---
title: "mlab-rng-polar — Mova code model"
description: "Mova code model of mlab/src/rng.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/mlab/src/rng.rs.groupant/polar.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: <https://groupants.elamur.ai/free/en/mova/mlab/src/rng.rs.groupant/polar.groupant/>

# mlab-rng-polar

The groupant beside mlab/src/rng.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:** [`mlab/src/rng.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/rng.rs)
- **source SHA-256:** `dccb613f518f3221…`
- **covers:** Normal takes spare first; otherwise samples u,v in [-1,1), rejects s<=0 or s>=1, emits u*sqrt(-2ln(s)/s), caches v times same scale. (bytes 1433–1911)
- **part of:** [mlab-rng](https://md.groupants.elamur.ai/free/en/mova/mlab/src/rng.rs.groupant/)
- **repository folder:** [`mlab/src/rng.rs.groupant/polar.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/rng.rs.groupant/polar.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** | partial | [approximant](#approximant) |
| **ast** | partial | `../syntax.json` |
| **cost** | symbolic source derived | [invariant](#invariant) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | partial bounded parent evidence | [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) |
| `rejection_domain` | rejection_domain | partial source derived model | [rejection_domain](#rejection-domain) |
| `cache_transport` | cache_transport | partial source derived model | [cache_transport](#cache-transport) |
| `branch_relation` | branch_relation | partial source derived model | [branch_relation](#branch-relation) |
| `resource_cost` | resource_cost | partial source derived model | [resource_cost](#resource-cost) |

## Model text


### descriptant

#### mlab-rng-polar

Normal takes spare first; otherwise samples u,v in [-1,1), rejects s<=0 or s>=1, emits u*sqrt(-2ln(s)/s), caches v times same scale.

Epoch 2026-10-31: isolated source-bound fragment over bytes [1433,1911); includes no claim beyond this relation. Source hash dccb613f518f32218a910c4eca3ad31df44347dd38b90d431833558e995a2046.

### approximant

#### polar: forward relation

Normal takes spare first; otherwise samples u,v in [-1,1), rejects s<=0 or s>=1, emits u*sqrt(-2ln(s)/s), caches v times same scale.

Domain: All u64 seeds; IEEE f64 libm operations. Cross-platform transcendental bit identity is not proved.

Executable surrogate gap: no measured cheaper implementation with a useful scoped metric is supplied. Categorical/error/effect relations are exact obligations, not percent losses. Future numeric caps only1/2/5/10%.

### invariant

#### polar: invariant and cost

s=0 and s=1 rejected; finite accepted s gives finite multiplier for this discrete generator.

Two consecutive accepted normals share one polar radius; cloning preserves spare and future stream.

Scope-specific cost: O(1) cached branch; each rejected pair costs two uniform draws. Expected O(1), unbounded worst-case loop.

### models

### behavior_complement

Cached branch excludes any state advance; rejected points exclude emission.

### reverse_reconstruction

Observed cached z admits any unchanged four-word state paired with spare=Some(z); fresh z admits many accepted (u,v) and prior rejection histories.

### rejection_domain

s=0 and s=1 rejected; finite accepted s gives finite multiplier for this discrete generator.

### cache_transport

Two consecutive accepted normals share one polar radius; cloning preserves spare and future stream.

### branch_relation

Normal takes spare first; otherwise samples u,v in [-1,1), rejects s<=0 or s>=1, emits u*sqrt(-2ln(s)/s), caches v times same scale.

### resource_cost

O(1) cached branch; each rejected pair costs two uniform draws. Expected O(1), unbounded worst-case loop.

### tests

#### Evidence boundary

See ../tests.md for the actual selected source test and mutant. These tests sample the file, not every fragment branch. Cached branch excludes any state advance; rejected points exclude emission. Other branches here are source-derived and unexecuted unless the parent test explicitly calls them.