diff --git a/qlib/backtest/high_performance_ds.py b/qlib/backtest/high_performance_ds.py
index 74927e2be..bb75ca8f6 100644
--- a/qlib/backtest/high_performance_ds.py
+++ b/qlib/backtest/high_performance_ds.py
@@ -167,11 +167,14 @@ class CN1minNumpyQuote(BaseQuote):
 
     def _agg_data(self, data: IndexData, method):
         """Agg data by specific method."""
+        # FIXME: why not call the method of data directly?
         if method == "sum":
             return np.nansum(data)
         elif method == "mean":
             return np.nanmean(data)
         elif method == "last":
+            # FIXME: I've never seen that this method was called.
+            # Please merge it with "ts_data_last"
             return data[-1]
         elif method == "all":
             return data.all()
diff --git a/qlib/utils/index_data.py b/qlib/utils/index_data.py
index 505f0dd33..c8d6bebee 100644
--- a/qlib/utils/index_data.py
+++ b/qlib/utils/index_data.py
@@ -10,7 +10,7 @@ Motivation of index_data
 """
 
 from functools import partial
-from typing import Tuple, Union, Callable, List
+from typing import Dict, Tuple, Union, Callable, List
 import bisect
 
 import numpy as np
@@ -128,8 +128,7 @@ class Index:
             raise KeyError(f"{item} can't be found in {self}")
 
     def __or__(self, other: "Index"):
-        idx = Index(idx_list=list(set(self.idx_list) | set(other.idx_list)))
-        return idx
+        return Index(idx_list=list(set(self.idx_list) | set(other.idx_list)))
 
     def __eq__(self, other: "Index"):
         # NOTE:  np.nan is not supported in the index
@@ -283,9 +282,8 @@ class BinaryOps:
         if isinstance(other, (int, float, np.number)):
             return self.obj.__class__(self_data_method(other))
         elif isinstance(other, self.obj.__class__):
-            # TODO: bad interface
-            tmp_data1, tmp_data2 = self.obj._align_indices(other)
-            return self.obj.__class__(self_data_method(tmp_data2.data), *self.obj.indices)
+            other_aligned = self.obj._align_indices(other)
+            return self.obj.__class__(self_data_method(other_aligned.data), *self.obj.indices)
         else:
             return NotImplemented
 
@@ -369,8 +367,21 @@ class IndexData(metaclass=index_data_ops_creator):
     def columns(self):
         return self.indices[1]
 
-    def _align_indices(self, other):
-        """Align index before performing the four arithmetic operations."""
+    def _align_indices(self, other: "IndexData") -> "IndexData":
+        """
+        Align all indices of `other` to `self` before performing the arithmetic operations.
+        This function will return a new IndexData rather than changing data in `other` inplace
+
+        Parameters
+        ----------
+        other : "IndexData"
+            the index in `other` is to be chagned
+
+        Returns
+        -------
+        IndexData:
+            the data in `other` with index aligned to `self`
+        """
         raise NotImplementedError(f"please implement _align_indices func")
 
     def sort_index(self, axis=0, inplace=True):
@@ -387,12 +398,12 @@ class IndexData(metaclass=index_data_ops_creator):
         tmp_data = np.absolute(self.data)
         return self.__class__(tmp_data, *self.indices)
 
-    def replace(self, to_replace: dict):
+    def replace(self, to_replace: Dict[np.number, np.number]):
         assert isinstance(to_replace, dict)
         tmp_data = self.data.copy()
         for num in to_replace:
             if num in tmp_data:
-                tmp_data[tmp_data == num] = to_replace[num]
+                tmp_data[self.data == num] = to_replace[num]
         return self.__class__(tmp_data, *self.indices)
 
     def apply(self, func: Callable):
@@ -411,6 +422,7 @@ class IndexData(metaclass=index_data_ops_creator):
         return len(self.data)
 
     def sum(self, axis=None):
+        # FIXME: weird logic and not general
         if axis is None:
             return np.nansum(self.data)
         elif axis == 0:
@@ -423,6 +435,7 @@ class IndexData(metaclass=index_data_ops_creator):
             raise ValueError(f"axis must be None, 0 or 1")
 
     def mean(self, axis=None):
+        # FIXME: weird logic and not general
         if axis is None:
             return np.nanmean(self.data)
         elif axis == 0:
@@ -479,9 +492,9 @@ class SingleData(IndexData):
 
     def _align_indices(self, other):
         if self.index == other.index:
-            return self, other
+            return other
         elif set(self.index) == set(other.index):
-            return self, other.reindex(self.index)
+            return other.reindex(self.index)
         else:
             raise ValueError(
                 f"The indexes of self and other do not meet the requirements of the four arithmetic operations"
@@ -563,7 +576,7 @@ class MultiData(IndexData):
 
     def _align_indices(self, other):
         if self.indices == other.indices:
-            return self, other
+            return other
         else:
             raise ValueError(
                 f"The indexes of self and other do not meet the requirements of the four arithmetic operations"
diff --git a/tests/misc/test_index_data.py b/tests/misc/test_index_data.py
index caa9b1897..c7a80fb0f 100644
--- a/tests/misc/test_index_data.py
+++ b/tests/misc/test_index_data.py
@@ -89,6 +89,12 @@ class IndexDataTest(unittest.TestCase):
         with self.assertRaises(KeyError):
             sd.loc["foo"]
 
+        # replace
+        sd = idd.SingleData([1, 2, 3, 4], index=["foo", "bar", "f", "g"])
+        sd = sd.replace(dict(zip(range(1, 5), range(2, 6))))
+        print(sd)
+        self.assertTrue(sd.iloc[0] == 2)
+
     def test_ops(self):
         sd1 = idd.SingleData([1, 2, 3, 4], index=["foo", "bar", "f", "g"])
         sd2 = idd.SingleData([1, 2, 3, 4], index=["foo", "bar", "f", "g"])