Bibliography on elementary functions

[1] Fredrik Johansson. Efficient implementation of elementary functions in the medium-precision range. In 22nd IEEE Symposium on Computer Arithmetic, 2015. [ bib ]
Keywords: multiple precision, exp, log, sincos, atan
[2] Olga Kupriianova and Christoph Quirin Lauter. A domain splitting algorithm for the mathematical functions code generator. In 2014 Asilomar Conference on Signals, Systems and Computers, 2014. [ bib ]
[3] Olga Kupriianova and Christoph Lauter. Replacing branches by polynomials in vectorizable elementary functions. In Book of abstracts for 16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, 2014. [ bib ]
[4] Marat Dukhan and Richard Vuduc. Methods for high-throughput computation of elementary functions. In Parallel Processing and Applied Mathematics, LNCS 8384, pages 86--95, 2014. [ bib ]
[5] Nicolas Brunie. Contributions to computer arithmetic and applications to embedded systems. Thèse de doctorat, École normale supérieure de Lyon, 2014. [ bib | http ]
Keywords: low-level optimization, tools, correct rounding
[6] Florent de Dinechin, Pedro Echeverría, Marisa López-Vallejo, and Bogdan Pasca. Floating-point exponentiation units for reconfigurable computing. ACM Transactions on Reconfigurable Technology and Systems, 6(1), 2013. [ bib | http | .pdf ]
Keywords: exp, log, pow, fixed-point, hardware, fpga
[7] Martin Langhammer and Bogdan Pasca. Faithful single-precision floating-point tangent for FPGAs. In Field Programmable Gate Arrays, pages 39--42, New York, NY, USA, 2013. ACM/SIGDA. [ bib | DOI | http ]
Keywords: floating-point, fpga, single-precision, tangent
[8] Marat Dukhan. PeachPy: A Python framework for developing high-performance assembly kernels. In Python for High Performance and Scientific Computing, 2013. [ bib ]
[9] Claude-Pierre Jeannerod and Jingyan Jourdan-Lu. Simultaneous floating-point sine and cosine for VLIW integer processors. In 23rd IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP 2012), pages 69--76, Delft, Netherlands, February 2012. [ bib | http ]
[10] Vincenzo Innocente. Floating point in experimental HEP data processing. In 2nd CERN Openlab/INTEL Workshop on Numerical Computing, 2012. [ bib | http | http ]
[11] Danilo Piparo. The VDT mathematical library. In 2nd CERN Openlab/INTEL Workshop on Numerical Computing, 2012. [ bib | http | http ]
[12] Claude-Pierre Jeannerod, Jingyan Jourdan-Lu, Christophe Monat, and Guillaume Revy. How to Square Floats Accurately and Efficiently on the ST231 Integer Processor. In 20th IEEE Symposium on Computer Arithmetic (ARITH), pages 77--81, Tübingen, Germany, August 2011. [ bib | DOI | http ]
[13] Christophe Mouilleron and Guillaume Revy. Automatic Generation of Fast and Certified Code for Polynomial Evaluation. In 20th Symposium on Computer Arithmetic , pages 233--242, Tübingen, Germany, August 2011. [ bib | DOI | http ]
[14] Florent de Dinechin and Bogdan Pasca. Designing custom arithmetic data paths with FloPoCo. IEEE Design & Test of Computers, 28(4):18--27, July 2011. [ bib | http | .pdf ]
[15] Sylvain Chevillard, Mioara Joldes, John Harrison, and Christoph Lauter. Efficient and accurate computation of upper bounds of approximation errors. Theoretical Computer Science, 412(16):1523--1543, April 2011. [ bib | DOI | http ]
Keywords: tools, approximation, formal proof, multiple precision
[16] Florent de Dinechin, Christoph Lauter, and Guillaume Melquiond. Certifying the floating-point implementation of an elementary function using Gappa. IEEE Transactions on Computers, 60(2):242--253, February 2011. [ bib | DOI | http | .pdf ]
Keywords: formal proofs
[17] Claude-Pierre Jeannerod, Hervé Knochel, Christophe Monat, and Guillaume Revy. Computing floating-point square roots via bivariate polynomial evaluation. IEEE Transactions on Computers, 60(2):214--227, February 2011. [ bib | DOI | http ]
[18] David R. Lutz. Fused multiply-add microarchitecture comprising separate early-normalizing multiply and add pipelines. In IEEE Symposium on Computer Arithmetic, pages 123--128, 2011. [ bib | http ]
[19] Hadi Parendeh-Afshar, Arkosnato Neogy, Philip Brisk, and Paolo Ienne. Compressor tree synthesis on commercial high-performance FPGAs. ACM Transactions on Reconfigurable Technology and Systems, 4(4):39:1--39:19, 2011. [ bib ]
[20] T. Hilaire and P. Chevrel. Sensitivity-based pole and input-output errors of linear filters as indicators of the implementation deterioration in fixed-point context. EURASIP Journal on Advances in Signal Processing, special issue on Quantization of VLSI Digital Signal Processing Systems, January 2011. [ bib ]
[21] Y. Feng, P. Chevrel, and T. Hilaire. Generalized modal realisation as a practical and efficient tool for FWL implementation. International Journal of Control, 84(1):66--77, 2011. [ bib ]
[22] Committee Draft, International C Standard. ISO/IEC 9899:201x, 2011. [ bib ]
[23] S. Boldo and G. Melquiond. Flocq: A unified library for proving floating-point algorithms in Coq. In ARITH 20, page 243–252, 2011. [ bib | .pdf ]
Keywords: formal proof
[24] Florent de Dinechin and Bogdan Pasca. Floating-point exponential functions for DSP-enabled FPGAs. In Field Programmable Technologies, pages 110--117, December 2010. [ bib | http | .pdf ]
Keywords: exp, fixed-point, hardware, fpga
[25] S. Chevillard, M. Joldes, and C. Lauter. Sollya: An environment for the development of numerical codes. In K. Fukuda, J. van der Hoeven, M. Joswig, and N. Takayama, editors, International Conference on Mathematical Software, volume 6327 of LNCS, pages 28--31, Heidelberg, Germany, September 2010. Springer. [ bib ]
Keywords: numerical software, faithful rounding, computer algebra, development tool, function approximation
[26] F. W. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors. NIST Handbook of Mathematical Functions. Cambridge University Press, 2010. [ bib ]
Keywords: textbook
[27] Florent de Dinechin. A flexible floating-point logarithm for reconfigurable computers. Lip research report rr2010-22, ENS-Lyon, 2010. [ bib | http ]
[28] Florent de Dinechin, Mioara Joldes, and Bogdan Pasca. Automatic generation of polynomial-based hardware architectures for function evaluation. In Application-specific Systems, Architectures and Processors. IEEE, 2010. [ bib | http | .pdf ]
[29] J. Apostolakis, A. Buckley, A. Dotti, and Z. Marshall. Final report of the ATLAS detector simulation performance assessment group. Cern-lcgapp-2010-01, CERN/PH/SFT, 2010. [ bib | http | .pdf ]
[30] Alexandre Benoit, Frédéric Chyzak, Alexis Darrasse, Stefan Gerhold, Marc Mezzarobba, and Bruno Salvy. The Dynamic Dictionary of Mathematical Functions (DDMF). In Fukuda et al. [31], pages 35--41. [ bib ]
[31] Komei Fukuda, Joris van der Hoeven, Michael Joswig, and Nobuki Takayama, editors. Mathematical Software -- ICMS 2010, volume 6327 of Lecture Notes in Computer Science. Springer, 2010. [ bib ]
[32] Ryan Kastner, Anup Hosangadi, and Farzan Fallah. Arithmetic Optimization Techniques for Hardware and Software Design. Cambridge University Press, New York, NY, USA, 1st edition, 2010. [ bib ]
Keywords: textbook
[33] J.-M. Muller, N. Brisebarre, F. de Dinechin, C.-P. Jeannerod, V. Lefèvre, G. Melquiond, N. Revol, D. Stehlé, and S. Torres. Handbook of Floating-Point Arithmetic. Birkhäuser, Boston, 2010. [ bib ]
Keywords: textbook
[34] Richard P. Brent and Paul Zimmermann. Modern Computer Arithmetic. Cambridge University Press, 2010. [ bib | .pdf ]
Keywords: textbook,multiple precision, division, sqrt, exp, log, sincos, tan
[35] Claude-Pierre Jeannerod, Hervé Knochel, Christophe Monat, Guillaume Revy, and Gilles Villard. A new binary floating-point division algorithm and its software implementation on the ST231 processor. In J.D. Bruguera, M. Cornea, D. DasSarma, and J. Harrison, editors, Proceedings of the 19th IEEE Symposium on Computer Arithmetic (ARITH'19), pages 95--103, Portland, OR, USA, June 2009. IEEE Computer Society. [ bib | DOI ]
Keywords: division, fixed-point, low-level optimization
[36] John Harrison. Fast and accurate Bessel function computation. In Proceedings of the 19th IEEE Symposium on Computer Arithmetic (ARITH'19). IEEE Computer Society, June 2009. [ bib | DOI ]
Keywords: special functions
[37] Toshio Fukushima. Fast computation of complete elliptic integrals and Jacobian elliptic functions. Celestial Mechanics and Dynamical Astronomy, 105(4):305--328, 2009. [ bib | DOI | http ]
Keywords: complete elliptic integrals, Jacobian elliptic functions, nome expansion, Innes’ method, Encke’s method, special functions
[38] Maciej Wielgosz, Ernest Jamro, and Kazimierz Wiatr. Accelerating calculations on the RASC platform: A case study of the exponential function. In Reconfigurable computing: architectures, tools and applications, LNCS 5453, pages 306--311. Springer-Verlag, 2009. [ bib ]
[39] Robin Pottathuparambil and Ron Sass. A parallel/vectorized double-precision exponential core to accelerate computational science applications. In Field Programmable Gate Arrays, pages 285--285. ACM, 2009. [ bib | DOI ]
[40] Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Damien Stehlé, and Serge Torres. Handbook of Floating-Point Arithmetic. Birkhauser Boston, 2009. [ bib ]
Keywords: textbook
[41] Nachiket Kapre and Andre DeHon. Accelerating SPICE model-evaluation using FPGAs. Field-Programmable Custom Computing Machines, pages 37--44, 2009. [ bib | DOI ]
[42] Nelson HF Beebe. A new math library. International Journal of Quantum Chemistry, 109(13):3008--3025, 2009. [ bib ]
[43] D-U Lee, P. Cheung, W. Luk, and J. Villasenor. Hierarchical segmentation schemes for function evaluation. IEEE Transactions on VLSI Systems, 17(1), 2009. [ bib ]
[44] Sylvain Chevillard. Évaluation efficace de fonctions numériques -- Outils et exemples. PhD thesis, École Normale Supérieure de Lyon, Lyon, France, 2009. [ bib ]
[45] Sylvain Chevillard, Mioara Joldes, and Christoph Quirin Lauter. Certified and fast computation of supremum norms of approximation errors. In 19th Symposium on Computer Arithmetic, pages 169--176. IEEE, 2009. [ bib | DOI ]
[46] IEEE standard for floating-point arithmetic. IEEE 754-2008, also ISO/IEC/IEEE 60559:2011, August 2008. [ bib | http ]
[47] N. Brisebarre and J.-M. Muller. Correctly rounded multiplication by arbitrary precision constants. IEEE Transactions on Computers, 57(2):165--174, February 2008. [ bib | DOI ]
[48] Samuel K. Moore. Intel makes a big jump in computer math. IEEE Spectrum, feb 2008. [ bib ]
[49] Maciej Wielgosz, Ernest Jamro, and Kazimierz Wiatr. Highly efficient structure of 64-bit exponential function implemented in FPGAs. In Reconfigurable computing: architectures, tools and applications, LNCS 4943, pages 274--279. Springer-Verlag, 2008. [ bib ]
[50] Altera. Floating Point Exponent (ALTFP_EXP) Megafunction User Guide, 2008. [ bib ]
[51] Altera. Floating Point Natural Logarithm (ALTFP_LOG) Megafunction User Guide, 2008. [ bib ]
[52] Roger Woods, John Mcallister, Richard Turner, Ying Yi, and Gaye Lightbody. FPGA-based Implementation of Signal Processing Systems. Wiley Publishing, 2008. [ bib ]
[53] Christoph Lauter. Arrondi correct de fonctions mathématiques. Fonctions univariées et bivariées, certification et automatisation. PhD thesis, École Normale Supérieure de Lyon, Lyon, France, 2008. [ bib ]
[54] Florent de Dinechin and Christoph Lauter. Optimizing polynomials for floating-point implementation. In Proceedings of the 8th Conference on Real Numbers and Computers, page 7–16, 2008. [ bib ]
Keywords: tools
[55] D. Karayannakis. An algorithm for evaluating the Gamma function and ramifications. ArXiv e-prints, December 2007. [ bib | arXiv ]
Keywords: special functions
[56] Jérémie Detrey and Florent de Dinechin. Parameterized floating-point logarithm and exponential functions for FPGAs. Microprocessors and Microsystems, Special Issue on FPGA-based Reconfigurable Computing, 31(8):537--545, December 2007. [ bib | DOI | .pdf ]
[57] Jérémie Detrey and Florent de Dinechin. Floating-point trigonometric functions for FPGAs. In Field-Programmable Logic and Applications, pages 29--34. IEEE, August 2007. [ bib | .pdf ]
[58] T. Hilaire, P. Chevrel, and J. Whidborne. Low parametric closed-loop sensitivity realizations using fixed-point and floating-point arithmetic. In Proc. European Control Conference (ECC'07), July 2007. [ bib ]
[59] Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, and Paul Zimmermann. MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Transactions on Mathematical Software, 33(2):13:1--13:15, June 2007. [ bib | http ]
Keywords: multiple precision, correct rounding
[60] Jérémie Detrey, Florent de Dinechin, and Xavier Pujol. Return of the hardware floating-point elementary function. In 18th Symposium on Computer Arithmetic, pages 161--168. IEEE, June 2007. [ bib | .pdf ]
[61] Nicolas Brisebarre and Sylvain Chevillard. Efficient polynomial L- approximations. In 18th Symposium on Computer Arithmetic, pages 169--176. IEEE, June 2007. [ bib ]
[62] D.U. Lee and John D. Villasenor. A bit-width optimization methodology for polynomial-based function evaluation. IEEE Transactions on Computers, 56(4):567--571, 2007. [ bib ]
[63] Maciej WIELGOSZ, Ernest JAMRO, and Kazimierz WIATR. Implementacja w układach fpga operacji eksponenty dla liczb w standardzie IEEE-754 o podwójnej precyzji. PAK, 53(5):126--128, 2007. [ bib ]
[64] L. Aksoy, E. Costa, P. Flores, and J. Monteiro. Optimization of area in digital FIR filters using gate-level metrics. In Design Automation Conference, pages 420--423, 2007. [ bib ]
[65] Florent de Dinechin, Christoph Quirin Lauter, and Jean-Michel Muller. Fast and correctly rounded logarithms in double-precision. Theoretical Informatics and Applications, 41:85--102, 2007. [ bib | .pdf ]
[66] S. Chevillard and Ch. Lauter. A certified infinite norm for the implementation of elementary functions. In A. Mathur, W. E. Wong, and M. F. Lau, editors, Seventh International Conference on Quality Software (QSIC 2007), pages 153--160. IEEE, 2007. [ bib ]
Keywords: tools
[67] Claude-Pierre Jeannerod, Hervé Knochel, Christophe Monat, and Guillaume Revy. Faster floating-point square root for integer processors. In IEEE Symposium on Industrial Embedded Systems (SIES'07), 2007. [ bib ]
[68] U. Meyer-Baese. Digital Signal Processing with Field Programmable Gate Arrays. Signals and Communication Technology. Springer, 2007. [ bib ]
[69] Sylvain Chevillard and Christoph Quirin Lauter. A certified infinite norm for the implementation of elementary functions. In Seventh International Conference on Quality Software (QSIC 2007), 11-12 October 2007, Portland, Oregon, USA, pages 153--160, 2007. [ bib | DOI ]
[70] Florent de Dinechin, Christoph Lauter, and Jean-Michel Muller. Fast and correctly rounded logarithms in double-precision. RAIRO - Theoretical Informatics and Applications, 41(1):85--102, 4 2007. [ bib ]
Keywords: correct rounding, log
[71] Florent de Dinechin and Sergey Maidanov. Software techniques for perfect elementary functions in floating-point interval arithmetic. In Real Numbers and Computers, July 2006. [ bib | .pdf ]
[72] T. Hilaire. Analyse et synthèse de l'implémentation de lois de contrôle-commande en précision finie (Étude dans le cadre des applications automobiles sur calculateur embarquée). PhD thesis, Université de Nantes, June 2006. [ bib ]
[73] T. Hilaire, P. Chevrel, and J-P. Clauzel. Low parametric sensitivity realization design for FWL implementation of MIMO controllers. In Proc. of Control Applications of Optimisation CAO'O6, April 2006. [ bib ]
[74] C. S. Anderson, Shane Story, and Nikita Astafiev. Accurate math functions on the Intel IA-32 architecture: A performance-driven design. In 7th Conference on Real Numbers and Computers, pages 93--105, 2006. [ bib ]
Keywords: low-level optimization, libm, log, cos
[75] The CMS Collaboration. CMS Physics: Technical Design Report Volume 1: Detector Performance and Software. Technical Design Report CMS. CERN, Geneva, 2006. [ bib ]
[76] Jean-Michel Muller. Elementary Functions: Algorithms and Implementation (2nd edition). Birkhauser, 2006. [ bib ]
Keywords: textbook
[77] Florent de Dinechin, Alexey Ershov, and Nicolas Gast. Towards the post-ultimate libm. In 17th Symposium on Computer Arithmetic, pages 288--295. IEEE, June 2005. [ bib | .pdf ]
[78] D. H. Bailey. High-precision floating-point arithmetic in scientific computation. Computing in Science and Engineering, 7(3):54--61, May 2005. [ bib ]
[79] R. Clint Whaley and Antoine Petitet. Minimizing development and maintenance costs in supporting persistently optimized BLAS. Software: Practice and Experience, 35(2):101--121, February 2005. http://www.cs.utsa.edu/~whaley/papers/spercw04.ps. [ bib ]
[80] A. G. Ershov and T. P. Kashevarova. Interval mathematical library based on Chebyshev and Taylor series expansion. Reliable Computing, 11(5):359--367, 2005. [ bib ]
[81] W. Hofschuster, W. Krämer, M. Lerch, G. Tischler, and J. Wolff v. Gudenberg. filib++ a fast interval library supporting containment computations. Transactions on Mathematical Software, 2005. [ bib ]
[82] Ian Bird et al. LHC computing grid: Technical design report. Technical Report LCG-TDR-001, CERN, 2005. [ bib ]
[83] Markus Püschel, José M. F. Moura, Jeremy Johnson, David Padua, Manuela Veloso, Bryan Singer, Jianxin Xiong, Franz Franchetti, Aca Gacic, Yevgen Voronenko, Kang Chen, Robert W. Johnson, and Nicholas Rizzolo. SPIRAL: Code generation for DSP transforms. Proceedings of the IEEE, 93(2):232-- 275, 2005. special issue on “Program Generation, Optimization, and Adaptation”. [ bib ]
[84] Matteo Frigo and Steven G. Johnson. The design and implementation of FFTW3. Proceedings of the IEEE, 93(2):216--231, 2005. Special issue on “Program Generation, Optimization, and Platform Adaptation”. [ bib ]
[85] James W. Thomas, John P. Okada, Peter Markstein, and Ren-Chang Li. The libm library and floating-point arithmetic in HP-UX for Itanium-based systems. Technical report, Hewlett-Packard Company, Palo Alto, CA, USA, December 2004. [ bib ]
[86] J. A. Pineiro, M. D. Ercegovac, and J. D. Bruguera. Algorithm and architecture for logarithm, exponential, and powering computation. IEEE Transactions on Computers, 53(9):1085--1096, September 2004. [ bib ]
[87] G. Li and Z. Zhao. On the generalized DFIIt structure and its state-space realization in digital filter implementation. IEEE Trans. on Circuits and Systems, 51(4):769--778, April 2004. [ bib ]
[88] David Harris. An exponentiation unit for an OpenGL lighting engine. Transactions on Computers, 53(3):251--258, March 2004. [ bib | DOI ]
Keywords: IEEE single-precision floating-point format; OpenGL hardware acceleration; OpenGL lighting engine; bipartite table; computer arithmetic; exponentiation unit; floating-point color component; geometry pipeline lighting stage; inverse log table; logarithm lookup table; table complexity; computational complexity; floating point arithmetic; pipeline arithmetic; software standards; table lookup;
[89] Peter Markstein. Accelerating sine and cosine evaluation with compiler assistance. In 2005. Proceedings. 8th Euromicro Conference on-Claude Bajard Jean and Michael Schulte, editors, 16th Symposium on Computer Arithmetic, pages 137--140. IEEE, June 2003. [ bib ]
Keywords: sin, cos, compiler
[90] J. Wu, S. Chen, J.F. Whidborne, and J. Chu. A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes. IEEE Trans. Automatic Control, 48(5):816--823, May 2003. [ bib ]
[91] Peter Markstein. A fast quad precision elementary function library for Itanium. In Real Numbers and Computers, pages 5--12, Lyon, France, 2003. [ bib ]
Keywords:
[92] M. D. Ercegovac and T. Lang. Digital Arithmetic. Morgan Kaufmann, 2003. [ bib ]
Keywords: textbook
[93] Álvaro Vázquez and Elisardo Antelo. Implementation of the exponential function in a floating-point unit. Journal of VLSI Signal Processing, 33(1-2):125--145, January 2003. [ bib ]
[94] J. Wu, S. Chen, G. Li, and J. Chu. Constructing sparse realizations of finite-precision digital controllers based on a closed-loop stability related measure. IEE Proc. Control Theory and Applications, 150(1):61--68, January 2003. [ bib ]
[95] David Defour. Fonctions élémentaires: algorithmes et implémentations efficaes pour l'arrondi correct en double précision. PhD thesis, École Normale Supérieure de Lyon, Lyon, France, 2003. [ bib ]
[96] A.A. Liddicoat. High-performance arithmetic for division and the elementary functions. PhD thesis, Stanford University, 2002. [ bib ]
[97] Marius Cornea, John Harrison, and Ping Tak Peter Tang. Scientific Computing on Itanium-based Systems. Intel Press, 2002. [ bib ]
Keywords: textbook
[98] Daniel Ménard and Olivier Sentieys. A methodology for evaluating the precision of fixed-point systems. In ICASSP, pages 3152--3155, 2002. [ bib ]
[99] J. Cao, B.W.Y. Wei, and J. Cheng. High-performance architectures for elementary function generation. In Neil Burgess and Luigi Ciminiera, editors, 15th Symposium on Computer Arithmetic, Vail, Colorado, June 2001. IEEE. [ bib ]
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Keywords:
[101] M. J. Flynn and S. F. Oberman. Advanced Computer Arithmetic Design. Wiley-Interscience, 2001. [ bib ]
Keywords: textbook
[102] Y. He and C. H. Q. Ding. Using accurate arithmetics to improve numerical reproducibility and stability in parallel applications. Journal of Supercomputing, 18:259--277, 2001. [ bib ]
[103] S. M. Rump. Rigorous and portable standard functions. BIT Numerical Mathematics, 41(3), 2001. [ bib ]
[104] R. Istepanian and J.F. Whidborne, editors. Digital Controller implementation and fragility. Springer, 2001. [ bib ]
[105] Michael L Overton. Numerical computing with IEEE floating point arithmetic. SIAM, 2001. [ bib ]
Keywords: textbook
[106] R.H. Istepanian, J. Wu, and S. Chen. Sparse realizations of optimal finite-precision teleoperation controller structures. pages 687--691, June 2000. [ bib ]
[107] John Harrison. Formal verification of floating point trigonometric functions. In Formal Methods in Computer-Aided Design: Third International Conference FMCAD 2000, volume 1954 of Lecture Notes in Computer Science, pages 217--233. Springer-Verlag, 2000. [ bib ]
Keywords: formal proof, sin, cos
[108] Marc Daumas and Claire Moreau-Finot. Exponential: implementation trade-offs for hundred bit precision. In Real Numbers and Computers, pages 61--74, Dagstuhl, Germany, 2000. [ bib ]
Keywords: exp, multiple precision
[109] B. Parhami. Computer Arithmetic, Algorithms and Hardware Designs. Oxford University Press, 2000. [ bib ]
Keywords: textbook
[110] Peter Markstein. IA-64 and Elementary Functions: Speed and Precision. Hewlett-Packard Professional Books. Prentice Hall, 2000. [ bib ]
Keywords: textbook
[111] Sergey P. Shary. Interval algebraic problems and their numerical solution. PhD thesis, Novosibirsk Institute of Computational Mathematics and Mathematical Geophysics, 2000. [ bib ]
[112] S. F. Oberman. Floating point division and square root algorithms and implementation in the amd-k7(tm) microprocessor. In 14th Symposium on Computer Arithmetic. IEEE, April 1999. [ bib ]
Keywords: division, sqrt, hardware
[113] S. Story and P.T.P. Tang. New algorithms for improved transcendental functions on IA-64. In 14th Symposium on Computer Arithmetic, pages 4---11. IEEE, April 1999. [ bib ]
Keywords:
[114] J. Harrison, T. Kubaska, S. Story, and P.T.P. Tang. The computation of transcendental functions on the IA-64 architecture. Intel Technology Journal, Q4, 1999. [ bib ]
Keywords:
[115] G. Li. On the structure of digital controllers with finite word length consideration. IEEE Trans. on Autom. Control, 43(5):689--693, May 1998. [ bib ]
[116] W. Hofschuster and W. Krämer. FI_LIB, eine schnelle und portable Funktionsbibliothek für reelle Argumente und reelle Intervalle im IEEE-double-Format. Technical Report Nr. 98/7, Institut für Wissenschaftliches Rechnen und Mathematische Modellbildung, Universität Karlsruhe, 1998. [ bib ]
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[117] R. Istepanian, G. Li, J. Wu, and J. Chu. Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds. In IEEE Proc. Control Theory and Appl., volume 145, 1998. [ bib ]
[118] John Harrison. Floating point verification in HOL light: The exponential function. In Algebraic Methodology and Software Technology, pages 246--260, 1997. [ bib | .html ]
Keywords: formal proof, exp
[119] Donald Knuth. The Art of Computer Programming, vol.2: Seminumerical Algorithms. Addison Wesley, 3rd edition, 1997. [ bib ]
Keywords: multiple precision, formal proof, division, textbook
[120] Jonathan R. Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. In Discrete and Computational Geometry, volume 18, pages 305--363, 1997. [ bib | .ps ]
[121] D.M. Priest. Fast table-driven algorithms for interval elementary functions. In 13th Symposium on Computer Arithmetic, pages 168--174. IEEE, 1997. [ bib ]
[122] Gang Li. On pole and zero sensitivity of linear systems. Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 44(7):583 --590, jul 1997. [ bib ]
[123] W. F. Wong and E. Goto. Fast evaluation of the elementary functions in single precision. IEEE Transactions on Computers, 44(3):453--457, March 1995. [ bib ]
Keywords: Add-Table Lookup-Add, ATA, hardware, division, sqrt, log, exp, sin, cos, atan
[124] W. F. Wong and E. Goto. Fast hardware-based algorithms for elementary function computations using rectangular multipliers. IEEE Transactions on Computers, 43(3):278--294, March 1994. [ bib ]
Keywords: hardware, division, log, sqrt, exp, atan, atan2, sin, cos
[125] M. D. Ercegovac and T. Lang. Division and Square Root: Digit-Recurrence Algorithms and Implementations. Kluwer Academic Publishers, Boston, 1994. [ bib ]
Keywords: textbook, division, sqrt
[126] W. F. Wong and E. Goto. Fast evaluation of the elementary functions in double precision. In Twenty-Seventh Annual Hawaii International Conference on System Sciences, pages 349--358, 1994. [ bib ]
Keywords: Add-Table Lookup-Add-Multiply, ATA-M, hardware, division, square root, exp, sin, cos, log, atan, sinh, cosh
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Keywords: textbook, 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
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