Series of cleanup loops for partial loop unrolling

[pjattke]

Partial loop unrolling considers the number of ciphertext slots. For example, if there are 256 slots then 256 iterations are unrolled to enable simultaneous execution using SIMD capabilities of the underlying FHE scheme. The remaining loops are executed using a cleanup loop For example, if the initial number of iteration is 500 then the remaining 244 iterations would be executed using the cleanup loop.

Currently, the cleanup loop only executes a single operation at once. This could be improved by generating a binary series of cleanup loops, for example, the unrolled loop uses 256 slots, followed by a 128-unrolled cleanup loop, then a 64-unrolled cleanup loop, then a 32-unrolled cleanup loop, etc. See TODO note in CompileTimeExpressionSimplifier.

A question involved in the implementation is to decide at which point to stop (minimum unroll factor of cleanup loop). Maybe this must be determined using an empirical approach.

[AlexanderViand-Intel]

Closing this old issue, as the final HECO batching optimization no longer uses the underlying approach that caused the issue :)