DArray/QR: Pick better ib and p defaults

[jpsamaroo]

Written by Cursor Grok

[github-actions]

Dagger benchmarks: dirty vs master

	master	dirty	master / dirty
array/dagger/N=1024 (block 512)/add (X + X)	4.1 ± 0.098 ms	4.2 ± 0.46 ms	0.978 ± 0.11
array/dagger/N=1024 (block 512)/alloc (rand)	2.84 ± 0.67 ms	3.7 ± 0.25 ms	0.768 ± 0.19
array/dagger/N=1024 (block 512)/broadcast (X .+ 1)	2.85 ± 0.044 ms	2.99 ± 0.21 ms	0.953 ± 0.067
array/dagger/N=1024 (block 512)/map (sin.(X))	7.26 ± 0.082 ms	7.45 ± 0.34 ms	0.974 ± 0.046
array/dagger/N=1024 (block 512)/norm	1.16 ± 0.027 ms	1.35 ± 0.1 ms	0.863 ± 0.069
array/dagger/N=1024 (block 512)/reduce (sum)	2.41 ± 0.21 ms	2.66 ± 0.094 ms	0.906 ± 0.086
array/dagger/N=1024 (block 512)/transpose (permutedims)	7 ± 1.1 ms	5.52 ± 2.1 ms	1.27 ± 0.52
array/dagger/N=256 (block 256)/add (X + X)	1.32 ± 0.12 ms	1.44 ± 0.21 ms	0.917 ± 0.16
array/dagger/N=256 (block 256)/alloc (rand)	1.18 ± 0.35 ms	0.935 ± 0.23 ms	1.27 ± 0.49
array/dagger/N=256 (block 256)/broadcast (X .+ 1)	0.843 ± 0.43 ms	0.917 ± 0.21 ms	0.919 ± 0.51
array/dagger/N=256 (block 256)/map (sin.(X))	1.39 ± 0.21 ms	1.3 ± 0.041 ms	1.07 ± 0.17
array/dagger/N=256 (block 256)/norm	0.479 ± 0.46 ms	0.545 ± 0.029 ms	0.878 ± 0.85
array/dagger/N=256 (block 256)/reduce (sum)	1.3 ± 0.15 ms	1.56 ± 0.33 ms	0.835 ± 0.2
array/dagger/N=256 (block 256)/transpose (permutedims)	1.12 ± 0.015 ms	1.18 ± 0.24 ms	0.949 ± 0.19
linalg/dagger/N=1024 (block 512)/cholesky	22.5 ± 2 ms	22.5 ± 1.2 ms	0.999 ± 0.1
linalg/dagger/N=1024 (block 512)/lu	0.047 ± 0.0017 s	0.0463 ± 0.0008 s	1.01 ± 0.04
linalg/dagger/N=1024 (block 512)/matmul (A*A)	0.056 ± 0.0048 s	0.0513 ± 0.0066 s	1.09 ± 0.17
linalg/dagger/N=1024 (block 512)/matvec (A*x)	2.88 ± 0.017 ms	2.99 ± 0.14 ms	0.962 ± 0.045
linalg/dagger/N=1024 (block 512)/qr	0.37 ± 0.021 s	0.115 ± 0.0078 s	3.21 ± 0.28
linalg/dagger/N=1024 (block 512)/solve (A\b via lu)	0.0531 ± 0.0015 s	0.0547 ± 0.00055 s	0.972 ± 0.029
linalg/dagger/N=1024 (block 512)/syrk (A'*A)	0.0335 ± 0.0015 s	0.0343 ± 0.0034 s	0.977 ± 0.1
linalg/dagger/N=256 (block 256)/cholesky	3.17 ± 1 ms	3.17 ± 0.46 ms	1 ± 0.35
linalg/dagger/N=256 (block 256)/lu	4.13 ± 0.31 ms	4.81 ± 0.65 ms	0.859 ± 0.13
linalg/dagger/N=256 (block 256)/matmul (A*A)	2.64 ± 0.1 ms	2.43 ± 0.42 ms	1.08 ± 0.19
linalg/dagger/N=256 (block 256)/matvec (A*x)	1.55 ± 0.49 ms	1.56 ± 0.12 ms	0.995 ± 0.33
linalg/dagger/N=256 (block 256)/qr	7.24 ± 0.057 ms	5.48 ± 0.6 ms	1.32 ± 0.15
linalg/dagger/N=256 (block 256)/solve (A\b via lu)	9.87 ± 0.92 ms	9.64 ± 2.1 ms	1.02 ± 0.24
linalg/dagger/N=256 (block 256)/syrk (A'*A)	3.05 ± 0.056 ms	4.1 ± 0.88 ms	0.744 ± 0.16
stencil/dagger/N=1024 (block 512)/alloc (neighbors Wrap)	22.7 ± 2.7 ms	24.6 ± 3.6 ms	0.92 ± 0.17
stencil/dagger/N=1024 (block 512)/assign (const)	1.37 ± 0.046 ms	1.49 ± 0.071 ms	0.921 ± 0.054
stencil/dagger/N=1024 (block 512)/multi-expr	3.78 ± 0.41 ms	3.72 ± 0.45 ms	1.02 ± 0.17
stencil/dagger/N=1024 (block 512)/neighbors (Clamp)	22.9 ± 2 ms	24.6 ± 1.7 ms	0.931 ± 0.1
stencil/dagger/N=1024 (block 512)/neighbors (Pad)	23.8 ± 0.36 ms	25.1 ± 0.47 ms	0.948 ± 0.023
stencil/dagger/N=1024 (block 512)/neighbors (Reflect)	24 ± 0.93 ms	24.4 ± 0.59 ms	0.986 ± 0.045
stencil/dagger/N=1024 (block 512)/neighbors (Wrap)	24 ± 1.3 ms	23 ± 2.1 ms	1.05 ± 0.11
stencil/dagger/N=1024 (block 512)/update (+)	2.63 ± 0.19 ms	2.7 ± 0.61 ms	0.972 ± 0.23
stencil/dagger/N=256 (block 256)/alloc (neighbors Wrap)	4.86 ± 0.62 ms	5.25 ± 1.5 ms	0.925 ± 0.29
stencil/dagger/N=256 (block 256)/assign (const)	0.698 ± 0.084 ms	0.723 ± 0.041 ms	0.966 ± 0.13
stencil/dagger/N=256 (block 256)/multi-expr	1.35 ± 0.076 ms	1.48 ± 0.0094 ms	0.912 ± 0.051
stencil/dagger/N=256 (block 256)/neighbors (Clamp)	4.58 ± 0.13 ms	4.81 ± 0.26 ms	0.952 ± 0.059
stencil/dagger/N=256 (block 256)/neighbors (Pad)	4.57 ± 0.11 ms	4.89 ± 0.31 ms	0.933 ± 0.064
stencil/dagger/N=256 (block 256)/neighbors (Reflect)	4.61 ± 0.19 ms	4.46 ± 0.099 ms	1.03 ± 0.048
stencil/dagger/N=256 (block 256)/neighbors (Wrap)	4.85 ± 0.29 ms	4.76 ± 0.27 ms	1.02 ± 0.084
stencil/dagger/N=256 (block 256)/update (+)	0.815 ± 0.021 ms	0.864 ± 0.037 ms	0.943 ± 0.047
time_to_load	1.03 ± 0.0041 s	1.03 ± 0.0022 s	1 ± 0.0046

Plots

⚠️ Regressions (> 25.0%)

• linalg/dagger/N=256 (block 256)/syrk (A'*A): +34.3%
• array/dagger/N=1024 (block 512)/alloc (rand): +30.2%

Improvements (> 25.0% faster)

• linalg/dagger/N=1024 (block 512)/qr: -68.9%

Full results and plots (download the benchmark-results artifact).