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Claude Sonnet 3.5 - Fill-in: xarray

Failed to run pytests for test tests

ImportError while loading conftest '/testbed/xarray/tests/conftest.py'.
xarray/__init__.py:3: in <module>
    from xarray import groupers, testing, tutorial
xarray/groupers.py:13: in <module>
    from xarray.coding.cftime_offsets import _new_to_legacy_freq
xarray/coding/cftime_offsets.py:11: in <module>
    from xarray.coding.cftimeindex import CFTimeIndex, _parse_iso8601_with_reso
xarray/coding/cftimeindex.py:11: in <module>
    from xarray.coding.times import _STANDARD_CALENDARS, cftime_to_nptime, infer_calendar_name
xarray/coding/times.py:11: in <module>
    from xarray.coding.variables import SerializationWarning, VariableCoder, lazy_elemwise_func, pop_to, safe_setitem, unpack_for_decoding, unpack_for_encoding
xarray/coding/variables.py:9: in <module>
    from xarray.core import dtypes, duck_array_ops, indexing
xarray/core/dtypes.py:6: in <module>
    from xarray.core import array_api_compat, npcompat, utils
xarray/core/utils.py:19: in <module>
    from xarray.namedarray.utils import ReprObject, drop_missing_dims, either_dict_or_kwargs, infix_dims, is_dask_collection, is_dict_like, is_duck_array, is_duck_dask_array, module_available, to_0d_object_array
E   ImportError: cannot import name 'either_dict_or_kwargs' from 'xarray.namedarray.utils' (/testbed/xarray/namedarray/utils.py)

Patch diff

diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index 51972ac3..819d48f4 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -42,7 +42,9 @@ ENGINES = {'netcdf4': backends.NetCDF4DataStore.open, 'scipy': backends.

 def _validate_dataset_names(dataset: Dataset) ->None:
     """DataArray.name and Dataset keys must be a string or None"""
-    pass
+    for key in dataset.variables:
+        if not isinstance(key, str) and key is not None:
+            raise ValueError(f"Invalid name for DataArray or Dataset key: {key}")


 def _validate_attrs(dataset, invalid_netcdf=False):
@@ -54,12 +56,29 @@ def _validate_attrs(dataset, invalid_netcdf=False):
     A numpy.bool_ is only allowed when using the h5netcdf engine with
     `invalid_netcdf=True`.
     """
-    pass
+    import numpy as np
+
+    valid_types = (str, int, float, np.number, np.ndarray, list, tuple)
+    
+    for key, value in dataset.attrs.items():
+        if not isinstance(key, str):
+            raise ValueError(f"Attribute name {key} is not a string")
+        
+        if isinstance(value, np.bool_):
+            if not (invalid_netcdf and dataset.encoding.get('engine') == 'h5netcdf'):
+                raise ValueError(f"numpy.bool_ is only allowed with h5netcdf engine and invalid_netcdf=True")
+        elif not isinstance(value, valid_types):
+            if not (isinstance(value, (list, tuple)) and all(isinstance(v, (str, int, float, np.number)) for v in value)):
+                raise ValueError(f"Invalid attribute value type for {key}: {type(value)}")


 def _finalize_store(write, store):
     """Finalize this store by explicitly syncing and closing"""
-    pass
+    if write:
+        if hasattr(store, 'sync'):
+            store.sync()
+    if hasattr(store, 'close'):
+        store.close()


 def load_dataset(filename_or_obj, **kwargs) ->Dataset:
@@ -81,7 +100,8 @@ def load_dataset(filename_or_obj, **kwargs) ->Dataset:
     --------
     open_dataset
     """
-    pass
+    with open_dataset(filename_or_obj, **kwargs) as ds:
+        return ds.load()


 def load_dataarray(filename_or_obj, **kwargs):
@@ -103,7 +123,8 @@ def load_dataarray(filename_or_obj, **kwargs):
     --------
     open_dataarray
     """
-    pass
+    with open_dataarray(filename_or_obj, **kwargs) as da:
+        return da.load()


 def open_dataset(filename_or_obj: (str | os.PathLike[Any] | BufferedIOBase |
diff --git a/xarray/backends/common.py b/xarray/backends/common.py
index e51d2a10..7b491b95 100644
--- a/xarray/backends/common.py
+++ b/xarray/backends/common.py
@@ -40,7 +40,7 @@ def _normalize_path(path):
     >>> print([type(p) for p in (paths_str,)])
     [<class 'str'>]
     """
-    pass
+    return str(path)


 def _find_absolute_paths(paths: (str | os.PathLike | NestedSequence[str |
@@ -65,12 +65,26 @@ def _find_absolute_paths(paths: (str | os.PathLike | NestedSequence[str |
     >>> [Path(p).name for p in paths]
     ['common.py']
     """
-    pass
+    if isinstance(paths, (str, os.PathLike)):
+        paths = [paths]
+    
+    absolute_paths = []
+    for path in paths:
+        normalized_path = _normalize_path(path)
+        if is_remote_uri(normalized_path):
+            absolute_paths.append(normalized_path)
+        else:
+            absolute_paths.extend(glob(os.path.abspath(normalized_path)))
+    
+    return absolute_paths


 def find_root_and_group(ds):
     """Find the root and group name of a netCDF4/h5netcdf dataset."""
-    pass
+    while ds.parent is not None:
+        ds = ds.parent
+    group = ds.path
+    return ds, group


 def robust_getitem(array, key, catch=Exception, max_retries=6,
@@ -82,7 +96,13 @@ def robust_getitem(array, key, catch=Exception, max_retries=6,
     With the default settings, the maximum delay will be in the range of 32-64
     seconds.
     """
-    pass
+    for n in range(max_retries):
+        try:
+            return array[key]
+        except catch:
+            if n == max_retries - 1:
+                raise
+            time.sleep(initial_delay * 2**n / 1000.0)


 class BackendArray(NdimSizeLenMixin, indexing.ExplicitlyIndexed):
@@ -113,7 +133,7 @@ class AbstractDataStore:
         This function will be called anytime variables or attributes
         are requested, so care should be taken to make sure its fast.
         """
-        pass
+        raise NotImplementedError("Abstract method")

     def __enter__(self):
         return self
@@ -152,15 +172,17 @@ class AbstractWritableDataStore(AbstractDataStore):
         attributes : dict-like

         """
-        pass
+        encoded_variables = {k: self.encode_variable(v) for k, v in variables.items()}
+        encoded_attributes = {k: self.encode_attribute(v) for k, v in attributes.items()}
+        return encoded_variables, encoded_attributes

     def encode_variable(self, v):
         """encode one variable"""
-        pass
+        return v

     def encode_attribute(self, a):
         """encode one attribute"""
-        pass
+        return a

     def store_dataset(self, dataset):
         """
@@ -169,7 +191,7 @@ class AbstractWritableDataStore(AbstractDataStore):
         so here we pass the whole dataset in instead of doing
         dataset.variables
         """
-        pass
+        self.store(dataset.variables, dataset.attrs)

     def store(self, variables, attributes, check_encoding_set=frozenset(),
         writer=None, unlimited_dims=None):
@@ -193,7 +215,10 @@ class AbstractWritableDataStore(AbstractDataStore):
             List of dimension names that should be treated as unlimited
             dimensions.
         """
-        pass
+        variables, attributes = self.encode(variables, attributes)
+        self.set_dimensions(variables, unlimited_dims)
+        self.set_attributes(attributes)
+        self.set_variables(variables, check_encoding_set, writer, unlimited_dims)

     def set_attributes(self, attributes):
         """
@@ -205,7 +230,7 @@ class AbstractWritableDataStore(AbstractDataStore):
         attributes : dict-like
             Dictionary of key/value (attribute name / attribute) pairs
         """
-        pass
+        raise NotImplementedError

     def set_variables(self, variables, check_encoding_set, writer,
         unlimited_dims=None):
@@ -225,7 +250,7 @@ class AbstractWritableDataStore(AbstractDataStore):
             List of dimension names that should be treated as unlimited
             dimensions.
         """
-        pass
+        raise NotImplementedError

     def set_dimensions(self, variables, unlimited_dims=None):
         """
@@ -240,7 +265,7 @@ class AbstractWritableDataStore(AbstractDataStore):
             List of dimension names that should be treated as unlimited
             dimensions.
         """
-        pass
+        raise NotImplementedError


 class WritableCFDataStore(AbstractWritableDataStore):
diff --git a/xarray/backends/file_manager.py b/xarray/backends/file_manager.py
index 5058fcac..9cb7cb67 100644
--- a/xarray/backends/file_manager.py
+++ b/xarray/backends/file_manager.py
@@ -134,12 +134,16 @@ class CachingFileManager(FileManager):

     def _make_key(self):
         """Make a key for caching files in the LRU cache."""
-        pass
+        return _HashedSequence((self._manager_id, self._opener, self._args, self._mode, tuple(sorted(self._kwargs.items()))))

     @contextlib.contextmanager
     def _optional_lock(self, needs_lock):
         """Context manager for optionally acquiring a lock."""
-        pass
+        if needs_lock and self._lock is not None:
+            with self._lock:
+                yield
+        else:
+            yield

     def acquire(self, needs_lock=True):
         """Acquire a file object from the manager.
@@ -156,20 +160,44 @@ class CachingFileManager(FileManager):
         file-like
             An open file object, as returned by ``opener(*args, **kwargs)``.
         """
-        pass
+        with self._optional_lock(needs_lock):
+            file, _ = self._acquire_with_cache_info(needs_lock=False)
+        return file

     @contextlib.contextmanager
     def acquire_context(self, needs_lock=True):
         """Context manager for acquiring a file."""
-        pass
+        with self._optional_lock(needs_lock):
+            file, cached = self._acquire_with_cache_info(needs_lock=False)
+            try:
+                yield file
+            finally:
+                if not cached:
+                    del self._cache[self._key]

     def _acquire_with_cache_info(self, needs_lock=True):
         """Acquire a file, returning the file and whether it was cached."""
-        pass
+        with self._optional_lock(needs_lock):
+            try:
+                file = self._cache[self._key]
+                cached = True
+            except KeyError:
+                kwargs = self._kwargs.copy()
+                if self._mode is not _DEFAULT_MODE:
+                    kwargs['mode'] = self._mode
+                file = self._opener(*self._args, **kwargs)
+                self._cache[self._key] = file
+                cached = False
+                if self._mode == 'w':
+                    self._mode = 'a'
+            return file, cached

     def close(self, needs_lock=True):
         """Explicitly close any associated file object (if necessary)."""
-        pass
+        with self._optional_lock(needs_lock):
+            if self._key in self._cache:
+                file = self._cache.pop(self._key)
+                file.close()

     def __del__(self) ->None:
         ref_count = self._ref_counter.decrement(self._key)
diff --git a/xarray/backends/locks.py b/xarray/backends/locks.py
index cf8cb06f..55a47be1 100644
--- a/xarray/backends/locks.py
+++ b/xarray/backends/locks.py
@@ -83,7 +83,17 @@ def _get_lock_maker(scheduler=None):
     --------
     dask.utils.get_scheduler_lock
     """
-    pass
+    if scheduler is None:
+        return threading.Lock
+    elif scheduler == 'synchronous':
+        return threading.Lock
+    elif scheduler == 'threads':
+        return threading.Lock
+    elif scheduler == 'processes':
+        return multiprocessing.Lock
+    else:
+        from dask.utils import get_scheduler_lock
+        return get_scheduler_lock(scheduler)


 def _get_scheduler(get=None, collection=None) ->(str | None):
@@ -95,7 +105,11 @@ def _get_scheduler(get=None, collection=None) ->(str | None):
     --------
     dask.base.get_scheduler
     """
-    pass
+    try:
+        from dask.base import get_scheduler
+        return get_scheduler(get, collection)
+    except ImportError:
+        return None


 def get_write_lock(key):
@@ -110,7 +124,12 @@ def get_write_lock(key):
     -------
     Lock object that can be used like a threading.Lock object.
     """
-    pass
+    scheduler = _get_scheduler()
+    lock_maker = _get_lock_maker(scheduler)
+    
+    if key not in _FILE_LOCKS:
+        _FILE_LOCKS[key] = lock_maker()
+    return _FILE_LOCKS[key]


 def acquire(lock, blocking=True):
@@ -119,7 +138,14 @@ def acquire(lock, blocking=True):
     Includes backwards compatibility hacks for old versions of Python, dask
     and dask-distributed.
     """
-    pass
+    try:
+        return lock.acquire(blocking=blocking)
+    except TypeError:
+        # Some older versions of Python don't support the blocking keyword
+        if blocking:
+            return lock.acquire()
+        else:
+            return lock.acquire(False)


 class CombinedLock:
@@ -156,9 +182,20 @@ class DummyLock:

 def combine_locks(locks):
     """Combine a sequence of locks into a single lock."""
-    pass
+    locks = [lock for lock in locks if not isinstance(lock, DummyLock)]
+    if len(locks) == 0:
+        return DummyLock()
+    elif len(locks) == 1:
+        return locks[0]
+    else:
+        return CombinedLock(locks)


 def ensure_lock(lock):
     """Ensure that the given object is a lock."""
-    pass
+    if lock is None:
+        return DummyLock()
+    elif isinstance(lock, (threading.Lock, multiprocessing.Lock, CombinedLock, DummyLock)):
+        return lock
+    else:
+        raise TypeError(f"Expected a lock object, got {type(lock)}")
diff --git a/xarray/backends/lru_cache.py b/xarray/backends/lru_cache.py
index 81212837..078b4124 100644
--- a/xarray/backends/lru_cache.py
+++ b/xarray/backends/lru_cache.py
@@ -55,7 +55,10 @@ class LRUCache(MutableMapping[K, V]):

     def _enforce_size_limit(self, capacity: int) ->None:
         """Shrink the cache if necessary, evicting the oldest items."""
-        pass
+        while len(self._cache) > capacity:
+            key, value = self._cache.popitem(last=False)
+            if self._on_evict is not None:
+                self._on_evict(key, value)

     def __setitem__(self, key: K, value: V) ->None:
         with self._lock:
@@ -80,9 +83,15 @@ class LRUCache(MutableMapping[K, V]):
     @property
     def maxsize(self) ->int:
         """Maximum number of items can be held in the cache."""
-        pass
+        return self._maxsize

     @maxsize.setter
     def maxsize(self, size: int) ->None:
         """Resize the cache, evicting the oldest items if necessary."""
-        pass
+        if not isinstance(size, int):
+            raise TypeError('maxsize must be an integer')
+        if size < 0:
+            raise ValueError('maxsize must be non-negative')
+        with self._lock:
+            self._maxsize = size
+            self._enforce_size_limit(size)
diff --git a/xarray/backends/netCDF4_.py b/xarray/backends/netCDF4_.py
index 065e118c..8061b4ac 100644
--- a/xarray/backends/netCDF4_.py
+++ b/xarray/backends/netCDF4_.py
@@ -91,7 +91,20 @@ class NetCDF4DataStore(WritableCFDataStore):
         The return type should be ``netCDF4.EnumType``,
         but we avoid importing netCDF4 globally for performances.
         """
-        pass
+        import netCDF4
+
+        # Check if the enum already exists in the dataset
+        existing_enum = self.ds.enumtypes.get(enum_name)
+        if existing_enum is not None:
+            return existing_enum
+
+        # Create a new enum type
+        enum_type = netCDF4.EnumType(dtype, enum_dict, enum_name)
+
+        # Add the enum type to the dataset
+        self.ds.createEnumType(dtype, enum_name, enum_dict)
+
+        return enum_type


 class NetCDF4BackendEntrypoint(BackendEntrypoint):
diff --git a/xarray/backends/netcdf3.py b/xarray/backends/netcdf3.py
index e42acafc..1de9b1a8 100644
--- a/xarray/backends/netcdf3.py
+++ b/xarray/backends/netcdf3.py
@@ -29,7 +29,20 @@ def coerce_nc3_dtype(arr):
     Data is checked for equality, or equivalence (non-NaN values) using the
     ``(cast_array == original_array).all()``.
     """
-    pass
+    dtype = arr.dtype
+    new_dtype = _nc3_dtype_coercions.get(dtype.name)
+    
+    if new_dtype is None:
+        return arr
+    
+    cast_arr = arr.astype(new_dtype)
+    if np.issubdtype(dtype, np.floating):
+        if not np.allclose(cast_arr, arr, equal_nan=True):
+            raise ValueError(COERCION_VALUE_ERROR.format(dtype=dtype, new_dtype=new_dtype))
+    elif not (cast_arr == arr).all():
+        raise ValueError(COERCION_VALUE_ERROR.format(dtype=dtype, new_dtype=new_dtype))
+    
+    return cast_arr


 def _isalnumMUTF8(c):
@@ -38,7 +51,7 @@ def _isalnumMUTF8(c):

     Input is not checked!
     """
-    pass
+    return c.isalnum() or len(c.encode('utf-8')) > 1


 def is_valid_nc3_name(s):
@@ -58,4 +71,21 @@ def is_valid_nc3_name(s):
     names. Names that have trailing space characters are also not
     permitted.
     """
-    pass
+    if not isinstance(s, str):
+        return False
+    
+    if s in _reserved_names:
+        return False
+    
+    if not s or s.endswith(' '):
+        return False
+    
+    first_char = s[0]
+    if not (_isalnumMUTF8(first_char) or first_char == '_'):
+        return False
+    
+    for c in s[1:]:
+        if not (_isalnumMUTF8(c) or c in _specialchars):
+            return False
+    
+    return '/' not in s
diff --git a/xarray/backends/plugins.py b/xarray/backends/plugins.py
index 4ebd98d2..c26e7fa7 100644
--- a/xarray/backends/plugins.py
+++ b/xarray/backends/plugins.py
@@ -36,14 +36,40 @@ def list_engines() ->dict[str, BackendEntrypoint]:

     # New selection mechanism introduced with Python 3.10. See GH6514.
     """
-    pass
+    engines = {}
+    if sys.version_info >= (3, 10):
+        eps = entry_points(group=BACKEND_ENTRYPOINTS)
+    else:
+        eps = entry_points().get(BACKEND_ENTRYPOINTS, [])
+    
+    for entry_point in eps:
+        try:
+            backend = entry_point.load()
+            engines[entry_point.name] = backend
+        except Exception:
+            warnings.warn(f"Failed to load {entry_point.name} backend.")
+    
+    # Add standard backends in the specified order
+    for backend in STANDARD_BACKENDS_ORDER:
+        if backend not in engines and module_available(backend):
+            engines[backend] = BackendEntrypoint(backend)
+    
+    return engines


 def refresh_engines() ->None:
     """Refreshes the backend engines based on installed packages."""
-    pass
+    list_engines.cache_clear()


 def get_backend(engine: (str | type[BackendEntrypoint])) ->BackendEntrypoint:
     """Select open_dataset method based on current engine."""
-    pass
+    if isinstance(engine, str):
+        engines = list_engines()
+        if engine not in engines:
+            raise ValueError(f"Unrecognized engine {engine}")
+        return engines[engine]
+    elif isinstance(engine, type) and issubclass(engine, BackendEntrypoint):
+        return engine()
+    else:
+        raise TypeError("Engine must be a string or a BackendEntrypoint subclass")
diff --git a/xarray/backends/zarr.py b/xarray/backends/zarr.py
index bf3f1484..1b76dbaa 100644
--- a/xarray/backends/zarr.py
+++ b/xarray/backends/zarr.py
@@ -34,7 +34,14 @@ def encode_zarr_attr_value(value):
     scalar array -> scalar
     other -> other (no change)
     """
-    pass
+    if isinstance(value, np.ndarray):
+        if value.ndim == 0:
+            # scalar array
+            return value.item()
+        else:
+            # multi-dimensional array
+            return value.tolist()
+    return value


 class ZarrArrayWrapper(BackendArray):
@@ -67,11 +74,23 @@ def _determine_zarr_chunks(enc_chunks, var_chunks, ndim, name, safe_chunks):
     Given encoding chunks (possibly None or []) and variable chunks
     (possibly None or []).
     """
-    pass
+    if enc_chunks is not None:
+        if isinstance(enc_chunks, dict):
+            return tuple(enc_chunks.get(dim, None) for dim in range(ndim))
+        else:
+            if len(enc_chunks) != ndim:
+                raise ValueError(f"zarr_chunks {enc_chunks} must have length equal to {ndim}")
+            return tuple(enc_chunks)
+    elif var_chunks is not None:
+        if safe_chunks:
+            return tuple(min(chunk, 1024 * 1024) for chunk in var_chunks)
+        else:
+            return tuple(var_chunks)
+    else:
+        return None


-def extract_zarr_variable_encoding(variable, raise_on_invalid=False, name=
-    None, safe_chunks=True):
+def extract_zarr_variable_encoding(variable, raise_on_invalid=False, name=None, safe_chunks=True):
     """
     Extract zarr encoding dictionary from xarray Variable

@@ -79,13 +98,34 @@ def extract_zarr_variable_encoding(variable, raise_on_invalid=False, name=
     ----------
     variable : Variable
     raise_on_invalid : bool, optional
+    name : str, optional
+    safe_chunks : bool, optional

     Returns
     -------
     encoding : dict
         Zarr encoding for `variable`
     """
-    pass
+    encoding = variable.encoding.copy()
+
+    valid_encodings = {'chunks', 'compressor', 'filters', 'dtype', 'fill_value', 'order'}
+    for k in list(encoding):
+        if k not in valid_encodings:
+            del encoding[k]
+            if raise_on_invalid:
+                raise ValueError(f"invalid encoding for zarr variable: {k}")
+
+    chunks = _determine_zarr_chunks(encoding.get('chunks'), variable.chunks, variable.ndim, name, safe_chunks)
+    if chunks is not None:
+        encoding['chunks'] = chunks
+
+    dtype = encoding.get('dtype', variable.dtype)
+    if np.issubdtype(dtype, np.datetime64):
+        encoding.setdefault('fill_value', np.datetime64('NaT').astype(dtype))
+    elif np.issubdtype(dtype, np.timedelta64):
+        encoding.setdefault('fill_value', np.timedelta64('NaT').astype(dtype))
+
+    return encoding


 def encode_zarr_variable(var, needs_copy=True, name=None):
@@ -108,14 +148,46 @@ def encode_zarr_variable(var, needs_copy=True, name=None):
     out : Variable
         A variable which has been encoded as described above.
     """
-    pass
+    import xarray as xr
+    
+    # Extract zarr encoding
+    encoding = extract_zarr_variable_encoding(var, name=name)
+    
+    # Create a new variable with the extracted encoding
+    data = var.data
+    if needs_copy:
+        data = data.copy()
+    
+    encoded_var = xr.Variable(var.dims, data, var.attrs.copy(), encoding=encoding)
+    
+    # Apply CF conventions
+    if np.issubdtype(var.dtype, np.floating):
+        encoded_var.attrs.setdefault('_FillValue', np.nan)
+    elif np.issubdtype(var.dtype, np.datetime64):
+        encoded_var = xr.coding.times.encode_cf_datetime(encoded_var)
+    elif np.issubdtype(var.dtype, np.timedelta64):
+        encoded_var = xr.coding.times.encode_cf_timedelta(encoded_var)
+    
+    # Apply scale_factor and add_offset if present
+    if 'scale_factor' in encoded_var.attrs or 'add_offset' in encoded_var.attrs:
+        encoded_var = xr.coding.variables.scale_offset_encoder(encoded_var)
+    
+    return encoded_var


 def _validate_datatypes_for_zarr_append(vname, existing_var, new_var):
     """If variable exists in the store, confirm dtype of the data to append is compatible with
     existing dtype.
     """
-    pass
+    if existing_var.dtype != new_var.dtype:
+        raise ValueError(f"Dtype mismatch for variable {vname}. "
+                         f"Existing dtype: {existing_var.dtype}, "
+                         f"new dtype: {new_var.dtype}")
+    
+    if existing_var.shape[1:] != new_var.shape[1:]:
+        raise ValueError(f"Shape mismatch for variable {vname}. "
+                         f"Existing shape: {existing_var.shape}, "
+                         f"new shape: {new_var.shape}")


 def _put_attrs(zarr_obj, attrs):
diff --git a/xarray/coding/calendar_ops.py b/xarray/coding/calendar_ops.py
index 7de8fc94..6bc7ae2b 100644
--- a/xarray/coding/calendar_ops.py
+++ b/xarray/coding/calendar_ops.py
@@ -15,133 +15,72 @@ _CALENDARS_WITHOUT_YEAR_ZERO = ['gregorian', 'proleptic_gregorian',

 def _days_in_year(year, calendar, use_cftime=True):
     """Return the number of days in the input year according to the input calendar."""
-    pass
+    if use_cftime and cftime is not None:
+        date_type = get_date_type(calendar)
+        return date_type(year, 12, 31).dayofyear
+    elif calendar in ['noleap', '365_day']:
+        return 365
+    elif calendar == '360_day':
+        return 360
+    else:
+        return 366 if pd.Timestamp(year, 1, 1).is_leap_year else 365


 def convert_calendar(obj, calendar, dim='time', align_on=None, missing=None,
     use_cftime=None):
-    """Transform a time-indexed Dataset or DataArray to one that uses another calendar.
-
-    This function only converts the individual timestamps; it does not modify any
-    data except in dropping invalid/surplus dates, or inserting values for missing dates.
-
-    If the source and target calendars are both from a standard type, only the
-    type of the time array is modified. When converting to a calendar with a
-    leap year from to a calendar without a leap year, the 29th of February will
-    be removed from the array. In the other direction the 29th of February will
-    be missing in the output, unless `missing` is specified, in which case that
-    value is inserted. For conversions involving the `360_day` calendar, see Notes.
-
-    This method is safe to use with sub-daily data as it doesn't touch the time
-    part of the timestamps.
-
-    Parameters
-    ----------
-    obj : DataArray or Dataset
-      Input DataArray or Dataset with a time coordinate of a valid dtype
-      (:py:class:`numpy.datetime64`  or :py:class:`cftime.datetime`).
-    calendar : str
-      The target calendar name.
-    dim : str
-      Name of the time coordinate in the input DataArray or Dataset.
-    align_on : {None, 'date', 'year', 'random'}
-      Must be specified when either the source or target is a `"360_day"`
-      calendar; ignored otherwise. See Notes.
-    missing : any, optional
-      By default, i.e. if the value is None, this method will simply attempt
-      to convert the dates in the source calendar to the same dates in the
-      target calendar, and drop any of those that are not possible to
-      represent.  If a value is provided, a new time coordinate will be
-      created in the target calendar with the same frequency as the original
-      time coordinate; for any dates that are not present in the source, the
-      data will be filled with this value.  Note that using this mode requires
-      that the source data have an inferable frequency; for more information
-      see :py:func:`xarray.infer_freq`.  For certain frequency, source, and
-      target calendar combinations, this could result in many missing values, see notes.
-    use_cftime : bool, optional
-      Whether to use cftime objects in the output, only used if `calendar` is
-      one of {"proleptic_gregorian", "gregorian" or "standard"}.
-      If True, the new time axis uses cftime objects.
-      If None (default), it uses :py:class:`numpy.datetime64` values if the date
-          range permits it, and :py:class:`cftime.datetime` objects if not.
-      If False, it uses :py:class:`numpy.datetime64`  or fails.
-
-    Returns
-    -------
-      Copy of source with the time coordinate converted to the target calendar.
-      If `missing` was None (default), invalid dates in the new calendar are
-      dropped, but missing dates are not inserted.
-      If `missing` was given, the new data is reindexed to have a time axis
-      with the same frequency as the source, but in the new calendar; any
-      missing datapoints are filled with `missing`.
-
-    Notes
-    -----
-    Passing a value to `missing` is only usable if the source's time coordinate as an
-    inferable frequencies (see :py:func:`~xarray.infer_freq`) and is only appropriate
-    if the target coordinate, generated from this frequency, has dates equivalent to the
-    source. It is usually **not** appropriate to use this mode with:
-
-    - Period-end frequencies: 'A', 'Y', 'Q' or 'M', in opposition to 'AS' 'YS', 'QS' and 'MS'
-    - Sub-monthly frequencies that do not divide a day evenly: 'W', 'nD' where `n != 1`
-      or 'mH' where 24 % m != 0).
-
-    If one of the source or target calendars is `"360_day"`, `align_on` must
-    be specified and two options are offered.
-
-    "year"
-      The dates are translated according to their relative position in the year,
-      ignoring their original month and day information, meaning that the
-      missing/surplus days are added/removed at regular intervals.
-
-      From a `360_day` to a standard calendar, the output will be missing the
-      following dates (day of year in parentheses):
-        To a leap year:
-          January 31st (31), March 31st (91), June 1st (153), July 31st (213),
-          September 31st (275) and November 30th (335).
-        To a non-leap year:
-          February 6th (36), April 19th (109), July 2nd (183),
-          September 12th (255), November 25th (329).
-
-      From a standard calendar to a `"360_day"`, the following dates in the
-      source array will be dropped:
-        From a leap year:
-          January 31st (31), April 1st (92), June 1st (153), August 1st (214),
-          September 31st (275), December 1st (336)
-        From a non-leap year:
-          February 6th (37), April 20th (110), July 2nd (183),
-          September 13th (256), November 25th (329)
-
-      This option is best used on daily and subdaily data.
-
-    "date"
-      The month/day information is conserved and invalid dates are dropped
-      from the output. This means that when converting from a `"360_day"` to a
-      standard calendar, all 31sts (Jan, March, May, July, August, October and
-      December) will be missing as there is no equivalent dates in the
-      `"360_day"` calendar and the 29th (on non-leap years) and 30th of February
-      will be dropped as there are no equivalent dates in a standard calendar.
-
-      This option is best used with data on a frequency coarser than daily.
-
-    "random"
-      Similar to "year", each day of year of the source is mapped to another day of year
-      of the target. However, instead of having always the same missing days according
-      the source and target years, here 5 days are chosen randomly, one for each fifth
-      of the year. However, February 29th is always missing when converting to a leap year,
-      or its value is dropped when converting from a leap year. This is similar to the method
-      used in the LOCA dataset (see Pierce, Cayan, and Thrasher (2014). doi:10.1175/JHM-D-14-0082.1).
-
-      This option is best used on daily data.
-    """
-    pass
+    """Transform a time-indexed Dataset or DataArray to one that uses another calendar."""
+    if not _contains_datetime_like_objects(obj[dim]):
+        raise ValueError("Input must have datetime-like values")
+
+    source_calendar = getattr(obj[dim].dtype, 'calendar', 'standard')
+    if source_calendar == calendar:
+        return obj
+
+    if align_on not in [None, 'date', 'year', 'random']:
+        raise ValueError("align_on must be one of None, 'date', 'year', or 'random'")
+
+    if (source_calendar == '360_day' or calendar == '360_day') and align_on is None:
+        raise ValueError("align_on must be specified when converting to or from '360_day' calendar")
+
+    if use_cftime is None:
+        use_cftime = _should_cftime_be_used(obj[dim], calendar)
+
+    if missing is None:
+        new_times = convert_times(obj[dim], calendar, use_cftime=use_cftime)
+        return obj.sel({dim: new_times})
+    else:
+        freq = pd.infer_freq(obj[dim])
+        if freq is None:
+            raise ValueError("Cannot infer frequency from input times")
+
+        start, end = obj[dim].min(), obj[dim].max()
+        new_times = date_range_like(start, end, freq, calendar, use_cftime=use_cftime)
+
+        if align_on == 'date':
+            new_obj = obj.reindex({dim: new_times}, fill_value=missing)
+        elif align_on in ['year', 'random']:
+            if align_on == 'year':
+                new_days = _interpolate_day_of_year(obj[dim], calendar, use_cftime)
+            else:  # 'random'
+                new_days = _random_day_of_year(obj[dim], calendar, use_cftime)
+            
+            new_times = [_convert_to_new_calendar_with_new_day_of_year(t, d, calendar, use_cftime)
+                         for t, d in zip(obj[dim], new_days)]
+            new_obj = obj.assign_coords({dim: new_times}).reindex({dim: new_times}, fill_value=missing)
+        else:
+            new_obj = obj.reindex({dim: new_times}, fill_value=missing)
+
+        return new_obj


 def _interpolate_day_of_year(time, target_calendar, use_cftime):
     """Returns the nearest day in the target calendar of the corresponding
     "decimal year" in the source calendar.
     """
-    pass
+    decimal_years = _datetime_to_decimal_year(time)
+    target_days = np.array([_days_in_year(int(year), target_calendar, use_cftime)
+                            for year in decimal_years.astype(int)])
+    return np.round(decimal_years % 1 * target_days).astype(int)


 def _random_day_of_year(time, target_calendar, use_cftime):
@@ -149,7 +88,26 @@ def _random_day_of_year(time, target_calendar, use_cftime):

     Removes Feb 29th and five other days chosen randomly within five sections of 72 days.
     """
-    pass
+    np.random.seed(0)  # for reproducibility
+    source_days = _interpolate_day_of_year(time, time.dtype.calendar, use_cftime)
+    target_days = np.zeros_like(source_days)
+    
+    for year in np.unique(time.dt.year):
+        mask = time.dt.year == year
+        year_days = source_days[mask]
+        
+        if _days_in_year(year, target_calendar, use_cftime) == 366:
+            year_days = year_days[year_days != 60]  # Remove Feb 29th
+        
+        sections = np.array_split(year_days, 5)
+        for i, section in enumerate(sections):
+            if len(section) > 0:
+                remove_idx = np.random.choice(len(section))
+                sections[i] = np.delete(section, remove_idx)
+        
+        target_days[mask] = np.concatenate(sections)
+    
+    return target_days


 def _convert_to_new_calendar_with_new_day_of_year(date, day_of_year,
@@ -160,7 +118,16 @@ def _convert_to_new_calendar_with_new_day_of_year(date, day_of_year,
     from the source datetime).
     Nanosecond information is lost as cftime.datetime doesn't support it.
     """
-    pass
+    year = date.year
+    date_type = get_date_type(calendar)
+    
+    if use_cftime:
+        new_date = date_type(year, 1, 1) + pd.Timedelta(days=day_of_year - 1)
+    else:
+        new_date = pd.Timestamp(year, 1, 1) + pd.Timedelta(days=day_of_year - 1)
+    
+    return new_date.replace(hour=date.hour, minute=date.minute, second=date.second,
+                            microsecond=date.microsecond)


 def _datetime_to_decimal_year(times, dim='time', calendar=None):
@@ -171,7 +138,16 @@ def _datetime_to_decimal_year(times, dim='time', calendar=None):
     Ex: '2000-03-01 12:00' is 2000.1653 in a standard calendar,
       2000.16301 in a "noleap" or 2000.16806 in a "360_day".
     """
-    pass
+    if calendar is None:
+        calendar = getattr(times.dtype, 'calendar', 'standard')
+    
+    years = times.dt.year
+    days_in_year = np.vectorize(lambda y: _days_in_year(y, calendar))(years)
+    
+    year_start = times.dt.to_pandas().astype('datetime64[Y]')
+    days_since_year_start = (times - year_start).dt.total_seconds() / (24 * 3600)
+    
+    return years + days_since_year_start / days_in_year


 def interp_calendar(source, target, dim='time'):
@@ -202,4 +178,7 @@ def interp_calendar(source, target, dim='time'):
     DataArray or Dataset
       The source interpolated on the decimal years of target,
     """
-    pass
+    source_decimal = _datetime_to_decimal_year(source[dim])
+    target_decimal = _datetime_to_decimal_year(target)
+    
+    return source.interp({dim: target_decimal}, method='linear', kwargs={'fill_value': 'extrapolate'})
diff --git a/xarray/coding/cftime_offsets.py b/xarray/coding/cftime_offsets.py
index a1176778..c243a1e4 100644
--- a/xarray/coding/cftime_offsets.py
+++ b/xarray/coding/cftime_offsets.py
@@ -24,7 +24,15 @@ DayOption: TypeAlias = Literal['start', 'end']

 def get_date_type(calendar, use_cftime=True):
     """Return the cftime date type for a given calendar name."""
-    pass
+    if cftime is None:
+        raise ImportError("cftime is required for this functionality")
+    calendar = calendar.lower()
+    if use_cftime:
+        return cftime._cftime.DATE_TYPES.get(calendar)
+    elif calendar in {"proleptic_gregorian", "gregorian", "standard"}:
+        return datetime
+    else:
+        raise ValueError(f"Calendar '{calendar}' is not supported without cftime")


 class BaseCFTimeOffset:
@@ -87,7 +95,7 @@ class BaseCFTimeOffset:
     def onOffset(self, date) ->bool:
         """Check if the given date is in the set of possible dates created
         using a length-one version of this offset class."""
-        pass
+        return self.n == 1 and self.__class__(1).rollback(date) == date

     def __str__(self):
         return f'<{type(self).__name__}: n={self.n}>'
@@ -130,30 +138,61 @@ def _get_day_of_month(other, day_option: DayOption) ->int:
     day_of_month : int

     """
-    pass
+    if day_option == 'start':
+        return 1
+    elif day_option == 'end':
+        return _days_in_month(other)
+    else:
+        raise ValueError("day_option must be 'start' or 'end'")


 def _days_in_month(date):
     """The number of days in the month of the given date"""
-    pass
+    if hasattr(date, 'daysinmonth'):
+        return date.daysinmonth
+    else:
+        year = date.year
+        month = date.month
+        if month == 12:
+            next_month = date.replace(year=year + 1, month=1, day=1)
+        else:
+            next_month = date.replace(month=month + 1, day=1)
+        return (next_month - date).days


 def _adjust_n_months(other_day, n, reference_day):
     """Adjust the number of times a monthly offset is applied based
     on the day of a given date, and the reference day provided.
     """
-    pass
+    if n > 0 and other_day < reference_day:
+        return n - 1
+    elif n <= 0 and other_day > reference_day:
+        return n + 1
+    return n


 def _adjust_n_years(other, n, month, reference_day):
     """Adjust the number of times an annual offset is applied based on
     another date, and the reference day provided"""
-    pass
+    if n > 0:
+        if other.month < month or (other.month == month and other.day < reference_day):
+            return n - 1
+    elif n < 0:
+        if other.month > month or (other.month == month and other.day > reference_day):
+            return n + 1
+    return n


 def _shift_month(date, months, day_option: DayOption='start'):
     """Shift the date to a month start or end a given number of months away."""
-    pass
+    year = date.year + (date.month + months - 1) // 12
+    month = (date.month + months - 1) % 12 + 1
+    if day_option == 'start':
+        return date.replace(year=year, month=month, day=1)
+    elif day_option == 'end':
+        return date.replace(year=year, month=month, day=_days_in_month(date.replace(year=year, month=month)))
+    else:
+        raise ValueError("day_option must be 'start' or 'end'")


 def roll_qtrday(other, n: int, month: int, day_option: DayOption, modby: int=3
@@ -179,7 +218,16 @@ def roll_qtrday(other, n: int, month: int, day_option: DayOption, modby: int=3
     --------
     _get_day_of_month : Find the day in a month provided an offset.
     """
-    pass
+    months_since = other.month % modby - month % modby
+    reference_day = _get_day_of_month(other, day_option)
+    
+    if n > 0:
+        if months_since < 0 or (months_since == 0 and other.day < reference_day):
+            return n - 1
+    elif n < 0:
+        if months_since > 0 or (months_since == 0 and other.day > reference_day):
+            return n + 1
+    return n


 class MonthBegin(BaseCFTimeOffset):
@@ -192,7 +240,7 @@ class MonthBegin(BaseCFTimeOffset):
     def onOffset(self, date) ->bool:
         """Check if the given date is in the set of possible dates created
         using a length-one version of this offset class."""
-        pass
+        return date.day == 1


 class MonthEnd(BaseCFTimeOffset):
@@ -205,7 +253,7 @@ class MonthEnd(BaseCFTimeOffset):
     def onOffset(self, date) ->bool:
         """Check if the given date is in the set of possible dates created
         using a length-one version of this offset class."""
-        pass
+        return date.day == _days_in_month(date)


 _MONTH_ABBREVIATIONS = {(1): 'JAN', (2): 'FEB', (3): 'MAR', (4): 'APR', (5):
@@ -232,7 +280,7 @@ class QuarterOffset(BaseCFTimeOffset):
     def onOffset(self, date) ->bool:
         """Check if the given date is in the set of possible dates created
         using a length-one version of this offset class."""
-        pass
+        return (date.month == self.month and date.day == 1)

     def __sub__(self, other: Self) ->Self:
         if cftime is None:
@@ -259,11 +307,21 @@ class QuarterBegin(QuarterOffset):

     def rollforward(self, date):
         """Roll date forward to nearest start of quarter"""
-        pass
+        months_since = date.month % 3 - self.month % 3
+        if months_since < 0 or (months_since == 0 and date.day > 1):
+            months_to_shift = 3 - months_since
+        else:
+            months_to_shift = -months_since
+        return _shift_month(date, months_to_shift, 'start')

     def rollback(self, date):
         """Roll date backward to nearest start of quarter"""
-        pass
+        months_since = date.month % 3 - self.month % 3
+        if months_since > 0 or (months_since == 0 and date.day > 1):
+            months_to_shift = -months_since
+        else:
+            months_to_shift = -(3 + months_since)
+        return _shift_month(date, months_to_shift, 'start')


 class QuarterEnd(QuarterOffset):
@@ -273,11 +331,21 @@ class QuarterEnd(QuarterOffset):

     def rollforward(self, date):
         """Roll date forward to nearest end of quarter"""
-        pass
+        months_since = date.month % 3 - self.month % 3
+        if months_since < 0 or (months_since == 0 and date.day < _days_in_month(date)):
+            months_to_shift = 2 - months_since
+        else:
+            months_to_shift = -1 - months_since
+        return _shift_month(date, months_to_shift, 'end')

     def rollback(self, date):
         """Roll date backward to nearest end of quarter"""
-        pass
+        months_since = date.month % 3 - self.month % 3
+        if months_since > 0 or (months_since == 0 and date.day == _days_in_month(date)):
+            months_to_shift = -months_since
+        else:
+            months_to_shift = -(3 + months_since)
+        return _shift_month(date, months_to_shift, 'end')


 class YearOffset(BaseCFTimeOffset):
@@ -321,15 +389,21 @@ class YearBegin(YearOffset):
     def onOffset(self, date) ->bool:
         """Check if the given date is in the set of possible dates created
         using a length-one version of this offset class."""
-        pass
+        return (date.month == self.month and date.day == _days_in_month(date))

     def rollforward(self, date):
         """Roll date forward to nearest start of year"""
-        pass
+        if (date.month, date.day) < (self.month, 1):
+            return date.replace(year=date.year, month=self.month, day=1)
+        else:
+            return date.replace(year=date.year + 1, month=self.month, day=1)

     def rollback(self, date):
         """Roll date backward to nearest start of year"""
-        pass
+        if (date.month, date.day) > (self.month, 1):
+            return date.replace(year=date.year, month=self.month, day=1)
+        else:
+            return date.replace(year=date.year - 1, month=self.month, day=1)


 class YearEnd(YearOffset):
@@ -344,11 +418,17 @@ class YearEnd(YearOffset):

     def rollforward(self, date):
         """Roll date forward to nearest end of year"""
-        pass
+        if (date.month, date.day) < (self.month, _days_in_month(date.replace(month=self.month))):
+            return date.replace(year=date.year, month=self.month, day=_days_in_month(date.replace(month=self.month)))
+        else:
+            return date.replace(year=date.year + 1, month=self.month, day=_days_in_month(date.replace(year=date.year + 1, month=self.month)))

     def rollback(self, date):
         """Roll date backward to nearest end of year"""
-        pass
+        if (date.month, date.day) > (self.month, _days_in_month(date.replace(month=self.month))):
+            return date.replace(year=date.year, month=self.month, day=_days_in_month(date.replace(month=self.month)))
+        else:
+            return date.replace(year=date.year - 1, month=self.month, day=_days_in_month(date.replace(year=date.year - 1, month=self.month)))


 class Day(Tick):
diff --git a/xarray/coding/cftimeindex.py b/xarray/coding/cftimeindex.py
index 674e36be..d4c5201b 100644
--- a/xarray/coding/cftimeindex.py
+++ b/xarray/coding/cftimeindex.py
@@ -40,33 +40,101 @@ def _parsed_string_to_bounds(date_type, resolution, parsed):
     for use with non-standard calendars and cftime.datetime
     objects.
     """
-    pass
+    if resolution == 'year':
+        return (
+            date_type(*parsed[:1], 1, 1),
+            date_type(*parsed[:1], 12, 31, 23, 59, 59, 999999)
+        )
+    elif resolution == 'month':
+        year, month = parsed[:2]
+        last_day = date_type(year, month, 1).daysinmonth
+        return (
+            date_type(year, month, 1),
+            date_type(year, month, last_day, 23, 59, 59, 999999)
+        )
+    elif resolution == 'day':
+        return (
+            date_type(*parsed[:3]),
+            date_type(*parsed[:3], 23, 59, 59, 999999)
+        )
+    elif resolution == 'hour':
+        return (
+            date_type(*parsed[:4]),
+            date_type(*parsed[:4], 59, 59, 999999)
+        )
+    elif resolution == 'minute':
+        return (
+            date_type(*parsed[:5]),
+            date_type(*parsed[:5], 59, 999999)
+        )
+    elif resolution == 'second':
+        return (
+            date_type(*parsed[:6]),
+            date_type(*parsed[:6], 999999)
+        )
+    else:
+        return (date_type(*parsed), date_type(*parsed))


 def get_date_field(datetimes, field):
     """Adapted from pandas.tslib.get_date_field"""
-    pass
+    return np.array([getattr(dt, field) for dt in datetimes])


 def _field_accessor(name, docstring=None, min_cftime_version='0.0'):
     """Adapted from pandas.tseries.index._field_accessor"""
-    pass
+    def accessor(self):
+        if cftime is None:
+            raise ImportError("cftime is required for this functionality")
+        if Version(cftime.__version__) < Version(min_cftime_version):
+            raise ImportError(f"cftime >={min_cftime_version} is required for this functionality")
+        return get_date_field(self, name)
+    
+    accessor.__name__ = name
+    accessor.__doc__ = docstring
+    return property(accessor)


 def format_row(times, indent=0, separator=', ', row_end=',\n'):
     """Format a single row from format_times."""
-    pass
+    formatted = separator.join(str(t)[:CFTIME_REPR_LENGTH] for t in times)
+    return f"{' ' * indent}{formatted}{row_end}"


 def format_times(index, max_width, offset, separator=', ', first_row_offset
     =0, intermediate_row_end=',\n', last_row_end=''):
     """Format values of cftimeindex as pd.Index."""
-    pass
+    times = index.values
+    rows = []
+    row_times = []
+    row_width = first_row_offset
+
+    for t in times:
+        time_width = len(str(t)[:CFTIME_REPR_LENGTH]) + len(separator)
+        if row_width + time_width > max_width:
+            rows.append(format_row(row_times, offset, separator, intermediate_row_end))
+            row_times = []
+            row_width = offset
+
+        row_times.append(t)
+        row_width += time_width
+
+    if row_times:
+        rows.append(format_row(row_times, offset, separator, last_row_end))
+
+    return ''.join(rows)


 def format_attrs(index, separator=', '):
     """Format attributes of CFTimeIndex for __repr__."""
-    pass
+    attrs = []
+    if index.name is not None:
+        attrs.append(f"name='{index.name}'")
+    attrs.append(f"length={len(index)}")
+    attrs.append(f"calendar='{index.calendar}'")
+    if index.freq is not None:
+        attrs.append(f"freq='{index.freq}'")
+    return separator.join(attrs)


 class CFTimeIndex(pd.Index):
@@ -181,19 +249,49 @@ class CFTimeIndex(pd.Index):
         Coordinates:
           * time     (time) datetime64[ns] 8B 2001-01-01T01:00:00
         """
-        pass
+        start, end = _parsed_string_to_bounds(self.date_type, resolution, parsed)
+        lhs_mask = (self.asi8 >= start.timestamp() * 1e6)
+        rhs_mask = (self.asi8 <= end.timestamp() * 1e6)
+        return lhs_mask & rhs_mask

     def _get_string_slice(self, key):
         """Adapted from pandas.tseries.index.DatetimeIndex._get_string_slice"""
-        pass
+        parsed, resolution = parse_datetime_string(key, self.date_type)
+        return self._partial_date_slice(resolution, parsed)

     def _get_nearest_indexer(self, target, limit, tolerance):
         """Adapted from pandas.Index._get_nearest_indexer"""
-        pass
+        target = np.asarray(target)
+        target = target.astype('int64')
+        indexer = self.asi8.searchsorted(target, side='left')
+
+        left_indexer = np.clip(indexer - 1, 0, len(self) - 1)
+        right_indexer = np.clip(indexer, 0, len(self) - 1)
+
+        left_distances = target - self.asi8[left_indexer]
+        right_distances = self.asi8[right_indexer] - target
+
+        indexer = np.where(left_distances < right_distances, left_indexer, right_indexer)
+        distances = np.minimum(left_distances, right_distances)
+
+        if tolerance is not None:
+            tolerance = tolerance.total_seconds() * 1e6
+            indexer = np.where(distances <= tolerance, indexer, -1)
+
+        if limit is not None:
+            outside_tolerance_mask = distances > limit
+            indexer[outside_tolerance_mask] = -1
+
+        return indexer

     def _filter_indexer_tolerance(self, target, indexer, tolerance):
         """Adapted from pandas.Index._filter_indexer_tolerance"""
-        pass
+        if tolerance is not None:
+            tolerance = tolerance.total_seconds() * 1e6
+            target = target.astype('int64')
+            distance = np.abs(self.asi8[indexer] - target)
+            indexer = indexer[distance <= tolerance]
+        return indexer

     def get_loc(self, key):
         """Adapted from pandas.tseries.index.DatetimeIndex.get_loc"""
diff --git a/xarray/coding/frequencies.py b/xarray/coding/frequencies.py
index 1ea6ec74..3b213c0b 100644
--- a/xarray/coding/frequencies.py
+++ b/xarray/coding/frequencies.py
@@ -35,7 +35,16 @@ def infer_freq(index):
     ValueError
         If there are fewer than three values or the index is not 1D.
     """
-    pass
+    if isinstance(index, CFTimeIndex):
+        return _CFTimeFrequencyInferer(index).get_freq()
+    elif isinstance(index, (pd.DatetimeIndex, pd.TimedeltaIndex)):
+        return pd.infer_freq(index)
+    elif isinstance(index, (pd.Series, xr.DataArray)):
+        return pd.infer_freq(index.values)
+    elif _contains_datetime_like_objects(index):
+        return pd.infer_freq(index)
+    else:
+        raise TypeError("Index must be datetime-like")


 class _CFTimeFrequencyInferer:
@@ -60,37 +69,102 @@ class _CFTimeFrequencyInferer:
         -------
         str or None
         """
-        pass
+        if not self.is_monotonic:
+            return None
+
+        delta = self.deltas[0]
+        if _is_multiple(delta, _ONE_DAY):
+            return self._infer_daily_freq()
+        elif _is_multiple(delta, _ONE_HOUR):
+            return self._infer_hourly_freq()
+        elif _is_multiple(delta, _ONE_MINUTE):
+            return self._infer_minute_freq()
+        elif _is_multiple(delta, _ONE_SECOND):
+            return self._infer_second_freq()
+        elif _is_multiple(delta, _ONE_MILLI):
+            return self._infer_milli_freq()
+        elif _is_multiple(delta, _ONE_MICRO):
+            return self._infer_micro_freq()
+        else:
+            return None
+
+    def _infer_daily_freq(self):
+        days = self.deltas[0] // _ONE_DAY
+        if days == 7:
+            return 'W'
+        elif days in [28, 29, 30, 31]:
+            return self._infer_monthly_freq()
+        else:
+            return _maybe_add_count('D', days)
+
+    def _infer_monthly_freq(self):
+        anchor = month_anchor_check(self.index)
+        if anchor:
+            return f'M{anchor}'
+        else:
+            months = self.month_deltas[0]
+            return _maybe_add_count('M', months)
+
+    def _infer_hourly_freq(self):
+        hours = self.deltas[0] // _ONE_HOUR
+        return _maybe_add_count('H', hours)
+
+    def _infer_minute_freq(self):
+        minutes = self.deltas[0] // _ONE_MINUTE
+        return _maybe_add_count('T', minutes)
+
+    def _infer_second_freq(self):
+        seconds = self.deltas[0] // _ONE_SECOND
+        return _maybe_add_count('S', seconds)
+
+    def _infer_milli_freq(self):
+        millis = self.deltas[0] // _ONE_MILLI
+        return _maybe_add_count('L', millis)
+
+    def _infer_micro_freq(self):
+        micros = self.deltas[0] // _ONE_MICRO
+        return _maybe_add_count('U', micros)

     @property
     def deltas(self):
         """Sorted unique timedeltas as microseconds."""
-        pass
+        if self._deltas is None:
+            deltas = np.diff(self.values)
+            self._deltas = _unique_deltas(deltas)
+        return self._deltas

     @property
     def year_deltas(self):
         """Sorted unique year deltas."""
-        pass
+        if self._year_deltas is None:
+            years = np.array([d.year for d in self.index])
+            self._year_deltas = _unique_deltas(np.diff(years))
+        return self._year_deltas

     @property
     def month_deltas(self):
         """Sorted unique month deltas."""
-        pass
+        if self._month_deltas is None:
+            months = np.array([d.year * 12 + d.month for d in self.index])
+            self._month_deltas = _unique_deltas(np.diff(months))
+        return self._month_deltas


 def _unique_deltas(arr):
     """Sorted unique deltas of numpy array"""
-    pass
+    return np.unique(arr)


 def _is_multiple(us, mult: int):
     """Whether us is a multiple of mult"""
-    pass
+    return us % mult == 0


 def _maybe_add_count(base: str, count: float):
     """If count is greater than 1, add it to the base offset string"""
-    pass
+    if count == 1:
+        return base
+    return f"{count}{base}"


 def month_anchor_check(dates):
@@ -103,4 +177,9 @@ def month_anchor_check(dates):
     Replicated pandas._libs.tslibs.resolution.month_position_check
     but without business offset handling.
     """
-    pass
+    if all(d.day == 1 for d in dates):
+        return "cs"
+    elif all(d.day == pd.Timestamp(d).days_in_month for d in dates):
+        return "ce"
+    else:
+        return None
diff --git a/xarray/coding/strings.py b/xarray/coding/strings.py
index 8a99b2a2..1d3d497f 100644
--- a/xarray/coding/strings.py
+++ b/xarray/coding/strings.py
@@ -20,7 +20,15 @@ class EncodedStringCoder(VariableCoder):

 def ensure_fixed_length_bytes(var: Variable) ->Variable:
     """Ensure that a variable with vlen bytes is converted to fixed width."""
-    pass
+    if var.dtype.kind == 'O':
+        # Variable-length bytes, need to convert to fixed-width
+        max_length = max(len(x) for x in var.data.ravel() if x is not None)
+        new_values = np.zeros(var.shape + (max_length,), dtype='S1')
+        for i, x in np.ndenumerate(var.data):
+            if x is not None:
+                new_values[i][:len(x)] = list(x)
+        return Variable(var.dims + ('string',), new_values)
+    return var


 class CharacterArrayCoder(VariableCoder):
@@ -29,22 +37,60 @@ class CharacterArrayCoder(VariableCoder):

 def bytes_to_char(arr):
     """Convert numpy/dask arrays from fixed width bytes to characters."""
-    pass
+    if isinstance(arr, np.ndarray):
+        return _numpy_bytes_to_char(arr)
+    elif is_chunked_array(arr):
+        ChunkedArray = get_chunked_array_type(arr)
+        return ChunkedArray(arr.chunks, bytes_to_char, dtype='S1',
+                            meta=_numpy_bytes_to_char(arr._meta))
+    else:
+        raise TypeError(f"Unsupported array type: {type(arr)}")


 def _numpy_bytes_to_char(arr):
     """Like netCDF4.stringtochar, but faster and more flexible."""
-    pass
+    # Ensure the input is a numpy array
+    arr = np.asarray(arr)
+    
+    if arr.dtype.kind == 'S':
+        # Convert bytes to characters
+        return arr.view('S1').reshape(arr.shape + (-1,))
+    elif arr.dtype == object:
+        # Handle object arrays (e.g., arrays of Python strings)
+        max_len = max(len(s) for s in arr.flat)
+        char_arr = np.zeros(arr.shape + (max_len,), dtype='S1')
+        for i, s in np.ndenumerate(arr):
+            char_arr[i][:len(s)] = list(s.encode('ascii'))
+        return char_arr
+    else:
+        raise ValueError(f"Unsupported dtype: {arr.dtype}")


 def char_to_bytes(arr):
     """Convert numpy/dask arrays from characters to fixed width bytes."""
-    pass
+    if isinstance(arr, np.ndarray):
+        return _numpy_char_to_bytes(arr)
+    elif is_chunked_array(arr):
+        ChunkedArray = get_chunked_array_type(arr)
+        return ChunkedArray(arr.chunks, char_to_bytes, dtype='S' + str(arr.shape[-1]),
+                            meta=_numpy_char_to_bytes(arr._meta))
+    else:
+        raise TypeError(f"Unsupported array type: {type(arr)}")


 def _numpy_char_to_bytes(arr):
     """Like netCDF4.chartostring, but faster and more flexible."""
-    pass
+    # Ensure the input is a numpy array
+    arr = np.asarray(arr)
+    
+    if arr.dtype.kind == 'S' and arr.dtype.itemsize == 1:
+        # Convert characters to bytes
+        return arr.view('S' + str(arr.shape[-1])).squeeze(axis=-1)
+    elif arr.dtype.kind in ('U', 'O'):
+        # Handle Unicode strings or object arrays
+        return np.char.encode(arr.astype('U'), encoding='ascii')
+    else:
+        raise ValueError(f"Unsupported dtype: {arr.dtype}")


 class StackedBytesArray(indexing.ExplicitlyIndexedNDArrayMixin):
diff --git a/xarray/coding/times.py b/xarray/coding/times.py
index 956c93ca..d7dc93c4 100644
--- a/xarray/coding/times.py
+++ b/xarray/coding/times.py
@@ -55,19 +55,63 @@ def decode_cf_datetime(num_dates, units: str, calendar: (str | None)=None,
     --------
     cftime.num2date
     """
-    pass
+    num_dates = np.asarray(num_dates)
+    units = units.strip()
+
+    if calendar is None:
+        calendar = 'standard'
+
+    if calendar.lower() in _STANDARD_CALENDARS and use_cftime is not True:
+        return decode_cf_datetime_numpy(num_dates, units)
+    else:
+        if cftime is None:
+            raise ImportError("cftime is required for non-standard calendars.")
+        return cftime.num2date(num_dates, units, calendar, only_use_cftime_datetimes=True)
+
+def decode_cf_datetime_numpy(num_dates, units):
+    """Helper function to decode CF datetimes using numpy for standard calendars."""
+    units_split = units.split(' since ')
+    if len(units_split) != 2:
+        raise ValueError(f"Invalid units string: {units}")
+    
+    unit, reference_date_string = units_split
+    reference_date = pd.Timestamp(reference_date_string)
+    
+    if unit not in _NS_PER_TIME_DELTA:
+        raise ValueError(f"Unsupported time unit: {unit}")
+    
+    time_delta = np.timedelta64(num_dates.astype('timedelta64[ns]') * _NS_PER_TIME_DELTA[unit])
+    return reference_date + time_delta


 def decode_cf_timedelta(num_timedeltas, units: str) ->np.ndarray:
     """Given an array of numeric timedeltas in netCDF format, convert it into a
     numpy timedelta64[ns] array.
     """
-    pass
+    num_timedeltas = np.asarray(num_timedeltas)
+    units = units.strip()
+
+    if units not in _NS_PER_TIME_DELTA:
+        raise ValueError(f"Unsupported time unit for timedelta: {units}")
+
+    return (num_timedeltas * _NS_PER_TIME_DELTA[units]).astype('timedelta64[ns]')


 def infer_calendar_name(dates) ->CFCalendar:
     """Given an array of datetimes, infer the CF calendar name"""
-    pass
+    if isinstance(dates, np.ndarray) and np.issubdtype(dates.dtype, np.datetime64):
+        return 'proleptic_gregorian'
+    elif cftime and isinstance(dates[0], cftime.datetime):
+        return dates[0].calendar
+    else:
+        try:
+            import pandas as pd
+            if isinstance(dates, pd.DatetimeIndex):
+                return 'proleptic_gregorian'
+        except ImportError:
+            pass
+    
+    raise ValueError("Unable to infer calendar name from input dates.")


 def infer_datetime_units(dates) ->str:
@@ -76,7 +120,18 @@ def infer_datetime_units(dates) ->str:
     'hours', 'minutes' or 'seconds' (the first one that can evenly divide all
     unique time deltas in `dates`)
     """
-    pass
+    dates = np.asarray(dates)
+    if len(dates) < 2:
+        return "seconds since " + format_timestamp(dates[0])
+
+    deltas = np.diff(dates)
+    unique_deltas = np.unique(deltas)
+
+    for unit in ['days', 'hours', 'minutes', 'seconds']:
+        if np.all(unique_deltas % np.timedelta64(1, unit[0].upper()) == np.timedelta64(0, 'ns')):
+            return f"{unit} since {format_timestamp(dates[0])}"
+
+    return f"seconds since {format_timestamp(dates[0])}"


 def format_cftime_datetime(date) ->str:
diff --git a/xarray/coding/variables.py b/xarray/coding/variables.py
index efe7890c..7d47ccf0 100644
--- a/xarray/coding/variables.py
+++ b/xarray/coding/variables.py
@@ -138,7 +138,11 @@ def lazy_elemwise_func(array, func: Callable, dtype: np.typing.DTypeLike):
     -------
     Either a dask.array.Array or _ElementwiseFunctionArray.
     """
-    pass
+    chunked_array_type = get_chunked_array_type(array)
+    if chunked_array_type is not None:
+        return chunked_array_type.map_overlap(array, func, dtype=dtype)
+    else:
+        return _ElementwiseFunctionArray(array, func, dtype)


 def pop_to(source: MutableMapping, dest: MutableMapping, key: Hashable,
@@ -148,23 +152,52 @@ def pop_to(source: MutableMapping, dest: MutableMapping, key: Hashable,
     None values are not passed on.  If k already exists in dest an
     error is raised.
     """
-    pass
+    value = source.pop(key, None)
+    if value is not None:
+        if key in dest:
+            raise ValueError(f"'{key}' already exists in dest")
+        dest[key] = value
+    return value


 def _apply_mask(data: np.ndarray, encoded_fill_values: list,
     decoded_fill_value: Any, dtype: np.typing.DTypeLike) ->np.ndarray:
     """Mask all matching values in a NumPy arrays."""
-    pass
+    if encoded_fill_values:
+        cond = False
+        for fv in encoded_fill_values:
+            cond |= data == fv
+        data = np.where(cond, decoded_fill_value, data)
+    
+    return data.astype(dtype)


 def _check_fill_values(attrs, name, dtype):
-    """ "Check _FillValue and missing_value if available.
+    """Check _FillValue and missing_value if available.

     Return dictionary with raw fill values and set with encoded fill values.

     Issue SerializationWarning if appropriate.
     """
-    pass
+    fill_values = {}
+    encoded_fill_values = set()
+
+    for attr in ['_FillValue', 'missing_value']:
+        value = attrs.get(attr)
+        if value is not None:
+            fill_values[attr] = value
+            encoded_fill_values.add(duck_array_ops.asarray(value).item())
+
+    if len(fill_values) > 1:
+        if fill_values['_FillValue'] != fill_values['missing_value']:
+            warnings.warn(
+                f"Variable '{name}' has multiple fill values {fill_values}, "
+                "decoding all values to NaN.",
+                SerializationWarning,
+                stacklevel=3,
+            )
+
+    return fill_values, encoded_fill_values


 class CFMaskCoder(VariableCoder):
@@ -174,7 +207,15 @@ class CFMaskCoder(VariableCoder):
 def _choose_float_dtype(dtype: np.dtype, mapping: MutableMapping) ->type[np
     .floating[Any]]:
     """Return a float dtype that can losslessly represent `dtype` values."""
-    pass
+    if np.issubdtype(dtype, np.floating):
+        return dtype.type
+    elif np.issubdtype(dtype, np.integer):
+        if dtype.itemsize <= 2:
+            return np.float32
+        else:
+            return np.float64
+    else:
+        raise ValueError(f"Unsupported dtype: {dtype}")


 class CFScaleOffsetCoder(VariableCoder):
diff --git a/xarray/conventions.py b/xarray/conventions.py
index de83ae8f..0e5e5b13 100644
--- a/xarray/conventions.py
+++ b/xarray/conventions.py
@@ -28,7 +28,19 @@ if TYPE_CHECKING:

 def _infer_dtype(array, name=None):
     """Given an object array with no missing values, infer its dtype from all elements."""
-    pass
+    if len(array) == 0:
+        return np.dtype(object)
+    
+    sample = array[0]
+    if isinstance(sample, (np.ndarray, list)):
+        first_dtype = np.array(sample).dtype
+        if all(np.array(item).dtype == first_dtype for item in array):
+            return np.dtype(object)
+    
+    try:
+        return np.array(array).dtype
+    except (ValueError, TypeError):
+        return np.dtype(object)


 def _copy_with_dtype(data, dtype: np.typing.DTypeLike):
@@ -37,7 +49,10 @@ def _copy_with_dtype(data, dtype: np.typing.DTypeLike):
     We use this instead of np.array() to ensure that custom object dtypes end
     up on the resulting array.
     """
-    pass
+    result = np.array(data, dtype=dtype, copy=True)
+    if dtype == object:
+        result[:] = data
+    return result


 def encode_cf_variable(var: Variable, needs_copy: bool=True, name: T_Name=None
@@ -61,7 +76,38 @@ def encode_cf_variable(var: Variable, needs_copy: bool=True, name: T_Name=None
     out : Variable
         A variable which has been encoded as described above.
     """
-    pass
+    original_dtype = var.dtype
+    encoded_dtype = var.encoding.get('dtype', original_dtype)
+    
+    if needs_copy:
+        var = var.copy(deep=True)
+    
+    if np.issubdtype(original_dtype, np.datetime64):
+        var = times.encode_cf_datetime(var)
+    elif np.issubdtype(original_dtype, np.timedelta64):
+        var = times.encode_cf_timedelta(var)
+    
+    if var.dtype != encoded_dtype:
+        var = var.astype(encoded_dtype)
+    
+    # Apply scale_factor and add_offset
+    scale_factor = var.encoding.get('scale_factor')
+    add_offset = var.encoding.get('add_offset')
+    if scale_factor is not None or add_offset is not None:
+        data = var.values
+        if scale_factor is not None:
+            data = data / scale_factor
+        if add_offset is not None:
+            data = data - add_offset
+        var = Variable(var.dims, data, var.attrs, var.encoding)
+    
+    # Handle _FillValue and missing_value
+    fill_value = var.encoding.get('_FillValue', var.attrs.get('_FillValue'))
+    if fill_value is not None:
+        var.encoding['_FillValue'] = fill_value
+        var.values[np.isnan(var.values)] = fill_value
+    
+    return var


 def decode_cf_variable(name: Hashable, var: Variable, concat_characters:
@@ -113,7 +159,42 @@ def decode_cf_variable(name: Hashable, var: Variable, concat_characters:
     out : Variable
         A variable holding the decoded equivalent of var.
     """
-    pass
+    # Handle endianness
+    if decode_endianness and var.dtype.byteorder not in ('=', '|'):
+        var = Variable(var.dims, var.values.byteswap().newbyteorder(), var.attrs, var.encoding)
+
+    # Handle masking and scaling
+    if mask_and_scale:
+        scale_factor = var.attrs.get('scale_factor') or var.encoding.get('scale_factor')
+        add_offset = var.attrs.get('add_offset') or var.encoding.get('add_offset')
+        fill_value = var.attrs.get('_FillValue') or var.encoding.get('_FillValue')
+
+        if scale_factor is not None or add_offset is not None:
+            data = var.values
+            if scale_factor is not None:
+                data = data * scale_factor
+            if add_offset is not None:
+                data = data + add_offset
+            var = Variable(var.dims, data, var.attrs, var.encoding)
+
+        if fill_value is not None:
+            var = Variable(var.dims, np.ma.masked_equal(var.values, fill_value), var.attrs, var.encoding)
+
+    # Handle time decoding
+    if decode_times:
+        if 'units' in var.attrs and 'since' in var.attrs['units']:
+            var = times.decode_cf_datetime(var, use_cftime=use_cftime)
+        elif decode_timedelta is not None and 'units' in var.attrs:
+            var = times.decode_cf_timedelta(var)
+
+    # Handle character concatenation
+    if concat_characters and var.dtype.kind == 'S':
+        if stack_char_dim:
+            var = strings.CharacterArrayCoder().decode(var)
+        else:
+            var = strings.EncodedStringCoder().decode(var)
+
+    return var


 def _update_bounds_attributes(variables: T_Variables) ->None:
diff --git a/xarray/convert.py b/xarray/convert.py
index d29fc8f6..13bcddf4 100644
--- a/xarray/convert.py
+++ b/xarray/convert.py
@@ -19,32 +19,69 @@ cell_methods_strings = {'point', 'sum', 'maximum', 'median', 'mid_range',

 def _filter_attrs(attrs, ignored_attrs):
     """Return attrs that are not in ignored_attrs"""
-    pass
+    return {k: v for k, v in attrs.items() if k not in ignored_attrs}


 def _pick_attrs(attrs, keys):
     """Return attrs with keys in keys list"""
-    pass
+    return {k: attrs[k] for k in keys if k in attrs}


 def _get_iris_args(attrs):
     """Converts the xarray attrs into args that can be passed into Iris"""
-    pass
+    iris_args = {}
+    for key in ['standard_name', 'long_name', 'units', 'bounds']:
+        if key in attrs:
+            iris_args[key] = attrs[key]
+    return iris_args


 def to_iris(dataarray):
     """Convert a DataArray into a Iris Cube"""
-    pass
+    import iris
+    
+    # Create the cube
+    cube = iris.cube.Cube(dataarray.values)
+    
+    # Set the dimensions
+    for dim, coord in dataarray.coords.items():
+        if dim in dataarray.dims:
+            iris_coord = iris.coords.DimCoord(coord.values, **_get_iris_args(coord.attrs))
+            cube.add_dim_coord(iris_coord, dataarray.get_axis_num(dim))
+        else:
+            iris_coord = iris.coords.AuxCoord(coord.values, **_get_iris_args(coord.attrs))
+            cube.add_aux_coord(iris_coord)
+    
+    # Set the attributes
+    filtered_attrs = _filter_attrs(dataarray.attrs, iris_forbidden_keys)
+    cube.attributes.update(filtered_attrs)
+    
+    # Set the name
+    cube.var_name = dataarray.name
+    
+    return cube


 def _iris_obj_to_attrs(obj):
     """Return a dictionary of attrs when given a Iris object"""
-    pass
+    attrs = {}
+    for key in ['standard_name', 'long_name', 'units', 'bounds']:
+        value = getattr(obj, key, None)
+        if value is not None:
+            attrs[key] = value
+    attrs.update(obj.attributes)
+    return attrs


 def _iris_cell_methods_to_str(cell_methods_obj):
     """Converts a Iris cell methods into a string"""
-    pass
+    cell_methods = []
+    for cm in cell_methods_obj:
+        method = f"{cm.coord_names[0]}: {cm.method}"
+        if cm.intervals:
+            method += f" (interval: {cm.intervals[0]})"
+        cell_methods.append(method)
+    return " ".join(cell_methods)


 def _name(iris_obj, default='unknown'):
@@ -53,9 +90,38 @@ def _name(iris_obj, default='unknown'):
     Similar to iris_obj.name() method, but using iris_obj.var_name first to
     enable roundtripping.
     """
-    pass
+    return (
+        iris_obj.var_name
+        or iris_obj.standard_name
+        or iris_obj.long_name
+        or default
+    )


 def from_iris(cube):
     """Convert a Iris cube into an DataArray"""
-    pass
+    import iris
+    
+    # Create coordinates
+    coords = {}
+    for coord in cube.coords():
+        coord_attrs = _iris_obj_to_attrs(coord)
+        if isinstance(coord, iris.coords.DimCoord):
+            coords[coord.name()] = (coord.name(), coord.points, coord_attrs)
+        else:
+            coords[coord.name()] = ([], coord.points, coord_attrs)
+    
+    # Create attributes
+    attrs = _iris_obj_to_attrs(cube)
+    if cube.cell_methods:
+        attrs['cell_methods'] = _iris_cell_methods_to_str(cube.cell_methods)
+    
+    # Create DataArray
+    da = DataArray(
+        data=cube.data,
+        coords=coords,
+        attrs=attrs,
+        name=_name(cube)
+    )
+    
+    return da
diff --git a/xarray/core/accessor_dt.py b/xarray/core/accessor_dt.py
index 87474ec9..fec61818 100644
--- a/xarray/core/accessor_dt.py
+++ b/xarray/core/accessor_dt.py
@@ -18,21 +18,26 @@ if TYPE_CHECKING:

 def _season_from_months(months):
     """Compute season (DJF, MAM, JJA, SON) from month ordinal"""
-    pass
+    seasons = {1: 'DJF', 2: 'DJF', 3: 'MAM', 4: 'MAM', 5: 'MAM', 6: 'JJA',
+               7: 'JJA', 8: 'JJA', 9: 'SON', 10: 'SON', 11: 'SON', 12: 'DJF'}
+    return np.vectorize(seasons.get)(months)


 def _access_through_cftimeindex(values, name):
     """Coerce an array of datetime-like values to a CFTimeIndex
     and access requested datetime component
     """
-    pass
+    from xarray.core.indexes import CFTimeIndex
+    index = CFTimeIndex(values)
+    return getattr(index, name)


 def _access_through_series(values, name):
     """Coerce an array of datetime-like values to a pandas Series and
     access requested datetime component
     """
-    pass
+    series = pd.Series(values)
+    return getattr(series.dt, name)


 def _get_date_field(values, name, dtype):
@@ -54,14 +59,23 @@ def _get_date_field(values, name, dtype):
         Array-like of datetime fields accessed for each element in values

     """
-    pass
+    if is_duck_dask_array(values):
+        import dask.array as da
+        return da.map_overlap(_access_through_series, values, name=name, dtype=dtype)
+    else:
+        return _access_through_series(values, name).astype(dtype)


 def _round_through_series_or_index(values, name, freq):
     """Coerce an array of datetime-like values to a pandas Series or xarray
     CFTimeIndex and apply requested rounding
     """
-    pass
+    from xarray.core.indexes import CFTimeIndex
+    if isinstance(values, CFTimeIndex):
+        index = values
+    else:
+        index = pd.Series(values)
+    return getattr(index, name)(freq)


 def _round_field(values, name, freq):
@@ -83,21 +97,28 @@ def _round_field(values, name, freq):
         Array-like of datetime fields accessed for each element in values

     """
-    pass
+    if is_duck_dask_array(values):
+        import dask.array as da
+        return da.map_overlap(_round_through_series_or_index, values, name=name, freq=freq)
+    else:
+        return _round_through_series_or_index(values, name, freq)


 def _strftime_through_cftimeindex(values, date_format: str):
     """Coerce an array of cftime-like values to a CFTimeIndex
     and access requested datetime component
     """
-    pass
+    from xarray.core.indexes import CFTimeIndex
+    index = CFTimeIndex(values)
+    return index.strftime(date_format)


 def _strftime_through_series(values, date_format: str):
     """Coerce an array of datetime-like values to a pandas Series and
     apply string formatting
     """
-    pass
+    series = pd.Series(values)
+    return series.dt.strftime(date_format)


 class TimeAccessor(Generic[T_DataArray]):
@@ -120,7 +141,7 @@ class TimeAccessor(Generic[T_DataArray]):
         floor-ed timestamps : same type as values
             Array-like of datetime fields accessed for each element in values
         """
-        pass
+        return self._obj.copy(data=_round_field(self._obj.data, "floor", freq))

     def ceil(self, freq: str) ->T_DataArray:
         """
@@ -136,7 +157,7 @@ class TimeAccessor(Generic[T_DataArray]):
         ceil-ed timestamps : same type as values
             Array-like of datetime fields accessed for each element in values
         """
-        pass
+        return self._obj.copy(data=_round_field(self._obj.data, "ceil", freq))

     def round(self, freq: str) ->T_DataArray:
         """
@@ -152,7 +173,7 @@ class TimeAccessor(Generic[T_DataArray]):
         rounded timestamps : same type as values
             Array-like of datetime fields accessed for each element in values
         """
-        pass
+        return self._obj.copy(data=_round_field(self._obj.data, "round", freq))


 class DatetimeAccessor(TimeAccessor[T_DataArray]):
@@ -215,7 +236,11 @@ class DatetimeAccessor(TimeAccessor[T_DataArray]):
         <xarray.DataArray 'strftime' ()> Size: 8B
         array('January 01, 2000, 12:00:00 AM', dtype=object)
         """
-        pass
+        values = self._obj.data
+        if is_np_datetime_like(self._obj.dtype):
+            return self._obj.copy(data=_strftime_through_series(values, date_format))
+        else:
+            return self._obj.copy(data=_strftime_through_cftimeindex(values, date_format))

     def isocalendar(self) ->Dataset:
         """Dataset containing ISO year, week number, and weekday.
@@ -224,125 +249,131 @@ class DatetimeAccessor(TimeAccessor[T_DataArray]):
         -----
         The iso year and weekday differ from the nominal year and weekday.
         """
-        pass
+        from xarray import Dataset
+        iso_calendar = _access_through_series(self._obj.data, 'isocalendar')
+        return Dataset({
+            'year': ('time', iso_calendar.year),
+            'week': ('time', iso_calendar.week),
+            'weekday': ('time', iso_calendar.day),
+        }, coords={'time': self._obj.coords['time']})

     @property
     def year(self) ->T_DataArray:
         """The year of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'year', 'int64'))

     @property
     def month(self) ->T_DataArray:
         """The month as January=1, December=12"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'month', 'int64'))

     @property
     def day(self) ->T_DataArray:
         """The days of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'day', 'int64'))

     @property
     def hour(self) ->T_DataArray:
         """The hours of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'hour', 'int64'))

     @property
     def minute(self) ->T_DataArray:
         """The minutes of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'minute', 'int64'))

     @property
     def second(self) ->T_DataArray:
         """The seconds of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'second', 'int64'))

     @property
     def microsecond(self) ->T_DataArray:
         """The microseconds of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'microsecond', 'int64'))

     @property
     def nanosecond(self) ->T_DataArray:
         """The nanoseconds of the datetime"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'nanosecond', 'int64'))

     @property
     def weekofyear(self) ->DataArray:
         """The week ordinal of the year"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'weekofyear', 'int64'))
     week = weekofyear

     @property
     def dayofweek(self) ->T_DataArray:
         """The day of the week with Monday=0, Sunday=6"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'dayofweek', 'int64'))
     weekday = dayofweek

     @property
     def dayofyear(self) ->T_DataArray:
         """The ordinal day of the year"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'dayofyear', 'int64'))

     @property
     def quarter(self) ->T_DataArray:
         """The quarter of the date"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'quarter', 'int64'))

     @property
     def days_in_month(self) ->T_DataArray:
         """The number of days in the month"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'days_in_month', 'int64'))
     daysinmonth = days_in_month

     @property
     def season(self) ->T_DataArray:
         """Season of the year"""
-        pass
+        return self._obj.copy(data=_season_from_months(_get_date_field(self._obj.data, 'month', 'int64')))

     @property
     def time(self) ->T_DataArray:
         """Timestamps corresponding to datetimes"""
-        pass
+        return self._obj.copy(data=_access_through_series(self._obj.data, 'time'))

     @property
     def date(self) ->T_DataArray:
         """Date corresponding to datetimes"""
-        pass
+        return self._obj.copy(data=_access_through_series(self._obj.data, 'date'))

     @property
     def is_month_start(self) ->T_DataArray:
         """Indicate whether the date is the first day of the month"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_month_start', 'bool'))

     @property
     def is_month_end(self) ->T_DataArray:
         """Indicate whether the date is the last day of the month"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_month_end', 'bool'))

     @property
     def is_quarter_start(self) ->T_DataArray:
         """Indicate whether the date is the first day of a quarter"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_quarter_start', 'bool'))

     @property
     def is_quarter_end(self) ->T_DataArray:
         """Indicate whether the date is the last day of a quarter"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_quarter_end', 'bool'))

     @property
     def is_year_start(self) ->T_DataArray:
         """Indicate whether the date is the first day of a year"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_year_start', 'bool'))

     @property
     def is_year_end(self) ->T_DataArray:
         """Indicate whether the date is the last day of the year"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_year_end', 'bool'))

     @property
     def is_leap_year(self) ->T_DataArray:
         """Indicate if the date belongs to a leap year"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'is_leap_year', 'bool'))

     @property
     def calendar(self) ->CFCalendar:
@@ -351,7 +382,10 @@ class DatetimeAccessor(TimeAccessor[T_DataArray]):
         Only relevant for arrays of :py:class:`cftime.datetime` objects,
         returns "proleptic_gregorian" for arrays of :py:class:`numpy.datetime64` values.
         """
-        pass
+        if is_np_datetime_like(self._obj.dtype):
+            return "proleptic_gregorian"
+        else:
+            return infer_calendar_name(self._obj.data)


 class TimedeltaAccessor(TimeAccessor[T_DataArray]):
@@ -404,26 +438,26 @@ class TimedeltaAccessor(TimeAccessor[T_DataArray]):
     @property
     def days(self) ->T_DataArray:
         """Number of days for each element"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'days', 'int64'))

     @property
     def seconds(self) ->T_DataArray:
         """Number of seconds (>= 0 and less than 1 day) for each element"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'seconds', 'int64'))

     @property
     def microseconds(self) ->T_DataArray:
         """Number of microseconds (>= 0 and less than 1 second) for each element"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'microseconds', 'int64'))

     @property
     def nanoseconds(self) ->T_DataArray:
         """Number of nanoseconds (>= 0 and less than 1 microsecond) for each element"""
-        pass
+        return self._obj.copy(data=_get_date_field(self._obj.data, 'nanoseconds', 'int64'))

     def total_seconds(self) ->T_DataArray:
         """Total duration of each element expressed in seconds."""
-        pass
+        return self._obj.copy(data=_access_through_series(self._obj.data, 'total_seconds'))


 class CombinedDatetimelikeAccessor(DatetimeAccessor[T_DataArray],
diff --git a/xarray/core/alignment.py b/xarray/core/alignment.py
index 3ec2a057..7818ce17 100644
--- a/xarray/core/alignment.py
+++ b/xarray/core/alignment.py
@@ -27,7 +27,18 @@ def reindex_variables(variables: Mapping[Any, Variable], dim_pos_indexers:
     Not public API.

     """
-    pass
+    new_variables = {}
+    for name, var in variables.items():
+        indexers = {k: v for k, v in dim_pos_indexers.items() if k in var.dims}
+        if indexers:
+            new_variables[name] = var.reindex(
+                indexers, copy=copy, fill_value=fill_value, sparse=sparse
+            )
+        elif copy:
+            new_variables[name] = var.copy(deep=False)
+        else:
+            new_variables[name] = var
+    return new_variables


 CoordNamesAndDims = tuple[tuple[Hashable, tuple[Hashable, ...]], ...]
@@ -110,7 +121,24 @@ class Aligner(Generic[T_Alignable]):
         such that we can group matching indexes based on the dictionary keys.

         """
-        pass
+        normalized_indexes = {}
+        normalized_index_vars = {}
+
+        for key, idx in indexes.items():
+            if isinstance(idx, Index):
+                index = idx
+                index_vars = idx.to_variables()
+            else:
+                index = PandasIndex(idx, name=key)
+                index_vars = {key: Variable((key,), idx)}
+
+            coord_names_and_dims = tuple((name, var.dims) for name, var in index_vars.items())
+            matching_key = (coord_names_and_dims, type(index))
+
+            normalized_indexes[matching_key] = index
+            normalized_index_vars[matching_key] = index_vars
+
+        return normalized_indexes, normalized_index_vars

     def assert_no_index_conflict(self) ->None:
         """Check for uniqueness of both coordinate and dimension names across all sets
@@ -126,7 +154,20 @@ class Aligner(Generic[T_Alignable]):
         (ref: https://github.com/pydata/xarray/issues/1603#issuecomment-442965602)

         """
-        pass
+        all_coord_names = set()
+        all_dim_names = set()
+
+        for (coord_names_and_dims, _), index in self.indexes.items():
+            coord_names = {name for name, _ in coord_names_and_dims}
+            dim_names = set(index.dims)
+
+            if not coord_names.isdisjoint(all_coord_names):
+                raise ValueError("Conflicting coordinate names found.")
+            if not dim_names.isdisjoint(all_dim_names):
+                raise ValueError("Conflicting dimension names found.")
+
+            all_coord_names.update(coord_names)
+            all_dim_names.update(dim_names)

     def _need_reindex(self, dim, cmp_indexes) ->bool:
         """Whether or not we need to reindex variables for a set of
@@ -139,11 +180,44 @@ class Aligner(Generic[T_Alignable]):
           pandas). This is useful, e.g., for overwriting such duplicate indexes.

         """
-        pass
+        if dim in self.exclude_dims:
+            return False
+
+        if self.join == "override":
+            return False
+
+        if self.join == "exact":
+            return not indexes_all_equal(cmp_indexes)
+
+        if len(cmp_indexes) == 1:
+            return False
+
+        first_index = cmp_indexes[0]
+        return any(not first_index.equals(other) for other in cmp_indexes[1:])

     def align_indexes(self) ->None:
         """Compute all aligned indexes and their corresponding coordinate variables."""
-        pass
+        for key, cmp_indexes in self.all_indexes.items():
+            dim = cmp_indexes[0].dim
+            if self._need_reindex(dim, cmp_indexes):
+                aligned_index = self._align_index(key, cmp_indexes)
+                self.aligned_indexes[key] = aligned_index
+                self.aligned_index_vars[key] = aligned_index.to_variables()
+                self.reindex[key] = True
+            else:
+                self.aligned_indexes[key] = cmp_indexes[0]
+                self.aligned_index_vars[key] = self.all_index_vars[key][0]
+                self.reindex[key] = False
+
+    def _align_index(self, key, cmp_indexes):
+        if self.join == "outer":
+            return Index.union(cmp_indexes)
+        elif self.join == "inner":
+            return Index.intersection(cmp_indexes)
+        elif self.join in ["left", "right"]:
+            return cmp_indexes[0 if self.join == "left" else -1]
+        else:
+            raise ValueError(f"Invalid join option: {self.join}")


 T_Obj1 = TypeVar('T_Obj1', bound='Alignable')
diff --git a/xarray/core/combine.py b/xarray/core/combine.py
index d78cb540..675036b6 100644
--- a/xarray/core/combine.py
+++ b/xarray/core/combine.py
@@ -35,7 +35,11 @@ def _infer_tile_ids_from_nested_list(entry, current_pos):
     -------
     combined_tile_ids : dict[tuple(int, ...), obj]
     """
-    pass
+    if isinstance(entry, list):
+        for i, item in enumerate(entry):
+            yield from _infer_tile_ids_from_nested_list(item, current_pos + (i,))
+    else:
+        yield current_pos, entry


 def _check_dimension_depth_tile_ids(combined_tile_ids):
@@ -43,12 +47,24 @@ def _check_dimension_depth_tile_ids(combined_tile_ids):
     Check all tuples are the same length, i.e. check that all lists are
     nested to the same depth.
     """
-    pass
+    depths = {len(key) for key in combined_tile_ids.keys()}
+    if len(depths) != 1:
+        raise ValueError("All lists must be nested to the same depth.")


 def _check_shape_tile_ids(combined_tile_ids):
     """Check all lists along one dimension are same length."""
-    pass
+    if not combined_tile_ids:
+        return
+
+    depths = max(len(key) for key in combined_tile_ids.keys())
+    for dim in range(depths):
+        lengths = set()
+        for key in combined_tile_ids.keys():
+            if len(key) > dim:
+                lengths.add(max(k[dim] for k in combined_tile_ids.keys() if len(k) > dim) + 1)
+        if len(lengths) != 1:
+            raise ValueError(f"Lists along dimension {dim} have inconsistent lengths.")


 def _combine_nd(combined_ids, concat_dims, data_vars='all', coords=
@@ -76,7 +92,25 @@ def _combine_nd(combined_ids, concat_dims, data_vars='all', coords=
     -------
     combined_ds : xarray.Dataset
     """
-    pass
+    if len(combined_ids) == 1:
+        return next(iter(combined_ids.values()))
+
+    dims = len(next(iter(combined_ids.keys())))
+    if len(concat_dims) != dims:
+        raise ValueError("Length of concat_dims must match the number of dimensions in combined_ids")
+
+    for dim in range(dims - 1, -1, -1):
+        if concat_dims[dim] is None:
+            combined_ids = {k[:-1]: merge([combined_ids[k[:-1] + (i,)] for i in range(max(k[dim] for k in combined_ids.keys()) + 1)],
+                                          compat=compat, join=join, fill_value=fill_value, combine_attrs=combine_attrs)
+                            for k in combined_ids.keys() if k[dim] == 0}
+        else:
+            combined_ids = {k[:-1]: concat([combined_ids[k[:-1] + (i,)] for i in range(max(k[dim] for k in combined_ids.keys()) + 1)],
+                                           dim=concat_dims[dim], data_vars=data_vars, coords=coords,
+                                           compat=compat, fill_value=fill_value, join=join, combine_attrs=combine_attrs)
+                            for k in combined_ids.keys() if k[dim] == 0}
+
+    return next(iter(combined_ids.values()))


 def _combine_1d(datasets, concat_dim, compat: CompatOptions='no_conflicts',
@@ -86,7 +120,11 @@ def _combine_1d(datasets, concat_dim, compat: CompatOptions='no_conflicts',
     Applies either concat or merge to 1D list of datasets depending on value
     of concat_dim
     """
-    pass
+    if concat_dim is None:
+        return merge(datasets, compat=compat, join=join, fill_value=fill_value, combine_attrs=combine_attrs)
+    else:
+        return concat(datasets, dim=concat_dim, data_vars=data_vars, coords=coords,
+                      compat=compat, fill_value=fill_value, join=join, combine_attrs=combine_attrs)


 DATASET_HYPERCUBE = Union[Dataset, Iterable['DATASET_HYPERCUBE']]
@@ -276,7 +314,15 @@ def combine_nested(datasets: DATASET_HYPERCUBE, concat_dim: (str |
     concat
     merge
     """
-    pass
+    if not isinstance(concat_dim, (list, tuple)):
+        concat_dim = [concat_dim]
+
+    combined_ids = dict(_infer_tile_ids_from_nested_list(datasets, ()))
+    _check_dimension_depth_tile_ids(combined_ids)
+    _check_shape_tile_ids(combined_ids)
+
+    return _combine_nd(combined_ids, concat_dim, data_vars=data_vars, coords=coords,
+                       compat=compat, fill_value=fill_value, join=join, combine_attrs=combine_attrs)


 def _combine_single_variable_hypercube(datasets, fill_value=dtypes.NA,
@@ -293,7 +339,38 @@ def _combine_single_variable_hypercube(datasets, fill_value=dtypes.NA,

     This function is NOT part of the public API.
     """
-    pass
+    if not datasets:
+        return Dataset()
+
+    first = datasets[0]
+    coords = set(first.coords)
+    dim_coords = {dim: coord for dim, coord in first.coords.items() if dim in first.dims}
+
+    # Determine the shape of the hypercube
+    hypercube_shape = {}
+    for ds in datasets:
+        for dim, coord in ds.coords.items():
+            if dim in dim_coords and not coord.equals(dim_coords[dim]):
+                if dim not in hypercube_shape:
+                    hypercube_shape[dim] = set()
+                hypercube_shape[dim].add(coord.values.tolist()[0])
+
+    # Create a new coordinate for each dimension of the hypercube
+    new_coords = {}
+    concat_dims = []
+    for dim, values in hypercube_shape.items():
+        new_coords[dim] = sorted(values)
+        concat_dims.append(dim)
+
+    # Assign each dataset to its position in the hypercube
+    positioned_datasets = {}
+    for ds in datasets:
+        position = tuple(new_coords[dim].index(ds.coords[dim].values.tolist()[0]) for dim in concat_dims)
+        positioned_datasets[position] = ds
+
+    # Combine the datasets
+    return _combine_nd(positioned_datasets, concat_dims, data_vars=data_vars, coords=coords,
+                       compat=compat, fill_value=fill_value, join=join, combine_attrs=combine_attrs)


 def combine_by_coords(data_objects: Iterable[Dataset | DataArray]=[],
@@ -551,4 +628,35 @@ def combine_by_coords(data_objects: Iterable[Dataset | DataArray]=[],
     Finally, if you attempt to combine a mix of unnamed DataArrays with either named
     DataArrays or Datasets, a ValueError will be raised (as this is an ambiguous operation).
     """
-    pass
+    if not data_objects:
+        return Dataset()
+
+    if all(isinstance(obj, DataArray) for obj in data_objects):
+        if all(obj.name is not None for obj in data_objects):
+            data_objects = [obj.to_dataset() for obj in data_objects]
+        elif any(obj.name is not None for obj in data_objects):
+            raise ValueError("Cannot combine mix of named and unnamed DataArrays.")
+        else:
+            return _combine_single_variable_hypercube(data_objects, fill_value=fill_value,
+                                                      data_vars=data_vars, coords=coords,
+                                                      compat=compat, join=join,
+                                                      combine_attrs=combine_attrs)
+
+    datasets = [obj if isinstance(obj, Dataset) else obj.to_dataset() for obj in data_objects]
+
+    # Identify the dimensions to concatenate along
+    concat_dims = set()
+    for ds in datasets:
+        for dim, coord in ds.coords.items():
+            if dim in ds.dims and not all(coord.equals(other_ds[dim]) for other_ds in datasets if dim in other_ds.dims):
+                concat_dims.add(dim)
+
+    # Sort datasets based on their coordinate values
+    sorted_datasets = sorted(datasets, key=lambda ds: tuple(ds[dim].values[0] for dim in concat_dims if dim in ds.dims))
+
+    # Combine the datasets
+    combined = _combine_nd({tuple(ds[dim].values[0] for dim in concat_dims if dim in ds.dims): ds for ds in sorted_datasets},
+                           list(concat_dims), data_vars=data_vars, coords=coords,
+                           compat=compat, fill_value=fill_value, join=join, combine_attrs=combine_attrs)
+
+    return combined
diff --git a/xarray/core/common.py b/xarray/core/common.py
index c819d798..042f0e97 100644
--- a/xarray/core/common.py
+++ b/xarray/core/common.py
@@ -127,7 +127,10 @@ class AbstractArray:
         int or tuple of int
             Axis number or numbers corresponding to the given dimensions.
         """
-        pass
+        if isinstance(dim, Iterable) and not isinstance(dim, str):
+            return tuple(self.get_axis_num(d) for d in dim)
+        else:
+            return self.dims.index(dim)

     @property
     def sizes(self: Any) ->Mapping[Hashable, int]:
@@ -139,7 +142,7 @@ class AbstractArray:
         --------
         Dataset.sizes
         """
-        pass
+        return Frozen(dict(zip(self.dims, self.shape)))


 class AttrAccessMixin:
@@ -166,12 +169,12 @@ class AttrAccessMixin:
     @property
     def _attr_sources(self) ->Iterable[Mapping[Hashable, Any]]:
         """Places to look-up items for attribute-style access"""
-        pass
+        return [self.attrs, self.coords, self.data_vars]

     @property
     def _item_sources(self) ->Iterable[Mapping[Hashable, Any]]:
         """Places to look-up items for key-autocompletion"""
-        pass
+        return [self.coords, self.data_vars]

     def __getattr__(self, name: str) ->Any:
         if name not in {'__dict__', '__setstate__'}:
@@ -213,7 +216,7 @@ class AttrAccessMixin:
         See http://ipython.readthedocs.io/en/stable/config/integrating.html#tab-completion
         For the details.
         """
-        pass
+        return list(itertools.chain.from_iterable(source.keys() for source in self._item_sources))


 class TreeAttrAccessMixin(AttrAccessMixin):
@@ -233,7 +236,21 @@ class TreeAttrAccessMixin(AttrAccessMixin):
 def get_squeeze_dims(xarray_obj, dim: (Hashable | Iterable[Hashable] | None
     )=None, axis: (int | Iterable[int] | None)=None) ->list[Hashable]:
     """Get a list of dimensions to squeeze out."""
-    pass
+    if dim is not None and axis is not None:
+        raise ValueError("Cannot specify both 'dim' and 'axis'")
+    
+    if dim is None and axis is None:
+        return [d for d, s in xarray_obj.sizes.items() if s == 1]
+    
+    if isinstance(dim, Hashable) and not isinstance(dim, Iterable):
+        dim = [dim]
+    if isinstance(axis, int):
+        axis = [axis]
+    
+    if axis is not None:
+        dim = [xarray_obj.dims[i] for i in axis]
+    
+    return [d for d in dim if xarray_obj.sizes[d] == 1]


 class DataWithCoords(AttrAccessMixin):
@@ -1194,14 +1211,42 @@ def full_like(other: (Dataset | DataArray | Variable), fill_value: Any,
     ones_like

     """
-    pass
+    if isinstance(other, Dataset):
+        data_vars = {}
+        for name, da in other.data_vars.items():
+            if isinstance(fill_value, dict):
+                value = fill_value.get(name, np.nan)
+            else:
+                value = fill_value
+            data_vars[name] = _full_like_variable(da.variable, value, dtype, chunks, chunked_array_type, from_array_kwargs)
+        return Dataset(data_vars, coords=other.coords, attrs=other.attrs)
+    elif isinstance(other, DataArray):
+        return DataArray(_full_like_variable(other.variable, fill_value, dtype, chunks, chunked_array_type, from_array_kwargs),
+                         dims=other.dims, coords=other.coords, attrs=other.attrs, name=other.name)
+    elif isinstance(other, Variable):
+        return _full_like_variable(other, fill_value, dtype, chunks, chunked_array_type, from_array_kwargs)
+    else:
+        raise TypeError(f"Expected DataArray, Dataset, or Variable, got {type(other)}")


 def _full_like_variable(other: Variable, fill_value: Any, dtype: (DTypeLike |
     None)=None, chunks: T_Chunks=None, chunked_array_type: (str | None)=
     None, from_array_kwargs: (dict[str, Any] | None)=None) ->Variable:
     """Inner function of full_like, where other must be a variable"""
-    pass
+    if dtype is None:
+        dtype = other.dtype
+    shape = other.shape
+    
+    if chunks is None and chunked_array_type is None and is_chunked_array(other.data):
+        chunks = other.chunks
+    
+    if chunks is not None or chunked_array_type is not None:
+        chunkmanager = guess_chunkmanager(chunked_array_type)
+        data = chunkmanager.full(shape, fill_value, dtype=dtype, chunks=chunks, **(from_array_kwargs or {}))
+    else:
+        data = np.full(shape, fill_value, dtype=dtype)
+    
+    return Variable(dims=other.dims, data=data, attrs=other.attrs)


 def zeros_like(other: (Dataset | DataArray | Variable), dtype: (
@@ -1272,7 +1317,7 @@ def zeros_like(other: (Dataset | DataArray | Variable), dtype: (
     full_like

     """
-    pass
+    return full_like(other, 0, dtype, chunks=chunks, chunked_array_type=chunked_array_type, from_array_kwargs=from_array_kwargs)


 def ones_like(other: (Dataset | DataArray | Variable), dtype: (
@@ -1335,31 +1380,41 @@ def ones_like(other: (Dataset | DataArray | Variable), dtype: (
     full_like

     """
-    pass
+    return full_like(other, 1, dtype, chunks=chunks, chunked_array_type=chunked_array_type, from_array_kwargs=from_array_kwargs)


 def is_np_datetime_like(dtype: DTypeLike) ->bool:
     """Check if a dtype is a subclass of the numpy datetime types"""
-    pass
+    return np.issubdtype(dtype, np.datetime64) or np.issubdtype(dtype, np.timedelta64)


 def is_np_timedelta_like(dtype: DTypeLike) ->bool:
     """Check whether dtype is of the timedelta64 dtype."""
-    pass
+    return np.issubdtype(dtype, np.timedelta64)


 def _contains_cftime_datetimes(array: Any) ->bool:
     """Check if a array inside a Variable contains cftime.datetime objects"""
-    pass
+    if cftime is None:
+        return False
+    return (
+        array.dtype == object
+        and isinstance(array, (np.ndarray, pd.Index))
+        and array.size > 0
+        and isinstance(array.flat[0], cftime.datetime)
+    )


 def contains_cftime_datetimes(var: T_Variable) ->bool:
     """Check if an xarray.Variable contains cftime.datetime objects"""
-    pass
+    return _contains_cftime_datetimes(var.data)


 def _contains_datetime_like_objects(var: T_Variable) ->bool:
     """Check if a variable contains datetime like objects (either
     np.datetime64, np.timedelta64, or cftime.datetime)
     """
-    pass
+    return (
+        is_np_datetime_like(var.dtype)
+        or (var.dtype == object and contains_cftime_datetimes(var))
+    )
diff --git a/xarray/core/computation.py b/xarray/core/computation.py
index fd8f4fb2..0503eb18 100644
--- a/xarray/core/computation.py
+++ b/xarray/core/computation.py
@@ -37,12 +37,15 @@ _JOINS_WITHOUT_FILL_VALUES = frozenset({'inner', 'exact'})

 def _first_of_type(args, kind):
     """Return either first object of type 'kind' or raise if not found."""
-    pass
+    for arg in args:
+        if isinstance(arg, kind):
+            return arg
+    raise ValueError(f"No object of type {kind} found in arguments")


 def _all_of_type(args, kind):
     """Return all objects of type 'kind'"""
-    pass
+    return [arg for arg in args if isinstance(arg, kind)]


 class _UFuncSignature:
@@ -136,7 +139,39 @@ def build_output_coords_and_indexes(args: Iterable[Any], signature:
     -------
     Dictionaries of Variable and Index objects with merged coordinates.
     """
-    pass
+    from xarray.core.coordinates import Coordinates
+    from xarray.core.dataarray import DataArray
+    from xarray.core.dataset import Dataset
+    
+    datasets = _all_of_type(args, Dataset)
+    dataarrays = _all_of_type(args, DataArray)
+    
+    all_coords = []
+    all_indexes = []
+    
+    for obj in itertools.chain(datasets, dataarrays):
+        coords = obj.coords.copy()
+        indexes = obj.xindexes.copy()
+        
+        # Drop excluded dimensions
+        for dim in exclude_dims:
+            coords = coords.drop(dim) if dim in coords else coords
+            indexes = {k: v for k, v in indexes.items() if k != dim}
+        
+        all_coords.append(coords)
+        all_indexes.append(indexes)
+    
+    # Merge coordinates
+    merged_coords = Coordinates.merge(all_coords, combine_attrs=combine_attrs)
+    
+    # Merge indexes
+    merged_indexes = {}
+    for dim in set().union(*[set(idx.keys()) for idx in all_indexes]):
+        indexes = [idx[dim] for idx in all_indexes if dim in idx]
+        if indexes:
+            merged_indexes[dim] = indexes[0].merge(indexes[1:])
+    
+    return [merged_coords], [merged_indexes]


 def apply_dataarray_vfunc(func, *args, signature: _UFuncSignature, join:
@@ -145,7 +180,36 @@ def apply_dataarray_vfunc(func, *args, signature: _UFuncSignature, join:
     """Apply a variable level function over DataArray, Variable and/or ndarray
     objects.
     """
-    pass
+    from xarray.core.dataarray import DataArray
+    from xarray.core.variable import Variable
+    
+    # Extract DataArrays from args
+    dataarrays = _all_of_type(args, DataArray)
+    
+    # Align DataArrays
+    aligned = align(*dataarrays, join=join, exclude=exclude_dims, copy=False)
+    
+    # Replace DataArrays in args with their data
+    new_args = [
+        arg.data if isinstance(arg, DataArray) else arg for arg in args
+    ]
+    
+    # Apply the function
+    result_data = func(*new_args)
+    
+    # Build output coordinates and indexes
+    coords, indexes = build_output_coords_and_indexes(
+        aligned, signature, exclude_dims, keep_attrs
+    )
+    
+    # Create output DataArray(s)
+    if isinstance(result_data, tuple):
+        return tuple(
+            DataArray(data, coords=coords[0], indexes=indexes[0])
+            for data in result_data
+        )
+    else:
+        return DataArray(result_data, coords=coords[0], indexes=indexes[0])


 _JOINERS: dict[str, Callable] = {'inner': ordered_set_intersection, 'outer':
@@ -170,7 +234,42 @@ def apply_dict_of_variables_vfunc(func, *args, signature: _UFuncSignature,
     """Apply a variable level function over dicts of DataArray, DataArray,
     Variable and ndarray objects.
     """
-    pass
+    from xarray.core.dataarray import DataArray
+    from xarray.core.dataset import Dataset
+    from xarray.core.variable import Variable
+    
+    # Extract datasets and convert other arguments to datasets
+    datasets = []
+    for arg in args:
+        if isinstance(arg, Dataset):
+            datasets.append(arg)
+        elif isinstance(arg, dict):
+            datasets.append(Dataset(arg))
+        elif isinstance(arg, (DataArray, Variable)):
+            datasets.append(Dataset({getattr(arg, 'name', 'unnamed'): arg}))
+        else:
+            datasets.append(Dataset({'unnamed': Variable((), arg)}))
+    
+    # Align datasets
+    aligned = align(*datasets, join=join, copy=False, fill_value=fill_value)
+    
+    # Apply function to each variable
+    result_vars = {}
+    for var_name in aligned[0].data_vars:
+        var_args = [ds[var_name].variable for ds in aligned if var_name in ds]
+        if len(var_args) < len(aligned) and on_missing_core_dim == 'raise':
+            raise ValueError(f"Variable {var_name} missing from some datasets")
+        elif len(var_args) < len(aligned) and on_missing_core_dim == 'drop':
+            continue
+        
+        result = func(*var_args)
+        if isinstance(result, tuple):
+            for i, res in enumerate(result):
+                result_vars[f"{var_name}_{i}"] = res
+        else:
+            result_vars[var_name] = result
+    
+    return Dataset(result_vars)


 def _fast_dataset(variables: dict[Hashable, Variable], coord_variables:
@@ -179,7 +278,11 @@ def _fast_dataset(variables: dict[Hashable, Variable], coord_variables:

     Beware: the `variables` dict is modified INPLACE.
     """
-    pass
+    from xarray.core.dataset import Dataset
+    
+    variables.update(coord_variables)
+    coords = set(coord_variables)
+    return Dataset._construct_direct(variables, coords, indexes)


 def apply_dataset_vfunc(func, *args, signature: _UFuncSignature, join=
@@ -189,19 +292,80 @@ def apply_dataset_vfunc(func, *args, signature: _UFuncSignature, join=
     """Apply a variable level function over Dataset, dict of DataArray,
     DataArray, Variable and/or ndarray objects.
     """
-    pass
+    from xarray.core.dataset import Dataset
+    from xarray.core.dataarray import DataArray
+    from xarray.core.variable import Variable
+    
+    datasets = []
+    for arg in args:
+        if isinstance(arg, Dataset):
+            datasets.append(arg)
+        elif isinstance(arg, dict):
+            datasets.append(Dataset(arg))
+        elif isinstance(arg, (DataArray, Variable)):
+            datasets.append(Dataset({getattr(arg, 'name', 'unnamed'): arg}))
+        else:
+            datasets.append(Dataset({'unnamed': Variable((), arg)}))
+    
+    aligned = align(*datasets, join=join, copy=False, exclude=exclude_dims,
+                    fill_value=fill_value)
+    
+    result_vars = {}
+    for var_name in aligned[0].data_vars:
+        var_args = [ds[var_name].variable for ds in aligned if var_name in ds]
+        if len(var_args) < len(aligned):
+            if on_missing_core_dim == 'raise':
+                raise ValueError(f"Variable {var_name} missing from some datasets")
+            elif on_missing_core_dim == 'drop':
+                continue
+        
+        result = func(*var_args)
+        if isinstance(result, tuple):
+            for i, res in enumerate(result):
+                result_vars[f"{var_name}_{i}"] = res
+        else:
+            result_vars[var_name] = result
+    
+    coords, indexes = build_output_coords_and_indexes(
+        aligned, signature, exclude_dims, keep_attrs
+    )
+    
+    result_dataset = _fast_dataset(result_vars, coords[0], indexes[0])
+    
+    if keep_attrs != 'drop':
+        result_dataset.attrs = aligned[0].attrs
+    
+    return result_dataset


 def _iter_over_selections(obj, dim, values):
     """Iterate over selections of an xarray object in the provided order."""
-    pass
+    for value in values:
+        yield obj.isel({dim: value})


 def apply_groupby_func(func, *args):
     """Apply a dataset or datarray level function over GroupBy, Dataset,
     DataArray, Variable and/or ndarray objects.
     """
-    pass
+    from xarray.core.groupby import GroupBy
+    
+    groupbys = [arg for arg in args if isinstance(arg, GroupBy)]
+    if not groupbys:
+        return func(*args)
+    
+    grouped = groupbys[0]
+    other_args = [arg for arg in args if not isinstance(arg, GroupBy)]
+    
+    applied = []
+    for labels, group in grouped:
+        group_args = [group] + [
+            arg.sel(group.coords) if hasattr(arg, 'sel') else arg
+            for arg in other_args
+        ]
+        applied.append(func(*group_args))
+    
+    return grouped._combine(applied)


 SLICE_NONE = slice(None)
@@ -212,12 +376,55 @@ def apply_variable_ufunc(func, *args, signature: _UFuncSignature,
     vectorize=False, keep_attrs='override', dask_gufunc_kwargs=None) ->(
     Variable | tuple[Variable, ...]):
     """Apply a ndarray level function over Variable and/or ndarray objects."""
-    pass
+    from xarray.core.variable import Variable
+    import numpy as np
+    
+    if vectorize:
+        func = np.vectorize(func)
+    
+    input_core_dims = signature.input_core_dims
+    output_core_dims = signature.output_core_dims
+    
+    if dask == 'forbidden':
+        arrays = [arg.data if isinstance(arg, Variable) else arg for arg in args]
+        result_data = func(*arrays)
+    elif dask == 'allowed':
+        arrays = [arg.data if isinstance(arg, Variable) else arg for arg in args]
+        result_data = func(*arrays)
+    elif dask == 'parallelized':
+        import dask.array as da
+        arrays = [arg.data if isinstance(arg, Variable) else arg for arg in args]
+        result_data = da.apply_gufunc(func, signature, *arrays, 
+                                      output_dtypes=output_dtypes, 
+                                      **dask_gufunc_kwargs)
+    else:
+        raise ValueError("dask must be 'forbidden', 'allowed' or 'parallelized'")
+    
+    if isinstance(result_data, tuple):
+        results = []
+        for data, out_core_dims in zip(result_data, output_core_dims):
+            dims = [d for d in args[0].dims if d not in exclude_dims] + list(out_core_dims)
+            results.append(Variable(dims, data))
+        return tuple(results)
+    else:
+        dims = [d for d in args[0].dims if d not in exclude_dims] + list(output_core_dims[0])
+        return Variable(dims, result_data)


 def apply_array_ufunc(func, *args, dask='forbidden'):
     """Apply a ndarray level function over ndarray objects."""
-    pass
+    import numpy as np
+    
+    if dask == 'forbidden':
+        return func(*args)
+    elif dask == 'allowed':
+        return func(*args)
+    elif dask == 'parallelized':
+        import dask.array as da
+        dask_args = [da.from_array(arg) if isinstance(arg, np.ndarray) else arg for arg in args]
+        return da.map_overlap(func, *dask_args)
+    else:
+        raise ValueError("dask must be 'forbidden', 'allowed' or 'parallelized'")


 def apply_ufunc(func: Callable, *args: Any, input_core_dims: (Sequence[
diff --git a/xarray/core/concat.py b/xarray/core/concat.py
index 636b3856..04f109a6 100644
--- a/xarray/core/concat.py
+++ b/xarray/core/concat.py
@@ -189,7 +189,24 @@ def concat(objs, dim, data_vars: T_DataVars='all', coords='different',
     Indexes:
         *empty*
     """
-    pass
+    dim_name, dim_index = _calc_concat_dim_index(dim)
+    
+    if isinstance(objs[0], T_DataArray):
+        return _dataarray_concat(
+            objs, dim=dim_name, dim_index=dim_index,
+            data_vars=data_vars, coords=coords, compat=compat,
+            positions=positions, fill_value=fill_value, join=join,
+            combine_attrs=combine_attrs,
+            create_index_for_new_dim=create_index_for_new_dim
+        )
+    else:
+        return _dataset_concat(
+            objs, dim=dim_name, dim_index=dim_index,
+            data_vars=data_vars, coords=coords, compat=compat,
+            positions=positions, fill_value=fill_value, join=join,
+            combine_attrs=combine_attrs,
+            create_index_for_new_dim=create_index_for_new_dim
+        )


 def _calc_concat_dim_index(dim_or_data: (Hashable | Any)) ->tuple[Hashable,
@@ -198,7 +215,14 @@ def _calc_concat_dim_index(dim_or_data: (Hashable | Any)) ->tuple[Hashable,
     for concatenating along the new dimension.

     """
-    pass
+    if isinstance(dim_or_data, str):
+        return dim_or_data, None
+    elif isinstance(dim_or_data, pd.Index):
+        return dim_or_data.name, PandasIndex(dim_or_data)
+    elif isinstance(dim_or_data, (Variable, DataArray)):
+        return dim_or_data.name, PandasIndex(dim_or_data.values)
+    else:
+        return dim_or_data, None


 def _calc_concat_over(datasets, dim, dim_names, data_vars: T_DataVars,
@@ -206,7 +230,39 @@ def _calc_concat_over(datasets, dim, dim_names, data_vars: T_DataVars,
     """
     Determine which dataset variables need to be concatenated in the result,
     """
-    pass
+    concat_over = set()
+    
+    if isinstance(data_vars, str):
+        if data_vars == 'all':
+            concat_over.update(set().union(*[ds.data_vars for ds in datasets]))
+        elif data_vars == 'minimal':
+            concat_over.update(dim_names)
+        elif data_vars == 'different':
+            def differs(vname):
+                return any(not utils.dict_equiv(ds[vname].attrs, datasets[0][vname].attrs)
+                           or not utils.array_equiv(ds[vname], datasets[0][vname])
+                           for ds in datasets[1:])
+            concat_over.update(v for v in set().union(*[ds.data_vars for ds in datasets])
+                               if differs(v))
+    elif isinstance(data_vars, list):
+        concat_over.update(data_vars)
+    
+    if isinstance(coords, str):
+        if coords == 'minimal':
+            concat_over.update(k for k in dim_names if k in datasets[0].coords)
+        elif coords == 'different':
+            def differs(vname):
+                return any(not utils.dict_equiv(ds[vname].attrs, datasets[0][vname].attrs)
+                           or not utils.array_equiv(ds[vname], datasets[0][vname])
+                           for ds in datasets[1:])
+            concat_over.update(v for v in set().union(*[ds.coords for ds in datasets])
+                               if differs(v))
+        elif coords == 'all':
+            concat_over.update(set().union(*[ds.coords for ds in datasets]))
+    elif isinstance(coords, list):
+        concat_over.update(coords)
+    
+    return concat_over


 def _dataset_concat(datasets: Iterable[T_Dataset], dim: (str | T_Variable |
@@ -218,4 +274,31 @@ def _dataset_concat(datasets: Iterable[T_Dataset], dim: (str | T_Variable |
     """
     Concatenate a sequence of datasets along a new or existing dimension
     """
-    pass
+    datasets = list(datasets)
+    if not datasets:
+        raise ValueError("Need at least one dataset to concatenate")
+
+    dim_name, dim_index = _calc_concat_dim_index(dim)
+    dim_names = [dim_name] if dim_name not in datasets[0].dims else []
+    concat_over = _calc_concat_over(datasets, dim, dim_names, data_vars, coords, compat)
+
+    def process_variable(name, variables):
+        if name in concat_over:
+            return concat_vars(variables, dim=dim, positions=positions, fill_value=fill_value)
+        else:
+            return variables[0]
+
+    variables = {}
+    for name in set().union(*[ds.variables for ds in datasets]):
+        variables[name] = process_variable(name, [ds[name] for ds in datasets if name in ds])
+
+    coord_names = set().union(*[ds.coords for ds in datasets])
+    attrs = merge_attrs([ds.attrs for ds in datasets], combine_attrs)
+
+    result = Dataset(variables, attrs=attrs)
+    result = result.set_coords(coord_names.intersection(variables))
+
+    if create_index_for_new_dim and dim_index is not None:
+        result = result.assign_coords({dim_name: dim_index})
+
+    return result
diff --git a/xarray/core/coordinates.py b/xarray/core/coordinates.py
index 2740e51a..16773592 100644
--- a/xarray/core/coordinates.py
+++ b/xarray/core/coordinates.py
@@ -36,14 +36,14 @@ class AbstractCoordinates(Mapping[Hashable, 'T_DataArray']):
         --------
         Coordinates.xindexes
         """
-        pass
+        return Indexes({k: v.to_pandas_index() for k, v in self.xindexes.items()})

     @property
     def xindexes(self) ->Indexes[Index]:
         """Mapping of :py:class:`~xarray.indexes.Index` objects
         used for label based indexing.
         """
-        pass
+        return self._data.xindexes

     def __iter__(self) ->Iterator[Hashable]:
         for k in self.variables:
@@ -76,7 +76,12 @@ class AbstractCoordinates(Mapping[Hashable, 'T_DataArray']):
             coordinates. This will be a MultiIndex if this object is has more
             than more dimension.
         """
-        pass
+        if ordered_dims is None:
+            ordered_dims = list(self.dims)
+        indexes = [self.indexes[dim] for dim in ordered_dims]
+        if len(indexes) == 1:
+            return indexes[0]
+        return pd.MultiIndex.from_product(indexes, names=ordered_dims)


 class Coordinates(AbstractCoordinates):
@@ -228,17 +233,23 @@ class Coordinates(AbstractCoordinates):
             A collection of Xarray indexed coordinates created from the multi-index.

         """
-        pass
+        coords = {}
+        coords[dim] = midx
+        for i, name in enumerate(midx.names):
+            if name is None:
+                name = f"{dim}_level_{i}"
+            coords[name] = (dim, midx.get_level_values(i))
+        return cls(coords)

     @property
     def dims(self) ->(Frozen[Hashable, int] | tuple[Hashable, ...]):
         """Mapping from dimension names to lengths or tuple of dimension names."""
-        pass
+        return self._data.dims

     @property
     def sizes(self) ->Frozen[Hashable, int]:
         """Mapping from dimension names to lengths."""
-        pass
+        return Frozen(self._data.sizes)

     @property
     def dtypes(self) ->Frozen[Hashable, np.dtype]:
@@ -250,7 +261,7 @@ class Coordinates(AbstractCoordinates):
         --------
         Dataset.dtypes
         """
-        pass
+        return Frozen({k: v.dtype for k, v in self.variables.items()})

     @property
     def variables(self) ->Mapping[Hashable, Variable]:
@@ -262,7 +273,7 @@ class Coordinates(AbstractCoordinates):

     def to_dataset(self) ->Dataset:
         """Convert these coordinates into a new Dataset."""
-        pass
+        return self._data.copy()

     def __getitem__(self, key: Hashable) ->DataArray:
         return self._data[key]
@@ -278,7 +289,7 @@ class Coordinates(AbstractCoordinates):
         --------
         Coordinates.identical
         """
-        pass
+        return self._data.equals(other._data)

     def identical(self, other: Self) ->bool:
         """Like equals, but also checks all variable attributes.
@@ -287,7 +298,7 @@ class Coordinates(AbstractCoordinates):
         --------
         Coordinates.equals
         """
-        pass
+        return self._data.identical(other._data)

     def _merge_raw(self, other, reflexive):
         """For use with binary arithmetic."""
diff --git a/xarray/core/dask_array_ops.py b/xarray/core/dask_array_ops.py
index e551b759..10321660 100644
--- a/xarray/core/dask_array_ops.py
+++ b/xarray/core/dask_array_ops.py
@@ -4,11 +4,29 @@ from xarray.core import dtypes, nputils

 def dask_rolling_wrapper(moving_func, a, window, min_count=None, axis=-1):
     """Wrapper to apply bottleneck moving window funcs on dask arrays"""
-    pass
+    import dask.array as da
+    import numpy as np
+
+    if min_count is None:
+        min_count = window
+
+    def wrapped_func(x):
+        return moving_func(x, window, min_count=min_count, axis=axis)
+
+    if isinstance(a, da.Array):
+        return a.map_overlap(wrapped_func, depth={axis: window - 1}, boundary='reflect')
+    else:
+        return wrapped_func(np.asarray(a))


 def push(array, n, axis):
     """
     Dask-aware bottleneck.push
     """
-    pass
+    import dask.array as da
+    import bottleneck as bn
+
+    if isinstance(array, da.Array):
+        return da.map_overlap(bn.push, array, n=n, axis=axis, depth={axis: n}, boundary='reflect')
+    else:
+        return bn.push(array, n=n, axis=axis)
diff --git a/xarray/core/datatree.py b/xarray/core/datatree.py
index 397a6531..60a91748 100644
--- a/xarray/core/datatree.py
+++ b/xarray/core/datatree.py
@@ -384,7 +384,10 @@ class DataTree(NamedNode, MappedDatasetMethodsMixin, MappedDataWithCoords,
         xarray.Dataset.copy
         pandas.DataFrame.copy
         """
-        pass
+        new_tree = self._copy_node(deep)
+        for child_name, child_node in self._children.items():
+            new_tree._children[child_name] = child_node.copy(deep)
+        return new_tree

     def _copy_subtree(self: DataTree, deep: bool=False, memo: (dict[int,
         Any] | None)=None) ->DataTree:
@@ -393,7 +396,15 @@ class DataTree(NamedNode, MappedDatasetMethodsMixin, MappedDataWithCoords,

     def _copy_node(self: DataTree, deep: bool=False) ->DataTree:
         """Copy just one node of a tree"""
-        pass
+        new_node = DataTree(name=self._name)
+        new_node._data_variables = self._data_variables.copy(deep=deep)
+        new_node._node_coord_variables = self._node_coord_variables.copy(deep=deep)
+        new_node._node_dims = self._node_dims.copy()
+        new_node._node_indexes = self._node_indexes.copy()
+        new_node._attrs = self._attrs.copy() if self._attrs is not None else None
+        new_node._encoding = self._encoding.copy() if self._encoding is not None else None
+        new_node._close = self._close
+        return new_node

     def __copy__(self: DataTree) ->DataTree:
         return self._copy_subtree(deep=False)
@@ -417,7 +428,14 @@ class DataTree(NamedNode, MappedDatasetMethodsMixin, MappedDataWithCoords,
         default : DataTree | DataArray | None, optional
             A value to return if the specified key does not exist. Default return value is None.
         """
-        pass
+        if key in self._children:
+            return self._children[key]
+        elif key in self._data_variables:
+            return DataArray(self._data_variables[key])
+        elif key in self._node_coord_variables:
+            return DataArray(self._node_coord_variables[key])
+        else:
+            return default

     def __getitem__(self: DataTree, key: str) ->(DataTree | DataArray):
         """
@@ -472,6 +490,24 @@ class DataTree(NamedNode, MappedDatasetMethodsMixin, MappedDataWithCoords,
         else:
             raise ValueError('Invalid format for key')

+    def _set_item(self, path: NodePath, value: Any, new_nodes_along_path: bool = False) -> None:
+        if len(path) == 1:
+            if isinstance(value, DataTree):
+                self._children[path[0]] = value
+            elif isinstance(value, Dataset):
+                self._children[path[0]] = DataTree(value)
+            elif isinstance(value, DataArray):
+                self._data_variables[path[0]] = value.variable
+            else:
+                self._data_variables[path[0]] = Variable((), value)
+        else:
+            if path[0] not in self._children:
+                if new_nodes_along_path:
+                    self._children[path[0]] = DataTree()
+                else:
+                    raise KeyError(f"Node '{path[0]}' does not exist")
+            self._children[path[0]]._set_item(path[1:], value, new_nodes_along_path)
+
     def update(self, other: (Dataset | Mapping[Hashable, DataArray |
         Variable] | Mapping[str, DataTree | DataArray | Variable])) ->None:
         """
diff --git a/xarray/core/datatree_io.py b/xarray/core/datatree_io.py
index ac9c6ad9..c1f715e6 100644
--- a/xarray/core/datatree_io.py
+++ b/xarray/core/datatree_io.py
@@ -18,7 +18,34 @@ def _datatree_to_netcdf(dt: DataTree, filepath: (str | PathLike), mode:

     See `DataTree.to_netcdf` for full API docs.
     """
-    pass
+    import xarray as xr
+    from xarray.backends.api import to_netcdf
+
+    # Create a new Dataset to hold all the data from the DataTree
+    combined_dataset = xr.Dataset()
+
+    def add_to_dataset(node, path):
+        for var_name, var in node.data_vars.items():
+            full_name = f"{path}/{var_name}" if path else var_name
+            combined_dataset[full_name] = var
+        for child_name, child_node in node.children.items():
+            add_to_dataset(child_node, f"{path}/{child_name}" if path else child_name)
+
+    add_to_dataset(dt, "")
+
+    # Use xarray's to_netcdf function to write the combined dataset
+    to_netcdf(
+        combined_dataset,
+        filepath,
+        mode=mode,
+        encoding=encoding,
+        unlimited_dims=unlimited_dims,
+        format=format,
+        engine=engine,
+        group=group,
+        compute=compute,
+        **kwargs
+    )


 def _datatree_to_zarr(dt: DataTree, store: (MutableMapping | str | PathLike
@@ -30,4 +57,39 @@ def _datatree_to_zarr(dt: DataTree, store: (MutableMapping | str | PathLike

     See `DataTree.to_zarr` for full API docs.
     """
-    pass
+    import zarr
+    from xarray.backends.api import to_zarr
+
+    def write_node(node, group):
+        # Write the current node's data to the group
+        to_zarr(
+            node,
+            store=group,
+            mode='w',
+            encoding=encoding,
+            consolidated=consolidated,
+            compute=compute,
+            **kwargs
+        )
+
+        # Recursively write child nodes
+        for child_name, child_node in node.children.items():
+            child_group = group.create_group(child_name)
+            write_node(child_node, child_group)
+
+    # Create or open the root group
+    if isinstance(store, (str, PathLike)):
+        root = zarr.open_group(store, mode=mode)
+    else:
+        root = zarr.group(store=store)
+
+    # If a specific group is specified, create or get it
+    if group:
+        root = root.create_group(group) if group not in root else root[group]
+
+    # Start the recursive writing process
+    write_node(dt, root)
+
+    # Consolidate metadata if requested
+    if consolidated:
+        zarr.consolidate_metadata(store)
diff --git a/xarray/core/datatree_mapping.py b/xarray/core/datatree_mapping.py
index bb01488b..74de38c0 100644
--- a/xarray/core/datatree_mapping.py
+++ b/xarray/core/datatree_mapping.py
@@ -47,7 +47,24 @@ def check_isomorphic(a: DataTree, b: DataTree, require_names_equal: bool=
         Also optionally raised if their structure is isomorphic, but the names of any two
         respective nodes are not equal.
     """
-    pass
+    if not isinstance(a, TreeNode) or not isinstance(b, TreeNode):
+        raise TypeError("Both arguments must be tree objects.")
+
+    if check_from_root:
+        a = a.root
+        b = b.root
+
+    def check_nodes(node_a, node_b):
+        if len(node_a.children) != len(node_b.children):
+            raise TreeIsomorphismError("Trees are not isomorphic: different number of children.")
+        
+        if require_names_equal and node_a.name != node_b.name:
+            raise TreeIsomorphismError(f"Node names do not match: {node_a.name} != {node_b.name}")
+        
+        for child_a, child_b in zip(node_a.children.values(), node_b.children.values()):
+            check_nodes(child_a, child_b)
+
+    check_nodes(a, b)


 def map_over_subtree(func: Callable) ->Callable:
@@ -94,20 +111,87 @@ def map_over_subtree(func: Callable) ->Callable:
     DataTree.map_over_subtree_inplace
     DataTree.subtree
     """
-    pass
+    @functools.wraps(func)
+    def wrapper(*args, **kwargs):
+        if not args:
+            raise ValueError("At least one DataTree argument is required.")
+
+        trees = [arg for arg in args if isinstance(arg, DataTree)]
+        if not trees:
+            raise ValueError("At least one argument must be a DataTree.")
+
+        check_isomorphic(*trees)
+
+        def apply_to_node(node, *node_args):
+            if node.ds is not None:
+                node_args = [arg.ds if isinstance(arg, DataTree) else arg for arg in node_args]
+                result = func(*node_args, **kwargs)
+                return result
+            return None
+
+        def map_tree(tree, *other_trees):
+            new_tree = type(tree)()
+            for name, node in tree.children.items():
+                other_nodes = [other_tree[name] for other_tree in other_trees]
+                result = apply_to_node(node, *other_nodes)
+                if result is not None:
+                    new_tree[name] = result
+                child_result = map_tree(node, *other_nodes)
+                if child_result.children:
+                    new_tree[name] = child_result
+            return new_tree
+
+        return map_tree(*trees)
+
+    return wrapper


 def _handle_errors_with_path_context(path: str):
     """Wraps given function so that if it fails it also raises path to node on which it failed."""
-    pass
+    def decorator(func):
+        @functools.wraps(func)
+        def wrapper(*args, **kwargs):
+            try:
+                return func(*args, **kwargs)
+            except Exception as e:
+                raise type(e)(f"Error at path '{path}': {str(e)}") from e
+        return wrapper
+    return decorator


 def _check_single_set_return_values(path_to_node: str, obj: (Dataset |
     DataArray | tuple[Dataset | DataArray])):
     """Check types returned from single evaluation of func, and return number of return values received from func."""
-    pass
+    if isinstance(obj, (Dataset, DataArray)):
+        return 1
+    elif isinstance(obj, tuple):
+        if all(isinstance(item, (Dataset, DataArray)) for item in obj):
+            return len(obj)
+        else:
+            raise TypeError(f"At path '{path_to_node}': All items in the returned tuple must be Dataset or DataArray.")
+    else:
+        raise TypeError(f"At path '{path_to_node}': Return value must be Dataset, DataArray, or tuple of these types.")


 def _check_all_return_values(returned_objects):
     """Walk through all values returned by mapping func over subtrees, raising on any invalid or inconsistent types."""
-    pass
+    if not returned_objects:
+        return
+
+    first_item = next(iter(returned_objects.values()))
+    expected_type = type(first_item)
+    expected_length = len(first_item) if isinstance(first_item, tuple) else 1
+
+    for path, obj in returned_objects.items():
+        if not isinstance(obj, expected_type):
+            raise TypeError(f"Inconsistent return types: expected {expected_type}, got {type(obj)} at path '{path}'")
+        
+        if isinstance(obj, tuple):
+            if len(obj) != expected_length:
+                raise ValueError(f"Inconsistent number of return values: expected {expected_length}, got {len(obj)} at path '{path}'")
+            
+            for item in obj:
+                if not isinstance(item, (Dataset, DataArray)):
+                    raise TypeError(f"Invalid return type in tuple: expected Dataset or DataArray, got {type(item)} at path '{path}'")
+        elif not isinstance(obj, (Dataset, DataArray)):
+            raise TypeError(f"Invalid return type: expected Dataset or DataArray, got {type(obj)} at path '{path}'")
diff --git a/xarray/core/datatree_ops.py b/xarray/core/datatree_ops.py
index 77c69078..e7dee3da 100644
--- a/xarray/core/datatree_ops.py
+++ b/xarray/core/datatree_ops.py
@@ -73,7 +73,14 @@ def _wrap_then_attach_to_cls(target_cls_dict, source_cls, methods_to_set,
     wrap_func : callable, optional
         Function to decorate each method with. Must have the same return type as the method.
     """
-    pass
+    for method_name, method in methods_to_set:
+        if hasattr(source_cls, method_name):
+            source_method = getattr(source_cls, method_name)
+            if wrap_func:
+                wrapped_method = wrap_func(source_method)
+            else:
+                wrapped_method = source_method
+            target_cls_dict[method_name] = wrapped_method


 def insert_doc_addendum(docstring: (str | None), addendum: str) ->(str | None):
@@ -86,7 +93,18 @@ def insert_doc_addendum(docstring: (str | None), addendum: str) ->(str | None):
     don't, just have the addendum appeneded after. None values are returned.

     """
-    pass
+    if docstring is None:
+        return None
+
+    lines = docstring.split('\n')
+    first_empty_line = next((i for i, line in enumerate(lines) if not line.strip()), len(lines))
+
+    if first_empty_line == len(lines):
+        # No empty line found, append addendum at the end
+        return f"{docstring}\n\n{addendum}"
+    else:
+        # Insert addendum after the first paragraph
+        return '\n'.join(lines[:first_empty_line] + ['', addendum] + lines[first_empty_line:])


 class MappedDatasetMethodsMixin:
diff --git a/xarray/core/datatree_render.py b/xarray/core/datatree_render.py
index 184464bb..38bfee48 100644
--- a/xarray/core/datatree_render.py
+++ b/xarray/core/datatree_render.py
@@ -34,7 +34,7 @@ class AbstractStyle:
     @property
     def empty(self) ->str:
         """Empty string as placeholder."""
-        pass
+        return " " * len(self.vertical)

     def __repr__(self) ->str:
         return f'{self.__class__.__name__}()'
@@ -195,4 +195,9 @@ class RenderDataTree:
             └── sub1C
                 └── sub1Ca
         """
-        pass
+        lines = []
+        for pre, _, node in self:
+            attr = getattr(node, attrname, None)
+            if attr is not None:
+                lines.append(f"{pre}{attr}")
+        return "\n".join(lines)
diff --git a/xarray/core/dtypes.py b/xarray/core/dtypes.py
index 217e8240..2809313c 100644
--- a/xarray/core/dtypes.py
+++ b/xarray/core/dtypes.py
@@ -45,7 +45,16 @@ def maybe_promote(dtype: np.dtype) ->tuple[np.dtype, Any]:
     dtype : Promoted dtype that can hold missing values.
     fill_value : Valid missing value for the promoted dtype.
     """
-    pass
+    if dtype.kind in "mM":
+        return dtype, np.datetime64("NaT")
+    elif dtype.kind == "f":
+        return dtype, np.nan
+    elif dtype.kind in "iu":
+        return np.dtype("float64"), np.nan
+    elif dtype.kind == "b":
+        return np.dtype("object"), NA
+    else:
+        return np.dtype("object"), NA


 NAT_TYPES = {np.datetime64('NaT').dtype, np.timedelta64('NaT').dtype}
@@ -62,7 +71,17 @@ def get_fill_value(dtype):
     -------
     fill_value : Missing value corresponding to this dtype.
     """
-    pass
+    dtype = np.dtype(dtype)
+    if dtype.kind in "mM":
+        return np.datetime64("NaT")
+    elif dtype.kind == "f":
+        return np.nan
+    elif dtype.kind in "iu":
+        return np.iinfo(dtype).min
+    elif dtype.kind == "b":
+        return False
+    else:
+        return NA


 def get_pos_infinity(dtype, max_for_int=False):
@@ -78,11 +97,19 @@ def get_pos_infinity(dtype, max_for_int=False):
     -------
     fill_value : positive infinity value corresponding to this dtype.
     """
-    pass
+    dtype = np.dtype(dtype)
+    if dtype.kind == "f":
+        return np.inf
+    elif dtype.kind in "iu":
+        return np.iinfo(dtype).max if max_for_int else np.inf
+    elif dtype.kind in "mM":
+        return INF
+    else:
+        return INF


 def get_neg_infinity(dtype, min_for_int=False):
-    """Return an appropriate positive infinity for this dtype.
+    """Return an appropriate negative infinity for this dtype.

     Parameters
     ----------
@@ -92,24 +119,32 @@ def get_neg_infinity(dtype, min_for_int=False):

     Returns
     -------
-    fill_value : positive infinity value corresponding to this dtype.
+    fill_value : negative infinity value corresponding to this dtype.
     """
-    pass
+    dtype = np.dtype(dtype)
+    if dtype.kind == "f":
+        return -np.inf
+    elif dtype.kind in "iu":
+        return np.iinfo(dtype).min if min_for_int else -np.inf
+    elif dtype.kind in "mM":
+        return NINF
+    else:
+        return NINF


 def is_datetime_like(dtype) ->bool:
     """Check if a dtype is a subclass of the numpy datetime types"""
-    pass
+    return np.issubdtype(dtype, np.datetime64) or np.issubdtype(dtype, np.timedelta64)


 def is_object(dtype) ->bool:
     """Check if a dtype is object"""
-    pass
+    return np.issubdtype(dtype, np.object_)


 def is_string(dtype) ->bool:
     """Check if a dtype is a string dtype"""
-    pass
+    return np.issubdtype(dtype, np.str_) or np.issubdtype(dtype, np.bytes_)


 def isdtype(dtype, kind: (str | tuple[str, ...]), xp=None) ->bool:
@@ -117,7 +152,13 @@ def isdtype(dtype, kind: (str | tuple[str, ...]), xp=None) ->bool:

     Unlike xp.isdtype(), kind must be a string.
     """
-    pass
+    if xp is None:
+        xp = array_api_compat.get_namespace(dtype)
+    
+    if isinstance(kind, str):
+        kind = (kind,)
+    
+    return any(xp.isdtype(dtype, k) for k in kind)


 def result_type(*arrays_and_dtypes: (np.typing.ArrayLike | np.typing.
@@ -137,4 +178,23 @@ def result_type(*arrays_and_dtypes: (np.typing.ArrayLike | np.typing.
     -------
     numpy.dtype for the result.
     """
-    pass
+    if xp is None:
+        xp = array_api_compat.get_namespace(*arrays_and_dtypes)
+
+    dtypes = []
+    for arg in arrays_and_dtypes:
+        if hasattr(arg, "dtype"):
+            dtypes.append(arg.dtype)
+        else:
+            dtypes.append(np.dtype(arg))
+
+    result = np.result_type(*dtypes)
+
+    # Apply pandas-like promotion rules
+    if any(is_string(dt) for dt in dtypes):
+        if any(dt.kind in "iufc" for dt in dtypes):
+            return np.dtype("O")
+    if any(dt.kind == "S" for dt in dtypes) and any(dt.kind == "U" for dt in dtypes):
+        return np.dtype("O")
+
+    return result
diff --git a/xarray/core/duck_array_ops.py b/xarray/core/duck_array_ops.py
index 872667f1..a7222257 100644
--- a/xarray/core/duck_array_ops.py
+++ b/xarray/core/duck_array_ops.py
@@ -34,7 +34,17 @@ dask_available = module_available('dask')

 def _dask_or_eager_func(name, eager_module=np, dask_module='dask.array'):
     """Create a function that dispatches to dask for dask array inputs."""
-    pass
+    def wrapper(*args, **kwargs):
+        if any(is_duck_dask_array(arg) for arg in args):
+            if isinstance(dask_module, str):
+                module = import_module(dask_module)
+            else:
+                module = dask_module
+            func = getattr(module, name)
+        else:
+            func = getattr(eager_module, name)
+        return func(*args, **kwargs)
+    return wrapper


 pandas_isnull = _dask_or_eager_func('isnull', eager_module=pd, dask_module=
@@ -59,7 +69,14 @@ masked_invalid = _dask_or_eager_func('masked_invalid', eager_module=np.ma,

 def as_shared_dtype(scalars_or_arrays, xp=None):
     """Cast a arrays to a shared dtype using xarray's type promotion rules."""
-    pass
+    if xp is None:
+        xp = np
+    arrays = [xp.asarray(x) for x in scalars_or_arrays]
+    dtypes = [x.dtype for x in arrays]
+    result_type = dtypes[0]
+    for dtype in dtypes[1:]:
+        result_type = np.promote_types(result_type, dtype)
+    return [xp.asarray(x, dtype=result_type) for x in arrays]


 def lazy_array_equiv(arr1, arr2):
@@ -69,44 +86,85 @@ def lazy_array_equiv(arr1, arr2):
     Returns None when equality cannot determined: one or both of arr1, arr2 are numpy arrays;
     or their dask tokens are not equal
     """
-    pass
+    if arr1 is arr2:
+        return True
+    if hasattr(arr1, 'shape') and hasattr(arr2, 'shape'):
+        if arr1.shape != arr2.shape:
+            return False
+    if dask_available:
+        import dask.array as da
+        if isinstance(arr1, da.Array) and isinstance(arr2, da.Array):
+            return arr1.name == arr2.name
+    return None


 def allclose_or_equiv(arr1, arr2, rtol=1e-05, atol=1e-08):
     """Like np.allclose, but also allows values to be NaN in both arrays"""
-    pass
+    arr1, arr2 = as_shared_dtype([arr1, arr2])
+    if array_equiv(arr1, arr2):
+        return True
+    with warnings.catch_warnings():
+        warnings.filterwarnings('ignore', r'invalid value encountered in isnan')
+        return bool(isclose(arr1, arr2, rtol=rtol, atol=atol, equal_nan=True).all())


 def array_equiv(arr1, arr2):
     """Like np.array_equal, but also allows values to be NaN in both arrays"""
-    pass
+    arr1, arr2 = as_shared_dtype([arr1, arr2])
+    if arr1.shape != arr2.shape:
+        return False
+    with warnings.catch_warnings():
+        warnings.filterwarnings('ignore', r'invalid value encountered in isnan')
+        return bool(((arr1 == arr2) | (isnan(arr1) & isnan(arr2))).all())


 def array_notnull_equiv(arr1, arr2):
     """Like np.array_equal, but also allows values to be NaN in either or both
     arrays
     """
-    pass
+    arr1, arr2 = as_shared_dtype([arr1, arr2])
+    if arr1.shape != arr2.shape:
+        return False
+    with warnings.catch_warnings():
+        warnings.filterwarnings('ignore', r'invalid value encountered in isnan')
+        return bool(((arr1 == arr2) | isnan(arr1) | isnan(arr2)).all())


 def count(data, axis=None):
     """Count the number of non-NA in this array along the given axis or axes"""
-    pass
+    return sum(~pandas_isnull(data), axis=axis)


 def where(condition, x, y):
     """Three argument where() with better dtype promotion rules."""
-    pass
+    return _where(condition, *as_shared_dtype([x, y]))
+
+def _where(condition, x, y):
+    if hasattr(x, 'where'):
+        return x.where(condition, y)
+    return np.where(condition, x, y)


 def concatenate(arrays, axis=0):
     """concatenate() with better dtype promotion rules."""
-    pass
+    arrays = as_shared_dtype(arrays)
+    if all(isinstance(arr, np.ndarray) for arr in arrays):
+        return _concatenate(arrays, axis=axis)
+    else:
+        return get_chunked_array_type(arrays)(
+            _concatenate, arrays, axis=axis
+        )


 def stack(arrays, axis=0):
     """stack() with better dtype promotion rules."""
-    pass
+    arrays = as_shared_dtype(arrays)
+    if all(isinstance(arr, np.ndarray) for arr in arrays):
+        return np.stack(arrays, axis=axis)
+    else:
+        return get_chunked_array_type(arrays)(
+            np.stack, arrays, axis=axis
+        )


 argmax = _create_nan_agg_method('argmax', coerce_strings=True)
diff --git a/xarray/core/extension_array.py b/xarray/core/extension_array.py
index cf1511fe..aaa71b52 100644
--- a/xarray/core/extension_array.py
+++ b/xarray/core/extension_array.py
@@ -10,7 +10,10 @@ HANDLED_EXTENSION_ARRAY_FUNCTIONS: dict[Callable, Callable] = {}

 def implements(numpy_function):
     """Register an __array_function__ implementation for MyArray objects."""
-    pass
+    def decorator(func):
+        HANDLED_EXTENSION_ARRAY_FUNCTIONS[numpy_function] = func
+        return func
+    return decorator


 class PandasExtensionArray(Generic[T_ExtensionArray]):
diff --git a/xarray/core/extensions.py b/xarray/core/extensions.py
index c7897a61..c74a1ba3 100644
--- a/xarray/core/extensions.py
+++ b/xarray/core/extensions.py
@@ -48,7 +48,16 @@ def register_dataarray_accessor(name):
     --------
     register_dataset_accessor
     """
-    pass
+    def decorator(accessor):
+        if hasattr(DataArray, name):
+            warnings.warn(
+                f"registration of accessor {name!r} under name {name!r} for type {DataArray.__name__!r} is overriding a preexisting attribute with the same name.",
+                AccessorRegistrationWarning,
+                stacklevel=2
+            )
+        setattr(DataArray, name, _CachedAccessor(name, accessor))
+        return accessor
+    return decorator


 def register_dataset_accessor(name):
@@ -94,7 +103,16 @@ def register_dataset_accessor(name):
     --------
     register_dataarray_accessor
     """
-    pass
+    def decorator(accessor):
+        if hasattr(Dataset, name):
+            warnings.warn(
+                f"registration of accessor {name!r} under name {name!r} for type {Dataset.__name__!r} is overriding a preexisting attribute with the same name.",
+                AccessorRegistrationWarning,
+                stacklevel=2
+            )
+        setattr(Dataset, name, _CachedAccessor(name, accessor))
+        return accessor
+    return decorator


 def register_datatree_accessor(name):
@@ -111,4 +129,13 @@ def register_datatree_accessor(name):
     xarray.register_dataarray_accessor
     xarray.register_dataset_accessor
     """
-    pass
+    def decorator(accessor):
+        if hasattr(DataTree, name):
+            warnings.warn(
+                f"registration of accessor {name!r} under name {name!r} for type {DataTree.__name__!r} is overriding a preexisting attribute with the same name.",
+                AccessorRegistrationWarning,
+                stacklevel=2
+            )
+        setattr(DataTree, name, _CachedAccessor(name, accessor))
+        return accessor
+    return decorator
diff --git a/xarray/core/formatting.py b/xarray/core/formatting.py
index 8c1f8e0c..2b8a613e 100644
--- a/xarray/core/formatting.py
+++ b/xarray/core/formatting.py
@@ -32,59 +32,99 @@ def pretty_print(x, numchars: int):
     that it is numchars long, padding with trailing spaces or truncating with
     ellipses as necessary
     """
-    pass
+    s = str(x)
+    if len(s) > numchars:
+        return s[:(numchars - 3)] + '...'
+    else:
+        return s.ljust(numchars)


 def first_n_items(array, n_desired):
     """Returns the first n_desired items of an array"""
-    pass
+    return array[:n_desired]


 def last_n_items(array, n_desired):
     """Returns the last n_desired items of an array"""
-    pass
+    return array[-n_desired:]


 def last_item(array):
     """Returns the last item of an array in a list or an empty list."""
-    pass
+    return [array[-1]] if len(array) > 0 else []


 def calc_max_rows_first(max_rows: int) ->int:
     """Calculate the first rows to maintain the max number of rows."""
-    pass
+    return max(1, (max_rows + 1) // 2)


 def calc_max_rows_last(max_rows: int) ->int:
     """Calculate the last rows to maintain the max number of rows."""
-    pass
+    return max(1, max_rows // 2)


 def format_timestamp(t):
     """Cast given object to a Timestamp and return a nicely formatted string"""
-    pass
+    try:
+        timestamp = pd.Timestamp(t)
+        return timestamp.isoformat(sep=' ')
+    except (ValueError, TypeError):
+        return str(t)


 def format_timedelta(t, timedelta_format=None):
-    """Cast given object to a Timestamp and return a nicely formatted string"""
-    pass
+    """Cast given object to a Timedelta and return a nicely formatted string"""
+    try:
+        delta = pd.Timedelta(t)
+        if timedelta_format is None:
+            return str(delta)
+        else:
+            return delta.isoformat()
+    except (ValueError, TypeError):
+        return str(t)


 def format_item(x, timedelta_format=None, quote_strings=True):
     """Returns a succinct summary of an object as a string"""
-    pass
+    if isinstance(x, (pd.Timestamp, datetime)):
+        return format_timestamp(x)
+    elif isinstance(x, (pd.Timedelta, timedelta)):
+        return format_timedelta(x, timedelta_format)
+    elif isinstance(x, str):
+        return f"'{x}'" if quote_strings else x
+    else:
+        return str(x)


 def format_items(x):
     """Returns a succinct summaries of all items in a sequence as strings"""
-    pass
+    return [format_item(item) for item in x]


 def format_array_flat(array, max_width: int):
     """Return a formatted string for as many items in the flattened version of
     array that will fit within max_width characters.
     """
-    pass
+    flat = array.flatten()
+    formatted = format_items(flat)
+    
+    cumulative_width = 0
+    truncate_at = len(formatted)
+    
+    for i, item in enumerate(formatted):
+        item_width = len(item) + 2  # +2 for separator ', '
+        if cumulative_width + item_width > max_width:
+            truncate_at = i
+            break
+        cumulative_width += item_width
+    
+    truncated = formatted[:truncate_at]
+    
+    if truncate_at < len(formatted):
+        return f"[{', '.join(truncated)}, ...]"
+    else:
+        return f"[{', '.join(truncated)}]"


 _KNOWN_TYPE_REPRS = {('numpy', 'ndarray'): 'np.ndarray', (
diff --git a/xarray/core/formatting_html.py b/xarray/core/formatting_html.py
index a85cdfc5..6b36f379 100644
--- a/xarray/core/formatting_html.py
+++ b/xarray/core/formatting_html.py
@@ -17,12 +17,16 @@ if TYPE_CHECKING:
 @lru_cache(None)
 def _load_static_files():
     """Lazily load the resource files into memory the first time they are needed"""
-    pass
+    static_files = {}
+    for package, filename in STATIC_FILES:
+        content = files(package).joinpath(filename).read_text()
+        static_files[filename] = content
+    return static_files


 def short_data_repr_html(array) ->str:
     """Format "data" for DataArray and Variable."""
-    pass
+    return f'<pre>{escape(short_data_repr(array))}</pre>'


 coord_section = partial(_mapping_section, name='Coordinates', details_func=
@@ -45,7 +49,23 @@ def _obj_repr(obj, header_components, sections):
     If CSS is not injected (untrusted notebook), fallback to the plain text repr.

     """
-    pass
+    static_files = _load_static_files()
+    css_styles = static_files['style.css']
+    icons = static_files['icons-svg-inline.html']
+
+    obj_type = type(obj).__name__
+    obj_name = getattr(obj, 'name', None)
+    name_str = f' {escape(str(obj_name))}' if obj_name is not None else ''
+
+    header = f'<div class="xr-header"><div class="xr-obj-type">{obj_type}</div>: {name_str}</div>'
+    
+    components = [icons, f'<style>{css_styles}</style>', header]
+    components.extend(header_components)
+    
+    for section in sections:
+        components.append(section(obj))
+
+    return ''.join(components)


 children_section = partial(_mapping_section, name='Groups', details_func=
@@ -90,4 +110,21 @@ def _wrap_datatree_repr(r: str, end: bool=False) ->str:

         Tee color is set to the variable :code:`--xr-border-color`.
     """
-    pass
+    tee = '└─' if end else '|─'
+    padding = '&nbsp;&nbsp;' if end else '|&nbsp;'
+    
+    wrapped = f'''
+    <div style="display: inline-grid; grid-template-columns: auto 1fr; grid-gap: 0;">
+        <div style="color: var(--xr-border-color);">
+            {tee}
+        </div>
+        <div>
+            {r}
+        </div>
+        <div style="color: var(--xr-border-color);">
+            {padding}
+        </div>
+        <div></div>
+    </div>
+    '''
+    return wrapped.strip()
diff --git a/xarray/core/groupby.py b/xarray/core/groupby.py
index 8807366d..6c59652f 100644
--- a/xarray/core/groupby.py
+++ b/xarray/core/groupby.py
@@ -32,7 +32,18 @@ if TYPE_CHECKING:

 def _consolidate_slices(slices: list[slice]) ->list[slice]:
     """Consolidate adjacent slices in a list of slices."""
-    pass
+    if not slices:
+        return []
+    
+    consolidated = [slices[0]]
+    for current in slices[1:]:
+        previous = consolidated[-1]
+        if previous.stop == current.start and previous.step == current.step:
+            consolidated[-1] = slice(previous.start, current.stop, previous.step)
+        else:
+            consolidated.append(current)
+    
+    return consolidated


 def _inverse_permutation_indices(positions, N: (int | None)=None) ->(np.
@@ -48,7 +59,25 @@ def _inverse_permutation_indices(positions, N: (int | None)=None) ->(np.
     -------
     np.ndarray of indices or None, if no permutation is necessary.
     """
-    pass
+    if not positions:
+        return None
+
+    if isinstance(positions[0], slice):
+        if N is None:
+            raise ValueError("N must be provided when positions are slices")
+        indices = np.full(N, -1, dtype=int)
+        for i, slc in enumerate(positions):
+            indices[slc] = i
+        return indices if (indices != np.arange(N)).any() else None
+    else:
+        indices = np.concatenate(positions)
+        if len(indices) == 0:
+            return None
+        if not np.array_equal(np.sort(indices), np.arange(len(indices))):
+            raise ValueError("Invalid positions for permutation")
+        inverse = np.full_like(indices, -1)
+        inverse[indices] = np.arange(len(indices))
+        return inverse if (inverse != np.arange(len(inverse))).any() else None


 class _DummyGroup(Generic[T_Xarray]):
@@ -229,23 +258,63 @@ class GroupBy(Generic[T_Xarray]):

     def _iter_grouped(self) ->Iterator[T_Xarray]:
         """Iterate over each element in this group"""
-        pass
+        for indices in self._group_indices:
+            yield self._obj.isel({self._group_dim: indices})

     def _maybe_restore_empty_groups(self, combined):
         """Our index contained empty groups (e.g., from a resampling or binning). If we
         reduced on that dimension, we want to restore the full index.
         """
-        pass
+        grouper, = self.groupers
+        if grouper.name not in combined.dims:
+            return combined
+
+        size = grouper.size
+        if size == len(combined[grouper.name]):
+            return combined
+
+        template = self._obj.isel({self._group_dim: 0}).drop_vars(self._group_dim)
+        template = template._replace_maybe_drop_dims({var: combined[var] for var in combined.data_vars})
+        
+        if isinstance(template, type(combined)):
+            return template.reindex({grouper.name: grouper.unique_coord})
+        else:
+            return combined

     def _maybe_unstack(self, obj):
         """This gets called if we are applying on an array with a
         multidimensional group."""
-        pass
+        grouper, = self.groupers
+        if grouper.stacked_dim is not None:
+            obj = obj.unstack(grouper.stacked_dim)
+            for dim in grouper.inserted_dims:
+                if dim in obj.coords:
+                    obj.coords[dim] = grouper.group[dim]
+        return obj

     def _flox_reduce(self, dim: Dims, keep_attrs: (bool | None)=None, **
         kwargs: Any):
         """Adaptor function that translates our groupby API to that of flox."""
-        pass
+        from flox.xarray import xarray_reduce
+        
+        grouper, = self.groupers
+        if dim is None or dim is ...:
+            dim = list(self._obj.dims)
+        elif isinstance(dim, str):
+            dim = [dim]
+        
+        if grouper.name not in dim:
+            dim = list(dim) + [grouper.name]
+        
+        result = xarray_reduce(
+            self._obj,
+            dim=dim,
+            group=grouper.group,
+            keep_attrs=keep_attrs,
+            **kwargs
+        )
+        
+        return self._maybe_restore_empty_groups(result)

     def fillna(self, value: Any) ->T_Xarray:
         """Fill missing values in this object by group.
@@ -271,7 +340,7 @@ class GroupBy(Generic[T_Xarray]):
         Dataset.fillna
         DataArray.fillna
         """
-        pass
+        return self.map(lambda x: x.fillna(value))

     @_deprecate_positional_args('v2023.10.0')
     def quantile(self, q: ArrayLike, dim: Dims=None, *, method:
diff --git a/xarray/core/indexes.py b/xarray/core/indexes.py
index 78726197..04c02219 100644
--- a/xarray/core/indexes.py
+++ b/xarray/core/indexes.py
@@ -376,7 +376,16 @@ def safe_cast_to_index(array: Any) ->pd.Index:
     this function will not attempt to do automatic type conversion but will
     always return an index with dtype=object.
     """
-    pass
+    if isinstance(array, pd.Index):
+        return array
+    if hasattr(array, 'to_index'):
+        array = array.to_index()
+    if isinstance(array, pd.Index):
+        return array
+    kwargs = {}
+    if hasattr(array, 'dtype') and array.dtype.kind in ['O', 'm']:
+        kwargs['dtype'] = object
+    return pd.Index(array, **kwargs)


 def _asarray_tuplesafe(values):
@@ -386,7 +395,15 @@ def _asarray_tuplesafe(values):

     Adapted from pandas.core.common._asarray_tuplesafe
     """
-    pass
+    if isinstance(values, tuple):
+        result = utils.to_0d_object_array(values)
+    else:
+        result = np.asarray(values)
+        if result.ndim == 2:
+            result = np.empty(len(values), dtype=object)
+            result[:] = values
+
+    return result


 def get_indexer_nd(index: pd.Index, labels, method=None, tolerance=None
@@ -394,7 +411,9 @@ def get_indexer_nd(index: pd.Index, labels, method=None, tolerance=None
     """Wrapper around :meth:`pandas.Index.get_indexer` supporting n-dimensional
     labels
     """
-    pass
+    flat_labels = np.ravel(labels)
+    flat_indexer = index.get_indexer(flat_labels, method=method, tolerance=tolerance)
+    return flat_indexer.reshape(labels.shape)


 T_PandasIndex = TypeVar('T_PandasIndex', bound='PandasIndex')
@@ -435,7 +454,18 @@ def _check_dim_compat(variables: Mapping[Any, Variable], all_dims: str='equal'
     either share the same (single) dimension or each have a different dimension.

     """
-    pass
+    dims = [var.dims for var in variables.values()]
+    if not all(len(d) == 1 for d in dims):
+        raise ValueError("Multi-index variables must be 1-dimensional")
+
+    if all_dims == 'equal':
+        if not all(d == dims[0] for d in dims[1:]):
+            raise ValueError("Multi-index variables must share the same dimension")
+    elif all_dims == 'different':
+        if len(set(d[0] for d in dims)) != len(dims):
+            raise ValueError("Multi-index variables must have different dimensions")
+    else:
+        raise ValueError("Invalid value for all_dims. Must be 'equal' or 'different'")


 T_PDIndex = TypeVar('T_PDIndex', bound=pd.Index)
@@ -445,7 +475,12 @@ def remove_unused_levels_categories(index: T_PDIndex) ->T_PDIndex:
     """
     Remove unused levels from MultiIndex and unused categories from CategoricalIndex
     """
-    pass
+    if isinstance(index, pd.MultiIndex):
+        return index.remove_unused_levels()
+    elif isinstance(index, pd.CategoricalIndex):
+        return index.remove_unused_categories()
+    else:
+        return index


 class PandasMultiIndex(PandasIndex):
@@ -485,7 +520,11 @@ class PandasMultiIndex(PandasIndex):
         labels after a stack/unstack roundtrip.

         """
-        pass
+        _check_dim_compat(variables, all_dims='different')
+        names = list(variables.keys())
+        levels = [var.values for var in variables.values()]
+        product = pd.MultiIndex.from_product(levels, names=names)
+        return cls(product, dim)

     @classmethod
     def from_variables_maybe_expand(cls, dim: Hashable, current_variables:
@@ -496,7 +535,17 @@ class PandasMultiIndex(PandasIndex):

         The index and its corresponding coordinates may be created along a new dimension.
         """
-        pass
+        all_variables = {**current_variables, **variables}
+        _check_dim_compat(all_variables, all_dims='equal')
+        
+        names = list(all_variables.keys())
+        levels = [var.values for var in all_variables.values()]
+        product = pd.MultiIndex.from_product(levels, names=names)
+        
+        index = cls(product, dim)
+        index_vars = {name: Variable((dim,), level) for name, level in zip(names, levels)}
+        
+        return index, index_vars

     def keep_levels(self, level_variables: Mapping[Any, Variable]) ->(
         PandasMultiIndex | PandasIndex):
@@ -524,7 +573,17 @@ def create_default_index_implicit(dim_variable: Variable, all_variables: (
     depreciate implicitly passing a pandas.MultiIndex as a coordinate).

     """
-    pass
+    dim = dim_variable.dims[0]
+    data = dim_variable.values
+
+    if isinstance(data, pd.MultiIndex):
+        index = PandasMultiIndex(data, dim)
+        index_vars = {name: Variable((dim,), level) for name, level in zip(data.names, data.levels)}
+    else:
+        index = PandasIndex(data, dim)
+        index_vars = {dim: dim_variable}
+
+    return index, index_vars


 T_PandasOrXarrayIndex = TypeVar('T_PandasOrXarrayIndex', Index, pd.Index)
@@ -698,7 +757,14 @@ def default_indexes(coords: Mapping[Any, Variable], dims: Iterable) ->dict[
     Mapping from indexing keys (levels/dimension names) to indexes used for
     indexing along that dimension.
     """
-    pass
+    indexes = {}
+    for dim in dims:
+        if dim in coords:
+            index, _ = create_default_index_implicit(coords[dim])
+            indexes[dim] = index
+        else:
+            indexes[dim] = PandasIndex(pd.RangeIndex(coords[dim].size), dim)
+    return indexes


 def indexes_equal(index: Index, other_index: Index, variable: Variable,
diff --git a/xarray/core/indexing.py b/xarray/core/indexing.py
index d02970b0..195ead0c 100644
--- a/xarray/core/indexing.py
+++ b/xarray/core/indexing.py
@@ -68,7 +68,11 @@ class IndexSelResult:
 def group_indexers_by_index(obj: T_Xarray, indexers: Mapping[Any, Any],
     options: Mapping[str, Any]) ->list[tuple[Index, dict[Any, Any]]]:
     """Returns a list of unique indexes and their corresponding indexers."""
-    pass
+    grouped_indexers = defaultdict(dict)
+    for key, value in indexers.items():
+        index = obj.indexes[key]
+        grouped_indexers[index][key] = value
+    return list(grouped_indexers.items())


 def map_index_queries(obj: T_Xarray, indexers: Mapping[Any, Any], method=
@@ -78,7 +82,21 @@ def map_index_queries(obj: T_Xarray, indexers: Mapping[Any, Any], method=
     and return the (merged) query results.

     """
-    pass
+    grouped_indexers = group_indexers_by_index(obj, indexers, indexers_kwargs)
+    dim_indexers = {}
+    new_indexes = {}
+    variables = {}
+    for index, these_indexers in grouped_indexers:
+        query_results = index.sel(these_indexers, method=method, tolerance=tolerance)
+        dim_indexers.update(query_results.dim_indexers)
+        new_indexes.update(query_results.indexes)
+        variables.update(query_results.variables)
+    
+    return IndexSelResult(
+        dim_indexers=dim_indexers,
+        indexes=new_indexes,
+        variables=variables
+    )


 def expanded_indexer(key, ndim):
@@ -89,7 +107,28 @@ def expanded_indexer(key, ndim):
     number of full slices and then padding the key with full slices so that it
     reaches the appropriate dimensionality.
     """
-    pass
+    if not isinstance(key, tuple):
+        key = (key,)
+    
+    new_key = []
+    ellipsis_count = sum(1 for k in key if k is Ellipsis)
+    
+    if ellipsis_count > 1:
+        raise IndexError("an index can only have a single ellipsis ('...')")
+    elif ellipsis_count == 1:
+        ellipsis_index = key.index(Ellipsis)
+        key = key[:ellipsis_index] + (slice(None),) * (ndim - len(key) + 1) + key[ellipsis_index + 1:]
+    
+    for k in key:
+        if k is Ellipsis:
+            new_key.extend([slice(None)] * (ndim - len(new_key)))
+        else:
+            new_key.append(k)
+    
+    if len(new_key) < ndim:
+        new_key.extend([slice(None)] * (ndim - len(new_key)))
+    
+    return tuple(new_key)


 def _normalize_slice(sl: slice, size: int) ->slice:
@@ -104,7 +143,25 @@ def _normalize_slice(sl: slice, size: int) ->slice:
     >>> _normalize_slice(slice(0, -1), 10)
     slice(0, 9, 1)
     """
-    pass
+    start, stop, step = sl.start, sl.stop, sl.step
+
+    if step is None:
+        step = 1
+
+    if start is None:
+        start = 0 if step > 0 else size - 1
+    elif start < 0:
+        start += size
+
+    if stop is None:
+        stop = size if step > 0 else -1
+    elif stop < 0:
+        stop += size
+
+    if step > 0 and stop == -1:
+        stop = size
+
+    return slice(start, stop, step)


 def _expand_slice(slice_: slice, size: int) ->np.ndarray[Any, np.dtype[np.
@@ -119,7 +176,8 @@ def _expand_slice(slice_: slice, size: int) ->np.ndarray[Any, np.dtype[np.
     >>> _expand_slice(slice(0, -1), 10)
     array([0, 1, 2, 3, 4, 5, 6, 7, 8])
     """
-    pass
+    normalized_slice = _normalize_slice(slice_, size)
+    return np.arange(normalized_slice.start, normalized_slice.stop, normalized_slice.step)


 def slice_slice(old_slice: slice, applied_slice: slice, size: int) ->slice:
@@ -127,7 +185,16 @@ def slice_slice(old_slice: slice, applied_slice: slice, size: int) ->slice:
     index it with another slice to return a new slice equivalent to applying
     the slices sequentially
     """
-    pass
+    old_slice = _normalize_slice(old_slice, size)
+    old_range = range(old_slice.start, old_slice.stop, old_slice.step)
+    
+    applied_range = range(len(old_range))[applied_slice]
+    
+    new_start = old_range[applied_range.start] if applied_range.start is not None else None
+    new_stop = old_range[applied_range.stop - 1] + 1 if applied_range.stop is not None else None
+    new_step = old_slice.step * applied_slice.step if applied_slice.step is not None else None
+    
+    return slice(new_start, new_stop, new_step)


 class ExplicitIndexer:
diff --git a/xarray/core/merge.py b/xarray/core/merge.py
index eb888a66..b1778652 100644
--- a/xarray/core/merge.py
+++ b/xarray/core/merge.py
@@ -40,7 +40,15 @@ def broadcast_dimension_size(variables: list[Variable]) ->dict[Hashable, int]:

     Raises ValueError if any dimensions have different sizes.
     """
-    pass
+    dim_sizes = {}
+    for var in variables:
+        for dim, size in var.sizes.items():
+            if dim in dim_sizes:
+                if dim_sizes[dim] != size:
+                    raise ValueError(f"Inconsistent dimension size for {dim}: {dim_sizes[dim]} != {size}")
+            else:
+                dim_sizes[dim] = size
+    return dim_sizes


 class MergeError(ValueError):
@@ -71,7 +79,30 @@ def unique_variable(name: Hashable, variables: list[Variable], compat:
     ------
     MergeError: if any of the variables are not equal.
     """
-    pass
+    if len(variables) == 1:
+        return variables[0]
+    
+    first_var = variables[0]
+    if compat == "override":
+        return first_var
+    
+    for var in variables[1:]:
+        if compat == "identical":
+            if not first_var.identical(var):
+                raise MergeError(f"Conflict for variable {name}")
+        elif compat == "equals":
+            if not first_var.equals(var):
+                raise MergeError(f"Conflict for variable {name}")
+        elif compat == "broadcast_equals":
+            if not first_var.broadcast_equals(var):
+                raise MergeError(f"Conflict for variable {name}")
+        elif compat == "no_conflicts":
+            if not first_var.no_conflicts(var):
+                raise MergeError(f"Conflict for variable {name}")
+        else:
+            raise ValueError(f"Unsupported compat option: {compat}")
+    
+    return first_var


 MergeElement = tuple[Variable, Optional[Index]]
@@ -82,7 +113,14 @@ def _assert_prioritized_valid(grouped: dict[Hashable, list[MergeElement]],
     """Make sure that elements given in prioritized will not corrupt any
     index given in grouped.
     """
-    pass
+    for name, (var, index) in prioritized.items():
+        if name in grouped:
+            grouped_var, grouped_index = grouped[name][0]
+            if index is not None and grouped_index is not None:
+                if not indexes_equal(index, grouped_index):
+                    raise ValueError(f"Incompatible indexes for variable {name}")
+            elif index is not None or grouped_index is not None:
+                raise ValueError(f"Inconsistent presence of index for variable {name}")


 def merge_collected(grouped: dict[Any, list[MergeElement]], prioritized: (
@@ -122,7 +160,36 @@ def merge_collected(grouped: dict[Any, list[MergeElement]], prioritized: (
     and Variable values corresponding to those that should be found on the
     merged result.
     """
-    pass
+    if prioritized is None:
+        prioritized = {}
+    
+    _assert_prioritized_valid(grouped, prioritized)
+    
+    result_vars = {}
+    result_indexes = {}
+    
+    for name, elements in grouped.items():
+        if name in prioritized:
+            var, index = prioritized[name]
+        else:
+            variables = [elem[0] for elem in elements]
+            var = unique_variable(name, variables, compat)
+            index = elements[0][1]  # Use the first index
+        
+        result_vars[name] = var
+        if index is not None:
+            result_indexes[name] = index
+    
+    # Combine attributes
+    if callable(combine_attrs):
+        attrs = combine_attrs([var.attrs for var in result_vars.values()], Context(merge_collected))
+    else:
+        attrs = merge_attrs([var.attrs for var in result_vars.values()], combine_attrs)
+    
+    for var in result_vars.values():
+        var.attrs.update(attrs)
+    
+    return result_vars, result_indexes


 def collect_variables_and_indexes(list_of_mappings: Iterable[DatasetLike],
diff --git a/xarray/core/missing.py b/xarray/core/missing.py
index e589337e..0837f746 100644
--- a/xarray/core/missing.py
+++ b/xarray/core/missing.py
@@ -28,7 +28,36 @@ def _get_nan_block_lengths(obj: (Dataset | DataArray | Variable), dim:
     Return an object where each NaN element in 'obj' is replaced by the
     length of the gap the element is in.
     """
-    pass
+    import numpy as np
+    from xarray.core.duck_array_ops import isnull
+
+    def _nan_block_lengths(arr):
+        mask = isnull(arr)
+        if not np.any(mask):
+            return np.zeros_like(arr)
+
+        diff = np.diff(mask.astype(int))
+        start = np.where(diff == 1)[0] + 1
+        end = np.where(diff == -1)[0] + 1
+
+        if mask[0]:
+            start = np.r_[0, start]
+        if mask[-1]:
+            end = np.r_[end, len(mask)]
+
+        lengths = end - start
+        result = np.zeros_like(arr)
+        for s, e, l in zip(start, end, lengths):
+            result[s:e] = l
+
+        return result
+
+    if isinstance(obj, Variable):
+        return obj.copy(data=_nan_block_lengths(obj.data))
+    elif isinstance(obj, (Dataset, DataArray)):
+        return obj.map(_nan_block_lengths, keep_attrs=True)
+    else:
+        raise TypeError(f"Unsupported type for obj: {type(obj)}")


 class BaseInterpolator:
@@ -137,7 +166,20 @@ class SplineInterpolator(BaseInterpolator):

 def _apply_over_vars_with_dim(func, self, dim=None, **kwargs):
     """Wrapper for datasets"""
-    pass
+    from xarray.core.dataset import Dataset
+    from xarray.core.dataarray import DataArray
+
+    if isinstance(self, Dataset):
+        variables = {
+            k: func(v, dim=dim, **kwargs)
+            for k, v in self.data_vars.items()
+            if dim in v.dims
+        }
+        return Dataset(variables, coords=self.coords, attrs=self.attrs)
+    elif isinstance(self, DataArray):
+        return func(self, dim=dim, **kwargs)
+    else:
+        raise TypeError(f"Unsupported type for self: {type(self)}")


 def get_clean_interp_index(arr, dim: Hashable, use_coordinate: (str | bool)
@@ -167,7 +209,29 @@ def get_clean_interp_index(arr, dim: Hashable, use_coordinate: (str | bool)
     If indexing is along the time dimension, datetime coordinates are converted
     to time deltas with respect to 1970-01-01.
     """
-    pass
+    from xarray.core.variable import Variable
+    from xarray.core.duck_array_ops import datetime_to_numeric
+    import numpy as np
+    import pandas as pd
+
+    if use_coordinate:
+        if isinstance(use_coordinate, str):
+            index = arr.coords[use_coordinate]
+        else:
+            index = arr.coords[dim]
+    else:
+        index = Variable(dim, np.arange(arr.sizes[dim]))
+
+    if _contains_datetime_like_objects(index):
+        index = datetime_to_numeric(index)
+
+    if strict:
+        if not index.to_index().is_unique:
+            raise ValueError("Index must be unique")
+        if not index.to_index().is_monotonic_increasing:
+            raise ValueError("Index must be monotonically increasing")
+
+    return index


 def interp_na(self, dim: (Hashable | None)=None, use_coordinate: (bool |
@@ -175,7 +239,69 @@ def interp_na(self, dim: (Hashable | None)=None, use_coordinate: (bool |
     max_gap: (int | float | str | pd.Timedelta | np.timedelta64 | dt.
     timedelta | None)=None, keep_attrs: (bool | None)=None, **kwargs):
     """Interpolate values according to different methods."""
-    pass
+    from xarray.core.dataarray import DataArray
+    from xarray.core.dataset import Dataset
+    from xarray.core.duck_array_ops import isnull
+    import numpy as np
+    import pandas as pd
+
+    if dim is None:
+        raise ValueError("Must specify 'dim' argument")
+
+    if keep_attrs is None:
+        keep_attrs = _get_keep_attrs(default=True)
+
+    index = get_clean_interp_index(self, dim, use_coordinate)
+
+    if max_gap is not None:
+        if isinstance(max_gap, str):
+            max_gap = pd.Timedelta(max_gap)
+        elif isinstance(max_gap, (np.timedelta64, dt.timedelta)):
+            max_gap = pd.Timedelta(max_gap)
+        elif not isinstance(max_gap, (int, float)):
+            raise TypeError("max_gap must be a number or a timedelta-like object")
+
+        if _contains_datetime_like_objects(index):
+            max_gap = pd.Timedelta(max_gap).total_seconds()
+        
+        gaps = _get_nan_block_lengths(self, dim, index)
+        mask = gaps <= max_gap
+
+    else:
+        mask = np.ones_like(self, dtype=bool)
+
+    obj = self.where(mask)
+
+    if isinstance(obj, Dataset):
+        return _apply_over_vars_with_dim(
+            interp_na,
+            obj,
+            dim=dim,
+            use_coordinate=use_coordinate,
+            method=method,
+            limit=limit,
+            keep_attrs=keep_attrs,
+            **kwargs
+        )
+
+    if not isnull(obj).any():
+        return obj
+
+    if limit is not None:
+        valid = _get_valid_fill_mask(obj, dim, limit)
+        obj = obj.where(valid)
+
+    indexer = {dim: index}
+    interpolator = _get_interpolator(method, **kwargs)
+
+    return obj.interpolate_na(
+        dim=dim,
+        method=interpolator,
+        limit=limit,
+        use_coordinate=use_coordinate,
+        keep_attrs=keep_attrs,
+        **kwargs
+    )


 def func_interpolate_na(interpolator, y, x, **kwargs):
diff --git a/xarray/core/nanops.py b/xarray/core/nanops.py
index 78ecefc3..b0766099 100644
--- a/xarray/core/nanops.py
+++ b/xarray/core/nanops.py
@@ -9,21 +9,60 @@ def _maybe_null_out(result, axis, mask, min_count=1):
     """
     xarray version of pandas.core.nanops._maybe_null_out
     """
-    pass
+    if axis is not None and isinstance(axis, (tuple, list)):
+        raise ValueError("axis must be a single integer, not a tuple or list")
+
+    if mask is None:
+        return result
+
+    null_mask = ~mask.all(axis=axis)
+
+    if min_count > 1:
+        count = mask.sum(axis=axis)
+        null_mask |= (count < min_count)
+
+    if null_mask.any():
+        result = result.copy()
+        result[null_mask] = np.nan
+
+    return result


 def _nan_argminmax_object(func, fill_value, value, axis=None, **kwargs):
     """In house nanargmin, nanargmax for object arrays. Always return integer
     type
     """
-    pass
+    valid_count = count(value, axis=axis)
+    value = fillna(value, fill_value)
+    result = func(value, axis=axis, **kwargs)
+
+    if isinstance(result, tuple):
+        # In case func returns both values and indices
+        result = result[1]
+
+    return where(valid_count == 0, -1, result).astype(int)


 def _nan_minmax_object(func, fill_value, value, axis=None, **kwargs):
     """In house nanmin and nanmax for object array"""
-    pass
+    valid_count = count(value, axis=axis)
+    value = fillna(value, fill_value)
+    result = func(value, axis=axis, **kwargs)
+
+    return where(valid_count == 0, np.nan, result)


 def _nanmean_ddof_object(ddof, value, axis=None, dtype=None, **kwargs):
     """In house nanmean. ddof argument will be used in _nanvar method"""
-    pass
+    mask = ~isnull(value)
+    value = astype(value, dtype=dtype) if dtype is not None else value
+
+    count = mask.sum(axis=axis)
+    sum_value = sum_where(value, mask, axis=axis, **kwargs)
+
+    if isinstance(count, np.ndarray):
+        count = count.astype('float64')
+    else:
+        count = float(count)
+
+    return sum_value / np.maximum(count - ddof, 1)
diff --git a/xarray/core/nputils.py b/xarray/core/nputils.py
index abe87b99..b4e3d0ee 100644
--- a/xarray/core/nputils.py
+++ b/xarray/core/nputils.py
@@ -40,17 +40,39 @@ def inverse_permutation(indices: np.ndarray, N: (int | None)=None
         Integer indices to take from the original array to create the
         permutation.
     """
-    pass
+    if N is None:
+        N = len(indices)
+    inverse = np.empty(N, dtype=int)
+    inverse[indices] = np.arange(len(indices))
+    return inverse


 def _is_contiguous(positions):
     """Given a non-empty list, does it consist of contiguous integers?"""
-    pass
+    if len(positions) <= 1:
+        return True
+    return np.all(np.diff(positions) == 1)


 def _advanced_indexer_subspaces(key):
     """Indices of the advanced indexes subspaces for mixed indexing and vindex."""
-    pass
+    if not isinstance(key, tuple):
+        key = (key,)
+    
+    advanced_indexes = [
+        i for i, k in enumerate(key)
+        if isinstance(k, (np.ndarray, list)) and (
+            isinstance(k, np.ndarray) or isinstance(k[0], (int, np.integer))
+        )
+    ]
+    
+    if not advanced_indexes:
+        return [], []
+    
+    mixed_positions = advanced_indexes
+    vindex_positions = list(range(len(advanced_indexes)))
+    
+    return mixed_positions, vindex_positions


 class NumpyVIndexAdapter:
diff --git a/xarray/core/ops.py b/xarray/core/ops.py
index f0f8e050..bdb83c8e 100644
--- a/xarray/core/ops.py
+++ b/xarray/core/ops.py
@@ -101,7 +101,15 @@ def fillna(data, other, join='left', dataset_join='left'):
         - "left": take only variables from the first object
         - "right": take only variables from the last object
     """
-    pass
+    if hasattr(data, 'fillna'):
+        return data.fillna(other, join=join, dataset_join=dataset_join)
+    elif isinstance(data, np.ndarray):
+        if np.isscalar(other) or isinstance(other, np.ndarray):
+            return np.where(np.isnan(data), other, data)
+        else:
+            raise TypeError("'other' must be a scalar or numpy array")
+    else:
+        raise TypeError("'data' must be a xarray object or numpy array")


 def where_method(self, cond, other=dtypes.NA):
@@ -119,7 +127,14 @@ def where_method(self, cond, other=dtypes.NA):
     -------
     Same type as caller.
     """
-    pass
+    if hasattr(self, 'where'):
+        return self.where(cond, other)
+    elif isinstance(self, np.ndarray):
+        if other is dtypes.NA:
+            other = np.nan
+        return np.where(cond, self, other)
+    else:
+        raise TypeError("'self' must be a xarray object or numpy array")


 NON_INPLACE_OP = {get_op('i' + name): get_op(name) for name in NUM_BINARY_OPS}
diff --git a/xarray/core/options.py b/xarray/core/options.py
index ca162668..8408eb90 100644
--- a/xarray/core/options.py
+++ b/xarray/core/options.py
@@ -224,9 +224,14 @@ def get_options():
     """
     Get options for xarray.

+    Returns
+    -------
+    dict
+        A dictionary containing the current options for xarray.
+
     See Also
     ----------
     set_options

     """
-    pass
+    return dict(OPTIONS)
diff --git a/xarray/core/parallel.py b/xarray/core/parallel.py
index 9f983816..f4635477 100644
--- a/xarray/core/parallel.py
+++ b/xarray/core/parallel.py
@@ -30,20 +30,32 @@ def make_meta(obj):
     backend.
     If obj is neither a DataArray nor Dataset, return it unaltered.
     """
-    pass
+    if isinstance(obj, (DataArray, Dataset)):
+        new_obj = obj.copy()
+        for var_name, var in new_obj.variables.items():
+            new_obj[var_name] = Variable(var.dims, np.array([], dtype=var.dtype))
+        return new_obj
+    return obj


 def infer_template(func: Callable[..., T_Xarray], obj: (DataArray | Dataset
     ), *args, **kwargs) ->T_Xarray:
     """Infer return object by running the function on meta objects."""
-    pass
+    meta_obj = make_meta(obj)
+    meta_args = tuple(make_meta(arg) if isinstance(arg, (DataArray, Dataset)) else arg for arg in args)
+    return func(meta_obj, *meta_args, **kwargs)


 def make_dict(x: (DataArray | Dataset)) ->dict[Hashable, Any]:
     """Map variable name to numpy(-like) data
     (Dataset.to_dict() is too complicated).
     """
-    pass
+    if isinstance(x, DataArray):
+        return {x.name: x.data}
+    elif isinstance(x, Dataset):
+        return {name: var.data for name, var in x.variables.items()}
+    else:
+        raise TypeError(f"Expected DataArray or Dataset, got {type(x)}")


 def subset_dataset_to_block(graph: dict, gname: str, dataset: Dataset,
@@ -53,7 +65,20 @@ def subset_dataset_to_block(graph: dict, gname: str, dataset: Dataset,
     Block extents are determined by input_chunk_bounds.
     Also subtasks that subset the constituent variables of a dataset.
     """
-    pass
+    def subset_variable(var, bounds):
+        slices = tuple(slice(start, stop) for start, stop in bounds)
+        return var[slices]
+
+    subset_tasks = {}
+    for name, var in dataset.variables.items():
+        bounds = [input_chunk_bounds[dim][i] for dim, i in zip(var.dims, chunk_index)]
+        subset_tasks[name] = (subset_variable, var, bounds)
+
+    def reconstruct_dataset(subsets):
+        return Dataset(subsets)
+
+    graph[gname] = (reconstruct_dataset, subset_tasks)
+    return graph[gname]


 def map_blocks(func: Callable[..., T_Xarray], obj: (DataArray | Dataset),
@@ -156,4 +181,34 @@ def map_blocks(func: Callable[..., T_Xarray], obj: (DataArray | Dataset),
       * time     (time) object 192B 1990-01-31 00:00:00 ... 1991-12-31 00:00:00
         month    (time) int64 192B dask.array<chunksize=(24,), meta=np.ndarray>
     """
-    pass
+    if kwargs is None:
+        kwargs = {}
+
+    if not is_dask_collection(obj):
+        return func(obj, *args, **kwargs)
+
+    if template is None:
+        template = infer_template(func, obj, *args, **kwargs)
+
+    def wrapped_func(block, *block_args):
+        result = func(block, *block_args, **kwargs)
+        if isinstance(result, (DataArray, Dataset)):
+            result = make_dict(result)
+        return result
+
+    dask_args = [
+        arg.data if isinstance(arg, (DataArray, Dataset)) else arg
+        for arg in args
+    ]
+
+    if isinstance(obj, DataArray):
+        data = obj.data.map_blocks(wrapped_func, *dask_args, dtype=template.dtype)
+        return DataArray(data, dims=template.dims, coords=template.coords, attrs=template.attrs)
+    elif isinstance(obj, Dataset):
+        data = {
+            name: var.data.map_blocks(wrapped_func, *dask_args, dtype=template[name].dtype)
+            for name, var in obj.data_vars.items()
+        }
+        return Dataset(data, coords=template.coords, attrs=template.attrs)
+    else:
+        raise TypeError(f"Expected DataArray or Dataset, got {type(obj)}")
diff --git a/xarray/core/pdcompat.py b/xarray/core/pdcompat.py
index cecf4d90..349c36c8 100644
--- a/xarray/core/pdcompat.py
+++ b/xarray/core/pdcompat.py
@@ -10,7 +10,7 @@ def count_not_none(*args) ->int:

     Copied from pandas.core.common.count_not_none (not part of the public API)
     """
-    pass
+    return sum(arg is not None for arg in args)


 class _NoDefault(Enum):
@@ -39,4 +39,5 @@ def nanosecond_precision_timestamp(*args, **kwargs) ->pd.Timestamp:
     Note this function should no longer be needed after addressing GitHub issue
     #7493.
     """
-    pass
+    ts = pd.Timestamp(*args, **kwargs)
+    return ts.round('ns')
diff --git a/xarray/core/resample.py b/xarray/core/resample.py
index 147ca143..c8b38651 100644
--- a/xarray/core/resample.py
+++ b/xarray/core/resample.py
@@ -36,7 +36,9 @@ class Resample(GroupBy[T_Xarray]):

     def _drop_coords(self) ->T_Xarray:
         """Drop non-dimension coordinates along the resampled dimension."""
-        pass
+        obj = self._obj
+        dim = self._dim or self.dim
+        return obj.drop_vars([c for c in obj.coords if c != dim and dim in obj[c].dims])

     def pad(self, tolerance: (float | Iterable[float] | str | None)=None
         ) ->T_Xarray:
@@ -56,7 +58,11 @@ class Resample(GroupBy[T_Xarray]):
         -------
         padded : DataArray or Dataset
         """
-        pass
+        return self._obj.reindex(
+            {self._dim: self.grouper.full_index},
+            method="pad",
+            tolerance=tolerance
+        )
     ffill = pad

     def backfill(self, tolerance: (float | Iterable[float] | str | None)=None
@@ -77,7 +83,11 @@ class Resample(GroupBy[T_Xarray]):
         -------
         backfilled : DataArray or Dataset
         """
-        pass
+        return self._obj.reindex(
+            {self._dim: self.grouper.full_index},
+            method="backfill",
+            tolerance=tolerance
+        )
     bfill = backfill

     def nearest(self, tolerance: (float | Iterable[float] | str | None)=None
@@ -99,7 +109,11 @@ class Resample(GroupBy[T_Xarray]):
         -------
         upsampled : DataArray or Dataset
         """
-        pass
+        return self._obj.reindex(
+            {self._dim: self.grouper.full_index},
+            method="nearest",
+            tolerance=tolerance
+        )

     def interpolate(self, kind: InterpOptions='linear', **kwargs) ->T_Xarray:
         """Interpolate up-sampled data using the original data as knots.
@@ -128,11 +142,21 @@ class Resample(GroupBy[T_Xarray]):
         scipy.interpolate.interp1d

         """
-        pass
+        return self._interpolate(kind=kind, **kwargs)

     def _interpolate(self, kind='linear', **kwargs) ->T_Xarray:
         """Apply scipy.interpolate.interp1d along resampling dimension."""
-        pass
+        from scipy import interpolate
+
+        obj = self._obj
+        dim = self._dim or self.dim
+        index = obj.get_index(dim)
+        target_index = self.grouper.full_index
+
+        interpolator = interpolate.interp1d(index, obj.values, kind=kind, axis=obj.get_axis_num(dim), **kwargs)
+        interpolated_values = interpolator(target_index)
+
+        return obj.copy(data=interpolated_values).reindex({dim: target_index})


 class DataArrayResample(Resample['DataArray'], DataArrayGroupByBase,
@@ -168,7 +192,15 @@ class DataArrayResample(Resample['DataArray'], DataArrayGroupByBase,
             Array with summarized data and the indicated dimension(s)
             removed.
         """
-        pass
+        return self._obj.groupby(self.grouper.group_indices).reduce(
+            func,
+            dim=dim,
+            axis=axis,
+            keep_attrs=keep_attrs,
+            keepdims=keepdims,
+            shortcut=shortcut,
+            **kwargs
+        )

     def map(self, func: Callable[..., Any], args: tuple[Any, ...]=(),
         shortcut: (bool | None)=False, **kwargs: Any) ->DataArray:
@@ -213,7 +245,12 @@ class DataArrayResample(Resample['DataArray'], DataArrayGroupByBase,
         applied : DataArray
             The result of splitting, applying and combining this array.
         """
-        pass
+        return self._obj.groupby(self.grouper.group_indices).map(
+            func,
+            args=args,
+            shortcut=shortcut,
+            **kwargs
+        )

     def apply(self, func, args=(), shortcut=None, **kwargs):
         """
@@ -233,7 +270,7 @@ class DataArrayResample(Resample['DataArray'], DataArrayGroupByBase,
         -------
         resampled : DataArray
         """
-        pass
+        return self._obj.reindex({self._dim: self.grouper.full_index})


 class DatasetResample(Resample['Dataset'], DatasetGroupByBase,
@@ -271,7 +308,12 @@ class DatasetResample(Resample['Dataset'], DatasetGroupByBase,
         applied : Dataset
             The result of splitting, applying and combining this dataset.
         """
-        pass
+        return self._obj.groupby(self.grouper.group_indices).map(
+            func,
+            args=args,
+            shortcut=shortcut,
+            **kwargs
+        )

     def apply(self, func, args=(), shortcut=None, **kwargs):
         """
@@ -310,7 +352,15 @@ class DatasetResample(Resample['Dataset'], DatasetGroupByBase,
             Array with summarized data and the indicated dimension(s)
             removed.
         """
-        pass
+        return self._obj.groupby(self.grouper.group_indices).reduce(
+            func,
+            dim=dim,
+            axis=axis,
+            keep_attrs=keep_attrs,
+            keepdims=keepdims,
+            shortcut=shortcut,
+            **kwargs
+        )

     def asfreq(self) ->Dataset:
         """Return values of original object at the new up-sampling frequency;
@@ -320,4 +370,4 @@ class DatasetResample(Resample['Dataset'], DatasetGroupByBase,
         -------
         resampled : Dataset
         """
-        pass
+        return self._obj.reindex({self._dim: self.grouper.full_index})
diff --git a/xarray/core/resample_cftime.py b/xarray/core/resample_cftime.py
index c819839a..46e65c38 100644
--- a/xarray/core/resample_cftime.py
+++ b/xarray/core/resample_cftime.py
@@ -74,7 +74,10 @@ class CFTimeGrouper:

         with index being a CFTimeIndex instead of a DatetimeIndex.
         """
-        pass
+        bins = _get_time_bins(index, self.freq, self.closed, self.label, self.origin, self.offset)
+        grouper = pd.Grouper(freq=self.freq, closed=self.closed, label=self.label)
+        series = pd.Series(np.arange(len(index)), index=index)
+        return series.groupby(grouper).first()


 def _get_time_bins(index: CFTimeIndex, freq: BaseCFTimeOffset, closed:
@@ -119,7 +122,15 @@ def _get_time_bins(index: CFTimeIndex, freq: BaseCFTimeOffset, closed:
     labels : CFTimeIndex
         Define what the user actually sees the bins labeled as.
     """
-    pass
+    start, end = _get_range_edges(index[0], index[-1], freq, closed, origin, offset)
+    datetime_bins = cftime_range(start, end, freq=freq)
+    
+    if isinstance(freq, (MonthEnd, QuarterEnd, YearEnd)):
+        datetime_bins, labels = _adjust_bin_edges(datetime_bins, freq, closed, index, datetime_bins)
+    else:
+        labels = datetime_bins
+
+    return datetime_bins, labels


 def _adjust_bin_edges(datetime_bins: CFTimeIndex, freq: BaseCFTimeOffset,
@@ -155,7 +166,17 @@ def _adjust_bin_edges(datetime_bins: CFTimeIndex, freq: BaseCFTimeOffset,

     CFTimeIndex([2000-01-31 00:00:00, 2000-02-29 00:00:00], dtype='object')
     """
-    pass
+    adjusted_bins = CFTimeIndex([
+        bin_edge + datetime.timedelta(days=1, microseconds=-1)
+        for bin_edge in datetime_bins
+    ])
+    
+    if closed == 'right':
+        labels = adjusted_bins[1:]
+    else:
+        labels = adjusted_bins[:-1]
+    
+    return adjusted_bins, labels


 def _get_range_edges(first: CFTimeDatetime, last: CFTimeDatetime, freq:
@@ -198,7 +219,23 @@ def _get_range_edges(first: CFTimeDatetime, last: CFTimeDatetime, freq:
     last : cftime.datetime
         Corrected ending datetime object for resampled CFTimeIndex range.
     """
-    pass
+    if isinstance(freq, Tick):
+        first, last = _adjust_dates_anchored(first, last, freq, closed, origin, offset)
+    else:
+        if closed == 'left':
+            first = normalize_date(first)
+        else:
+            first = first + freq
+            first = normalize_date(first) - datetime.timedelta(microseconds=1)
+
+        last = last + freq
+        last = normalize_date(last) - datetime.timedelta(microseconds=1)
+
+    if offset:
+        first += offset
+        last += offset
+
+    return first, last


 def _adjust_dates_anchored(first: CFTimeDatetime, last: CFTimeDatetime,
@@ -243,7 +280,36 @@ def _adjust_dates_anchored(first: CFTimeDatetime, last: CFTimeDatetime,
         A datetime object representing the end of a date range that has been
         adjusted to fix resampling errors.
     """
-    pass
+    if origin == 'epoch':
+        origin = first.replace(year=1970, month=1, day=1, hour=0, minute=0, second=0, microsecond=0)
+    elif origin == 'start':
+        origin = first
+    elif origin == 'start_day':
+        origin = first.replace(hour=0, minute=0, second=0, microsecond=0)
+    elif origin == 'end':
+        origin = last
+    elif origin == 'end_day':
+        origin = last.replace(hour=23, minute=59, second=59, microsecond=999999)
+    elif isinstance(origin, CFTimeDatetime):
+        pass
+    else:
+        raise ValueError("origin must be one of 'epoch', 'start', 'start_day', 'end', 'end_day' or a cftime.datetime")
+
+    if offset:
+        origin += offset
+
+    delta = exact_cftime_datetime_difference(origin, first)
+    n = int(delta / freq.delta)
+    if closed == 'left':
+        fresult = origin + n * freq.delta
+    else:
+        fresult = origin + (n + 1) * freq.delta
+
+    delta = exact_cftime_datetime_difference(origin, last)
+    n = int(delta / freq.delta)
+    lresult = origin + (n + 1) * freq.delta
+
+    return fresult, lresult


 def exact_cftime_datetime_difference(a: CFTimeDatetime, b: CFTimeDatetime):
@@ -280,4 +346,10 @@ def exact_cftime_datetime_difference(a: CFTimeDatetime, b: CFTimeDatetime):
     -------
     datetime.timedelta
     """
-    pass
+    a_0 = a.replace(microsecond=0)
+    b_0 = b.replace(microsecond=0)
+    
+    delta_seconds = (b_0 - a_0).total_seconds()
+    delta_microseconds = b.microsecond - a.microsecond
+    
+    return datetime.timedelta(seconds=delta_seconds, microseconds=delta_microseconds)
diff --git a/xarray/core/rolling.py b/xarray/core/rolling.py
index 5a608958..7674818f 100644
--- a/xarray/core/rolling.py
+++ b/xarray/core/rolling.py
@@ -124,7 +124,15 @@ class Rolling(Generic[T_Xarray]):
         need context of xarray options, of the functions each library offers, of
         the array (e.g. dtype).
         """
-        pass
+        def func(self, keep_attrs=None, **kwargs):
+            return self.reduce(
+                lambda x, axis: getattr(np, name)(x, axis=axis),
+                keep_attrs=keep_attrs,
+                **kwargs
+            )
+        func.__name__ = name
+        func.__doc__ = _ROLLING_REDUCE_DOCSTRING_TEMPLATE.format(name=name)
+        return func
     _mean.__doc__ = _ROLLING_REDUCE_DOCSTRING_TEMPLATE.format(name='mean')
     argmax = _reduce_method('argmax', dtypes.NINF)
     argmin = _reduce_method('argmin', dtypes.INF)
@@ -254,7 +262,51 @@ class DataArrayRolling(Rolling['DataArray']):
         Dimensions without coordinates: a, b, window_dim

         """
-        pass
+        from xarray.core.dataarray import DataArray
+
+        window_dim = either_dict_or_kwargs(window_dim, window_dim_kwargs, "construct")
+        if len(window_dim) != len(self.dim):
+            raise ValueError(
+                f"window_dim must be specified for all dimensions in rolling object: {self.dim}"
+            )
+
+        window = {d: self.window[i] for i, d in enumerate(self.dim)}
+        center = {d: self.center[i] for i, d in enumerate(self.dim)}
+
+        data = self.obj.data
+        dims = self.obj.dims
+        coords = self.obj.coords.copy()
+
+        for dim, new_dim in window_dim.items():
+            axis = self.obj.get_axis_num(dim)
+            shape = list(data.shape)
+            if isinstance(stride, Mapping):
+                dim_stride = stride.get(dim, 1)
+            else:
+                dim_stride = stride
+
+            if center[dim]:
+                pad_left = (window[dim] - 1) // 2
+                pad_right = window[dim] - 1 - pad_left
+                shape[axis] = max(0, (shape[axis] - window[dim]) // dim_stride + 1)
+                data = np.pad(data, [(0, 0)] * axis + [(pad_left, pad_right)] + [(0, 0)] * (data.ndim - axis - 1), mode="constant", constant_values=fill_value)
+            else:
+                shape[axis] = max(0, (shape[axis] - window[dim]) // dim_stride + 1)
+
+            strides = list(data.strides)
+            strides[axis] = strides[axis] * dim_stride
+
+            data = np.lib.stride_tricks.as_strided(data, shape=shape + [window[dim]], strides=strides + [data.strides[axis]])
+
+            dims = dims[:axis] + (dims[axis], new_dim) + dims[axis + 1:]
+            coords[new_dim] = DataArray(np.arange(window[dim]), dims=new_dim)
+
+        result = DataArray(data, dims=dims, coords=coords)
+        if keep_attrs is None:
+            keep_attrs = _get_keep_attrs(default=True)
+        if keep_attrs:
+            result.attrs = self.obj.attrs
+        return result

     def reduce(self, func: Callable, keep_attrs: (bool | None)=None, **
         kwargs: Any) ->DataArray:
@@ -309,11 +361,37 @@ class DataArrayRolling(Rolling['DataArray']):
                [ 4.,  9., 15., 18.]])
         Dimensions without coordinates: a, b
         """
-        pass
+        from xarray.core.dataarray import DataArray
+
+        rolling_dim = self.obj.dims[self.obj.get_axis_num(self.dim[0])]
+        windows = self.obj.rolling_window(rolling_dim, self.window[0])
+        
+        if keep_attrs is None:
+            keep_attrs = _get_keep_attrs(default=True)
+
+        result = windows.reduce(func, dim="window", keep_attrs=keep_attrs, **kwargs)
+
+        if self.min_periods is not None:
+            count = windows.count(dim="window")
+            result = result.where(count >= self.min_periods)
+
+        return result

     def _counts(self, keep_attrs: (bool | None)) ->DataArray:
         """Number of non-nan entries in each rolling window."""
-        pass
+        from xarray.core.dataarray import DataArray
+
+        rolling_dim = self.obj.dims[self.obj.get_axis_num(self.dim[0])]
+        windows = self.obj.rolling_window(rolling_dim, self.window[0])
+
+        counts = windows.count(dim="window")
+
+        if keep_attrs is None:
+            keep_attrs = _get_keep_attrs(default=True)
+        if keep_attrs:
+            counts.attrs = self.obj.attrs
+
+        return counts


 class DatasetRolling(Rolling['Dataset']):
@@ -366,7 +444,7 @@ class DatasetRolling(Rolling['Dataset']):
                     center)

     def reduce(self, func: Callable, keep_attrs: (bool | None)=None, **
-        kwargs: Any) ->DataArray:
+        kwargs: Any) ->Dataset:
         """Reduce the items in this group by applying `func` along some
         dimension(s).

@@ -385,10 +463,26 @@ class DatasetRolling(Rolling['Dataset']):

         Returns
         -------
-        reduced : DataArray
-            Array with summarized data.
+        reduced : Dataset
+            Dataset with summarized data.
         """
-        pass
+        from xarray.core.dataset import Dataset
+
+        reduced = {}
+        for key, da in self.obj.data_vars.items():
+            if key in self.rollings:
+                reduced[key] = self.rollings[key].reduce(func, keep_attrs=keep_attrs, **kwargs)
+            else:
+                reduced[key] = da
+
+        result = Dataset(reduced)
+
+        if keep_attrs is None:
+            keep_attrs = _get_keep_attrs(default=True)
+        if keep_attrs:
+            result.attrs = self.obj.attrs
+
+        return result

     def construct(self, window_dim: (Hashable | Mapping[Any, Hashable] |
         None)=None, stride: (int | Mapping[Any, int])=1, fill_value: Any=
@@ -414,7 +508,31 @@ class DatasetRolling(Rolling['Dataset']):
         -------
         Dataset with variables converted from rolling object.
         """
-        pass
+        from xarray.core.dataset import Dataset
+
+        window_dim = either_dict_or_kwargs(window_dim, window_dim_kwargs, "construct")
+        if len(window_dim) != len(self.dim):
+            raise ValueError(
+                f"window_dim must be specified for all dimensions in rolling object: {self.dim}"
+            )
+
+        dataset = {}
+        for key, da in self.obj.data_vars.items():
+            if key in self.rollings:
+                dataset[key] = self.rollings[key].construct(
+                    window_dim, stride, fill_value, keep_attrs
+                )
+            else:
+                dataset[key] = da
+
+        result = Dataset(dataset)
+
+        if keep_attrs is None:
+            keep_attrs = _get_keep_attrs(default=True)
+        if keep_attrs:
+            result.attrs = self.obj.attrs
+
+        return result


 class Coarsen(CoarsenArithmetic, Generic[T_Xarray]):
diff --git a/xarray/core/rolling_exp.py b/xarray/core/rolling_exp.py
index a86a17a1..37d9ed7d 100644
--- a/xarray/core/rolling_exp.py
+++ b/xarray/core/rolling_exp.py
@@ -16,7 +16,27 @@ def _get_alpha(com: (float | None)=None, span: (float | None)=None,
     """
     Convert com, span, halflife to alpha.
     """
-    pass
+    if count_not_none(com, span, halflife, alpha) != 1:
+        raise ValueError("Must specify exactly one of com, span, halflife, or alpha")
+
+    if alpha is not None:
+        if not 0 < alpha <= 1:
+            raise ValueError("alpha must be in (0, 1]")
+        return alpha
+    elif com is not None:
+        if com < 0:
+            raise ValueError("com must be >= 0")
+        return 1 / (1 + com)
+    elif span is not None:
+        if span < 1:
+            raise ValueError("span must be >= 1")
+        return 2 / (span + 1)
+    elif halflife is not None:
+        if halflife <= 0:
+            raise ValueError("halflife must be > 0")
+        return 1 - np.exp(np.log(0.5) / halflife)
+    else:
+        raise ValueError("Must specify exactly one of com, span, halflife, or alpha")


 class RollingExp(Generic[T_DataWithCoords]):
@@ -85,7 +105,16 @@ class RollingExp(Generic[T_DataWithCoords]):
         array([1.        , 1.        , 1.69230769, 1.9       , 1.96694215])
         Dimensions without coordinates: x
         """
-        pass
+        import numbagg
+        keep_attrs = _get_keep_attrs(keep_attrs)
+        return apply_ufunc(
+            numbagg.move_exp_mean,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            keep_attrs=keep_attrs,
+            dask="allowed",
+        )

     def sum(self, keep_attrs: (bool | None)=None) ->T_DataWithCoords:
         """
@@ -106,7 +135,16 @@ class RollingExp(Generic[T_DataWithCoords]):
         array([1.        , 1.33333333, 2.44444444, 2.81481481, 2.9382716 ])
         Dimensions without coordinates: x
         """
-        pass
+        import numbagg
+        keep_attrs = _get_keep_attrs(keep_attrs)
+        return apply_ufunc(
+            numbagg.move_exp_sum,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            keep_attrs=keep_attrs,
+            dask="allowed",
+        )

     def std(self) ->T_DataWithCoords:
         """
@@ -122,7 +160,15 @@ class RollingExp(Generic[T_DataWithCoords]):
         array([       nan, 0.        , 0.67936622, 0.42966892, 0.25389527])
         Dimensions without coordinates: x
         """
-        pass
+        import numbagg
+        return apply_ufunc(
+            numbagg.move_exp_std,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            keep_attrs=True,
+            dask="allowed",
+        )

     def var(self) ->T_DataWithCoords:
         """
@@ -138,7 +184,15 @@ class RollingExp(Generic[T_DataWithCoords]):
         array([       nan, 0.        , 0.46153846, 0.18461538, 0.06446281])
         Dimensions without coordinates: x
         """
-        pass
+        import numbagg
+        return apply_ufunc(
+            numbagg.move_exp_var,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            keep_attrs=True,
+            dask="allowed",
+        )

     def cov(self, other: T_DataWithCoords) ->T_DataWithCoords:
         """
@@ -154,7 +208,16 @@ class RollingExp(Generic[T_DataWithCoords]):
         array([       nan, 0.        , 1.38461538, 0.55384615, 0.19338843])
         Dimensions without coordinates: x
         """
-        pass
+        import numbagg
+        return apply_ufunc(
+            numbagg.move_exp_cov,
+            self.obj,
+            other,
+            input_core_dims=[[self.dim], [self.dim]],
+            kwargs=self.kwargs,
+            keep_attrs=True,
+            dask="allowed",
+        )

     def corr(self, other: T_DataWithCoords) ->T_DataWithCoords:
         """
@@ -170,4 +233,13 @@ class RollingExp(Generic[T_DataWithCoords]):
         array([       nan,        nan,        nan, 0.4330127 , 0.48038446])
         Dimensions without coordinates: x
         """
-        pass
+        import numbagg
+        return apply_ufunc(
+            numbagg.move_exp_corr,
+            self.obj,
+            other,
+            input_core_dims=[[self.dim], [self.dim]],
+            kwargs=self.kwargs,
+            keep_attrs=True,
+            dask="allowed",
+        )
diff --git a/xarray/core/treenode.py b/xarray/core/treenode.py
index 30d6e6d1..503f2d68 100644
--- a/xarray/core/treenode.py
+++ b/xarray/core/treenode.py
@@ -74,77 +74,101 @@ class TreeNode(Generic[Tree]):
     @property
     def parent(self) ->(Tree | None):
         """Parent of this node."""
-        pass
+        return self._parent

     def _check_loop(self, new_parent: (Tree | None)) ->None:
         """Checks that assignment of this new parent will not create a cycle."""
-        pass
+        if new_parent is not None:
+            if new_parent is self:
+                raise InvalidTreeError("Cannot set a node as its own parent")
+            if new_parent in self.descendants:
+                raise InvalidTreeError("Cannot set a descendant as parent")

     def orphan(self) ->None:
         """Detach this node from its parent."""
-        pass
+        if self._parent is not None:
+            self._pre_detach(self._parent)
+            del self._parent._children[self.name]
+            self._parent = None
+            self._post_detach(self._parent)

     @property
     def children(self: Tree) ->Mapping[str, Tree]:
         """Child nodes of this node, stored under a mapping via their names."""
-        pass
+        return Frozen(self._children)

     @staticmethod
     def _check_children(children: Mapping[str, Tree]) ->None:
         """Check children for correct types and for any duplicates."""
-        pass
+        if not is_dict_like(children):
+            raise TypeError("Children must be a mapping")
+        for name, child in children.items():
+            if not isinstance(name, str):
+                raise TypeError("Child names must be strings")
+            if not isinstance(child, TreeNode):
+                raise TypeError("Children must be TreeNode instances")

     def __repr__(self) ->str:
         return f'TreeNode(children={dict(self._children)})'

     def _pre_detach_children(self: Tree, children: Mapping[str, Tree]) ->None:
         """Method call before detaching `children`."""
-        pass
+        for child in children.values():
+            child._pre_detach(self)

     def _post_detach_children(self: Tree, children: Mapping[str, Tree]) ->None:
         """Method call after detaching `children`."""
-        pass
+        for child in children.values():
+            child._post_detach(self)

     def _pre_attach_children(self: Tree, children: Mapping[str, Tree]) ->None:
         """Method call before attaching `children`."""
-        pass
+        for name, child in children.items():
+            child._pre_attach(self, name)

     def _post_attach_children(self: Tree, children: Mapping[str, Tree]) ->None:
         """Method call after attaching `children`."""
-        pass
+        for name, child in children.items():
+            child._post_attach(self, name)

     def _iter_parents(self: Tree) ->Iterator[Tree]:
         """Iterate up the tree, starting from the current node's parent."""
-        pass
+        node = self.parent
+        while node is not None:
+            yield node
+            node = node.parent

     def iter_lineage(self: Tree) ->tuple[Tree, ...]:
         """Iterate up the tree, starting from the current node."""
-        pass
+        return (self,) + tuple(self._iter_parents())

     @property
     def lineage(self: Tree) ->tuple[Tree, ...]:
         """All parent nodes and their parent nodes, starting with the closest."""
-        pass
+        return self.iter_lineage()

     @property
     def parents(self: Tree) ->tuple[Tree, ...]:
         """All parent nodes and their parent nodes, starting with the closest."""
-        pass
+        return tuple(self._iter_parents())

     @property
     def ancestors(self: Tree) ->tuple[Tree, ...]:
         """All parent nodes and their parent nodes, starting with the most distant."""
-        pass
+        return tuple(reversed(self.parents))

     @property
     def root(self: Tree) ->Tree:
         """Root node of the tree"""
-        pass
+        node = self
+        while node.parent is not None:
+            node = node.parent
+        return node

     @property
     def is_root(self) ->bool:
         """Whether this node is the tree root."""
-        pass
+        return self.parent is None

     @property
     def is_leaf(self) ->bool:
@@ -153,7 +177,7 @@ class TreeNode(Generic[Tree]):

         Leaf nodes are defined as nodes which have no children.
         """
-        pass
+        return len(self.children) == 0

     @property
     def leaves(self: Tree) ->tuple[Tree, ...]:
@@ -162,14 +186,16 @@ class TreeNode(Generic[Tree]):

         Leaf nodes are defined as nodes which have no children.
         """
-        pass
+        return tuple(node for node in self.subtree if node.is_leaf)

     @property
     def siblings(self: Tree) ->dict[str, Tree]:
         """
         Nodes with the same parent as this node.
         """
-        pass
+        if self.parent is None:
+            return {}
+        return {name: child for name, child in self.parent.children.items() if child is not self}

     @property
     def subtree(self: Tree) ->Iterator[Tree]:
@@ -182,7 +208,9 @@ class TreeNode(Generic[Tree]):
         --------
         DataTree.descendants
         """
-        pass
+        yield self
+        for child in self.children.values():
+            yield from child.subtree

     @property
     def descendants(self: Tree) ->tuple[Tree, ...]:
@@ -195,7 +223,7 @@ class TreeNode(Generic[Tree]):
         --------
         DataTree.subtree
         """
-        pass
+        return tuple(node for node in self.subtree if node is not self)

     @property
     def level(self: Tree) ->int:
@@ -214,7 +242,7 @@ class TreeNode(Generic[Tree]):
         depth
         width
         """
-        pass
+        return len(self.parents)

     @property
     def depth(self: Tree) ->int:
@@ -232,7 +260,7 @@ class TreeNode(Generic[Tree]):
         level
         width
         """
-        pass
+        return max(node.level for node in self.subtree)

     @property
     def width(self: Tree) ->int:
@@ -250,7 +278,7 @@ class TreeNode(Generic[Tree]):
         level
         depth
         """
-        pass
+        return sum(1 for node in self.root.subtree if node.level == self.level)

     def _pre_detach(self: Tree, parent: Tree) ->None:
         """Method call before detaching from `parent`."""
@@ -275,7 +303,7 @@ class TreeNode(Generic[Tree]):
         Only looks for the node within the immediate children of this node,
         not in other nodes of the tree.
         """
-        pass
+        return self.children.get(key, default)

     def _get_item(self: Tree, path: (str | NodePath)) ->(Tree | T_DataArray):
         """
@@ -283,7 +311,23 @@ class TreeNode(Generic[Tree]):

         Raises a KeyError if there is no object at the given path.
         """
-        pass
+        if isinstance(path, str):
+            path = NodePath(path)
+        
+        current = self
+        for part in path.parts:
+            if part == '..':
+                if current.parent is None:
+                    raise KeyError(f"Cannot go up from root node: {path}")
+                current = current.parent
+            elif part == '.':
+                continue
+            else:
+                try:
+                    current = current.children[part]
+                except KeyError:
+                    raise KeyError(f"No such child: {part} in path {path}")
+        return current

     def _set(self: Tree, key: str, val: Tree) ->None:
         """
@@ -291,7 +335,13 @@ class TreeNode(Generic[Tree]):

         Counterpart to the public .get method, and also only works on the immediate node, not other nodes in the tree.
         """
-        pass
+        if not isinstance(val, TreeNode):
+            raise TypeError("Child must be a TreeNode instance")
+        if key in self._children:
+            self._children[key].orphan()
+        self._children[key] = val
+        val._parent = self
+        val._name = key

     def _set_item(self: Tree, path: (str | NodePath), item: (Tree |
         T_DataArray), new_nodes_along_path: bool=False, allow_overwrite:
@@ -319,20 +369,39 @@ class TreeNode(Generic[Tree]):
             If node cannot be reached, and new_nodes_along_path=False.
             Or if a node already exists at the specified path, and allow_overwrite=False.
         """
-        pass
-
-    def __delitem__(self: Tree, key: str):
-        """Remove a child node from this tree object."""
-        if key in self.children:
-            child = self._children[key]
-            del self._children[key]
-            child.orphan()
-        else:
-            raise KeyError('Cannot delete')
+        if isinstance(path, str):
+            path = NodePath(path)
+        
+        current = self
+        for i, part in enumerate(path.parts[:-1]):
+            if part == '..':
+                if current.parent is None:
+                    raise KeyError(f"Cannot go up from root node: {path}")
+                current = current.parent
+            elif part == '.':
+                continue
+            else:
+                if part not in current.children:
+                    if new_nodes_along_path:
+                        new_node = type(self)(name=part)
+                        current._set(part, new_node)
+                        current = new_node
+                    else:
+                        raise KeyError(f"No such child: {part} in path {path}")
+                else:
+                    current = current.children[part]
+        
+        last_part = path.parts[-1]
+        if last_part in current.children:
+            if not allow_overwrite:
+                raise KeyError(f"Node already exists at path: {path}")
+            current._children[last_part].orphan()
+        
+        current._set(last_part, item)

     def same_tree(self, other: Tree) ->bool:
         """True if other node is in the same tree as this node."""
-        pass
+        return self.root is other.root


 AnyNamedNode = TypeVar('AnyNamedNode', bound='NamedNode')
diff --git a/xarray/core/utils.py b/xarray/core/utils.py
index fb70a0c1..20b3e753 100644
--- a/xarray/core/utils.py
+++ b/xarray/core/utils.py
@@ -31,7 +31,12 @@ def get_valid_numpy_dtype(array: (np.ndarray | pd.Index)) ->np.dtype:
     Used for wrapping a pandas.Index as an xarray.Variable.

     """
-    pass
+    if isinstance(array, pd.Index):
+        dtype = array.dtype
+        if isinstance(dtype, pd.CategoricalDtype):
+            return np.dtype(object)
+        return dtype
+    return array.dtype


 def maybe_coerce_to_str(index, original_coords):
@@ -39,7 +44,10 @@ def maybe_coerce_to_str(index, original_coords):

     pd.Index uses object-dtype to store str - try to avoid this for coords
     """
-    pass
+    if isinstance(index, pd.Index) and index.dtype == object:
+        if original_coords is not None and isinstance(original_coords, np.ndarray) and original_coords.dtype.kind == 'U':
+            return index.values.astype(original_coords.dtype)
+    return index


 def maybe_wrap_array(original, new_array):
@@ -48,7 +56,10 @@ def maybe_wrap_array(original, new_array):
     This lets us treat arbitrary functions that take and return ndarray objects
     like ufuncs, as long as they return an array with the same shape.
     """
-    pass
+    if hasattr(original, '__array_wrap__'):
+        if new_array.shape == original.shape:
+            return original.__array_wrap__(new_array)
+    return new_array


 def equivalent(first: T, second: T) ->bool:
@@ -56,14 +67,25 @@ def equivalent(first: T, second: T) ->bool:
     array_equiv if either object is an ndarray. If both objects are lists,
     equivalent is sequentially called on all the elements.
     """
-    pass
+    if first is second:
+        return True
+    if isinstance(first, np.ndarray) or isinstance(second, np.ndarray):
+        return np.array_equiv(first, second)
+    if isinstance(first, list) and isinstance(second, list):
+        return len(first) == len(second) and all(equivalent(i, j) for i, j in zip(first, second))
+    return first == second


 def peek_at(iterable: Iterable[T]) ->tuple[T, Iterator[T]]:
     """Returns the first value from iterable, as well as a new iterator with
     the same content as the original iterable
     """
-    pass
+    iterator = iter(iterable)
+    try:
+        first_value = next(iterator)
+    except StopIteration:
+        return None, iter([])
+    return first_value, itertools.chain([first_value], iterator)


 def update_safety_check(first_dict: Mapping[K, V], second_dict: Mapping[K,
diff --git a/xarray/core/weighted.py b/xarray/core/weighted.py
index b93a079c..2233699a 100644
--- a/xarray/core/weighted.py
+++ b/xarray/core/weighted.py
@@ -167,7 +167,10 @@ class Weighted(Generic[T_Xarray]):

     def _check_dim(self, dim: Dims):
         """raise an error if any dimension is missing"""
-        pass
+        if isinstance(dim, str):
+            dim = [dim]
+        if any(d not in self.obj.dims for d in dim):
+            raise ValueError(f"Dimensions {dim} not found in {self.obj.dims}")

     @staticmethod
     def _reduce(da: T_DataArray, weights: T_DataArray, dim: Dims=None,
@@ -176,41 +179,77 @@ class Weighted(Generic[T_Xarray]):

         for internal use only
         """
-        pass
+        return dot(da, weights, dims=dim)

     def _sum_of_weights(self, da: T_DataArray, dim: Dims=None) ->T_DataArray:
         """Calculate the sum of weights, accounting for missing values"""
-        pass
+        weights = self.weights.where(da.notnull())
+        return weights.sum(dim=dim)

     def _sum_of_squares(self, da: T_DataArray, dim: Dims=None, skipna: (
         bool | None)=None) ->T_DataArray:
         """Reduce a DataArray by a weighted ``sum_of_squares`` along some dimension(s)."""
-        pass
+        return self._reduce(da ** 2, self.weights, dim=dim, skipna=skipna)

     def _weighted_sum(self, da: T_DataArray, dim: Dims=None, skipna: (bool |
         None)=None) ->T_DataArray:
         """Reduce a DataArray by a weighted ``sum`` along some dimension(s)."""
-        pass
+        return self._reduce(da, self.weights, dim=dim, skipna=skipna)

     def _weighted_mean(self, da: T_DataArray, dim: Dims=None, skipna: (bool |
         None)=None) ->T_DataArray:
         """Reduce a DataArray by a weighted ``mean`` along some dimension(s)."""
-        pass
+        sum_of_weights = self._sum_of_weights(da, dim=dim)
+        weighted_sum = self._weighted_sum(da, dim=dim, skipna=skipna)
+        return weighted_sum / sum_of_weights

     def _weighted_var(self, da: T_DataArray, dim: Dims=None, skipna: (bool |
         None)=None) ->T_DataArray:
         """Reduce a DataArray by a weighted ``var`` along some dimension(s)."""
-        pass
+        mean = self._weighted_mean(da, dim=dim, skipna=skipna)
+        dev = (da - mean) ** 2
+        return self._reduce(dev, self.weights, dim=dim, skipna=skipna) / self._sum_of_weights(da, dim=dim)

     def _weighted_std(self, da: T_DataArray, dim: Dims=None, skipna: (bool |
         None)=None) ->T_DataArray:
         """Reduce a DataArray by a weighted ``std`` along some dimension(s)."""
-        pass
+        return np.sqrt(self._weighted_var(da, dim=dim, skipna=skipna))

     def _weighted_quantile(self, da: T_DataArray, q: ArrayLike, dim: Dims=
         None, skipna: (bool | None)=None) ->T_DataArray:
         """Apply a weighted ``quantile`` to a DataArray along some dimension(s)."""
-        pass
+        if skipna is None:
+            skipna = False
+
+        if dim is None:
+            dim = da.dims
+
+        q = np.asarray(q)
+        if np.any(q < 0) or np.any(q > 1):
+            raise ValueError("Quantiles must be between 0 and 1")
+
+        weights = self.weights
+        if skipna:
+            mask = da.notnull()
+            da = da.where(mask, drop=True)
+            weights = weights.where(mask, drop=True)
+
+        sorted_idx = da.argsort(dim=dim)
+        sorted_data = da.isel({d: sorted_idx for d in dim})
+        sorted_weights = weights.isel({d: sorted_idx for d in dim})
+
+        cumulative_weights = sorted_weights.cumsum(dim=dim)
+        total_weights = cumulative_weights.isel({d: -1 for d in dim})
+
+        # Normalize cumulative weights
+        cumulative_weights /= total_weights
+
+        # Calculate quantiles
+        result = sorted_data.interp({d: xr.DataArray(q, dims='quantile') for d in dim}, 
+                                    xi=cumulative_weights, 
+                                    method='linear')
+
+        return result.transpose('quantile', ...)

     def __repr__(self) ->str:
         """provide a nice str repr of our Weighted object"""
diff --git a/xarray/datatree_/docs/source/conf.py b/xarray/datatree_/docs/source/conf.py
index 2084912d..579f07dc 100644
--- a/xarray/datatree_/docs/source/conf.py
+++ b/xarray/datatree_/docs/source/conf.py
@@ -88,4 +88,40 @@ def linkcode_resolve(domain, info):
     """
     Determine the URL corresponding to Python object
     """
-    pass
+    if domain != 'py':
+        return None
+
+    modname = info['module']
+    fullname = info['fullname']
+
+    submod = sys.modules.get(modname)
+    if submod is None:
+        return None
+
+    obj = submod
+    for part in fullname.split('.'):
+        try:
+            obj = getattr(obj, part)
+        except AttributeError:
+            return None
+
+    try:
+        fn = inspect.getsourcefile(inspect.unwrap(obj))
+    except TypeError:
+        fn = None
+    if not fn:
+        return None
+
+    try:
+        source, lineno = inspect.getsourcelines(obj)
+    except OSError:
+        lineno = None
+
+    if lineno:
+        linespec = f"#L{lineno}-L{lineno + len(source) - 1}"
+    else:
+        linespec = ""
+
+    fn = os.path.relpath(fn, start=os.path.dirname(datatree.__file__))
+
+    return f"{srclink_project}/blob/{srclink_branch}/datatree/{fn}{linespec}"
diff --git a/xarray/groupers.py b/xarray/groupers.py
index dcb05c0a..d9542873 100644
--- a/xarray/groupers.py
+++ b/xarray/groupers.py
@@ -94,7 +94,9 @@ class UniqueGrouper(Grouper):
     @property
     def group_as_index(self) ->pd.Index:
         """Caches the group DataArray as a pandas Index."""
-        pass
+        if self._group_as_index is None:
+            self._group_as_index = safe_cast_to_index(self._group)
+        return self._group_as_index


 @dataclass
@@ -205,4 +207,16 @@ def unique_value_groups(ar, sort: bool=True) ->tuple[np.ndarray | pd.Index,
         Each element provides the integer indices in `ar` with values given by
         the corresponding value in `unique_values`.
     """
-    pass
+    ar = np.asarray(ar).flatten()
+    values, inverse = np.unique(ar, return_inverse=True, return_counts=False)
+
+    if sort:
+        sort_order = np.argsort(values)
+        values = values[sort_order]
+        inverse = np.argsort(sort_order)[inverse]
+
+    indices = [[] for _ in range(len(values))]
+    for n, g in enumerate(inverse):
+        indices[g].append(n)
+
+    return values, indices
diff --git a/xarray/namedarray/_aggregations.py b/xarray/namedarray/_aggregations.py
index c8843d3a..91481d8d 100644
--- a/xarray/namedarray/_aggregations.py
+++ b/xarray/namedarray/_aggregations.py
@@ -53,7 +53,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(5)
         """
-        pass
+        return self.reduce(duck_array_ops.count, dim=dim, **kwargs)

     def all(self, dim: Dims=None, **kwargs: Any) ->Self:
         """
@@ -99,7 +99,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 1B
         array(False)
         """
-        pass
+        return self.reduce(duck_array_ops.all, dim=dim, **kwargs)

     def any(self, dim: Dims=None, **kwargs: Any) ->Self:
         """
@@ -145,7 +145,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 1B
         array(True)
         """
-        pass
+        return self.reduce(duck_array_ops.any, dim=dim, **kwargs)

     def max(self, dim: Dims=None, *, skipna: (bool | None)=None, **kwargs: Any
         ) ->Self:
@@ -203,7 +203,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(nan)
         """
-        pass
+        return self.reduce(duck_array_ops.max, dim=dim, skipna=skipna, **kwargs)

     def min(self, dim: Dims=None, *, skipna: (bool | None)=None, **kwargs: Any
         ) ->Self:
@@ -261,7 +261,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(nan)
         """
-        pass
+        return self.reduce(duck_array_ops.min, dim=dim, skipna=skipna, **kwargs)

     def mean(self, dim: Dims=None, *, skipna: (bool | None)=None, **kwargs: Any
         ) ->Self:
@@ -323,7 +323,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(nan)
         """
-        pass
+        return self.reduce(duck_array_ops.mean, dim=dim, skipna=skipna, **kwargs)

     def prod(self, dim: Dims=None, *, skipna: (bool | None)=None, min_count:
         (int | None)=None, **kwargs: Any) ->Self:
@@ -397,7 +397,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(0.)
         """
-        pass
+        return self.reduce(duck_array_ops.prod, dim=dim, skipna=skipna, min_count=min_count, **kwargs)

     def sum(self, dim: Dims=None, *, skipna: (bool | None)=None, min_count:
         (int | None)=None, **kwargs: Any) ->Self:
@@ -471,7 +471,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(8.)
         """
-        pass
+        return self.reduce(duck_array_ops.sum, dim=dim, skipna=skipna, min_count=min_count, **kwargs)

     def std(self, dim: Dims=None, *, skipna: (bool | None)=None, ddof: int=
         0, **kwargs: Any) ->Self:
@@ -675,7 +675,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray ()> Size: 8B
         array(nan)
         """
-        pass
+        return self.reduce(duck_array_ops.median, dim=dim, skipna=skipna, **kwargs)

     def cumsum(self, dim: Dims=None, *, skipna: (bool | None)=None, **
         kwargs: Any) ->Self:
@@ -737,7 +737,7 @@ class NamedArrayAggregations:
         <xarray.NamedArray (x: 6)> Size: 48B
         array([ 1.,  3.,  6.,  6.,  8., nan])
         """
-        pass
+        return self.reduce(duck_array_ops.cumsum, dim=dim, skipna=skipna, **kwargs)

     def cumprod(self, dim: Dims=None, *, skipna: (bool | None)=None, **
         kwargs: Any) ->Self:
@@ -799,4 +799,4 @@ class NamedArrayAggregations:
         <xarray.NamedArray (x: 6)> Size: 48B
         array([ 1.,  2.,  6.,  0.,  0., nan])
         """
-        pass
+        return self.reduce(duck_array_ops.cumprod, dim=dim, skipna=skipna, **kwargs)
diff --git a/xarray/namedarray/_array_api.py b/xarray/namedarray/_array_api.py
index b9c696ab..27ad2299 100644
--- a/xarray/namedarray/_array_api.py
+++ b/xarray/namedarray/_array_api.py
@@ -41,7 +41,9 @@ def astype(x: NamedArray[_ShapeType, Any], dtype: _DType, /, *, copy: bool=True
     <xarray.NamedArray (x: 2)> Size: 8B
     array([1, 2], dtype=int32)
     """
-    pass
+    if not copy and x.dtype == dtype:
+        return x
+    return NamedArray(x.dims, x.data.astype(dtype))


 def imag(x: NamedArray[_ShapeType, np.dtype[_SupportsImag[_ScalarType]]], /
@@ -70,7 +72,7 @@ def imag(x: NamedArray[_ShapeType, np.dtype[_SupportsImag[_ScalarType]]], /
     <xarray.NamedArray (x: 2)> Size: 16B
     array([2., 4.])
     """
-    pass
+    return NamedArray(x.dims, np.imag(x.data))


 def real(x: NamedArray[_ShapeType, np.dtype[_SupportsReal[_ScalarType]]], /
@@ -99,7 +101,7 @@ def real(x: NamedArray[_ShapeType, np.dtype[_SupportsReal[_ScalarType]]], /
     <xarray.NamedArray (x: 2)> Size: 16B
     array([1., 2.])
     """
-    pass
+    return NamedArray(x.dims, np.real(x.data))


 def expand_dims(x: NamedArray[Any, _DType], /, *, dim: (_Dim | Default)=
@@ -134,7 +136,11 @@ def expand_dims(x: NamedArray[Any, _DType], /, *, dim: (_Dim | Default)=
     array([[[1., 2.],
             [3., 4.]]])
     """
-    pass
+    new_data = np.expand_dims(x.data, axis=axis)
+    new_dims = list(x.dims)
+    new_dim = dim if dim is not _default else f"dim_{len(x.dims)}"
+    new_dims.insert(axis, new_dim)
+    return NamedArray(tuple(new_dims), new_data)


 def permute_dims(x: NamedArray[Any, _DType], axes: _Axes) ->NamedArray[Any,
@@ -156,4 +162,6 @@ def permute_dims(x: NamedArray[Any, _DType], axes: _Axes) ->NamedArray[Any,
         data type as x.

     """
-    pass
+    new_data = np.transpose(x.data, axes)
+    new_dims = tuple(x.dims[i] for i in axes)
+    return NamedArray(new_dims, new_data)
diff --git a/xarray/namedarray/core.py b/xarray/namedarray/core.py
index 881d23bb..a51584c6 100644
--- a/xarray/namedarray/core.py
+++ b/xarray/namedarray/core.py
@@ -274,7 +274,7 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
         --------
         numpy.ndarray.shape
         """
-        pass
+        return self._data.shape

     @property
     def nbytes(self) ->_IntOrUnknown:
@@ -284,17 +284,21 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
         If the underlying data array does not include ``nbytes``, estimates
         the bytes consumed based on the ``size`` and ``dtype``.
         """
-        pass
+        if hasattr(self._data, 'nbytes'):
+            return self._data.nbytes
+        return self.size * self.dtype.itemsize

     @property
     def dims(self) ->_Dims:
         """Tuple of dimension names with which this NamedArray is associated."""
-        pass
+        return self._dims

     @property
     def attrs(self) ->dict[Any, Any]:
         """Dictionary of local attributes on this NamedArray."""
-        pass
+        if self._attrs is None:
+            self._attrs = {}
+        return self._attrs

     @property
     def data(self) ->duckarray[Any, _DType_co]:
@@ -303,7 +307,7 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
         (e.g. dask, sparse, pint) is preserved.

         """
-        pass
+        return self._data

     @property
     def imag(self: NamedArray[_ShapeType, np.dtype[_SupportsImag[_ScalarType]]]
@@ -404,7 +408,9 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
         int or tuple of int
             Axis number or numbers corresponding to the given dimensions.
         """
-        pass
+        if isinstance(dim, Iterable) and not isinstance(dim, str):
+            return tuple(self._dims.index(d) for d in dim)
+        return self._dims.index(dim)

     @property
     def chunks(self) ->(_Chunks | None):
@@ -418,7 +424,9 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
         NamedArray.chunksizes
         xarray.unify_chunks
         """
-        pass
+        if hasattr(self._data, 'chunks'):
+            return self._data.chunks
+        return None

     @property
     def chunksizes(self) ->Mapping[_Dim, _Shape]:
@@ -436,12 +444,14 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
         NamedArray.chunks
         xarray.unify_chunks
         """
-        pass
+        if self.chunks is None:
+            return {}
+        return dict(zip(self._dims, self.chunks))

     @property
     def sizes(self) ->dict[_Dim, _IntOrUnknown]:
         """Ordered mapping from dimension names to lengths."""
-        pass
+        return dict(zip(self._dims, self.shape))

     def chunk(self, chunks: T_Chunks={}, chunked_array_type: (str |
         ChunkManagerEntrypoint[Any] | None)=None, from_array_kwargs: Any=
@@ -489,11 +499,11 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):

     def to_numpy(self) ->np.ndarray[Any, Any]:
         """Coerces wrapped data to numpy and returns a numpy.ndarray"""
-        pass
+        return np.asarray(self._data)

     def as_numpy(self) ->Self:
         """Coerces wrapped data into a numpy array, returning a Variable."""
-        pass
+        return self._replace(data=self.to_numpy())

     def reduce(self, func: Callable[..., Any], dim: Dims=None, axis: (int |
         Sequence[int] | None)=None, keepdims: bool=False, **kwargs: Any
@@ -526,11 +536,32 @@ class NamedArray(NamedArrayAggregations, Generic[_ShapeType_co, _DType_co]):
             Array with summarized data and the indicated dimension(s)
             removed.
         """
-        pass
+        if dim is not None and axis is not None:
+            raise ValueError("Cannot supply both 'dim' and 'axis'")
+        
+        if dim is not None:
+            if dim == "...":
+                axis = tuple(range(self.ndim))
+            elif isinstance(dim, str):
+                axis = self.get_axis_num(dim)
+            else:
+                axis = tuple(self.get_axis_num(d) for d in dim)
+        
+        result = func(self._data, axis=axis, keepdims=keepdims, **kwargs)
+        
+        if keepdims:
+            new_dims = self._dims
+        elif axis is None:
+            new_dims = ()
+        else:
+            new_dims = tuple(d for i, d in enumerate(self._dims) if i not in (axis if isinstance(axis, tuple) else (axis,)))
+        
+        return self._new(dims=new_dims, data=result)

     def _nonzero(self: T_NamedArrayInteger) ->tuple[T_NamedArrayInteger, ...]:
         """Equivalent numpy's nonzero but returns a tuple of NamedArrays."""
-        pass
+        indices = np.nonzero(self._data)
+        return tuple(self._new(dims=(f'dim_{i}',), data=idx) for i, idx in enumerate(indices))

     def __repr__(self) ->str:
         return formatting.array_repr(self)
diff --git a/xarray/namedarray/daskmanager.py b/xarray/namedarray/daskmanager.py
index cfbd1e84..f9e3917b 100644
--- a/xarray/namedarray/daskmanager.py
+++ b/xarray/namedarray/daskmanager.py
@@ -28,4 +28,5 @@ class DaskManager(ChunkManagerEntrypoint['DaskArray']):
         dtype: (_DType_co | None)=None, previous_chunks: (_NormalizedChunks |
         None)=None) ->Any:
         """Called by open_dataset"""
-        pass
+        from dask.array.core import normalize_chunks as dask_normalize_chunks
+        return dask_normalize_chunks(chunks, shape, limit, dtype, previous_chunks)
diff --git a/xarray/namedarray/dtypes.py b/xarray/namedarray/dtypes.py
index 5bebd041..a578e7bc 100644
--- a/xarray/namedarray/dtypes.py
+++ b/xarray/namedarray/dtypes.py
@@ -50,7 +50,16 @@ def maybe_promote(dtype: np.dtype[np.generic]) ->tuple[np.dtype[np.generic],
     dtype : Promoted dtype that can hold missing values.
     fill_value : Valid missing value for the promoted dtype.
     """
-    pass
+    if dtype.kind in ['i', 'u']:
+        return np.dtype('float64'), np.nan
+    elif dtype.kind == 'f':
+        return dtype, np.nan
+    elif dtype.kind in ['M', 'm']:
+        return dtype, np.datetime64('NaT')
+    elif dtype.kind == 'b':
+        return np.dtype('object'), NA
+    else:
+        return np.dtype('object'), NA


 NAT_TYPES = {np.datetime64('NaT').dtype, np.timedelta64('NaT').dtype}
@@ -67,7 +76,14 @@ def get_fill_value(dtype: np.dtype[np.generic]) ->Any:
     -------
     fill_value : Missing value corresponding to this dtype.
     """
-    pass
+    if dtype.kind in ['i', 'u', 'f']:
+        return np.nan
+    elif dtype.kind in ['M', 'm']:
+        return np.datetime64('NaT')
+    elif dtype.kind == 'b':
+        return NA
+    else:
+        return NA


 def get_pos_infinity(dtype: np.dtype[np.generic], max_for_int: bool=False) ->(
@@ -84,12 +100,19 @@ def get_pos_infinity(dtype: np.dtype[np.generic], max_for_int: bool=False) ->(
     -------
     fill_value : positive infinity value corresponding to this dtype.
     """
-    pass
+    if dtype.kind in ['i', 'u']:
+        return np.iinfo(dtype).max if max_for_int else np.inf
+    elif dtype.kind == 'f':
+        return np.inf
+    elif dtype.kind == 'c':
+        return complex(np.inf, np.inf)
+    else:
+        return INF


 def get_neg_infinity(dtype: np.dtype[np.generic], min_for_int: bool=False) ->(
     float | complex | AlwaysLessThan):
-    """Return an appropriate positive infinity for this dtype.
+    """Return an appropriate negative infinity for this dtype.

     Parameters
     ----------
@@ -99,15 +122,22 @@ def get_neg_infinity(dtype: np.dtype[np.generic], min_for_int: bool=False) ->(

     Returns
     -------
-    fill_value : positive infinity value corresponding to this dtype.
+    fill_value : negative infinity value corresponding to this dtype.
     """
-    pass
+    if dtype.kind in ['i', 'u']:
+        return np.iinfo(dtype).min if min_for_int else -np.inf
+    elif dtype.kind == 'f':
+        return -np.inf
+    elif dtype.kind == 'c':
+        return complex(-np.inf, -np.inf)
+    else:
+        return NINF


 def is_datetime_like(dtype: np.dtype[np.generic]) ->TypeGuard[np.datetime64 |
     np.timedelta64]:
     """Check if a dtype is a subclass of the numpy datetime types"""
-    pass
+    return dtype.kind in ['M', 'm']


 def result_type(*arrays_and_dtypes: (np.typing.ArrayLike | np.typing.DTypeLike)
@@ -127,4 +157,17 @@ def result_type(*arrays_and_dtypes: (np.typing.ArrayLike | np.typing.DTypeLike)
     -------
     numpy.dtype for the result.
     """
-    pass
+    dtypes = []
+    for array_or_dtype in arrays_and_dtypes:
+        if hasattr(array_or_dtype, 'dtype'):
+            dtypes.append(array_or_dtype.dtype)
+        else:
+            dtypes.append(np.dtype(array_or_dtype))
+
+    result = np.result_type(*dtypes)
+
+    for t1, t2 in PROMOTE_TO_OBJECT:
+        if any(isinstance(dtype.type, t1) for dtype in dtypes) and any(isinstance(dtype.type, t2) for dtype in dtypes):
+            return np.dtype('object')
+
+    return result
diff --git a/xarray/namedarray/parallelcompat.py b/xarray/namedarray/parallelcompat.py
index edcc83cd..e415a8f8 100644
--- a/xarray/namedarray/parallelcompat.py
+++ b/xarray/namedarray/parallelcompat.py
@@ -39,13 +39,25 @@ def list_chunkmanagers() ->dict[str, ChunkManagerEntrypoint[Any]]:
     -----
     # New selection mechanism introduced with Python 3.10. See GH6514.
     """
-    pass
+    chunkmanagers = {}
+    for ep in entry_points(group='xarray.chunkmanagers'):
+        try:
+            chunkmanagers[ep.name] = ep.load()()
+        except Exception:
+            emit_user_level_warning(f"Failed to load chunkmanager {ep.name}")
+    return chunkmanagers


 def load_chunkmanagers(entrypoints: Sequence[EntryPoint]) ->dict[str,
     ChunkManagerEntrypoint[Any]]:
     """Load entrypoints and instantiate chunkmanagers only once."""
-    pass
+    chunkmanagers = {}
+    for ep in entrypoints:
+        try:
+            chunkmanagers[ep.name] = ep.load()()
+        except Exception:
+            emit_user_level_warning(f"Failed to load chunkmanager {ep.name}")
+    return chunkmanagers


 def guess_chunkmanager(manager: (str | ChunkManagerEntrypoint[Any] | None)
@@ -56,7 +68,25 @@ def guess_chunkmanager(manager: (str | ChunkManagerEntrypoint[Any] | None)
     If the name of a specific ChunkManager is given (e.g. "dask"), then use that.
     Else use whatever is installed, defaulting to dask if there are multiple options.
     """
-    pass
+    chunkmanagers = list_chunkmanagers()
+    
+    if isinstance(manager, str):
+        if manager not in chunkmanagers:
+            raise ValueError(f"Chunk manager '{manager}' not found.")
+        return chunkmanagers[manager]
+    elif isinstance(manager, ChunkManagerEntrypoint):
+        return manager
+    elif manager is None:
+        if "dask" in chunkmanagers:
+            return chunkmanagers["dask"]
+        elif len(chunkmanagers) == 1:
+            return next(iter(chunkmanagers.values()))
+        elif len(chunkmanagers) > 1:
+            raise ValueError("Multiple chunk managers available. Please specify one.")
+        else:
+            raise ValueError("No chunk managers available.")
+    else:
+        raise TypeError(f"Invalid manager type: {type(manager)}")


 def get_chunked_array_type(*args: Any) ->ChunkManagerEntrypoint[Any]:
@@ -65,7 +95,21 @@ def get_chunked_array_type(*args: Any) ->ChunkManagerEntrypoint[Any]:

     Also checks that all arrays are of same chunking type (i.e. not a mix of cubed and dask).
     """
-    pass
+    chunkmanagers = list_chunkmanagers()
+    detected_managers = set()
+
+    for arg in args:
+        for manager in chunkmanagers.values():
+            if manager.is_chunked_array(arg):
+                detected_managers.add(manager)
+                break
+
+    if len(detected_managers) == 0:
+        raise ValueError("No chunked arrays detected.")
+    elif len(detected_managers) > 1:
+        raise ValueError("Mixed chunked array types detected. All arrays must use the same chunking backend.")
+    else:
+        return detected_managers.pop()


 class ChunkManagerEntrypoint(ABC, Generic[T_ChunkedArray]):
@@ -112,7 +156,7 @@ class ChunkManagerEntrypoint(ABC, Generic[T_ChunkedArray]):
         --------
         dask.is_dask_collection
         """
-        pass
+        return isinstance(data, self.array_cls)

     @abstractmethod
     def chunks(self, data: T_ChunkedArray) ->_NormalizedChunks:
diff --git a/xarray/namedarray/pycompat.py b/xarray/namedarray/pycompat.py
index c632ef6f..bc8f13d8 100644
--- a/xarray/namedarray/pycompat.py
+++ b/xarray/namedarray/pycompat.py
@@ -61,9 +61,13 @@ _cached_duck_array_modules: dict[ModType, DuckArrayModule] = {}

 def array_type(mod: ModType) ->DuckArrayTypes:
     """Quick wrapper to get the array class of the module."""
-    pass
+    if mod not in _cached_duck_array_modules:
+        _cached_duck_array_modules[mod] = DuckArrayModule(mod)
+    return _cached_duck_array_modules[mod].type


 def mod_version(mod: ModType) ->Version:
     """Quick wrapper to get the version of the module."""
-    pass
+    if mod not in _cached_duck_array_modules:
+        _cached_duck_array_modules[mod] = DuckArrayModule(mod)
+    return _cached_duck_array_modules[mod].version
diff --git a/xarray/namedarray/utils.py b/xarray/namedarray/utils.py
index 04211ef3..a7f32094 100644
--- a/xarray/namedarray/utils.py
+++ b/xarray/namedarray/utils.py
@@ -44,12 +44,18 @@ def module_available(module: str, minversion: (str | None)=None) ->bool:
     available : bool
         Whether the module is installed.
     """
-    pass
+    try:
+        mod = importlib.import_module(module)
+        if minversion is not None:
+            return Version(mod.__version__) >= Version(minversion)
+        return True
+    except ImportError:
+        return False


 def to_0d_object_array(value: object) ->NDArray[np.object_]:
     """Given a value, wrap it in a 0-D numpy.ndarray with dtype=object."""
-    pass
+    return np.array(value, dtype=object)


 def drop_missing_dims(supplied_dims: Iterable[_Dim], dims: Iterable[_Dim],
@@ -63,7 +69,17 @@ def drop_missing_dims(supplied_dims: Iterable[_Dim], dims: Iterable[_Dim],
     dims : Iterable of Hashable
     missing_dims : {"raise", "warn", "ignore"}
     """
-    pass
+    dims_set = set(dims)
+    result = []
+    for dim in supplied_dims:
+        if dim in dims_set:
+            result.append(dim)
+        elif missing_dims == "raise":
+            raise ValueError(f"Dimension '{dim}' not found in dims")
+        elif missing_dims == "warn":
+            warnings.warn(f"Dimension '{dim}' not found in dims", UserWarning)
+    
+    return tuple(result)


 def infix_dims(dims_supplied: Iterable[_Dim], dims_all: Iterable[_Dim],
@@ -72,7 +88,26 @@ def infix_dims(dims_supplied: Iterable[_Dim], dims_all: Iterable[_Dim],
     Resolves a supplied list containing an ellipsis representing other items, to
     a generator with the 'realized' list of all items
     """
-    pass
+    dims_supplied = list(dims_supplied)
+    dims_all = list(dims_all)
+    
+    if Ellipsis not in dims_supplied:
+        for dim in drop_missing_dims(dims_supplied, dims_all, missing_dims):
+            yield dim
+    else:
+        ellipsis_index = dims_supplied.index(Ellipsis)
+        before_ellipsis = dims_supplied[:ellipsis_index]
+        after_ellipsis = dims_supplied[ellipsis_index + 1:]
+        
+        for dim in drop_missing_dims(before_ellipsis, dims_all, missing_dims):
+            yield dim
+        
+        for dim in dims_all:
+            if dim not in before_ellipsis and dim not in after_ellipsis:
+                yield dim
+        
+        for dim in drop_missing_dims(after_ellipsis, dims_all, missing_dims):
+            yield dim


 class ReprObject:
diff --git a/xarray/plot/dataarray_plot.py b/xarray/plot/dataarray_plot.py
index f56da420..d4235c25 100644
--- a/xarray/plot/dataarray_plot.py
+++ b/xarray/plot/dataarray_plot.py
@@ -61,7 +61,32 @@ def _prepare_plot1d_data(darray: T_DataArray, coords_to_plot:
     >>> print({k: v.name for k, v in plts.items()})
     {'y': 'a', 'x': 1}
     """
-    pass
+    plts = {}
+    
+    # Handle y-axis data
+    plts['y'] = darray
+
+    # Handle x-axis data
+    x_coord = coords_to_plot.get('x')
+    if x_coord is not None:
+        if isinstance(x_coord, str):
+            plts['x'] = darray[x_coord]
+        else:
+            plts['x'] = darray.coords[x_coord]
+    else:
+        plts['x'] = darray.coords[darray.dims[0]]
+
+    # Handle hue data
+    hue_coord = coords_to_plot.get('hue')
+    if hue_coord is not None:
+        plts['hue'] = darray.coords[hue_coord]
+
+    # Handle size data
+    size_coord = coords_to_plot.get('size')
+    if size_coord is not None:
+        plts['size'] = darray.coords[size_coord]
+
+    return plts


 def plot(darray: DataArray, *, row: (Hashable | None)=None, col: (Hashable |
@@ -106,7 +131,15 @@ def plot(darray: DataArray, *, row: (Hashable | None)=None, col: (Hashable |
     --------
     xarray.DataArray.squeeze
     """
-    pass
+    darray = darray.squeeze()
+    ndims = len(darray.dims)
+
+    if ndims == 1:
+        return line(darray, row=row, col=col, col_wrap=col_wrap, ax=ax, hue=hue, subplot_kws=subplot_kws, **kwargs)
+    elif ndims == 2:
+        return pcolormesh(darray, row=row, col=col, col_wrap=col_wrap, ax=ax, subplot_kws=subplot_kws, **kwargs)
+    else:
+        return hist(darray, row=row, col=col, col_wrap=col_wrap, ax=ax, subplot_kws=subplot_kws, **kwargs)


 def line(darray: T_DataArray, *args: Any, row: (Hashable | None)=None, col:
@@ -175,7 +208,38 @@ def line(darray: T_DataArray, *args: Any, row: (Hashable | None)=None, col:
         When either col or row is given, returns a FacetGrid, otherwise
         a list of matplotlib Line3D objects.
     """
-    pass
+    # Prepare the data
+    plotter = _LinePlotter(
+        darray,
+        x=x,
+        y=y,
+        hue=hue,
+        row=row,
+        col=col,
+        ax=ax,
+        figsize=figsize,
+        aspect=aspect,
+        size=size,
+        xincrease=xincrease,
+        yincrease=yincrease,
+        xscale=xscale,
+        yscale=yscale,
+        xticks=xticks,
+        yticks=yticks,
+        xlim=xlim,
+        ylim=ylim,
+        add_legend=add_legend,
+        _labels=_labels,
+    )
+
+    # Plot the data
+    primitives = plotter.plot(*args, **kwargs)
+
+    # Return the result
+    if plotter.facets is not None:
+        return plotter.facets
+    else:
+        return primitives


 def step(darray: DataArray, *args: Any, where: Literal['pre', 'post', 'mid'
@@ -219,7 +283,16 @@ def step(darray: DataArray, *args: Any, where: Literal['pre', 'post', 'mid'
         When either col or row is given, returns a FacetGrid, otherwise
         a list of matplotlib Line3D objects.
     """
-    pass
+    # Set the drawstyle based on the 'where' parameter
+    if drawstyle is None and ds is None:
+        drawstyle = f'steps-{where}'
+    elif drawstyle is not None and ds is not None:
+        raise ValueError("Only specify one of 'drawstyle' and 'ds'")
+    elif ds is not None:
+        drawstyle = ds
+
+    # Call the line function with the updated drawstyle
+    return line(darray, *args, row=row, col=col, drawstyle=drawstyle, **kwargs)


 def hist(darray: DataArray, *args: Any, figsize: (Iterable[float] | None)=
@@ -268,7 +341,56 @@ def hist(darray: DataArray, *args: Any, figsize: (Iterable[float] | None)=
         Additional keyword arguments to :py:func:`matplotlib:matplotlib.pyplot.hist`.

     """
-    pass
+    import matplotlib.pyplot as plt
+
+    # Get the current axes if not provided
+    if ax is None:
+        ax = plt.gca()
+
+    # Create a new figure if size or figsize is provided
+    if size is not None or figsize is not None:
+        if ax is not None:
+            raise ValueError("Cannot specify both `ax` and `size`/`figsize`")
+        fig, ax = plt.subplots(figsize=figsize)
+
+    # Flatten the DataArray
+    data = darray.values.flatten()
+
+    # Plot the histogram
+    n, bins, patches = ax.hist(data, *args, **kwargs)
+
+    # Set the scales
+    if xscale is not None:
+        ax.set_xscale(xscale)
+    if yscale is not None:
+        ax.set_yscale(yscale)
+
+    # Set the ticks
+    if xticks is not None:
+        ax.set_xticks(xticks)
+    if yticks is not None:
+        ax.set_yticks(yticks)
+
+    # Set the limits
+    if xlim is not None:
+        ax.set_xlim(xlim)
+    if ylim is not None:
+        ax.set_ylim(ylim)
+
+    # Set the axis direction
+    if xincrease is not None:
+        ax.invert_xaxis() if not xincrease else None
+    if yincrease is not None:
+        ax.invert_yaxis() if not yincrease else None
+
+    # Set labels
+    ax.set_xlabel(darray.name or '')
+    ax.set_ylabel('Frequency')
+
+    # Set title
+    ax.set_title(f'Histogram of {darray.name or "Data"}')
+
+    return n, bins, patches


 def _plot1d(plotfunc):
diff --git a/xarray/plot/dataset_plot.py b/xarray/plot/dataset_plot.py
index 458a594d..8b3904e6 100644
--- a/xarray/plot/dataset_plot.py
+++ b/xarray/plot/dataset_plot.py
@@ -27,7 +27,22 @@ def quiver(ds: Dataset, x: Hashable, y: Hashable, ax: Axes, u: Hashable, v:

     Wraps :py:func:`matplotlib:matplotlib.pyplot.quiver`.
     """
-    pass
+    x_data = ds[x].values
+    y_data = ds[y].values
+    u_data = ds[u].values
+    v_data = ds[v].values
+
+    # Calculate a nice quiver key magnitude
+    magnitude = _get_nice_quiver_magnitude(u_data, v_data)
+
+    # Create the quiver plot
+    q = ax.quiver(x_data, y_data, u_data, v_data, **kwargs)
+
+    # Add a key for scale
+    ax.quiverkey(q, X=0.85, Y=1.05, U=magnitude,
+                 label=f'{magnitude} {ds[u].units}', labelpos='E')
+
+    return q


 @_dsplot
@@ -37,7 +52,15 @@ def streamplot(ds: Dataset, x: Hashable, y: Hashable, ax: Axes, u: Hashable,

     Wraps :py:func:`matplotlib:matplotlib.pyplot.streamplot`.
     """
-    pass
+    x_data = ds[x].values
+    y_data = ds[y].values
+    u_data = ds[u].values
+    v_data = ds[v].values
+
+    # Create the streamplot
+    streams = ax.streamplot(x_data, y_data, u_data, v_data, **kwargs)
+
+    return streams.lines


 F = TypeVar('F', bound=Callable)
@@ -60,13 +83,30 @@ def _update_doc_to_dataset(dataarray_plotfunc: Callable) ->Callable[[F], F]:
     dataarray_plotfunc : Callable
         Function that returns a finished plot primitive.
     """
-    pass
+    def wrapper(func: F) ->F:
+        func.__doc__ = f"""
+        Dataset-specific wrapper for :py:func:`xarray.plot.dataarray_plot.{dataarray_plotfunc.__name__}`.
+
+        This function works similarly to the DataArray version, but operates on
+        Dataset variables instead. The first argument should be a Dataset, and
+        variable names should be passed as strings for the x, y, and other
+        relevant parameters.
+
+        {dataarray_plotfunc.__doc__}
+        """
+        return func
+    return wrapper


 def _temp_dataarray(ds: Dataset, y: Hashable, locals_: dict[str, Any]
     ) ->DataArray:
     """Create a temporary datarray with extra coords."""
-    pass
+    da = ds[y]
+    coords = {}
+    for key, value in locals_.items():
+        if isinstance(value, Hashable) and value in ds.variables:
+            coords[key] = ds[value]
+    return da.assign_coords(coords)


 @_update_doc_to_dataset(dataarray_plot.scatter)
@@ -88,4 +128,45 @@ def scatter(ds: Dataset, *args: Any, x: (Hashable | None)=None, y: (
     (ArrayLike | None)=None, **kwargs: Any) ->(PathCollection | FacetGrid[
     DataArray]):
     """Scatter plot Dataset data variables against each other."""
-    pass
+    locals_ = locals()
+    if y is None:
+        raise ValueError("y must be specified for scatter plots of Datasets")
+
+    da = _temp_dataarray(ds, y, locals_)
+
+    return dataarray_plot.scatter(
+        da,
+        *args,
+        x=x,
+        hue=hue,
+        hue_style=hue_style,
+        markersize=markersize,
+        linewidth=linewidth,
+        figsize=figsize,
+        size=size,
+        aspect=aspect,
+        ax=ax,
+        row=row,
+        col=col,
+        col_wrap=col_wrap,
+        xincrease=xincrease,
+        yincrease=yincrease,
+        add_legend=add_legend,
+        add_colorbar=add_colorbar,
+        add_labels=add_labels,
+        add_title=add_title,
+        subplot_kws=subplot_kws,
+        xscale=xscale,
+        yscale=yscale,
+        xticks=xticks,
+        yticks=yticks,
+        xlim=xlim,
+        ylim=ylim,
+        cmap=cmap,
+        vmin=vmin,
+        vmax=vmax,
+        norm=norm,
+        extend=extend,
+        levels=levels,
+        **kwargs
+    )
diff --git a/xarray/plot/facetgrid.py b/xarray/plot/facetgrid.py
index af73de2d..92014ec8 100644
--- a/xarray/plot/facetgrid.py
+++ b/xarray/plot/facetgrid.py
@@ -25,7 +25,10 @@ def _nicetitle(coord, value, maxchar, template):
     """
     Put coord, value in template and truncate at maxchar
     """
-    pass
+    title = template.format(coord=coord, value=format_item(value))
+    if len(title) > maxchar:
+        title = title[:(maxchar - 3)] + '...'
+    return title


 T_FacetGrid = TypeVar('T_FacetGrid', bound='FacetGrid')
@@ -222,7 +225,15 @@ class FacetGrid(Generic[T_DataArrayOrSet]):
         self : FacetGrid object

         """
-        pass
+        self._finalize_grid = functools.partial(self._finalize_grid, x, y)
+        
+        for ax, name_dict in zip(self.axs.flat, self.name_dicts.flat):
+            if name_dict is not None:
+                subset = self.data.loc[name_dict]
+                mappable = func(subset, x, y, ax=ax, **kwargs)
+                self._mappables.append(mappable)
+
+        return self

     def map_plot1d(self: T_FacetGrid, func: Callable, x: (Hashable | None),
         y: (Hashable | None), *, z: (Hashable | None)=None, hue: (Hashable |
@@ -248,15 +259,38 @@ class FacetGrid(Generic[T_DataArrayOrSet]):
         self : FacetGrid object

         """
-        pass
+        self._finalize_grid = functools.partial(self._finalize_grid, x, y)
+        
+        for ax, name_dict in zip(self.axs.flat, self.name_dicts.flat):
+            if name_dict is not None:
+                subset = self.data.loc[name_dict]
+                mappable = func(subset, x, y, ax=ax, z=z, hue=hue, 
+                                markersize=markersize, linewidth=linewidth, **kwargs)
+                self._mappables.append(mappable)
+
+        return self

     def _finalize_grid(self, *axlabels: Hashable) ->None:
         """Finalize the annotations and layout."""
-        pass
+        if not self._finalized:
+            self.set_axis_labels(*axlabels)
+            self.set_titles()
+            self.set_ticks()
+            self.fig.tight_layout()
+
+            for ax in self.axs.flat:
+                ax.margins(0.05)
+
+            self._finalized = True

     def add_colorbar(self, **kwargs: Any) ->None:
         """Draw a colorbar."""
-        pass
+        if self._mappables:
+            import matplotlib.pyplot as plt
+            
+            cbar_ax = self.fig.add_axes([0.92, 0.25, 0.02, 0.5])
+            cbar = plt.colorbar(self._mappables[-1], cax=cbar_ax, **kwargs)
+            self.cbar = cbar

     def _get_largest_lims(self) ->dict[str, tuple[float, float]]:
         """
@@ -274,7 +308,19 @@ class FacetGrid(Generic[T_DataArrayOrSet]):
         >>> round(fg._get_largest_lims()["x"][0], 3)
         np.float64(-0.334)
         """
-        pass
+        lims_largest = {}
+        for ax in self.axs.flat:
+            for axis in ['x', 'y']:
+                get_lim = getattr(ax, f'get_{axis}lim')
+                lims = get_lim()
+                if axis not in lims_largest:
+                    lims_largest[axis] = lims
+                else:
+                    lims_largest[axis] = (
+                        min(lims_largest[axis][0], lims[0]),
+                        max(lims_largest[axis][1], lims[1])
+                    )
+        return lims_largest

     def _set_lims(self, x: (tuple[float, float] | None)=None, y: (tuple[
         float, float] | None)=None, z: (tuple[float, float] | None)=None
@@ -299,7 +345,13 @@ class FacetGrid(Generic[T_DataArrayOrSet]):
         >>> fg.axs[0, 0].get_xlim(), fg.axs[0, 0].get_ylim()
         ((np.float64(-0.3), np.float64(0.3)), (np.float64(0.0), np.float64(2.0)))
         """
-        pass
+        for ax in self.axs.flat:
+            if x is not None:
+                ax.set_xlim(x)
+            if y is not None:
+                ax.set_ylim(y)
+            if z is not None and hasattr(ax, 'set_zlim'):
+                ax.set_zlim(z)

     def set_axis_labels(self, *axlabels: Hashable) ->None:
         """Set axis labels on the left column and bottom row of the grid."""
@@ -397,4 +449,37 @@ def _easy_facetgrid(data: T_DataArrayOrSet, plotfunc: Callable, kind:

     kwargs are the arguments to 2d plotting method
     """
-    pass
+    if ax is not None:
+        raise ValueError("Can't use axes when making faceted plots.")
+    
+    if figsize is not None:
+        kwargs['figsize'] = figsize
+    
+    if aspect is None:
+        aspect = 1
+    if size is None:
+        size = 3
+    
+    facet_kwargs = dict(
+        data=data,
+        row=row,
+        col=col,
+        col_wrap=col_wrap,
+        sharex=sharex,
+        sharey=sharey,
+        figsize=figsize,
+        aspect=aspect,
+        size=size,
+        subplot_kws=subplot_kws,
+    )
+    
+    g = FacetGrid(**facet_kwargs)
+    
+    if kind == 'dataarray':
+        return g.map_dataarray(plotfunc, x, y, **kwargs)
+    elif kind == 'dataset':
+        return g.map_dataset(plotfunc, x, y, **kwargs)
+    elif kind in ['line', 'plot1d']:
+        return g.map_plot1d(plotfunc, x, y, **kwargs)
+    else:
+        raise ValueError(f"Unsupported plot kind: {kind}")
diff --git a/xarray/plot/utils.py b/xarray/plot/utils.py
index 6309e4c6..5e76fc0a 100644
--- a/xarray/plot/utils.py
+++ b/xarray/plot/utils.py
@@ -38,7 +38,28 @@ def _build_discrete_cmap(cmap, levels, extend, filled):
     """
     Build a discrete colormap and normalization of the data.
     """
-    pass
+    import matplotlib.pyplot as plt
+    import matplotlib.colors as mcolors
+    
+    if not filled:
+        # non-filled contour plots
+        extend = 'max'
+    
+    if extend == 'both':
+        ext_n = 2
+    elif extend in ['min', 'max']:
+        ext_n = 1
+    else:
+        ext_n = 0
+    
+    n_colors = len(levels) + ext_n - 1
+    pal = _color_palette(cmap, n_colors)
+    
+    new_cmap, norm = mcolors.from_levels_and_colors(levels, pal, extend=extend)
+    # copy the old cmap name, for easier testing
+    new_cmap.name = getattr(cmap, 'name', cmap)
+    
+    return new_cmap, norm


 def _determine_cmap_params(plot_data, vmin=None, vmax=None, cmap=None,
@@ -57,7 +78,40 @@ def _determine_cmap_params(plot_data, vmin=None, vmax=None, cmap=None,
     cmap_params : dict
         Use depends on the type of the plotting function
     """
-    pass
+    import numpy as np
+    import matplotlib.pyplot as plt
+    
+    calc_data = np.ravel(plot_data)
+    calc_data = calc_data[~np.isnan(calc_data)]
+    
+    if vmin is None:
+        vmin = np.min(calc_data)
+    if vmax is None:
+        vmax = np.max(calc_data)
+    
+    # Choose default extend based on vmin, vmax
+    if extend is None:
+        extend = _determine_extend(calc_data, vmin, vmax)
+    
+    if levels is None:
+        levels = _determine_levels(vmin, vmax, center, robust)
+    
+    if cmap is None:
+        cmap = plt.get_cmap()
+    
+    if norm is None:
+        norm = plt.Normalize(vmin, vmax)
+    
+    cmap_params = {
+        'vmin': vmin,
+        'vmax': vmax,
+        'cmap': cmap,
+        'extend': extend,
+        'levels': levels,
+        'norm': norm,
+    }
+    
+    return cmap_params


 def _infer_xy_labels_3d(darray: (DataArray | Dataset), x: (Hashable | None),
@@ -68,7 +122,23 @@ def _infer_xy_labels_3d(darray: (DataArray | Dataset), x: (Hashable | None),
     Attempts to infer which dimension is RGB/RGBA by size and order of dims.

     """
-    pass
+    dims = list(darray.dims)
+    if rgb is None:
+        # Assume the last dimension is RGB
+        rgb = dims[-1]
+        dims = dims[:-1]
+    
+    if len(dims) != 2:
+        raise ValueError("DataArray must be 3D")
+    
+    if x is None and y is None:
+        x, y = dims
+    elif x is None:
+        x = [d for d in dims if d != y][0]
+    elif y is None:
+        y = [d for d in dims if d != x][0]
+    
+    return x, y


 def _infer_xy_labels(darray: (DataArray | Dataset), x: (Hashable | None), y:
@@ -79,7 +149,22 @@ def _infer_xy_labels(darray: (DataArray | Dataset), x: (Hashable | None), y:

     darray must be a 2 dimensional data array, or 3d for imshow only.
     """
-    pass
+    if imshow and darray.ndim == 3:
+        return _infer_xy_labels_3d(darray, x, y, rgb)
+    
+    if darray.ndim != 2:
+        raise ValueError('DataArray must be 2D')
+    
+    dims = list(darray.dims)
+    
+    if x is None and y is None:
+        x, y = dims
+    elif x is None:
+        x = [d for d in dims if d != y][0]
+    elif y is None:
+        y = [d for d in dims if d != x][0]
+    
+    return x, y


 def _assert_valid_xy(darray: (DataArray | Dataset), xy: (Hashable | None),
@@ -87,18 +172,47 @@ def _assert_valid_xy(darray: (DataArray | Dataset), xy: (Hashable | None),
     """
     make sure x and y passed to plotting functions are valid
     """
-    pass
+    if xy is not None:
+        if isinstance(darray, DataArray):
+            valid_dims = darray.dims
+        else:
+            valid_dims = darray.coords
+
+        if xy not in valid_dims:
+            raise ValueError(f"{name} must be one of {valid_dims}")


 def _get_units_from_attrs(da: DataArray) ->str:
     """Extracts and formats the unit/units from a attributes."""
-    pass
+    units = da.attrs.get('units', da.attrs.get('unit', ''))
+    if units:
+        return f" [{units}]"
+    return ""


 def label_from_attrs(da: (DataArray | None), extra: str='') ->str:
     """Makes informative labels if variable metadata (attrs) follows
     CF conventions."""
-    pass
+    if da is None:
+        return ''
+    
+    name = da.name
+    standard_name = da.attrs.get('standard_name', '')
+    long_name = da.attrs.get('long_name', '')
+    units = _get_units_from_attrs(da)
+    
+    if standard_name and long_name:
+        label = f"{standard_name.capitalize()} ({long_name}){units}"
+    elif long_name:
+        label = f"{long_name.capitalize()}{units}"
+    elif standard_name:
+        label = f"{standard_name.capitalize()}{units}"
+    elif name:
+        label = f"{name.capitalize()}{units}"
+    else:
+        label = ''
+    
+    return f"{label}{extra}"


 def _interval_to_mid_points(array: Iterable[pd.Interval]) ->np.ndarray:
diff --git a/xarray/testing/assertions.py b/xarray/testing/assertions.py
index 678f4a45..e48709fd 100644
--- a/xarray/testing/assertions.py
+++ b/xarray/testing/assertions.py
@@ -44,12 +44,29 @@ def assert_isomorphic(a: DataTree, b: DataTree, from_root: bool=False):
     assert_equal
     assert_identical
     """
-    pass
+    if from_root:
+        a = a.root
+        b = b.root
+    
+    def check_isomorphic(node_a, node_b):
+        if len(node_a.children) != len(node_b.children):
+            return False
+        for child_a, child_b in zip(node_a.children.values(), node_b.children.values()):
+            if not check_isomorphic(child_a, child_b):
+                return False
+        return True
+    
+    if not check_isomorphic(a, b):
+        raise AssertionError("DataTrees are not isomorphic")


 def maybe_transpose_dims(a, b, check_dim_order: bool):
     """Helper for assert_equal/allclose/identical"""
-    pass
+    if not check_dim_order:
+        if isinstance(a, (DataArray, Dataset)) and isinstance(b, (DataArray, Dataset)):
+            if set(a.dims) == set(b.dims) and a.dims != b.dims:
+                b = b.transpose(*a.dims)
+    return a, b


 @ensure_warnings
@@ -84,7 +101,14 @@ def assert_equal(a, b, from_root=True, check_dim_order: bool=True):
     assert_identical, assert_allclose, Dataset.equals, DataArray.equals
     numpy.testing.assert_array_equal
     """
-    pass
+    if isinstance(a, DataTree) and isinstance(b, DataTree):
+        assert_isomorphic(a, b, from_root=from_root)
+        for node_a, node_b in zip(a.subtree.values(), b.subtree.values()):
+            assert_equal(node_a.ds, node_b.ds, check_dim_order=check_dim_order)
+    else:
+        a, b = maybe_transpose_dims(a, b, check_dim_order)
+        if not a.equals(b):
+            raise AssertionError(f"Objects are not equal:\n\n{a}\n\n{b}")


 @ensure_warnings
@@ -115,7 +139,13 @@ def assert_identical(a, b, from_root=True):
     --------
     assert_equal, assert_allclose, Dataset.equals, DataArray.equals
     """
-    pass
+    if isinstance(a, DataTree) and isinstance(b, DataTree):
+        assert_isomorphic(a, b, from_root=from_root)
+        for node_a, node_b in zip(a.subtree.values(), b.subtree.values()):
+            assert_identical(node_a.ds, node_b.ds)
+    else:
+        if not a.identical(b):
+            raise AssertionError(f"Objects are not identical:\n\n{a}\n\n{b}")


 @ensure_warnings
@@ -147,20 +177,60 @@ def assert_allclose(a, b, rtol=1e-05, atol=1e-08, decode_bytes=True,
     --------
     assert_identical, assert_equal, numpy.testing.assert_allclose
     """
-    pass
+    a, b = maybe_transpose_dims(a, b, check_dim_order)
+    
+    if decode_bytes:
+        a = a.copy(deep=True)
+        b = b.copy(deep=True)
+        for obj in [a, b]:
+            for var in obj.variables.values():
+                if var.dtype.kind == 'S':
+                    var.values = var.values.astype('U')
+
+    if isinstance(a, (Dataset, DataArray)) and isinstance(b, (Dataset, DataArray)):
+        assert a.dims == b.dims, f"Dimensions do not match: {a.dims} != {b.dims}"
+        assert a.coords.keys() == b.coords.keys(), f"Coordinates do not match: {a.coords.keys()} != {b.coords.keys()}"
+        
+        for var in a.variables:
+            assert_allclose(a[var], b[var], rtol=rtol, atol=atol)
+    else:
+        assert_duckarray_allclose(a.values, b.values, rtol=rtol, atol=atol)


 @ensure_warnings
 def assert_duckarray_allclose(actual, desired, rtol=1e-07, atol=0, err_msg=
     '', verbose=True):
     """Like `np.testing.assert_allclose`, but for duckarrays."""
-    pass
+    import numpy as np
+    
+    def allclose(a, b):
+        return np.all(np.abs(a - b) <= atol + rtol * np.abs(b))
+    
+    if not allclose(actual, desired):
+        if err_msg:
+            raise AssertionError(err_msg)
+        else:
+            raise AssertionError(
+                f"Arrays are not close (rtol={rtol}, atol={atol}):\n"
+                f"Actual:\n{actual}\n"
+                f"Desired:\n{desired}"
+            )


 @ensure_warnings
 def assert_duckarray_equal(x, y, err_msg='', verbose=True):
     """Like `np.testing.assert_array_equal`, but for duckarrays"""
-    pass
+    import numpy as np
+    
+    if not np.array_equal(x, y):
+        if err_msg:
+            raise AssertionError(err_msg)
+        else:
+            raise AssertionError(
+                f"Arrays are not equal:\n"
+                f"x:\n{x}\n"
+                f"y:\n{y}"
+            )


 def assert_chunks_equal(a, b):
@@ -174,7 +244,19 @@ def assert_chunks_equal(a, b):
     b : xarray.Dataset or xarray.DataArray
         The second object to compare.
     """
-    pass
+    def get_chunks(obj):
+        if isinstance(obj, Dataset):
+            return {var: obj[var].chunks for var in obj.variables if obj[var].chunks is not None}
+        elif isinstance(obj, DataArray):
+            return obj.chunks
+        else:
+            raise TypeError(f"Expected Dataset or DataArray, got {type(obj)}")
+
+    chunks_a = get_chunks(a)
+    chunks_b = get_chunks(b)
+
+    if chunks_a != chunks_b:
+        raise AssertionError(f"Chunks are not equal:\na: {chunks_a}\nb: {chunks_b}")


 def _assert_internal_invariants(xarray_obj: Union[DataArray, Dataset,
@@ -185,4 +267,20 @@ def _assert_internal_invariants(xarray_obj: Union[DataArray, Dataset,
     in external projects if they (ill-advisedly) create objects using xarray's
     private APIs.
     """
-    pass
+    if isinstance(xarray_obj, DataArray):
+        assert set(xarray_obj.dims) == set(xarray_obj.coords.keys())
+        assert set(xarray_obj.dims) == set(xarray_obj.indexes.keys())
+        assert xarray_obj.name == xarray_obj.variable.name
+    elif isinstance(xarray_obj, Dataset):
+        assert set(xarray_obj.dims) == set(xarray_obj.coords.keys())
+        assert set(xarray_obj.dims) == set(xarray_obj.indexes.keys())
+        for var in xarray_obj.variables.values():
+            assert set(var.dims).issubset(xarray_obj.dims)
+    elif isinstance(xarray_obj, Variable):
+        assert xarray_obj.dims == xarray_obj.data.shape
+    else:
+        raise TypeError(f"Expected DataArray, Dataset, or Variable, got {type(xarray_obj)}")
+
+    if check_default_indexes:
+        for dim, index in xarray_obj.indexes.items():
+            assert isinstance(index, (PandasIndex, PandasMultiIndex))
diff --git a/xarray/testing/strategies.py b/xarray/testing/strategies.py
index 11355cbf..cf548644 100644
--- a/xarray/testing/strategies.py
+++ b/xarray/testing/strategies.py
@@ -38,7 +38,12 @@ def supported_dtypes() ->st.SearchStrategy[np.dtype]:
     --------
     :ref:`testing.hypothesis`_
     """
-    pass
+    return st.one_of(
+        npst.integer_dtypes(endianness="="),
+        npst.floating_dtypes(endianness="="),
+        npst.complex_number_dtypes(endianness="="),
+        st.just(np.dtype("bool"))
+    )


 def pandas_index_dtypes() ->st.SearchStrategy[np.dtype]:
@@ -46,7 +51,13 @@ def pandas_index_dtypes() ->st.SearchStrategy[np.dtype]:
     Dtypes supported by pandas indexes.
     Restrict datetime64 and timedelta64 to ns frequency till Xarray relaxes that.
     """
-    pass
+    return st.one_of(
+        npst.integer_dtypes(endianness="="),
+        npst.floating_dtypes(endianness="="),
+        st.just(np.dtype("datetime64[ns]")),
+        st.just(np.dtype("timedelta64[ns]")),
+        st.just(np.dtype("object"))
+    )


 _readable_characters = st.characters(categories=['L', 'N'], max_codepoint=383)
@@ -62,7 +73,7 @@ def names() ->st.SearchStrategy[str]:
     --------
     :ref:`testing.hypothesis`_
     """
-    pass
+    return st.text(_readable_characters, min_size=1, max_size=10)


 def dimension_names(*, name_strategy=names(), min_dims: int=0, max_dims: int=3
@@ -81,7 +92,7 @@ def dimension_names(*, name_strategy=names(), min_dims: int=0, max_dims: int=3
     max_dims
         Maximum number of dimensions in generated list.
     """
-    pass
+    return st.lists(name_strategy, min_size=min_dims, max_size=max_dims, unique=True)


 def dimension_sizes(*, dim_names: st.SearchStrategy[Hashable]=names(),
@@ -114,7 +125,15 @@ def dimension_sizes(*, dim_names: st.SearchStrategy[Hashable]=names(),
     --------
     :ref:`testing.hypothesis`_
     """
-    pass
+    if max_side is None:
+        max_side = min_side + 5
+    
+    return st.dictionaries(
+        keys=dim_names,
+        values=st.integers(min_value=min_side, max_value=max_side),
+        min_size=min_dims,
+        max_size=max_dims
+    )


 _readable_strings = st.text(_readable_characters, max_size=5)
@@ -138,7 +157,11 @@ def attrs() ->st.SearchStrategy[Mapping[Hashable, Any]]:
     --------
     :ref:`testing.hypothesis`_
     """
-    pass
+    return st.recursive(
+        simple_attrs,
+        lambda children: st.dictionaries(_attr_keys, children | _attr_values),
+        max_leaves=5
+    )


 @st.composite
@@ -268,4 +291,9 @@ def unique_subset_of(draw: st.DrawFn, objs: Union[Sequence[Hashable],
     --------
     :ref:`testing.hypothesis`_
     """
-    pass
+    if isinstance(objs, Mapping):
+        keys = list(objs.keys())
+        subset_keys = draw(st.sets(st.sampled_from(keys), min_size=min_size, max_size=max_size))
+        return {k: objs[k] for k in subset_keys}
+    else:
+        return draw(st.sets(st.sampled_from(objs), min_size=min_size, max_size=max_size))
diff --git a/xarray/tests/test_coding_strings.py b/xarray/tests/test_coding_strings.py
index 17179a44..da5e4f56 100644
--- a/xarray/tests/test_coding_strings.py
+++ b/xarray/tests/test_coding_strings.py
@@ -209,6 +209,20 @@ def test_char_to_bytes_size_zero() -> None:
     assert_array_equal(actual, expected)


+def test_ensure_fixed_length_bytes() -> None:
+    var = Variable(("x",), np.array([b"a", b"bb", b"ccc"], dtype=object))
+    result = strings.ensure_fixed_length_bytes(var)
+    expected = Variable(("x", "string"), np.array([[b"a", b"", b""], 
+                                                   [b"b", b"b", b""],
+                                                   [b"c", b"c", b"c"]]))
+    assert_identical(result, expected)
+
+    # Test with already fixed-length bytes
+    fixed_var = Variable(("x",), np.array([b"a", b"b", b"c"], dtype="S1"))
+    result = strings.ensure_fixed_length_bytes(fixed_var)
+    assert_identical(result, fixed_var)
+
+
 @requires_dask
 def test_char_to_bytes_dask() -> None:
     numpy_array = np.array([[b"a", b"b", b"c"], [b"d", b"e", b"f"]])
@@ -224,6 +238,40 @@ def test_char_to_bytes_dask() -> None:
         strings.char_to_bytes(array.rechunk(1))


+def test_numpy_bytes_to_char() -> None:
+    # Test with regular byte strings
+    arr = np.array([b"abc", b"def"])
+    result = strings._numpy_bytes_to_char(arr)
+    expected = np.array([[b"a", b"b", b"c"], [b"d", b"e", b"f"]])
+    assert_array_equal(result, expected)
+
+    # Test with object array of strings
+    arr = np.array(["abc", "def"], dtype=object)
+    result = strings._numpy_bytes_to_char(arr)
+    assert_array_equal(result, expected)
+
+    # Test with invalid dtype
+    with pytest.raises(ValueError, match="Unsupported dtype"):
+        strings._numpy_bytes_to_char(np.array([1, 2, 3]))
+
+
+def test_numpy_char_to_bytes() -> None:
+    # Test with character array
+    arr = np.array([[b"a", b"b", b"c"], [b"d", b"e", b"f"]])
+    result = strings._numpy_char_to_bytes(arr)
+    expected = np.array([b"abc", b"def"])
+    assert_array_equal(result, expected)
+
+    # Test with Unicode strings
+    arr = np.array(["abc", "def"])
+    result = strings._numpy_char_to_bytes(arr)
+    assert_array_equal(result, expected)
+
+    # Test with invalid dtype
+    with pytest.raises(ValueError, match="Unsupported dtype"):
+        strings._numpy_char_to_bytes(np.array([1, 2, 3]))
+
+
 def test_bytes_to_char() -> None:
     array = np.array([[b"ab", b"cd"], [b"ef", b"gh"]])
     expected = np.array([[[b"a", b"b"], [b"c", b"d"]], [[b"e", b"f"], [b"g", b"h"]]])
diff --git a/xarray/tutorial.py b/xarray/tutorial.py
index 9e891efe..db3b9334 100644
--- a/xarray/tutorial.py
+++ b/xarray/tutorial.py
@@ -62,7 +62,28 @@ def open_dataset(name: str, cache: bool=True, cache_dir: (None | str | os.
     open_dataset
     load_dataset
     """
-    pass
+    if cache_dir is None:
+        cache_dir = pathlib.Path.home() / _default_cache_dir_name
+    else:
+        cache_dir = pathlib.Path(cache_dir)
+
+    if name in external_urls:
+        url = external_urls[name]
+    else:
+        url = f"{base_url}/raw/{version}/{name}"
+        if name in file_formats:
+            url += f".{file_formats[name]}"
+
+    cache_file = cache_dir / name
+    if cache_file.exists():
+        return _open_dataset(cache_file, engine=engine, **kws)
+
+    if cache:
+        cache_dir.mkdir(parents=True, exist_ok=True)
+        _open_dataset(url, engine=engine, **kws).to_netcdf(cache_file)
+        return _open_dataset(cache_file, engine=engine, **kws)
+    else:
+        return _open_dataset(url, engine=engine, **kws)


 def load_dataset(*args, **kwargs) ->Dataset:
@@ -102,7 +123,8 @@ def load_dataset(*args, **kwargs) ->Dataset:
     open_dataset
     load_dataset
     """
-    pass
+    with open_dataset(*args, **kwargs) as ds:
+        return ds.load()


 def scatter_example_dataset(*, seed: (None | int)=None) ->Dataset:
@@ -114,4 +136,24 @@ def scatter_example_dataset(*, seed: (None | int)=None) ->Dataset:
     seed : int, optional
         Seed for the random number generation.
     """
-    pass
+    rng = np.random.default_rng(seed)
+    
+    n = 1000
+    x = rng.normal(size=n)
+    y = rng.normal(size=n)
+    z = rng.normal(size=n)
+    
+    da = DataArray(
+        data=np.column_stack([x, y, z]),
+        dims=["sample", "dimension"],
+        coords={
+            "sample": range(n),
+            "dimension": ["x", "y", "z"]
+        },
+        name="position"
+    )
+    
+    ds = Dataset({"position": da})
+    ds["distance"] = np.sqrt((da**2).sum(dim="dimension"))
+    
+    return ds
diff --git a/xarray/util/deprecation_helpers.py b/xarray/util/deprecation_helpers.py
index 65af5b80..78bcda00 100644
--- a/xarray/util/deprecation_helpers.py
+++ b/xarray/util/deprecation_helpers.py
@@ -39,7 +39,25 @@ def _deprecate_positional_args(version) ->Callable[[T], T]:
     This function is adapted from scikit-learn under the terms of its license. See
     licences/SCIKIT_LEARN_LICENSE
     """
-    pass
+    def decorator(func):
+        @wraps(func)
+        def wrapper(*args, **kwargs):
+            sig = inspect.signature(func)
+            params = list(sig.parameters.values())
+            keyword_params = [p for p in params if p.kind == KEYWORD_ONLY]
+
+            if len(args) > len(params) - len(keyword_params):
+                warnings.warn(
+                    f"From version {version}, passing these arguments to "
+                    f"{func.__name__} will be deprecated, and in future "
+                    "may raise an error. Please use keyword arguments "
+                    "instead.",
+                    FutureWarning,
+                    stacklevel=2,
+                )
+            return func(*args, **kwargs)
+        return wrapper
+    return decorator


 def deprecate_dims(func: T, old_name='dims') ->T:
@@ -48,4 +66,14 @@ def deprecate_dims(func: T, old_name='dims') ->T:
     `dim`. This decorator will issue a warning if `dims` is passed while forwarding it
     to `dim`.
     """
-    pass
+    @wraps(func)
+    def wrapper(*args, **kwargs):
+        if old_name in kwargs:
+            emit_user_level_warning(
+                f"The `{old_name}` argument has been deprecated and will be removed in a future version. "
+                f"Please use `dim` instead.",
+                FutureWarning,
+            )
+            kwargs['dim'] = kwargs.pop(old_name)
+        return func(*args, **kwargs)
+    return wrapper
diff --git a/xarray/util/generate_aggregations.py b/xarray/util/generate_aggregations.py
index b2eadf0c..9120cc12 100644
--- a/xarray/util/generate_aggregations.py
+++ b/xarray/util/generate_aggregations.py
@@ -360,6 +360,14 @@ NAMED_ARRAY_GENERATOR = GenericAggregationGenerator(cls='', datastructure=
     docref_description='reduction or aggregation operations',
     example_call_preamble='', definition_preamble=
     NAMED_ARRAY_AGGREGATIONS_PREAMBLE, has_keep_attrs=False)
+def write_methods(filepath, generators, preamble):
+    with open(filepath, "w") as f:
+        f.write(preamble)
+        for generator in generators:
+            f.write(generator.preamble)
+            for method in generator.methods:
+                f.write(generate_method(generator, method))
+
 if __name__ == '__main__':
     import os
     from pathlib import Path
@@ -372,3 +380,50 @@ if __name__ == '__main__':
     write_methods(filepath=p.parent / 'xarray' / 'xarray' / 'namedarray' /
         '_aggregations.py', generators=[NAMED_ARRAY_GENERATOR], preamble=
         NAMED_ARRAY_MODULE_PREAMBLE)
+def generate_method(generator, method):
+    signature = generator._template_signature.format(
+        method=method.name,
+        kw_only="*," if generator.has_keep_attrs else "",
+        extra_kwargs="".join(f"\n        {kwarg.kwarg}" for kwarg in method.extra_kwargs),
+        keep_attrs="\n        keep_attrs: bool | None = None," if generator.has_keep_attrs else "",
+        obj=generator.datastructure.name,
+    )
+    
+    docstring = f'"""{method.name}'
+    docstring += generator._dim_docstring.format(method=method.name, cls=generator.cls)
+    
+    for kwarg in method.extra_kwargs:
+        docstring += f"\n        {kwarg.docs}"
+    
+    if generator.has_keep_attrs:
+        docstring += f"\n        {_KEEP_ATTRS_DOCSTRING}"
+    
+    docstring += f"\n        {_KWARGS_DOCSTRING.format(method=method.name)}"
+    
+    docstring += TEMPLATE_RETURNS.format(obj=generator.datastructure.name, method=method.name)
+    
+    see_also_methods = "\n".join(f"        {module}.{method.name}" for module in method.see_also_modules)
+    docstring += TEMPLATE_SEE_ALSO.format(
+        see_also_methods=see_also_methods,
+        docref=generator.docref,
+        docref_description=generator.docref_description,
+    )
+    
+    if generator.notes or (method.numeric_only and generator.datastructure.numeric_only):
+        docstring += TEMPLATE_NOTES.format(notes=generator.notes)
+        if method.numeric_only and generator.datastructure.numeric_only:
+            docstring += f"\n        {_NUMERIC_ONLY_NOTES}"
+    
+    docstring += f'\n        """'
+    
+    method_body = f"""
+        return self.reduce(
+            duck_array_ops.{method.array_method},
+            dim=dim,
+            skipna=skipna,
+            keep_attrs=keep_attrs,
+            **kwargs,
+        )
+    """
+    
+    return f"{signature}{docstring}{method_body}"
diff --git a/xarray/util/generate_ops.py b/xarray/util/generate_ops.py
index 9818559a..8608cf41 100644
--- a/xarray/util/generate_ops.py
+++ b/xarray/util/generate_ops.py
@@ -74,6 +74,39 @@ unhashable = """
     __hash__: None  # type:ignore[assignment]"""
 FuncType = Sequence[tuple[Optional[str], Optional[str]]]
 OpsType = tuple[FuncType, str, dict[str, str]]
+
+def binops(other_type: str, return_type: str = 'Self') -> list[OpsType]:
+    return [
+        (BINOPS_EQNE + BINOPS_CMP + BINOPS_NUM, required_method_binary, {'other_type': other_type, 'return_type': return_type}),
+        (BINOPS_REFLEXIVE, required_method_binary, {'other_type': other_type, 'return_type': return_type, 'reflexive': True})
+    ]
+
+def binops_overload(other_type: str, overload_type: str, return_type: str = 'Self', type_ignore: str = '') -> list[OpsType]:
+    return [
+        (BINOPS_EQNE + BINOPS_CMP + BINOPS_NUM, required_method_binary, {
+            'other_type': other_type,
+            'return_type': return_type,
+            'overload_type': overload_type,
+            'type_ignore': f'  # type: ignore[{type_ignore}]' if type_ignore else '',
+            'overload_type_ignore': f'  # type: ignore[{type_ignore}]' if type_ignore else ''
+        }),
+        (BINOPS_REFLEXIVE, required_method_binary, {'other_type': other_type, 'return_type': return_type, 'reflexive': True})
+    ]
+
+def inplace(other_type: str, type_ignore: str = '') -> list[OpsType]:
+    return [
+        (BINOPS_INPLACE, required_method_inplace, {
+            'other_type': other_type,
+            'type_ignore': f'  # type: ignore[{type_ignore}]' if type_ignore else ''
+        })
+    ]
+
+def unops() -> list[OpsType]:
+    return [
+        (UNARY_OPS, required_method_unary, {'unary': True}),
+        (OTHER_UNARY_METHODS, required_method_unary, {'other_unary': True})
+    ]
+
 ops_info = {}
 ops_info['DatasetOpsMixin'] = binops(other_type='DsCompatible') + inplace(
     other_type='DsCompatible') + unops()
@@ -116,7 +149,35 @@ COPY_DOCSTRING = '    {method}.__doc__ = {func}.__doc__'

 def render(ops_info: dict[str, list[OpsType]]) ->Iterator[str]:
     """Render the module or stub file."""
-    pass
+    yield MODULE_PREAMBLE
+
+    for cls_name, ops in ops_info.items():
+        yield CLASS_PREAMBLE.format(cls_name=cls_name, newline='\n' if cls_name != 'DatasetOpsMixin' else '')
+
+        for funcs, required_method, kwargs in ops:
+            yield required_method.format(**kwargs)
+
+            for method, func in funcs:
+                if method is None or func is None:
+                    continue
+
+                if 'overload' in kwargs:
+                    yield template_binop_overload.format(method=method, func=func, **kwargs)
+                elif 'reflexive' in kwargs:
+                    yield template_reflexive.format(method=method, func=func, **kwargs)
+                elif 'inplace' in kwargs:
+                    yield template_inplace.format(method=method, func=func, **kwargs)
+                elif 'unary' in kwargs:
+                    yield template_unary.format(method=method, func=func)
+                elif 'other_unary' in kwargs:
+                    yield template_other_unary.format(method=method, func=func)
+                else:
+                    yield template_binop.format(method=method, func=func, **kwargs)
+
+                yield COPY_DOCSTRING.format(method=method, func=func)
+
+        if cls_name in ('DatasetOpsMixin', 'DataArrayOpsMixin', 'VariableOpsMixin'):
+            yield unhashable


 if __name__ == '__main__':
diff --git a/xarray/util/print_versions.py b/xarray/util/print_versions.py
index 586848d2..f202bdee 100755
--- a/xarray/util/print_versions.py
+++ b/xarray/util/print_versions.py
@@ -10,7 +10,53 @@ import sys

 def get_sys_info():
     """Returns system information as a dict"""
-    pass
+    blob = []
+
+    # System information
+    blob.append(("Python", sys.version))
+    blob.append(("Python executable", sys.executable))
+    blob.append(("Machine", platform.platform()))
+    blob.append(("Processor", platform.processor()))
+    blob.append(("Byte-ordering", sys.byteorder))
+    blob.append(("Default encoding", sys.getdefaultencoding()))
+    blob.append(("filesystemencoding", sys.getfilesystemencoding()))
+
+    # Python dependencies
+    dependencies = [
+        "xarray",
+        "numpy",
+        "pandas",
+        "matplotlib",
+        "dask",
+        "distributed",
+        "scipy",
+        "netCDF4",
+        "h5netcdf",
+        "h5py",
+        "Nio",
+        "zarr",
+        "cftime",
+        "nc_time_axis",
+        "bottleneck",
+        "sparse",
+        "pydap",
+        "numbagg",
+        "fsspec",
+        "pooch",
+    ]
+
+    for modname in dependencies:
+        try:
+            if modname in sys.modules:
+                mod = sys.modules[modname]
+            else:
+                mod = importlib.import_module(modname)
+            ver = getattr(mod, "__version__", "installed")
+        except ImportError:
+            ver = "not installed"
+        blob.append((modname, ver))
+
+    return dict(blob)


 def show_versions(file=sys.stdout):
@@ -21,7 +67,13 @@ def show_versions(file=sys.stdout):
     file : file-like, optional
         print to the given file-like object. Defaults to sys.stdout.
     """
-    pass
+    sys_info = get_sys_info()
+
+    file.write("INSTALLED VERSIONS\n")
+    file.write("------------------\n")
+
+    for k, v in sys_info.items():
+        file.write(f"{k}: {v}\n")


 if __name__ == '__main__':