
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
J.A. Pi?eiro, M.D. Ercegovac, J.D. Bruguera, "Algorithm and Architecture for Logarithm, Exponential, and Powering Computation," IEEE Transactions on Computers, vol. 53, no. 9, pp. 10851096, September, 2004.  
BibTex  x  
@article{ 10.1109/TC.2004.53, author = {J.A. Pi?eiro and M.D. Ercegovac and J.D. Bruguera}, title = {Algorithm and Architecture for Logarithm, Exponential, and Powering Computation}, journal ={IEEE Transactions on Computers}, volume = {53}, number = {9}, issn = {00189340}, year = {2004}, pages = {10851096}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2004.53}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Algorithm and Architecture for Logarithm, Exponential, and Powering Computation IS  9 SN  00189340 SP1085 EP1096 EPD  10851096 A1  J.A. Pi?eiro, A1  M.D. Ercegovac, A1  J.D. Bruguera, PY  2004 KW  Computer arithmetic KW  elementary function approximation KW  digitrecurrence algorithms KW  logarithm KW  exponential KW  powering KW  highradix KW  LRCF multiplication KW  online arithmetic. VL  53 JA  IEEE Transactions on Computers ER   
[1] E. Antelo, T. Lang, and J.D. Bruguera, VeryHigh Radix CORDIC Vectoring with Scalings andSelection by Rounding Proc. 14th Int'l Symp. Computer Arithmetic (ARITH14), pp. 204213, Apr. 1999.
[2] J.C. Bajard, S. Kla, and J.M. Muller, BKM: A New Hardware Algorithm for Complex Elementary Functions IEEE Trans. Computers, vol. 43, no. 8, pp. 955964, Aug. 1994.
[3] W. Cody and W. Waite, Software Manual for the Elementary Functions. Prentice Hall, 1980.
[4] M.D. Ercegovac and T. Lang, OntheFly Conversion of Redundant into Conventiona lRepresentations IEEE Trans. Computers, vol. 36, no. 7, pp. 895897, July 1987.
[5] M.D. Ercegovac et al., Fast Multiplication without CarryPropagate Addition , IEEE Trans. Computers, vol. 39, no. 11, Nov. 1990.
[6] M.D. Ercegovac and T. Lang, "OntheFly Rounding," IEEE Trans. Computers, vol. 41, no. 12, pp. 1,4971,503, Dec. 1992.
[7] M.D. Ercegovac and T. Lang, Division and Square Root: Digit Recurrence Algorithms and Implementations. Kluwer Academic, 1994.
[8] M.D. Ercegovac, T. Lang, J.M. Muller, and A. Tisserand, “Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers,” IEEE Trans. Computers, vol. 49, no. 7, pp. 628637, July 2000.
[9] C.T. Fike, Computer Evaluation of Mathematical Functions. Prentice Hall, 1968.
[10] S. Gal and B. Bachelis, An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard ACM Trans. Math. Software, vol. 17, no. 1, pp. 2645, Mar. 1991.
[11] R.E. Goldschmidt, Applications of Division by Convergence MS thesis, Electrical Eng. Dept., Massachussets Inst. of Technology (MIT), June 1964.
[12] D. Harris, A Powering Unit for an OpenGL Lighting Engine Proc. 35th Asilomar Conf. Signals, Systems, and Computers, pp. 16411645, 2001.
[13] J.F. Hart, E.W. Cheney, C.L. Lawson, H.J. Maehly, C.K. Mesztenyi, J.R. Rice, H.G. Thacher, and C. Witzgall, Computer Approximations. New York: Wiley, 1968.
[14] R.K. Kolagotla et al., VLSI Implementation of a 200Mhz 16$\times$16 LefttoRight CarryFree Multiplier in 0.35$\mu \rm m$CMOS Technology for NextGeneration DSPs , Proc. IEEE 1997 Custom Integrated Circuits Conf., pp. 469472, 1997.
[15] P. Kornerup, Reviewing 4to2 Adders for MultiOperand Addition Proc. IEEE 13th Int'l Conf. ApplicationSpecific Systems, Architectures and Processors (ASAP '02), pp. 218229, 2002.
[16] D.M. Lewis, “114 MFLOPS Logarithmic Number System Arithmetic Unit for DSP Applications,” IEEE J. SolidState Circuits, vol. 30, pp. 1,5471,553, 1995.
[17] J.M. Muller, Elementary Functions. Algorithms and Implementation. Birkhauser, 1997.
[18] S.F. Oberman, “Floating Point Division and Square Root Algorithms and Implementation in the AMDK7 Microprocessor,” Proc. 14th Symp. Computer Arithmetic (ARITH14), pp. 106115, Apr. 1999.
[19] J.A. Piñeiro, Algorithms and Architectures for Elementary Function Computation PhD dissertation, Dept. of Electronics and Computer Eng., Univ. Santiago de Compostela, June 2003, http://www.ac.usc.es~alex.
[20] J.A. Pineiro and J.D. Bruguera, HighSpeed DoublePrecision Computation of Reciprocal, Division, Square Root, and Inverse Square Root IEEE Trans. Computers, vol. 51, no. 12, pp. 13771388, Dec. 2002.
[21] J.A. Piñeiro, J.D. Bruguera, and J.M. Muller, “Faithful Powering Computation Using Table LookUp and a Fused Accumulation Tree,” Proc. IEEE 15th Int'l Symp. Computer Arithmetic (ARITH15), pp. 4047, 2001.
[22] J.A. Piñeiro, M.D. Ercegovac, and J.D. Bruguera, HighRadix Logarithm with Selection by Rounding Proc. IEEE 13th Int'l Conf. ApplicationSpecific Systems, Architectures and Processors (ASAP '02), pp. 101110, July 2002.
[23] J.A. Piñeiro, M.D. Ercegovac, and J.D. Bruguera, HighRadix Iterative Algorithm for Powering Computation Proc. IEEE 16th Int'l Symp. Computer Arithmetic (ARITH16), pp. 204211, June 2003.
[24] J.A. Piñeiro, M.D. Ercegovac, and J.D. Bruguera, OnLine HighRadix Exponential with Selection by Rounding Proc. IEEE Int'l Symp. Circuits And Systems (ISCAS 2003), May 2003.
[25] M.J. Schulte and J.E. Stine, Approximating Elementary Functions with Symmetric Bipartite Tables IEEE Trans. Computers, vol. 48, no. 8, pp. 842847, Aug. 1999.
[26] H.C. Shin, J.A. Lee, and L.S. Kim, A Minimized Hardware Architecture of Fast Phong Shader Using Taylor Series Approximation in 3D Graphics Proc. Int'l Conf. Computer Design, VLSI in Computers and Processors, pp. 286291, 1998.
[27] N. Takagi, “Powering by a Table LookUp and a Multiplication with Operand Modification,” IEEE Trans. Computers, vol. 47, no. 11, pp. 12161222, Nov. 1998.
[28] P.T.P. Tang, “TableLookup Algorithms for Elementary Functions and Their Error Analysis,” Proc. 10th Symp. Computer Arithmetic, pp. 232236, 1991.
[29] M. Zhang, S. Vassiliadis, and J.G. DelgadoFrias, Sigmoid Generators for Neural Computing Using Piecewise Approximations IEEE Trans. Computers, vol. 45, no. 9, pp. 10451050, Sept. 1996.