--- a/src/frontc/clexer.mll
+++ b/src/frontc/clexer.mll
@@ -134,9 +134,11 @@ let init_lexicon _ =
       (* WW: see /usr/include/sys/cdefs.h for why __signed and __volatile
        * are accepted GCC-isms *)
       ("_Bool", fun loc -> BOOL loc);
+      ("_Complex", fun loc -> COMPLEX loc);
       ("char", fun loc -> CHAR loc);
       ("int", fun loc -> INT loc);
       ("float", fun loc -> FLOAT loc);
+      ("__float128", fun loc -> FLOAT128 loc);
       ("double", fun loc -> DOUBLE loc);
       ("void", fun loc -> VOID loc);
       ("enum", fun loc -> ENUM loc);
--- a/src/frontc/cparser.mly
+++ b/src/frontc/cparser.mly
@@ -269,6 +269,8 @@ let oblivState (s:statement): statement =
 %token<Cabs.cabsloc> VOLATILE EXTERN STATIC CONST RESTRICT AUTO REGISTER FROZEN
 %token<Cabs.cabsloc> THREAD
 
+%token<Cabs.cabsloc> COMPLEX FLOAT128
+
 %token<Cabs.cabsloc> SIZEOF ALIGNOF
 
 %token EQ PLUS_EQ MINUS_EQ STAR_EQ SLASH_EQ PERCENT_EQ
@@ -1002,7 +1004,11 @@ type_spec:   /* ISO 6.7.2 */
 |   LONG            { Tlong, $1 }
 |   INT64           { Tint64, $1 }
 |   FLOAT           { Tfloat, $1 }
+|   FLOAT128        { Tfloat, $1 }
 |   DOUBLE          { Tdouble, $1 }
+|   COMPLEX FLOAT   { Tfloat, $2 }
+|   COMPLEX FLOAT128{ Tfloat, $2 }
+|   COMPLEX DOUBLE  { Tdouble, $2 }
 |   SIGNED          { Tsigned, $1 }
 |   UNSIGNED        { Tunsigned, $1 }
 |   STRUCT                 id_or_typename