order - fuse - order kernel logic#74
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Jutho
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Jul 15, 2026
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| g = 8 * sizeof(Int) - leading_zeros(M + 1) | ||
| importance = 2 .* (1 .<< (g .* (N .- indexorder(strides[1])))) | ||
| for k in 2:M | ||
| importance = importance .+ (1 .<< (g .* (N .- indexorder(strides[k])))) | ||
| end |
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I have to admit that I forgot exactly how this cost model works 😄
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Something like, the importance of a dimension is
sum over arrays of 2^(log2(M+2) * (N - indexorder of dimension in array))
So if an index is the first index in each of the arrays, its importance is
(M+1) * (M+2)^((N-1))
Jutho
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| # ceil(Int, log2(M+2)) # to account for the fact that there are M arrays, where the first one is counted with a factor 2 | ||
| g = 8 * sizeof(Int) - leading_zeros(M + 1) |
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Suggested change
| # ceil(Int, log2(M+2)) # to account for the fact that there are M arrays, where the first one is counted with a factor 2 | |
| g = 8 * sizeof(Int) - leading_zeros(M + 1) | |
| g = 8 * sizeof(Int) - leading_zeros(M + 1) # = ceil(Int, log2(M+2)) | |
| # to account for the fact that there are M arrays, where the first one is counted with a factor 2 |
Jutho
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Jul 15, 2026
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Closes #72.
The previous approach was
fuse-order, where thefuseonly works if at least one of the input arrays is ordered in increasing strides. The pathological case beingpermutedims(A, (2,1)) .= permutedims(B, (2, 1)), where fusion is trivial but never happened.Here, I simply first order, then fuse, and then finally order again to make sure the leftover dim 1's from the fusion are migrated to the end.