Brouwer

[davidamarquis]

This PR adds a new iterator SubsetGrayCode that has useful features vs. the existing GrayCode iterator.

The reasons for using SubsetGrayCode are
-so we iterate over the indexs of a binary vector that have changed rather than the entire vector
-so we can use rank/unrank functions
Respectively, these will let us speed up Brouwer's algorithm by eliminating matrix muls, and for multithreading will let us equalize the number of vectors visited per thread.

As a sanity check on the new iterator I benchmarked both iterators to make sure performance is in the same ballpark on a simple loop. Specifically, I tested with length=25, weight=12 which has about 5 million entries. I found they were close: GrayCode is slightly faster and SubsetGrayCode uses slightly less memory.

SubsetGrayCode:

BenchmarkTools.Trial: 54 samples with 1 evaluation.
 Range (min … max):  66.365 ms … 219.557 ms  ┊ GC (min … max):  0.00% … 34.15%
 Time  (median):     92.912 ms               ┊ GC (median):    26.24%
 Time  (mean ± σ):   93.526 ms ±  27.981 ms  ┊ GC (mean ± σ):  19.78% ± 13.74%
Memory estimate: 158.70 MiB, allocs estimate: 5200322.

GrayCode:

BenchmarkTools.Trial: 65 samples with 1 evaluation.
 Range (min … max):  51.159 ms … 103.931 ms  ┊ GC (min … max):  0.00% … 50.88%
 Time  (median):     77.176 ms               ┊ GC (median):    31.98%
 Time  (mean ± σ):   77.271 ms ±   6.824 ms  ┊ GC (mean ± σ):  31.52% ±  7.35%
Memory estimate: 238.05 MiB, allocs estimate: 5200308.

[davidamarquis]

the repetition of in causes a precompile error. Probably its there because of a merge error so I deleted one of them

[davidamarquis]

this iterator has maximum distance 2 meaning that at most 2 entries of the current v are different from the previous v. This means inds will end each iteration holding at most 2 positive values.

The reason inds has length 3 is each iteration changes the indexs of v in two positions. Each change corresponds to one 'addition' and one 'subtraction' (but we're over F2 so those ops are the same). During the second change inds sometimes has 3 positive values temporarily.

[davidamarquis]

the update we're doing here corresponds to binary addition at the index x. If x is already set in indexs this corresponds to two binary additions. These cancel out so we remove x from indexs

[davidamarquis]

The rest of this file is the old GrayCode. I did not change anything except for adding one reference to the paper the algorithm was initially based on

[davidamarquis]

to keep SubsetGrayCode simpler I did not add a mutate keyword. I could not see a need for it because if we need a collection of all subsets we can use subsets() from Hecke (its faster)