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MPIR - Parallel Algorithms and CUDA

Present : Carl Witty, Bill Hart, Michael Abshoff, Glenn Tarbox Virtually Present : Jeff Gilchrist, Gonzalo Tornaria

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Parallel algorithms:

* Multimodular algorithms * Scalar algorithms * Peter Montgomery's remainder algorithm a mod b, precompute b1 = B mod b, b2 = B^{2 mod b, b3 = B}3 mod b, then write a = a0 + a1*B + a2*B^2 +..., then compute a0 + a1*b1 + a2*b2 +.... and do final reduction mod b. Multiplications can be done in parallel.

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Parallel algorithms:

• Multimodular algorithms
• Scalar algorithms

• Peter Montgomery's remainder algorithm a mod b, precompute b1 = B mod b, b2 = B^{2 mod b, b3 = B}3 mod b, then write a = a0 + a1*B + a2*B^2 +..., then compute a0 + a1*b1 + a2*b2 +.... and do final reduction mod b. Multiplications can be done in parallel.

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