📐algorithm-pollard-rho-tests

The groupant beside algorithms/src/pollard_rho/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

Components

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.

Model text

descriptant

pollard_rho tests.rs

Source SHA-256: 9d6b40e7ef478d6bb079264ef0fdfff255d6bd70cb38b38b56f66da49dff01fa.

Execute five tests, requiring every assertion to hold. Independent trial division produces full small-number prime multisets; known full-width factorizations and exact u128 reconstruction cover larger cases. The modular step is compared to repeated modular addition, independent of multiplication.

Epoch 2026-10-30: prospective model retained before implementation. Independent bounded oracles, extreme arithmetic fixtures and compiled intentional mutations test the claim. Five owned tests pass twice each in debug and release, with identical normalized records. Finite results do not prove all inputs.

For pollard_rho the initial test incorrectly assumed n=9 needs more than one iteration; actual first iteration finds divisor three. The exhaustion witness was corrected to n=25,budget=1. Production logic was unchanged by that correction.

model

pollard_rho tests.rs model

Domain

Five tests: independent trial factorization n=1..4999; zero/cap/exhaustion, free prime/even cases; u64::MAX known factors, 3^40, 1000000007*1000000009, largest known prime below u64::MAX; seven deterministic replay/budget-extension cases; additive modular-product oracle for n=3..29,x<n,c=1..9.

Forward

Execute five tests, requiring every assertion to hold. Independent trial division produces full small-number prime multisets; known full-width factorizations and exact u128 reconstruction cover larger cases. The modular step is compared to repeated modular addition, independent of multiplication.

Invariant

Independent oracles do not call the implementation under test. Full-width product reconstruction using production primality is only a consistency check; independent small trial oracles are separate.

Cost

Finite fixture harness only; oracle loops are explicitly bounded by the source fixtures. Production cost: At most budget Floyd iterations across splits and restarts, each three modular squarings and one Euclidean gcd. At most 127 pending-node visits for a u64 factor tree, each Miller-Rabin O(log(n+1)) word work. Conservative O((budget+64)*log(n+1)) word operations, O(log(n+1)) pending/output words. This is a hard work cap, not an expected success claim.

nonbehavior

Type: behavior_complement. Over terminating candidate implementations and pass/fail observations, exclude pass when any assertion fails and failure when all assertions hold. Nontermination and abort are outside this binary observation domain.

implementation_fibers

Type: reverse_reconstruction. Pass reconstructs the set of implementations agreeing on every observed fixture; off-fixture behavior is unconstrained. Failure reconstructs implementations or incorrect oracle premises that cause a mismatch, not a unique defect.

oracle

Type: oracle_correspondence. Independent trial division produces full small-number prime multisets; known full-width factorizations and exact u128 reconstruction cover larger cases. The modular step is compared to repeated modular addition, independent of multiplication.

mutation

Type: counterfactual_boundary. Emit three on the even-composite split instead of two; boundaries_and_budget must fail on 2^63.

replay

Type: metamorphic_relation. Single-thread runs twice each in debug and release must have identical ordered normalized test records. Build output and timing are excluded. Finite agreement is not universal equivalence.

Composition and gaps

The source is a small leaf; its validation, core arithmetic and result assembly compose under the invariant above. Tests observe the public operation plus any private helper explicitly named by tests. Partial syntax does not expand macros or provide a semantic AST. No useful certified approximate metric is supplied for exact discrete outputs; executable numerical approximants are an explicit gap. No performance benchmark or formal proof is claimed.

evidence

Evidence — 2026-10-30

Source SHA-256: 9dc84e061044dd0f0e915c268668164c34130d6537f59051a60e0500c20d689c. Five tests per algorithm pass twice in debug and twice in release; normalized records compared by a Rust driver. Strict library Clippy and owned-file formatting pass. One compiled production mutation per algorithm fails a named assertion and restored bytes pass the positive suite.

Five tests: independent trial factorization n=1..4999; zero/cap/exhaustion, free prime/even cases; u64::MAX known factors, 3^40, 1000000007*1000000009, largest known prime below u64::MAX; seven deterministic replay/budget-extension cases; additive modular-product oracle for n=3..29,x<n,c=1..9.

Emit three on the even-composite split instead of two; boundaries_and_budget must fail on 2^63.

External evidence under $MOVA_DATA/runs/octopus-wave18-numbers-2026-10-30/:

• pollard_rho-debug-1.log: SHA-256 9758cfd6078528c523f63a8f6c72a6b7ec1ebdec37387a29d1ead040046a2c14.
• pollard_rho-debug-2.log: SHA-256 598d3a802e75de03bb0c4041d4fdc2ab2e3665fd621138f0e54afe5979cce6fd.
• pollard_rho-release-1.log: SHA-256 64ef2510ce388035d3c0c867ba97cd62b37873a00126afebc5044d395ecba5b5.
• pollard_rho-release-2.log: SHA-256 c2cfed586585fe3197a7de263072894817e4c6775abe3c5662850e64d6f9c0dc.
• pollard_rho-mutant.log: SHA-256 f161e35f0867062da3e0f6365170332fe3505bd58bdc1f560d3cf5d0e89721c5.
• pollard_rho-restored.log: SHA-256 a9a907a93f31a6cd5e17d3f4303f37a20f05f256c1102ade91f760144b632baf.

Syntax extraction is run twice and compared exactly; syntax.json is a partial Rust syntax projection, not semantic AST analysis. Root integration supplies registry validation; this branch does not modify the shared registry.

prospective

Prospective model — 2026-10-30

Domain n:u64 and budget<=10^7 Floyd iterations; zero invalid (before budget validation), one yields empty. Prime inputs require no rho budget. Reuse deterministic Miller-Rabin and Euclidean gcd, exact u128 square plus c modular arithmetic. Deterministic c restarts on collision, with global consumed iteration count; no guarantee of success within any budget. Each iteration performs three polynomial evaluations plus gcd; pending split stack and output have <=64 entries. Invariant product(pending)*product(primes)=original and each emitted factor is prime. O((budget+64)*log(n)) word-operation conservative bound including primality; O(log n) words. Complement excludes incomplete successful factors and hangs. Successful output reconstructs n uniquely by multiplication but not budget; exhausted output cannot identify n. Prime-power, product reconstruction, budget monotonic success, and deterministic replay specialize model.

root-wave18

Root integration refinement — 2026-10-30

Strict all-target Clippy exposed a test-only style issue after the owner library-only check. The source now uses the equivalent standard slice/divisibility helper. Old test source SHA-256: 9dc84e061044dd0f0e915c268668164c34130d6537f59051a60e0500c20d689c; current SHA-256: 9d6b40e7ef478d6bb079264ef0fdfff255d6bd70cb38b38b56f66da49dff01fa. Owner receipts remain historical and are not rewritten. Final root execution is recorded in models/algorithm-library.groupant/model.md#wave18-evidence; raw receipts are under $MOVA_DATA/runs/octopus-wave18-integration-2026-10-30/native-final. Syntax was projected twice identically after this edit. No production algorithm changed.

This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/pollard_rho/tests.rs.groupant/