A new polynomial factorization algorithm and its implementation
Journal of Symbolic Computation
Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Optimizing compilers for modern architectures: a dependence-based approach
Optimizing compilers for modern architectures: a dependence-based approach
Register tiling in nonrectangular iteration spaces
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computer architecture: a quantitative approach
Computer architecture: a quantitative approach
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Modular Algorithms In Symbolic Summation And Symbolic Integration (Lecture Notes in Computer Science)
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Implementation techniques for fast polynomial arithmetic in a high-level programming environment
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
High-performance implementations of the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast arithmetic for triangular sets: from theory to practice
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Multithreaded parallel implementation of arithmetic operations modulo a triangular set
Proceedings of the 2007 international workshop on Parallel symbolic computation
Fast arithmetic for triangular sets: From theory to practice
Journal of Symbolic Computation
Isolating real roots of real polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Cache complexity and multicore implementation for univariate real root isolation
ACM Communications in Computer Algebra
On the computing time of the continued fractions method
Journal of Symbolic Computation
ACM Communications in Computer Algebra
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We present algorithms that outperform straightforward implementations of classical Taylor shift by 1. For input poly-nomials of low degrees a method of the SACLIB library is faster than straightforward implementations by a factor of at least 2; for higher degrees we develop a method that is faster than straightforward implementations by a factor of up to 7. Our Taylor shift algorithm requires more word additions than straightforward methods but it reduces the number of cycles per word addition by reducing memory traffic and the number of carry computations. The introduction of signed digits, suspended normalization, radix reduction, and delayed carry propagation enables our algorithm to take advantage of the technique of register tiling which is commonly used by optimizing compilers. While our algorithm is written in a high-level language, it depends on several parameters that can be tuned to the underlying architecture.