--- title: "algorithm-neville-interpolation-tests — Mova code model" description: "Mova code model of algorithms/src/neville_interpolation/tests.rs: components with their labels, obernants and the model text." url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/neville_interpolation/tests.rs.groupant/" --- Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants** This page as HTML: # algorithm-neville-interpolation-tests The groupant beside algorithms/src/neville_interpolation/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 descriptive instance - **source:** [`algorithms/src/neville_interpolation/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/neville_interpolation/tests.rs) - **source SHA-256:** `25044ad8fe42b6c0…` - **repository folder:** [`algorithms/src/neville_interpolation/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/neville_interpolation/tests.rs.groupant) - **repository commit:** `48f2e6f74146` > **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](#approximant) | | **ast** | partial | `syntax.json` | | **descriptant** | present | [descriptant](#descriptant) | | **invariant** | partial | [approximant](#approximant) | | **tests** | existing checks referenced | [tests](#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](#behavior-complement) | | `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) | | `oracle_independence` | oracle_independence | partial source derived model | [oracle_independence](#oracle-independence) | | `mutation_sensitivity` | mutation_sensitivity | partial source derived model | [mutation_sensitivity](#mutation-sensitivity) | | `finite_scope` | finite_scope | partial source derived model | [finite_scope](#finite-scope) | ## Model text ### descriptant #### neville_interpolation: tests.rs Original std-only Rust. References: Neville/Newton: Stoer and Bulirsch, Introduction to Numerical Analysis, interpolation chapter; spline: de Boor, A Practical Guide to Splines; trapezoid: Davis and Rabinowitz, Methods of Numerical Integration; tanh-sinh: Takahasi and Mori (1974), Double exponential formulas for numerical integration. No copied implementation. ##### Prospective epoch (before implementation) Before implementation: finite strictly increasing nonempty interpolation nodes, matched finite ordinates; spline at least two. Neville triangular O(n^2) time/O(n) memory, P_i,j=((x_j-x)P_i,j-1+(x-x_i)P_i+1,j)/(x_j-x_i). Newton backward divided differences O(n^2)/O(n), nested product evaluation O(n). Natural spline Thomas solve for second derivatives, zero endpoint curvatures, O(n) construction and binary interval evaluation. Reject nonfinite intermediate states and undefined spacing; no conditioning promise. Quadrature endpoints strictly ordered finite, finite positive tolerance, finite span; callbacks finite, deterministic and resource bounded by caller. Adaptive trapezoid dyadically doubles grid reusing samples, /3 consecutive difference heuristic; bounded evaluations and stagnation. Tanh sinh fixed transformed truncation [-3,3], dyadic h, samples strictly inside endpoints in ascending transformed order per level, no reuse; error is consecutive difference only and excludes truncation error. Both no arbitrary-function accuracy bound: zero and unsampled bump share sample trace. Expected gain: Neville O(n) storage versus full tableau, Newton O(n) repeated evaluation, spline linear solve; no measured speed claim or executable approximation percentage. Validation independent polynomial/analytic fixtures, domain/overflow/status/count and alias witnesses; compiled production mutants and repeats. ##### Mathematical combiner Raw source and partial syntax anchor the f64 transition F; forward model predicts F, typed views describe its excluded pairs and preimage fibers; independent tests evaluate finite projections of F. Their conjunction narrows compatible implementations but is not a proof. No semantic AST resolution or macro expansion. Leaf children=[]; crate wiring is parent-owned. ##### Observed epoch 2026-10-30 15 focused tests pass twice debug and twice optimized release with identical normalized outcomes. Five compiled production mutants fail oracle assertions; original bytes restored and positives rerun. No benchmark or speed claim. Finite arithmetic, allocations and callback limitations remain. ### model ### behavior_complement Observed Pass excludes implementations violating any asserted result on these fixtures, including compiled mutant: Change left+right to left-right; polynomial_oracle assertion fails. Pass does not exclude bugs outside tested cases; it is not a universal theorem. ### reverse_reconstruction Pass has many preimages: exact implementations and implementations agreeing only on this finite fixture set. Untested q=12345 behavior can change while all assertions pass. At q=0, nodes [-1,1], ordinates [-1,1] and [0,0] both yield 0. A scalar query cannot recover ordinates or nodes. At known distinct nodes, real exact interpolation is unique for degree