PERF: ArrowDtype.__eq__ (pandas-dev#54223)

* PERF: ArrowDtype.__eq__

* cleanup

Author: lukemanley

pandas/core/dtypes/dtypes.py

@@ -2056,6 +2056,15 @@ def __init__(self, pyarrow_dtype: pa.DataType) -> None:
     def __repr__(self) -> str:
         return self.name
 
+    def __hash__(self) -> int:
+        # make myself hashable
+        return hash(str(self))
+
+    def __eq__(self, other: Any) -> bool:
+        if not isinstance(other, type(self)):
+            return super().__eq__(other)
+        return self.pyarrow_dtype == other.pyarrow_dtype
+
     @property
     def type(self):
         """