rand: add non uniform distributions in the rand.dist module (#9274)

vlib/rand/dist/dist_test.v

@@ -0,0 +1,111 @@
+import math
+import rand
+import rand.dist
+
+const (
+	// The sample size to be used
+	count = 2000
+	// Accepted error is within 5% of the actual values.
+	error = 0.05
+	// The seeds used (for reproducible testing)
+	seeds = [[u32(0xffff24), 0xabcd], [u32(0x141024), 0x42851],
+		[u32(0x1452), 0x90cd],
+	]
+)
+
+fn test_bernoulli() {
+	ps := [0.0, 0.1, 1.0 / 3.0, 0.5, 0.8, 17.0 / 18.0, 1.0]
+
+	for seed in seeds {
+		rand.seed(seed)
+		for p in ps {
+			mut successes := 0
+			for _ in 0 .. count {
+				if dist.bernoulli(p) {
+					successes++
+				}
+			}
+			assert math.abs(f64(successes) / count - p) < error
+		}
+	}
+}
+
+fn test_binomial() {
+	ns := [100, 200, 1000]
+	ps := [0.0, 0.5, 0.95, 1.0]
+
+	for seed in seeds {
+		rand.seed(seed)
+		for n in ns {
+			for p in ps {
+				np := n * p
+				npq := np * (1 - p)
+
+				mut sum := 0
+				mut var := 0.0
+				for _ in 0 .. count {
+					x := dist.binomial(n, p)
+					sum += x
+					dist := (x - np)
+					var += dist * dist
+				}
+
+				assert math.abs(f64(sum / count) - np) / n < error
+				assert math.abs(f64(var / count) - npq) / n < error
+			}
+		}
+	}
+}
+
+fn test_normal_pair() {
+	mus := [0, 10, 100, -40]
+	sigmas := [1, 2, 40, 5]
+	total := 2 * count
+
+	for seed in seeds {
+		rand.seed(seed)
+		for mu in mus {
+			for sigma in sigmas {
+				mut sum := 0.0
+				mut var := 0.0
+				for _ in 0 .. count {
+					x, y := dist.normal_pair(mu: mu, sigma: sigma)
+					sum += x + y
+					dist_x := x - mu
+					dist_y := y - mu
+					var += dist_x * dist_x
+					var += dist_y * dist_y
+				}
+
+				variance := sigma * sigma
+				assert math.abs(f64(sum / total) - mu) / sigma < 1
+				assert math.abs(f64(var / total) - variance) / variance < 2 * error
+			}
+		}
+	}
+}
+
+fn test_normal() {
+	mus := [0, 10, 100, -40, 20]
+	sigmas := [1, 2, 5]
+
+	for seed in seeds {
+		rand.seed(seed)
+		for mu in mus {
+			for sigma in sigmas {
+				mut sum := 0.0
+				mut var := 0.0
+				for _ in 0 .. count {
+					x := dist.normal(mu: mu, sigma: sigma)
+					sum += x
+					dist := x - mu
+					var += dist * dist
+				}
+
+				variance := sigma * sigma
+				assert math.abs(f64(sum / count) - mu) / sigma < 1
+				assert math.abs(f64(var / count) - variance) / variance < 2 * error
+			}
+		}
+	}
+}