Reorganize the test suite to reduce code duplication

[DilumAluthge]

@chriselrod This should make it much easier to change the matrix sizes we test. We just edit the contents of https://github.com/JuliaLinearAlgebra/Octavian.jl/blob/dpa/coverage/test/matmul.jl and/or https://github.com/JuliaLinearAlgebra/Octavian.jl/blob/dpa/coverage/test/matmul_coverage.jl.

test/matmul.jl: (code coverage is disabled, so we can test really big matrices) https://github.com/JuliaLinearAlgebra/Octavian.jl/blob/46d21b23ade288f420140d134a1608b8d3d9d9f2/test/matmul.jl#L1-L7

test/matmul_coverage.jl: (code coverage is enabled) https://github.com/JuliaLinearAlgebra/Octavian.jl/blob/46d21b23ade288f420140d134a1608b8d3d9d9f2/test/matmul_coverage.jl#L1-L7

[codecov[bot]]

Codecov Report

Merging #45 (c6574ee) into master (174fe57) will increase coverage by 28.73%. The diff coverage is n/a.

@@             Coverage Diff             @@
##           master      #45       +/-   ##
===========================================
+ Coverage   12.23%   40.97%   +28.73%     
===========================================
  Files          12       12               
  Lines         719      715        -4     
===========================================
+ Hits           88      293      +205     
+ Misses        631      422      -209     

Impacted Files	Coverage Δ
src/staticfloats.jl	36.66% <0.00%> (+3.33%)	:arrow_up:
src/macrokernels.jl	15.70% <0.00%> (+9.42%)	:arrow_up:
src/utils.jl	79.31% <0.00%> (+10.34%)	:arrow_up:
src/memory_buffer.jl	13.79% <0.00%> (+10.34%)	:arrow_up:
src/global_constants.jl	85.71% <0.00%> (+14.28%)	:arrow_up:
src/matmul.jl	41.97% <0.00%> (+35.09%)	:arrow_up:
src/integerdivision.jl	66.66% <0.00%> (+44.44%)	:arrow_up:
src/funcptrs.jl	50.00% <0.00%> (+45.34%)	:arrow_up:
src/types.jl	75.00% <0.00%> (+75.00%)	:arrow_up:
src/block_sizes.jl	77.19% <0.00%> (+77.19%)	:arrow_up:

---

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[chriselrod]

Someone else to consider, related to your Preferences.jl PR, is that the L3 cash readings we have are those for large server CPUs, shared among all their cores. But we only have access to 2 or so of those cores, and (similarly) only a correspondingly small slice of the total L3.

Which means our blocking sizes here should be smaller than they are, which would decrease the size of the matrices needed to hit all code paths.

[DilumAluthge]

Oh interesting. So the L3 cache size that we get from Hwloc.jl/VectorizationBase.jl is for the entire CPU?

So maybe the logic should be something like this:

1. Use Hwloc.jl/VectorizationBase.jl to get the size of the L3 cache (shared among all cores)
2. Use ??? to get the total number of cores on this machine
3. VectorizationBase.NUM_CORES is the number of cores that we actually have access to (is this correct?)
4. Divide (VectorizationBase.NUM_CORES)/(answer from number 2) to compute the proportion of cores that we have
5. Multiple (answer from number 4)*(answer from number 1) to figure out how much L3 cache we actually have access to.

Does this look right?

Couple questions:

• Am I right in number 3 when I say that VectorizationBase.NUM_CORES` is the number of cores that we actually have access to (not the total number of cores)
• How do we figure out number 2?

[chriselrod]

2. Maybe CpuId.jl can help:

   
   julia> using CpuId

julia> cpucores() 10

Worth trying.

3. Not in general, but it seems to on GitHub CI.

Example of where it doesn't (VectorizationBase uses Hwloc, but worse than that precompiles one static value; changing it would require re-precompiling VectorizationBase):
```julia
# > taskset -c 0,1 julia

julia> using Hwloc
[ Info: Precompiling Hwloc [0e44f5e4-bd66-52a0-8798-143a42290a1d]

julia> Hwloc.topology_load()
D0: L0 P0 Machine
    D1: L0 P0 Package
        D2: L0 P-1 L3Cache  Cache{size=14417920,depth=3,linesize=64,associativity=11,type=Unified}
            D3: L0 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L0 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L0 P0 Core
                        D6: L0 P0 PU
                        D6: L1 P10 PU
            D3: L1 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L1 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L1 P1 Core
                        D6: L2 P1 PU
                        D6: L3 P11 PU
            D3: L2 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L2 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L2 P2 Core
                        D6: L4 P2 PU
                        D6: L5 P12 PU
            D3: L3 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L3 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L3 P3 Core
                        D6: L6 P3 PU
                        D6: L7 P13 PU
            D3: L4 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L4 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L4 P4 Core
                        D6: L8 P4 PU
                        D6: L9 P14 PU
            D3: L5 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L5 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L5 P8 Core
                        D6: L10 P5 PU
                        D6: L11 P15 PU
            D3: L6 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L6 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L6 P9 Core
                        D6: L12 P6 PU
                        D6: L13 P16 PU
            D3: L7 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L7 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L7 P10 Core
                        D6: L14 P7 PU
                        D6: L15 P17 PU
            D3: L8 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L8 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L8 P11 Core
                        D6: L16 P8 PU
                        D6: L17 P18 PU
            D3: L9 P-1 L2Cache  Cache{size=1048576,depth=2,linesize=64,associativity=16,type=Unified}
                D4: L9 P-1 L1Cache  Cache{size=32768,depth=1,linesize=64,associativity=8,type=Data}
                    D5: L9 P12 Core
                        D6: L18 P9 PU
                        D6: L19 P19 PU

julia> run(`taskset -p $(getpid())`)
pid 193828's current affinity mask: 3
Process(`taskset -p 193828`, ProcessExited(0))

We're pinned to cores 0 and 1, but Hwloc still shows 10 cores.

But it's probably correct if we're running in a virtual machine that's only given a few cores.