prefix tests

collatz/prefix.go

@@ -44,12 +44,12 @@ func PrefixIterate(n *big.Int, pf []uint) *big.Int {
 	n = Copy(n)
 
 	// R_0 function
-	n.Div(n, new(big.Int).Rsh(ONE, pf[0]))
+	n.Div(n, new(big.Int).Lsh(ONE, pf[0]))
 
 	// R function
 	for i := 1; i < len(pf); i++ {
 		n.Mul(n, THREE).Add(n, ONE)
-		n.Div(n, new(big.Int).Rsh(ONE, pf[i]-pf[i-1]))
+		n.Div(n, new(big.Int).Lsh(ONE, pf[i]-pf[i-1]))
 	}
 	return n
 }

collatz/prefix_test.go

@@ -5,8 +5,57 @@ import (
 	"testing"
 )
 
+// Find Prefix by simply comparing the ECFs
+func prefixBrute(a []uint, b []uint) []uint {
+	// get the minimum length
+	l := len(a)
+	if len(b) < l {
+		l = len(b)
+	}
+
+	ans := make([]uint, 0)
+	for i := 0; i < l; i++ {
+		if a[i] == b[i] {
+			ans = append(ans, a[i])
+		} else {
+			break
+		}
+	}
+
+	return ans
+}
+
 func TestPrefix(t *testing.T) {
+	cases := []struct {
+		n *big.Int
+		m *big.Int
+	}{
+		{big.NewInt(1), big.NewInt(2)},
+		{big.NewInt(3), big.NewInt(12)},
+		{big.NewInt(8), big.NewInt(16)},
+		{big.NewInt(27), big.NewInt(37)},
+	}
 
+	for _, test := range cases {
+		// expected prefix found via ECFs
+		pf := prefixBrute(CollatzECF(test.n), CollatzECF(test.m))
+
+		if !EqualUints(pf, PrefixFind(test.n, test.m)) {
+			t.Errorf("Prefix is wrong.")
+		}
+
+		if !EqualUints(pf, PrefixFind(test.m, test.n)) {
+			t.Errorf("PrefixFind should be commutative.")
+		}
+
+		// test both numbers for ECF iteration
+		if PrefixIterate(test.n, CollatzECF(test.n)).Cmp(big.NewInt(1)) != 0 {
+			t.Errorf("Iterating over ECF should result in 1.")
+		}
+		if PrefixIterate(test.m, CollatzECF(test.m)).Cmp(big.NewInt(1)) != 0 {
+			t.Errorf("Iterating over ECF should result in 1.")
+		}
+	}
 }
 
 func TestPrefixAdd(t *testing.T) {
@@ -22,6 +71,7 @@ func TestPrefixAdd(t *testing.T) {
 		{[]uint{1}, nil, []uint{1}},
 		// normal cases
 		{[]uint{2, 4}, []uint{4}, []uint{2, 8}},
+		{[]uint{4}, []uint{2, 4}, []uint{6, 8}},
 		{[]uint{0, 1, 5}, []uint{0, 1, 3}, []uint{0, 1, 5, 6, 8}},
 	}