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Moebius and Mertens functions #90

Merged
merged 10 commits into from
Jan 19, 2018
Merged

Moebius and Mertens functions #90

merged 10 commits into from
Jan 19, 2018

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Bodigrim
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This PR aims to fulfil Step 2 from #60: sublinear summation of Mobius function (so called Mertens function).

  • Introduce a special type for values of Mobius function. Mobius function returns only in -1, 0 or 1, so it is convenient to denote them by three-valued enum.
  • Write a specialised, space-effective and fast version of sieveBlock for Mobius function. It is 5x faster than generic sieveBlockUnboxed.
  • Implement sublinear Mertens function with time and space complexity O(n^(2/3)).

Reference: https://arxiv.org/abs/1610.08551v2

@Bodigrim Bodigrim merged commit 09dbf9c into Bodigrim:master Jan 19, 2018
@Bodigrim Bodigrim deleted the moebius branch January 19, 2018 23:19
@Bodigrim Bodigrim mentioned this pull request Jan 19, 2018
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