Abstract
The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coefficients. The code is mainly written in CilkPlus [10] targeting multicore processors. The current distribution focuses on dense polynomials and the sparse case is work in progress. A strong emphasis is put on adaptive algorithms as the library aims at supporting a wide variety of situations in terms of problem sizes and available computing resources. One of the purposes of the BPAS project is to take advantage of hardware accelerators in the development of polynomial systems solvers. The BPAS library is publicly available in source at www.bpaslib.org .
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24(3-4), 235–265 (1997)
Chen, C., Mansouri, F., Moreno Maza, M., Xie, N., Xie, Y.: Parallel Multiplication of Dense Polynomials with Integer Coefficient. Technical report, The University of Western Ontario (2013)
Chen, C., Moreno Maza, M., Xie, Y.: Cache complexity and multicore implementation for univariate real root isolation. J. of Physics: Conf. Series 341 (2011)
Frigo, M., Johnson, S.G.: The design and implementation of FFTW3 93(2), 216–231 (2005)
Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. ACM Transactions on Algorithms 8(1), 4 (2012)
Gastineau, M., Laskar, J.: Highly scalable multiplication for distributed sparse multivariate polynomials on many-core systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 100–115. Springer, Heidelberg (2013)
von zur Gathen, J., Gerhard, J.: Fast algorithms for taylor shifts and certain difference equations. In: ISSAC, pp. 40–47 (1997)
Hart, W., Johansson, F., Pancratz, S.: FLINT: Fast Library for Number Theory. V. 2.4.3, http://flintlib.org
Jenks, R.D., Sutor, R.S.: AXIOM, The Scientific Computation System. Springer (1992)
Leiserson, C.E.: The Cilk++ concurrency platform. The Journal of Supercomputing 51(3), 244–257 (2010)
Li, X., Moreno Maza, M., Rasheed, R., Schost, É.: The modpn library: Bringing fast polynomial arithmetic into maple. J. Symb. Comput. 46(7), 841–858 (2011)
Mansouri, F.: On the parallelization of integer polynomial multiplication. Master’s thesis, The University of Western Ontario, London, ON, Canada (2014), http://www.csd.uwo.ca/~moreno/Publications/farnam-thesis.pdf
Monagan, M.B., Pearce, R.: Parallel sparse polynomial multiplication using heaps. In: ISSAC, pp. 263–270. ACM (2009)
Moreno Maza, M., Xie, Y.: FFT-based dense polynomial arithmetic on multi-cores. In: Mewhort, D.J.K., Cann, N.M., Slater, G.W., Naughton, T.J. (eds.) HPCS 2009. LNCS, vol. 5976, pp. 378–399. Springer, Heidelberg (2010)
Moreno Maza, M., Xie, Y.: Balanced dense polynomial multiplication on multi-cores. Int. J. Found. Comput. Sci. 22(5), 1035–1055 (2011)
Schönhage, A., Strassen, V.: Schnelle multiplikation großer zahlen. Computing 7(3-4), 281–292 (1971)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, C., Covanov, S., Mansouri, F., Maza, M.M., Xie, N., Xie, Y. (2014). The Basic Polynomial Algebra Subprograms. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_100
Download citation
DOI: https://doi.org/10.1007/978-3-662-44199-2_100
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44198-5
Online ISBN: 978-3-662-44199-2
eBook Packages: Computer ScienceComputer Science (R0)