---
title: "algorithm-integer-sqrt-tests — Mova code model"
description: "Mova code model of algorithms/src/integer_sqrt/tests.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/integer_sqrt/tests.rs.groupant/"
---
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# algorithm-integer-sqrt-tests

The groupant beside algorithms/src/integer_sqrt/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

- **kind:** groupant
- **status:** partial source derived instance
- **source:** [`algorithms/src/integer_sqrt/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/integer_sqrt/tests.rs)
- **source SHA-256:** `5fddfd2e52bb4fd9…`
- **repository folder:** [`algorithms/src/integer_sqrt/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/integer_sqrt/tests.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **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](#forward) |
| **ast** | partial | `syntax.json` |
| **cost** | symbolic unmeasured | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | source derived | [Invariant](#invariant) |
| **tests** | bounded executed | [evidence](#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](#nonbehavior) |
| `failure_fibers` | reverse_reconstruction | partial source derived | [failure_fibers](#failure-fibers) |
| `oracle` | oracle_correspondence | partial source derived | [oracle](#oracle) |
| `mutation` | counterfactual_boundary | partial source derived | [mutation](#mutation) |
| `schedule` | resource_observation | partial source derived | [schedule](#schedule) |

## Model text


### descriptant

#### integer_sqrt tests epoch

2026-10-29. Repository search found math/src/calc.rs delegating arbitrary-precision roots to a dependency. This fixed-width binary search is newly authored; standard isqrt is test-only. 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.

Replacing <= by < in the square predicate compiled and exactly tests::square_neighbors_and_maximum failed (exit 101; one failed, two filtered).

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

## integer_sqrt tests model

### Forward

Accept exactly when all oracle assertions and metamorphic conditions succeed on this explicit finite fixture set: 65,537 inputs 0..=65536, nine square-root values with square/neighbor cases, u64::MAX and 4,096 fixed-seed full-width inputs with adjacent monotonicity.

### 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: 65,537 inputs 0..=65536, nine square-root values with square/neighbor cases, u64::MAX and 4,096 fixed-seed full-width inputs with adjacent monotonicity. 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. Standard u64::isqrt is independent of this source; u128 square bounds provide a second constraint. Finite correspondence assumes the oracle; no universal proof.

### mutation

Type: counterfactual_boundary. Replacing <= by < in the square predicate compiled and exactly tests::square_neighbors_and_maximum failed (exit 101; one failed, two filtered). Intervention changes source operations with fixture inputs fixed.

### schedule

Type: resource_observation. 65,537 inputs 0..=65536, nine square-root values with square/neighbor cases, u64::MAX and 4,096 fixed-seed full-width inputs with adjacent monotonicity. 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. 65,537 inputs 0..=65536, nine square-root values with square/neighbor cases, u64::MAX and 4,096 fixed-seed full-width inputs with adjacent monotonicity.

Standard u64::isqrt is independent of this source; u128 square bounds provide a second constraint.

Replacing <= by < in the square predicate compiled and exactly tests::square_neighbors_and_maximum failed (exit 101; one failed, two filtered).

Commands: cargo test -p mova-algorithms --offline integer_sqrt::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.