diff --git a/lmathlib.c b/lmathlib.c
index 3454c41f..f6f0b426 100644
--- a/lmathlib.c
+++ b/lmathlib.c
@@ -276,7 +276,7 @@ static int math_type (lua_State *L) {
 /* there is a 'long long' type (which must have at least 64 bits) */
 #define Rand64		unsigned long long
 
-#elif (LUA_MAXINTEGER >> 30 >> 30) >= 7
+#elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3
 
 /* 'lua_Integer' has at least 64 bits */
 #define Rand64		lua_Unsigned
@@ -538,7 +538,7 @@ static lua_Unsigned project (lua_Unsigned ran, lua_Unsigned n,
     lim |= (lim >> 4);
     lim |= (lim >> 8);
     lim |= (lim >> 16);
-#if (LUA_MAXINTEGER >> 30) >= 3
+#if (LUA_MAXUNSIGNED >> 31) >= 3
     lim |= (lim >> 32);  /* integer type has more than 32 bits */
 #endif
   }
diff --git a/luaconf.h b/luaconf.h
index e6271b80..66dca6bf 100644
--- a/luaconf.h
+++ b/luaconf.h
@@ -515,7 +515,6 @@
 */
 #define LUA_UNSIGNED		unsigned LUAI_UACINT
 
-#define LUA_MAXUNSIGNED		(~(lua_Unsigned)0)
 
 #define LUA_UNSIGNEDBITS	(sizeof(LUA_UNSIGNED) * CHAR_BIT)
 
@@ -530,6 +529,8 @@
 #define LUA_MAXINTEGER		INT_MAX
 #define LUA_MININTEGER		INT_MIN
 
+#define LUA_MAXUNSIGNED		UINT_MAX
+
 #elif LUA_INT_TYPE == LUA_INT_LONG	/* }{ long */
 
 #define LUA_INTEGER		long
@@ -538,6 +539,8 @@
 #define LUA_MAXINTEGER		LONG_MAX
 #define LUA_MININTEGER		LONG_MIN
 
+#define LUA_MAXUNSIGNED		ULONG_MAX
+
 #elif LUA_INT_TYPE == LUA_INT_LONGLONG	/* }{ long long */
 
 /* use presence of macro LLONG_MAX as proxy for C99 compliance */
@@ -550,6 +553,8 @@
 #define LUA_MAXINTEGER		LLONG_MAX
 #define LUA_MININTEGER		LLONG_MIN
 
+#define LUA_MAXUNSIGNED		ULLONG_MAX
+
 #elif defined(LUA_USE_WINDOWS) /* }{ */
 /* in Windows, can use specific Windows types */
 
@@ -559,6 +564,8 @@
 #define LUA_MAXINTEGER		_I64_MAX
 #define LUA_MININTEGER		_I64_MIN
 
+#define LUA_MAXUNSIGNED		_UI64_MAX
+
 #else				/* }{ */
 
 #error "Compiler does not support 'long long'. Use option '-DLUA_32BITS' \