BUG: intersection of decreasing RangeIndexes

closes #17296

doc/source/whatsnew/v0.21.0.txt

@@ -359,6 +359,7 @@ Indexing
 - Bug in ``.iloc`` when used with inplace addition or assignment and an int indexer on a ``MultiIndex`` causing the wrong indexes to be read from and written to (:issue:`17148`)
 - Bug in ``.isin()`` in which checking membership in empty ``Series`` objects raised an error (:issue:`16991`)
 - Bug in ``CategoricalIndex`` reindexing in which specified indices containing duplicates were not being respected (:issue:`17323`)
+- Bug in intersection of ``RangeIndex`` with negative step (:issue:`17296`)
 
 I/O
 ^^^

pandas/core/indexes/range.py

@@ -324,34 +324,38 @@ def intersection(self, other):
         if not len(self) or not len(other):
             return RangeIndex._simple_new(None)
 
+        first = self[::-1] if self._step < 0 else self
+        second = other[::-1] if other._step < 0 else other
+
         # check whether intervals intersect
         # deals with in- and decreasing ranges
-        int_low = max(min(self._start, self._stop + 1),
-                      min(other._start, other._stop + 1))
-        int_high = min(max(self._stop, self._start + 1),
-                       max(other._stop, other._start + 1))
+        int_low = max(first._start, second._start)
+        int_high = min(first._stop, second._stop)
         if int_high <= int_low:
             return RangeIndex._simple_new(None)
 
         # Method hint: linear Diophantine equation
         # solve intersection problem
         # performance hint: for identical step sizes, could use
         # cheaper alternative
-        gcd, s, t = self._extended_gcd(self._step, other._step)
+        gcd, s, t = first._extended_gcd(first._step, second._step)
 
         # check whether element sets intersect
-        if (self._start - other._start) % gcd:
+        if (first._start - second._start) % gcd:
             return RangeIndex._simple_new(None)
 
         # calculate parameters for the RangeIndex describing the
         # intersection disregarding the lower bounds
-        tmp_start = self._start + (other._start - self._start) * \
-            self._step // gcd * s
-        new_step = self._step * other._step // gcd
+        tmp_start = first._start + (second._start - first._start) * \
+            first._step // gcd * s
+        new_step = first._step * second._step // gcd
         new_index = RangeIndex(tmp_start, int_high, new_step, fastpath=True)
 
         # adjust index to limiting interval
         new_index._start = new_index._min_fitting_element(int_low)
+
+        if (self._step < 0 and other._step < 0) is not (new_index._step < 0):
+            new_index = new_index[::-1]
         return new_index
 
     def _min_fitting_element(self, lower_limit):

pandas/tests/indexes/test_range.py

@@ -609,6 +609,19 @@ def test_intersection(self):
         expected = Index(np.sort(np.intersect1d(self.index.values,
                                                 other.values)))
         tm.assert_index_equal(result, expected)
+        # reversed (GH 17296)
+        result = other.intersection(self.index)
+        tm.assert_index_equal(result, expected)
+
+        # GH 17296: intersect two decreasing RangeIndexes
+        first = RangeIndex(10, -2, -2)
+        other = RangeIndex(5, -4, -1)
+        expected = first.astype(int).intersection(other.astype(int))
+        result = first.intersection(other).astype(int)
+        tm.assert_index_equal(result, expected)
+        # reversed
+        result = other.intersection(first).astype(int)
+        tm.assert_index_equal(result, expected)
 
         index = RangeIndex(5)