FFTs in external or hierarchical memory
The Journal of Supercomputing
Discrete weighted transforms and large-integer arithmetic
Mathematics of Computation
High-precision division and square root
ACM Transactions on Mathematical Software (TOMS)
Modern computer algebra
Rapid multiplication modulo the sum and difference of highly composite numbers
Mathematics of Computation
The truncated fourier transform and applications
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Integer and polynomial multiplication: towards optimal toom-cook matrices
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Time-and space-efficient evaluation of some hypergeometric constants
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Faster multiplication in GF(2)[x]
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Fast Mersenne prime testing on the GPU
Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units
Schönhage-Strassen algorithm with MapReduce for multiplying terabit integers
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
| Hi-index | 0.00 |
Schönhage-Strassen's algorithm is one of the best known algorithms for multiplying large integers. Implementing it ef?ciently is of utmost importance, since many other algorithms rely on it as a subroutine. We present here an improved implementation, based on the one distributed within the GMP library. The following ideas and techniques were used or tried: faster arithmetic modulo 2n + 1, improved cache locality, Mersenne transforms, Chinese Remainder Reconstruction, the √2 trick, Harley's and Granlund's tricks, improved tuning.