Implementation of BMat16

[Victorin-Brunel]

Here are the additions regarding BMat16 :

• Creation of BMat16
• Various constructors (with a vector register of 256 bits, 4 64 bits uint, or a two-dimensional vector)
• Comparison operators (==, !=, <, >)
• Acces operator to a particular bit at a position (i, j)
• Method to set a bit at a position (i, j)
• A convertor to a two-dimensional array
• Bitwise or operator between two matrices
• Naive transposition
• Optimized transposition with vector instructions
• Optimized matrix multplication
• Optimized matrix multplication using BMat8 matrix multiplication
• Two naive multiplications (one with the acces operator, the other with the array conversion)
• Number of non-zero rows
• Vector of rows
• Identity matrix of size 0 to 16
• Random matrix, and the possibility to specify a size from 1 to 16
• Swap of two matrices
• Display operator

[james-d-mitchell]

Closing and reopening to trigger the ci again

[james-d-mitchell]

I've tried BMat16's with libsemigroups (basically dropping it in everywhere we use HPCombi::BMat8 in the tests) and found no issues whatsoever. So I'm happy to merge this if you are @hivert ?

[hivert]

I've tried BMat16's with libsemigroups (basically dropping it in everywhere we use HPCombi::BMat8 in the tests) and found no issues whatsoever. So I'm happy to merge this if you are @hivert ?

I'd like to look a little at the generated assembly code to check that some think are properly optimized by the (a) compiler (notably some product by power of 2 which could be written as shift). I try to do it either during the week-end or next week. Other than that, I'm Ok to merge.

[hivert]

The code looks good. I checked:

• product in the BMat16::BMat16, BMat16::operator(), BMat16::set and BMat16::to_array are properly optimized with shift.
• the loop in BMat16::mult_transpose is properly unrolled.

This should be fixed easily

• The doc of operator< doesn't specify the order;
• the is a bitwise | on matrices but not & of bitwise complement.

There are finally some possible improvements which needs to be fixed:

• This should be fixed as soon as simde provides the implementation

inline size_t BMat16::nr_rows() const noexcept {
  [...] 
  //// Vectorized version which doesn't work due to the absence of popcnt in
   /// simde
   // xpu16 tmp = _data, zero = simde_mm256_setzero_si256();
   // xpu16 x = (tmp != zero);
   // return simde_mm256_popcnt_epi16(x);
}

• This one is low priority (in random which is now that used and probably a little time consuming):

    // TO DO : Instead of nulling all the cols/rows one by one, one could do
    // that at once with the proper mask

[james-d-mitchell]

Great! Thanks @hivert, should we then: merge this PR, and add issues for the TODOs that you mention, or would you rather that the TODOs are addressed in this PR first?

[james-d-mitchell]

I just rebased onto the most recent versions on main