Rotom: Rolled Layout Representation - #3170
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Two roll-semantics extensions that make diagonal packings expressible beyond the square, equal-extent case: - The roll-by (second) dim may be any kind. Rolling by a replication or gap dim shifts by that dim's block index, so each block holds a distinct cyclic rotation of the rolled dim -- the layout materializes every rotation and downstream alignment becomes block selection (the replicate-then-roll expansion of a compact operand is pure rotations). A rolled-by gap claims its blocks: it contributes an existential address term and counts toward the ciphertext count, unlike a plain gap. Rolls apply on both the ciphertext and slot address lines, so a roll can place a diagonal on the ciphertext axis (one ciphertext per diagonal); a from-dim absent from a line drops out of that line's address. - Roll extents need not match: roll(i, j) rewrites dims[i]'s index to (idx_i - idx_j) mod extent(dims[i]), well-defined for any partner extent -- a smaller partner covers a prefix of the rotations, a larger one wraps. This unlocks rolled placements for rectangular (non-square k) contractions. A rolled-by gap is bounded to the rolled dim's extent (larger gaps would claim blocks holding repeated rotations that the accounting was never audited for); larger replication partners are the intended replicate-then-roll form and stay unbounded. Materialization unit tests cover roll-by-replication, roll-by-gap (claimed blocks), both unequal-extent orientations, and the verifier rules; lit tests cover the mod-from positive case and the gap bound.
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Part 2 of #2980 and stacked on #3169
Two extensions to roll(from, by) semantics that make diagonal packings expressible beyond the square, equal-extent case.
Roll partners may be replication or gap dims. Previously both roll operands had to be traversal dims. Now the by (second) dim may also be a replication or gap dim.
Roll extents need not match (mod-from). roll(i, j) now rewrites dims[i]'s index to (idx_i - idx_j) mod extent(dims[i]), well-defined for any partner extent - a smaller partner covers a prefix of the rotations, a larger one wraps. This unlocks rolled placements for rectangular (non-square-k) contractions.
Rolled-by-gap bound. A rolled-by gap partner is bounded to the rolled dim's extent.