Elamur Groupantsalgorithm-modular-power-tests
The groupant beside algorithms/src/modular_power/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 | bounded checked | Forward |
| ast | partial | syntax.json |
| cost | symbolic unmeasured | Cost |
| descriptant | present | descriptant |
| invariant | source derived | Invariant |
| tests | bounded executed | 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 |
|---|---|---|---|
nonbehavior | behavior_complement | partial source derived | nonbehavior |
failure_fibers | reverse_reconstruction | partial source derived | failure_fibers |
oracle | oracle_correspondence | partial source derived | oracle |
mutation | counterfactual_boundary | partial source derived | mutation |
schedule | resource_observation | partial source derived | schedule |
Model text
descriptant
modular_power tests epoch
2026-10-29. Repository search found math/src/nt.rs::modpow_plain; this unsigned specialization composes its repository-owned square-and-multiply idea with exact u128 products. No external solutions or LeetCode imports.
Prospective assumptions are retained in ../mod.rs.groupant/model.md#prospective. The mathematical combiner reviews source, partial syntax, forward/typed models, invariants and finite evidence. It preserves predictions and failed controls when revising claims; it is not an autonomous proof generator.
Narrowing power squaring or accumulator multiplication to wrapping u64 compiled; each exactly filtered tests::zero_identity_and_full_width_products failed (exit 101; one failed, two filtered). Initial parity-only cases missed accumulator narrowing; the added (-2)^3 identity closed that observed gap.
Implementation and tests form separate leaf groupants. Parent registry wiring remains integration work. Partial syntax has opaque macros and no semantic/type resolution. No universal proof or application behavior is claimed.
model
modular_power tests model
Forward
Accept exactly when all oracle assertions and metamorphic conditions succeed on this explicit finite fixture set: 10,200 small repeated-multiplication cases (25 bases x17 exponents x24 positive moduli), zero/one modulus and exponent-zero boundaries, full-width parity/products, and 1,024 fixed-seed reduction/addition cases.
Invariant
Expected independent-oracle values do not invoke the tested routine; metamorphic sides explicitly do. Inputs are deterministic and all arithmetic bounded, checked or widened.
Cost
Fixed finite work: 10,200 small repeated-multiplication cases (25 bases x17 exponents x24 positive moduli), zero/one modulus and exponent-zero boundaries, full-width parity/products, and 1,024 fixed-seed reduction/addition cases. No measured speed claim.
nonbehavior
Type: behavior_complement. U is candidate implementations paired with pass/fail on the finite fixture set F. R(P,pass) iff all assertions succeed; R(P,fail) iff a terminating call/assertion panics or a mismatch occurs. U minus R comprises false passes despite failure and false failures despite all assertions holding. Harness crashes/nontermination are excluded.
failure_fibers
Type: reverse_reconstruction. A pass admits all implementations agreeing on F with arbitrary off-fixture behavior. A failure admits all faulty implementations or faulty oracles producing that mismatch/panic; no unique defect reconstruction.
oracle
Type: oracle_correspondence. Small exponents use repeated multiplication, no binary exponent decomposition or repeated squaring. Parity, identity and exponent-addition laws add explicit algebraic constraints. Finite correspondence assumes the oracle; no universal proof.
mutation
Type: counterfactual_boundary. Narrowing power squaring or accumulator multiplication to wrapping u64 compiled; each exactly filtered tests::zero_identity_and_full_width_products failed (exit 101; one failed, two filtered). Initial parity-only cases missed accumulator narrowing; the added (-2)^3 identity closed that observed gap. Intervention changes source operations with fixture inputs fixed.
schedule
Type: resource_observation. 10,200 small repeated-multiplication cases (25 bases x17 exponents x24 positive moduli), zero/one modulus and exponent-zero boundaries, full-width parity/products, and 1,024 fixed-seed reduction/addition cases. Fixed seed, wrapping generator and loop bounds determine observations; wall-clock time is not part of the deterministic output.
evidence
Evidence 2026-10-29
Three focused tests pass twice with identical normalized statuses. 10,200 small repeated-multiplication cases (25 bases x17 exponents x24 positive moduli), zero/one modulus and exponent-zero boundaries, full-width parity/products, and 1,024 fixed-seed reduction/addition cases.
Small exponents use repeated multiplication, no binary exponent decomposition or repeated squaring. Parity, identity and exponent-addition laws add explicit algebraic constraints.
Narrowing power squaring or accumulator multiplication to wrapping u64 compiled; each exactly filtered tests::zero_identity_and_full_width_products failed (exit 101; one failed, two filtered). Initial parity-only cases missed accumulator narrowing; the added (-2)^3 identity closed that observed gap.
Commands: cargo test -p mova-algorithms --offline modular_power::tests:: -- --test-threads=1; cargo clippy -p mova-algorithms --offline --all-targets -- -D warnings. Owned-source rustfmt checks pass. Temporary library exports permit local crate checks but are not committed; parent owns integration. External copies compile with rustc --edition 2024 --test and run with --exact. Production sources stay unchanged.
Source-bound syntax is generated twice after formatting and compared. Structural evidence does not establish semantic correctness, school/inference wiring or throughput.
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