Speicalize copy! for triangular, and use copy! in ldiv

[jishnub]

Currently, we specialize copyto! for a triangular source. However, this has two branches, depending on whether the axes match. In the branch where the axes do match, we may use copy! instead, and specialize this in terms of the internal _copyto! which is identical in implementation.

We also use copy! in ldiv instead of copyto!. These should be equivalent in most cases, barring one extra axes check in copy!, as the fallback method for copy! calls copyto! internally. However, the advantage comes for triangular matrices, where copy! doesn't have branches, as the axes necessarily match.

As a consequence, this reduces the TTFX in operations like

julia> using Random, LinearAlgebra

julia> A = rand(4,4);

julia> @time A \ UpperTriangular(A);
  0.598575 seconds (1.28 M allocations: 61.788 MiB, 98.57% compilation time: 3% of which was recompilation) # master
  0.487267 seconds (1.01 M allocations: 49.726 MiB, 3.54% gc time, 98.95% compilation time) # this PR

julia> @time UpperTriangular(A) / A;
  0.826212 seconds (1.45 M allocations: 71.427 MiB, 16.96% gc time, 84.47% compilation time) # master
  0.616258 seconds (1.28 M allocations: 63.135 MiB, 2.65% gc time, 99.19% compilation time) # this PR

I've renamed the internal functions as _copyto! -> _copy! and copyto_unaliased! -> copy_unaliased!, as these are closer to the meaning of copy! than to copyto!.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.97%. Comparing base (925acef) to head (56aacff).
Report is 24 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1263      +/-   ##
==========================================
- Coverage   92.03%   91.97%   -0.07%     
==========================================
  Files          34       34              
  Lines       15475    15479       +4     
==========================================
- Hits        14243    14237       -6     
- Misses       1232     1242      +10     

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[jishnub]

Gentle bump

[dkarrasch]

SGTM

I haven't looked into the copy! and copyto! dispatch in a while and don't have the bandwidth to do that now, but this either doesn't change anything (like renaming or being led to the same implementation by multiple dispatch), or improves ttfx and/or runtime, right?

[jishnub]

Yes, I think this should be a harmless change