Add examples for random number generation and statistical tests

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();
+    }
+}
+