Memory map rotated TIFF images at stored size

Tests/test_file_tiff.py

@@ -556,6 +556,27 @@ def test_exif_frames(self) -> None:
             im.seek(1)
             assert im.getexif()[273] == (1408, 1907)
 
+    @pytest.mark.parametrize(
+        "orientation, method",
+        (
+            (5, Image.Transpose.TRANSPOSE),
+            (6, Image.Transpose.ROTATE_270),
+            (7, Image.Transpose.TRANSVERSE),
+            (8, Image.Transpose.ROTATE_90),
+        ),
+    )
+    def test_orientation_mmap(
+        self, orientation: int, method: Image.Transpose, tmp_path: Path
+    ) -> None:
+        im = hopper("L").crop((0, 0, 128, 64))
+        filename = tmp_path / "temp.tif"
+        im.save(filename, tiffinfo={274: orientation})
+
+        with Image.open(filename) as reloaded:
+            assert reloaded.size == (64, 128)
+            reloaded.load()
+            assert_image_equal(reloaded, im.transpose(method))
+
     @pytest.mark.parametrize("mode", ("1", "L"))
     def test_photometric(self, mode: str, tmp_path: Path) -> None:
         filename = tmp_path / "temp.tif"

src/PIL/ImageFile.py

@@ -346,18 +346,19 @@ def load(self) -> Image.core.PixelAccess | None:
                     with open(self.filename) as fp:
                         self.map = mmap.mmap(fp.fileno(), 0, access=mmap.ACCESS_READ)
 
+                    size = getattr(self, "_tile_size", self.size)
                     if self.mode in {"L", "P"}:
                         pixelsize = 1
                     elif self.mode.startswith("I;16"):
                         pixelsize = 2
                     else:
                         pixelsize = 4
-                    stride = max(args[1], self.size[0] * pixelsize)
-                    if offset + self.size[1] * stride > self.map.size():
+                    stride = max(args[1], size[0] * pixelsize)
+                    if offset + size[1] * stride > self.map.size():
                         msg = "buffer is not large enough"
                         raise OSError(msg)
                     self.im = Image.core.map_buffer(
-                        self.map, self.size, decoder_name, offset, args
+                        self.map, size, decoder_name, offset, args
                     )
                     readonly = 1
                     # After trashing self.im,