Elamur Groupantsalgorithm-horner-tests
The groupant beside algorithms/src/horner/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 | approximant |
| tests | focused executed full pending | wave20-evidence |
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 |
oracle_independence | oracle_independence | partial source derived model | oracle_independence |
mutation_sensitivity | mutation_sensitivity | partial source derived model | mutation_sensitivity |
finite_scope | finite_scope | partial source derived model | finite_scope |
reference_observation_equivalence | bitwise_differential_relation | partial source derived model | reference_observation_equivalence |
Model text
descriptant
horner tests.rs
Executable finite checks for horner: power_oracle independently computes powers and differentiated powers, degrees 0..14 over 17 dyadic points; invalid/overflow cases.
Original std-only implementation. Literature: see module-level Clenshaw (1955), Horner (1819), Neumaier (1974), or Lyness (1969) citation as applicable; citations are algorithm references, not copied code.
Epoch 2026-10-30: independent polynomial/basis/integer fixtures and explicit finite-error partitions. Simpson hidden bump demonstrates limits of sampled estimates. An initial correction-denominator mutant survived tight-tolerance tests; a loose-tolerance quartic assertion was added to isolate the correction, and that mutant was then rejected. No speed claim; no percentages inferred from finite observations. Rust syntax projection is partial, without macro expansion, type resolution or semantic proof.
model
behavior_complement
For fixed fixtures, complement consists of assertion traces differing from the required exact errors, statuses or tolerance comparisons; implementations agreeing only here remain possible. A passing trace excludes the compiled mutant but not arbitrary bugs outside fixtures.
reverse_reconstruction
Pass reconstructs the set of implementations consistent with these finite assertions; it does not identify one implementation. Untested inputs remain arbitrary. At x=0 value=c0 and derivative=c1; all higher coefficients remain free. [2,3,7] and [2,3,99] have identical outputs. With fixed degree and x, real fiber is intersection of two affine constraints; dependent constraints and f64 rounding require separate treatment.
oracle_independence
power_oracle independently computes powers and differentiated powers, coefficient lengths 0..14 over 17 dyadic points; invalid/overflow cases.
mutation_sensitivity
Replace derivative +value with -value; power_oracle fails
finite_scope
Finite fixture agreement supplies empirical observations, not a semantic proof or universal error cap. Different implementations with the same fixture outputs remain in the pass fiber.
reference_observation_equivalence
Compare original per-step and final gates on 133332 combinations (coefficient lengths 0..4, ten values, twelve arguments), two invalid-coefficient cases and derivative-only overflow. Compare both success bit patterns including signed zero, and exact error variants. The shared recurrence reference is complemented by the independent power oracle.
approximant
Forward model and invariant
Three tests combine independent power/derivative observations, boundary/fiber witnesses and full-width comparison with original gate placement. Success bits and error variants remain distinct.
Invariant: 133332 deterministic loop cases compare success bits and exact errors. The missing-derivative-gate mutant must fail W20-HORNER-DERIVATIVE-GATE.
Cost: Fixed corpus: 133332 comparisons with at most four coefficients, 255 independent power-oracle cases of lengths 0..14, and boundaries. Oracle cost is distinct from production.
IEEE-754 assumptions; no universal real accuracy guarantee. Wave20 is exact in its Result observation, not an approximate surrogate.
tests
Evidence
power_oracle independently computes powers and differentiated powers, degrees 0..14 over 17 dyadic points; invalid/overflow cases.
Compiled production negative control: Replace derivative +value with -value; power_oracle fails. Original bytes restored and named positive test rerun. Full algorithms library passes twice debug and twice release with identical sorted test-name/results; receipts bind logs under $MOVA_DATA/runs/octopus-wave19-numeric-2026-10-30. Source projection generated twice and compared before installation. Strict crate all-target Clippy attempted; outcome in receipt.
wave20-evidence
Horner optimization evidence — 2026-10-30
One final finite-pair gate replaces per-coefficient output gates after finite input validation. Under ordinary IEEE-754 arithmetic, nonfinite recurrence states cannot recover to an admitted finite final pair. Successful arithmetic order and Result variants are retained; failure can traverse more coefficients. Root's compiled production mutant rejects; restored code passes four integrated algorithm profiles. Source SHA-256 751f5de9220401aea97bd6d76e421eb99102a06168dd1bb848757d5b8d26f0a5.
Native receipts and actual CPU report distinguish the scoped absorption argument, finite observations and measured work. Historical wave19 measurements remain unchanged.
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