Architecture-aware classical taylor shift by 1

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 2005, Issue , 2005, Pages 200-207

  Johnson, Jeremy R ^a   Krandick, Werner ^a   Ruslanov, Anatole D ^a  

^a Drexel University   (United States)

Author keywords

Code generation; Delayed carry propagation; High performance computing; ILP scheduling; Loop unrolling; Memory hierarchy; Multiprecision arithmetic; Performance tuning; Polynomials; Register tiling; Taylor shift

Indexed keywords

ALGORITHMS; HIERARCHICAL SYSTEMS; HIGH LEVEL LANGUAGES; POLYNOMIALS; STORAGE ALLOCATION (COMPUTER);

CODE GENERATION; DELAYED CARRY PROPAGATION; HIGH PERFORMANCE COMPUTING; LOOP UNROLLING; MEMORY HIERARCHY; MULTIPRECISION ARITHMETIC; PERFORMANCE TUNING; REGISTER TILING; TAYLOR SHIFT;

COMPUTER ARCHITECTURE;

EID: 33748970197     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1073884.1073913     Document Type: Conference Paper

References (22)

1. Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullrnan. The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1974.
2. Randy Allen and Ken Kennedy, Optimizing Compilers for Modern Architecture: A Dependence-Based Approach, Morgan Kaufmann Publishers, New York, 2002.
3. Jacques Borowczyk. Sur la vie et l'œuvre de François Budan (1761-1840). Historia Mathematics 18:129-157, 1991.
4. Randal E. Bryant, and David R. O'Hallaron. Computer Systems: A Programmer's Perspective. Prentice Hall, 2003.
5. G. E. Collins and R. G. K. Loos. Specifications and index of SAC-2 algorithms. Technical Report WSI-90-4, Wilhelm-Schickard-Institut für Informatik, Universität; Tübingen, 1990.
6. George E. Collins. The computing time of the Euclidean algorithm. SIAM Journal on Computing, 3(1):1-10, 1974.
7. George E. Collins and Alkiviadis G. Akritas. Polynomial real root isolation using Descartes' rule of signs. In R. D. Jenks, editor, Proceedings of the 1976 ACM Symposium on Symbolic, and Algebraic Computation, pages 272-275. ACM Press, 1976.
8. George E. Collins et al. SACLIB User's Guide, Technical Report 93-19, Research Institute for Symbolic Computation, RISC-Linz, Johannes Kepler University, A-4040 Linz, Austria, 1993.
9. Jürgen Gerhard. Modular Algorithms in Symbolic Summation and Symbolic Integration, volume 3218 of Lecture Notes in Computer Science. Springer-Verlag, 2004.
10. Jürgen Gerhard. Personal communication, 2005.
11. Torbjörn Granlund. GNU MP: The GNU Multiple Precision Arithmetic Library. Swox AB, September 2004. Edition 4.1.4.
12. John L. Hennessy, David A. Patterson, and David Goldberg. Computer Architecture: A Quantitative Approach. Morgan Kaufmann, 3rd edition, 2002.
13. Tim Horel and Gary Lauterbach. UltraSPARC-III: Designing third-generation 64-bit performance. IEEE MICRO, 19(3):73-85, 1999.
14. Marta Jiménez, José M. Llabería, and Agustín Fernández. Register tiling in nonrectangular iteration spaces. ACM Transactions on Programming Languages and Systems, 24(4):409-453, 2002.
15. Maplesoft. Maple 9: Learning Guide, 2003.
16. M. B. Monagan, K. O. Geddes, K. M. Heal, G. Labahn, S. M. Vorkootter, J. McCarron, and P. DeMarco, Maple 9: Advanced Programming Guide. Maplesoft, 2003.
17. M. B. Monagan, K. O. Geddes, K. M. Heal, G. Labahn, S. M. Vorkoetter, J. McCarron, and P. DeMarco. Maple 9: Introductory Programming Guide. Maplesoft, 2003.
18. Victor Shoup. NTL: A Library for Doing Number Theory. http://www.shoup.net/nt1.
19. Victor Shoup. A new polynomial factorization algorithm and its implementation. Journal of Symbolic Computation, 20(4):363-397, 1995.
20. Sun Microsystems, Sun Studio Collection. http://www.sun.com/software/products/studio/.
21. Sun Microsystems. UltraSPARC III Cu: User's Manual, 2004.
22. Joachim von zur Gathen and Jürgen Gerhard. Fast algorithms for Taylor shifts and certain difference equations. In W. W. Küchlin, editor, International Symposium on Symbolic and Algebraic Computation, pages 40-47, ACM Press, 1997.