Fix PCGRandom.integer() bias: use Lemire rejection sampling

[Zelys-DFKH]

Summary

PCGRandom.integer() used Math.round(this.number() * Number.MAX_SAFE_INTEGER) % max, which baked two sources of statistical bias into one expression and consumed twice the PRNG state per call.

Closes #6184

ryanleecode's comment in the thread spotted and quantified the bias clearly. I wanted to make sure a fix landed.

Problem

Math.round boundary bias: Math.round maps [0, 1) to integers non-uniformly. Buckets at each end of the range receive half the probability mass of interior values.

Modulo bias: Number.MAX_SAFE_INTEGER is not evenly divisible by most values of max, so some output values have one extra preimage in the modulo cycle and are overrepresented.

Double state consumption: number() calls _next() twice to build a 53-bit float. Integer generation only needs one 32-bit draw.

The practical bias magnitude is tiny (ryanleecode's analysis put it at ~10^-16), but a PRNG that is correct-by-construction is worth having.

Fix

For max <= 2^32: Lemire (2018) rejection sampling on raw 32-bit output (arXiv:1805.10941). Same approach as OpenBSD's arc4random_uniform and the PCG reference implementation. Every value in [0, max) gets exactly floor((2^32 - threshold) / max) accepting preimages, provably uniform.

For max > 2^32 (e.g. nextInt passing Number.MAX_SAFE_INTEGER): falls back to Math.floor(this.number() * max). Math.floor removes the Math.round boundary bias; residual floating-point discretization bias at that scale is negligible.

Tests

• Bounds test: nextIntBetween stays in [min, max) across several small ranges, where rejection sampling is most aggressively exercised.
• Deterministic test against a known seed to catch regressions in output sequence.

[changeset-bot]

🦋 Changeset detected

Latest commit: 53025fd

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 36 packages

Name	Type
effect	Patch
@effect/cli	Patch
@effect/cluster	Patch
@effect/experimental	Patch
@effect/opentelemetry	Patch
@effect/platform-browser	Patch
@effect/platform-bun	Patch
@effect/platform-node-shared	Patch
@effect/platform-node	Patch
@effect/platform	Patch
@effect/printer-ansi	Patch
@effect/printer	Patch
@effect/rpc	Patch
@effect/sql-clickhouse	Patch
@effect/sql-d1	Patch
@effect/sql-drizzle	Patch
@effect/sql-kysely	Patch
@effect/sql-libsql	Patch
@effect/sql-mssql	Patch
@effect/sql-mysql2	Patch
@effect/sql-pg	Patch
@effect/sql-sqlite-bun	Patch
@effect/sql-sqlite-do	Patch
@effect/sql-sqlite-node	Patch
@effect/sql-sqlite-react-native	Patch
@effect/sql-sqlite-wasm	Patch
@effect/sql	Patch
@effect/typeclass	Patch
@effect/vitest	Patch
@effect/workflow	Patch
@effect/ai	Patch
@effect/ai-amazon-bedrock	Patch
@effect/ai-anthropic	Patch
@effect/ai-google	Patch
@effect/ai-openai	Patch
@effect/ai-openrouter	Patch

Not sure what this means? Click here to learn what changesets are.

Click here if you're a maintainer who wants to add another changeset to this PR