diff --git a/torch/_inductor/codegen/common.py b/torch/_inductor/codegen/common.py
index 6bf3104d150..77fe55d11a7 100644
--- a/torch/_inductor/codegen/common.py
+++ b/torch/_inductor/codegen/common.py
@@ -605,51 +605,16 @@ class PythonPrinter(_PythonPrinter):
         return super().doprint(expr)
 
 
-class OpOverrides:
-    def __init__(self, parent):
-        super().__init__()
-        self._parent = parent
-
-    @staticmethod
-    def paren(string: str) -> str:
-        def all_in_parens(string: str) -> bool:
-            if string[0] != "(" or len(string) < 2:
-                return False
-            count = 1
-            for i, char in enumerate(string[1:]):
-                if char == "(":
-                    count += 1
-                elif char == ")":
-                    count -= 1
-                if count == 0 and i != len(string) - 2:
-                    return False
-            assert count == 0
-            return True
-
-        if (
-            isinstance(string, CSEVariable)
-            or re.match(r"^[a-z0-9_.]+$", string, re.IGNORECASE)
-            or re.match(r"^\([^)]*\)$", string, re.IGNORECASE)
-            or string == ""
-        ):
-            return string
-        # don't put extra parens for strings that are already wrapped in parens
-        if all_in_parens(string):
-            return string
-        return f"({string})"
-
-    def __getattr__(self, item):
-        return getattr(self._parent, item)
+class OpDecompositions:
+    """
+    Decomposes inductor ops
+    """
 
     @staticmethod
     def identity(value):
         # used to trigger cse
         return value
 
-    @staticmethod
-    def constant(value, dtype):
-        return repr(value)
-
     @staticmethod
     def reciprocal(x):
         return ops.truediv(ops.constant(1, torch.int32), x)
@@ -691,15 +656,86 @@ class OpOverrides:
         one = ops.constant(1, torch.int32)
         return ops.truediv(one, ops.add(one, ops.exp(ops.neg(x))))
 
+    @staticmethod
+    def relu(x):
+        return ops.maximum(x, ops.constant(0, torch.int32))
+
+    @staticmethod
+    def fma(x, y, z):
+        # for backends that don't override this (halide)
+        return ops.add(ops.mul(x, y), z)
+
+    @staticmethod
+    def floor_to_int(a, dtype):
+        return ops.to_dtype(ops.floor(a), dtype)
+
+    @staticmethod
+    def ceil_to_int(a, dtype):
+        return ops.to_dtype(ops.ceil(a), dtype)
+
+    @staticmethod
+    def trunc_to_int(a, dtype):
+        return ops.to_dtype(ops.trunc(a), dtype)
+
+    @staticmethod
+    def remainder(a, b):
+        r = ops.mod(a, b)
+        cond = ops.and_(
+            ops.ne(r, ops.constant(0, torch.int32)),
+            ops.ne(ops.signbit(r), ops.signbit(b)),
+        )
+        return ops.where(cond, ops.add(r, b), r)
+
+    @staticmethod
+    def round_to_int(a, dtype):
+        return ops.to_dtype(ops.round(a), dtype)
+
+
+class OpOverrides(OpDecompositions):
+    def __init__(self, parent):
+        super().__init__()
+        self._parent = parent
+
+    @staticmethod
+    def paren(string: str) -> str:
+        def all_in_parens(string: str) -> bool:
+            if string[0] != "(" or len(string) < 2:
+                return False
+            count = 1
+            for i, char in enumerate(string[1:]):
+                if char == "(":
+                    count += 1
+                elif char == ")":
+                    count -= 1
+                if count == 0 and i != len(string) - 2:
+                    return False
+            assert count == 0
+            return True
+
+        if (
+            isinstance(string, CSEVariable)
+            or re.match(r"^[a-z0-9_.]+$", string, re.IGNORECASE)
+            or re.match(r"^\([^)]*\)$", string, re.IGNORECASE)
+            or string == ""
+        ):
+            return string
+        # don't put extra parens for strings that are already wrapped in parens
+        if all_in_parens(string):
+            return string
+        return f"({string})"
+
+    def __getattr__(self, item):
+        return getattr(self._parent, item)
+
+    @staticmethod
+    def constant(value, dtype):
+        return repr(value)
+
     @staticmethod
     def libdevice_sigmoid(x):
         one = ops.constant(1, torch.int32)
         return ops.truediv(one, ops.add(one, ops.libdevice_exp(ops.neg(x))))
 
-    @staticmethod
-    def relu(x):
-        return ops.maximum(x, ops.constant(0, torch.int32))
-
     @staticmethod
     def libdevice_abs(x):
         return ops.abs(x)
@@ -752,36 +788,6 @@ class OpOverrides:
     def bitwise_right_shift(x, y):
         return f"{OpOverrides.paren(x)} >> {OpOverrides.paren(y)}"
 
-    @staticmethod
-    def remainder(a, b):
-        r = ops.mod(a, b)
-        cond = ops.and_(
-            ops.ne(r, ops.constant(0, torch.int32)),
-            ops.ne(ops.signbit(r), ops.signbit(b)),
-        )
-        return ops.where(cond, ops.add(r, b), r)
-
-    @staticmethod
-    def fma(x, y, z):
-        # for backends that don't override this (halide)
-        return ops.add(ops.mul(x, y), z)
-
-    @staticmethod
-    def trunc_to_int(a, dtype):
-        return ops.to_dtype(ops.trunc(a), dtype)
-
-    @staticmethod
-    def floor_to_int(a, dtype):
-        return ops.to_dtype(ops.floor(a), dtype)
-
-    @staticmethod
-    def ceil_to_int(a, dtype):
-        return ops.to_dtype(ops.ceil(a), dtype)
-
-    @staticmethod
-    def round_to_int(a, dtype):
-        return ops.to_dtype(ops.round(a), dtype)
-
     @staticmethod
     def int_truediv(a, b):
         # TODO: this is wrong
diff --git a/torch/_inductor/ops_handler.py b/torch/_inductor/ops_handler.py
index b31f64872d8..1ae590d444f 100644
--- a/torch/_inductor/ops_handler.py
+++ b/torch/_inductor/ops_handler.py
@@ -51,8 +51,7 @@ def _arg_str(a) -> str:
 # implementations make heavy use of __getattr__ magic, and pre-existing
 # stubs for methods would interfere with this mechanism.
 #
-# TODO: A superclass that does desugaring for operations like
-# reciprocal/square might be useful.
+# See OpDecompositions for superclass that desugars operations like reciprocal/square.
 class OpsHandler(Protocol[T]):
     """
     Protocol describing the set of valid operations on ``torch._inductor.virtualized.ops``,