Elamur Groupantsalgorithm-quantized-dot-tests
The groupant beside algorithms/src/quantized_dot/tests.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | syntax.json |
| descriptant | present | descriptant |
| invariant | partial | model |
| tests | existing checks referenced | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
independent_oracle | independent_oracle | partial source derived model | independent_oracle |
boundary_refusal_fiber | boundary_refusal_fiber | partial source derived model | boundary_refusal_fiber |
compiled_fault_separation | compiled_fault_separation | partial source derived model | compiled_fault_separation |
Model text
descriptant
quantized_dot: tests.rs
Deterministic executable assertions for quantized_dot; finite fixtures observe production outputs against independent masks or exact arithmetic. Passing is a finite evidence claim, not universal correctness.
Epoch2026-10-30
Prospective model was saved before implementation. Independent finite fixtures and exact integer arithmetic retain explicit domain boundaries. Initial cancellation test incorrectly expected10% rejection for a1.97% residual; corrected to1%. This was a fixture error, not a reason to weaken the certificate. Four full library runs passed502tests; focused module contains3tests. Compiled production mutation: Disable certificate rejection; unsupported5% result violates named boundary assertion. No live workload, end-to-end gain or universal numerical guarantee measured.
model
Mathematical model
Deterministic executable assertions for quantized_dot; finite fixtures observe production outputs against independent masks or exact arithmetic. Passing is a finite evidence claim, not universal correctness.
Invariant
Exact identity ab-qaqb=qarb+qbra+rarb gives |exact-approx|<=E by triangle inequality. Quantization preserves sign or becomes zero. Normalized error is E/L1 when L1>0; L1=0 forces E=0. Cancellation of dot terms does not invalidate an L1 certificate.
Cost and resources
O(n) time, O(1) storage, no allocation. Checked i128 accumulation and u128 certificate sums. Quotient/remainder certification avoids overflow from multiplying L1 by100. Work budget bounds pairs; unsupported and uncertified domains fail with no hidden fallback.
Observation limits
Integer certificates are scoped to successful calls and stated premises, with categorical validation, budget, allocation and overflow errors. usize targets up to64 bits are modeled. No floating approximation, timing benefit or universal error theorem inferred from tests. No retained selected subset witness.
Literature
Higham, Accuracy and Stability of Numerical Algorithms, perturbation/error analysis of dot products; here the residual identity is exact integer arithmetic.
Executable companion gap
The production kernel already realizes the scoped approximation. No separate cheaper Rust surrogate has been measured; no fake exact wrapper or speed claim is attached.
approximant
Mathematical model
Deterministic executable assertions for quantized_dot; finite fixtures observe production outputs against independent masks or exact arithmetic. Passing is a finite evidence claim, not universal correctness.
Invariant
Exact identity ab-qaqb=qarb+qbra+rarb gives |exact-approx|<=E by triangle inequality. Quantization preserves sign or becomes zero. Normalized error is E/L1 when L1>0; L1=0 forces E=0. Cancellation of dot terms does not invalidate an L1 certificate.
Cost and resources
O(n) time, O(1) storage, no allocation. Checked i128 accumulation and u128 certificate sums. Quotient/remainder certification avoids overflow from multiplying L1 by100. Work budget bounds pairs; unsupported and uncertified domains fail with no hidden fallback.
Observation limits
Integer certificates are scoped to successful calls and stated premises, with categorical validation, budget, allocation and overflow errors. usize targets up to64 bits are modeled. No floating approximation, timing benefit or universal error theorem inferred from tests. No retained selected subset witness.
Literature
Higham, Accuracy and Stability of Numerical Algorithms, perturbation/error analysis of dot products; here the residual identity is exact integer arithmetic.
Executable companion gap
The production kernel already realizes the scoped approximation. No separate cheaper Rust surrogate has been measured; no fake exact wrapper or speed claim is attached.
models
Typed obernants: quantized_dot tests.rs
Source SHA256: 1c8d36000e8b7236183612e5eb877fabb6f5c0063bdf07f6e16ab9b3864a7e81. Partial source-derived relations; finite checks are not proofs.
behavior_complement
Observation is a vector of named assertion outcomes. The pass fiber contains implementations agreeing on every exercised fixture; its complement contains at least one failing assertion, panic or error mismatch. A surviving mutant outside the tested domain can remain in the pass fiber. This relation explicitly leaves untested behavior unknown.
reverse_reconstruction
All implementations producing the same finite assertion vector belong to one nonunique fiber. Original production and a mutant differing only on untested data may both pass; the compiled mutant (Disable certificate rejection; unsupported5% result violates named boundary assertion.) is separated by tier_boundary_and_validation. A pass vector cannot reconstruct source, runtime or behavior on unseen inputs.
independent_oracle
Fixtures target the mathematical observation directly: Equal-length i64 arrays, positive u64 step and supported percent. Let qa=trunc(a/step)step and ra=a-qa. Accumulate approximate sum qaqb and E=sum(|qa||rb|+|qb||ra|+|rarb|). L1=sum|ab|. Return only if E<=floor(percent*L1/100). Small mask enumeration is structurally independent of scaled/trimmed DP; exact integer formulas are independent of interpolation lookup and quantization branches. These finite witnesses falsify implementation claims without promoting sample agreement to proof.
boundary_refusal_fiber
The validation/budget fixtures distinguish supported success from invalid tiers, dimensions, resource or overflow failures where relevant. Inputs sharing Error variants lose original details. Boundary assertions are executable witnesses of the broader production relation: checked_accumulation_fiber|Three MINMIN products overflow signed i128 and return Overflow. One MIN1 is represented exactly. Budget and length checks precede arithmetic. Arithmetic failure cannot be relabeled as a small numerical error.
compiled_fault_separation
Disable certificate rejection; unsupported5% result violates named boundary assertion. The intentional production edit must compile and fail tier_boundary_and_validation; restored byte hash and positive rerun close the experiment. It only demonstrates sensitivity to this fault, not mutation completeness.
tests
Executable evidence
Run cargo test -p mova-algorithms quantized_dot::tests (also --release). Module has 3 tests. Twice debug and twice release full library502-test runs have equal normalized test names/results. Strict all-target Clippy passed.
Compiled mutant: Disable certificate rejection; unsupported5% result violates named boundary assertion. Named assertion test: tier_boundary_and_validation. Production bytes restored and focused positive suite passed.
External logs: $MOVA_DATA/runs/octopus-wave19-approx-2026-10-30. receipt.json binds file hashes. Syntax projections are generated independently twice and compared; partial syntax only, not semantic AST. Allocation refusal is not deterministically injected.
prospective
Before implementation: knapsack uses exact rational profit scaling K=epsilonvmax/n, minimum-weight DP, loss<=nK<=epsilon OPT. Subset sum uses rational trimmed sorted lists delta=epsilon/n and retains feasible lower representatives; (1+delta)^-n>=1-epsilon. Tiers exactly 1/2/5/10%, zeros exact. Checked work/state budgets and fallible allocation, no speed claims. Piecewise interpolation uses integer knots/query and exact rational values, conditional on caller's C² function, exact samples and |f''|<=M; absolute bound Mh²/8 only. Quantized dot uses integer truncation and exact absolute residual bound, normalized by sum|a_i b_i| with exact zero convention, never cancellation-sensitive scalar relative metric. All arithmetic checked. Tests compare exhaustive or independent arithmetic oracles, exercise invalid/overflow/budget boundaries and compiled production mutants.
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