Ramanujan, modular equations, and approximations to Pi or how to compute one billion digits of Pi
American Mathematical Monthly
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
A gmp-based implementation of schönhage-strassen's large integer multiplication algorithm
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast integer multiplication using modular arithmetic
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Hadoop Distributed File System
MSST '10 Proceedings of the 2010 IEEE 26th Symposium on Mass Storage Systems and Technologies (MSST)
Modern Computer Arithmetic
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We present MapReduce-SSA, an integer multiplication algorithm using the ideas from Schönhage-Strassen algorithm (SSA) on MapReduce. SSA is one of the most commonly used large integer multiplication algorithms. MapReduce is a programming model invented for distributed data processing on large clusters. MapReduce-SSA is designed for multiplying integers in terabit scale on clusters of commodity machines. As parts of MapReduce-SSA, two algorithms, MapReduce-FFT and MapReduce-Sum, are created for computing discrete Fourier transforms and summations. These mathematical algorithms match the model of MapReduce seamlessly.