Add ILP bootstrap placement pass

[edwjchen]

This PR is an initial attempt at implementing a naive ILP-based bootstrap placement pass for more efficient bootstrap and secret-mgmt operation placement. The pass does not rely on the current secret-mgmt-insert-pass, as the pass initially solves for the level of each op, thereby determining the bootstrap and other secret-mgmt operation placement.

• New pass --ilp-bootstrap-placement with option bootstrap-waterline
• LIT tests: bootstrap_placement_comparison.mlir, ilp_relin_modreduce_placement.mlir.

At a high-level, the formulation is as follows:

• Variables
  • the input level of each op, the output level of each op, and whether a bootstrap is placed on an op.
• Constraints
  • Level bounds: 0 <= op.level <= bootstrapWaterline
  • Operand matching: operand levels must be equal
  • Multiplication: assumes multiplications consume 1 level
  • Non-mult: all other operations forward the operand level
  • Bootstrap (big-M): if bootstrap, then the output level is the bootstrapWaterline, otherwise the input level is forwarded to the output level.
• Objective: minimize number of bootstrap operations

Note: This is still a naive ILP implementation and there are concerns yet to be addressed.

• This ILP formulation relies on the assumption that every multiplication consumes a level. This can be relaxed with more fine-grain scale analysis, (e.g., that delays multiple multiplications before a rescale instruction).
• The ILP formulation only considers the input and output level of each vertex. However, this misses potential level changes along edges (e.g., when two independent data paths converge at an op with a level mismatch). The assumption assumes a modReduce operation after every multiplication, and all operands levels are equal without additional modReduce operations.

These limitations will be addressed in the future.

[j2kun]

Looking pretty good! I have a few performance comments on the ILP, one major organizational comment on the IR update itself, and the rest are nitpicks.

[j2kun]

Please run pre-commit run --all-files to fix the linter errors. You can set it up to run automatically as a git hook via https://heir.dev/docs/development/#pre-commit

[edwjchen]

Please run pre-commit run --all-files to fix the linter errors. You can set it up to run automatically as a git hook via https://heir.dev/docs/development/#pre-commit

Updated!