---
title: "mlab-numerics-elem-gamma — Mova code model"
description: "Mova code model of mlab/src/builtins/elem.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/mlab/src/builtins/elem.rs.groupant/elem-gamma.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**

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# mlab-numerics-elem-gamma

The groupant beside mlab/src/builtins/elem.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/builtins/elem.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/elem.rs)
- **source SHA-256:** `09570b244d52019b…`
- **covers:** gamma(x) returns Inf when x==trunc(x) and x<=0; otherwise returns libm::tgamma(x). (bytes 15486–15612)
- **part of:** [mlab-numerics-elem](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/elem.rs.groupant/)
- **repository folder:** [`mlab/src/builtins/elem.rs.groupant/elem-gamma.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/elem.rs.groupant/elem-gamma.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` |
| **cost** | symbolic source derived | [invariant](#invariant) |
| **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) |
| `pole_boundary` | pole_boundary | partial source derived model | [pole_boundary](#pole-boundary) |
| `positive_factorial` | positive_factorial | partial source derived model | [positive_factorial](#positive-factorial) |
| `nan_branch` | nan_branch | partial source derived model | [nan_branch](#nan-branch) |
| `library_dependency` | library_dependency | partial source derived model | [library_dependency](#library-dependency) |

## Model text


### descriptant

#### mlab-numerics-elem-gamma

gamma(x) returns Inf when x==trunc(x) and x<=0; otherwise returns libm::tgamma(x).

##### Modeling epoch 2026-10-31

Prospective source reading preceded inline tests. This node records implementation behavior, not a complete MATLAB compatibility contract. Models retain limits discovered in source reading, including real-only projections and warning-only result gates. Synthetic CPU fixtures are independent of frozen suites. No external effects, teacher, corpora or benchmark main are executed.

### approximant

#### Forward relation

gamma(x) returns Inf when x==trunc(x) and x<=0; otherwise returns libm::tgamma(x).

Executable Rust surrogate gap: no calibrated replacement is attached. Exact test calls are evidence for the reference, not a fast approximant. Numerical approximants would need a named domain, zero convention and metric at supported caps 1/2/5/10%; categorical errors/effects have no percent surrogate here.

### invariant

#### Invariants and cost

Exact pole policy precedes library evaluation; no rejection Result.

##### Cost

Constant wrapper work plus libm implementation.

Allocation failure, unchecked usize dimension arithmetic and IEEE nonfinite propagation are outside finite fixture guarantees. No measured throughput or global accuracy claim.

### models

## Typed source models: mlab-numerics-elem-gamma

### behavior_complement

Nonpositive integer poles exclude a finite result. No reflected approximation is implemented here.

### reverse_reconstruction

All nonpositive integers belong to the positive-Inf output fiber, along with possible overflow inputs; a gamma value generally has multiple real antecedents.

### pole_boundary

gamma(-2)=Inf and gamma(0)=Inf.

### positive_factorial

For fixture x=5, gamma=4!=24; this does not certify every integer.

### nan_branch

NaN fails equality and reaches libm; no custom NaN error.

### library_dependency

Accuracy outside poles is delegated to libm; no Boost held-out suite executed.


### tests

#### Evidence and limits

Selected wave30_tests exercise this source; fragment-specific limits are stated in its operators.

Native command specifications, numeric exits, profile-paired logs, compiled controls and exact-restoration receipts are retained externally in the wave30 numerics run. Tests exercise actual source, not a copied model. The selected finite fixtures do not prove full convergence, backend accuracy on all matrices, resource exhaustion or side-effectful callback behavior.