Implementing a Mersenne Twister Generator in?Rust
Luis Soares, M.Sc.
Lead Software Engineer | Blockchain & ZK Protocol Engineer | ?? Rust | C++ | Web3 | Solidity | Golang | Cryptography | Author
The Mersenne Twister is a widely used pseudorandom number generator (PRNG) known for its fast generation and high-quality randomness. Developed by Makoto Matsumoto and Takuji Nishimura, it produces a sequence of 32-bit integers with a very long period of 2^19937?1 and a high degree of uniformity and independence among the values.
In this article, we explore the implementation of a Mersenne Twister generator in Rust, covering the algorithm, implementation details, and usage examples! ??
Concepts Behind the Mersenne?Twister
The Mersenne Twister is a pseudorandom number generator (PRNG) widely used because of its long period and high quality of randomness. The key idea is to produce a sequence of numbers that appear random and are suitable for use in simulations, games, and other applications.
Key Characteristics
Mersenne Twister Algorithm
Key Features
Algorithm Steps
Parameters
The Mersenne Twister uses several parameters for its internal operations:
Implementing the Mersenne Twister in?Rust
Step 1: Define the Mersenne Twister?Struct
First, we define a struct to hold the state of the generator.
const N: usize = 624;
const M: usize = 397;
const MATRIX_A: u32 = 0x9908B0DF;
const UPPER_MASK: u32 = 0x80000000;
const LOWER_MASK: u32 = 0x7FFFFFFF;
struct MersenneTwister {
mt: [u32; N],
index: usize,
}
impl MersenneTwister {
fn new(seed: u32) -> Self {
let mut mt = [0u32; N];
let mut twister = MersenneTwister { mt, index: N + 1 };
twister.initialize(seed);
twister
}
fn initialize(&mut self, seed: u32) {
self.mt[0] = seed;
for i in 1..N {
self.mt[i] = (1812433253u32)
.wrapping_mul(self.mt[i - 1] ^ (self.mt[i - 1] >> 30))
.wrapping_add(i as u32);
}
}
fn generate_numbers(&mut self) {
for i in 0..N {
let y = (self.mt[i] & UPPER_MASK) | (self.mt[(i + 1) % N] & LOWER_MASK);
self.mt[i] = self.mt[(i + M) % N] ^ (y >> 1);
if y % 2 != 0 {
self.mt[i] ^= MATRIX_A;
}
}
}
fn extract_number(&mut self) -> u32 {
if self.index >= N {
if self.index > N {
panic!("Generator was never seeded");
}
self.generate_numbers();
self.index = 0;
}
let mut y = self.mt[self.index];
self.index += 1;
y ^= (y >> 11);
y ^= (y << 7) & 0x9D2C5680;
y ^= (y << 15) & 0xEFC60000;
y ^= (y >> 18);
y
}
}
Step 2: Initialization
The initialization function sets the initial state of the generator using a given seed value.
impl MersenneTwister {
fn initialize(&mut self, seed: u32) {
self.mt[0] = seed;
for i in 1..N {
self.mt[i] = (1812433253u32)
.wrapping_mul(self.mt[i - 1] ^ (self.mt[i - 1] >> 30))
.wrapping_add(i as u32);
}
}
}
Step 3: Twist Transformation
The generate_numbers function performs the twist transformation to generate new values in the state array.
impl MersenneTwister {
fn generate_numbers(&mut self) {
for i in 0..N {
let y = (self.mt[i] & UPPER_MASK) | (self.mt[(i + 1) % N] & LOWER_MASK);
self.mt[i] = self.mt[(i + M) % N] ^ (y >> 1);
if y % 2 != 0 {
self.mt[i] ^= MATRIX_A;
}
}
}
}
Step 4: Extracting Random?Numbers
The extract_number function returns a random 32-bit integer and applies tempering to improve the distribution of the output values.
impl MersenneTwister {
fn extract_number(&mut self) -> u32 {
if self.index >= N {
if self.index > N {
panic!("Generator was never seeded");
}
self.generate_numbers();
self.index = 0;
}
let mut y = self.mt[self.index];
self.index += 1;
y ^= (y >> 11);
y ^= (y << 7) & 0x9D2C5680;
y ^= (y << 15) & 0xEFC60000;
y ^= (y >> 18);
y
}
}
Step 5: Usage?Example
Here’s how you can use the MersenneTwister struct to generate random numbers.
fn main() {
let mut rng = MersenneTwister::new(5489);
for _ in 0..10 {
println!("{}", rng.extract_number());
}
}
Full Implementation
Here is the complete code for the Mersenne Twister implementation in Rust:
const N: usize = 624;
const M: usize = 397;
const MATRIX_A: u32 = 0x9908B0DF;
const UPPER_MASK: u32 = 0x80000000;
const LOWER_MASK: u32 = 0x7FFFFFFF;
struct MersenneTwister {
mt: [u32; N],
index: usize,
}
impl MersenneTwister {
fn new(seed: u32) -> Self {
let mut mt = [0u32; N];
let mut twister = MersenneTwister { mt, index: N + 1 };
twister.initialize(seed);
twister
}
fn initialize(&mut self, seed: u32) {
self.mt[0] = seed;
for i in 1..N {
self.mt[i] = (1812433253u32)
.wrapping_mul(self.mt[i - 1] ^ (self.mt[i - 1] >> 30))
.wrapping_add(i as u32);
}
}
fn generate_numbers(&mut self) {
for i in 0..N {
let y = (self.mt[i] & UPPER_MASK) | (self.mt[(i + 1) % N] & LOWER_MASK);
self.mt[i] = self.mt[(i + M) % N] ^ (y >> 1);
if y % 2 != 0 {
self.mt[i] ^= MATRIX_A;
}
}
}
fn extract_number(&mut self) -> u32 {
if self.index >= N {
if self.index > N {
panic!("Generator was never seeded");
}
self.generate_numbers();
self.index = 0;
}
// Tempering Process
let mut y = self.mt[self.index];
self.index += 1;
y ^= (y >> 11);
y ^= (y << 7) & 0x9D2C5680;
y ^= (y << 15) & 0xEFC60000;
y ^= (y >> 18);
y
}
}
fn main() {
let mut rng = MersenneTwister::new(5489);
for _ in 0..10 {
println!("{}", rng.extract_number());
}
}
The tempering process
The tempering process in the Mersenne Twister algorithm is a final transformation applied to the generated number before it is returned as the output. This process improves the statistical properties of the generated numbers, making them appear more uniformly distributed and reducing any detectable patterns or correlations.
Let’s break down each step of the tempering process:
Tempering Steps
The tempering process involves a series of bitwise operations (shifts and XORs) on the 32-bit integer y. The specific constants and bitwise operations were chosen empirically to improve the distribution of the output values.
let mut y = self.mt[self.index];
This initializes y with the current state value from the state vector.
2. First Tempering Operation:
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y ^= (y >> 11);
3. Second Tempering Operation:
y ^= (y << 7) & 0x9D2C5680;
4. Third Tempering Operation:
y ^= (y << 15) & 0xEFC60000;
5. Fourth Tempering Operation:
y ^= (y >> 18);
Understanding the?Masks
In the context of the Mersenne Twister algorithm, the masks are applied during the tempering process to selectively modify certain bits of the intermediate value y. The masks used are:
These masks are used in conjunction with bitwise AND operations to selectively influence the bits at specific positions.
Purpose of the?Masks
The main goal of the tempering process is to improve the distribution of the generated random numbers by ensuring that the bits are well-mixed. Each mask contributes to this goal in a specific way:
y ^= (y << 7) & 0x9D2C5680;
2. 0xEFC60000:
y ^= (y << 15) & 0xEFC60000;
Why These Specific?Masks?
The choice of these specific masks (0x9D2C5680 and 0xEFC60000) is based on empirical testing and theoretical analysis by the algorithm's creators, Makoto Matsumoto and Takuji Nishimura. The goal was to find masks that:
These specific masks were found to be effective in achieving these goals, leading to the high-quality random numbers produced by the Mersenne Twister.
Full Tempering Process?Code
Here is the full tempering process as seen in the Mersenne Twister implementation:
impl MersenneTwister {
fn extract_number(&mut self) -> u32 {
if self.index >= N {
if self.index > N {
panic!("Generator was never seeded");
}
self.generate_numbers();
self.index = 0;
}
let mut y = self.mt[self.index];
self.index += 1;
// Tempering
y ^= (y >> 11);
y ^= (y << 7) & 0x9D2C5680;
y ^= (y << 15) & 0xEFC60000;
y ^= (y >> 18);
y
}
}
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All the best,
Luis Soares [email protected]
Lead Software Engineer | Blockchain & ZKP Protocol Engineer | ?? Rust | Web3 | Solidity | Golang | Cryptography | Author
AI/LLM Disruptive Leader | GenAI Tech Lab
3 个月See my new random number generator framework (featuring issues of Mersenne Twister), at https://mltblog.com/4fGDLu0