diff --git a/cloudpickle/cloudpickle.py b/cloudpickle/cloudpickle.py
index 654b8aacf..563f1af55 100644
--- a/cloudpickle/cloudpickle.py
+++ b/cloudpickle/cloudpickle.py
@@ -77,6 +77,13 @@
 _DYNAMIC_CLASS_TRACKER_BY_ID = weakref.WeakValueDictionary()
 _DYNAMIC_CLASS_TRACKER_LOCK = threading.Lock()
 
+PYPY = platform.python_implementation() == "PyPy"
+
+builtin_code_type = None
+if PYPY:
+    # builtin-code objects only exist in pypy
+    builtin_code_type = type(float.__new__.__code__)
+
 if sys.version_info[0] < 3:  # pragma: no branch
     from pickle import Pickler
     try:
@@ -453,12 +460,40 @@ def save_function(self, obj, name=None):
         Determines what kind of function obj is (e.g. lambda, defined at
         interactive prompt, etc) and handles the pickling appropriately.
         """
-        if not _is_global(obj, name=name):
+        if _is_global(obj, name=name):
+            return Pickler.save_global(self, obj, name=name)
+        elif PYPY and isinstance(obj.__code__, builtin_code_type):
+            return self.save_pypy_builtin_func(obj)
+        else:
             return self.save_function_tuple(obj)
-        return Pickler.save_global(self, obj, name=name)
 
     dispatch[types.FunctionType] = save_function
 
+    def save_pypy_builtin_func(self, obj):
+        """Save pypy equivalent of builtin functions.
+
+        PyPy does not have the concept of builtin-functions. Instead,
+        builtin-functions are simple function instances, but with a
+        builtin-code attribute.
+        Most of the time, builtin functions should be pickled by attribute. But
+        PyPy has flaky support for __qualname__, so some builtin functions such
+        as float.__new__ will be classified as dynamic. For this reason only,
+        we created this special routine. Because builtin-functions are not
+        expected to have closure or globals, there is no additional hack
+        (compared the one already implemented in pickle) to protect ourselves
+        from reference cycles. A simple (reconstructor, newargs, obj.__dict__)
+        tuple is save_reduced.
+
+        Note also that PyPy improved their support for __qualname__ in v3.6, so
+        this routing should be removed when cloudpickle supports only PyPy 3.6
+        and later.
+        """
+        rv = (types.FunctionType, (obj.__code__, {}, obj.__name__,
+                                   obj.__defaults__, obj.__closure__),
+              obj.__dict__)
+        self.save_reduce(*rv, obj=obj)
+
+
     def _save_subimports(self, code, top_level_dependencies):
         """
         Save submodules used by a function but not listed in its globals.
@@ -676,10 +711,7 @@ def save_function_tuple(self, func):
         write(pickle.TUPLE)
         write(pickle.REDUCE)  # applies _fill_function on the tuple
 
-    _extract_code_globals_cache = (
-        weakref.WeakKeyDictionary()
-        if not hasattr(sys, "pypy_version_info")
-        else {})
+    _extract_code_globals_cache = weakref.WeakKeyDictionary()
 
     @classmethod
     def extract_code_globals(cls, co):
@@ -688,19 +720,14 @@ def extract_code_globals(cls, co):
         """
         out_names = cls._extract_code_globals_cache.get(co)
         if out_names is None:
-            try:
-                names = co.co_names
-            except AttributeError:
-                # PyPy "builtin-code" object
-                out_names = set()
-            else:
-                out_names = {names[oparg] for _, oparg in _walk_global_ops(co)}
-
-                # see if nested function have any global refs
-                if co.co_consts:
-                    for const in co.co_consts:
-                        if type(const) is types.CodeType:
-                            out_names |= cls.extract_code_globals(const)
+            names = co.co_names
+            out_names = {names[oparg] for _, oparg in _walk_global_ops(co)}
+
+            # see if nested function have any global refs
+            if co.co_consts:
+                for const in co.co_consts:
+                    if isinstance(const, types.CodeType):
+                        out_names |= cls.extract_code_globals(const)
 
             cls._extract_code_globals_cache[co] = out_names