[do-not-merge] approximate non-linearities and CKKS management for Transformers

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[do-not-merge] approximate non-linearities and CKKS management for Transformers

Introduce polynomial approximation pipelines, numerical stability passes,
padding tracking, and scale/bootstrap management optimizations required for
evaluating deep CKKS Transformer models (e.g. BERT-tiny SST-2):

• Frontend canonicalization & domain stamping:

  • Add PrepareForLayoutPropagation to canonicalize PyTorch and torch-mlir
    export idioms before layout assignment (folding unit-dimension reshapes
    and transposes, bias additions into matmuls, and raising generic
    subgraphs to linalg).
  • Add StampApproximationDomains to attach calibrated approximation interval
    attributes to bare math.rsqrt and math.erf ops from unannotated PyTorch
    exports, supplying domain bounds and degrees for Chebyshev approximations.

• Numerically stable non-linearities (Softmax, GELU, & Reciprocal):

  • Add SoftmaxToNsSoftmax to lower Softmax to normalize-and-square form with
    exact compile-time zero-padding cancellation, preventing exponential
    overflow in attention matrices.
  • Add LowerRecip to lower math_ext.reciprocal using self-correcting
    Goldschmidt iterations with calibrated polynomial seeds, preventing NaN
    divergence across stacked transformer layers.
  • Extend PolynomialApproximation to support operations pinning
    approximation_method = "chebyshev" (and "hermite") to enforce
    Carathéodory-Fejér minimax polynomial fitting over Taylor series.

• Padding semantics propagation:

  • Introduce #tensor_ext.padding attribute, PaddingSemanticsOpInterface, and
    PropagatePadding pass to derive trailing zero-padding metadata across
    matmuls, transposes, broadcasts, reductions, and elementwise ops.
  • Prevent interleaved padding elements in CRT slot layouts from corrupting
    reduction statistics in LayerNorm and Softmax.
  • Strip padding attributes during TensorExtToTensor conversion.

• CKKS scale management & underdetermined scale resolution:

  • Extend ScaleAnalysis and PopulateScaleCKKS to resolve underdetermined
    adjust_scale operations in multi-branch DAGs where both join operands
    arrive through adjust_scale and modreduce chains.
  • Assign consistent canonical target scales (logDefaultScale + logq before
    modreduce, or logDefaultScale) to prevent scale inference failures and
    mismatches at residual addition joins.

• Secret insert management & bootstrap optimizations:

  • Hoist shared bootstraps before rotation fan-out operations when sibling
    bootstraps share a common source root in SecretInsertMgmtCKKS.
  • Skip terminal refreshes when remaining multiplicative depth is sufficient
    to complete the computation without an extra bootstrap.
  • Emit adjust_scale and modreduce before bootstrap operations so
    bootstrapped ciphertexts are guaranteed to be at base scale, preventing
    runtime modulus panics in Lattigo.
  • Fix waterline calculation when levelBudget == -1 to prevent spurious
    bootstraps in unbudgeted modules.

• Testing:

  • Add lit test suites for prepare_for_layout_propagation,
    stamp_approximation_domains, polynomial_approximation, propagate_padding,
    softmax_to_ns_softmax, lower_recip, and populate_scale.
  • Add targeted SecretInsertMgmt lit tests for fan-out bootstrap hoisting,
    skipping terminal refreshes, and base-scale bootstrap insertion.
  • Align bootstrap_placement_comparison greedy budget with ILP waterline 3.