---
title: "math-calc-checks — Mova code model"
description: "Mova code model of math/src/calc.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/math/src/calc.rs.groupant/checks.groupant/"
---
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# math-calc-checks

The groupant beside math/src/calc.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_fragment
- **status:** partial source bound model
- **source:** [`math/src/calc.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/calc.rs)
- **source SHA-256:** `81be7f264f451792…`
- **covers:** approx computes supported f64 expressions; fingerprint computes integer residues; independent prefers exact integer residues then finite f64. Matching is many-to-one, tolerance1e-9 max(1,|result|). Unavailable or matching checks are not global numerical guarantees. (bytes 55308–62082)
- **part of:** [math-calc](https://md.groupants.elamur.ai/free/en/mova/math/src/calc.rs.groupant/)
- **repository folder:** [`math/src/calc.rs.groupant/checks.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/calc.rs.groupant/checks.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` |
| **composition** | partial | `model.md` |
| **cost** | partial | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [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) |
| `priority_relation` | priority_relation | partial source derived model | [priority_relation](#priority-relation) |
| `finite_tolerance` | finite_tolerance | partial source derived model | [finite_tolerance](#finite-tolerance) |
| `factorial_operand_domain` | factorial_operand_domain | partial source derived model | [factorial_operand_domain](#factorial-operand-domain) |
| `availability_boundary` | availability_boundary | partial source derived model | [availability_boundary](#availability-boundary) |

## Parts

- [math-calc-checks-residue-fibers](https://md.groupants.elamur.ai/free/en/mova/math/src/calc.rs.groupant/checks.groupant/residue-fibers.groupant/)

## Model text


### descriptant

#### math-calc-checks

approx computes supported f64 expressions; fingerprint computes integer residues; independent prefers exact integer residues then finite f64. Matching is many-to-one, tolerance1e-9 max(1,|result|). Unavailable or matching checks are not global numerical guarantees.

Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.

### approximant

#### Scoped forward and cost

approx computes supported f64 expressions; fingerprint computes integer residues; independent prefers exact integer residues then finite f64. Matching is many-to-one, tolerance1e-9 max(1,|result|). Unavailable or matching checks are not global numerical guarantees.

No executable percent surrogate claimed.

### invariant

#### Scoped invariant

approx computes supported f64 expressions; fingerprint computes integer residues; independent prefers exact integer residues then finite f64. Matching is many-to-one, tolerance1e-9 max(1,|result|). Unavailable or matching checks are not global numerical guarantees.

Source range[55308,62082) bound by manifest digest. Parent domain applies, not arbitrary public states.

Additional source limits from independent review: range converts span through z_to_u64(...).unwrap_or(0); a positive span>u64 charges0 then loops without per-iteration ticks. Fingerprint factorial reduces its operand first: original operand P61+1 yields residue argument1 and result1, whereas mathematical factorial residue is0. Restrict original factorial operand domain; residue<=2M alone is insufficient. No huge input was executed.

### models

## Source-scoped typed relations

### behavior_complement

For integer result x, a supported fingerprint excludes acceptance when x mod P61 differs from computed fp. Matching excludes no error by a multiple of P61. Unsupported paths return None, not Check{ok:false}.

### reverse_reconstruction

Given fingerprint r, compatible claimed integers are {r+k*P61 | k integer}. A finite f64 check admits results within its scaled tolerance. Neither relation identifies the original E or exact result.

### priority_relation

independent checks integer fingerprint first and returns it immediately. Only unavailable fingerprint reaches finite f64 comparison; a failing supported fingerprint is not rescued by a floating match.

### finite_tolerance

For Q fallback require both a and fx finite and |fx|<1e300, then |a-fx|<=1e-9 max(|fx|,1). R branch compares without this explicit finite prefilter; unsupported approx remains None.

### factorial_operand_domain

fingerprint(Fact(a)) fingerprints a first, then computes factorial of residue if <=2M. Correctness needs the original operand admitted in the small natural domain; original P61+1 maps to1! residue1 although true factorial residue0. This huge case is source-derived, not executed.

### availability_boundary

approx supports arithmetic/selected calls but not lists/booleans/index/ranged functions; mod/floor/ceil reject magnitudes>=4.5e15. fingerprint supports integer addition, subtraction, multiplication, natural powers, factorial and negation; division returns None, so independent may instead use its floating fallback. Power evaluates the exponent via a fresh Env.

### tests

#### Evidence

See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.

approx computes supported f64 expressions; fingerprint computes integer residues; independent prefers exact integer residues then finite f64. Matching is many-to-one, tolerance1e-9 max(1,|result|). Unavailable or matching checks are not global numerical guarantees.

### wave34-composition

## Check descendant composition

The residue-fibers child feeds independent only for an integer exact result. A supported residue comparison returns immediately even on disagreement; f64 fallback runs only when fingerprint is unavailable. The integer result is reduced by the same modulus, so accepted claims inhabit a residue class and may differ by P61. Unsupported result types yield no check. The child also evaluates power exponents in a fresh Env and the factorial argument reduction remains a documented domain gap.

Parent compatible antecedents must preserve the supported/unsupported branch, not only the numeric residue. A failed fingerprint cannot be repaired by a favorable floating recomputation in the parent. Historical approximate and finite-tolerance models remain distinct; no total numerical certificate is inferred.

### Cost

Use the reached fingerprint cost, then one result reduction and comparison. Only an unavailable fingerprint adds approximate-expression traversal. Avoid adding both branches when fingerprint succeeds. Big-integer reduction and cloned exponent variables contribute outside the modular multiplication count.