Merge pull request #66 from Magnus167/update-readme

Update README

.github/runners/runner-x64/Dockerfile

@@ -7,7 +7,7 @@ ARG DEBIAN_FRONTEND=noninteractive
 
 RUN apt update -y && apt upgrade -y && useradd -m docker
 RUN apt install -y --no-install-recommends \
-    curl jq git unzip \
+    curl jq git zip unzip \
     # dev dependencies
     build-essential libssl-dev libffi-dev python3 python3-venv python3-dev python3-pip \
     # dot net core dependencies

.github/scripts/run_examples.sh

@@ -0,0 +1,16 @@
+cargo build --release --examples 
+
+for ex in examples/*.rs; do
+  name=$(basename "$ex" .rs)
+  echo
+  echo "🟡 Running example: $name"
+
+  if ! cargo run --release --example "$name" -- --debug; then
+    echo
+    echo "❌ Example '$name' failed. Aborting."
+    exit 1
+  fi
+done
+
+echo
+echo "✅ All examples ran successfully."

.github/workflows/docs-and-testcov.yml

@@ -151,6 +151,8 @@ jobs:
           mkdir -p target/doc/docs
           mv target/doc/rustframe/* target/doc/docs/
 
+          echo "<meta http-equiv=\"refresh\" content=\"0; url=../docs/index.html\">" > target/doc/rustframe/index.html
+
           mkdir output
           cp tarpaulin-report.html target/doc/docs/
           cp tarpaulin-report.json target/doc/docs/

.github/workflows/run-unit-tests.yml

@@ -12,14 +12,12 @@ concurrency:
 
 jobs:
   pick-runner:
-
     if: github.event.pull_request.draft == false
 
     runs-on: ubuntu-latest
     outputs:
       runner: ${{ steps.choose.outputs.use-runner }}
     steps:
-
       - uses: actions/checkout@v4
       - id: choose
         uses: ./.github/actions/runner-fallback
@@ -27,7 +25,6 @@ jobs:
           primary-runner: "self-hosted"
           fallback-runner: "ubuntu-latest"
           github-token: ${{ secrets.CUSTOM_GH_TOKEN }}
-          
 
   run-unit-tests:
     needs: pick-runner
@@ -56,6 +53,20 @@ jobs:
       - name: Test docs generation
         run: cargo doc --no-deps --release
 
+      - name: Test examples
+        run: cargo test --examples --release
+
+      - name: Run all examples
+        run: |
+          for example in examples/*.rs; do
+            name=$(basename "$example" .rs)
+            echo "Running example: $name"
+            cargo run --release --example "$name" -- --debug || exit 1
+          done
+
+      - name: Cargo test all targets
+        run: cargo test --all-targets --release
+
       - name: Upload coverage to Codecov
         uses: codecov/codecov-action@v3
         with:

Cargo.toml

@@ -1,5 +1,6 @@
 [package]
 name = "rustframe"
+authors = ["Palash Tyagi (https://github.com/Magnus167)"]
 version = "0.0.1-a.20250716"
 edition = "2021"
 license = "GPL-3.0-or-later"
@@ -14,7 +15,6 @@ crate-type = ["cdylib", "lib"]
 [dependencies]
 chrono = "^0.4.10"
 criterion = { version = "0.5", features = ["html_reports"], optional = true }
-rand = "^0.9.1"
 
 [features]
 bench = ["dep:criterion"]

README.md

@@ -1,9 +1,5 @@
 # rustframe
 
-<!-- # <img align="center" alt="Rustframe" src=".github/rustframe_logo.png" height="50px" /> rustframe -->
-
-<!-- though the centre tag doesn't work as it would normally, it achieves the desired effect -->
-
 📚 [Docs](https://magnus167.github.io/rustframe/) | 🐙 [GitHub](https://github.com/Magnus167/rustframe) | 🌐 [Gitea mirror](https://gitea.nulltech.uk/Magnus167/rustframe) | 🦀 [Crates.io](https://crates.io/crates/rustframe) | 🔖 [docs.rs](https://docs.rs/rustframe/latest/rustframe/)
 
 <!-- [![Last commit](https://img.shields.io/endpoint?url=https://magnus167.github.io/rustframe/rustframe/last-commit-date.json)](https://github.com/Magnus167/rustframe) -->
@@ -27,11 +23,9 @@ Rustframe is an educational project, and is not intended for production use. It
 - **Math that reads like math** - element-wise `+`, `−`, `×`, `÷` on entire frames or scalars.
 - **Frames** - Column major data structure for single-type data, with labeled columns and typed row indices.
 - **Compute module** - Implements various statistical computations and machine learning models.
-
+- **Random number utils** - Built-in pseudo and cryptographically secure generators for simulations.
 - **[Coming Soon]** _DataFrame_ - Multi-type data structure for heterogeneous data, with labeled columns and typed row indices.
 
-- **[Coming Soon]** _Random number utils_ - Random number generation utilities for statistical sampling and simulations. (Currently using the [`rand`](https://crates.io/crates/rand) crate.)
-
 #### Matrix and Frame functionality
 
 - **Matrix operations** - Element-wise arithmetic, boolean logic, transpose, and more.
@@ -131,10 +125,6 @@ let mc: Matrix<f64> = Matrix::from_cols(vec![vec![1.0, 2.0], vec![3.0, 4.0]]);
 let md: Matrix<f64> = Matrix::from_cols(vec![vec![5.0, 6.0], vec![7.0, 8.0]]);
 let mul_result: Matrix<f64> = mc.matrix_mul(&md);
 // Expected:
-// 1*5 + 3*6 = 5 + 18 = 23
-// 2*5 + 4*6 = 10 + 24 = 34
-// 1*7 + 3*8 = 7 + 24 = 31
-// 2*7 + 4*8 = 14 + 32 = 46
 assert_eq!(mul_result.data(), &[23.0, 34.0, 31.0, 46.0]);
 
 // Dot product (alias for matrix_mul for FloatMatrix)
@@ -143,14 +133,7 @@ assert_eq!(dot_result, mul_result);
 
 // Transpose
 let original_matrix: Matrix<f64> = Matrix::from_cols(vec![vec![1.0, 2.0, 3.0], vec![4.0, 5.0, 6.0]]);
-// Original:
-// 1 4
-// 2 5
-// 3 6
 let transposed_matrix: Matrix<f64> = original_matrix.transpose();
-// Transposed:
-// 1 2 3
-// 4 5 6
 assert_eq!(transposed_matrix.rows(), 2);
 assert_eq!(transposed_matrix.cols(), 3);
 assert_eq!(transposed_matrix.data(), &[1.0, 4.0, 2.0, 5.0, 3.0, 6.0]);
@@ -159,10 +142,6 @@ assert_eq!(transposed_matrix.data(), &[1.0, 4.0, 2.0, 5.0, 3.0, 6.0]);
 let matrix = Matrix::from_cols(vec![vec![1.0, 2.0, 3.0], vec![4.0, 5.0, 6.0]]);
 // Map function to double each value
 let mapped_matrix = matrix.map(|x| x * 2.0);
-// Expected data after mapping
-// 2 8
-// 4 10
-// 6 12
 assert_eq!(mapped_matrix.data(), &[2.0, 4.0, 6.0, 8.0, 10.0, 12.0]);
 
 // Zip
@@ -170,9 +149,6 @@ let a = Matrix::from_cols(vec![vec![1.0, 2.0], vec![3.0, 4.0]]); // 2x2 matrix
 let b = Matrix::from_cols(vec![vec![5.0, 6.0], vec![7.0, 8.0]]); // 2x2 matrix
                                                                    // Zip function to add corresponding elements
 let zipped_matrix = a.zip(&b, |x, y| x + y);
-// Expected data after zipping
-// 6 10
-// 8 12
 assert_eq!(zipped_matrix.data(), &[6.0, 8.0, 10.0, 12.0]);
 ```
 
@@ -192,6 +168,29 @@ E.g. to run the `game_of_life` example:
 cargo run --example game_of_life
 ```
 
+More demos:
+
+```bash
+cargo run --example linear_regression
+cargo run --example logistic_regression
+cargo run --example k_means
+cargo run --example pca
+cargo run --example stats_overview
+cargo run --example descriptive_stats
+cargo run --example correlation
+cargo run --example inferential_stats
+cargo run --example distributions
+```
+
+To simply list all available examples, you can run:
+
+```bash
+# this technically raises an error, but it will list all examples
+cargo run --example
+```
+
+Each demo runs a couple of mini-scenarios showcasing the APIs.
+
 ### Running benchmarks
 
 To run the benchmarks, use:

examples/correlation.rs

@@ -0,0 +1,45 @@
+use rustframe::compute::stats::{covariance, covariance_matrix, pearson};
+use rustframe::matrix::{Axis, Matrix};
+
+/// Demonstrates covariance and correlation utilities.
+fn main() {
+    pairwise_cov();
+    println!("\n-----\n");
+    matrix_cov();
+}
+
+fn pairwise_cov() {
+    println!("Covariance & Pearson r\n----------------------");
+    let x = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
+    let y = Matrix::from_vec(vec![1.0, 2.0, 3.0, 5.0], 2, 2);
+    println!("covariance : {:.2}", covariance(&x, &y));
+    println!("pearson r  : {:.3}", pearson(&x, &y));
+}
+
+fn matrix_cov() {
+    println!("Covariance matrix\n-----------------");
+    let data = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
+    let cov = covariance_matrix(&data, Axis::Col);
+    println!("cov matrix : {:?}", cov.data());
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    const EPS: f64 = 1e-8;
+
+    #[test]
+    fn test_pairwise_cov() {
+        let x = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
+        let y = Matrix::from_vec(vec![1.0, 2.0, 3.0, 5.0], 2, 2);
+        assert!((covariance(&x, &y) - 1.625).abs() < EPS);
+        assert!((pearson(&x, &y) - 0.9827076298239908).abs() < 1e-5,);
+    }
+
+    #[test]
+    fn test_matrix_cov() {
+        let data = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
+        let cov = covariance_matrix(&data, Axis::Col);
+        assert_eq!(cov.data(), &[2.0, 2.0, 2.0, 2.0]);
+    }
+}

examples/descriptive_stats.rs

@@ -0,0 +1,56 @@
+use rustframe::compute::stats::{mean, mean_horizontal, mean_vertical, median, percentile, stddev};
+use rustframe::matrix::Matrix;
+
+/// Demonstrates descriptive statistics utilities.
+///
+/// Part 1: simple mean/stddev/median/percentile on a vector.
+/// Part 2: mean across rows and columns.
+fn main() {
+    simple_stats();
+    println!("\n-----\n");
+    axis_stats();
+}
+
+fn simple_stats() {
+    println!("Basic stats\n-----------");
+    let data = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+    println!("mean      : {:.2}", mean(&data));
+    println!("stddev    : {:.2}", stddev(&data));
+    println!("median    : {:.2}", median(&data));
+    println!("90th pct. : {:.2}", percentile(&data, 90.0));
+}
+
+fn axis_stats() {
+    println!("Row/column means\n----------------");
+    // 2x3 matrix
+    let data = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0], 2, 3);
+    let v = mean_vertical(&data); // 1x3
+    let h = mean_horizontal(&data); // 2x1
+    println!("vertical means  : {:?}", v.data());
+    println!("horizontal means: {:?}", h.data());
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    const EPS: f64 = 1e-8;
+
+    #[test]
+    fn test_simple_stats() {
+        let data = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+        assert!((mean(&data) - 3.0).abs() < EPS);
+        assert!((stddev(&data) - 1.4142135623730951).abs() < EPS);
+        assert!((median(&data) - 3.0).abs() < EPS);
+        assert!((percentile(&data, 90.0) - 5.0).abs() < EPS);
+    }
+
+    #[test]
+    fn test_axis_stats() {
+        let data = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0], 2, 3);
+        let v = mean_vertical(&data);
+        assert_eq!(v.data(), &[2.5, 3.5, 4.5]);
+        let h = mean_horizontal(&data);
+        assert_eq!(h.data(), &[2.0, 5.0]);
+    }
+}
+

examples/distributions.rs

@@ -0,0 +1,66 @@
+use rustframe::compute::stats::{binomial_cdf, binomial_pmf, normal_cdf, normal_pdf, poisson_pmf};
+use rustframe::matrix::Matrix;
+
+/// Demonstrates some probability distribution helpers.
+fn main() {
+    normal_example();
+    println!("\n-----\n");
+    binomial_example();
+    println!("\n-----\n");
+    poisson_example();
+}
+
+fn normal_example() {
+    println!("Normal distribution\n-------------------");
+    let x = Matrix::from_vec(vec![0.0, 1.0], 1, 2);
+    let pdf = normal_pdf(x.clone(), 0.0, 1.0);
+    let cdf = normal_cdf(x, 0.0, 1.0);
+    println!("pdf : {:?}", pdf.data());
+    println!("cdf : {:?}", cdf.data());
+}
+
+fn binomial_example() {
+    println!("Binomial distribution\n---------------------");
+    let k = Matrix::from_vec(vec![0_u64, 1, 2], 1, 3);
+    let pmf = binomial_pmf(4, k.clone(), 0.5);
+    let cdf = binomial_cdf(4, k, 0.5);
+    println!("pmf : {:?}", pmf.data());
+    println!("cdf : {:?}", cdf.data());
+}
+
+fn poisson_example() {
+    println!("Poisson distribution\n--------------------");
+    let k = Matrix::from_vec(vec![0_u64, 1, 2], 1, 3);
+    let pmf = poisson_pmf(3.0, k);
+    println!("pmf : {:?}", pmf.data());
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_normal_example() {
+        let x = Matrix::from_vec(vec![0.0, 1.0], 1, 2);
+        let pdf = normal_pdf(x.clone(), 0.0, 1.0);
+        let cdf = normal_cdf(x, 0.0, 1.0);
+        assert!((pdf.get(0, 0) - 0.39894228).abs() < 1e-6);
+        assert!((cdf.get(0, 1) - 0.8413447).abs() < 1e-6);
+    }
+
+    #[test]
+    fn test_binomial_example() {
+        let k = Matrix::from_vec(vec![0_u64, 1, 2], 1, 3);
+        let pmf = binomial_pmf(4, k.clone(), 0.5);
+        let cdf = binomial_cdf(4, k, 0.5);
+        assert!((pmf.get(0, 2) - 0.375).abs() < 1e-6);
+        assert!((cdf.get(0, 2) - 0.6875).abs() < 1e-6);
+    }
+
+    #[test]
+    fn test_poisson_example() {
+        let k = Matrix::from_vec(vec![0_u64, 1, 2], 1, 3);
+        let pmf = poisson_pmf(3.0, k);
+        assert!((pmf.get(0, 1) - 3.0_f64 * (-3.0_f64).exp()).abs() < 1e-6);
+    }
+}

examples/game_of_life.rs

@@ -1,13 +1,26 @@
-use rand::{self, Rng};
+//! Conway's Game of Life Example
+//! This example implements Conway's Game of Life using a `BoolMatrix` to represent the game board.
+//! It demonstrates matrix operations like shifting, counting neighbors, and applying game rules.
+//! The game runs in a loop, updating the board state and printing it to the console.
+//! To modify the behaviour of the example, please change the constants at the top of this file.
+
+
 use rustframe::matrix::{BoolMatrix, BoolOps, IntMatrix, Matrix};
+use rustframe::random::{rng, Rng};
 use std::{thread, time};
 
-const BOARD_SIZE: usize = 50; // Size of the board (50x50)
-const TICK_DURATION_MS: u64 = 10; // Milliseconds per frame
+const BOARD_SIZE: usize = 20; // Size of the board (50x50)
+const MAX_FRAMES: u32 = 1000;
+
+const TICK_DURATION_MS: u64 = 0; // Milliseconds per frame
+const SKIP_FRAMES: u32 = 1;
+const PRINT_BOARD: bool = true; // Set to false to disable printing the board
 
 fn main() {
-    // Initialize the game board.
-    // This demonstrates `BoolMatrix::from_vec`.
+    let args = std::env::args().collect::<Vec<String>>();
+    let debug_mode = args.contains(&"--debug".to_string());
+    let print_mode = if debug_mode { false } else { PRINT_BOARD };
+
     let mut current_board =
         BoolMatrix::from_vec(vec![false; BOARD_SIZE * BOARD_SIZE], BOARD_SIZE, BOARD_SIZE);
 
@@ -16,31 +29,18 @@ fn main() {
     add_simulated_activity(&mut current_board, BOARD_SIZE);
 
     let mut generation_count: u32 = 0;
-    // `previous_board_state` will store a clone of the board.
-    // This demonstrates `Matrix::clone()` and later `PartialEq` for `Matrix`.
     let mut previous_board_state: Option<BoolMatrix> = None;
     let mut board_hashes = Vec::new();
-    // let mut print_board_bool = true;
     let mut print_bool_int = 0;
 
     loop {
-        // print!("{}[2J", 27 as char); // Clear screen and move cursor to top-left
+        if print_bool_int % SKIP_FRAMES == 0 {
+            print_board(&current_board, generation_count, print_mode);
 
-        // if print_board_bool {
-        if print_bool_int % 10 == 0 {
-            print!("{}[2J", 27 as char);
-            println!("Conway's Game of Life - Generation: {}", generation_count);
-
-            print_board(&current_board);
-            println!("Alive cells: {}", &current_board.count());
-
-            // print_board_bool = false;
             print_bool_int = 0;
         } else {
-            // print_board_bool = true;
             print_bool_int += 1;
         }
-        // `current_board.count()` demonstrates a method from `BoolOps`.
         board_hashes.push(hash_board(&current_board, primes.clone()));
         if detect_stable_state(&current_board, &previous_board_state) {
             println!(
@@ -61,20 +61,18 @@ fn main() {
             add_simulated_activity(&mut current_board, BOARD_SIZE);
         }
 
-        // `current_board.clone()` demonstrates `Clone` for `Matrix`.
         previous_board_state = Some(current_board.clone());
 
-        // This is the core call to your game logic.
         let next_board = game_of_life_next_frame(&current_board);
         current_board = next_board;
 
         generation_count += 1;
         thread::sleep(time::Duration::from_millis(TICK_DURATION_MS));
 
-        // if generation_count > 500 { // Optional limit
-        //     println!("\nReached generation limit.");
-        //     break;
-        // }
+        if (MAX_FRAMES > 0) && (generation_count > MAX_FRAMES) {
+            println!("\nReached generation limit.");
+            break;
+        }
     }
 }
 
@@ -82,7 +80,13 @@ fn main() {
 ///
 /// - `board`: A reference to the `BoolMatrix` representing the current game state.
 /// This function demonstrates `board.rows()`, `board.cols()`, and `board[(r, c)]` (Index trait).
-fn print_board(board: &BoolMatrix) {
+fn print_board(board: &BoolMatrix, generation_count: u32, print_mode: bool) {
+    if !print_mode {
+        return;
+    }
+
+    print!("{}[2J", 27 as char);
+    println!("Conway's Game of Life - Generation: {}", generation_count);
     let mut print_str = String::new();
     print_str.push_str("+");
     for _ in 0..board.cols() {
@@ -93,7 +97,6 @@ fn print_board(board: &BoolMatrix) {
         print_str.push_str("| ");
         for c in 0..board.cols() {
             if board[(r, c)] {
-                // Using Index trait for Matrix<bool>
                 print_str.push_str("██");
             } else {
                 print_str.push_str("  ");
@@ -107,6 +110,8 @@ fn print_board(board: &BoolMatrix) {
     }
     print_str.push_str("+\n\n");
     print!("{}", print_str);
+
+    println!("Alive cells: {}", board.count());
 }
 
 /// Helper function to create a shifted version of the game board.
@@ -173,74 +178,38 @@ pub fn game_of_life_next_frame(current_game: &BoolMatrix) -> BoolMatrix {
     if rows == 0 && cols == 0 {
         return BoolMatrix::from_vec(vec![], 0, 0); // Return an empty BoolMatrix
     }
-    // Assuming valid non-empty dimensions (e.g., 25x25) as per typical GOL.
-    // Your Matrix::from_vec would panic for other invalid 0-dim cases.
-
     // Define the 8 neighbor offsets (row_delta, col_delta)
     let neighbor_offsets: [(isize, isize); 8] = [
         (-1, -1),
         (-1, 0),
-        (-1, 1), // Top row (NW, N, NE)
+        (-1, 1),
         (0, -1),
-        (0, 1), // Middle row (W, E)
+        (0, 1),
         (1, -1),
         (1, 0),
-        (1, 1), // Bottom row (SW, S, SE)
+        (1, 1),
     ];
 
-    // 1. Initialize `neighbor_counts` with the first shifted layer.
-    //    This demonstrates creating an IntMatrix from a function and using it as a base.
     let (first_dr, first_dc) = neighbor_offsets[0];
     let mut neighbor_counts = get_shifted_neighbor_layer(current_game, first_dr, first_dc);
 
-    // 2. Add the remaining 7 neighbor layers.
-    //    This demonstrates element-wise addition of matrices (`Matrix + Matrix`).
     for i in 1..neighbor_offsets.len() {
         let (dr, dc) = neighbor_offsets[i];
         let next_neighbor_layer = get_shifted_neighbor_layer(current_game, dr, dc);
-        // `neighbor_counts` (owned IntMatrix) + `next_neighbor_layer` (owned IntMatrix)
-        // uses `impl Add for Matrix`, consumes both, returns new owned `IntMatrix`.
         neighbor_counts = neighbor_counts + next_neighbor_layer;
     }
 
-    // 3. Apply Game of Life rules using element-wise operations.
-
-    // Rule: Survival or Birth based on neighbor counts.
-    // A cell is alive in the next generation if:
-    //   (it's currently alive AND has 2 or 3 neighbors) OR
-    //   (it's currently dead AND has exactly 3 neighbors)
-
-    // `neighbor_counts.eq_elem(scalar)`:
-    //   Demonstrates element-wise comparison of a Matrix with a scalar (broadcast).
-    //   Returns an owned `BoolMatrix`.
     let has_2_neighbors = neighbor_counts.eq_elem(2);
-    let has_3_neighbors = neighbor_counts.eq_elem(3); // This will be reused
+    let has_3_neighbors = neighbor_counts.eq_elem(3);
 
-    // `has_2_neighbors | has_3_neighbors`:
-    //   Demonstrates element-wise OR (`Matrix<bool> | Matrix<bool>`).
-    //   Consumes both operands, returns an owned `BoolMatrix`.
-    let has_2_or_3_neighbors = has_2_neighbors | has_3_neighbors.clone(); // Clone has_3_neighbors as it's used again
+    let has_2_or_3_neighbors = has_2_neighbors | has_3_neighbors.clone();
 
-    // `current_game & &has_2_or_3_neighbors`:
-    //   `current_game` is `&BoolMatrix`. `has_2_or_3_neighbors` is owned.
-    //   Demonstrates element-wise AND (`&Matrix<bool> & &Matrix<bool>`).
-    //   Borrows both operands, returns an owned `BoolMatrix`.
     let survives = current_game & &has_2_or_3_neighbors;
 
-    // `!current_game`:
-    //   Demonstrates element-wise NOT (`!&Matrix<bool>`).
-    //   Borrows operand, returns an owned `BoolMatrix`.
     let is_dead = !current_game;
 
-    // `is_dead & &has_3_neighbors`:
-    //   `is_dead` is owned. `has_3_neighbors` is owned.
-    //   Demonstrates element-wise AND (`Matrix<bool> & &Matrix<bool>`).
-    //   Consumes `is_dead`, borrows `has_3_neighbors`, returns an owned `BoolMatrix`.
     let births = is_dead & &has_3_neighbors;
 
-    // `survives | births`:
-    //   Demonstrates element-wise OR (`Matrix<bool> | Matrix<bool>`).
-    //   Consumes both operands, returns an owned `BoolMatrix`.
     let next_frame_game = survives | births;
 
     next_frame_game
@@ -250,7 +219,7 @@ pub fn generate_glider(board: &mut BoolMatrix, board_size: usize) {
     // Initialize with a Glider pattern.
     // It demonstrates how to set specific cells in the matrix.
     // This demonstrates `IndexMut` for `current_board[(r, c)] = true;`.
-    let mut rng = rand::rng();
+    let mut rng = rng();
     let r_offset = rng.random_range(0..(board_size - 3));
     let c_offset = rng.random_range(0..(board_size - 3));
     if board.rows() >= r_offset + 3 && board.cols() >= c_offset + 3 {
@@ -266,7 +235,7 @@ pub fn generate_pulsar(board: &mut BoolMatrix, board_size: usize) {
     // Initialize with a Pulsar pattern.
     // This demonstrates how to set specific cells in the matrix.
     // This demonstrates `IndexMut` for `current_board[(r, c)] = true;`.
-    let mut rng = rand::rng();
+    let mut rng = rng();
     let r_offset = rng.random_range(0..(board_size - 17));
     let c_offset = rng.random_range(0..(board_size - 17));
     if board.rows() >= r_offset + 17 && board.cols() >= c_offset + 17 {

examples/inferential_stats.rs

@@ -0,0 +1,66 @@
+use rustframe::compute::stats::{anova, chi2_test, t_test};
+use rustframe::matrix::Matrix;
+
+/// Demonstrates simple inferential statistics tests.
+fn main() {
+    t_test_demo();
+    println!("\n-----\n");
+    chi2_demo();
+    println!("\n-----\n");
+    anova_demo();
+}
+
+fn t_test_demo() {
+    println!("Two-sample t-test\n-----------------");
+    let a = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+    let b = Matrix::from_vec(vec![6.0, 7.0, 8.0, 9.0, 10.0], 1, 5);
+    let (t, p) = t_test(&a, &b);
+    println!("t statistic: {:.2}, p-value: {:.4}", t, p);
+}
+
+fn chi2_demo() {
+    println!("Chi-square test\n---------------");
+    let observed = Matrix::from_vec(vec![12.0, 5.0, 8.0, 10.0], 2, 2);
+    let (chi2, p) = chi2_test(&observed);
+    println!("chi^2: {:.2}, p-value: {:.4}", chi2, p);
+}
+
+fn anova_demo() {
+    println!("One-way ANOVA\n-------------");
+    let g1 = Matrix::from_vec(vec![1.0, 2.0, 3.0], 1, 3);
+    let g2 = Matrix::from_vec(vec![2.0, 3.0, 4.0], 1, 3);
+    let g3 = Matrix::from_vec(vec![3.0, 4.0, 5.0], 1, 3);
+    let (f, p) = anova(vec![&g1, &g2, &g3]);
+    println!("F statistic: {:.2}, p-value: {:.4}", f, p);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_t_test_demo() {
+        let a = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+        let b = Matrix::from_vec(vec![6.0, 7.0, 8.0, 9.0, 10.0], 1, 5);
+        let (t, _p) = t_test(&a, &b);
+        assert!((t + 5.0).abs() < 1e-5);
+    }
+
+    #[test]
+    fn test_chi2_demo() {
+        let observed = Matrix::from_vec(vec![12.0, 5.0, 8.0, 10.0], 2, 2);
+        let (chi2, p) = chi2_test(&observed);
+        assert!(chi2 > 0.0);
+        assert!(p > 0.0 && p < 1.0);
+    }
+
+    #[test]
+    fn test_anova_demo() {
+        let g1 = Matrix::from_vec(vec![1.0, 2.0, 3.0], 1, 3);
+        let g2 = Matrix::from_vec(vec![2.0, 3.0, 4.0], 1, 3);
+        let g3 = Matrix::from_vec(vec![3.0, 4.0, 5.0], 1, 3);
+        let (f, p) = anova(vec![&g1, &g2, &g3]);
+        assert!(f > 0.0);
+        assert!(p > 0.0 && p < 1.0);
+    }
+}

examples/k_means.rs

@@ -0,0 +1,65 @@
+use rustframe::compute::models::k_means::KMeans;
+use rustframe::matrix::Matrix;
+
+/// Two quick K-Means clustering demos.
+///
+/// Example 1 groups store locations on a city map.
+/// Example 2 segments customers by annual spending habits.
+fn main() {
+    city_store_example();
+    println!("\n-----\n");
+    customer_spend_example();
+}
+
+fn city_store_example() {
+    println!("Example 1: store locations");
+
+    // (x, y) coordinates of stores around a city
+    let raw = vec![
+        1.0, 2.0, 1.5, 1.8, 5.0, 8.0, 8.0, 8.0, 1.0, 0.6, 9.0, 11.0, 8.0, 2.0, 10.0, 2.0, 9.0, 3.0,
+    ];
+    let x = Matrix::from_rows_vec(raw, 9, 2);
+
+    // Group stores into two areas
+    let (model, labels) = KMeans::fit(&x, 2, 100, 1e-4);
+
+    println!("Centres: {:?}", model.centroids.data());
+    println!("Labels: {:?}", labels);
+
+    let new_points = Matrix::from_rows_vec(vec![0.0, 0.0, 8.0, 3.0], 2, 2);
+    let pred = model.predict(&new_points);
+    println!("New store assignments: {:?}", pred);
+}
+
+fn customer_spend_example() {
+    println!("Example 2: customer spending");
+
+    // (grocery spend, electronics spend) in dollars
+    let raw = vec![
+        200.0, 150.0, 220.0, 170.0, 250.0, 160.0, 800.0, 750.0, 820.0, 760.0, 790.0, 770.0,
+    ];
+    let x = Matrix::from_rows_vec(raw, 6, 2);
+
+    let (model, labels) = KMeans::fit(&x, 2, 100, 1e-4);
+
+    println!("Centres: {:?}", model.centroids.data());
+    println!("Labels: {:?}", labels);
+
+    let new_customers = Matrix::from_rows_vec(vec![230.0, 155.0, 810.0, 760.0], 2, 2);
+    let pred = model.predict(&new_customers);
+    println!("Cluster of new customers: {:?}", pred);
+}
+
+#[test]
+fn k_means_store_locations() {
+    let raw = vec![
+        1.0, 2.0, 1.5, 1.8, 5.0, 8.0, 8.0, 8.0, 1.0, 0.6, 9.0, 11.0, 8.0, 2.0, 10.0, 2.0, 9.0, 3.0,
+    ];
+    let x = Matrix::from_rows_vec(raw, 9, 2);
+    let (model, labels) = KMeans::fit(&x, 2, 100, 1e-4);
+    assert_eq!(labels.len(), 9);
+    assert_eq!(model.centroids.rows(), 2);
+    let new_points = Matrix::from_rows_vec(vec![0.0, 0.0, 8.0, 3.0], 2, 2);
+    let pred = model.predict(&new_points);
+    assert_eq!(pred.len(), 2);
+}

examples/linear_regression.rs

@@ -0,0 +1,118 @@
+use rustframe::compute::models::linreg::LinReg;
+use rustframe::matrix::Matrix;
+
+/// Two quick linear regression demonstrations.
+///
+/// Example 1 fits a model to predict house price from floor area.
+/// Example 2 adds number of bedrooms as a second feature.
+fn main() {
+    example_one_feature();
+    println!("\n-----\n");
+    example_two_features();
+}
+
+/// Price ~ floor area
+fn example_one_feature() {
+    println!("Example 1: predict price from floor area only");
+
+    // Square meters of floor area for a few houses
+    let sizes = vec![50.0, 60.0, 70.0, 80.0, 90.0, 100.0];
+    // Thousands of dollars in sale price
+    let prices = vec![150.0, 180.0, 210.0, 240.0, 270.0, 300.0];
+
+    // Each row is a sample with one feature
+    let x = Matrix::from_vec(sizes.clone(), sizes.len(), 1);
+    let y = Matrix::from_vec(prices.clone(), prices.len(), 1);
+
+    // Train with a small learning rate
+    let mut model = LinReg::new(1);
+    model.fit(&x, &y, 0.0005, 20000);
+
+    let preds = model.predict(&x);
+    println!("Size (m^2) -> predicted price (k) vs actual");
+    for i in 0..x.rows() {
+        println!(
+            "{:>3} -> {:>6.1} | {:>6.1}",
+            sizes[i],
+            preds[(i, 0)],
+            prices[i]
+        );
+    }
+
+    let new_house = Matrix::from_vec(vec![120.0], 1, 1);
+    let pred = model.predict(&new_house);
+    println!("Predicted price for 120 m^2: {:.1}k", pred[(0, 0)]);
+}
+
+/// Price ~ floor area + bedrooms
+fn example_two_features() {
+    println!("Example 2: price from area and bedrooms");
+
+    // (size m^2, bedrooms) for each house
+    let raw_x = vec![
+        50.0, 2.0, 70.0, 2.0, 90.0, 3.0, 110.0, 3.0, 130.0, 4.0, 150.0, 4.0,
+    ];
+    let prices = vec![160.0, 195.0, 250.0, 285.0, 320.0, 350.0];
+
+    let x = Matrix::from_rows_vec(raw_x, 6, 2);
+    let y = Matrix::from_vec(prices.clone(), prices.len(), 1);
+
+    let mut model = LinReg::new(2);
+    model.fit(&x, &y, 0.0001, 50000);
+
+    let preds = model.predict(&x);
+    println!("size, beds -> predicted | actual (k)");
+    for i in 0..x.rows() {
+        let size = x[(i, 0)];
+        let beds = x[(i, 1)];
+        println!(
+            "{:>3} m^2, {:>1} -> {:>6.1} | {:>6.1}",
+            size,
+            beds,
+            preds[(i, 0)],
+            prices[i]
+        );
+    }
+
+    let new_home = Matrix::from_rows_vec(vec![120.0, 3.0], 1, 2);
+    let pred = model.predict(&new_home);
+    println!(
+        "Predicted price for 120 m^2 with 3 bedrooms: {:.1}k",
+        pred[(0, 0)]
+    );
+}
+
+#[test]
+fn test_linear_regression_one_feature() {
+    let sizes = vec![50.0, 60.0, 70.0, 80.0, 90.0, 100.0];
+    let prices = vec![150.0, 180.0, 210.0, 240.0, 270.0, 300.0];
+    let scaled: Vec<f64> = sizes.iter().map(|s| s / 100.0).collect();
+    let x = Matrix::from_vec(scaled, sizes.len(), 1);
+    let y = Matrix::from_vec(prices.clone(), prices.len(), 1);
+    let mut model = LinReg::new(1);
+    model.fit(&x, &y, 0.1, 2000);
+    let preds = model.predict(&x);
+    for i in 0..y.rows() {
+        assert!((preds[(i, 0)] - prices[i]).abs() < 1.0);
+    }
+}
+
+#[test]
+fn test_linear_regression_two_features() {
+    let raw_x = vec![
+        50.0, 2.0, 70.0, 2.0, 90.0, 3.0, 110.0, 3.0, 130.0, 4.0, 150.0, 4.0,
+    ];
+    let prices = vec![170.0, 210.0, 270.0, 310.0, 370.0, 410.0];
+    let scaled_x: Vec<f64> = raw_x
+        .chunks(2)
+        .flat_map(|pair| vec![pair[0] / 100.0, pair[1]])
+        .collect();
+    let x = Matrix::from_rows_vec(scaled_x, 6, 2);
+    let y = Matrix::from_vec(prices.clone(), prices.len(), 1);
+    let mut model = LinReg::new(2);
+    model.fit(&x, &y, 0.01, 50000);
+    let preds = model.predict(&x);
+    for i in 0..y.rows() {
+        assert!((preds[(i, 0)] - prices[i]).abs() < 1.0);
+    }
+}

examples/logistic_regression.rs

@@ -0,0 +1,101 @@
+use rustframe::compute::models::logreg::LogReg;
+use rustframe::matrix::Matrix;
+
+/// Two binary classification demos using logistic regression.
+///
+/// Example 1 predicts exam success from hours studied.
+/// Example 2 predicts whether an online shopper will make a purchase.
+fn main() {
+    student_passing_example();
+    println!("\n-----\n");
+    purchase_prediction_example();
+}
+
+fn student_passing_example() {
+    println!("Example 1: exam pass prediction");
+
+    // Hours studied for each student
+    let hours = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0];
+    // Label: 0 denotes failure and 1 denotes success
+    let passed = vec![0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0];
+
+    let x = Matrix::from_vec(hours.clone(), hours.len(), 1);
+    let y = Matrix::from_vec(passed.clone(), passed.len(), 1);
+
+    let mut model = LogReg::new(1);
+    model.fit(&x, &y, 0.1, 10000);
+
+    let preds = model.predict(&x);
+    println!("Hours -> pred | actual");
+    for i in 0..x.rows() {
+        println!(
+            "{:>2} -> {} | {}",
+            hours[i] as i32,
+            preds[(i, 0)] as i32,
+            passed[i] as i32
+        );
+    }
+
+    // Probability estimate for a new student
+    let new_student = Matrix::from_vec(vec![5.5], 1, 1);
+    let p = model.predict_proba(&new_student);
+    println!("Probability of passing with 5.5h study: {:.2}", p[(0, 0)]);
+}
+
+fn purchase_prediction_example() {
+    println!("Example 2: purchase likelihood");
+
+    // minutes on site, pages viewed -> made a purchase?
+    let raw_x = vec![1.0, 2.0, 3.0, 1.0, 2.0, 4.0, 5.0, 5.0, 3.5, 2.0, 6.0, 6.0];
+    let bought = vec![0.0, 0.0, 0.0, 1.0, 0.0, 1.0];
+
+    let x = Matrix::from_rows_vec(raw_x, 6, 2);
+    let y = Matrix::from_vec(bought.clone(), bought.len(), 1);
+
+    let mut model = LogReg::new(2);
+    model.fit(&x, &y, 0.05, 20000);
+
+    let preds = model.predict(&x);
+    println!("time, pages -> pred | actual");
+    for i in 0..x.rows() {
+        println!(
+            "{:>4}m, {:>2} -> {} | {}",
+            x[(i, 0)],
+            x[(i, 1)] as i32,
+            preds[(i, 0)] as i32,
+            bought[i] as i32
+        );
+    }
+
+    let new_visit = Matrix::from_rows_vec(vec![4.0, 4.0], 1, 2);
+    let p = model.predict_proba(&new_visit);
+    println!("Prob of purchase for 4min/4pages: {:.2}", p[(0, 0)]);
+}
+
+#[test]
+fn test_student_passing_example() {
+    let hours = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0];
+    let passed = vec![0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0];
+    let x = Matrix::from_vec(hours.clone(), hours.len(), 1);
+    let y = Matrix::from_vec(passed.clone(), passed.len(), 1);
+    let mut model = LogReg::new(1);
+    model.fit(&x, &y, 0.1, 10000);
+    let preds = model.predict(&x);
+    for i in 0..y.rows() {
+        assert_eq!(preds[(i, 0)], passed[i]);
+    }
+}
+
+#[test]
+fn test_purchase_prediction_example() {
+    let raw_x = vec![1.0, 2.0, 3.0, 1.0, 2.0, 4.0, 5.0, 5.0, 3.5, 2.0, 6.0, 6.0];
+    let bought = vec![0.0, 0.0, 0.0, 1.0, 0.0, 1.0];
+    let x = Matrix::from_rows_vec(raw_x, 6, 2);
+    let y = Matrix::from_vec(bought.clone(), bought.len(), 1);
+    let mut model = LogReg::new(2);
+    model.fit(&x, &y, 0.05, 20000);
+    let preds = model.predict(&x);
+    for i in 0..y.rows() {
+        assert_eq!(preds[(i, 0)], bought[i]);
+    }
+}

examples/pca.rs

@@ -0,0 +1,60 @@
+use rustframe::compute::models::pca::PCA;
+use rustframe::matrix::Matrix;
+
+/// Two dimensionality reduction examples using PCA.
+///
+/// Example 1 reduces 3D sensor readings to two components.
+/// Example 2 compresses a small four-feature dataset.
+fn main() {
+    sensor_demo();
+    println!("\n-----\n");
+    finance_demo();
+}
+
+fn sensor_demo() {
+    println!("Example 1: 3D sensor data");
+
+    // Ten 3D observations from an accelerometer
+    let raw = vec![
+        2.5, 2.4, 0.5, 0.5, 0.7, 1.5, 2.2, 2.9, 0.7, 1.9, 2.2, 1.0, 3.1, 3.0, 0.6, 2.3, 2.7, 0.9,
+        2.0, 1.6, 1.1, 1.0, 1.1, 1.9, 1.5, 1.6, 2.2, 1.1, 0.9, 2.1,
+    ];
+    let x = Matrix::from_rows_vec(raw, 10, 3);
+
+    let pca = PCA::fit(&x, 2, 0);
+    let reduced = pca.transform(&x);
+
+    println!("Components: {:?}", pca.components.data());
+    println!("First row -> {:.2?}", [reduced[(0, 0)], reduced[(0, 1)]]);
+}
+
+fn finance_demo() {
+    println!("Example 2: 4D finance data");
+
+    // Four daily percentage returns of different stocks
+    let raw = vec![
+        0.2, 0.1, -0.1, 0.0, 0.3, 0.2, -0.2, 0.1, 0.1, 0.0, -0.1, -0.1, 0.4, 0.3, -0.3, 0.2, 0.0,
+        -0.1, 0.1, -0.1,
+    ];
+    let x = Matrix::from_rows_vec(raw, 5, 4);
+
+    // Keep two principal components
+    let pca = PCA::fit(&x, 2, 0);
+    let reduced = pca.transform(&x);
+
+    println!("Reduced shape: {:?}", reduced.shape());
+    println!("First row -> {:.2?}", [reduced[(0, 0)], reduced[(0, 1)]]);
+}
+
+#[test]
+fn test_sensor_demo() {
+    let raw = vec![
+        2.5, 2.4, 0.5, 0.5, 0.7, 1.5, 2.2, 2.9, 0.7, 1.9, 2.2, 1.0, 3.1, 3.0, 0.6, 2.3, 2.7, 0.9,
+        2.0, 1.6, 1.1, 1.0, 1.1, 1.9, 1.5, 1.6, 2.2, 1.1, 0.9, 2.1,
+    ];
+    let x = Matrix::from_rows_vec(raw, 10, 3);
+    let pca = PCA::fit(&x, 2, 0);
+    let reduced = pca.transform(&x);
+    assert_eq!(reduced.rows(), 10);
+    assert_eq!(reduced.cols(), 2);
+}

examples/random_demo.rs

@@ -0,0 +1,67 @@
+use rustframe::random::{crypto_rng, rng, Rng, SliceRandom};
+
+/// Demonstrates basic usage of the random number generators.
+///
+/// It showcases uniform ranges, booleans, normal distribution,
+/// shuffling and the cryptographically secure generator.
+fn main() {
+    basic_usage();
+    println!("\n-----\n");
+    normal_demo();
+    println!("\n-----\n");
+    shuffle_demo();
+}
+
+fn basic_usage() {
+    println!("Basic PRNG usage\n----------------");
+    let mut prng = rng();
+    println!("random u64   : {}", prng.next_u64());
+    println!("range [10,20): {}", prng.random_range(10..20));
+    println!("bool         : {}", prng.gen_bool());
+}
+
+fn normal_demo() {
+    println!("Normal distribution\n-------------------");
+    let mut prng = rng();
+    for _ in 0..3 {
+        let v = prng.normal(0.0, 1.0);
+        println!("sample: {:.3}", v);
+    }
+}
+
+fn shuffle_demo() {
+    println!("Slice shuffling\n----------------");
+    let mut prng = rng();
+    let mut data = [1, 2, 3, 4, 5];
+    data.shuffle(&mut prng);
+    println!("shuffled: {:?}", data);
+
+    let mut secure = crypto_rng();
+    let byte = secure.random_range(0..256usize);
+    println!("crypto byte: {}", byte);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use rustframe::random::{CryptoRng, Prng};
+
+    #[test]
+    fn test_basic_usage_range_bounds() {
+        let mut rng = Prng::new(1);
+        for _ in 0..50 {
+            let v = rng.random_range(5..10);
+            assert!(v >= 5 && v < 10);
+        }
+    }
+
+    #[test]
+    fn test_crypto_byte_bounds() {
+        let mut rng = CryptoRng::new();
+        for _ in 0..50 {
+            let v = rng.random_range(0..256usize);
+            assert!(v < 256);
+        }
+    }
+}
+

examples/random_stats.rs

@@ -0,0 +1,57 @@
+use rustframe::random::{crypto_rng, rng, Rng};
+
+/// Demonstrates simple statistical checks on random number generators.
+fn main() {
+    chi_square_demo();
+    println!("\n-----\n");
+    monobit_demo();
+}
+
+fn chi_square_demo() {
+    println!("Chi-square test on PRNG");
+    let mut rng = rng();
+    let mut counts = [0usize; 10];
+    let samples = 10000;
+    for _ in 0..samples {
+        let v = rng.random_range(0..10usize);
+        counts[v] += 1;
+    }
+    let expected = samples as f64 / 10.0;
+    let chi2: f64 = counts
+        .iter()
+        .map(|&c| {
+            let diff = c as f64 - expected;
+            diff * diff / expected
+        })
+        .sum();
+    println!("counts: {:?}", counts);
+    println!("chi-square: {:.3}", chi2);
+}
+
+fn monobit_demo() {
+    println!("Monobit test on crypto RNG");
+    let mut rng = crypto_rng();
+    let mut ones = 0usize;
+    let samples = 1000;
+    for _ in 0..samples {
+        ones += rng.next_u64().count_ones() as usize;
+    }
+    let ratio = ones as f64 / (samples as f64 * 64.0);
+    println!("ones ratio: {:.4}", ratio);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_chi_square_demo_runs() {
+        chi_square_demo();
+    }
+
+    #[test]
+    fn test_monobit_demo_runs() {
+        monobit_demo();
+    }
+}
+

examples/stats_overview.rs

@@ -0,0 +1,93 @@
+use rustframe::compute::stats::{
+    chi2_test, covariance, covariance_matrix, mean, median, pearson, percentile, stddev, t_test,
+};
+use rustframe::matrix::{Axis, Matrix};
+
+/// Demonstrates some of the statistics utilities in Rustframe.
+///
+/// The example is split into three parts:
+///   - Basic descriptive statistics on a small data set
+///   - Covariance and correlation calculations
+///   - Simple inferential tests (t-test and chi-square)
+fn main() {
+    descriptive_demo();
+    println!("\n-----\n");
+    correlation_demo();
+    println!("\n-----\n");
+    inferential_demo();
+}
+
+fn descriptive_demo() {
+    println!("Descriptive statistics\n----------------------");
+    let data = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+    println!("mean           : {:.2}", mean(&data));
+    println!("std dev        : {:.2}", stddev(&data));
+    println!("median         : {:.2}", median(&data));
+    println!("25th percentile: {:.2}", percentile(&data, 25.0));
+}
+
+fn correlation_demo() {
+    println!("Covariance and Correlation\n--------------------------");
+    let x = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
+    let y = Matrix::from_vec(vec![1.0, 2.0, 3.0, 5.0], 2, 2);
+    let cov = covariance(&x, &y);
+    let cov_mat = covariance_matrix(&x, Axis::Col);
+    let corr = pearson(&x, &y);
+    println!("covariance : {:.2}", cov);
+    println!("cov matrix : {:?}", cov_mat.data());
+    println!("pearson r  : {:.2}", corr);
+}
+
+fn inferential_demo() {
+    println!("Inferential statistics\n----------------------");
+    let s1 = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+    let s2 = Matrix::from_vec(vec![6.0, 7.0, 8.0, 9.0, 10.0], 1, 5);
+    let (t_stat, t_p) = t_test(&s1, &s2);
+    println!("t statistic : {:.2}, p-value: {:.4}", t_stat, t_p);
+
+    let observed = Matrix::from_vec(vec![12.0, 5.0, 8.0, 10.0], 2, 2);
+    let (chi2, chi_p) = chi2_test(&observed);
+    println!("chi^2       : {:.2}, p-value: {:.4}", chi2, chi_p);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    const EPS: f64 = 1e-8;
+
+    #[test]
+    fn test_descriptive_demo() {
+        let data = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+        assert!((mean(&data) - 3.0).abs() < EPS);
+        assert!((stddev(&data) - 1.4142135623730951).abs() < EPS);
+        assert!((median(&data) - 3.0).abs() < EPS);
+        assert!((percentile(&data, 25.0) - 2.0).abs() < EPS);
+    }
+
+    #[test]
+    fn test_correlation_demo() {
+        let x = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
+        let y = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 5.0], 2, 2);
+        let cov = covariance(&x, &y);
+        assert!((cov - 1.625).abs() < EPS);
+        let cov_mat = covariance_matrix(&x, Axis::Col);
+        assert!((cov_mat.get(0, 0) - 2.0).abs() < EPS);
+        assert!((cov_mat.get(1, 1) - 2.0).abs() < EPS);
+        let corr = pearson(&x, &y);
+        assert!((corr - 0.9827076298239908).abs() < 1e-6);
+    }
+
+    #[test]
+    fn test_inferential_demo() {
+        let s1 = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0, 5.0], 1, 5);
+        let s2 = Matrix::from_rows_vec(vec![6.0, 7.0, 8.0, 9.0, 10.0], 1, 5);
+        let (t_stat, p_value) = t_test(&s1, &s2);
+        assert!((t_stat + 5.0).abs() < 1e-5);
+        assert!(p_value > 0.0 && p_value < 1.0);
+
+        let observed = Matrix::from_rows_vec(vec![12.0, 5.0, 8.0, 10.0], 2, 2);
+        let (chi2, p) = chi2_test(&observed);
+        assert!(chi2 > 0.0);
+        assert!(p > 0.0 && p < 1.0);
+    }
+}

src/compute/models/activations.rs

@@ -25,6 +25,7 @@ pub fn dleaky_relu(x: &Matrix<f64>) -> Matrix<f64> {
     x.map(|v| if v > 0.0 { 1.0 } else { 0.01 })
 }
 
+#[cfg(test)]
 mod tests {
     use super::*;
 

src/compute/models/dense_nn.rs

@@ -1,6 +1,6 @@
 use crate::compute::models::activations::{drelu, relu, sigmoid};
 use crate::matrix::{Matrix, SeriesOps};
-use rand::prelude::*;
+use crate::random::prelude::*;
 
 /// Supported activation functions
 #[derive(Clone)]
@@ -46,7 +46,7 @@ pub enum InitializerKind {
 
 impl InitializerKind {
     pub fn initialize(&self, rows: usize, cols: usize) -> Matrix<f64> {
-        let mut rng = rand::rng();
+        let mut rng = rng();
         let fan_in = rows;
         let fan_out = cols;
         let limit = match self {

src/compute/models/k_means.rs

@@ -1,7 +1,6 @@
 use crate::compute::stats::mean_vertical;
 use crate::matrix::Matrix;
-use rand::rng;
-use rand::seq::SliceRandom;
+use crate::random::prelude::*;
 
 pub struct KMeans {
     pub centroids: Matrix<f64>, // (k, n_features)
@@ -193,7 +192,8 @@ mod tests {
                                 break;
                             }
                         }
-                        assert!(matches_data_point, "Centroid {} (empty cluster) does not match any data point", c);
+                        // "Centroid {} (empty cluster) does not match any data point",c
+                        assert!(matches_data_point);
                     }
                 }
                 break;
@@ -360,5 +360,4 @@ mod tests {
         assert_eq!(predicted_label.len(), 1);
         assert!(predicted_label[0] < k);
     }
-
 }

src/compute/models/pca.rs

@@ -44,11 +44,7 @@ mod tests {
 
     #[test]
     fn test_pca_basic() {
-        // Simple 2D data, points along y=x line
-        // Data:
-        // 1.0, 1.0
-        // 2.0, 2.0
-        // 3.0, 3.0
+        // Simple 2D data with points along the y = x line
         let data = Matrix::from_rows_vec(vec![1.0, 1.0, 2.0, 2.0, 3.0, 3.0], 3, 2);
         let (_n_samples, _n_features) = data.shape();
 
@@ -71,15 +67,7 @@ mod tests {
         assert!((pca.components.get(0, 0) - 1.0).abs() < EPSILON);
         assert!((pca.components.get(0, 1) - 1.0).abs() < EPSILON);
 
-        // Test transform
-        // Centered data:
-        // -1.0, -1.0
-        //  0.0,  0.0
-        //  1.0,  1.0
-        // Projected: (centered_data * components.transpose())
-        // (-1.0 * 1.0 + -1.0 * 1.0) = -2.0
-        // ( 0.0 * 1.0 +  0.0 * 1.0) =  0.0
-        // ( 1.0 * 1.0 +  1.0 * 1.0) =  2.0
+        // Test transform: centered data projects to [-2.0, 0.0, 2.0]
         let transformed_data = pca.transform(&data);
         assert_eq!(transformed_data.rows(), 3);
         assert_eq!(transformed_data.cols(), 1);

src/compute/stats/correlation.rs

@@ -137,10 +137,7 @@ mod tests {
 
     #[test]
     fn test_covariance_scalar_same_matrix() {
-        // M =
-        // 1,2
-        // 3,4
-        // mean = 2.5
+        // Matrix with rows [1, 2] and [3, 4]; mean is 2.5
         let data = vec![1.0, 2.0, 3.0, 4.0];
         let m = Matrix::from_vec(data.clone(), 2, 2);
 
@@ -152,10 +149,7 @@ mod tests {
 
     #[test]
     fn test_covariance_scalar_diff_matrix() {
-        // x =
-        // 1,2
-        // 3,4
-        // y = 2*x
+        // Matrix x has rows [1, 2] and [3, 4]; y is two times x
         let x = Matrix::from_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
         let y = Matrix::from_vec(vec![2.0, 4.0, 6.0, 8.0], 2, 2);
 
@@ -167,10 +161,7 @@ mod tests {
 
     #[test]
     fn test_covariance_vertical() {
-        // M =
-        // 1,2
-        // 3,4
-        // cols are [1,3] and [2,4], each var=1, cov=1
+        // Matrix with rows [1, 2] and [3, 4]; columns are [1,3] and [2,4], each var=1, cov=1
         let m = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
         let cov_mat = covariance_vertical(&m);
 
@@ -184,10 +175,7 @@ mod tests {
 
     #[test]
     fn test_covariance_horizontal() {
-        // M =
-        // 1,2
-        // 3,4
-        // rows are [1,2] and [3,4], each var=0.25, cov=0.25
+        // Matrix with rows [1,2] and [3,4], each var=0.25, cov=0.25
         let m = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
         let cov_mat = covariance_horizontal(&m);
 
@@ -201,10 +189,7 @@ mod tests {
 
     #[test]
     fn test_covariance_matrix_vertical() {
-        // Test with a simple 2x2 matrix
-        // M =
-        // 1, 2
-        // 3, 4
+        // Test with a simple 2x2 matrix with rows [1, 2] and [3, 4]
         // Expected covariance matrix (vertical, i.e., between columns):
         // Col1: [1, 3], mean = 2
         // Col2: [2, 4], mean = 3
@@ -212,9 +197,7 @@ mod tests {
         // Cov(Col2, Col2) = ((2-3)^2 + (4-3)^2) / (2-1) = (1+1)/1 = 2
         // Cov(Col1, Col2) = ((1-2)*(2-3) + (3-2)*(4-3)) / (2-1) = ((-1)*(-1) + (1)*(1))/1 = (1+1)/1 = 2
         // Cov(Col2, Col1) = 2
-        // Expected:
-        // 2, 2
-        // 2, 2
+        // Expected matrix filled with 2
         let m = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
         let cov_mat = covariance_matrix(&m, Axis::Col);
 
@@ -226,10 +209,7 @@ mod tests {
 
     #[test]
     fn test_covariance_matrix_horizontal() {
-        // Test with a simple 2x2 matrix
-        // M =
-        // 1, 2
-        // 3, 4
+        // Test with a simple 2x2 matrix with rows [1, 2] and [3, 4]
         // Expected covariance matrix (horizontal, i.e., between rows):
         // Row1: [1, 2], mean = 1.5
         // Row2: [3, 4], mean = 3.5
@@ -237,9 +217,7 @@ mod tests {
         // Cov(Row2, Row2) = ((3-3.5)^2 + (4-3.5)^2) / (2-1) = (0.25+0.25)/1 = 0.5
         // Cov(Row1, Row2) = ((1-1.5)*(3-3.5) + (2-1.5)*(4-3.5)) / (2-1) = ((-0.5)*(-0.5) + (0.5)*(0.5))/1 = (0.25+0.25)/1 = 0.5
         // Cov(Row2, Row1) = 0.5
-        // Expected:
-        // 0.5, -0.5
-        // -0.5, 0.5
+        // Expected matrix: [[0.5, -0.5], [-0.5, 0.5]]
         let m = Matrix::from_rows_vec(vec![1.0, 2.0, 3.0, 4.0], 2, 2);
         let cov_mat = covariance_matrix(&m, Axis::Row);
 

src/compute/stats/descriptive.rs

@@ -350,11 +350,7 @@ mod tests {
         let data: Vec<f64> = (1..=24).map(|x| x as f64).collect();
         let x = Matrix::from_vec(data, 4, 6);
 
-        // columns:
-        //  1,  5,  9, 13, 17, 21
-        //  2,  6, 10, 14, 18, 22
-        //  3,  7, 11, 15, 19, 23
-        //  4,  8, 12, 16, 20, 24
+        // columns contain sequences increasing by four starting at 1 through 4
 
         let er0 = vec![1., 5., 9., 13., 17., 21.];
         let er50 = vec![3., 7., 11., 15., 19., 23.];

src/lib.rs

@@ -11,3 +11,6 @@ pub mod utils;
 
 /// Documentation for the [`crate::compute`] module.
 pub mod compute;
+
+/// Documentation for the [`crate::random`] module.
+pub mod random;

src/matrix/mat.rs

@@ -1028,9 +1028,7 @@ mod tests {
 
     #[test]
     fn test_from_rows_vec() {
-        // Representing:
-        // 1 2 3
-        // 4 5 6
+        // Matrix with rows [1, 2, 3] and [4, 5, 6]
         let rows_data = vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0];
         let matrix = Matrix::from_rows_vec(rows_data, 2, 3);
 
@@ -1042,19 +1040,14 @@ mod tests {
 
     // Helper function to create a basic Matrix for testing
     fn static_test_matrix() -> Matrix<i32> {
-        // Column-major data:
-        // 1 4 7
-        // 2 5 8
-        // 3 6 9
+        // Column-major data representing a 3x3 matrix of sequential integers
         let data = vec![1, 2, 3, 4, 5, 6, 7, 8, 9];
         Matrix::from_vec(data, 3, 3)
     }
 
     // Another helper for a different size
     fn static_test_matrix_2x4() -> Matrix<i32> {
-        // Column-major data:
-        // 1 3 5 7
-        // 2 4 6 8
+        // Column-major data representing a 2x4 matrix of sequential integers
         let data = vec![1, 2, 3, 4, 5, 6, 7, 8];
         Matrix::from_vec(data, 2, 4)
     }
@@ -1132,10 +1125,7 @@ mod tests {
 
     #[test]
     fn test_from_cols_basic() {
-        // Representing:
-        // 1 4 7
-        // 2 5 8
-        // 3 6 9
+        // Matrix with columns forming a 3x3 sequence
         let cols_data = vec![vec![1, 2, 3], vec![4, 5, 6], vec![7, 8, 9]];
         let matrix = Matrix::from_cols(cols_data);
 
@@ -1512,8 +1502,7 @@ mod tests {
 
         // Delete the first row
         matrix.delete_row(0);
-        // Should be:
-        // 3 6 9
+        // Resulting data should be [3, 6, 9]
         assert_eq!(matrix.rows(), 1);
         assert_eq!(matrix.cols(), 3);
         assert_eq!(matrix.data(), &[3, 6, 9]);

src/matrix/seriesops.rs

@@ -215,20 +215,13 @@ mod tests {
 
     // Helper function to create a FloatMatrix for SeriesOps testing
     fn create_float_test_matrix() -> FloatMatrix {
-        // 3x3 matrix (column-major) with some NaNs
-        // 1.0  4.0  7.0
-        // 2.0  NaN  8.0
-        // 3.0  6.0  NaN
+        // 3x3 column-major matrix containing a few NaN values
         let data = vec![1.0, 2.0, 3.0, 4.0, f64::NAN, 6.0, 7.0, 8.0, f64::NAN];
         FloatMatrix::from_vec(data, 3, 3)
     }
 
     fn create_float_test_matrix_4x4() -> FloatMatrix {
-        // 4x4 matrix (column-major) with some NaNs
-        // 1.0  5.0  9.0  13.0
-        // 2.0  NaN  10.0 NaN
-        // 3.0  6.0  NaN  14.0
-        // NaN  7.0  11.0 NaN
+        // 4x4 column-major matrix with NaNs inserted at positions where index % 5 == 0
         // first make array with 16 elements
         FloatMatrix::from_vec(
             (0..16)

src/random/crypto.rs

@@ -0,0 +1,227 @@
+#[cfg(unix)]
+use std::{fs::File, io::Read};
+
+use crate::random::Rng;
+
+#[cfg(unix)]
+pub struct CryptoRng {
+    file: File,
+}
+
+#[cfg(unix)]
+impl CryptoRng {
+    /// Open `/dev/urandom`.
+    pub fn new() -> Self {
+        let file = File::open("/dev/urandom").expect("failed to open /dev/urandom");
+        Self { file }
+    }
+}
+
+#[cfg(unix)]
+impl Rng for CryptoRng {
+    fn next_u64(&mut self) -> u64 {
+        let mut buf = [0u8; 8];
+        self.file
+            .read_exact(&mut buf)
+            .expect("failed reading from /dev/urandom");
+        u64::from_ne_bytes(buf)
+    }
+}
+
+#[cfg(windows)]
+pub struct CryptoRng;
+
+#[cfg(windows)]
+impl CryptoRng {
+    /// No handle is needed on Windows.
+    pub fn new() -> Self {
+        Self
+    }
+}
+
+#[cfg(windows)]
+impl Rng for CryptoRng {
+    fn next_u64(&mut self) -> u64 {
+        let mut buf = [0u8; 8];
+        win_fill(&mut buf).expect("BCryptGenRandom failed");
+        u64::from_ne_bytes(buf)
+    }
+}
+
+/// Fill `buf` with cryptographically secure random bytes using CNG.
+///
+/// * `BCryptGenRandom(NULL, buf, len, BCRYPT_USE_SYSTEM_PREFERRED_RNG)`
+///   asks the OS for its system‑preferred DRBG (CTR_DRBG on modern
+///   Windows).
+#[cfg(windows)]
+fn win_fill(buf: &mut [u8]) -> Result<(), ()> {
+    use core::ffi::c_void;
+
+    type BcryptAlgHandle = *mut c_void;
+    type NTSTATUS = i32;
+
+    const BCRYPT_USE_SYSTEM_PREFERRED_RNG: u32 = 0x0000_0002;
+
+    #[link(name = "bcrypt")]
+    extern "system" {
+        fn BCryptGenRandom(
+            hAlgorithm: BcryptAlgHandle,
+            pbBuffer: *mut u8,
+            cbBuffer: u32,
+            dwFlags: u32,
+        ) -> NTSTATUS;
+    }
+
+    // NT_SUCCESS(status) == status >= 0
+    let status = unsafe {
+        BCryptGenRandom(
+            core::ptr::null_mut(),
+            buf.as_mut_ptr(),
+            buf.len() as u32,
+            BCRYPT_USE_SYSTEM_PREFERRED_RNG,
+        )
+    };
+
+    if status >= 0 {
+        Ok(())
+    } else {
+        Err(())
+    }
+}
+
+/// Convenience constructor for [`CryptoRng`].
+pub fn crypto_rng() -> CryptoRng {
+    CryptoRng::new()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::random::Rng;
+    use std::collections::HashSet;
+
+    #[test]
+    fn test_crypto_rng_nonzero() {
+        let mut rng = CryptoRng::new();
+        let mut all_same = true;
+        let mut prev = rng.next_u64();
+        for _ in 0..5 {
+            let val = rng.next_u64();
+            if val != prev {
+                all_same = false;
+            }
+            prev = val;
+        }
+        assert!(!all_same, "CryptoRng produced identical values");
+    }
+
+    #[test]
+    fn test_crypto_rng_variation_large() {
+        let mut rng = CryptoRng::new();
+        let mut values = HashSet::new();
+        for _ in 0..100 {
+            values.insert(rng.next_u64());
+        }
+        assert!(values.len() > 90, "CryptoRng output not varied enough");
+    }
+
+    #[test]
+    fn test_crypto_rng_random_range_uniform() {
+        let mut rng = CryptoRng::new();
+        let mut counts = [0usize; 10];
+        for _ in 0..1000 {
+            let v = rng.random_range(0..10usize);
+            counts[v] += 1;
+        }
+        for &c in &counts {
+            // "Crypto RNG counts far from uniform: {c}"
+            assert!((c as isize - 100).abs() < 50);
+        }
+    }
+
+    #[test]
+    fn test_crypto_normal_distribution() {
+        let mut rng = CryptoRng::new();
+        let mean = 0.0;
+        let sd = 1.0;
+        let n = 2000;
+        let mut sum = 0.0;
+        let mut sum_sq = 0.0;
+        for _ in 0..n {
+            let val = rng.normal(mean, sd);
+            sum += val;
+            sum_sq += val * val;
+        }
+        let sample_mean = sum / n as f64;
+        let sample_var = sum_sq / n as f64 - sample_mean * sample_mean;
+        assert!(sample_mean.abs() < 0.1);
+        assert!((sample_var - 1.0).abs() < 0.2);
+    }
+
+    #[test]
+    fn test_two_instances_different_values() {
+        let mut a = CryptoRng::new();
+        let mut b = CryptoRng::new();
+        let va = a.next_u64();
+        let vb = b.next_u64();
+        assert_ne!(va, vb);
+    }
+
+    #[test]
+    fn test_crypto_rng_helper_function() {
+        let mut rng = crypto_rng();
+        let _ = rng.next_u64();
+    }
+
+    #[test]
+    fn test_crypto_normal_zero_sd() {
+        let mut rng = CryptoRng::new();
+        for _ in 0..5 {
+            let v = rng.normal(10.0, 0.0);
+            assert_eq!(v, 10.0);
+        }
+    }
+
+    #[test]
+    fn test_crypto_shuffle_empty_slice() {
+        use crate::random::SliceRandom;
+        let mut rng = CryptoRng::new();
+        let mut arr: [u8; 0] = [];
+        arr.shuffle(&mut rng);
+        assert!(arr.is_empty());
+    }
+
+    #[test]
+    fn test_crypto_chi_square_uniform() {
+        let mut rng = CryptoRng::new();
+        let mut counts = [0usize; 10];
+        let samples = 10000;
+        for _ in 0..samples {
+            let v = rng.random_range(0..10usize);
+            counts[v] += 1;
+        }
+        let expected = samples as f64 / 10.0;
+        let chi2: f64 = counts
+            .iter()
+            .map(|&c| {
+                let diff = c as f64 - expected;
+                diff * diff / expected
+            })
+            .sum();
+        assert!(chi2 < 40.0, "chi-square statistic too high: {chi2}");
+    }
+
+    #[test]
+    fn test_crypto_monobit() {
+        let mut rng = CryptoRng::new();
+        let mut ones = 0usize;
+        let samples = 1000;
+        for _ in 0..samples {
+            ones += rng.next_u64().count_ones() as usize;
+        }
+        let total_bits = samples * 64;
+        let ratio = ones as f64 / total_bits as f64;
+        // "bit ratio far from 0.5: {ratio}"
+        assert!((ratio - 0.5).abs() < 0.02);
+    }
+}

src/random/mod.rs

@@ -0,0 +1,14 @@
+pub mod crypto;
+pub mod prng;
+pub mod random_core;
+pub mod seq;
+
+pub use crypto::{crypto_rng, CryptoRng};
+pub use prng::{rng, Prng};
+pub use random_core::{RangeSample, Rng};
+pub use seq::SliceRandom;
+
+pub mod prelude {
+    pub use super::seq::SliceRandom;
+    pub use super::{crypto_rng, rng, CryptoRng, Prng, RangeSample, Rng};
+}

src/random/prng.rs

@@ -0,0 +1,227 @@
+use std::time::{SystemTime, UNIX_EPOCH};
+
+use crate::random::Rng;
+
+/// Simple XorShift64-based pseudo random number generator.
+#[derive(Clone)]
+pub struct Prng {
+    state: u64,
+}
+
+impl Prng {
+    /// Create a new generator from the given seed.
+    pub fn new(seed: u64) -> Self {
+        Self { state: seed }
+    }
+
+    /// Create a generator seeded from the current time.
+    pub fn from_entropy() -> Self {
+        let nanos = SystemTime::now()
+            .duration_since(UNIX_EPOCH)
+            .unwrap()
+            .as_nanos() as u64;
+        Self::new(nanos)
+    }
+}
+
+impl Rng for Prng {
+    fn next_u64(&mut self) -> u64 {
+        let mut x = self.state;
+        x ^= x << 13;
+        x ^= x >> 7;
+        x ^= x << 17;
+        self.state = x;
+        x
+    }
+}
+
+/// Convenience constructor using system entropy.
+pub fn rng() -> Prng {
+    Prng::from_entropy()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::random::Rng;
+
+    #[test]
+    fn test_prng_determinism() {
+        let mut a = Prng::new(42);
+        let mut b = Prng::new(42);
+        for _ in 0..5 {
+            assert_eq!(a.next_u64(), b.next_u64());
+        }
+    }
+
+    #[test]
+    fn test_random_range_f64() {
+        let mut rng = Prng::new(1);
+        for _ in 0..10 {
+            let v = rng.random_range(-1.0..1.0);
+            assert!(v >= -1.0 && v < 1.0);
+        }
+    }
+
+    #[test]
+    fn test_random_range_usize() {
+        let mut rng = Prng::new(9);
+        for _ in 0..100 {
+            let v = rng.random_range(10..20);
+            assert!(v >= 10 && v < 20);
+        }
+    }
+
+    #[test]
+    fn test_gen_bool_balance() {
+        let mut rng = Prng::new(123);
+        let mut trues = 0;
+        for _ in 0..1000 {
+            if rng.gen_bool() {
+                trues += 1;
+            }
+        }
+        let ratio = trues as f64 / 1000.0;
+        assert!(ratio > 0.4 && ratio < 0.6);
+    }
+
+    #[test]
+    fn test_normal_distribution() {
+        let mut rng = Prng::new(7);
+        let mut sum = 0.0;
+        let mut sum_sq = 0.0;
+        let mean = 5.0;
+        let sd = 2.0;
+        let n = 5000;
+        for _ in 0..n {
+            let val = rng.normal(mean, sd);
+            sum += val;
+            sum_sq += val * val;
+        }
+        let sample_mean = sum / n as f64;
+        let sample_var = sum_sq / n as f64 - sample_mean * sample_mean;
+        assert!((sample_mean - mean).abs() < 0.1);
+        assert!((sample_var - sd * sd).abs() < 0.2 * sd * sd);
+    }
+
+    #[test]
+    fn test_prng_from_entropy_unique() {
+        use std::{collections::HashSet, thread, time::Duration};
+        let mut seen = HashSet::new();
+        for _ in 0..5 {
+            let mut rng = Prng::from_entropy();
+            seen.insert(rng.next_u64());
+            thread::sleep(Duration::from_micros(1));
+        }
+        assert!(seen.len() > 1, "Entropy seeds produced identical outputs");
+    }
+
+    #[test]
+    fn test_prng_uniform_distribution() {
+        let mut rng = Prng::new(12345);
+        let mut counts = [0usize; 10];
+        for _ in 0..10000 {
+            let v = rng.random_range(0..10usize);
+            counts[v] += 1;
+        }
+        for &c in &counts {
+            // "PRNG counts far from uniform: {c}"
+            assert!((c as isize - 1000).abs() < 150);
+        }
+    }
+
+    #[test]
+    fn test_prng_different_seeds_different_output() {
+        let mut a = Prng::new(1);
+        let mut b = Prng::new(2);
+        let va = a.next_u64();
+        let vb = b.next_u64();
+        assert_ne!(va, vb);
+    }
+
+    #[test]
+    fn test_prng_gen_bool_varies() {
+        let mut rng = Prng::new(99);
+        let mut seen_true = false;
+        let mut seen_false = false;
+        for _ in 0..100 {
+            if rng.gen_bool() {
+                seen_true = true;
+            } else {
+                seen_false = true;
+            }
+        }
+        assert!(seen_true && seen_false);
+    }
+
+    #[test]
+    fn test_random_range_single_usize() {
+        let mut rng = Prng::new(42);
+        for _ in 0..10 {
+            let v = rng.random_range(5..6);
+            assert_eq!(v, 5);
+        }
+    }
+
+    #[test]
+    fn test_random_range_single_f64() {
+        let mut rng = Prng::new(42);
+        for _ in 0..10 {
+            let v = rng.random_range(1.234..1.235);
+            assert!(v >= 1.234 && v < 1.235);
+        }
+    }
+
+    #[test]
+    fn test_prng_normal_zero_sd() {
+        let mut rng = Prng::new(7);
+        for _ in 0..5 {
+            let v = rng.normal(3.0, 0.0);
+            assert_eq!(v, 3.0);
+        }
+    }
+
+    #[test]
+    fn test_random_range_extreme_usize() {
+        let mut rng = Prng::new(5);
+        for _ in 0..10 {
+            let v = rng.random_range(0..usize::MAX);
+            assert!(v < usize::MAX);
+        }
+    }
+
+    #[test]
+    fn test_prng_chi_square_uniform() {
+        let mut rng = Prng::new(12345);
+        let mut counts = [0usize; 10];
+        let samples = 10000;
+        for _ in 0..samples {
+            let v = rng.random_range(0..10usize);
+            counts[v] += 1;
+        }
+        let expected = samples as f64 / 10.0;
+        let chi2: f64 = counts
+            .iter()
+            .map(|&c| {
+                let diff = c as f64 - expected;
+                diff * diff / expected
+            })
+            .sum();
+        //  "chi-square statistic too high: {chi2}"
+        assert!(chi2 < 20.0);
+    }
+
+    #[test]
+    fn test_prng_monobit() {
+        let mut rng = Prng::new(42);
+        let mut ones = 0usize;
+        let samples = 1000;
+        for _ in 0..samples {
+            ones += rng.next_u64().count_ones() as usize;
+        }
+        let total_bits = samples * 64;
+        let ratio = ones as f64 / total_bits as f64;
+        // "bit ratio far from 0.5: {ratio}"
+        assert!((ratio - 0.5).abs() < 0.01);
+    }
+}

src/random/random_core.rs

@@ -0,0 +1,98 @@
+use std::f64::consts::PI;
+use std::ops::Range;
+
+/// Trait implemented by random number generators.
+pub trait Rng {
+    /// Generate the next random `u64` value.
+    fn next_u64(&mut self) -> u64;
+
+    /// Generate a value uniformly in the given range.
+    fn random_range<T>(&mut self, range: Range<T>) -> T
+    where
+        T: RangeSample,
+    {
+        T::from_u64(self.next_u64(), &range)
+    }
+
+    /// Generate a boolean with probability 0.5 of being `true`.
+    fn gen_bool(&mut self) -> bool {
+        self.random_range(0..2usize) == 1
+    }
+
+    /// Sample from a normal distribution using the Box-Muller transform.
+    fn normal(&mut self, mean: f64, sd: f64) -> f64 {
+        let u1 = self.random_range(0.0..1.0);
+        let u2 = self.random_range(0.0..1.0);
+        mean + sd * (-2.0 * u1.ln()).sqrt() * (2.0 * PI * u2).cos()
+    }
+}
+
+/// Conversion from a raw `u64` into a type within a range.
+pub trait RangeSample: Sized {
+    fn from_u64(value: u64, range: &Range<Self>) -> Self;
+}
+
+impl RangeSample for usize {
+    fn from_u64(value: u64, range: &Range<Self>) -> Self {
+        let span = range.end - range.start;
+        (value as usize % span) + range.start
+    }
+}
+
+impl RangeSample for f64 {
+    fn from_u64(value: u64, range: &Range<Self>) -> Self {
+        let span = range.end - range.start;
+        range.start + (value as f64 / u64::MAX as f64) * span
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_range_sample_usize_boundary() {
+        assert_eq!(<usize as RangeSample>::from_u64(0, &(0..1)), 0);
+        assert_eq!(<usize as RangeSample>::from_u64(u64::MAX, &(0..1)), 0);
+    }
+
+    #[test]
+    fn test_range_sample_f64_boundary() {
+        let v0 = <f64 as RangeSample>::from_u64(0, &(0.0..1.0));
+        let vmax = <f64 as RangeSample>::from_u64(u64::MAX, &(0.0..1.0));
+        assert!(v0 >= 0.0 && v0 < 1.0);
+        assert!(vmax > 0.999999999999 && vmax <= 1.0);
+    }
+
+    #[test]
+    fn test_range_sample_usize_varied() {
+        for i in 0..5 {
+            let v = <usize as RangeSample>::from_u64(i, &(10..15));
+            assert!(v >= 10 && v < 15);
+        }
+    }
+
+    #[test]
+    fn test_range_sample_f64_span() {
+        for val in [0, u64::MAX / 2, u64::MAX] {
+            let f = <f64 as RangeSample>::from_u64(val, &(2.0..4.0));
+            assert!(f >= 2.0 && f <= 4.0);
+        }
+    }
+
+    #[test]
+    fn test_range_sample_usize_single_value() {
+        for val in [0, 1, u64::MAX] {
+            let n = <usize as RangeSample>::from_u64(val, &(5..6));
+            assert_eq!(n, 5);
+        }
+    }
+
+    #[test]
+    fn test_range_sample_f64_negative_range() {
+        for val in [0, u64::MAX / 3, u64::MAX] {
+            let f = <f64 as RangeSample>::from_u64(val, &(-2.0..2.0));
+            assert!(f >= -2.0 && f <= 2.0);
+        }
+    }
+}

src/random/seq.rs

@@ -0,0 +1,105 @@
+use crate::random::Rng;
+
+/// Trait for randomizing slices.
+pub trait SliceRandom {
+    /// Shuffle the slice in place using the provided RNG.
+    fn shuffle<R: Rng>(&mut self, rng: &mut R);
+}
+
+impl<T> SliceRandom for [T] {
+    fn shuffle<R: Rng>(&mut self, rng: &mut R) {
+        for i in (1..self.len()).rev() {
+            let j = rng.random_range(0..(i + 1));
+            self.swap(i, j);
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::random::{CryptoRng, Prng};
+
+    #[test]
+    fn test_shuffle_slice() {
+        let mut rng = Prng::new(3);
+        let mut arr = [1, 2, 3, 4, 5];
+        let orig = arr.clone();
+        arr.shuffle(&mut rng);
+        assert_eq!(arr.len(), orig.len());
+        let mut sorted = arr.to_vec();
+        sorted.sort();
+        assert_eq!(sorted, orig.to_vec());
+    }
+
+    #[test]
+    fn test_slice_shuffle_deterministic_with_prng() {
+        let mut rng1 = Prng::new(11);
+        let mut rng2 = Prng::new(11);
+        let mut a = [1u8, 2, 3, 4, 5, 6, 7, 8, 9];
+        let mut b = a.clone();
+        a.shuffle(&mut rng1);
+        b.shuffle(&mut rng2);
+        assert_eq!(a, b);
+    }
+
+    #[test]
+    fn test_slice_shuffle_crypto_random_changes() {
+        let mut rng1 = CryptoRng::new();
+        let mut rng2 = CryptoRng::new();
+        let orig = [1u8, 2, 3, 4, 5, 6, 7, 8, 9];
+        let mut a = orig.clone();
+        let mut b = orig.clone();
+        a.shuffle(&mut rng1);
+        b.shuffle(&mut rng2);
+        assert!(a != orig || b != orig, "Shuffles did not change order");
+        assert_ne!(a, b, "Two Crypto RNG shuffles produced same order");
+    }
+
+    #[test]
+    fn test_shuffle_single_element_no_change() {
+        let mut rng = Prng::new(1);
+        let mut arr = [42];
+        arr.shuffle(&mut rng);
+        assert_eq!(arr, [42]);
+    }
+
+    #[test]
+    fn test_multiple_shuffles_different_results() {
+        let mut rng = Prng::new(5);
+        let mut arr1 = [1, 2, 3, 4];
+        let mut arr2 = [1, 2, 3, 4];
+        arr1.shuffle(&mut rng);
+        arr2.shuffle(&mut rng);
+        assert_ne!(arr1, arr2);
+    }
+
+    #[test]
+    fn test_shuffle_empty_slice() {
+        let mut rng = Prng::new(1);
+        let mut arr: [i32; 0] = [];
+        arr.shuffle(&mut rng);
+        assert!(arr.is_empty());
+    }
+
+    #[test]
+    fn test_shuffle_three_uniform() {
+        use std::collections::HashMap;
+        let mut rng = Prng::new(123);
+        let mut counts: HashMap<[u8; 3], usize> = HashMap::new();
+        for _ in 0..6000 {
+            let mut arr = [1u8, 2, 3];
+            arr.shuffle(&mut rng);
+            *counts.entry(arr).or_insert(0) += 1;
+        }
+        let expected = 1000.0;
+        let chi2: f64 = counts
+            .values()
+            .map(|&c| {
+                let diff = c as f64 - expected;
+                diff * diff / expected
+            })
+            .sum();
+        assert!(chi2 < 30.0, "shuffle chi-square too high: {chi2}");
+    }
+}