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NormalRandom

struct NormalRandom[rounds: Int = 10]

A high-performance random number generator using the Box-Muller transform.

The Box-Muller transform is a method for generating pairs of independent standard normal random variables. Works efficiently on both CPU and GPU.

Parameters​

  • ​rounds (Int): Number of mixing rounds to perform for the underlying random uniform generator that serves as input to the Box-Muller transform. Higher values provide better statistical quality at the cost of performance. Default is 10.

Implemented traits​

AnyType, Copyable, ImplicitlyDestructible, Movable

Methods​

__init__​

def __init__(out self, *, seed: UInt64 = UInt64(67280421310721), subsequence: UInt64 = UInt64(0), offset: UInt64 = UInt64(0))

Initializes the normal distribution random number generator.

Args:

  • ​seed (UInt64): Seed value for the RNG.
  • ​subsequence (UInt64): Subsequence number for the RNG.
  • ​offset (UInt64): Offset value for the RNG.

step_normal​

def step_normal(mut self, mean: Float32 = 0, stddev: Float32 = 1) -> SIMD[DType.float32, 8]

Generate 8 normally distributed random numbers using Box-Muller transform.

Args:

  • ​mean (Float32): Mean of the normal distribution.
  • ​stddev (Float32): Standard deviation of the normal distribution.

Returns:

SIMD[DType.float32, 8]: SIMD vector containing 8 random float32 values from a normal distribution with mean mean and standard deviation stddev.

step_normal_4​

def step_normal_4(mut self, mean: Float32 = 0, stddev: Float32 = 1) -> SIMD[DType.float32, 4]

Generate 4 normal floats from a single Philox step.

Pairs adjacent uint32 outputs (raw[0], raw[1]) and (raw[2], raw[3]) into Box-Muller pairs (one Philox step total, vs two for step_normal). Uses the unbiased (raw + 0.5) / 2^32 uniform conversion, which is bounded away from 0 — no 1.0 - u guard before log(u) is needed.

Result lane order: (sin(v_0)*s_0, cos(v_0)*s_0, sin(v_1)*s_1, cos(v_1)*s_1) — sin/cos interleaved per pair, matching the natural output of a single Box-Muller call.

Args:

  • ​mean (Float32): Mean of the normal distribution.
  • ​stddev (Float32): Standard deviation of the normal distribution.

Returns:

SIMD[DType.float32, 4]: SIMD vector of 4 normal float32 values.

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