Struct `Lcg128CmDxsm64`

pub struct Lcg128CmDxsm64 { /* private fields */ }

A PCG random number generator (CM DXSM 128/64 (LCG) variant).

Permuted Congruential Generator with 128-bit state, internal Linear Congruential Generator, and 64-bit output via "double xorshift multiply" output function.

This is a 128-bit LCG with explicitly chosen stream with the PCG-DXSM output function. This corresponds to pcg_engines::cm_setseq_dxsm_128_64 from pcg_cpp and PCG64DXSM from NumPy.

Despite the name, this implementation uses 32 bytes (256 bit) space comprising 128 bits of state and 128 bits stream selector. These are both set by SeedableRng, using a 256-bit seed.

Note that while two generators with different stream parameter may be closely correlated, this is mitigated by the DXSM output function.

Implementations

`impl Lcg128CmDxsm64`

fn state(&self) -> u128

Current state of the generator

fn stream(&self) -> u128

Stream parameter of the generator

Note that PCG only stores an increment, which is always odd. Self::from_state discards the highest bit from the stream by shifting it to the left, so this method shifts the increment by one bit to the right.

fn from_state(state: u128, stream: u128) -> Self

Construct an instance using a pre-initialized state

Unlike Self::new, this method does not mutate state. It may therefore be used with Self::state and Self::stream to reconstruct an RNG.

Note that the highest bit of the stream parameter is discarded to simplify upholding internal invariants.

`impl Lcg128CmDxsm64`

fn advance(&mut self, delta: u128)

Multi-step advance functions (jump-ahead, jump-back)

The method used here is based on Brown, "Random Number Generation with Arbitrary Stride,", Transactions of the American Nuclear Society (Nov. 1994). The algorithm is very similar to fast exponentiation.

Even though delta is an unsigned integer, we can pass a signed integer to go backwards, it just goes "the long way round".

Using this function is equivalent to calling next_64() delta number of times.

fn new(state: u128, stream: u128) -> Self

Construct an instance compatible with PCG seed and stream.

Note that the highest bit of the stream parameter is discarded to simplify upholding internal invariants.

Note that while two generators with different stream parameter may be closely correlated, this is mitigated by the DXSM output function.

PCG specifies the following default values for both parameters:

state = 0xcafef00dd15ea5e5
stream = 0xa02bdbf7bb3c0a7ac28fa16a64abf96

Trait Implementations

`impl Clone for Lcg128CmDxsm64`

fn clone(&self) -> Lcg128CmDxsm64

`impl Debug for Lcg128CmDxsm64`

fn fmt(&self, f: &mut Formatter<'_>) -> Result

`impl Eq for Lcg128CmDxsm64`

`impl PartialEq for Lcg128CmDxsm64`

fn eq(&self, other: &Lcg128CmDxsm64) -> bool

`impl SeedableRng for Lcg128CmDxsm64`

type Seed = [u8; 32];
fn from_seed(seed: Self::Seed) -> Self: We use a single 255-bit seed to initialise the state and select a stream. One seed bit (lowest bit of seed[8]) is ignored.