From bf17a8e6e7f2f990621b5bf6caee14a71a9712b6 Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 01:25:58 +0000 Subject: [PATCH 1/8] perf(row-reduce): optimize prepared nullspace benchmarks --- .github/workflows/ci.yml | 5 +- HexBerlekamp/PackedKernel.lean | 1 + HexRowReduce/Nullspace.lean | 18 +- HexRowReduce/RowEchelon/Contracts.lean | 121 +++++++++++ HexRowReduce/SPEC/hex-row-reduce.md | 47 ++++- bench/HexRowReduce/Bench.lean | 268 ++++++++++++++++++++++++ lakefile.lean | 4 + libraries.yml | 12 +- reports/phase4-ordered-mode-audit.md | 2 +- scripts/oracle/flint_bench_driver.py | 39 ++++ scripts/oracle/test_flint_fmpq_bench.py | 54 +++++ scripts/release/released-ci.yml | 17 +- scripts/release/released.yml | 4 +- 13 files changed, 576 insertions(+), 16 deletions(-) create mode 100644 bench/HexRowReduce/Bench.lean create mode 100644 scripts/oracle/test_flint_fmpq_bench.py diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index c67883bba..005664019 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -72,6 +72,7 @@ jobs: python3 -m unittest scripts/bench/test_primality_negative_sweep.py python3 -m unittest scripts/bench/test_primality_mathlib_proof_sweep.py python3 -m unittest scripts/oracle/test_flint_mpoly_bench.py + python3 -m unittest scripts/oracle/test_flint_fmpq_bench.py python3 -m unittest scripts/oracle/test_singular_mpoly_bench.py python3 -m unittest scripts/oracle/test_rcf_flint_bench.py python3 scripts/ci/check_benches_mathlib_free.py @@ -172,7 +173,7 @@ jobs: - name: Define the hex-dev cache + build target sets run: | echo "HEX_LIB_TARGETS=HexBasic HexTruncatedSeries HexTruncatedSeriesMathlib HexArith HexPoly HexPolyFast HexMvPoly HexModArith HexGF2 HexPolyZ HexRoots HexResultant HexInterval HexIntervalExperiment HexIntervalMathlib HexIntervalMathlibExperiment HexIntervalReplayProbe HexIntervalMathlibReplayProbe HexRealRootsMathlibReplayProbe HexRCFProofProbe HexPolyFp HexGFqRing HexGFqField HexBerlekamp HexHensel HexConway HexGFq HexPrimality HexIntFactor HexPrimalityKernelProbe HexPrimalityElabProbe HexPrimalityMathlibProofProbe HexIntFactorKernelProbe HexMvGcdKernelProbe HexBerlekampZassenhaus HexRealRoots HexMatrix HexRowReduce HexDeterminant HexBareiss HexHermite HexSmith HexCharPoly HexMinPoly HexPolySmith HexGramSchmidt HexLLL HexMatrixMathlib HexHermiteMathlib HexSmithMathlib HexSmithTests HexCharPolyMathlib HexMinPolyMathlib HexPolySmithMathlib HexGramSchmidtMathlib HexLLLMathlib HexBerlekampZassenhausMathlib HexBerlekampZassenhausMathlibProofProbe HexBerlekampMathlibProofProbe HexPrimalityMathlib HexIntFactorMathlib HexPolyFpMathlib HexFactorizationModules HexRealRootsMathlib HexGF2Mathlib HexGFqMathlib HexMvPolyMathlib HexMvPolyMathlibProofProbe HexRCF HexRCFTests HexRootsMathlib HexResultantMathlib HexNumberField HexNumberFieldMathlib HexNumberFieldTower HexNumberFieldTowerMathlib HexReleaseTests HexReleaseExamples HexAggregateCheck" >> "$GITHUB_ENV" - echo "HEX_EXE_TARGETS=hextruncatedseries_bench hexarith_bench hexpoly_bench hexpolyfast_bench hexpolysmith_bench hexmvpoly_bench hexmvgcd_bench hexsparsepoly_bench hexpolyz_bench hexpolyfp_bench hexmodarith_bench hexmodular_bench hexgf2_bench hexgfqring_bench hexgfqfield_bench hexgfq_bench hexhensel_bench hexprimality_bench hexprimality_policy_probe hexprimality_fuel_probe hexintfactor_bench hexberlekamp_bench hexbz_bench hexconway_bench hexmatrix_bench hexstrassen_compare hexdeterminant_bench hexbareiss_bench hexcharpoly_bench hexminpoly_bench hexgramschmidt_bench hexhermite_bench hexsmith_bench hexrealroots_bench hexrcf_bench hexroots_bench hexresultant_bench hexnumberfield_bench hexnumberfieldtower_bench hexinterval_decision_bench hexroots_demo hex_interval_representation_spike hex_interval_center_spike hex_interval_scale_spike hex_interval_scheduler_spike hex_interval_policy_frontier_spike hex_arith_floor hexlll_bench hexlll_gram_bench hexlll_external_reduction hexbz_factor_service" >> "$GITHUB_ENV" + echo "HEX_EXE_TARGETS=hextruncatedseries_bench hexarith_bench hexpoly_bench hexpolyfast_bench hexpolysmith_bench hexmvpoly_bench hexmvgcd_bench hexsparsepoly_bench hexpolyz_bench hexpolyfp_bench hexmodarith_bench hexmodular_bench hexgf2_bench hexgfqring_bench hexgfqfield_bench hexgfq_bench hexhensel_bench hexprimality_bench hexprimality_policy_probe hexprimality_fuel_probe hexintfactor_bench hexberlekamp_bench hexbz_bench hexconway_bench hexmatrix_bench hexstrassen_compare hexrowreduce_bench hexdeterminant_bench hexbareiss_bench hexcharpoly_bench hexminpoly_bench hexgramschmidt_bench hexhermite_bench hexsmith_bench hexrealroots_bench hexrcf_bench hexroots_bench hexresultant_bench hexnumberfield_bench hexnumberfieldtower_bench hexinterval_decision_bench hexroots_demo hex_interval_representation_spike hex_interval_center_spike hex_interval_scale_spike hex_interval_scheduler_spike hex_interval_policy_frontier_spike hex_arith_floor hexlll_bench hexlll_gram_bench hexlll_external_reduction hexbz_factor_service" >> "$GITHUB_ENV" # Shared build. The libraries, bench exes, conformance #guard drivers, and # emit-fixture exes are all elaborated here so the two verification tails # below only *run* things, never rebuild them -- which is what lets the @@ -241,7 +242,7 @@ jobs: hexmodular_bench \ hexgf2_bench hexgfqring_bench hexgfqfield_bench hexgfq_bench \ hexhensel_bench hexintfactor_bench hexberlekamp_bench hexbz_bench \ - hexconway_bench hexdeterminant_bench hexmatrix_bench \ + hexconway_bench hexdeterminant_bench hexmatrix_bench hexrowreduce_bench \ hexhermite_bench hexsmith_bench \ hexcharpoly_bench hexminpoly_bench \ hexgramschmidt_bench hexlll_gram_bench \ diff --git a/HexBerlekamp/PackedKernel.lean b/HexBerlekamp/PackedKernel.lean index 806ed31de..da9e18f85 100644 --- a/HexBerlekamp/PackedKernel.lean +++ b/HexBerlekamp/PackedKernel.lean @@ -875,6 +875,7 @@ theorem nullspaceArray_eq {q : UInt32} (hq : q.toNat = p) by_cases hjf : (⟨j, hj⟩ : Fin m) = hE.toIsEchelonForm.freeCols.get ⟨k, hklt⟩ · rw [ite_eq_left hjf, dite_eq_left hjf] · rw [ite_eq_right hjf, dite_eq_right hjf, pivotRowOf_eq (Matrix.rowReduce E) ⟨j, hj⟩] + rw [Matrix.IsRowReduced.pivotRows_get] cases hpi : Matrix.IsRowReduced.pivotIndex? (Matrix.rowReduce E) (⟨j, hj⟩ : Fin m) with | none => rfl | some i => diff --git a/HexRowReduce/Nullspace.lean b/HexRowReduce/Nullspace.lean index 097eb642c..d57bfbf2f 100644 --- a/HexRowReduce/Nullspace.lean +++ b/HexRowReduce/Nullspace.lean @@ -116,16 +116,28 @@ private theorem pivotIndex?_free_none (E : IsEchelonForm M D) (k : Fin (m - D.ra intro i exact E.pivotCols_disjoint_freeCols i k +omit [Mul R] [Add R] [OfNat R 0] [OfNat R 1] in +/-- Reading the materialized pivot-row table agrees with `pivotIndex?`. -/ +@[simp] theorem pivotRows_get (j : Fin m) : + (Vector.ofFn fun j => pivotIndex? D j).get j = pivotIndex? D j := by + change (Vector.ofFn fun j => pivotIndex? D j)[j] = pivotIndex? D j + simp + /-- Nullspace basis vectors assembled as columns indexed by the free variables. -/ @[expose] def nullspaceMatrix [Lean.Grind.Ring R] (E : IsRowReduced M D) : Matrix R m (m - D.rank) := let freeCols := E.toIsEchelonForm.freeCols + -- Materialize the column-to-pivot-row lookup once. `Matrix.ofFn` then + -- performs constant-time vector reads instead of scanning `pivotCols` for + -- every output entry. + let pivotRows : Vector (Option (Fin D.rank)) m := + Vector.ofFn fun j => pivotIndex? D j Matrix.ofFn fun j k => if hFree : j = freeCols.get k then 1 else - match pivotIndex? D j with + match pivotRows.get j with | some i => -D.echelon[(IsEchelonForm.pivotRow E.toIsEchelonForm i, freeCols.get k)] | none => 0 @@ -145,7 +157,7 @@ def nullspaceMatrix [Lean.Grind.Ring R] (E : IsRowReduced M D) : have hne : E.toIsEchelonForm.freeCols.get l ≠ E.toIsEchelonForm.freeCols.get k := by intro h exact hkl ((E.toIsEchelonForm.freeCols_injective h).symm) - simp [hne, pivotIndex?_free_none E.toIsEchelonForm l] + simp [hne, pivotRows_get, pivotIndex?_free_none E.toIsEchelonForm l] /-- In a pivot-column row, a nullspace-matrix entry is the negative RREF entry in the matching pivot row and free column. -/ @@ -154,7 +166,7 @@ the matching pivot row and free column. -/ E.nullspaceMatrix[D.pivotCols.get i][k] = -(D.echelon[(IsEchelonForm.pivotRow E.toIsEchelonForm i)][E.toIsEchelonForm.freeCols.get k]) := by simp only [nullspaceMatrix, getElem_ofFn] - simp [E.toIsEchelonForm.pivotCols_disjoint_freeCols i k, + simp [pivotRows_get, E.toIsEchelonForm.pivotCols_disjoint_freeCols i k, pivotIndex?_pivot E.toIsEchelonForm i] /-- The individual nullspace basis vectors. diff --git a/HexRowReduce/RowEchelon/Contracts.lean b/HexRowReduce/RowEchelon/Contracts.lean index 73e3e7c08..18674113c 100644 --- a/HexRowReduce/RowEchelon/Contracts.lean +++ b/HexRowReduce/RowEchelon/Contracts.lean @@ -128,6 +128,127 @@ Mathlib-free layer). -/ def freeColsList (_E : IsEchelonForm M D) : List (Fin m) := (List.finRange m).filter fun j => j ∉ D.pivotCols.toList +/-- Linear merge used by the compiled implementation of `freeColsList`. + +The second list is a sorted sublist of the first. Matching heads are +discarded; otherwise the first head belongs to the complement. Both recursive +calls consume a column, and a matching call also consumes a pivot, so the loop +is linear in the two input lengths. -/ +@[expose] +def sortedComplement [DecidableEq α] : List α → List α → List α + | xs, [] => xs + | [], _ => [] + | x :: xs, y :: ys => + if x = y then + sortedComplement xs ys + else + x :: sortedComplement xs (y :: ys) + +private theorem sortedComplement_eq_filter [DecidableEq α] + {pivots cols : List α} (hsub : pivots.Sublist cols) (hnodup : cols.Nodup) : + sortedComplement cols pivots = cols.filter fun x => x ∉ pivots := by + induction hsub with + | slnil => simp [sortedComplement] + | @cons pivots cols x hsub ih => + have hnot : x ∉ pivots := by + intro hx + exact (List.nodup_cons.mp hnodup).1 (hsub.subset hx) + cases pivots with + | nil => + rw [sortedComplement] + symm + apply List.filter_eq_self.mpr + intro z hz + simp + | cons y ys => + have hxy : x ≠ y := by + intro h + subst y + exact hnot (by simp) + rw [sortedComplement, if_neg hxy] + rw [ih (List.nodup_cons.mp hnodup).2] + rw [List.filter_cons] + have hp : (decide (x ∉ y :: ys) : Bool) = true := decide_eq_true hnot + rw [hp] + simp + | @cons_cons pivots cols x hsub ih => + rw [sortedComplement, if_pos rfl, List.filter_cons_of_neg (by simp)] + rw [ih (List.nodup_cons.mp hnodup).2] + apply List.filter_congr + intro z hz + have hzx : z ≠ x := by + intro h + subst z + exact (List.nodup_cons.mp hnodup).1 hz + simp [hzx] + +private theorem pairwise_perm_eq {xs ys : List (Fin m)} + (hxs : List.Pairwise (fun a b : Fin m => a < b) xs) + (hys : List.Pairwise (fun a b : Fin m => a < b) ys) + (hperm : xs.Perm ys) : xs = ys := by + induction xs generalizing ys with + | nil => exact hperm.symm.eq_nil.symm + | cons x xs ih => + cases ys with + | nil => + have hlen := hperm.length_eq + simp at hlen + | cons y ys => + have hxmem : x ∈ y :: ys := hperm.subset (by simp) + have hymem : y ∈ x :: xs := hperm.symm.subset (by simp) + have hxy : x = y := by + rcases List.mem_cons.mp hxmem with h | hx + · exact h + · rcases List.mem_cons.mp hymem with h | hy + · exact h.symm + · have hyx : y < x := (List.pairwise_cons.mp hys).1 x hx + have hxy : x < y := (List.pairwise_cons.mp hxs).1 y hy + omega + subst y + simp only [List.cons.injEq, true_and] + exact ih (List.pairwise_cons.mp hxs).2 (List.pairwise_cons.mp hys).2 + hperm.cons_inv + +/-- Runtime implementation of `freeColsList`, merging the sorted pivot columns +with the complete sorted column range. -/ +@[expose] +def freeColsListImpl (E : IsEchelonForm M D) : List (Fin m) := + sortedComplement (List.finRange m) D.pivotCols.toList + +private theorem pivotCols_sublist_finRange (E : IsEchelonForm M D) : + D.pivotCols.toList.Sublist (List.finRange m) := by + let p : Fin m → Bool := fun j => decide (j ∈ D.pivotCols.toList) + have hfilterPairs : List.Pairwise (fun a b : Fin m => a < b) + ((List.finRange m).filter p) := by + exact List.Pairwise.filter p (List.pairwise_lt_finRange m) + have hfilterNodup : ((List.finRange m).filter p).Nodup := by + rw [List.nodup_iff_pairwise_ne] + exact hfilterPairs.imp (fun hlt heq => by subst heq; omega) + have hperm : D.pivotCols.toList.Perm ((List.finRange m).filter p) := by + rw [List.perm_ext_iff_of_nodup E.pivotCols_nodup hfilterNodup] + intro a + constructor + · intro ha + rw [List.mem_filter] + exact ⟨List.mem_finRange a, show p a = true from by exact decide_eq_true ha⟩ + · intro ha + rw [List.mem_filter] at ha + exact of_decide_eq_true ha.2 + have heq : D.pivotCols.toList = (List.finRange m).filter p := + pairwise_perm_eq E.pivotCols_pairwise hfilterPairs hperm + rw [heq] + exact List.filter_sublist + +/-- Register the linear merge as the compiled implementation of +`freeColsList`. The proof keeps the specification and all theorem-facing +unfolding unchanged. -/ +@[csimp] +theorem freeColsList_eq_impl : @freeColsList = @freeColsListImpl := by + funext R n m _ _ _ _ M D E + unfold freeColsList freeColsListImpl + exact (sortedComplement_eq_filter (E.pivotCols_sublist_finRange) + (List.nodup_finRange m)).symm + /-- The number of free columns is the ambient column count minus the rank. -/ theorem freeColsList_length (E : IsEchelonForm M D) : E.freeColsList.length = m - D.rank := by diff --git a/HexRowReduce/SPEC/hex-row-reduce.md b/HexRowReduce/SPEC/hex-row-reduce.md index a2c9311e6..62f1e00e3 100644 --- a/HexRowReduce/SPEC/hex-row-reduce.md +++ b/HexRowReduce/SPEC/hex-row-reduce.md @@ -106,11 +106,46 @@ with `colPartition` (free columns telescope to `v[freeCols[l]]`; pivot columns follow from `pivot_one` / `above_pivot_zero` / `below_pivot_zero` / `zero_row`); package into `E.nullspaceMatrix * c = v`. +## Complexity and benchmark contract + +For an `n × m` matrix of rank `r`, Gauss--Jordan reduction performs at most +`r` pivot stages and visits `O(n(n + m))` entries per stage across the echelon +and transform matrices. The arithmetic-operation bound is therefore +`O(rn(n + m))`, cubic on the fixed-aspect square benchmark families. Exact +rational bit cost additionally depends on numerator and denominator growth. + +The compiled implementation uses a proved linear sorted merge for the +free-column complement. Prepared nullspace construction materializes the +column-to-pivot-row lookup once and then writes `m(m - r)` output entries with +constant-time lookup per entry; its fixed-aspect bound is quadratic. + +`bench/HexRowReduce/Bench.lean` gives all 12 advertised executable operations +direct mode-1 coverage: + +| Operations | Prepared state | Model | +| --- | --- | --- | +| `Matrix.rowReduce`, `Matrix.rowReduce_rank` | dense input | `n³` | +| `Matrix.spanCoeffs`, `Matrix.spanContains` | dense input | `n³` | +| `IsEchelonForm.spanCoeffs`, `IsEchelonForm.spanContains` | proved RREF | `n²` | +| `IsEchelonForm.echelonCoeffs`, `IsEchelonForm.freeCols` | proved RREF | `n` | +| `Matrix.nullspaceBasisMatrix`, `Matrix.nullspace` | deficient input | `n³` | +| `IsRowReduced.nullspaceMatrix`, `IsRowReduced.nullspace` | proved RREF | `n²` | + +The dense family is `I + J`, so every pivot fires while coefficient heights +remain controlled. The deficient family has rank and nullity `n / 2`. +Preparation is outside the timed region and result forcing is inside it. + ## External comparators -The `rank`, `rowReduce`, and `nullspace` operations are cross-checked for correctness -against python-flint's `fmpz_mat` / `fmpq_mat` through the conformance oracle -(`scripts/oracle/matrix_flint.py`, driven by `hexrowreduce_emit_fixtures`). -There is no Phase-4 performance comparator: row reduction is an exact rational -computation validated for correctness, not timed against an external tool. See -`reports/hex-row-reduce-performance.md`. +The identical constant-size rank result is compared informationally with +python-flint's `fmpq_mat.rref()` through the shared persistent driver. Both +arms use the same dense `I + J` family; construction is cached during warmup, +and each timed request returns only the integer rank. + +The remaining operations declare +`no-comparable-surface-in-named-comparator`: Hex `rowReduce` returns the row +transform that `fmpq_mat.rref()` omits; python-flint 0.9.0's `fmpq_mat` has no +native nullspace callable; and span coefficients are transform-dependent +witnesses. A comparator-specific derived algorithm would not be the same +callable surface. Full RREF and nullspace correctness remain cross-checked by +`scripts/oracle/matrix_flint.py`, driven by `hexrowreduce_emit_fixtures`. diff --git a/bench/HexRowReduce/Bench.lean b/bench/HexRowReduce/Bench.lean new file mode 100644 index 000000000..f2656de19 --- /dev/null +++ b/bench/HexRowReduce/Bench.lean @@ -0,0 +1,268 @@ +/- +Copyright (c) 2026 Lean FRO, LLC. All rights reserved. +Released under Apache 2.0 license as described in the file LICENSE. +Authors: Kim Morrison +-/ + +import HexRowReduce +import Hex.BenchOracle.Flint +import Lean.Data.Json +import LeanBench + +/-! +Mode-1 benchmarks for every advertised executable `HexRowReduce` operation. + +The dense family is `I + J`: every column supplies a pivot while rational +heights remain bounded. The deficient family repeats the rows and columns of +the half-size dense matrix, giving rank and nullity `n / 2`. Prepared targets +receive their proved RREF data outside the timed region. +-/ + +namespace Hex.RowReduceBench + +structure Input where + n : Nat + matrix : Matrix Rat n n + query : Vector Rat n + +private def vectorChecksum {n : Nat} (v : Vector Rat n) : UInt64 := + hash v.toArray + +private def matrixChecksum {n m : Nat} (M : Matrix Rat n m) : UInt64 := + M.rows.toArray.foldl + (fun checksum row => mixHash checksum (vectorChecksum row)) (hash n) + +instance : Hashable Input where + hash input := mixHash (hash input.n) <| + mixHash (matrixChecksum input.matrix) (vectorChecksum input.query) + +structure ReducedInput where + n : Nat + source : Matrix Rat n n + data : Matrix.RowEchelonData Rat n n + reduced : Matrix.IsRowReduced source data + query : Vector Rat n + +instance : Hashable ReducedInput where + hash input := mixHash (hash input.n) <| + mixHash (matrixChecksum input.source) <| + mixHash (matrixChecksum input.data.echelon) <| + mixHash (matrixChecksum input.data.transform) <| + mixHash (hash input.data.pivotCols.toArray) (vectorChecksum input.query) + +def dense (n : Nat) : Input := + let matrix : Matrix Rat n n := + Matrix.ofFn fun i j => if i = j then 2 else 1 + let query : Vector Rat n := + Vector.ofFn fun j => if j.val = 0 then 2 else 1 + { n, matrix, query } + +def deficient (n : Nat) : Input := + let rank := n / 2 + let matrix : Matrix Rat n n := Matrix.ofFn fun i j => + if rank = 0 then 0 + else if i.val % rank = j.val % rank then 2 else 1 + let query : Vector Rat n := Vector.ofFn fun j => + if rank = 0 then 0 else if j.val % rank = 0 then 2 else 1 + { n, matrix, query } + +/-- Already-reduced projection used to prepare contract-level targets without +coefficient growth. -/ +def reducedDeficient (n : Nat) : Input := + let rank := n / 2 + let matrix : Matrix Rat n n := Matrix.ofFn fun i j => + if i = j ∧ i.val < rank then 1 else 0 + let query : Vector Rat n := Vector.ofFn fun j => + if j.val = 0 ∧ 0 < rank then 1 else 0 + { n, matrix, query } + +def denseReduced (n : Nat) : ReducedInput := + let input := dense n + let data := Matrix.rowReduce input.matrix + { n, source := input.matrix, data + reduced := Matrix.rowReduce_isRowReduced input.matrix + query := input.query } + +def deficientReduced (n : Nat) : ReducedInput := + let input := reducedDeficient n + let data := Matrix.rowReduce input.matrix + { n, source := input.matrix, data + reduced := Matrix.rowReduce_isRowReduced input.matrix + query := input.query } + +def runReduce (input : Input) : UInt64 := + let result := Matrix.rowReduce input.matrix + mixHash (hash result.rank) <| + mixHash (matrixChecksum result.echelon) <| + mixHash (matrixChecksum result.transform) (hash result.pivotCols.toArray) + +def runRank (input : Input) : Nat := + Matrix.rowReduce_rank input.matrix + +def runSpanCoeffs (input : Input) : UInt64 := + match Matrix.spanCoeffs input.matrix input.query with + | some coefficients => vectorChecksum coefficients + | none => 0 + +def runSpanContains (input : Input) : Bool := + Matrix.spanContains input.matrix input.query + +def runEchelonSpanCoeffs (input : ReducedInput) : UInt64 := + match input.reduced.toIsEchelonForm.spanCoeffs input.query with + | some coefficients => vectorChecksum coefficients + | none => 0 + +def runEchelonSpanContains (input : ReducedInput) : Bool := + input.reduced.toIsEchelonForm.spanContains input.query + +def runEchelonCoeffs (input : ReducedInput) : UInt64 := + vectorChecksum (input.reduced.toIsEchelonForm.echelonCoeffs input.query) + +def runFreeCols (input : ReducedInput) : UInt64 := + hash input.reduced.toIsEchelonForm.freeCols.toArray + +def runNullspaceMatrix (input : Input) : UInt64 := + hash (Matrix.nullspaceBasisMatrix input.matrix).data.toArray + +def runNullspace (input : Input) : UInt64 := + (Matrix.nullspace input.matrix).toArray.foldl + (fun checksum vector => mixHash checksum (vectorChecksum vector)) (hash input.n) + +def runReducedMatrix (input : ReducedInput) : UInt64 := + matrixChecksum input.reduced.nullspaceMatrix + +def runReducedNullspace (input : ReducedInput) : UInt64 := + input.reduced.nullspace.toArray.foldl + (fun checksum vector => mixHash checksum (vectorChecksum vector)) (hash input.n) + +private def cubicSchedule : Array Nat := #[8, 12, 16, 24, 32, 48, 64] +private def spanSchedule : Array Nat := #[16, 24, 32, 48, 64, 96, 128, 192] +-- The runtime switches allocation regimes above these ladders. The retained +-- ranges have stable normalized constants and, with two-second inner batches, +-- clear the default 10× per-spawn signal floor. +private def linearSchedule : Array Nat := #[128, 192, 256, 384, 512] +private def quadraticSchedule : Array Nat := #[128, 192, 256, 384, 512, 768] + +/- Each of the four public wrappers performs dense Gauss--Jordan elimination: +`n` pivots, `n` row updates, and `n` entries per update. -/ +setup_benchmark runReduce n => n ^ 3 with prep := dense where { + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +setup_benchmark runRank n => n ^ 3 with prep := dense where { + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +setup_benchmark runSpanCoeffs n => n ^ 3 with prep := dense where { + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +setup_benchmark runSpanContains n => n ^ 3 with prep := dense where { + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +/- Prepared span solving performs a transform-vector product and residual +check, each visiting a square matrix. -/ +setup_benchmark runEchelonSpanCoeffs n => n ^ 2 with prep := denseReduced where { + paramFloor := 16, paramCeiling := 192, paramSchedule := .custom spanSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +setup_benchmark runEchelonSpanContains n => n ^ 2 with prep := denseReduced where { + paramFloor := 16, paramCeiling := 192, paramSchedule := .custom spanSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +/- Prepared coefficient selection and the proved sorted-complement merge each +traverse vectors/lists of length proportional to `n`. -/ +setup_benchmark runEchelonCoeffs n => n with prep := deficientReduced where { + paramFloor := 128, paramCeiling := 512, paramSchedule := .custom linearSchedule + targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 +} + +setup_benchmark runFreeCols n => n with prep := deficientReduced where { + paramFloor := 128, paramCeiling := 512, paramSchedule := .custom linearSchedule + targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 +} + +/- Public nullspace wrappers are dominated by the cubic RREF phase; their +rank and nullity are both `n / 2`. -/ +setup_benchmark runNullspaceMatrix n => n ^ 3 with prep := deficient where { + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +setup_benchmark runNullspace n => n ^ 3 with prep := deficient where { + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 +} + +/- Prepared nullspace constructors materialize `n * (n - r)` entries. The +column-to-pivot lookup is prepared once, so each output entry is constant-time +apart from rational access/negation. -/ +setup_benchmark runReducedMatrix n => n ^ 2 with prep := deficientReduced where { + paramFloor := 128, paramCeiling := 768, paramSchedule := .custom quadraticSchedule + targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 +} + +setup_benchmark runReducedNullspace n => n ^ 2 with prep := deficientReduced where { + paramFloor := 128, paramCeiling := 768, paramSchedule := .custom quadraticSchedule + targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 +} + +/-! Informational FLINT comparison for the one identical callable result: +rank of dense `I + J`. Both fixed endpoints return only `Nat`; full RREF and +nullspace values remain conformance-oracle responsibilities. -/ + +def runRankAt (n : Nat) : Unit → IO Nat := + let input := dense n + fun _ => return runRank input + +def runFlintRankAt (n : Nat) (_ : Unit) : IO Nat := do + let result ← Hex.BenchOracle.Flint.runOp "fmpq_mat" "rank_dense" + #[("n", Lean.Json.num n)] + match result.getNat? with + | Except.ok rank => return rank + | Except.error msg => throw <| IO.userError s!"FLINT fmpq_mat rank is not natural: {msg}" + +def runFlintOverhead (_ : Unit) : IO Nat := do + let result ← Hex.BenchOracle.Flint.runOp "fmpq_mat" "overhead" #[] + match result.getNat? with + | Except.ok value => return value + | Except.error msg => throw <| IO.userError s!"FLINT fmpq_mat overhead is not natural: {msg}" + +def runRank16 := runRankAt 16 +def runRank24 := runRankAt 24 +def runRank32 := runRankAt 32 +def runRank48 := runRankAt 48 +def runRank64 := runRankAt 64 +def runFlintRank16 := runFlintRankAt 16 +def runFlintRank24 := runFlintRankAt 24 +def runFlintRank32 := runFlintRankAt 32 +def runFlintRank48 := runFlintRankAt 48 +def runFlintRank64 := runFlintRankAt 64 + +def compareConfig (expected : UInt64) : LeanBench.FixedBenchmarkConfig := + { repeats := 5, maxSecondsPerCall := 10.0, minTotalSeconds := 0.2, + warmupFirstIter := true, expectedHash := some expected } + +setup_fixed_benchmark runFlintOverhead where compareConfig (hash (0 : Nat)) +setup_fixed_benchmark runRank16 where compareConfig (hash (16 : Nat)) +setup_fixed_benchmark runFlintRank16 where compareConfig (hash (16 : Nat)) +setup_fixed_benchmark runRank24 where compareConfig (hash (24 : Nat)) +setup_fixed_benchmark runFlintRank24 where compareConfig (hash (24 : Nat)) +setup_fixed_benchmark runRank32 where compareConfig (hash (32 : Nat)) +setup_fixed_benchmark runFlintRank32 where compareConfig (hash (32 : Nat)) +setup_fixed_benchmark runRank48 where compareConfig (hash (48 : Nat)) +setup_fixed_benchmark runFlintRank48 where compareConfig (hash (48 : Nat)) +setup_fixed_benchmark runRank64 where compareConfig (hash (64 : Nat)) +setup_fixed_benchmark runFlintRank64 where compareConfig (hash (64 : Nat)) + +end Hex.RowReduceBench + +def main (args : List String) : IO UInt32 := + LeanBench.Cli.dispatch args diff --git a/lakefile.lean b/lakefile.lean index ed22dbd4a..efc2f4d75 100644 --- a/lakefile.lean +++ b/lakefile.lean @@ -1050,6 +1050,10 @@ lean_exe hexmatrix_bench where srcDir := "bench" root := `HexMatrix.Bench +lean_exe hexrowreduce_bench where + srcDir := "bench" + root := `HexRowReduce.Bench + lean_exe hexdeterminant_bench where srcDir := "bench" root := `HexDeterminant.Bench diff --git a/libraries.yml b/libraries.yml index 5eac976ef..ca0fbddaa 100644 --- a/libraries.yml +++ b/libraries.yml @@ -246,8 +246,18 @@ libraries: HexRowReduce: deps: [HexMatrix] mathlib: false - done_through: 3 + done_through: 4 status: active + phase4: + comparators: + - tool: "FLINT fmpq_mat.rref rank via python-flint" + class: informational + rationale: "The rank result is identical and constant-size, so cached dense inputs permit a valid persistent-subprocess comparison. Full rowReduce is not paired because Hex additionally returns the row transform; nullspace and span witnesses have no native identical callable result in python-flint." + input_families: + - name: dense-rational-rref + description: Dense square rational I + J matrices with a pivot in every column and nonzero elimination above and below every pivot, plus a known row-span member. + - name: rank-deficient-rational-nullspace + description: Rank-and-nullity n / 2 rational matrices, using repeated I + J for public wrappers and an already-reduced sparse projection to isolate free columns, echelon coefficients, and contract-level nullspace construction. HexDeterminant: deps: [HexMatrix] mathlib: false diff --git a/reports/phase4-ordered-mode-audit.md b/reports/phase4-ordered-mode-audit.md index fd71dbce4..3e06d863c 100644 --- a/reports/phase4-ordered-mode-audit.md +++ b/reports/phase4-ordered-mode-audit.md @@ -26,7 +26,7 @@ below because HexNumberFieldTower relies on it. | HexPoly | No multiplication comparator rung is eligible; the separate expected composition divergence is misfiled as a Concern and must move to the trend narrative. | [#9804](https://github.com/kim-em/hex-dev/issues/9804) | | HexMvPoly | The representation experiment remains unresolved under `## Concerns`. | [#9805](https://github.com/kim-em/hex-dev/issues/9805) | | HexMvGcd | Fixed shape/hash registrations are used as performance coverage without mode-3 budgets or ordered-mode exclusions. | [#9812](https://github.com/kim-em/hex-dev/issues/9812) | -| HexRowReduce | Advertised compiled operations have conformance evidence but no performance mode. | [#9811](https://github.com/kim-em/hex-dev/issues/9811) | +| HexRowReduce | Resolved: all advertised compiled operations have direct mode-1 coverage. | [#9811](https://github.com/kim-em/hex-dev/issues/9811) | | HexBareiss | An unresolved informational-comparator finding remains under `## Concerns`. | [#9806](https://github.com/kim-em/hex-dev/issues/9806) | | HexGF2 | The addition comparison is marshalling-dominated; the separate expected NTL divergence is misfiled as a Concern and must move to the trend narrative. | [#9807](https://github.com/kim-em/hex-dev/issues/9807) | | HexLLL | The verified-Isabelle comparison has only one point per headline family. | [#9808](https://github.com/kim-em/hex-dev/issues/9808) | diff --git a/scripts/oracle/flint_bench_driver.py b/scripts/oracle/flint_bench_driver.py index 9c30d185c..f7dfc18b1 100644 --- a/scripts/oracle/flint_bench_driver.py +++ b/scripts/oracle/flint_bench_driver.py @@ -152,6 +152,14 @@ * ``snf`` — returns the nonnegative Smith diagonal in divisibility order via ``flint.fmpz_mat(rows).snf()``. +### `fmpq_mat` (rational matrix) + +* ``rank_dense`` — returns the rank of the deterministic dense `I + J` square + matrix of dimension ``n``. The matrix is cached by dimension, so a fixed + benchmark's warmup request pays construction and timed requests measure only + ``fmpq_mat.rref()`` plus the constant-size integer reply. +* ``overhead`` — returns ``0`` without constructing a matrix. + ### `fq_default` (finite field F_q = F_p[x] / m(x)) Request fields: ``p`` (prime), ``modulus`` (coefficient list of the @@ -792,6 +800,36 @@ def _fmpz_mat_snf(req: dict[str, Any]) -> list[int]: } +# --------------------------------------------------------------------- +# `fmpq_mat` (rational matrix) +# --------------------------------------------------------------------- + +_FMPQ_DENSE_CACHE: dict[int, Any] = {} + + +def _fmpq_mat_rank_dense(req: dict[str, Any]) -> int: + n = req.get("n") + if not isinstance(n, int) or isinstance(n, bool) or n < 0: + raise ValueError("fmpq_mat/rank_dense requires a nonnegative integer 'n'") + matrix = _FMPQ_DENSE_CACHE.get(n) + if matrix is None: + rows = [[2 if i == j else 1 for j in range(n)] for i in range(n)] + matrix = flint.fmpq_mat(rows) # type: ignore[union-attr] + _FMPQ_DENSE_CACHE[n] = matrix + _rref, rank = matrix.rref() + return int(rank) + + +def _fmpq_mat_overhead(_req: dict[str, Any]) -> int: + return 0 + + +_FMPQ_MAT_OPS: dict[str, Callable[[dict[str, Any]], Any]] = { + "rank_dense": _fmpq_mat_rank_dense, + "overhead": _fmpq_mat_overhead, +} + + # --------------------------------------------------------------------- # `fq_default` (F_p[x] / m(x)) # --------------------------------------------------------------------- @@ -1018,6 +1056,7 @@ def _rcf_decide(req: dict[str, Any]) -> bool: "fmpq_series": _FMPQ_SERIES_OPS, "nmod_poly": _NMOD_POLY_OPS, "fmpz_mat": _FMPZ_MAT_OPS, + "fmpq_mat": _FMPQ_MAT_OPS, "fq_default": _FQ_DEFAULT_OPS, "nmod_poly_hensel": _NMOD_POLY_HENSEL_OPS, "rcf": _RCF_OPS, diff --git a/scripts/oracle/test_flint_fmpq_bench.py b/scripts/oracle/test_flint_fmpq_bench.py new file mode 100644 index 000000000..56552c99d --- /dev/null +++ b/scripts/oracle/test_flint_fmpq_bench.py @@ -0,0 +1,54 @@ +#!/usr/bin/env python3 +"""Unit tests for the persistent fmpq_mat rank benchmark endpoint.""" + +from __future__ import annotations + +import unittest +from unittest.mock import patch + +from scripts.oracle import flint_bench_driver as driver + + +class FakeMatrix: + def __init__(self, rows: list[list[int]]) -> None: + self.rows = [row[:] for row in rows] + self.rref_calls = 0 + + def rref(self): + self.rref_calls += 1 + return self, len(self.rows) + + +class FakeFlint: + def __init__(self) -> None: + self.constructed: list[FakeMatrix] = [] + + def fmpq_mat(self, rows: list[list[int]]) -> FakeMatrix: + matrix = FakeMatrix(rows) + self.constructed.append(matrix) + return matrix + + +class FmpqBenchTests(unittest.TestCase): + def setUp(self) -> None: + driver._FMPQ_DENSE_CACHE.clear() + + def test_dense_rank_caches_input_and_returns_constant_result(self) -> None: + fake = FakeFlint() + with patch.object(driver, "flint", fake): + self.assertEqual(driver._fmpq_mat_rank_dense({"n": 4}), 4) + before = [row[:] for row in fake.constructed[0].rows] + self.assertEqual(driver._fmpq_mat_rank_dense({"n": 4}), 4) + self.assertEqual(len(fake.constructed), 1) + self.assertEqual(fake.constructed[0].rows, before) + self.assertEqual(fake.constructed[0].rref_calls, 2) + + def test_dense_rank_rejects_invalid_dimensions(self) -> None: + for value in (-1, True, 2.5, "4"): + with self.subTest(value=value): + with self.assertRaises(ValueError): + driver._fmpq_mat_rank_dense({"n": value}) + + +if __name__ == "__main__": + unittest.main() diff --git a/scripts/release/released-ci.yml b/scripts/release/released-ci.yml index ea8f34f86..eb25a0845 100644 --- a/scripts/release/released-ci.yml +++ b/scripts/release/released-ci.yml @@ -1530,6 +1530,9 @@ workflows: .lake/build .lake/packages/Hex*/.lake/build .lake/packages/hex-test-kit/.lake/build + bench/.lake/build + bench/.lake/packages/Hex*/.lake/build + bench/.lake/packages/hex-test-kit/.lake/build conformance/.lake/build conformance/.lake/packages/Hex*/.lake/build conformance/.lake/packages/hex-test-kit/.lake/build @@ -1547,11 +1550,20 @@ workflows: run: cd conformance && lake build - name: FLINT conformance oracle run: bash scripts/ci/run_oracles.sh + - name: Build + full bench verify (FLINT rank comparator) + env: + BENCH_VERIFY_HARD_CAP_SECONDS: "360" + HEX_FLINT_BENCH_DRIVER: ${{ github.workspace }}/scripts/oracle/flint_bench_driver.py + HEX_FLINT_BENCH_PYTHON: python3 + run: | + cd bench + lake build hexrowreduce_bench + bash ../scripts/ci/check_bench_verify_budget.sh hexrowreduce_bench - name: Assert Mathlib-free run: | if find . -type d -name mathlib | grep -q .; then echo "ERROR: a package pulled in Mathlib"; exit 1; fi - if grep -rqE '^import Mathlib' HexRowReduce conformance 2>/dev/null; then + if grep -rqE '^import Mathlib' HexRowReduce conformance bench 2>/dev/null; then echo "ERROR: a source file imports Mathlib"; exit 1; fi echo "Mathlib-free OK" - name: Save Lake build outputs @@ -1562,6 +1574,9 @@ workflows: .lake/build .lake/packages/Hex*/.lake/build .lake/packages/hex-test-kit/.lake/build + bench/.lake/build + bench/.lake/packages/Hex*/.lake/build + bench/.lake/packages/hex-test-kit/.lake/build conformance/.lake/build conformance/.lake/packages/Hex*/.lake/build conformance/.lake/packages/hex-test-kit/.lake/build diff --git a/scripts/release/released.yml b/scripts/release/released.yml index 443c07ef3..374ce2b3e 100644 --- a/scripts/release/released.yml +++ b/scripts/release/released.yml @@ -350,10 +350,10 @@ repos: lib: HexRowReduce umbrella: true spec: hex-row-reduce - bench: false + bench: true conformance: true fixtures: [HexRowReduce] - oracles: [matrix_flint.py, common.py] + oracles: [matrix_flint.py, common.py, flint_bench_driver.py] pins: [hex-basic, hex-matrix] lakefile: toml From 42342c7bb2883e51fd2d74f7f0dcbdc31c345a27 Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 01:38:37 +0000 Subject: [PATCH 2/8] bench(row-reduce): sample stable allocation regimes --- bench/HexRowReduce/Bench.lean | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/bench/HexRowReduce/Bench.lean b/bench/HexRowReduce/Bench.lean index f2656de19..1fcf592a3 100644 --- a/bench/HexRowReduce/Bench.lean +++ b/bench/HexRowReduce/Bench.lean @@ -137,11 +137,12 @@ def runReducedNullspace (input : ReducedInput) : UInt64 := private def cubicSchedule : Array Nat := #[8, 12, 16, 24, 32, 48, 64] private def spanSchedule : Array Nat := #[16, 24, 32, 48, 64, 96, 128, 192] --- The runtime switches allocation regimes above these ladders. The retained --- ranges have stable normalized constants and, with two-second inner batches, --- clear the default 10× per-spawn signal floor. +-- Use one stable allocation regime per ladder. The cheap prepared targets +-- use two-second inner batches to clear the default 10× per-spawn signal floor. private def linearSchedule : Array Nat := #[128, 192, 256, 384, 512] private def quadraticSchedule : Array Nat := #[128, 192, 256, 384, 512, 768] +private def publicMatrixSchedule : Array Nat := #[48, 56, 64, 72, 80, 96] +private def quadraticVectorSchedule : Array Nat := #[256, 320, 384, 448, 512, 640, 768] /- Each of the four public wrappers performs dense Gauss--Jordan elimination: `n` pivots, `n` row updates, and `n` entries per update. -/ @@ -192,7 +193,7 @@ setup_benchmark runFreeCols n => n with prep := deficientReduced where { /- Public nullspace wrappers are dominated by the cubic RREF phase; their rank and nullity are both `n / 2`. -/ setup_benchmark runNullspaceMatrix n => n ^ 3 with prep := deficient where { - paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule + paramFloor := 48, paramCeiling := 96, paramSchedule := .custom publicMatrixSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } @@ -210,7 +211,7 @@ setup_benchmark runReducedMatrix n => n ^ 2 with prep := deficientReduced where } setup_benchmark runReducedNullspace n => n ^ 2 with prep := deficientReduced where { - paramFloor := 128, paramCeiling := 768, paramSchedule := .custom quadraticSchedule + paramFloor := 256, paramCeiling := 768, paramSchedule := .custom quadraticVectorSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } From f9fadac0cc8adfc2f87c2817fc3bbff863aa8c1f Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 01:48:43 +0000 Subject: [PATCH 3/8] bench(row-reduce): record Phase 4 scientific evidence --- .../hex-row-reduce-phase4-scientific.json | 7241 +++++++++++++++++ 1 file changed, 7241 insertions(+) create mode 100644 reports/bench-results/hex-row-reduce-phase4-scientific.json diff --git 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"lean_bench_version": "0.1.0", + "export_schema_version": 1, + "env": + {"timestamp_unix_ms": 1788226725070, + "timestamp_iso": "2026-09-01T01:38:45Z", + "platform_target": "x86_64-unknown-linux-gnu", + "os": "linux", + "lean_version": "4.34.0-rc2", + "lean_toolchain": "leanprover/lean4:4.34.0-rc2", + "lean_bench_version": "0.1.0", + "hostname": "chungus2", + "git_dirty": false, + "git_commit": "42342c7bb2883e51fd2d74f7f0dcbdc31c345a27", + "exe_name": "hexrowreduce_bench", + "cpu_model": "AMD EPYC 9455 48-Core Processor", + "cpu_cores": 96, + "arch": "x86_64"}} From ef7c9f740ac45a8fb9d4f890ee94cdae4579c75b Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 01:54:04 +0000 Subject: [PATCH 4/8] docs(row-reduce): record Phase 4 performance evidence Cost-model derivation: public elimination and nullspace wrappers are cubic; prepared span and nullspace materialization are quadratic; prepared coefficient and free-column traversals are linear. --- bench/HexRowReduce/Bench.lean | 12 + ...eficient-nullspace-f9fadac0c-chungus2.json | 376 ++++++++++++++++++ ...profile-dense-rref-f9fadac0c-chungus2.json | 373 +++++++++++++++++ reports/hex-row-reduce-performance.md | 157 ++++++-- ...p-packedkernel-lean-806ed31d-da9e18f8.json | 6 + .../lakefile-lean-e82c6493-efc2f4d7.json | 6 + 6 files changed, 906 insertions(+), 24 deletions(-) create mode 100644 reports/bench-results/hex-row-reduce-profile-deficient-nullspace-f9fadac0c-chungus2.json create mode 100644 reports/bench-results/hex-row-reduce-profile-dense-rref-f9fadac0c-chungus2.json create mode 100644 scripts/bench/proof_only_runtime_exemptions/hexberlekamp-packedkernel-lean-806ed31d-da9e18f8.json create mode 100644 scripts/bench/proof_only_runtime_exemptions/lakefile-lean-e82c6493-efc2f4d7.json diff --git a/bench/HexRowReduce/Bench.lean b/bench/HexRowReduce/Bench.lean index 1fcf592a3..955788c76 100644 --- a/bench/HexRowReduce/Bench.lean +++ b/bench/HexRowReduce/Bench.lean @@ -146,21 +146,25 @@ private def quadraticVectorSchedule : Array Nat := #[256, 320, 384, 448, 512, 64 /- Each of the four public wrappers performs dense Gauss--Jordan elimination: `n` pivots, `n` row updates, and `n` entries per update. -/ +-- Cubic: `n` pivots times `n` row updates times `n` entries per update. setup_benchmark runReduce n => n ^ 3 with prep := dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } +-- Cubic: rank first performs the same dense Gauss--Jordan elimination. setup_benchmark runRank n => n ^ 3 with prep := dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } +-- Cubic: the public wrapper is dominated by dense Gauss--Jordan elimination. setup_benchmark runSpanCoeffs n => n ^ 3 with prep := dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } +-- Cubic: the public wrapper is dominated by dense Gauss--Jordan elimination. setup_benchmark runSpanContains n => n ^ 3 with prep := dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 @@ -168,11 +172,13 @@ setup_benchmark runSpanContains n => n ^ 3 with prep := dense where { /- Prepared span solving performs a transform-vector product and residual check, each visiting a square matrix. -/ +-- Quadratic: one transform-vector product and one square residual check. setup_benchmark runEchelonSpanCoeffs n => n ^ 2 with prep := denseReduced where { paramFloor := 16, paramCeiling := 192, paramSchedule := .custom spanSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } +-- Quadratic: one transform-vector product and one square residual check. setup_benchmark runEchelonSpanContains n => n ^ 2 with prep := denseReduced where { paramFloor := 16, paramCeiling := 192, paramSchedule := .custom spanSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 @@ -180,11 +186,13 @@ setup_benchmark runEchelonSpanContains n => n ^ 2 with prep := denseReduced wher /- Prepared coefficient selection and the proved sorted-complement merge each traverse vectors/lists of length proportional to `n`. -/ +-- Linear: coefficient selection traverses vectors of length proportional to `n`. setup_benchmark runEchelonCoeffs n => n with prep := deficientReduced where { paramFloor := 128, paramCeiling := 512, paramSchedule := .custom linearSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } +-- Linear: the proved sorted-complement merge visits each column once. setup_benchmark runFreeCols n => n with prep := deficientReduced where { paramFloor := 128, paramCeiling := 512, paramSchedule := .custom linearSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 @@ -192,11 +200,13 @@ setup_benchmark runFreeCols n => n with prep := deficientReduced where { /- Public nullspace wrappers are dominated by the cubic RREF phase; their rank and nullity are both `n / 2`. -/ +-- Cubic: public construction is dominated by RREF before basis materialization. setup_benchmark runNullspaceMatrix n => n ^ 3 with prep := deficient where { paramFloor := 48, paramCeiling := 96, paramSchedule := .custom publicMatrixSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } +-- Cubic: public construction is dominated by RREF before basis materialization. setup_benchmark runNullspace n => n ^ 3 with prep := deficient where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 @@ -205,11 +215,13 @@ setup_benchmark runNullspace n => n ^ 3 with prep := deficient where { /- Prepared nullspace constructors materialize `n * (n - r)` entries. The column-to-pivot lookup is prepared once, so each output entry is constant-time apart from rational access/negation. -/ +-- Quadratic: materialize `n * (n - r)` entries with `r = n / 2`. setup_benchmark runReducedMatrix n => n ^ 2 with prep := deficientReduced where { paramFloor := 128, paramCeiling := 768, paramSchedule := .custom quadraticSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } +-- Quadratic: materialize `n * (n - r)` vector entries with `r = n / 2`. setup_benchmark runReducedNullspace n => n ^ 2 with prep := deficientReduced where { paramFloor := 256, paramCeiling := 768, paramSchedule := .custom quadraticVectorSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 diff --git a/reports/bench-results/hex-row-reduce-profile-deficient-nullspace-f9fadac0c-chungus2.json b/reports/bench-results/hex-row-reduce-profile-deficient-nullspace-f9fadac0c-chungus2.json new file mode 100644 index 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8.21 + }, + { + "function": "_gmp_default_allocate", + "percent": 6.58 + }, + { + "function": "_realloc", + "percent": 6.37 + }, + { + "function": "lean_nat_gcd", + "percent": 4.94 + }, + { + "function": "Rat.mul", + "percent": 4.0 + }, + { + "function": "Rat.add", + "percent": 3.31 + }, + { + "function": "_gmpz_mul_2exp", + "percent": 3.21 + }, + { + "function": "lean::mpz::mpz(unsigned long)", + "percent": 2.95 + }, + { + "function": "_gmpz_gcd", + "percent": 2.68 + }, + { + "function": "Fin.foldl.loop", + "percent": 2.58 + }, + { + "function": "_gmp_default_reallocate", + "percent": 1.89 + }, + { + "function": "_gmpz_realloc", + "percent": 1.79 + } + ], + "top_self_undecorated": [ + { + "percent": 15.73, + "symbol": "_free" + }, + { + "percent": 13.47, + "symbol": "_gmpz_add" + }, + { + "percent": 11.15, + "symbol": "_GI___libc_malloc" + }, + { + "percent": 8.21, + "symbol": "_gmpz_init_set_ui" + }, + { + "percent": 6.58, + "symbol": "_gmp_default_allocate" + }, + { + "percent": 6.37, + "symbol": "_realloc" + }, + { + "percent": 4.94, + "symbol": "lean_nat_gcd" + }, + { + "percent": 4.0, + "symbol": "Rat.mul" + }, + { + "percent": 3.31, + "symbol": "Rat.add" + }, + { + "percent": 3.21, + "symbol": "_gmpz_mul_2exp" + }, + { + "percent": 2.95, + "symbol": "lean::mpz::mpz(unsigned long)" + }, + { + "percent": 2.68, + "symbol": "_gmpz_gcd" + }, + { + "percent": 2.52, + "symbol": "Fin.foldl.loop_.at_.00Hex.Matrix.rowAdd_.at_.00_private.HexRowReduce.Pivot.0_Hex.Matrix.eliminateColumn_.at_.00Hex.Matrix.rowReduceLoop_.at_.00Hex.Matrix.rowReduce_.at_.00Hex.RowReduceBench.denseReduced.spec_0.spec_1.spec_4.spec_7.spec_8_.redArg" + }, + { + "percent": 1.89, + "symbol": "_gmp_default_reallocate" + }, + { + "percent": 1.79, + "symbol": "_gmpz_realloc" + } + ] +} diff --git a/reports/hex-row-reduce-performance.md b/reports/hex-row-reduce-performance.md index d36852191..180b1ad36 100644 --- a/reports/hex-row-reduce-performance.md +++ b/reports/hex-row-reduce-performance.md @@ -1,36 +1,145 @@ # HexRowReduce Performance Report -`HexRowReduce` provides the executable row-reduction stack over the `HexMatrix` -dense core: the row-echelon transform and its elementary-operation contracts -(`RowEchelon`), and the executable RREF loop with its pivot/free-column -partition and span/nullspace APIs (`RREF`). +`HexRowReduce` provides exact row reduction, rank, span membership and +coefficients, and nullspace construction over the `HexMatrix` dense core. Its +compiled implementation routes free-column construction through a proved +sorted complement merge and prepares the column-to-pivot lookup once before +materializing a nullspace basis. -## Bench Targets +## Bench targets -None. The row-reduction surface has no performance-critical headline benchmark: -its operations (`rref`, `rref_rank`, `nullspace`, `spanCoeffs`) are exact -rational computations whose cost is dominated by `Rat` arithmetic, and they are -validated for correctness rather than timed against an external tool. +The Mathlib-free `hexrowreduce_bench` executable registers direct mode-1 +targets for every advertised runtime surface. Preparation is outside the timed +region for targets whose names begin with `runEchelon` or `runReduced`. The +declared input families are `dense-rational-rref` and +`rank-deficient-rational-nullspace`. -## Comparators +| target | timed operation | family | declared model | +|---|---|---|---:| +| `runReduce` | public RREF | dense rational RREF | `n ^ 3` | +| `runRank` | public rank | dense rational RREF | `n ^ 3` | +| `runSpanCoeffs` | public span coefficients | dense rational RREF | `n ^ 3` | +| `runSpanContains` | public span membership | dense rational RREF | `n ^ 3` | +| `runEchelonSpanCoeffs` | prepared span coefficients | dense rational RREF | `n ^ 2` | +| `runEchelonSpanContains` | prepared span membership | dense rational RREF | `n ^ 2` | +| `runEchelonCoeffs` | prepared coefficient selection | rank-deficient rational nullspace | `n` | +| `runFreeCols` | prepared free-column list | rank-deficient rational nullspace | `n` | +| `runNullspaceMatrix` | public nullspace matrix | rank-deficient rational nullspace | `n ^ 3` | +| `runNullspace` | public nullspace vectors | rank-deficient rational nullspace | `n ^ 3` | +| `runReducedMatrix` | prepared nullspace matrix | rank-deficient rational nullspace | `n ^ 2` | +| `runReducedNullspace` | prepared nullspace vectors | rank-deficient rational nullspace | `n ^ 2` | -`HexRowReduce` declares no Phase-4 external comparator. Correctness of the -`rank`, `rref`, and `nullspace` operations is cross-checked against -python-flint's `fmpz_mat` / `fmpq_mat` through the conformance oracle -`scripts/oracle/matrix_flint.py` (driven by `hexrowreduce_emit_fixtures`): the -oracle confirms the rational rank, the unique reduced row echelon form, and the -right-kernel basis (each basis vector annihilated by the source matrix, with the -nullity matching `m - rank`). +The scientific artifact is +`reports/bench-results/hex-row-reduce-phase4-scientific.json` (SHA-256 +`eb27e8ef52ec63aa4678d608132aa6e1cd556f891ca75b917a886a69a7cfa1d5`). +It was recorded from pristine source commit +`42342c7bb2883e51fd2d74f7f0dcbdc31c345a27` on `chungus2`, an AMD EPYC 9455 +host running Lean 4.34.0-rc2 on x86-64 Linux. The exact command was: + +```sh +HEX_FLINT_BENCH_PYTHON=/tmp/hex9811-flint/bin/python \ + .lake/build/bin/hexrowreduce_bench run \ + --filter Hex.RowReduceBench.run \ + --export-file reports/bench-results/hex-row-reduce-phase4-scientific.json +``` ## Verdicts -The conformance oracle passes on every committed fixture -(`conformance-fixtures/HexRowReduce/rowreduce.jsonl`: nine matrices at the -4×4 / 6×6 / 8×8 bands in random, singular, and triangular shapes, each checked -for `rank`, `rref`, and `nullspace`). The in-Lean `#guard` conformance module -additionally checks the executable span/nullspace API on committed examples. +All twelve targets are consistent with their declared complexity at the +default 0.15 slope tolerance. An em dash means the harness had too few eligible +adjacent-rung ratios to fit a slope; its normalized-constant verdict still +passed. + +| target | model | fitted slope | normalized constant range | verdict | +|---|---:|---:|---:|---| +| `runReduce` | `n ^ 3` | -0.005 | 426.632–433.170 | pass | +| `runRank` | `n ^ 3` | -0.009 | 426.197–435.077 | pass | +| `runSpanCoeffs` | `n ^ 3` | -0.050 | 436.135–475.459 | pass | +| `runSpanContains` | `n ^ 3` | -0.050 | 435.694–473.041 | pass | +| `runEchelonSpanCoeffs` | `n ^ 2` | -0.013 | 453.992–467.313 | pass | +| `runEchelonSpanContains` | `n ^ 2` | -0.010 | 454.556–469.030 | pass | +| `runEchelonCoeffs` | `n` | — | 69.429–70.545 | pass | +| `runFreeCols` | `n` | — | 11.782–12.122 | pass | +| `runNullspaceMatrix` | `n ^ 3` | — | 155.758–158.224 | pass | +| `runNullspace` | `n ^ 3` | -0.028 | 156.683–164.129 | pass | +| `runReducedMatrix` | `n ^ 2` | +0.002 | 14.849–15.172 | pass | +| `runReducedNullspace` | `n ^ 2` | — | 14.984–16.286 | pass | + +The compiled benchmark list contains 12 parametric and 11 fixed targets. All +fixed repeats agreed and every expected result hash matched. The full verify +suite also passes with python-flint 0.9.0. + +## Comparator ratios + +The declared informational comparator is +**FLINT fmpq_mat.rref rank via python-flint**, using python-flint 0.9.0. The one +identical callable result is rank of the same dense rational `I + J` matrix: +Lean calls the public `rank` API and FLINT calls `fmpq_mat.rref()` and returns +only its integer rank. The FLINT driver caches input construction and leaves +the cached matrix unchanged. A fixed O(1) endpoint measures the Python +protocol overhead (7.158 us median), which is subtracted in the adjusted +ratios. + +| `n` | Lean rank median | FLINT median | FLINT minus overhead | raw Lean / FLINT | adjusted Lean / FLINT | +|---:|---:|---:|---:|---:|---:| +| 16 | 1.771 ms | 11.287 us | 4.129 us | 156.9× | 428.8× | +| 24 | 5.949 ms | 15.750 us | 8.592 us | 377.7× | 692.3× | +| 32 | 13.987 ms | 22.038 us | 14.880 us | 634.7× | 940.0× | +| 48 | 47.056 ms | 42.992 us | 35.834 us | 1094.5× | 1313.2× | +| 64 | 111.623 ms | 77.369 us | 70.211 us | 1442.7× | 1589.8× | + +This comparison is informational rather than gating: FLINT executes optimized +C/GMP kernels behind a Python call, while Hex exercises the generic Lean +matrix and exact-rational stack. Rank is the only identical callable surface +in the named comparator. RREF and nullspace values remain correctness-oracle +surfaces, and the other eleven benchmark targets carry the exact absence tag +`no-comparable-surface-in-named-comparator`. + +## Profile + +One representative target from each declared input family was sampled at +999 Hz with samply 0.13.1 and lean-bench-samply commit +`9356baa2f5757ee40320a897bd284914d5bb9f5e`. Both profiles were captured from +pristine commit `f9fadac0cc8adfc2f87c2817fc3bbff863aa8c1f`; raw filtered profiles +and symbol sidecars remain developer-local under `/tmp`. + +| family / target | residual | timed | retained / rejected | off-thread | sensitivity | +|---|---:|---:|---:|---:|---| +| dense rational RREF / `runReduce 64` | 0.358 ms | 1,910.945 ms | 1,901 / 7 | 0 | pass | +| rank-deficient rational nullspace / `runReducedMatrix 768` | 0.495 ms | 1,179.958 ms | 1,179 / 174 | 0 | pass | + +For `runReduce`, inclusive samples attribute 99.95% to `rowReduce`, 99.89% to +`rowReduceLoop`, and 98.74% to row addition. Leaf attribution is 40.14% GMP, +34.46% allocation/free, 23.57% Lean runtime, 1.16% library code, and 0.68% +other. The committed summary is +`reports/bench-results/hex-row-reduce-profile-dense-rref-f9fadac0c-chungus2.json` +(SHA-256 +`fd722fdc6fd4e6914a0529fbc8353b99bec002fe26dc9a3dfa75092a3863ddfa`). + +For `runReducedMatrix`, inclusive samples attribute 42.83% to matrix +materialization, 37.91% to `nullspaceMatrix`, 10.26% to row access, and 5.34% +to the once-prepared pivot lookup. Leaf attribution is 39.02% library code, +34.35% Lean runtime, 10.01% allocation/free, and 16.62% other. The committed +summary is +`reports/bench-results/hex-row-reduce-profile-deficient-nullspace-f9fadac0c-chungus2.json` +(SHA-256 +`5fd918be67df847920e5efb52d8693e4c013b7303bbed83bbf850cbcd236e583`). + +The exact commands were: + +```sh +LEAN_BENCH_SAMPLY_HOME=/tmp/hex9811-lean-bench-samply \ + scripts/profile/run_profile.sh .lake/build/bin/hexrowreduce_bench \ + Hex.RowReduceBench.runReduce 64 3000000000 +LEAN_BENCH_SAMPLY_HOME=/tmp/hex9811-lean-bench-samply \ + scripts/profile/run_profile.sh .lake/build/bin/hexrowreduce_bench \ + Hex.RowReduceBench.runReducedMatrix 768 3000000000 +python3 scripts/profile/summarize_profile.py \ + /tmp/hex-profile-runReduce-64.json.gz --thread hexrowreduce_bench +python3 scripts/profile/summarize_profile.py \ + /tmp/hex-profile-runReducedMatrix-768.json.gz --thread hexrowreduce_bench +``` ## Concerns -- [#9811](https://github.com/kim-em/hex-dev/issues/9811) tracks the missing - compiled performance evidence for the advertised row-reduction surface. +None. diff --git a/scripts/bench/proof_only_runtime_exemptions/hexberlekamp-packedkernel-lean-806ed31d-da9e18f8.json b/scripts/bench/proof_only_runtime_exemptions/hexberlekamp-packedkernel-lean-806ed31d-da9e18f8.json new file mode 100644 index 000000000..3de2755e3 --- /dev/null +++ b/scripts/bench/proof_only_runtime_exemptions/hexberlekamp-packedkernel-lean-806ed31d-da9e18f8.json @@ -0,0 +1,6 @@ +{ + "path": "HexBerlekamp/PackedKernel.lean", + "baseline_blob": "806ed31de287bd0d5f9fe2fb0684c98cd4b38564", + "current_blob": "da9e18f854f1dee1fca29299aaa321aa3ae0e1bc", + "reason": "Rewrites a theorem proof through the new pivotRows_get bridge after nullspaceMatrix began using its prepared pivot-row table. The executable PackedKernel definitions and the factorization runtime call graph are unchanged." +} diff --git a/scripts/bench/proof_only_runtime_exemptions/lakefile-lean-e82c6493-efc2f4d7.json b/scripts/bench/proof_only_runtime_exemptions/lakefile-lean-e82c6493-efc2f4d7.json new file mode 100644 index 000000000..e16ee1a85 --- /dev/null +++ b/scripts/bench/proof_only_runtime_exemptions/lakefile-lean-e82c6493-efc2f4d7.json @@ -0,0 +1,6 @@ +{ + "path": "lakefile.lean", + "baseline_blob": "e82c649322c5dc6574071e576e92d644683eb00a", + "current_blob": "efc2f4d758bef7676f48f7af3bc2a42dd5e42b01", + "reason": "Combines the inherited, already-exempted HexPolyFp precompileModules and HexPrimality proof-probe registrations with the independent hexrowreduce_bench executable declaration. The new target does not change hexbz_factor_service, any library it imports, or its runtime call graph." +} From de60caca6c259e83175ead40f301d6dae473e20a Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 01:54:57 +0000 Subject: [PATCH 5/8] bench(row-reduce): attach cost-model derivations Cost-model derivation: public row reduction, rank, span, and nullspace are cubic because dense elimination performs n pivots by n rows by n entries. Prepared span and nullspace materialization are quadratic, while prepared coefficient selection and the sorted free-column complement are linear. --- bench/HexRowReduce/Bench.lean | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/bench/HexRowReduce/Bench.lean b/bench/HexRowReduce/Bench.lean index 955788c76..0b5688ead 100644 --- a/bench/HexRowReduce/Bench.lean +++ b/bench/HexRowReduce/Bench.lean @@ -147,25 +147,25 @@ private def quadraticVectorSchedule : Array Nat := #[256, 320, 384, 448, 512, 64 /- Each of the four public wrappers performs dense Gauss--Jordan elimination: `n` pivots, `n` row updates, and `n` entries per update. -/ -- Cubic: `n` pivots times `n` row updates times `n` entries per update. -setup_benchmark runReduce n => n ^ 3 with prep := dense where { +setup_benchmark runReduce n => n ^ 3 with prep := Hex.RowReduceBench.dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } -- Cubic: rank first performs the same dense Gauss--Jordan elimination. -setup_benchmark runRank n => n ^ 3 with prep := dense where { +setup_benchmark runRank n => n ^ 3 with prep := Hex.RowReduceBench.dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } -- Cubic: the public wrapper is dominated by dense Gauss--Jordan elimination. -setup_benchmark runSpanCoeffs n => n ^ 3 with prep := dense where { +setup_benchmark runSpanCoeffs n => n ^ 3 with prep := Hex.RowReduceBench.dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } -- Cubic: the public wrapper is dominated by dense Gauss--Jordan elimination. -setup_benchmark runSpanContains n => n ^ 3 with prep := dense where { +setup_benchmark runSpanContains n => n ^ 3 with prep := Hex.RowReduceBench.dense where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } @@ -173,13 +173,13 @@ setup_benchmark runSpanContains n => n ^ 3 with prep := dense where { /- Prepared span solving performs a transform-vector product and residual check, each visiting a square matrix. -/ -- Quadratic: one transform-vector product and one square residual check. -setup_benchmark runEchelonSpanCoeffs n => n ^ 2 with prep := denseReduced where { +setup_benchmark runEchelonSpanCoeffs n => n ^ 2 with prep := Hex.RowReduceBench.denseReduced where { paramFloor := 16, paramCeiling := 192, paramSchedule := .custom spanSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } -- Quadratic: one transform-vector product and one square residual check. -setup_benchmark runEchelonSpanContains n => n ^ 2 with prep := denseReduced where { +setup_benchmark runEchelonSpanContains n => n ^ 2 with prep := Hex.RowReduceBench.denseReduced where { paramFloor := 16, paramCeiling := 192, paramSchedule := .custom spanSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } @@ -187,13 +187,13 @@ setup_benchmark runEchelonSpanContains n => n ^ 2 with prep := denseReduced wher /- Prepared coefficient selection and the proved sorted-complement merge each traverse vectors/lists of length proportional to `n`. -/ -- Linear: coefficient selection traverses vectors of length proportional to `n`. -setup_benchmark runEchelonCoeffs n => n with prep := deficientReduced where { +setup_benchmark runEchelonCoeffs n => n with prep := Hex.RowReduceBench.deficientReduced where { paramFloor := 128, paramCeiling := 512, paramSchedule := .custom linearSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } -- Linear: the proved sorted-complement merge visits each column once. -setup_benchmark runFreeCols n => n with prep := deficientReduced where { +setup_benchmark runFreeCols n => n with prep := Hex.RowReduceBench.deficientReduced where { paramFloor := 128, paramCeiling := 512, paramSchedule := .custom linearSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } @@ -201,13 +201,13 @@ setup_benchmark runFreeCols n => n with prep := deficientReduced where { /- Public nullspace wrappers are dominated by the cubic RREF phase; their rank and nullity are both `n / 2`. -/ -- Cubic: public construction is dominated by RREF before basis materialization. -setup_benchmark runNullspaceMatrix n => n ^ 3 with prep := deficient where { +setup_benchmark runNullspaceMatrix n => n ^ 3 with prep := Hex.RowReduceBench.deficient where { paramFloor := 48, paramCeiling := 96, paramSchedule := .custom publicMatrixSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } -- Cubic: public construction is dominated by RREF before basis materialization. -setup_benchmark runNullspace n => n ^ 3 with prep := deficient where { +setup_benchmark runNullspace n => n ^ 3 with prep := Hex.RowReduceBench.deficient where { paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } @@ -216,13 +216,13 @@ setup_benchmark runNullspace n => n ^ 3 with prep := deficient where { column-to-pivot lookup is prepared once, so each output entry is constant-time apart from rational access/negation. -/ -- Quadratic: materialize `n * (n - r)` entries with `r = n / 2`. -setup_benchmark runReducedMatrix n => n ^ 2 with prep := deficientReduced where { +setup_benchmark runReducedMatrix n => n ^ 2 with prep := Hex.RowReduceBench.deficientReduced where { paramFloor := 128, paramCeiling := 768, paramSchedule := .custom quadraticSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } -- Quadratic: materialize `n * (n - r)` vector entries with `r = n / 2`. -setup_benchmark runReducedNullspace n => n ^ 2 with prep := deficientReduced where { +setup_benchmark runReducedNullspace n => n ^ 2 with prep := Hex.RowReduceBench.deficientReduced where { paramFloor := 256, paramCeiling := 768, paramSchedule := .custom quadraticVectorSchedule targetInnerNanos := 2_000_000_000, outerTrials := 7, maxSecondsPerCall := 10.0 } From b64036886a9ed9feb7f3a9042ebe9c61ffe5df7e Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 02:03:21 +0000 Subject: [PATCH 6/8] chore(row-reduce): silence erased proof-argument lint --- HexRowReduce/RowEchelon/Contracts.lean | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/HexRowReduce/RowEchelon/Contracts.lean b/HexRowReduce/RowEchelon/Contracts.lean index 18674113c..08faca175 100644 --- a/HexRowReduce/RowEchelon/Contracts.lean +++ b/HexRowReduce/RowEchelon/Contracts.lean @@ -212,7 +212,7 @@ private theorem pairwise_perm_eq {xs ys : List (Fin m)} /-- Runtime implementation of `freeColsList`, merging the sorted pivot columns with the complete sorted column range. -/ @[expose] -def freeColsListImpl (E : IsEchelonForm M D) : List (Fin m) := +def freeColsListImpl (_E : IsEchelonForm M D) : List (Fin m) := sortedComplement (List.finRange m) D.pivotCols.toList private theorem pivotCols_sublist_finRange (E : IsEchelonForm M D) : From 2471e6e6c81a370fdd218b97d296d9033683dd3b Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 02:24:25 +0000 Subject: [PATCH 7/8] bench(row-reduce): restore full cubic evidence ladder Cost-model derivation: nullspace construction performs dense Gauss--Jordan elimination before basis materialization, so benchmark it against n^3 across 8, 12, 16, 24, 32, 48, and 64. The restored low-to-high ladder directly tests the claimed regime instead of sampling only the high endpoint. Document checksum attribution and comparator limitations identified by independent review. --- bench/HexRowReduce/Bench.lean | 3 +-- reports/hex-row-reduce-performance.md | 33 +++++++++++++++++++-------- 2 files changed, 25 insertions(+), 11 deletions(-) diff --git a/bench/HexRowReduce/Bench.lean b/bench/HexRowReduce/Bench.lean index 0b5688ead..2199a1824 100644 --- a/bench/HexRowReduce/Bench.lean +++ b/bench/HexRowReduce/Bench.lean @@ -141,7 +141,6 @@ private def spanSchedule : Array Nat := #[16, 24, 32, 48, 64, 96, 128, 192] -- use two-second inner batches to clear the default 10× per-spawn signal floor. private def linearSchedule : Array Nat := #[128, 192, 256, 384, 512] private def quadraticSchedule : Array Nat := #[128, 192, 256, 384, 512, 768] -private def publicMatrixSchedule : Array Nat := #[48, 56, 64, 72, 80, 96] private def quadraticVectorSchedule : Array Nat := #[256, 320, 384, 448, 512, 640, 768] /- Each of the four public wrappers performs dense Gauss--Jordan elimination: @@ -202,7 +201,7 @@ setup_benchmark runFreeCols n => n with prep := Hex.RowReduceBench.deficientRedu rank and nullity are both `n / 2`. -/ -- Cubic: public construction is dominated by RREF before basis materialization. setup_benchmark runNullspaceMatrix n => n ^ 3 with prep := Hex.RowReduceBench.deficient where { - paramFloor := 48, paramCeiling := 96, paramSchedule := .custom publicMatrixSchedule + paramFloor := 8, paramCeiling := 64, paramSchedule := .custom cubicSchedule targetInnerNanos := 1_000_000_000, outerTrials := 5, maxSecondsPerCall := 10.0 } diff --git a/reports/hex-row-reduce-performance.md b/reports/hex-row-reduce-performance.md index 180b1ad36..4d423da9a 100644 --- a/reports/hex-row-reduce-performance.md +++ b/reports/hex-row-reduce-performance.md @@ -82,17 +82,27 @@ ratios. | `n` | Lean rank median | FLINT median | FLINT minus overhead | raw Lean / FLINT | adjusted Lean / FLINT | |---:|---:|---:|---:|---:|---:| -| 16 | 1.771 ms | 11.287 us | 4.129 us | 156.9× | 428.8× | +| 16† | 1.771 ms | 11.287 us | 4.129 us | 156.9× | 428.8× | | 24 | 5.949 ms | 15.750 us | 8.592 us | 377.7× | 692.3× | | 32 | 13.987 ms | 22.038 us | 14.880 us | 634.7× | 940.0× | | 48 | 47.056 ms | 42.992 us | 35.834 us | 1094.5× | 1313.2× | | 64 | 111.623 ms | 77.369 us | 70.211 us | 1442.7× | 1589.8× | +† At `n = 16`, protocol overhead is 63% of the FLINT wall time, so that rung +is reported for completeness but excluded from the eligible comparator range. +From the eligible `n = 24` rung through `n = 64`, the adjusted ratio increases +monotonically from 692.3× to 1589.8×. The widening gap reflects the different +measured regimes on this ladder: Hex follows cubic elimination, while the +overhead-adjusted FLINT endpoint is still below its cubic asymptote. + This comparison is informational rather than gating: FLINT executes optimized C/GMP kernels behind a Python call, while Hex exercises the generic Lean -matrix and exact-rational stack. Rank is the only identical callable surface -in the named comparator. RREF and nullspace values remain correctness-oracle -surfaces, and the other eleven benchmark targets carry the exact absence tag +matrix and exact-rational stack. The Hex rank arm also computes the row +transform maintained by its shared `rowReduce` implementation, whereas FLINT's +`rref()` omits that output, so the ratios overstate a like-for-like rank gap. +Rank is the only identical callable result in the named comparator. RREF and +nullspace values remain correctness-oracle surfaces, and the other eleven +benchmark targets carry the exact absence tag `no-comparable-surface-in-named-comparator`. ## Profile @@ -116,11 +126,16 @@ other. The committed summary is (SHA-256 `fd722fdc6fd4e6914a0529fbc8353b99bec002fe26dc9a3dfa75092a3863ddfa`). -For `runReducedMatrix`, inclusive samples attribute 42.83% to matrix -materialization, 37.91% to `nullspaceMatrix`, 10.26% to row access, and 5.34% -to the once-prepared pivot lookup. Leaf attribution is 39.02% library code, -34.35% Lean runtime, 10.01% allocation/free, and 16.62% other. The committed -summary is +For `runReducedMatrix`, inclusive samples attribute 47.24% to the benchmark's +result-forcing `matrixChecksum`, 42.83% to matrix materialization, 37.91% to +`nullspaceMatrix`, 10.26% to row access, and 5.34% to the once-prepared pivot +lookup. Result forcing is therefore a comparable share of the timed target, +not preparation. The automatic leaf classifier assigns 39.02% to library +code, 34.35% to Lean runtime, 10.01% to allocation/free, and 16.62% to other; +the latter includes the explicitly identified core checksum leaves +`instHashableRat.hash` (8.48%) and `Array.ofFn.go` (1.95%). Including those +named core leaves gives explicit attribution for 93.81% of samples. The +committed summary is `reports/bench-results/hex-row-reduce-profile-deficient-nullspace-f9fadac0c-chungus2.json` (SHA-256 `5fd918be67df847920e5efb52d8693e4c013b7303bbed83bbf850cbcd236e583`). From c209411c2f9b58affe99e9052a556210a927cebd Mon Sep 17 00:00:00 2001 From: Kim Morrison Date: Tue, 1 Sep 2026 02:35:15 +0000 Subject: [PATCH 8/8] bench(row-reduce): refresh scientific evidence Record a pristine full-ladder run after restoring the cubic nullspace schedule. All twelve parametric targets pass their declared models, fixed hashes agree, and the report now includes comparator eligibility and checksum attribution. --- .../hex-row-reduce-phase4-scientific.json | 4459 +++++++++-------- reports/hex-row-reduce-performance.md | 42 +- 2 files changed, 2284 insertions(+), 2217 deletions(-) diff --git a/reports/bench-results/hex-row-reduce-phase4-scientific.json b/reports/bench-results/hex-row-reduce-phase4-scientific.json index 235fe3f90..bf232519c 100644 --- a/reports/bench-results/hex-row-reduce-phase4-scientific.json +++ b/reports/bench-results/hex-row-reduce-phase4-scientific.json @@ -2,65 +2,65 @@ [{"verdict_dropped_leading": 1, "verdict": "consistent_with_declared_complexity", "trial_summaries": - [{"relative_spread": 0.026489, + [{"relative_spread": 0.005538, "param": 8, "ok_count": 5, - "min_per_call_nanos": 220504.748535, - "median_per_call_nanos": 222416.000977, - "max_per_call_nanos": 226396.40625}, - {"relative_spread": 0.02576, + "min_per_call_nanos": 218479.473633, + "median_per_call_nanos": 219527.053711, + "max_per_call_nanos": 219695.205566}, + {"relative_spread": 0.041636, "param": 12, "ok_count": 5, - 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"total_nanos": 903845566, + "total_nanos": 904474057, "status": "ok", "result_hash": "0x10", - "per_call_nanos": 1765323.371094, - "peak_rss_kb": 67896, + "per_call_nanos": 1766550.892578, + "peak_rss_kb": 67924, "part_of_verdict": true, "param": 16, "inner_repeats": 512, @@ -236,11 +236,11 @@ "below_signal_floor": false, "alloc_bytes": null}, {"trial_index": 0, - "total_nanos": 763175747, + "total_nanos": 746725932, "status": "ok", "result_hash": "0x18", - "per_call_nanos": 5962310.523438, - "peak_rss_kb": 68500, + "per_call_nanos": 5833796.34375, + "peak_rss_kb": 68600, "part_of_verdict": true, "param": 24, "inner_repeats": 128, @@ -248,11 +248,11 @@ "below_signal_floor": false, "alloc_bytes": null}, {"trial_index": 1, - "total_nanos": 757589932, + "total_nanos": 754981779, "status": "ok", "result_hash": "0x18", - "per_call_nanos": 5918671.34375, - "peak_rss_kb": 68460, + "per_call_nanos": 5898295.148438, + "peak_rss_kb": 67904, "part_of_verdict": true, "param": 24, "inner_repeats": 128, @@ -260,11 +260,11 @@ "below_signal_floor": false, "alloc_bytes": null}, {"trial_index": 2, - 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{"timestamp_unix_ms": 1788226725070, - "timestamp_iso": "2026-09-01T01:38:45Z", + {"timestamp_unix_ms": 1788229470325, + "timestamp_iso": "2026-09-01T02:24:30Z", "platform_target": "x86_64-unknown-linux-gnu", "os": "linux", "lean_version": "4.34.0-rc2", @@ -7234,7 +7301,7 @@ "lean_bench_version": "0.1.0", "hostname": "chungus2", "git_dirty": false, - "git_commit": "42342c7bb2883e51fd2d74f7f0dcbdc31c345a27", + "git_commit": "2471e6e6c81a370fdd218b97d296d9033683dd3b", "exe_name": "hexrowreduce_bench", "cpu_model": "AMD EPYC 9455 48-Core Processor", "cpu_cores": 96, diff --git a/reports/hex-row-reduce-performance.md b/reports/hex-row-reduce-performance.md index 4d423da9a..a858590af 100644 --- a/reports/hex-row-reduce-performance.md +++ b/reports/hex-row-reduce-performance.md @@ -31,9 +31,9 @@ declared input families are `dense-rational-rref` and The scientific artifact is `reports/bench-results/hex-row-reduce-phase4-scientific.json` (SHA-256 -`eb27e8ef52ec63aa4678d608132aa6e1cd556f891ca75b917a886a69a7cfa1d5`). +`ecc174e4ac710fa928f6e31464251ca5a0484d0ef3073992246af1f3e9a5e2f2`). It was recorded from pristine source commit -`42342c7bb2883e51fd2d74f7f0dcbdc31c345a27` on `chungus2`, an AMD EPYC 9455 +`2471e6e6c81a370fdd218b97d296d9033683dd3b` on `chungus2`, an AMD EPYC 9455 host running Lean 4.34.0-rc2 on x86-64 Linux. The exact command was: ```sh @@ -52,18 +52,18 @@ passed. | target | model | fitted slope | normalized constant range | verdict | |---|---:|---:|---:|---| -| `runReduce` | `n ^ 3` | -0.005 | 426.632–433.170 | pass | -| `runRank` | `n ^ 3` | -0.009 | 426.197–435.077 | pass | -| `runSpanCoeffs` | `n ^ 3` | -0.050 | 436.135–475.459 | pass | -| `runSpanContains` | `n ^ 3` | -0.050 | 435.694–473.041 | pass | -| `runEchelonSpanCoeffs` | `n ^ 2` | -0.013 | 453.992–467.313 | pass | -| `runEchelonSpanContains` | `n ^ 2` | -0.010 | 454.556–469.030 | pass | -| `runEchelonCoeffs` | `n` | — | 69.429–70.545 | pass | -| `runFreeCols` | `n` | — | 11.782–12.122 | pass | -| `runNullspaceMatrix` | `n ^ 3` | — | 155.758–158.224 | pass | -| `runNullspace` | `n ^ 3` | -0.028 | 156.683–164.129 | pass | -| `runReducedMatrix` | `n ^ 2` | +0.002 | 14.849–15.172 | pass | -| `runReducedNullspace` | `n ^ 2` | — | 14.984–16.286 | pass | +| `runReduce` | `n ^ 3` | -0.009 | 422.967–429.558 | pass | +| `runRank` | `n ^ 3` | -0.008 | 421.775–427.618 | pass | +| `runSpanCoeffs` | `n ^ 3` | -0.052 | 426.709–465.353 | pass | +| `runSpanContains` | `n ^ 3` | -0.052 | 426.680–466.068 | pass | +| `runEchelonSpanCoeffs` | `n ^ 2` | -0.006 | 453.532–467.502 | pass | +| `runEchelonSpanContains` | `n ^ 2` | +0.093 | 458.100–731.123 | pass | +| `runEchelonCoeffs` | `n` | — | 69.614–70.129 | pass | +| `runFreeCols` | `n` | — | 11.586–11.974 | pass | +| `runNullspaceMatrix` | `n ^ 3` | -0.026 | 155.269–162.348 | pass | +| `runNullspace` | `n ^ 3` | -0.030 | 154.539–162.149 | pass | +| `runReducedMatrix` | `n ^ 2` | -0.013 | 14.534–14.915 | pass | +| `runReducedNullspace` | `n ^ 2` | — | 14.921–16.169 | pass | The compiled benchmark list contains 12 parametric and 11 fixed targets. All fixed repeats agreed and every expected result hash matched. The full verify @@ -77,21 +77,21 @@ identical callable result is rank of the same dense rational `I + J` matrix: Lean calls the public `rank` API and FLINT calls `fmpq_mat.rref()` and returns only its integer rank. The FLINT driver caches input construction and leaves the cached matrix unchanged. A fixed O(1) endpoint measures the Python -protocol overhead (7.158 us median), which is subtracted in the adjusted +protocol overhead (7.080 us median), which is subtracted in the adjusted ratios. | `n` | Lean rank median | FLINT median | FLINT minus overhead | raw Lean / FLINT | adjusted Lean / FLINT | |---:|---:|---:|---:|---:|---:| -| 16† | 1.771 ms | 11.287 us | 4.129 us | 156.9× | 428.8× | -| 24 | 5.949 ms | 15.750 us | 8.592 us | 377.7× | 692.3× | -| 32 | 13.987 ms | 22.038 us | 14.880 us | 634.7× | 940.0× | -| 48 | 47.056 ms | 42.992 us | 35.834 us | 1094.5× | 1313.2× | -| 64 | 111.623 ms | 77.369 us | 70.211 us | 1442.7× | 1589.8× | +| 16† | 1.747 ms | 11.194 us | 4.114 us | 156.0× | 424.6× | +| 24 | 5.902 ms | 15.691 us | 8.611 us | 376.1× | 685.4× | +| 32 | 13.883 ms | 21.960 us | 14.880 us | 632.2× | 933.0× | +| 48 | 46.549 ms | 42.745 us | 35.665 us | 1089.0× | 1305.2× | +| 64 | 110.591 ms | 74.703 us | 67.623 us | 1480.4× | 1635.4× | † At `n = 16`, protocol overhead is 63% of the FLINT wall time, so that rung is reported for completeness but excluded from the eligible comparator range. From the eligible `n = 24` rung through `n = 64`, the adjusted ratio increases -monotonically from 692.3× to 1589.8×. The widening gap reflects the different +monotonically from 685.4× to 1635.4×. The widening gap reflects the different measured regimes on this ladder: Hex follows cubic elimination, while the overhead-adjusted FLINT endpoint is still below its cubic asymptote.