Add needed files

Signed-off-by: Jakub Sztandera <kubuxu@protocol.ai>

chain/messagepool/block_proba.go

@@ -0,0 +1,71 @@
+package messagepool
+
+import "math"
+
+func noWinnersProb() []float64 {
+	poissPdf := func(x float64) float64 {
+		const Mu = 5
+		lg, _ := math.Lgamma(x + 1)
+		result := math.Exp((math.Log(Mu) * x) - lg - Mu)
+		return result
+	}
+
+	out := make([]float64, 0, MaxBlocks)
+	for i := 0; i < MaxBlocks; i++ {
+		out = append(out, poissPdf(float64(i)))
+	}
+	return out
+}
+
+func binomialCoefficient(n, k float64) float64 {
+	if k > n {
+		return math.NaN()
+	}
+	r := 1.0
+	for d := 1.0; d <= k; d++ {
+		r *= n
+		r /= d
+		n -= 1
+	}
+	return r
+}
+
+func (mp *MessagePool) blockProbabilities(tq float64) []float64 {
+	noWinners := noWinnersProb() // cache this
+
+	p := 1 - tq
+	binoPdf := func(x, trials float64) float64 {
+		// based on https://github.com/atgjack/prob
+		if x > trials {
+			return 0
+		}
+		if p == 0 {
+			if x == 0 {
+				return 1.0
+			}
+			return 0.0
+		}
+		if p == 1 {
+			if x == trials {
+				return 1.0
+			}
+			return 0.0
+		}
+		coef := binomialCoefficient(trials, x)
+		pow := math.Pow(p, x) * math.Pow(1-p, trials-x)
+		if math.IsInf(coef, 0) {
+			return 0
+		}
+		return coef * pow
+	}
+
+	out := make([]float64, 0, MaxBlocks)
+	for place := 0; place < MaxBlocks; place++ {
+		var pPlace float64
+		for otherWinners, pCase := range noWinners {
+			pPlace += pCase * binoPdf(float64(place), float64(otherWinners+1))
+		}
+		out = append(out, pPlace)
+	}
+	return out
+}

chain/messagepool/block_proba_test.go

@@ -0,0 +1,8 @@
+package messagepool
+
+import "testing"
+
+func TestBlockProbability(t *testing.T) {
+	mp := &MessagePool{}
+	t.Logf("%+v\n", mp.blockProbabilities(1-0.15))
+}