year =         2007,
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  longPUBLISHER =	 {IEEE Computer Society Press},
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@TechReport{CretDinechin2007,
  author = {I. Trestian and  O. Cre\c{t}
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  title = {{FPGA}-BASED COMPUTATION OF THE INDUCTANCE OF COILS
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  number = {ensl-00169909},
  note = {http://prunel.ccsd.cnrs.fr/ensl-00169909/},
  institution =  {\'Ecole Normale Sup\'erieure de Lyon},
  year = 2007
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  booktitle =    {18th Symposium on Computer Arithmetic},
  year =         2007,
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  longPUBLISHER =	 {IEEE Computer Society Press},
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@inproceedings{WangSchulte2007,
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}

@INPROCEEDINGS{Chu98,
  AUTHOR =	 {M. Chu and N. Weaver and K. Sulimma and A. DeHon and
                  J. Wawrzynek},
  TITLE =	 {Object Oriented Circuit-Generators in Java},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1998}
}

@INPROCEEDINGS{Luk98,
  AUTHOR =	 {N. Shirazi and W. Luk and P.Y.K. Cheung},
  TITLE =	 {Automating Production of Run-Time Reconfigurable
                  Designs},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1998}
}

@INPROCEEDINGS{Ligon98,
  AUTHOR =	 {W. B. Ligon and S. McMillan and G. Monn and
                  K. Schoonover and F. Stivers and K. D. Underwood},
  TITLE =	 {A Re-evaluation of the Practicality of
                  Floating-Point Operations on {FPGAs}},
  BOOKTITLE =	 {{FPGAs} for Custom Computing
                  Machines},
publisher={IEEE},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1998}
}


@INPROCEEDINGS{Walters98,
  AUTHOR =	 {A. Walters and P. Athanas},
  TITLE =	 {A Scalable {FIR} Filter Using 32-bit Floating-Point Complex Arithmetic on a Configurable Computing Machine},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1998}
}

@INPROCEEDINGS{Ercegovac98,
  AUTHOR =	 {A.F. Tenca and M.D. Ercegovac},
  TITLE =	 {A Variable Long-Precision Arithmetic Unit Design
                  Suitable for Reconfigurable Coprocessor
                  Architectures},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1998}
}

@manual{Virtex,
  organization = {Xilinx Corporation},
  title =	 {{Virtex 2.5V} Field Programmable Gate Arrays},
  NOmonth =	 jan,
  year =	 {2000}
}

@manual{VirtexE,
  organization = {Xilinx Corporation},
  title =	 {{Virtex E 1.8V} Field Programmable Gate Arrays},
  NOmonth =	 feb,
  year =	 {2000}
}

@manual{Virtex2,
  organization = {Xilinx Corporation},
  title =	 {{Virtex-II} Platform {FPGA} Handbook},
  NOmonth =	 dec,
  year =	 {2000}
}


@manual{XilinxKCMVirtex,
  organization = {Xilinx Corporation},
  title =	 {Constant (K) Coefficient Multiplier Generator for
                  Virtex},
  NOmonth =	 mar,
  year =	 {1999}
}

@manual{XilinxLogicore2002,
  organization = {Xilinx Corporation},
  title =	 {Sine/Cosine Lookup Table V4.2},
  NOmonth =	 nov,
  year =	 {2002},
  url = {www.xilinx.com/ipcenter/}
}

@INPROCEEDINGS{Brebner98,
  AUTHOR =	 {Brebner, Gordon},
  TITLE =	 {Field-Programmable Logic: Catalyst for New Computing
                  Paradigms},
  BOOKTITLE =	 {International Workshop on Field Programmable Logic
                  and Applications},
  YEAR =	 {1998},
 NOADDRESS =	 {Tallin, Estonia}
}

@INPROCEEDINGS{Radunovic98,
  AUTHOR =	 {Radunovic, B. and Milutinovic, V.},
  TITLE =	 {A Survey of Reconfigurable Computing Architectures},
  BOOKTITLE =	 {International Workshop on Field Programmable Logic
                  and Applications},
  YEAR =	 {1998},
 NOADDRESS =	 {Tallin, Estonia}
}

@INPROCEEDINGS{McKeever98,
  AUTHOR =	 {Luk, W. and McKeever, S.},
  TITLE =	 {Pebble: a Language for Parameterized and
                  Reconfigurable Hardware Design},
  BOOKTITLE =	 {International Workshop on Field Programmable Logic
                  and Applications},
  YEAR =	 {1998},
 NOADDRESS =	 {Tallin, Estonia}
}

@INPROCEEDINGS{LiuZhuWong98,
  AUTHOR =	 {Liu, H. and Zhu, K. and Wong, D. F.},
  TITLE =	 {Circuit Partitioning with Complex Resource
                  Constraints in {FPGAs}},
  BOOKTITLE =	 {FPGA'98, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {77-84},
  YEAR =	 {1998}
}

@INPROCEEDINGS{Takahara98,
  AUTHOR =	 {Takahara, A. and Miyazaki, T. and Murooka, T. and
                  Katayama, M. and Hayashi, K. and Tsutsui, A. and
                  Ichimori, T. and Fukami, K.},
  TITLE =	 {More Wires and Fewer {LUT}s: a Design Methodology
                  for {FPGA}s},
  BOOKTITLE =	 {FPGA'98, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {12-19},
  YEAR =	 {1998}
}

@INPROCEEDINGS{Senouci98,
  AUTHOR =	 {Senouci, S. A. and Amoura, A. and Krupnova, H. and
                  Saucier, G.},
  TITLE =	 {Timing Driven Floorplanning on Programmable
                  Hierarchical Targets},
  BOOKTITLE =	 {FPGA'98, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {85-92},
  YEAR =	 {1998}
}

@INPROCEEDINGS{DeHon99,
  AUTHOR =	 {A. DeHon},
  TITLE =	 {Balancing Interconnect and Computation in a
                  Reconfigurable Computing Array (or, why you don't
                  really want 100\% {LUT} utilization},
  BOOKTITLE =	 {FPGA'99, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {69-77},
  YEAR =	 {1999}
}

@INPROCEEDINGS{DeHon99b,
  AUTHOR =	 {W. Tsu and K. Macy and A. Joshi and R. Huang and N. Walker and T. Tung and O. Rowhani and V. George and J. Wawrzynek and A. DeHon},
  TITLE =	 {{HSRA}: High-Speed, Hierarchical Synchronous Reconfigurable Array},
  BOOKTITLE =	 {FPGA'99, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {125-133},
  YEAR =	 {1999}
}

@INPROCEEDINGS{Vuillemin99,
  AUTHOR =	 {A. Marshall and T. Stansfield and I. Kostarnov and
                  J. Vuillemin and B. Hutchings},
  TITLE =	 {A Reconfigurable Arithmetic Array for Multimedia
                  Applications},
  BOOKTITLE =	 {FPGA'99, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {135-143},
  YEAR =	 {1999}
}

@INPROCEEDINGS{Kaptanoglu99,
  AUTHOR =	 {S. Kaptanoglu and G. Bakker and A. Kundu and
                  I. Corneillet and B. Ting},
  TITLE =	 {A New High Density and Very Low Cost Reprogrammable
                  {FPGA} Architecture},
  BOOKTITLE =	 {FPGA'99, ACM/SIGDA International Symposium on
                  {FPGAs}},
 NOADDRESS =	 {Monterey, CA},
  PAGES =	 {3-12},
  YEAR =	 {1999}
}

@INPROCEEDINGS{Benyamin99,
  AUTHOR =	 {D. Benyamin and W. Luk and J. Villasenor},
  TITLE =	 {Optimizing {FPGA}-Based Vector Product Designs},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1999},
  ANNOTE= {distributed arithmetic}
}

@INPROCEEDINGS{Orlando99,
  AUTHOR =	 {G. Orlando and C. Paar},
  TITLE =	 {A Super-Serial Galois Fields Multiplier for {FPGAs}
                  and its Application to Public-Key Algorithms},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1999}
}

@INPROCEEDINGS{Leong99,
  AUTHOR =	 {M.P. Leong and M.Y. Yeung and C.K. Yeung and C.W. Fu
                  and P.A. Heng and P.H.W. Leong},
  TITLE =	 {Automatic Floating to Fixed Point Translation and
                  its Application to Post-Rendering 3D Warping},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {1999}
}

@INPROCEEDINGS{Guccione99,
  AUTHOR =	 {Guccione, S. A. and Levi, D.},
  TITLE =	 {Run-Time Parameterizable Cores},
  BOOKTITLE =	 {International Workshop on Field Programmable Logic
                  and Applications},
  PUBLISHER =	 {Springer Verlag, LNCS 1673},
 NOADDRESS =	 {Glascow},
  PAGES =	 {215-222},
  YEAR =	 {1999}
}

@article{Marchal99,
  author =	 {Marchal, P.},
  title =	 {Field-Programmable Gate Arrays},
  journal =	 {Communication of the ACM},
  volume =	 42,
  number =	 4,
  pages =	 {57-59},
  NOmonth =	 apr,
  year =	 1999
}

@article{Stewart2000,
  author =	 {Stewart, D.},
  title =	 {L'Ouest américain menacé par le béton},
  journal =	 {Le Monde Diplomatique},
  volume = 47,
  number =	 556,
  pages =	 {14},
  NOmonth =	 jul,
  year =	 2000
}



@INPROCEEDINGS{Scalera00,
  AUTHOR =	 {J. Scalera and M. Jones},
  TITLE =	 {A Run-Time Reconfigurable Plug-In for the Winamp {MP3} Player},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {2000}
}

@INPROCEEDINGS{Singh00,
  AUTHOR =	 {Satnam Singh},
  TITLE =	 {Death of the {RLOC}?},
  BOOKTITLE =	 {IEEE Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {2000}
}

@INPROCEEDINGS{Patterson00,
  AUTHOR =	 {Cameron Patterson},
  TITLE =	 {High Performance {DES} Encryption in {Virtex}(tm) {FPGAs} Using {JBits}(tm)},
  BOOKTITLE =	 {{IEEE} Symposium on {FPGAs} for Custom Computing
                  Machines},
 NOADDRESS =	 {Napa Valley, CA},
  YEAR =	 {2000}
}


@INPROCEEDINGS{Keller00,
  AUTHOR =	 {Eric Keller },
  TITLE =	 {{JRoute}: A Run-Time Routing {API} for {FPGA} Hardware},
  BOOKTITLE =	 {7th Reconfigurable Architectures Workshop},
  PUBLISHER = {LNCS 1800},
 NOADDRESS =	 {Cancun, Mexico},
  NOMONTH = may,
  YEAR =	 {2000}
}

@manual{JBits27manual,
  organization = {Xilinx Corporation},
  title =	 {The JBits 2.7 SDK for Virtex},
  year =	 {2001}
}


@INPROCEEDINGS{Downs01,
  AUTHOR =	 {J. Scalera and M. Jones},
  TITLE =	 {Cores and anti-cores: Using {JBits} as part of a mainstream design flow},
  BOOKTITLE =	 {8th Reconfigurable Architectures Workshop},
 NOADDRESS =	 {San Francisco, CA},
  NOMONTH = apr,
  YEAR =	 {2001}
}


@INPROCEEDINGS{Belanovic2002,
  AUTHOR =	 {Belanovi\'c, P. and Leeser, M.},
  TITLE =	 {A Library of Parameterized Floating-Point Modules and Their Use},
  BOOKTITLE =	 {Field Programmable Logic and Applications},
  PAGES =	 {657-666},
  SERIES       = {LNCS},
  VOLUME       = 2438,
  PUBLISHER =	 {Springer},
  NoNOMONTH        = sep,
  YEAR =	 {2002}
}

@INPROCEEDINGS{Shirazi2002,
  AUTHOR =	 {Gaffar, A. A. and Luk, W. and Cheung, P. Y. K. and Shirazi, N. and Hwang, J.},
  TITLE =	 {Automating Customisation of Floating-Point Designs},
  BOOKTITLE =	 {Field Programmable Logic and Applications},
  PAGES =	 {523-533},
  SERIES       = {LNCS},
  VOLUME       = 2438,
  PUBLISHER =	 {Springer},
   NOMONTH        = sep,
  YEAR =	 {2002}
}

@INPROCEEDINGS{Roesler2002,
  AUTHOR =	 {Roesler, E. and Nelson, B.},
  TITLE =	 {Novel Optimizations for Hardware Floating-Point Units in a Modern {FPGA} Architecture},
  BOOKTITLE =	 {Field Programmable Logic and Applications},
  PAGES =	 {637-646},
  SERIES       = {LNCS},
  VOLUME       = 2438,
  PUBLISHER =	 {Springer, Berlin},
   NOMONTH        = sep,
  YEAR =	 {2002}
}


@INPROCEEDINGS{Dido2002,
  AUTHOR =	 {J. Dido and N. Geraudie and L. Loiseau and O. Payeur and Y. Savaria and D. Poirier},
  booktitle = {Field-Programmable Gate Arrays},
  NOLocation =	 {Monterey, CA},
  PAGES =        {50--55},
  TITLE =	 {A Flexible Floating-Point Format for Optimizing Data-Paths and Operators in {FPGA} Based {DSP}s},
  NoNOMONTH =	 feb,
  publisher = {ACM},
  YEAR =	 2002
}


@INPROCEEDINGS{Lienhart2002,
  AUTHOR =	 {G. Lienhart and A. Kugel and R. M\"anner},
  TITLE =	 {Using Floating-Point Arithmetic on {FPGA}s to Accelerate Scientific {N}-Body Simulations},
  BOOKTITLE =	 {{FPGAs} for Custom Computing Machines},
  NOlocation =	 {Napa Valley, CA},
  publisher={IEEE},
  YEAR =	 2002
}


@InProceedings{DossRiley2004:fccm,
  author =	 {Doss, C. and Riley, Jr., R.~L.},
  title =	 {{FPGA}-based implementation of a robust {IEEE}-754 exponential unit},
  booktitle =	 {Field-Programmable Custom Computing Machines},
  pages =        {229-238},
  Noeditor =	 {Arnold, J.M. and Pocek, K.L.},
  publisher =	 {IEEE},
  noNOmonth =        apr,
  year =	 {2004},
  doi =          {10.1109/FCCM.2004.38}
}




@InProceedings{OrtHumDurPra2003:fpl,
  author = 	 {F. Ortiz and J. Humphrey  and J. Durbano  and D. Prather},
  title = 	 {A Study on the Design of Floating-Point Functions in {FPGAs}},
  booktitle =	 {Field Programmable Logic and Applications},
  pages =	 {1131--1135},
  year =	 2003,
   PUBLISHER    = {Springer, Berlin},
   SERIES       = {LNCS},
   VOLUME       = 2778,
  nolocation =	 {Lisbon, Portugal},
  NOmonth =	 sep
}

@inproceedings{deLorimier2005,
 author = {M. deLorimier and A. DeHon},
 title = {Floating-point sparse matrix-vector multiply for {FPGAs}},
 booktitle = {Field-Programmable Gate Arrays},
 year = {2005},
 isbn = {1-59593-029-9},
 pages = {75--85},
 NOlocation = {Monterey, CA},
 doi = {http://doi.acm.org/10.1145/1046192.1046203},
 publisher = {ACM},
 NOaddress = {New York, NY}
 }

@inproceedings{DouEtc2005,
 author = {Dou, Y. and S. Vassiliadis and G. K. Kuzmanov and G. N. Gaydadjiev},
 title = {64-bit floating-point {FPGA} matrix multiplication},
 booktitle = {Field-Programmable Gate Arrays},
 year = {2005},
 isbn = {1-59593-029-9},
 pages = {86--95},
 NOlocation = {Monterey, CA},
 doi = {http://doi.acm.org/10.1145/1046192.1046204},
 publisher = {ACM},
 NOaddress = {New York, NY}
 }

@inproceedings{Underwood2004,
 author = {K. Underwood},
 title = {{FPGA}s vs. {CPU}s: Trends in Peak Floating-Point
                Performance},
 booktitle = {ACM/SIGDA Field-Programmable Gate Arrays},
 year = {2004},
 isbn = {1-59593-029-9},
 NOlocation = {Monterey, CA},
 doi = {http://doi.acm.org/10.1145/1046192.1046204},
 publisher = {ACM},
 NOaddress = {New York, NY}
 }


@InProceedings{HasemlanEtc2005,
  author = 	 {Haselman, M and Beauchamp, M. and Underwood, K. and Hemmert, K. S.},
  title = 	 {A Comparison of Floating-Point and Logarithmic Number Systems for {FPGA}s},
  BOOKTITLE =	 {{FPGAs} for Custom Computing Machines},
  year =	 2005
}


@inproceedings{HemmertUnderwood2005,
  author    = {K. Scott Hemmert and
               K. D. Underwood},
  title     = {An Analysis of the Double-Precision Floating-Point {FFT} on
               {FPGA}s.},
  booktitle = {13th IEEE Symposium on Field-Programmable Custom Computing
               Machines},
  year      = {2005},
  NOmonth = apr,
  nopages     = {171-180},
  ee        = {http://doi.ieeecomputersociety.org/10.1109/FCCM.2005.16}
}


@inproceedings{ZhuoPrasanna2004,
author = {L. Zhuo and V. Prasanna},
title = {Scalable and Modular Algorithms for Floating-Point Matrix Multiplication on {FPGAs}},
booktitle = {Reconfigurable Architecture Workshop},
year = {2004},
publisher = {IEEE}
}

@inproceedings{GovinduEtAl2004,
author = {G. Govindu and L. Zhuo and S. Choi and V. Prasanna},
title = {Analysis of High-Performance Floating-Point Arithmetic on {FPGAs}},
booktitle = {Reconfigurable Architecture Workshop},
year = {2004},
publisher = {IEEE Computer Society}
}


@proceedings{DBLP:conf/fccm/2005,
  title     = {, 17-20 April 2005, Napa, CA, Proceedings},
  booktitle = {FCCM},
  publisher = {IEEE Computer Society},
  year      = {2005},
  isbn      = {0-7695-2445-1}
}

@InProceedings{BeauchampEtAl2006:fpl,
  author = 	 {Beauchamp, M.J.  and  Hauck, S. and   Underwood, K.D. and   Hemmert, K.S.},
  title = 	 {Architectural Modifications to Improve Floating-Point Unit Efficiency in {FPGA}s},
  booktitle =	 {Field Programmable Logic and Applications},
  pages =	 {1--6},
  year =	 2005,
  NOmonth =	 aug
}


@inproceedings{ChongEtc2007,
 author = {Yee Jern Chong and Sri Parameswaran},
 title = {Automatic application specific floating-point unit generation},
 booktitle = {Design, automation and test in Europe},
 year = {2007},
 pages = {461--466},
 nolocation = {Nice, France},
 doi = {http://doi.acm.org/10.1145/1266366.1266464},
 publisher = {ACM},
noaddress = {New York, NY},
 }



@inproceedings{RoyBanerjee2004:DAC,
 author = {Sanghamitra Roy and Prith Banerjee},
 title = {An algorithm for converting floating-point computations to fixed-point in {MATLAB} based {FPGA} design},
 booktitle = {Design Automation Conference},
 year = {2004},
 pages = {484--487},
 nolocation = {San Diego, CA},
 doi = {http://doi.acm.org/10.1145/996566.996701},
 publisher = {ACM},
noaddress = {New York, NY},
 }


@inproceedings{BeauchampEtc2006:fpga,
 author = {Michael J. Beauchamp and Scott Hauck and Keith D. Underwood and K. Scott Hemmert},
 title = {Embedded floating-point units in {FPGA}s},
 booktitle = {ACM/SIGDA international symposium on Field programmable gate arrays},
 year = {2006},
 pages = {12--20},
 nolocation = {Monterey, CA},
 doi = {http://doi.acm.org/10.1145/1117201.1117204},
 publisher = {ACM},
 noaddress = {New York, NY},
 }

@inproceedings{1188571,
 author = {Keith D. Underwood and K. Scott Hemmert and Craig Ulmer},
 title = {Architectures and {API}s: assessing requirements for delivering {FPGA} performance to applications},
 booktitle = {ACM/IEEE conference on Supercomputing},
 year = {2006},
 pages = {111},
 nolocation = {Tampa, Florida},
 doi = {http://doi.acm.org/10.1145/1188455.1188571},
 publisher = {ACM},
 noaddress = {New York, NY},
 }

@inproceedings{ZhouPrasanna2005:FPGA,
 author = {L. Zhuo and V. K. Prasanna},
 title = {Sparse Matrix-Vector multiplication on {FPGA}s},
 booktitle = {Field-Programmable Gate Arrays},
 year = {2005},
 pages = {63--74},
 nolocation = {Monterey, CA},
 doi = {http://doi.acm.org/10.1145/1046192.1046202},
 publisher = {ACM},
 noaddress = {New York, NY}
}



@inproceedings{ZhuoPrasanna2005:SC,
 author = {L. Zhuo and V. K. Prasanna},
 title = {High Performance Linear Algebra Operations on Reconfigurable Systems},
 booktitle = {Supercomputing},
 year = {2005},
 doi = {http://dx.doi.org/10.1109/SC.2005.31},
 longpublisher = {IEEE Computer Society},
 publisher = {IEEE},
 noaddress = {Washington, DC},
 }



@inproceedings{Catanzaro2005:fccm,
  author    = {Bryan Catanzaro and Brent Nelson},
  title     = {Higher Radix Floating-Point Representations for {FPGA}-Based Arithmetic},
  booktitle = {13th IEEE Symposium on Field-Programmable Custom Computing
               Machines},
  year      = {2005},
  NOmonth = apr,
  nopages     = {161-170},
  ee        = {http://doi.ieeecomputersociety.org/10.1109/FCCM.2005.16}
}

@inproceedings{Liu2006:fpga,
 author = {J. Liu and M. Chang and C.-K. Cheng},
 title = {An iterative division algorithm for {FPGA}s},
 booktitle = {Field-Programmable Gate Arrays},
 year = {2006},
 isbn = {1-59593-292-5},
 pages = {83--89},
 nolocation = {Monterey, CA},
 doi = {http://doi.acm.org/10.1145/1117201.1117213},
 publisher = {ACM},
 noaddress = {New York, NY},
 }


@InProceedings{NicholsEtAl2002,
  author = 	 {K. R. Nichols and M. A. Moussa and S. M. Areibi},
  title = 	 {FEASIBILITY OF FLOATING-POINT ARITHMETIC IN {FPGA} BASED ARTIFICIAL NEURAL
                               NETWORKS
},
  booktitle =	 {CAINE},
  pages =	 {8-13},
  year =	 2002
}


@Manual{AlteraFFT2005,
  title = 	 {{FFT}/{IFFT} Block Floating Point Scaling},
  organization =	 {Altera Corporation},
  year =	 2005,
  note =	 {Application note 404-1.0}
}

@InProceedings{Andraka2006,
  author = 	 {Ray Andraka},
  title = 	 {Hybrid Floating Point Technique Yields 1.2 Gigasample Per Second 32 to 2048 point Floating Point {FFT} in a single {FPGA}},
  booktitle =	 {High Performance Embedded Computing Workshop},
  year =	 2006
}

@inproceedings{HeEtal2006:ERSA,
  author    = {C. He and
               G. Qin and
               M. Lu and
               W. Zhao},
  title     = {Group-Alignment based Accurate Floating-Point Summation
               on {FPGA}s},
  booktitle = {Engineering of Reconfigurable Systems and Algorithms},
  year      = {2006},
  pages     = {136-142}
}

@Article{wittigEtAl2008:HPCWire,
  author =	 {D. Strenski and J. Simkins and R. Walke and R. Wittig},
  title =	 {Revaluating {FPGA}s for 64-bit Floating-Point Calculations},
  journal =	 {HPC wire},
  year =	 2008,
  month =	 may,
  day = 14,
  url={http://www.hpcwire.com/features/Revaluating_FPGAs_for_64-bit_Floating-Point_Calculations.html}
}

@INPROCEEDINGS{Langhammer2008,
  AUTHOR =	 {Martin Langhammer},
  TITLE =	 {Floating Point Datapath Synthesis for {FPGA}s},
  BOOKTITLE =	 {Field Programmable Logic and Applications},
  PAGES =	 {355-360},
  YEAR =	 {2008}
}

@inproceedings{Lee2002,
  author =       {B.~Lee and N.~Burgess},
  title =        {Parameterisable Floating-Point Operations on {FPGA}},
  booktitle =    {Thirty-Sixth Asilomar Conference on Signals, Systems, and Computers},
  pages =        {1064-1068},
  month= nov,
  volume=2,
  location =      {Pacific Grove, California},
  year =         2002
}


@inproceedings{BrisebarreMullerDinechin2008:ASAP,
  author    =  {N. Brisebarre and   de Dinechin, F. and Muller, J.-M.},
  title     =   {Integer and Floating-Point Constant Multipliers for {FPGA}s},
  booktitle = {Application-specific Systems, Architectures and Processors},
  pages = {239--244},
  PUBLISHER =	 {IEEE},
  year      =    {2008}
  }


@InProceedings{GuntoroGlesner2008,
title={High-performance {FPGA}-based floating-point adder with three inputs},
author={Guntoro, A. and Glesner, M.},
booktitle={Field Programmable Logic and Applications},
year={2008},
pages={627-630},
}

@Manual{ARMDSCLG,
	AUTHOR		= {{ARM}},
	TITLE		= {{ARM} Developer Suite: {Compilers} and Libraries Guide},
	VERSION		= {1.2},
	NUMBER		= {ARM DUI 0067D},
	ORGANIZATION	= {ARM Limited},
	MONTH		= nov,
	YEAR		= {2001},
	NOTE		= {Available at \url{http://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.dui0067d/index.html} or in PDF at \url{http://infocenter.arm.com/help/topic/com.arm.doc.dui0067d/DUI0067.pdf}.}
}

@Manual{ARMDSDG,
	AUTHOR		= {{ARM}},
	TITLE		= {{ARM} Developer Suite: {Developer} Guide},
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	ORGANIZATION	= {ARM Limited},
	MONTH		= nov,
	YEAR		= {2001},
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}

@Manual{SunNCG2005,
	AUTHOR		= {Sun},
	TITLE		= {Numerical Computation Guide -- Sun\texttrademark\ Studio 11},
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}

@Manual{SPARC64VI,
	AUTHOR		= {Fujitsu},
	TITLE		= {{SPARC64}\texttrademark\ {VI} Extensions},
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%misc{mpfr,
%        author="{The Spaces project}",
%        howpublished="\url{http://www.mpfr.org}",
%        title="{MPFR}, the multiple precision floating point reliable library, version 2.0.3", 
%        year="2004",
%}



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@misc{polylib,
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%%%%%%%%%%
%%%%%%%%%% Ajout biblio 
%%%%%%%%%%

\Sort{
  Mode{on}
  Collation{mixed}
  SortTypeOrder{pattern,key,name}
  NameOrder{ascending}
  Key{{author,editor},\year{year,note}}
  KeyOrder{descending,nulls first}
  Pattern{author+editor: "doron"}
  PatternOrder{first}
}

\@string{LNCS="Lecture Notes in Computer Science"}		  
\@string{Springer="Springer-Verlag"}	
\@string{IEEE="IEEE Computer Society Press"}
\@String{j-NUM-MATH="Numerische Mathematik"}


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  publisher =	 {IEEE}
}

@inproceedings{Rump-Habilitation83,
        AUTHOR             = {S.~Rump},
        TITLE            = {Solving Algebraic Problems with High Accuracy (Habilitationsschrift)},
        PAGES              = {51--120},
        PUBLISHER          = {Academic Press, New york, NY},
         BOOKTITLE              = {A New Approach to Scientific Computation},
        EDITOR = {Kulisch and Miranker},
        YEAR               = {1983}
}

@article{RumpZimmermannBoldoMelquiond2009,
    author = {S. Rump and P. Zimmermann and S. Boldo and G. Melquiond},
    title = {Interval Operations in Rounding to Nearest},
    journal = {BIT},
    note = {To appear},
    year = {2009}
}

@Article{collangeEtAl:TSI2008,
  author = 		  {S. Collange and M. Daumas and D. Defour},
  title = 		  {{\'E}tat de l'int\'egration de la virgule flottante dans les processeurs graphiques},
  journal = 	  {Technique et Science Informatiques},
  year = 		  2008,
  volume = 	  27,
  number = 	  6,
  pages = 	  {719--733},
  note = {In French}
}

@inproceedings{Oberman2005,
    author={Oberman, S.~F.  and  Siu, M.~Y.},
    title={A High-Performance Area-Efficient Multifunction Interpolator},
    booktitle={Proceedings of the 17th {IEEE} Symposium on Computer Arithmetic (ARITH-17)},
    year={2005},
    month= jun,
    publisher={IEEE Computer Society Press},
    nolocation={Cape Cod, MA}
}

@article{Wirthlin2004,
  author    = {Wirthlin, M. J. },
  title     = {Constant Coefficient Multiplication Using Look-Up Tables},
  journal   = {{VLSI} Signal Processing},
  volume    = 36,
  number    = 1,
  year      = 2004,
  pages     = {7-15}
}

@Article{Gustafsson2006,
  author = 		  {O. Gustafsson and  Dempster, A. G. and  K. Johansson and Macleod, M. D. },
  title = 		  {Simplified design of constant coefficient multipliers},
  journal = 	  {Circuits, Systems, and Signal Processing},
  year = 		  2006,
  volume = 	  25,
  number = 	  2,
  pages = 	  {225--251}}