Tier 3: integer fast paths for mixed-grid add and cross-grid stores#20
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Two of the three Tier-3 follow-ups from the performance pass, both measured with the nanobench suite and gated to be bit-identical: - addition.hpp: mixed integer-aligned / notch-offset operands with a unit-numerator result notch 1/d compute both offsets as pure integer math ((to_value - Lower)*d and raw*widen) instead of the 3-op exact rational branch. New bench row: 146 -> 31 ns, 2107 -> 415 ins (4.7x). Gated on an index-raw result, imax-safe slot counts, and NON-fp operands (a double raw has no integer offset - test_real_exact's oracle caught that during development; a pinning test keeps it out). - assignment.hpp: the non-integer cross-grid store folds Offset + Factor*raw to one integer multiply-add plus the same round_quotient. The gate proves every product (including the worst-case runtime numerator over R's raw range) fits imax AND mirrors round_quotient's internal value-index branch-choice checks, so reduced and unreduced forms take the same branch - bit-identical results incl. negative ties. Bench row: 156 -> 99 ns, 2144 -> 1351 ins. The third follow-up (folding the constant offset math in the remaining rational branch) is intentionally skipped: after the mixed-add path landed that branch only serves rational-raw operands, no benchmark exercises it, and the fold would save one rational op on a path dominated by the rational add itself. Recorded in bench.cpp's known-slow-paths note. tests/test_cross_grid.cpp pins both gates engaged for their shapes and the fp exclusion; docs/performance.md regenerated with the new rows. Verified: full suite green in default + BND_MATH_FIXED configs, fuzz seed 777 x 40k iters clean (128.8M checks), accuracy tables bit-identical, amalgamation + codegen guard green. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Implements two of the three Tier-3 follow-ups from the performance pass (#18), both measured with the nanobench suite and gated to be bit-identical to the rational paths they replace.
Mixed integer/notch-offset add (
addition.hpp)With a unit-numerator result notch
1/d, both operand offsets in result-notch units are pure integer math —(to_value − Lower)·dfor the integer-aligned operand,raw·widenfor the notch-offset one — replacing the 3-op exact-rational branch.146 → 31 ns, 2107 → 415 ins (4.7×) on the new bench row (A/B with the gate disabled).
Gated on an index-raw result, imax-safe slot counts, and non-fp operands: a real-backed operand whose result grid drops to integer storage past the 2^53 exactness limit would have its double raw truncated —
test_real_exact's oracle caught exactly that during development, and a[perf-paths]pinning test keeps fp shapes excluded.Affine-folded cross-grid store (
assignment.hpp)The non-integer
Offset + Factor·rawrational chain folds to one integer multiply-add plus the sameround_quotient. The gate proves every product (including the worst-case runtime numerator over R's raw range) fitsimaxand mirrorsround_quotient's internal value-index branch-choice fit checks — rounding is reduction-invariant, but the branch choice is not (negative ties differ across branches), so both forms are forced onto the same branch.156 → 99 ns, 2144 → 1351 ins on the existing
cross-grid assign :: non-integer snaprow (which includes source construction, so the store itself improved more).Third follow-up: intentionally skipped
Folding the constant offset math in the remaining rational branch is dropped: after the mixed-add path lands, that branch only serves rational-raw operands, no benchmark exercises it, and the fold would save one rational op on a path dominated by the rational add itself. Recorded in bench.cpp's known-slow-paths note.
Verification
Full suite green in default +
BND_MATH_FIXEDconfigs (incl. new[perf-paths]pinning tests) · fuzz seed 777 × 40k iters clean (128.8M checks) · accuracy tables bit-identical · amalgamation + codegen guard green ·docs/performance.mdregenerated with the new rows. The armed cachegrind gates (#19) run against this PR.🤖 Generated with Claude Code