diff --git a/container/intsets/sparse.go b/container/intsets/sparse.go
index be14d0559..763b38485 100644
--- a/container/intsets/sparse.go
+++ b/container/intsets/sparse.go
@@ -698,19 +698,44 @@ func (s *Sparse) String() string {
 	return buf.String()
 }
 
-// BitString returns the set s as a non-empty string of 1s and 0s.
-// The ith character is 1 if the set contains i.
+// BitString returns the set as a string of 1s and 0s denoting the sum
+// of the i'th powers of 2, for each i in s.  A radix point, always
+// preceded by a digit, appears if the sum is non-integral.
+//
+// Examples:
+//              {}.BitString() =      "0"
+//	     {4,5}.BitString() = "110000"
+//            {-3}.BitString() =      "0.001"
+//      {-3,0,4,5}.BitString() = "110001.001"
 //
 func (s *Sparse) BitString() string {
 	if s.IsEmpty() {
 		return "0"
 	}
-	b := make([]byte, s.Max()+1)
+
+	min, max := s.Min(), s.Max()
+	var nbytes int
+	if max > 0 {
+		nbytes = max
+	}
+	nbytes++ // zero bit
+	radix := nbytes
+	if min < 0 {
+		nbytes += len(".") - min
+	}
+
+	b := make([]byte, nbytes)
 	for i := range b {
 		b[i] = '0'
 	}
+	if radix < nbytes {
+		b[radix] = '.'
+	}
 	s.forEach(func(x int) {
-		b[x] = '1'
+		if x >= 0 {
+			x += len(".")
+		}
+		b[radix-x] = '1'
 	})
 	return string(b)
 }
diff --git a/container/intsets/sparse_test.go b/container/intsets/sparse_test.go
index 258291af1..bdbb8dfd5 100644
--- a/container/intsets/sparse_test.go
+++ b/container/intsets/sparse_test.go
@@ -23,9 +23,6 @@ func TestBasics(t *testing.T) {
 	if s := s.String(); s != "{}" {
 		t.Errorf("String({}): got %q, want \"{}\"", s)
 	}
-	if s := s.BitString(); s != "0" {
-		t.Errorf("BitString({}): got %q, want \"0\"", s)
-	}
 	if s.Has(3) {
 		t.Errorf("Has(3): got true, want false")
 	}
@@ -421,13 +418,24 @@ func TestIntersectionWith(t *testing.T) {
 }
 
 func TestBitString(t *testing.T) {
-	var set intsets.Sparse
-	set.Insert(0)
-	set.Insert(7)
-	set.Insert(177)
-	want := "10000001" + strings.Repeat("0", 169) + "1"
-	if got := set.BitString(); got != want {
-		t.Errorf("BitString: got %s, want %s", got, want)
+	for _, test := range []struct {
+		input []int
+		want  string
+	}{
+		{nil, "0"},
+		{[]int{0}, "1"},
+		{[]int{0, 4, 5}, "110001"},
+		{[]int{0, 7, 177}, "1" + strings.Repeat("0", 169) + "10000001"},
+		{[]int{-3, 0, 4, 5}, "110001.001"},
+		{[]int{-3}, "0.001"},
+	} {
+		var set intsets.Sparse
+		for _, x := range test.input {
+			set.Insert(x)
+		}
+		if got := set.BitString(); got != test.want {
+			t.Errorf("BitString(%s) = %s, want %s", set.String(), got, test.want)
+		}
 	}
 }