Binary Linear Algebra

[federico-bongiorno]

An implementation of sparse binary vectors and matrices with linear algebra solver.

[Bodigrim]

Please rebase your branch atop of master.

[Bodigrim]

Could you please check that time grows proportionally to n^2, benchmarking matrices of growing sizes? If this is the case, then having a large constant factor is eventually manageable, but if it is not so, we are in a bigger trouble.

[Bodigrim]

There is a couple of hlint suggestions: https://travis-ci.org/github/Bodigrim/arithmoi/jobs/709224118#L1018

[Bodigrim]

And one more thing to make Travis build happy: add mod-0.1.2.0 to extra-deps in stack-8.8.3.yaml.

[Bodigrim]

Continuing our discussion elsewhere. The current submission does not eat all the RAM. Yes, allocating 5 millions of (Integer, SignedPrimeIntSet) takes quite a lot of space, more than 500 Mb, but it works fine (and returns correct answer) with 2 Gb limit.

While you generate sievingInterval of length 5000000 further computations operate over much smaller subset of smooth numbers, about 30000 elements. Instead of sieving 5000000 elements in one go (which causes a spike in memory allocations and does not scale), you can take first 10^5 values, sieve out non-smooth ones, than take next 10^5 elements and sieve them, etc., concatenating smooth vectors together.

[Bodigrim]

This is really unexpected semantics for a function, named binarySearch. If users of this function need indices starting from 1, they can apply map (+1) themselves.

[federico-bongiorno]

I added a comment to explain it better. Suppose I have Prime 2, Prime 3 and Prime 5. I want to send them respectively to 1,2,3. I use 0 to when the number is negative (its sign is true).

[federico-bongiorno]

To make it clearer 30 would be given by [1,2,3] whereas -30 by [0,1,2,3].

[Bodigrim]

Yay! Thanks!