# Fixtures, Numerical Tolerances, and Property Tests

`D00-F12-A09` · Financial Mathematics, Statistics, and Data Foundations → Statistical Computing and Reproducibility · archetype `record-transform` · difficulty 1/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { fixturesNumericalTolerancesAndPropertyTests } from "fintech-algorithms/foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests";
```

## Signature

```ts
fixturesNumericalTolerancesAndPropertyTests(input)
```

Compares an actual vector against an expected one under an absolute tolerance, the way a fixture check does.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `D00Input` | yes | Reads `actual` and `expected`, two aligned lists of finite numbers, and `tolerance`, the largest absolute error still counted as a match. A non-empty `values` list of finite numbers must also be present; it is validated but not compared. |

## Returns

`D00Output`

`allClose` is true when every absolute error is within `tolerance`, `maximumError` is the largest of them, `tolerance` is echoed back, and `properties` carries `finite` and `sameLength`.

## Errors

- When `values` is absent, empty, or holds a non-finite number — throws RangeError
- When `actual` and `expected` have different lengths — throws RangeError
- When `tolerance` is negative — throws RangeError

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

### Input

`input`:

```json
{
  "values": [1, 2, 3, 4, 5],
  "floatingValue": 0.1,
  "maxSafeMagnitude": 1.7976931348623157e+308,
  "window": 3,
  "rawValues": [1, null, 2, "bad", 3],
  "invalidPolicy": "drop-and-report",
  "seed": 42,
  "sampleCount": 5,
  "leftVector": [
    {
      "index": "A",
      "value": 1
    },
    {
      "index": "B",
      "value": 2
    }
  ],
  "rightVector": [
    {
      "index": "B",
      "value": 20
    },
    {
      "index": "C",
      "value": 30
    }
  ],
  "train": [10, 12, 14, 16],
  "test": [18, 20],
  "actual": [1, 2.0000001, 3],
  "expected": [1, 2, 3]
}
```

Showing 14 of 18 fields.

### Call

```ts
fixturesNumericalTolerancesAndPropertyTests(input)
```

### Returns

object with 2 fields: allClose, maximumError

```json
{
  "allClose": true,
  "maximumError": 9.999999983634211e-8
}
```

## Verification and provenance

Tier: **verified** (via input-expected).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/foundations/llms.txt