Module quasirandom 

Quasi-random low-discrepancy sequences (feature quasirandom). Quasi-random (low-discrepancy) sequences.

Quasi-random sequences cover the unit cube [0, 1)^D more evenly than uniform PRNG draws - variance for Monte Carlo integration scales O((log n)^d / n) rather than O(1/√n). They’re standard tools for ray-tracing, financial simulation, and high-dimensional numerical integration.

Three constructions are shipped:

• VanDerCorputSequence
  • 1-D, any prime base.
• HaltonSequence
  • multi-dim, Van der Corput across the first primes. Supports up to 32 dimensions.
• SobolSequence
  • multi-dim, uses precomputed direction numbers. Supports up to 6 dimensions out of the box; the Joe-Kuo D6 file would extend this past 21 000.

These are not PRNGs and live alongside, not inside, crate::Random. Use a PRNG when you want unpredictability; use a quasi-random sequence when you want even coverage.

Structs

HaltonSequence

Multi-dimensional Halton sequence - Van der Corput across the first HALTON_MAX_DIM primes. Discrepancy is excellent for dimensions up to ~10; beyond that consider SobolSequence or scrambled Halton.

SobolSequence

Multi-dimensional Sobol sequence (Bratley-Fox 1988 starter set, dimensions 1–6). For higher-dimensional uses, switch to a Joe-Kuo D6 direction-number table (out of scope here).

VanDerCorputSequence

1-D Van der Corput sequence in a given prime base. Each step reverses the index’s base-b digit expansion and reads it as a fraction in [0, 1).

Constants

HALTON_MAX_DIM

Maximum number of dimensions supported by HaltonSequence.

SOBOL_MAX_DIM

Maximum number of dimensions SobolSequence supports with the shipped direction-number table.