compute totient with trial division

cmd/primitiveRoot.go

@@ -29,15 +29,34 @@ var modulus string
 var tpf []string
 
 func totient(n *big.Int) *big.Int {
-	total := big.NewInt(0)
+	N := new(big.Int).Set(n)
-	for a := big.NewInt(1); a.Cmp(n) == -1; a.Add(a, big.NewInt(1)) {
+
-		gcd := new(big.Int).GCD(nil, nil, a, n)
+	phi := new(big.Int).Set(N)
-		if gcd.Cmp(big.NewInt(1)) == 0 {
+
-			total.Add(total, big.NewInt(1))
+	sqrtn := new(big.Int).Sqrt(N)
+	for i := big.NewInt(2); i.Cmp(sqrtn) != 1; i.Add(i, big.NewInt(1)) {
+		mod := new(big.Int).Mod(N, i)
+		if mod.Cmp(big.NewInt(0)) != 0 {
+			continue
+		}
+
+		// phi -= phi // i
+		tmp := new(big.Int).Div(phi, i)
+		phi.Sub(phi, tmp)
+
+		for mod.Cmp(big.NewInt(0)) == 0 {
+			N.Div(N, i)
+			mod.Mod(N, i)
 		}
 	}
 
-	return total
+	if N.Cmp(big.NewInt(1)) == 1 {
+		// phi -= phi // N
+		tmp := new(big.Int).Div(phi, N)
+		phi.Sub(phi, tmp)
+	}
+
+	return phi
 }
 
 func multiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {