tweak: move to log scale

probppl.go

@@ -13,17 +13,39 @@ import rand "math/rand/v2"
 type src = *rand.Rand
 
 func generateRandomMapping(r src) map[int]float64 {
-	current_probability := 0.0
 	mapping := make(map[int]float64)
-	for i := 0; i <= 1000; i++ {
-		if current_probability < 1.0 {
-			num_possible_steps := int((1-current_probability)/0.001) + 1
-			fmt.Println("num possible steps: %d", num_possible_steps)
-			step := float64(r.IntN(num_possible_steps)) * 0.001
-			current_probability += step
-		}
-		mapping[i] = current_probability
+	sum := 0.0
+
+	// Consider zero case separately
+	p0 := r.Float64()
+	mapping[0.0] = p0
+	sum += p0
+
+	// Consider successive exponents of 1.5
+	l := 1.0
+	m := 1.5
+	for i := 1; i < 22; i++ {
+		l = l * m
+		p := r.Float64()
+		mapping[int(l)] = p
+		sum += p
+	}
+
+	for key, value := range mapping {
+		mapping[key] = value / sum
 	}
+
+	/*
+		for i := 0; i <= 1000; i++ {
+			if current_probability < 1.0 {
+				num_possible_steps := int((1-current_probability)/0.001) + 1
+				fmt.Println("num possible steps: %d", num_possible_steps)
+				step := float64(r.IntN(num_possible_steps)) * 0.001
+				current_probability += step
+			}
+			mapping[i] = current_probability
+		}
+	*/
 	return mapping
 }
 
@@ -32,8 +54,8 @@ func main() {
 
 	var r = rand.New(rand.NewPCG(uint64(1), uint64(2)))
 	randomMapping := generateRandomMapping(r)
-	for i := 0; i <= 1000; i++ {
-		fmt.Printf("%d: %.4f\n", i, randomMapping[i])
+	for i, value := range randomMapping {
+		fmt.Printf("%d: %.4f\n", i, value)
 	}
 
 }

todo.md

@@ -0,0 +1,5 @@
+- [ ] MVP of mappings
+- [ ] Try as cdfs: too much prob at the beginning
+- [ ] Try as pdfs: too evenly distributed
+- [ ] Try as pdfs over log space; 1, 2, 4, 8, 16, 32, ...
+  - Or maybe even more coarse, 1.x^n