BUG: Period + np.timedelta64(nat) (#47196)

* BUG: Period + np.timedelta64(nat)

* GH ref

* test reversed subtraction raises

* parametrize over unit

Author: jbrockmendel

doc/source/whatsnew/v1.5.0.rst

@@ -828,6 +828,7 @@ Period
 - Bug in :meth:`Period.strftime` and :meth:`PeriodIndex.strftime`, directives ``%l`` and ``%u`` were giving wrong results (:issue:`46252`)
 - Bug in inferring an incorrect ``freq`` when passing a string to :class:`Period` microseconds that are a multiple of 1000 (:issue:`46811`)
 - Bug in constructing a :class:`Period` from a :class:`Timestamp` or ``np.datetime64`` object with non-zero nanoseconds and ``freq="ns"`` incorrectly truncating the nanoseconds (:issue:`46811`)
+- Bug in adding ``np.timedelta64("NaT", "ns")`` to a :class:`Period` with a timedelta-like freq incorrectly raising ``IncompatibleFrequency`` instead of returning ``NaT`` (:issue:`47196`)
 -
 
 Plotting

pandas/_libs/tslibs/period.pyx

@@ -50,6 +50,7 @@ from pandas._libs.tslibs.np_datetime cimport (
     check_dts_bounds,
     dt64_to_dtstruct,
     dtstruct_to_dt64,
+    get_timedelta64_value,
     npy_datetimestruct,
     npy_datetimestruct_to_datetime,
     pandas_datetime_to_datetimestruct,
@@ -1682,17 +1683,22 @@ cdef class _Period(PeriodMixin):
         cdef:
             int64_t inc
 
-        if is_tick_object(self.freq):
-            try:
-                inc = delta_to_nanoseconds(other, reso=self.freq._reso, round_ok=False)
-            except ValueError as err:
-                raise IncompatibleFrequency("Input cannot be converted to "
-                                            f"Period(freq={self.freqstr})") from err
-            # TODO: overflow-check here
-            ordinal = self.ordinal + inc
-            return Period(ordinal=ordinal, freq=self.freq)
-        raise IncompatibleFrequency("Input cannot be converted to "
-                                    f"Period(freq={self.freqstr})")
+        if not is_tick_object(self.freq):
+            raise IncompatibleFrequency("Input cannot be converted to "
+                                        f"Period(freq={self.freqstr})")
+
+        if util.is_timedelta64_object(other) and get_timedelta64_value(other) == NPY_NAT:
+            # i.e. np.timedelta64("nat")
+            return NaT
+
+        try:
+            inc = delta_to_nanoseconds(other, reso=self.freq._reso, round_ok=False)
+        except ValueError as err:
+            raise IncompatibleFrequency("Input cannot be converted to "
+                                        f"Period(freq={self.freqstr})") from err
+        # TODO: overflow-check here
+        ordinal = self.ordinal + inc
+        return Period(ordinal=ordinal, freq=self.freq)
 
     def _add_offset(self, other) -> "Period":
         # Non-Tick DateOffset other

pandas/tests/scalar/period/test_period.py

@@ -1187,6 +1187,19 @@ def test_comparison_numpy_zerodim_arr(self, zerodim_arr, expected):
 
 
 class TestArithmetic:
+    @pytest.mark.parametrize("unit", ["ns", "us", "ms", "s", "m"])
+    def test_add_sub_td64_nat(self, unit):
+        # GH#47196
+        per = Period("2022-06-01", "D")
+        nat = np.timedelta64("NaT", unit)
+
+        assert per + nat is NaT
+        assert nat + per is NaT
+        assert per - nat is NaT
+
+        with pytest.raises(TypeError, match="unsupported operand"):
+            nat - per
+
     def test_sub_delta(self):
         left, right = Period("2011", freq="A"), Period("2007", freq="A")
         result = left - right