The Cilkview scalability analyzer
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Solving bivariate polynomial systems on a GPU
ACM Communications in Computer Algebra
FFT-based dense polynomial arithmetic on multi-cores
HPCS'09 Proceedings of the 23rd international conference on High Performance Computing Systems and Applications
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In symbolic computation, polynomial multiplication is a fundamental operation akin to matrix multiplication in numerical computation. We present efficient implementation strategies for FFT-based dense polynomial multiplication targeting multi-cores. We show that {\it balanced input data} can maximize parallel speedup and minimize cache complexity for bivariate multiplication. However, unbalanced input data, which are common in symbolic computation, are challenging. We provide efficient techniques, what we call {\it contraction} and {\it extension}, to reduce multivariate (and univariate) multiplication to {\it balanced bivariate multiplication}. Our implementation in {\tt Cilk++} demonstrates good speed upon multi-cores.