Space- and time-efficient polynomial multiplication
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
NumGfun: a package for numerical and analytic computation with D-finite functions
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
LEMA: towards a language for reliable arithmetic
ACM Communications in Computer Algebra
Arithmetic operations beyond floating point number precision
International Journal of Computational Science and Engineering
New higher-order methods for the simultaneous inclusion of polynomial zeros
Numerical Algorithms
FPGA implementation of variable-precision floating-point arithmetic
APPT'11 Proceedings of the 9th international conference on Advanced parallel processing technologies
Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”
SIAM Journal on Numerical Analysis
Constant-optimized quantum circuits for modular multiplication and exponentiation
Quantum Information & Computation
Schönhage-Strassen algorithm with MapReduce for multiplying terabit integers
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Software implementation of modular exponentiation, using advanced vector instructions architectures
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Square root algorithms for the number field sieve
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
A note on the space complexity of fast D-finite function evaluation
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
On construction of a library of formally verified low-level arithmetic functions
Innovations in Systems and Software Engineering
VLIW coprocessor for IEEE-754 quadruple-precision elementary functions
ACM Transactions on Architecture and Code Optimization (TACO)
Exact and efficient generation of geometric random variates and random graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
SN-SEC: a secure wireless sensor platform with hardware cryptographic primitives
Personal and Ubiquitous Computing
Classical simulations of Abelian-group normalizer circuits with intermediate measurements
Quantum Information & Computation
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Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors.