What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Algorithms for computer algebra
Algorithms for computer algebra
Discrete weighted transforms and large-integer arithmetic
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
The twenty-fourth fermat number is composite
Mathematics of Computation
A gmp-based implementation of schönhage-strassen's large integer multiplication algorithm
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Efficient Multiplication of Polynomials on Graphics Hardware
APPT '09 Proceedings of the 8th International Symposium on Advanced Parallel Processing Technologies
Fast Mersenne prime testing on the GPU
Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units
Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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We extend the work of Richard Crandall et al. to demonstrate how the Discrete Weighted Transform (DWT) can be applied to speed up multiplication modulo any number of the form a ± b where Πp|abP is small. In particular this allows rapid computation modulo numbers of the form k.2n ± 1.In addition, we prove tight bounds on the rounding errors which naturally occur in floating-point implementations of FFT and DWT multiplications. This makes it possible for FFT multiplications to be used in situations where correctness is essential, for example in computer algebra packages.