datadeps: Parallelize analysis and scheduling via hierarchical scheduling

[jpsamaroo]

This allows Datadeps analysis and scheduling (ordinarily sequential operations) to be parallelized by multiple threads and/or multiple workers, greatly improving performance and scalability.

Written by Claude

[github-actions]

Dagger benchmarks: dirty vs master

	master	dirty	master / dirty
array/dagger/N=1024 (block 512)/add (X + X)	10.4 ± 0.25 ms
array/dagger/N=1024 (block 512)/alloc (rand)	4.26 ± 0.18 ms
array/dagger/N=1024 (block 512)/broadcast (X .+ 1)	7.59 ± 0.71 ms
array/dagger/N=1024 (block 512)/map (sin.(X))	11.4 ± 0.6 ms
array/dagger/N=1024 (block 512)/norm	3.8 ± 0.23 ms
array/dagger/N=1024 (block 512)/reduce (sum)	7.23 ± 0.74 ms
array/dagger/N=1024 (block 512)/transpose (permutedims)	9.35 ± 2.1 ms
array/dagger/N=256 (block 256)/add (X + X)	3.03 ± 0.65 ms
array/dagger/N=256 (block 256)/alloc (rand)	1.16 ± 0.22 ms
array/dagger/N=256 (block 256)/broadcast (X .+ 1)	3.28 ± 0.18 ms
array/dagger/N=256 (block 256)/map (sin.(X))	3.5 ± 0.12 ms
array/dagger/N=256 (block 256)/norm	1.95 ± 0.028 ms
array/dagger/N=256 (block 256)/reduce (sum)	4.09 ± 0.63 ms
array/dagger/N=256 (block 256)/transpose (permutedims)	2.41 ± 0.11 ms
linalg/dagger/N=1024 (block 512)/cholesky	31.5 ± 1.3 ms
linalg/dagger/N=1024 (block 512)/lu	7.65 s
linalg/dagger/N=1024 (block 512)/matmul (A*A)	0.0585 ± 0.0069 s
linalg/dagger/N=1024 (block 512)/matvec (A*x)	9.34 ± 0.79 ms
linalg/dagger/N=1024 (block 512)/qr	0.381 ± 0.0033 s
linalg/dagger/N=1024 (block 512)/solve (A\b via lu)	10.9 s
linalg/dagger/N=1024 (block 512)/syrk (A'*A)	0.0439 ± 0.0052 s
linalg/dagger/N=256 (block 256)/cholesky	6.43 ± 2.3 ms
linalg/dagger/N=256 (block 256)/lu	1.31 ± 0.02 s
linalg/dagger/N=256 (block 256)/matmul (A*A)	3.91 ± 0.038 ms
linalg/dagger/N=256 (block 256)/matvec (A*x)	3.63 ± 0.49 ms
linalg/dagger/N=256 (block 256)/qr	11.1 ± 0.9 ms
linalg/dagger/N=256 (block 256)/solve (A\b via lu)	2.23 ± 0.018 s
linalg/dagger/N=256 (block 256)/syrk (A'*A)	6.34 ± 0.87 ms
stencil/dagger/N=1024 (block 512)/alloc (neighbors Wrap)	0.0517 ± 0.0023 s
stencil/dagger/N=1024 (block 512)/assign (const)	4 ± 0.3 ms
stencil/dagger/N=1024 (block 512)/multi-expr	10.6 ± 1.3 ms
stencil/dagger/N=1024 (block 512)/neighbors (Clamp)	0.0557 ± 0.0027 s
stencil/dagger/N=1024 (block 512)/neighbors (Pad)	0.101 ± 0.011 s
stencil/dagger/N=1024 (block 512)/neighbors (Reflect)	0.0922 ± 0.012 s
stencil/dagger/N=1024 (block 512)/neighbors (Wrap)	0.092 ± 0.016 s
stencil/dagger/N=1024 (block 512)/update (+)	6.08 ± 0.14 ms
stencil/dagger/N=256 (block 256)/alloc (neighbors Wrap)	14.4 ± 0.66 ms
stencil/dagger/N=256 (block 256)/assign (const)	2.51 ± 0.15 ms
stencil/dagger/N=256 (block 256)/multi-expr	4.85 ± 0.27 ms
stencil/dagger/N=256 (block 256)/neighbors (Clamp)	13.2 ± 0.23 ms
stencil/dagger/N=256 (block 256)/neighbors (Pad)	15.9 ± 0.23 ms
stencil/dagger/N=256 (block 256)/neighbors (Reflect)	15.4 ± 0.12 ms
stencil/dagger/N=256 (block 256)/neighbors (Wrap)	15.7 ± 0.67 ms
stencil/dagger/N=256 (block 256)/update (+)	2.65 ± 1 ms
time_to_load	0.985 ± 0.0068 s	1.02 ± 0.013 s	0.961 ± 0.014

No regressions beyond 25.0% 🎉

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