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Faster Chinese remaindering

Abstract : The Chinese remainder theorem is a key tool for the design of efficient multi-modular algorithms. In this paper, we study the case when the moduli m_1,…,m_ℓ are fixed and can even be chosen by the user. Through an appropriate use of the technique of FFT-trading, we will show that this assumption allows for the gain of an asymptotic factor O(log log ℓ) in the complexity of “Chinese remaindering”. For small ℓ, we will also show how to choose “gentle moduli” that allow for further gains at the other end. The multiplication of integer matrices is one typical application where we expect practical gains for various common matrix dimensions and integer bitsizes.
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https://hal.archives-ouvertes.fr/hal-01403810
Contributor : Joris van der Hoeven Connect in order to contact the contributor
Submitted on : Sunday, November 27, 2016 - 7:46:32 PM
Last modification on : Wednesday, November 18, 2020 - 10:32:05 PM
Long-term archiving on: : Tuesday, March 21, 2017 - 1:50:49 PM

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  • HAL Id : hal-01403810, version 1

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Joris van der Hoeven. Faster Chinese remaindering. 2016. ⟨hal-01403810⟩

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