{"longStrinGwitHmixofsmaLLandcAps", "LONGSTRINGWITHMIXOFSMALLANDCAPS"},
        {"long\u0250string\u0250with\u0250nonascii\u2C6Fchars", "LONG\u2C6FSTRING\u2C6FWITH\u2C6FNONASCII\u2C6FCHARS"},
        {"\u0250\u0250\u0250\u0250\u0250", "\u2C6F\u2C6F\u2C6F\u2C6F\u2C6F"}, // grows one byte per char
+       {"a\u0080\U0010FFFF", "A\u0080\U0010FFFF"},                           // test utf8.RuneSelf and utf8.MaxRune
 }
 
 var lowerTests = []StringTest{
        {"longStrinGwitHmixofsmaLLandcAps", "longstringwithmixofsmallandcaps"},
        {"LONG\u2C6FSTRING\u2C6FWITH\u2C6FNONASCII\u2C6FCHARS", "long\u0250string\u0250with\u0250nonascii\u0250chars"},
        {"\u2C6D\u2C6D\u2C6D\u2C6D\u2C6D", "\u0251\u0251\u0251\u0251\u0251"}, // shrinks one byte per char
+       {"A\u0080\U0010FFFF", "a\u0080\U0010FFFF"},                           // test utf8.RuneSelf and utf8.MaxRune
 }
 
 const space = "\t\v\r\f\n\u0085\u00a0\u2000\u3000"
        if m != expect {
                t.Errorf("replace invalid sequence: expected %q got %q", expect, m)
        }
+
+       // 8. Check utf8.RuneSelf and utf8.MaxRune encoding
+       encode := func(r rune) rune {
+               switch r {
+               case utf8.RuneSelf:
+                       return unicode.MaxRune
+               case unicode.MaxRune:
+                       return utf8.RuneSelf
+               }
+               return r
+       }
+       s := string(utf8.RuneSelf) + string(utf8.MaxRune)
+       r := string(utf8.MaxRune) + string(utf8.RuneSelf) // reverse of s
+       m = Map(encode, s)
+       if m != r {
+               t.Errorf("encoding not handled correctly: expected %q got %q", r, m)
+       }
+       m = Map(encode, r)
+       if m != s {
+               t.Errorf("encoding not handled correctly: expected %q got %q", s, m)
+       }
 }
 
 func TestToUpper(t *testing.T) { runStringTests(t, ToUpper, "ToUpper", upperTests) }