BUG - remove scaling multiplier from Period diff result

doc/source/whatsnew/v0.24.0.rst

@@ -1056,7 +1056,7 @@ from :class:`Period`, :class:`PeriodIndex`, and in some cases
 :class:`Timestamp`, :class:`DatetimeIndex` and :class:`TimedeltaIndex`.
 
 This usage is now deprecated.  Instead add or subtract integer multiples of
-the object's ``freq`` attribute (:issue:`21939`)
+the object's ``freq`` attribute (:issue:`21939`) / (:issue:`23878`)
 
 Previous Behavior:
 

pandas/_libs/tslibs/period.pyx

@@ -1685,7 +1685,7 @@ cdef class _Period(object):
                 if other.freq != self.freq:
                     msg = _DIFFERENT_FREQ.format(self.freqstr, other.freqstr)
                     raise IncompatibleFrequency(msg)
-                return (self.ordinal - other.ordinal) * self.freq
+                return (self.ordinal - other.ordinal) * type(self.freq)()
             elif getattr(other, '_typ', None) == 'periodindex':
                 # GH#21314 PeriodIndex - Period returns an object-index
                 # of DateOffset objects, for which we cannot use __neg__

pandas/tests/arithmetic/test_period.py

@@ -1085,3 +1085,21 @@ def test_pi_sub_period_nat(self):
         exp = pd.TimedeltaIndex([np.nan, np.nan, np.nan, np.nan], name='idx')
         tm.assert_index_equal(idx - pd.Period('NaT', freq='M'), exp)
         tm.assert_index_equal(pd.Period('NaT', freq='M') - idx, exp)
+
+
+class TestPeriodArithmetic(object):
+
+    @pytest.mark.parametrize('n', [1, 2, 3, 4])
+    @pytest.mark.parametrize('freq,expected', [
+        (pd.offsets.Second, 18489600),
+        (pd.offsets.Minute, 308160),
+        (pd.offsets.Hour, 5136),
+        (pd.offsets.Day, 214),
+        (pd.offsets.MonthEnd, 7),
+        (pd.offsets.YearEnd, 1),
+    ])
+    def test_period_diff(self, freq, expected, n):
+        # GH 23878
+        p1 = pd.Period('19910905', freq=freq(n))
+        p2 = pd.Period('19920406', freq=freq(n))
+        assert (p2 - p1) == freq(expected)