auth: fix range handling bugs.

Test 15, counting from zero, in TestGetMergedPerms
in etcd/auth/range_perm_cache_test.go, was trying
incorrectly assert that [a, b) merged with [b, "")
should be [a, b). Added a test specifically for
this. This patch fixes the incorrect larger test
and the bugs in the code that it was hiding.

Fixes etcd-io#6359

auth/range_perm_cache.go

@@ -22,7 +22,10 @@ import (
 	"github.com/coreos/etcd/mvcc/backend"
 )
 
-// isSubset returns true if a is a subset of b
+// isSubset returns true if a is a subset of b.
+// If a is a prefix of b, then a is a subset of b.
+// Given intervals [a1,a2) and [b1,b2), is
+// the a interval a subset of b?
 func isSubset(a, b *rangePerm) bool {
 	switch {
 	case len(a.end) == 0 && len(b.end) == 0:
@@ -32,9 +35,11 @@ func isSubset(a, b *rangePerm) bool {
 		// b is a key, a is a range
 		return false
 	case len(a.end) == 0:
-		return 0 <= bytes.Compare(a.begin, b.begin) && bytes.Compare(a.begin, b.end) <= 0
+		// a is a key, b is a range. need b1 <= a1 and a1 < b2
+		return bytes.Compare(b.begin, a.begin) <= 0 && bytes.Compare(a.begin, b.end) < 0
 	default:
-		return 0 <= bytes.Compare(a.begin, b.begin) && bytes.Compare(a.end, b.end) <= 0
+		// both are ranges. need b1 <= a1 and a2 <= b2
+		return bytes.Compare(b.begin, a.begin) <= 0 && bytes.Compare(a.end, b.end) <= 0
 	}
 }
 
@@ -88,12 +93,18 @@ func mergeRangePerms(perms []*rangePerm) []*rangePerm {
 	i := 0
 	for i < len(perms) {
 		begin, next := i, i
-		for next+1 < len(perms) && bytes.Compare(perms[next].end, perms[next+1].begin) != -1 {
+		for next+1 < len(perms) && bytes.Compare(perms[next].end, perms[next+1].begin) >= 0 {
 			next++
 		}
-
-		merged = append(merged, &rangePerm{begin: perms[begin].begin, end: perms[next].end})
-
+		// don't merge ["a", "b") with ["b", ""), because perms[next+1].end is empty.
+		if next != begin && len(perms[next].end) > 0 {
+			merged = append(merged, &rangePerm{begin: perms[begin].begin, end: perms[next].end})
+		} else {
+			merged = append(merged, perms[begin])
+			if next != begin {
+				merged = append(merged, perms[next])
+			}
+		}
 		i = next + 1
 	}
 

auth/range_perm_cache_test.go

@@ -46,6 +46,10 @@ func TestGetMergedPerms(t *testing.T) {
 			[]*rangePerm{{[]byte("a"), []byte("b")}},
 			[]*rangePerm{{[]byte("a"), []byte("b")}},
 		},
+		{
+			[]*rangePerm{{[]byte("a"), []byte("b")}, {[]byte("b"), []byte("")}},
+			[]*rangePerm{{[]byte("a"), []byte("b")}, {[]byte("b"), []byte("")}},
+		},
 		{
 			[]*rangePerm{{[]byte("a"), []byte("b")}, {[]byte("b"), []byte("c")}},
 			[]*rangePerm{{[]byte("a"), []byte("c")}},
@@ -106,7 +110,7 @@ func TestGetMergedPerms(t *testing.T) {
 		},
 		{
 			[]*rangePerm{{[]byte("a"), []byte("")}, {[]byte("b"), []byte("c")}, {[]byte("b"), []byte("")}, {[]byte("c"), []byte("")}, {[]byte("d"), []byte("")}},
-			[]*rangePerm{{[]byte("a"), []byte("")}, {[]byte("b"), []byte("c")}, {[]byte("d"), []byte("")}},
+			[]*rangePerm{{[]byte("a"), []byte("")}, {[]byte("b"), []byte("c")}, {[]byte("c"), []byte("")}, {[]byte("d"), []byte("")}},
 		},
 		// duplicate ranges
 		{