BUGFIX: rank with object dtype and small values #62036

Changes :
- Removed the Cython helper function `are_diff` since a direct comparison would suffice. This removes tolerance/error based float equality under object dtype.
- Also, removed the special-case path for `numeric_object_t is object` and used a single comparison for both types. This aligns ranking semantics with Python equality across dtypes.
- Near-equal floats previously collapsed by FP_ERR will no longer tie when ranking object-dtype Series.

Author: Tejaswini V

doc/source/whatsnew/v3.0.0.rst

@@ -1122,6 +1122,7 @@ Other
 - Bug in printing a :class:`DataFrame` with a :class:`DataFrame` stored in :attr:`DataFrame.attrs` raised a ``ValueError`` (:issue:`60455`)
 - Bug in printing a :class:`Series` with a :class:`DataFrame` stored in :attr:`Series.attrs` raised a ``ValueError`` (:issue:`60568`)
 - Fixed bug where the :class:`DataFrame` constructor misclassified array-like objects with a ``.name`` attribute as :class:`Series` or :class:`Index` (:issue:`61443`)
+- Fixed bug where the :meth:`Series.rank` doesn't rank the values with object dtype and small values properly (:issue:`62036`)
 - Fixed regression in :meth:`DataFrame.from_records` not initializing subclasses properly (:issue:`57008`)
 
 .. ***DO NOT USE THIS SECTION***

pandas/_libs/algos.pyx

@@ -1,7 +1,6 @@
 cimport cython
 from cython cimport Py_ssize_t
 from libc.math cimport (
-    fabs,
     sqrt,
 )
 from libc.stdlib cimport (
@@ -72,13 +71,6 @@ tiebreakers = {
 }
 
 
-cdef bint are_diff(object left, object right):
-    try:
-        return fabs(left - right) > FP_ERR
-    except TypeError:
-        return left != right
-
-
 class Infinity:
     """
     Provide a positive Infinity comparison method for ranking.
@@ -1135,12 +1127,8 @@ cdef void rank_sorted_1d(
             dups += 1
             sum_ranks += i - grp_start + 1
 
-            if numeric_object_t is object:
-                next_val_diff = at_end or are_diff(masked_vals[sort_indexer[i]],
-                                                   masked_vals[sort_indexer[i+1]])
-            else:
-                next_val_diff = at_end or (masked_vals[sort_indexer[i]]
-                                           != masked_vals[sort_indexer[i+1]])
+            next_val_diff = at_end or (masked_vals[sort_indexer[i]]
+                                       != masked_vals[sort_indexer[i+1]])
 
             # We'll need this check later anyway to determine group size, so just
             # compute it here since shortcircuiting won't help

pandas/tests/test_algos.py

@@ -1809,6 +1809,16 @@ def test_uint64_overflow(self, dtype):
         s = Series([1, 2**63], dtype=dtype)
         tm.assert_numpy_array_equal(algos.rank(s), exp)
 
+    @pytest.mark.parametrize("method", ["average", "min", "max"])
+    def test_object_dtype(self, method):
+        exp = np.array([4.0, 1.0, 3.0, np.nan, 2.0], dtype=np.float64)
+        s = Series(
+            [5.4954145e29, -9.791984e-21, 9.3715776e-26, pd.NA, 1.8790257e-28],
+            dtype="Float64",
+        )
+        s = s.astype(object)
+        tm.assert_numpy_array_equal(algos.rank(s, method=method), exp)
+
     def test_too_many_ndims(self):
         arr = np.array([[[1, 2, 3], [4, 5, 6], [7, 8, 9]]])
         msg = "Array with ndim > 2 are not supported"