# Design: enterprise-random-family

## Context

`@suaveplan/types` defines `Rng = { nextUint32(): number; nextFloat(): number }` but ships zero implementations. The genesis `@suaveplan/testing` package contains an inline Mulberry32 `seededRng` for test fixtures — this inline copy stays (testing packages cannot take workspace deps), but the canonical implementations live here. The games codebase runs five different hand-rolled PRNG algorithms across bingo, baccarat, rummy, minesweeper, and fruit-machine — this change provides the single canonical set they all migrate to.

Three packages with zero inter-dependency between them at the leaf level: `pseudo-random` has no workspace deps, `random` depends on `@suaveplan/types` and `@suaveplan/error`, and `noise` depends only on `@suaveplan/error`.

## Goals / Non-Goals

**Goals:**

- Ship `SeededRng` interface and four algorithm implementations (Mulberry32, SFC32, Xoshiro256++, CounterRng) with full offset/fork/checkpoint support
- Ship the full high-level random utilities surface: strings, IDs, collections, objects, game primitives, and all statistical distributions with `DistributionConfig` serializable dispatch
- Ship spatial noise functions (Perlin, Simplex, Value, Worley, fBm, Blue noise)
- All three packages at 100% coverage (foundational layer)
- Full enterprise checklist for each

**Non-Goals:**

- Cryptographic PRNGs (ChaCha20-DRBG, HMAC-DRBG) — belong in `@suaveplan/crypto-sodium`/`crypto-browser`
- Gaussian Process regression, Monte Carlo integration, statistical hypothesis testing — future `@suaveplan/stats`
- Geo random geometry (`randomPoint`, `randomPolygon`) — deferred to `@suaveplan/geo/random`
- Changing `@suaveplan/testing`'s inline Mulberry32 — testing rule holds; it stays inline

## Decisions

### Package: `@suaveplan/pseudo-random`

```text
src/
  types/
    seeded-rng.types.ts / seeded-rng.md     # SeededRng interface + RngCheckpoint
  algorithms/
    mulberry32.ts / mulberry32.test.ts / mulberry32.md
    sfc32.ts / sfc32.test.ts / sfc32.md
    xoshiro256.ts / xoshiro256.test.ts / xoshiro256.md
    counter-rng.ts / counter-rng.test.ts / counter-rng.md
  seed/
    normalize.ts / normalize.test.ts / normalize.md   # normalizeSeed(string|number): number
  utils/
    shuffle.ts / shuffle.test.ts / shuffle.md         # shuffle, shuffleInPlace
    sample.ts / sample.test.ts / sample.md            # sample, weightedSample
    distributions.ts / distributions.test.ts / distributions.md  # uniform int/float helpers
  errors/
    codes.ts / pseudo-random-error.ts / index.ts
  constants/index.ts
  index.ts
```

**`SeededRng` interface:**

```ts
interface SeededRng extends Rng {
  readonly seed: number
  readonly position: number
  skip(n: number): this
  reset(): this
  at(offset: number): SeededRng
  fork(id: number | string): SeededRng
  checkpoint(): RngCheckpoint
  restore(checkpoint: RngCheckpoint): this
}
```

**Algorithm selection guide** (exported as docs, not enforced):

- `Mulberry32Rng` — 32-bit state, ~2^32 period. Best for trivial use cases, minimal memory footprint.
- `Sfc32Rng` — 128-bit state, period >2^127. Best default for games and simulations.
- `Xoshiro256Rng` — 256-bit state, period 2^256-1, supports fixed-size jump (2^128 and 2^192 steps). Best when independent parallel streams are needed at scale.
- `CounterRng` — splitmix64-based hash counter. O(1) seek to any position. Best for direct-address use cases like bingo ticket generation.

**Seed normalization** — `normalizeSeed(seed: string | number): number`:

- String seeds: splitmix64 mixing over char codes (replaces djb2/FNV-1a used in bingo)
- Numeric seeds: splitmix64 single-round mixing to avalanche input bias
- Rejects NaN, Infinity, non-safe-integers

**`fork(id)`** — derives a child seed via `splitmix64(parentSeed ^ hash(id))`. Child streams are statistically independent from the parent and from each other. Critical for game use cases:

```ts
const master = new Sfc32Rng(gameSeed)
const weather = master.fork('weather')
const enemies = master.fork('enemies')
const loot    = master.fork('loot')
```

**`at(offset)`** — for linear-burn algorithms (Mulberry32, SFC32): constructs a new instance at `seed` and burns `offset` values at construction time (O(offset), cost paid once). For CounterRng: O(1), directly sets the counter.

**Offset validation** — no hard cap (the bingo 1,000,000 limit was app-specific). Throws `PRNG.OFFSET.OUT_OF_RANGE` only for negative values.

### Package: `@suaveplan/random`

```text
src/
  source/
    crypto-rng.ts / crypto-rng.test.ts / crypto-rng.md     # cryptoRng(): Rng
    default-rng.ts / default-rng.test.ts / default-rng.md  # getDefaultRng / setDefaultRng
  bytes/
    random-bytes.ts / random-bytes.test.ts / random-bytes.md
  strings/
    random-string.ts / random-string.test.ts / random-string.md  # presets + custom charset
  ids/
    uuid.ts / uuid.test.ts / uuid.md        # randomUUID (v4+v7), randomULID, randomNanoid
  numbers/
    random-int.ts / random-int.test.ts / random-int.md
    random-float.ts / random-float.test.ts / random-float.md
  collections/
    shuffle.ts / shuffle.test.ts / shuffle.md
    sample.ts / sample.test.ts / sample.md
    choice.ts / choice.test.ts / choice.md
    weighted.ts / weighted.test.ts / weighted.md   # weightedChoice, weightedSample
  objects/
    random-key.ts / random-key.test.ts / random-key.md
    random-value.ts / ...
    random-entry.ts / ...
    random-subset.ts / ...
  game/
    dice.ts / dice.test.ts / dice.md    # coin, dice, roll
  distributions/
    continuous/
      normal.ts / normal.test.ts / normal.md
      log-normal.ts / ...
      exponential.ts / ...
      gamma.ts / ...
      beta.ts / ...
      pareto.ts / ...
      weibull.ts / ...
      cauchy.ts / ...
      logistic.ts / ...
    discrete/
      bernoulli.ts / bernoulli.test.ts / bernoulli.md
      geometric.ts / ...
      binomial.ts / ...
      poisson.ts / ...
    sampler.ts / sampler.test.ts / sampler.md  # createSampler, sample, DistributionConfig
  errors/
    codes.ts / random-error.ts / index.ts
  constants/index.ts
  index.ts
```

**`cryptoRng()` factory** — returns an object implementing `@suaveplan/types`'s `Rng` interface backed by `crypto.getRandomValues`:

```ts
{
  nextUint32: () => { const buf = new Uint32Array(1); crypto.getRandomValues(buf); return buf[0] },
  nextFloat:  function() { return this.nextUint32() / 0x1_0000_0000 }
}
```

This is the **only** callsite for `crypto.getRandomValues` in `@suaveplan/random`. Guarded by `tests/no-disallowed.test.ts`.

**Default source** — module-level mutable (non-exported) singleton. `getDefaultRng()` returns it; `setDefaultRng(rng)` replaces it (test hook). Default is `cryptoRng()`.

**String presets** (`randomString(length, { type, rng? })`):

| type | charset |
|---|---|
| `hex` | `0-9a-f` |
| `base64` | A-Z, a-z, 0-9, +, / |
| `base64url` | A-Z, a-z, 0-9, -, _ |
| `url-safe` | A-Z, a-z, 0-9, -, _, . |
| `numeric` | `0-9` |
| `alphanumeric` | A-Z, a-z, 0-9 |
| `distinguishable` | `CDEHKMPRTUWXY012458` (no I/O/0/1 confusion) |
| `ascii-printable` | all printable ASCII 0x20-0x7E |

Custom charset via `{ characters: string }` option.

**UUID v7** — time-ordered, 48-bit millisecond timestamp in high bits, 74 random bits. Monotonically increasing within the same millisecond via sequence counter.

**`DistributionConfig` tagged union** — every distribution has a named-parameter config object. The `type` discriminant selects the algorithm; all other fields are the algorithm's parameters. `createSampler(config, rng?)` returns `() => number`. `sample(config, rng?)` is a one-shot convenience. Config objects are plain JSON-serializable data — `rng` is always external.

**Implementation notes for distributions:**

- Normal: Box-Muller transform
- LogNormal: `exp(normal(mu, sigma))`
- Gamma: Marsaglia-Tsang method (k ≥ 1); Ahrens-Dieter for k < 1
- Beta: ratio of two Gamma samples
- Poisson: Knuth algorithm for λ ≤ 30; rejection method for larger λ
- All discrete distributions use `nextUint32()` not `nextFloat()` for the base draw

### Package: `@suaveplan/noise`

```text
src/
  perlin/
    perlin.ts / perlin.test.ts / perlin.md      # perlin2, perlin3 with seed
  simplex/
    simplex.ts / simplex.test.ts / simplex.md   # simplex2, simplex3, simplex4
  value/
    value.ts / value.test.ts / value.md         # value2, value3
  worley/
    worley.ts / worley.test.ts / worley.md      # worley2, worley3, WorleyMode (F1|F2|F1-F2)
  fbm/
    fbm.ts / fbm.test.ts / fbm.md              # fbm compositor, FbmOptions
  blue/
    blue.ts / blue.test.ts / blue.md            # blueNoiseSample, Poisson disk sampling
  errors/
    codes.ts / noise-error.ts / index.ts
  constants/index.ts
  index.ts
```

All noise functions accept a `seed: number` parameter and return values normalised to `[-1, 1]` (except Worley which returns `[0, 1]` distances). No dependency on `@suaveplan/pseudo-random` — noise uses its own internal seeded hash permutation tables, which is the standard noise implementation pattern.

**fBm compositor:**

```ts
fbm(noiseFn, x, y, {
  octaves: 6,
  lacunarity: 2.0,
  gain: 0.5,
  seed: 0
}): number
```

Composes any 2D noise function with octave summation.

**Blue noise** — Bridson's Poisson disk sampling algorithm:

```ts
blueNoiseSample(width, height, minDistance, { seed?, rng? }): [number, number][]
```

## Risks / Trade-offs

| Risk | Mitigation |
|---|---|
| `at(offset)` is O(offset) for Mulberry32/SFC32 | Document clearly; `CounterRng` is the O(1) alternative; no silent perf traps |
| `setDefaultRng` is global mutable state | Documented as test-only; tests restore previous value with `afterEach`; not exported from subpath exports |
| `fork` child streams not proven independent | Use `normalizeSeed` mixing + test with fast-check that `fork('a')` and `fork('b')` produce uncorrelated sequences across 10k samples |
| Simplex noise patent (expired 2022) | US patent 6,867,776 expired April 2022 — safe to use |
| Blue noise is O(n) output size | Cap at 100k points; throw `NOISE.BLUE.SAMPLE_LIMIT_EXCEEDED` above |