core.py

# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
The astropy.time package provides functionality for manipulating times and
dates. Specific emphasis is placed on supporting time scales (e.g. UTC, TAI,
UT1) and time representations (e.g. JD, MJD, ISO 8601) that are used in
astronomy.
"""
from __future__ import annotations

import copy
import enum
import operator
import os
import threading
from collections import defaultdict
from datetime import date, datetime, timezone
from time import strftime
from typing import TYPE_CHECKING
from warnings import warn
from weakref import WeakValueDictionary

import erfa
import numpy as np

from astropy import constants as const
from astropy import units as u
from astropy.extern import _strptime
from astropy.units import UnitConversionError
from astropy.utils import ShapedLikeNDArray, lazyproperty
from astropy.utils.compat import PYTHON_LT_3_11
from astropy.utils.data_info import MixinInfo, data_info_factory
from astropy.utils.exceptions import AstropyDeprecationWarning, AstropyWarning
from astropy.utils.masked import Masked

# Below, import TimeFromEpoch to avoid breaking code that followed the old
# example of making a custom timescale in the documentation.
from . import conf
from .formats import (
    TIME_DELTA_FORMATS,
    TIME_FORMATS,
    TimeAstropyTime,
    TimeDatetime,
    TimeDeltaNumeric,
    TimeFromEpoch,  # noqa: F401
    TimeJD,
    TimeUnique,
)
from .time_helper.function_helpers import CUSTOM_FUNCTIONS, UNSUPPORTED_FUNCTIONS
from .utils import day_frac

if TYPE_CHECKING:
    from astropy.coordinates import EarthLocation
__all__ = [
    "TimeBase",
    "Time",
    "TimeDelta",
    "TimeInfo",
    "TimeInfoBase",
    "update_leap_seconds",
    "TIME_SCALES",
    "STANDARD_TIME_SCALES",
    "TIME_DELTA_SCALES",
    "ScaleValueError",
    "OperandTypeError",
    "TimeDeltaMissingUnitWarning",
]


STANDARD_TIME_SCALES = ("tai", "tcb", "tcg", "tdb", "tt", "ut1", "utc")
LOCAL_SCALES = ("local",)
TIME_TYPES = {
    scale: scales for scales in (STANDARD_TIME_SCALES, LOCAL_SCALES) for scale in scales
}
TIME_SCALES = STANDARD_TIME_SCALES + LOCAL_SCALES
MULTI_HOPS = {
    ("tai", "tcb"): ("tt", "tdb"),
    ("tai", "tcg"): ("tt",),
    ("tai", "ut1"): ("utc",),
    ("tai", "tdb"): ("tt",),
    ("tcb", "tcg"): ("tdb", "tt"),
    ("tcb", "tt"): ("tdb",),
    ("tcb", "ut1"): ("tdb", "tt", "tai", "utc"),
    ("tcb", "utc"): ("tdb", "tt", "tai"),
    ("tcg", "tdb"): ("tt",),
    ("tcg", "ut1"): ("tt", "tai", "utc"),
    ("tcg", "utc"): ("tt", "tai"),
    ("tdb", "ut1"): ("tt", "tai", "utc"),
    ("tdb", "utc"): ("tt", "tai"),
    ("tt", "ut1"): ("tai", "utc"),
    ("tt", "utc"): ("tai",),
}
GEOCENTRIC_SCALES = ("tai", "tt", "tcg")
BARYCENTRIC_SCALES = ("tcb", "tdb")
ROTATIONAL_SCALES = ("ut1",)
TIME_DELTA_TYPES = {
    scale: scales
    for scales in (
        GEOCENTRIC_SCALES,
        BARYCENTRIC_SCALES,
        ROTATIONAL_SCALES,
        LOCAL_SCALES,
    )
    for scale in scales
}
TIME_DELTA_SCALES = (
    GEOCENTRIC_SCALES + BARYCENTRIC_SCALES + ROTATIONAL_SCALES + LOCAL_SCALES
)
# For time scale changes, we need L_G and L_B, which are stored in erfam.h as
#   /* L_G = 1 - d(TT)/d(TCG) */
#   define ERFA_ELG (6.969290134e-10)
#   /* L_B = 1 - d(TDB)/d(TCB), and TDB (s) at TAI 1977/1/1.0 */
#   define ERFA_ELB (1.550519768e-8)
# These are exposed in erfa as erfa.ELG and erfa.ELB.
# Implied: d(TT)/d(TCG) = 1-L_G
# and      d(TCG)/d(TT) = 1/(1-L_G) = 1 + (1-(1-L_G))/(1-L_G) = 1 + L_G/(1-L_G)
# scale offsets as second = first + first * scale_offset[(first,second)]
SCALE_OFFSETS = {
    ("tt", "tai"): None,
    ("tai", "tt"): None,
    ("tcg", "tt"): -erfa.ELG,
    ("tt", "tcg"): erfa.ELG / (1.0 - erfa.ELG),
    ("tcg", "tai"): -erfa.ELG,
    ("tai", "tcg"): erfa.ELG / (1.0 - erfa.ELG),
    ("tcb", "tdb"): -erfa.ELB,
    ("tdb", "tcb"): erfa.ELB / (1.0 - erfa.ELB),
}

# triple-level dictionary, yay!
SIDEREAL_TIME_MODELS = {
    "mean": {
        "IAU2006": {"function": erfa.gmst06, "scales": ("ut1", "tt")},
        "IAU2000": {"function": erfa.gmst00, "scales": ("ut1", "tt")},
        "IAU1982": {"function": erfa.gmst82, "scales": ("ut1",), "include_tio": False},
    },
    "apparent": {
        "IAU2006A": {"function": erfa.gst06a, "scales": ("ut1", "tt")},
        "IAU2000A": {"function": erfa.gst00a, "scales": ("ut1", "tt")},
        "IAU2000B": {"function": erfa.gst00b, "scales": ("ut1",)},
        "IAU1994": {"function": erfa.gst94, "scales": ("ut1",), "include_tio": False},
    },
}


class _LeapSecondsCheck(enum.Enum):
    NOT_STARTED = 0  # No thread has reached the check
    RUNNING = 1  # A thread is running update_leap_seconds (_LEAP_SECONDS_LOCK is held)
    DONE = 2  # update_leap_seconds has completed


_LEAP_SECONDS_CHECK = _LeapSecondsCheck.NOT_STARTED
_LEAP_SECONDS_LOCK = threading.RLock()


def _compress_array_dims(arr):
    """Compress array by allowing at most 2 * edgeitems + 1 in each dimension.

    Parameters
    ----------
    arr : array-like
        Array to compress.

    Returns
    -------
    out : array-like
        Compressed array.
    """
    idxs = []
    edgeitems = np.get_printoptions()["edgeitems"]

    # Build up a list of index arrays for each dimension, allowing no more than
    # 2 * edgeitems + 1 elements in each dimension.
    for dim in range(arr.ndim):
        if arr.shape[dim] > 2 * edgeitems:
            # The middle [edgeitems] value does not matter as it gets replaced
            # by ... in the output.
            idxs.append(
                np.concatenate(
                    [np.arange(edgeitems), [edgeitems], np.arange(-edgeitems, 0)]
                )
            )
        else:
            idxs.append(np.arange(arr.shape[dim]))

    # Use the magic np.ix_ function to effectively treat each index array as a
    # slicing operator.
    idxs_ix = np.ix_(*idxs)
    out = arr[idxs_ix]
    return out


class TimeInfoBase(MixinInfo):
    """
    Container for meta information like name, description, format.  This is
    required when the object is used as a mixin column within a table, but can
    be used as a general way to store meta information.

    This base class is common between TimeInfo and TimeDeltaInfo.
    """

    attr_names = MixinInfo.attr_names | {"serialize_method"}
    _supports_indexing = True

    # The usual tuple of attributes needed for serialization is replaced
    # by a property, since Time can be serialized different ways.
    _represent_as_dict_extra_attrs = (
        "format",
        "scale",
        "precision",
        "in_subfmt",
        "out_subfmt",
        "location",
        "_delta_ut1_utc",
        "_delta_tdb_tt",
    )

    # When serializing, write out the `value` attribute using the column name.
    _represent_as_dict_primary_data = "value"

    mask_val = np.ma.masked

    @property
    def _represent_as_dict_attrs(self):
        method = self.serialize_method[self._serialize_context]

        if method == "formatted_value":
            out = ("value",)
        elif method == "jd1_jd2":
            out = ("jd1", "jd2")
        else:
            raise ValueError("serialize method must be 'formatted_value' or 'jd1_jd2'")

        return out + self._represent_as_dict_extra_attrs

    def __init__(self, bound=False):
        super().__init__(bound)

        # If bound to a data object instance then create the dict of attributes
        # which stores the info attribute values.
        if bound:
            # Specify how to serialize this object depending on context.
            # If ``True`` for a context, then use formatted ``value`` attribute
            # (e.g. the ISO time string).  If ``False`` then use float jd1 and jd2.
            self.serialize_method = {
                "fits": "jd1_jd2",
                "ecsv": "formatted_value",
                "hdf5": "jd1_jd2",
                "yaml": "jd1_jd2",
                "parquet": "jd1_jd2",
                None: "jd1_jd2",
            }

    def get_sortable_arrays(self):
        """
        Return a list of arrays which can be lexically sorted to represent
        the order of the parent column.

        Returns
        -------
        arrays : list of ndarray
        """
        parent = self._parent
        jd_approx = parent.jd
        jd_remainder = (parent - parent.__class__(jd_approx, format="jd")).jd
        return [jd_approx, jd_remainder]

    @property
    def unit(self):
        return None

    info_summary_stats = staticmethod(
        data_info_factory(
            names=MixinInfo._stats,
            funcs=[getattr(np, stat) for stat in MixinInfo._stats],
        )
    )
    # When Time has mean, std, min, max methods:
    # funcs = [lambda x: getattr(x, stat)() for stat_name in MixinInfo._stats])

    def _construct_from_dict(self, map):
        if "jd1" in map and "jd2" in map:
            # Initialize as JD but revert to desired format and out_subfmt (if needed)
            format = map.pop("format")
            out_subfmt = map.pop("out_subfmt", None)
            map["format"] = "jd"
            map["val"] = map.pop("jd1")
            map["val2"] = map.pop("jd2")
            out = self._parent_cls(**map)
            out.format = format
            if out_subfmt is not None:
                out.out_subfmt = out_subfmt

        else:
            map["val"] = map.pop("value")
            out = self._parent_cls(**map)

        return out

    def new_like(self, cols, length, metadata_conflicts="warn", name=None):
        """
        Return a new Time instance which is consistent with the input Time objects
        ``cols`` and has ``length`` rows.

        This is intended for creating an empty Time instance whose elements can
        be set in-place for table operations like join or vstack.  It checks
        that the input locations and attributes are consistent.  This is used
        when a Time object is used as a mixin column in an astropy Table.

        Parameters
        ----------
        cols : list
            List of input columns (Time objects)
        length : int
            Length of the output column object
        metadata_conflicts : str ('warn'|'error'|'silent')
            How to handle metadata conflicts
        name : str
            Output column name

        Returns
        -------
        col : Time (or subclass)
            Empty instance of this class consistent with ``cols``

        """
        # Get merged info attributes like shape, dtype, format, description, etc.
        attrs = self.merge_cols_attributes(
            cols, metadata_conflicts, name, ("meta", "description")
        )
        attrs.pop("dtype")  # Not relevant for Time
        col0 = cols[0]

        # Check that location is consistent for all Time objects
        for col in cols[1:]:
            # This is the method used by __setitem__ to ensure that the right side
            # has a consistent location (and coerce data if necessary, but that does
            # not happen in this case since `col` is already a Time object).  If this
            # passes then any subsequent table operations via setitem will work.
            try:
                col0._make_value_equivalent(slice(None), col)
            except ValueError:
                raise ValueError("input columns have inconsistent locations")

        # Make a new Time object with the desired shape and attributes
        shape = (length,) + attrs.pop("shape")
        jd2000 = 2451544.5  # Arbitrary JD value J2000.0 that will work with ERFA
        jd1 = np.full(shape, jd2000, dtype="f8")
        jd2 = np.zeros(shape, dtype="f8")
        tm_attrs = {
            attr: getattr(col0, attr) for attr in ("scale", "location", "precision")
        }
        out = self._parent_cls(jd1, jd2, format="jd", **tm_attrs)
        out.format = col0.format
        out.out_subfmt = col0.out_subfmt
        out.in_subfmt = col0.in_subfmt

        # Set remaining info attributes
        for attr, value in attrs.items():
            setattr(out.info, attr, value)

        return out


class TimeInfo(TimeInfoBase):
    """
    Container for meta information like name, description, format.  This is
    required when the object is used as a mixin column within a table, but can
    be used as a general way to store meta information.
    """

    def _represent_as_dict(self, attrs=None):
        """Get the values for the parent ``attrs`` and return as a dict.

        By default, uses '_represent_as_dict_attrs'.
        """
        map = super()._represent_as_dict(attrs=attrs)

        # TODO: refactor these special cases into the TimeFormat classes?

        # The datetime64 format requires special handling for ECSV (see #12840).
        # The `value` has numpy dtype datetime64 but this is not an allowed
        # datatype for ECSV. Instead convert to a string representation.
        if (
            self._serialize_context == "ecsv"
            and map["format"] == "datetime64"
            and "value" in map
        ):
            map["value"] = map["value"].astype("U")

        # The datetime format is serialized as ISO with no loss of precision.
        if map["format"] == "datetime" and "value" in map:
            map["value"] = np.vectorize(lambda x: x.isoformat())(map["value"])

        return map

    def _construct_from_dict(self, map):
        # See comment above. May need to convert string back to datetime64.
        # Note that _serialize_context is not set here so we just look for the
        # string value directly.
        if (
            map["format"] == "datetime64"
            and "value" in map
            and map["value"].dtype.kind == "U"
        ):
            map["value"] = map["value"].astype("datetime64")

        # Convert back to datetime objects for datetime format.
        if map["format"] == "datetime" and "value" in map:
            from datetime import datetime

            map["value"] = np.vectorize(datetime.fromisoformat)(map["value"])

        delta_ut1_utc = map.pop("_delta_ut1_utc", None)
        delta_tdb_tt = map.pop("_delta_tdb_tt", None)

        out = super()._construct_from_dict(map)

        if delta_ut1_utc is not None:
            out._delta_ut1_utc = delta_ut1_utc
        if delta_tdb_tt is not None:
            out._delta_tdb_tt = delta_tdb_tt

        return out


class TimeDeltaInfo(TimeInfoBase):
    """
    Container for meta information like name, description, format.  This is
    required when the object is used as a mixin column within a table, but can
    be used as a general way to store meta information.
    """

    _represent_as_dict_extra_attrs = ("format", "scale")

    def new_like(self, cols, length, metadata_conflicts="warn", name=None):
        """
        Return a new TimeDelta instance which is consistent with the input Time objects
        ``cols`` and has ``length`` rows.

        This is intended for creating an empty Time instance whose elements can
        be set in-place for table operations like join or vstack.  It checks
        that the input locations and attributes are consistent.  This is used
        when a Time object is used as a mixin column in an astropy Table.

        Parameters
        ----------
        cols : list
            List of input columns (Time objects)
        length : int
            Length of the output column object
        metadata_conflicts : str ('warn'|'error'|'silent')
            How to handle metadata conflicts
        name : str
            Output column name

        Returns
        -------
        col : Time (or subclass)
            Empty instance of this class consistent with ``cols``

        """
        # Get merged info attributes like shape, dtype, format, description, etc.
        attrs = self.merge_cols_attributes(
            cols, metadata_conflicts, name, ("meta", "description")
        )
        attrs.pop("dtype")  # Not relevant for Time
        col0 = cols[0]

        # Make a new Time object with the desired shape and attributes
        shape = (length,) + attrs.pop("shape")
        jd1 = np.zeros(shape, dtype="f8")
        jd2 = np.zeros(shape, dtype="f8")
        out = self._parent_cls(jd1, jd2, format="jd", scale=col0.scale)
        out.format = col0.format

        # Set remaining info attributes
        for attr, value in attrs.items():
            setattr(out.info, attr, value)

        return out


class TimeBase(ShapedLikeNDArray):
    """Base time class from which Time and TimeDelta inherit."""

    # Make sure that reverse arithmetic (e.g., TimeDelta.__rmul__)
    # gets called over the __mul__ of Numpy arrays.
    __array_priority__ = 20000

    # Declare that Time can be used as a Table column by defining the
    # attribute where column attributes will be stored.
    _astropy_column_attrs = None

    def __getnewargs__(self):
        return (self._time,)

    def __getstate__(self):
        # For pickling, we remove the cache from what's pickled
        state = (self.__dict__ if PYTHON_LT_3_11 else super().__getstate__()).copy()
        state.pop("_id_cache", None)
        state.pop("cache", None)
        return state

    def _init_from_vals(
        self,
        val,
        val2,
        format,
        scale,
        copy,
        precision=None,
        in_subfmt=None,
        out_subfmt=None,
    ):
        """
        Set the internal _format, scale, and _time attrs from user
        inputs.  This handles coercion into the correct shapes and
        some basic input validation.
        """
        if in_subfmt is None:
            in_subfmt = "*"
        if out_subfmt is None:
            out_subfmt = "*"

        # Coerce val into an array
        val = _make_array(val, copy)

        # If val2 is not None, ensure consistency
        if val2 is not None:
            val2 = _make_array(val2, copy)
            try:
                np.broadcast(val, val2)
            except ValueError:
                raise ValueError(
                    "Input val and val2 have inconsistent shape; "
                    "they cannot be broadcast together."
                )

        if scale is not None:
            if not (isinstance(scale, str) and scale.lower() in self.SCALES):
                raise ScaleValueError(
                    f"Scale {scale!r} is not in the allowed scales "
                    f"{sorted(self.SCALES)}"
                )

        # If either of the input val, val2 are masked arrays then
        # find the masked elements and fill them.
        mask = False
        mask, val_data = get_mask_and_data(mask, val)
        mask, val_data2 = get_mask_and_data(mask, val2)

        # Parse / convert input values into internal jd1, jd2 based on format
        self._time = self._get_time_fmt(
            val_data, val_data2, format, scale, precision, in_subfmt, out_subfmt, mask
        )
        self._format = self._time.name

        # Hack from #9969 to allow passing the location value that has been
        # collected by the TimeAstropyTime format class up to the Time level.
        # TODO: find a nicer way.
        if hasattr(self._time, "_location"):
            self._location = self._time._location
            del self._time._location

        # If any inputs were masked then masked jd2 accordingly.  From above
        # routine ``mask`` must be either Python bool False or an bool ndarray
        # with shape broadcastable to jd2.
        if mask is not False:
            # Ensure that if the class is already masked, we do not lose it.
            self._time.jd1 = Masked(self._time.jd1, copy=False)
            self._time.jd1.mask |= mask
            # Ensure we share the mask (it may have been broadcast).
            self._time.jd2 = Masked(
                self._time.jd2, mask=self._time.jd1.mask, copy=False
            )

    def _get_time_fmt(
        self, val, val2, format, scale, precision, in_subfmt, out_subfmt, mask
    ):
        """
        Given the supplied val, val2, format and scale try to instantiate
        the corresponding TimeFormat class to convert the input values into
        the internal jd1 and jd2.

        If format is `None` and the input is a string-type or object array then
        guess available formats and stop when one matches.
        """
        if format is None:
            # If val and val2 broadcasted shape is (0,) (i.e. empty array input) then we
            # cannot guess format from the input values. But a quantity is fine (as
            # long as it has time units, but that will be checked later).
            empty_array = val.size == 0 and (val2 is None or val2.size == 0)
            if not (isinstance(self, TimeDelta) and isinstance(val, u.Quantity)) and (
                empty_array or np.all(mask)
            ):
                raise ValueError(
                    "cannot guess format from input values with zero-size array"
                    " or all elements masked"
                )
            formats = [
                (name, cls)
                for name, cls in self.FORMATS.items()
                if issubclass(cls, TimeUnique)
            ]

            # AstropyTime is a pseudo-format that isn't in the TIME_FORMATS registry,
            # but try to guess it at the end.
            if isinstance(self, Time):
                formats.append(("astropy_time", TimeAstropyTime))

        elif not isinstance(format, str):
            raise TypeError("format must be a string")

        elif format.lower() not in self.FORMATS:
            raise ValueError(
                f"Format {format!r} is not one of the allowed formats "
                f"{sorted(self.FORMATS)}"
            )
        else:
            formats = [(format, self.FORMATS[format])]

        masked = np.any(mask)
        oval, oval2 = val, val2
        problems = {}
        for name, cls in formats:
            try:
                if masked:
                    val, val2 = cls._fill_masked_values(oval, oval2, mask, in_subfmt)
                return cls(val, val2, scale, precision, in_subfmt, out_subfmt)
            except UnitConversionError:
                raise
            except (ValueError, TypeError) as err:
                # If ``format`` specified then there is only one possibility, so raise
                # immediately and include the upstream exception message to make it
                # easier for user to see what is wrong.
                if len(formats) == 1:
                    raise ValueError(
                        f"Input values did not match the format class {format}:"
                        + os.linesep
                        + f"{err.__class__.__name__}: {err}"
                    ) from err
                else:
                    problems[name] = err

        message = (
            "Input values did not match any of the formats where the format "
            "keyword is optional:\n"
        ) + "\n".join(f"- '{name}': {err}" for name, err in problems.items())
        raise ValueError(message)

    @property
    def writeable(self):
        return self._time.jd1.flags.writeable & self._time.jd2.flags.writeable

    @writeable.setter
    def writeable(self, value):
        self._time.jd1.flags.writeable = value
        self._time.jd2.flags.writeable = value

    @property
    def format(self):
        """
        Get or set time format.

        The format defines the way times are represented when accessed via the
        ``.value`` attribute.  By default it is the same as the format used for
        initializing the `Time` instance, but it can be set to any other value
        that could be used for initialization.  These can be listed with::

          >>> list(Time.FORMATS)
          ['jd', 'mjd', 'decimalyear', 'unix', 'unix_tai', 'cxcsec', 'gps', 'plot_date',
           'stardate', 'datetime', 'ymdhms', 'iso', 'isot', 'yday', 'datetime64',
           'fits', 'byear', 'jyear', 'byear_str', 'jyear_str']
        """
        return self._format

    @format.setter
    def format(self, format):
        """Set time format."""
        if format not in self.FORMATS:
            raise ValueError(f"format must be one of {list(self.FORMATS)}")
        format_cls = self.FORMATS[format]

        # Get the new TimeFormat object to contain time in new format.  Possibly
        # coerce in/out_subfmt to '*' (default) if existing subfmt values are
        # not valid in the new format.
        self._time = format_cls(
            self._time.jd1,
            self._time.jd2,
            self._time._scale,
            self.precision,
            in_subfmt=format_cls._get_allowed_subfmt(self.in_subfmt),
            out_subfmt=format_cls._get_allowed_subfmt(self.out_subfmt),
            from_jd=True,
        )

        self._format = format

    def to_string(self):
        """Output a string representation of the Time or TimeDelta object.

        Similar to ``str(self.value)`` (which uses numpy array formatting) but
        array values are evaluated only for the items that actually are output.
        For large arrays this can be a substantial performance improvement.

        Returns
        -------
        out : str
            String representation of the time values.

        """
        npo = np.get_printoptions()
        if self.size < npo["threshold"]:
            out = str(self.value)
        else:
            # Compress time object by allowing at most 2 * npo["edgeitems"] + 1
            # in each dimension. Then force numpy to use "summary mode" of
            # showing only the edge items by setting the size threshold to 0.
            # TODO: use np.core.arrayprint._leading_trailing if we have support for
            # np.concatenate. See #8610.
            tm = _compress_array_dims(self)
            with np.printoptions(threshold=0):
                out = str(tm.value)
        return out

    def __repr__(self):
        return "<{} object: scale='{}' format='{}' value={}>".format(
            self.__class__.__name__, self.scale, self.format, self.to_string()
        )

    def __str__(self):
        return self.to_string()

    def __hash__(self):
        try:
            loc = getattr(self, "location", None)
            if loc is not None:
                loc = loc.x.to_value(u.m), loc.y.to_value(u.m), loc.z.to_value(u.m)

            return hash((self.jd1, self.jd2, self.scale, loc))

        except TypeError:
            if self.ndim != 0:
                reason = "(must be scalar)"
            elif self.masked:
                reason = "(value is masked)"
            else:
                raise

            raise TypeError(f"unhashable type: '{self.__class__.__name__}' {reason}")

    @property
    def location(self) -> EarthLocation | None:
        return self._location

    @location.setter
    def location(self, value):
        if hasattr(self, "_location"):
            # since astropy 6.1.0
            warn(
                "Setting the location attribute post initialization will be "
                "disallowed in a future version of Astropy. "
                "Instead you should set the location when creating the Time object. "
                "In the future, this will raise an AttributeError.",
                category=FutureWarning,
                stacklevel=2,
            )
        self._location = value

    @property
    def scale(self):
        """Time scale."""
        return self._time.scale

    def _set_scale(self, scale):
        """
        This is the key routine that actually does time scale conversions.
        This is not public and not connected to the read-only scale property.
        """
        if scale == self.scale:
            return
        if scale not in self.SCALES:
            raise ValueError(
                f"Scale {scale!r} is not in the allowed scales {sorted(self.SCALES)}"
            )

        if scale == "utc" or self.scale == "utc":
            # If doing a transform involving UTC then check that the leap
            # seconds table is up to date.
            _check_leapsec()

        # Determine the chain of scale transformations to get from the current
        # scale to the new scale.  MULTI_HOPS contains a dict of all
        # transformations (xforms) that require intermediate xforms.
        # The MULTI_HOPS dict is keyed by (sys1, sys2) in alphabetical order.
        xform = (self.scale, scale)
        xform_sort = tuple(sorted(xform))
        multi = MULTI_HOPS.get(xform_sort, ())
        xforms = xform_sort[:1] + multi + xform_sort[-1:]
        # If we made the reverse xform then reverse it now.
        if xform_sort != xform:
            xforms = tuple(reversed(xforms))

        # Transform the jd1,2 pairs through the chain of scale xforms.
        jd1, jd2 = self._time.jd1, self._time.jd2
        for sys1, sys2 in zip(xforms[:-1], xforms[1:]):
            # Some xforms require an additional delta_ argument that is
            # provided through Time methods.  These values may be supplied by
            # the user or computed based on available approximations.  The
            # get_delta_ methods are available for only one combination of
            # sys1, sys2 though the property applies for both xform directions.
            args = [jd1, jd2]
            for sys12 in ((sys1, sys2), (sys2, sys1)):
                dt_method = "_get_delta_{}_{}".format(*sys12)
                try:
                    get_dt = getattr(self, dt_method)
                except AttributeError:
                    pass
                else:
                    args.append(get_dt(jd1, jd2))
                    break

            conv_func = getattr(erfa, sys1 + sys2)
            jd1, jd2 = conv_func(*args)

        jd1, jd2 = day_frac(jd1, jd2)

        self._time = self.FORMATS[self.format](
            jd1,
            jd2,
            scale,
            self.precision,
            self.in_subfmt,
            self.out_subfmt,
            from_jd=True,
        )

    @property
    def precision(self):
        """
        Decimal precision when outputting seconds as floating point (int
        value between 0 and 9 inclusive).
        """
        return self._time.precision

    @precision.setter
    def precision(self, val):
        del self.cache
        self._time.precision = val

    @property
    def in_subfmt(self):
        """
        Unix wildcard pattern to select subformats for parsing string input
        times.
        """
        return self._time.in_subfmt

    @in_subfmt.setter
    def in_subfmt(self, val):
        self._time.in_subfmt = val
        del self.cache

    @property
    def out_subfmt(self):
        """
        Unix wildcard pattern to select subformats for outputting times.
        """
        return self._time.out_subfmt

    @out_subfmt.setter
    def out_subfmt(self, val):
        # Setting the out_subfmt property here does validation of ``val``
        self._time.out_subfmt = val
        del self.cache

    @property
    def shape(self):
        """The shape of the time instances.

        Like `~numpy.ndarray.shape`, can be set to a new shape by assigning a
        tuple.  Note that if different instances share some but not all
        underlying data, setting the shape of one instance can make the other
        instance unusable.  Hence, it is strongly recommended to get new,
        reshaped instances with the ``reshape`` method.

        Raises
        ------
        ValueError
            If the new shape has the wrong total number of elements.
        AttributeError
            If the shape of the ``jd1``, ``jd2``, ``location``,
            ``delta_ut1_utc``, or ``delta_tdb_tt`` attributes cannot be changed
            without the arrays being copied.  For these cases, use the
            `Time.reshape` method (which copies any arrays that cannot be
            reshaped in-place).
        """
        return self._time.jd1.shape

    @shape.setter
    def shape(self, shape):
        del self.cache

        # We have to keep track of arrays that were already reshaped,
        # since we may have to return those to their original shape if a later
        # shape-setting fails.
        reshaped = []
        oldshape = self.shape

        # In-place reshape of data/attributes.  Need to access _time.jd1/2 not
        # self.jd1/2 because the latter are not guaranteed to be the actual
        # data, and in fact should not be directly changeable from the public
        # API.
        for obj, attr in (
            (self._time, "jd1"),
            (self._time, "jd2"),
            (self, "_delta_ut1_utc"),
            (self, "_delta_tdb_tt"),
            (self, "location"),
        ):
            val = getattr(obj, attr, None)
            if val is not None and val.size > 1:
                try:
                    val.shape = shape
                except Exception:
                    for val2 in reshaped:
                        val2.shape = oldshape
                    raise
                else:
                    reshaped.append(val)

    def _shaped_like_input(self, value):
        if self.masked:
            # Ensure the mask is independent.
            value = conf._masked_cls(value, mask=self.mask.copy())
            # For new-style, we do not treat masked scalars differently from arrays.
            if isinstance(value, Masked):
                return value

        if self._time.jd1.shape:
            if isinstance(value, np.ndarray):
                return value
            else:
                raise TypeError(
                    f"JD is an array ({self._time.jd1!r}) but value is not ({value!r})"
                )
        else:
            # zero-dimensional array, is it safe to unbox?  The tricky comparison
            # of the mask is for the case that value is structured; otherwise, we
            # could just use np.ma.is_masked(value).
            if (
                isinstance(value, np.ndarray)
                and not value.shape
                and (
                    (mask := getattr(value, "mask", np.False_)) == np.zeros_like(mask)
                ).all()
            ):
                if value.dtype.kind == "M":
                    # existing test doesn't want datetime64 converted
                    return value[()]
                elif value.dtype.fields:
                    # Unpack but keep field names; .item() doesn't
                    # Still don't get python types in the fields
                    return value[()]
                else:
                    return value.item()
            else:
                return value

    @property
    def jd1(self):
        """
        First of the two doubles that internally store time value(s) in JD.
        """
        return self._shaped_like_input(self._time.jd1)

    @property
    def jd2(self):
        """
        Second of the two doubles that internally store time value(s) in JD.
        """
        return self._shaped_like_input(self._time.jd2)

    def to_value(self, format, subfmt="*"):
        """Get time values expressed in specified output format.

        This method allows representing the ``Time`` object in the desired
        output ``format`` and optional sub-format ``subfmt``.  Available
        built-in formats include ``jd``, ``mjd``, ``iso``, and so forth. Each
        format can have its own sub-formats

        For built-in numerical formats like ``jd`` or ``unix``, ``subfmt`` can
        be one of 'float', 'long', 'decimal', 'str', or 'bytes'.  Here, 'long'
        uses ``numpy.longdouble`` for somewhat enhanced precision (with
        the enhancement depending on platform), and 'decimal'
        :class:`decimal.Decimal` for full precision.  For 'str' and 'bytes', the
        number of digits is also chosen such that time values are represented
        accurately.

        For built-in date-like string formats, one of 'date_hms', 'date_hm', or
        'date' (or 'longdate_hms', etc., for 5-digit years in
        `~astropy.time.TimeFITS`).  For sub-formats including seconds, the
        number of digits used for the fractional seconds is as set by
        `~astropy.time.Time.precision`.

        Parameters
        ----------
        format : str
            The format in which one wants the time values. Default: the current
            format.
        subfmt : str or None, optional
            Value or wildcard pattern to select the sub-format in which the
            values should be given.  The default of '*' picks the first
            available for a given format, i.e., 'float' or 'date_hms'.
            If `None`, use the instance's ``out_subfmt``.

        """
        # TODO: add a precision argument (but ensure it is keyword argument
        # only, to make life easier for TimeDelta.to_value()).
        if format not in self.FORMATS:
            raise ValueError(f"format must be one of {list(self.FORMATS)}")

        if subfmt is None:
            if format == self.format:
                subfmt = self.out_subfmt
            else:
                subfmt = self.FORMATS[format]._get_allowed_subfmt(self.out_subfmt)

        cache = self.cache["format"]
        key = format, subfmt, conf.masked_array_type
        value = cache.get(key)
        if value is None:
            if format == self.format:
                tm = self
            else:
                tm = self.replicate(format=format)

            # Some TimeFormat subclasses may not be able to handle being passes
            # on a out_subfmt. This includes some core classes like
            # TimeBesselianEpochString that do not have any allowed subfmts. But
            # those do deal with `self.out_subfmt` internally, so if subfmt is
            # the same, we do not pass it on.
            kwargs = {}
            if subfmt is not None and subfmt != tm.out_subfmt:
                kwargs["out_subfmt"] = subfmt
            try:
                value = tm._time.to_value(parent=tm, **kwargs)
            except TypeError as exc:
                # Try validating subfmt, e.g. for formats like 'jyear_str' that
                # do not implement out_subfmt in to_value() (because there are
                # no allowed subformats).  If subfmt is not valid this gives the
                # same exception as would have occurred if the call to
                # `to_value()` had succeeded.
                tm._time._select_subfmts(subfmt)

                # Subfmt was valid, so fall back to the original exception to see
                # if it was lack of support for out_subfmt as a call arg.
                if "unexpected keyword argument 'out_subfmt'" in str(exc):
                    raise ValueError(
                        f"to_value() method for format {format!r} does not "
                        "support passing a 'subfmt' argument"
                    ) from None
                else:
                    # Some unforeseen exception so raise.
                    raise

            value = tm._shaped_like_input(value)
            cache[key] = value

        return value

    @property
    def value(self):
        """Time value(s) in current format."""
        return self.to_value(self.format, None)

    @property
    def mask(self):
        if "mask" not in self.cache:
            mask = getattr(self._time.jd2, "mask", None)
            if mask is None:
                mask = np.broadcast_to(np.False_, self._time.jd2.shape)
            else:
                # Take a view of any existing mask, so we can set it to readonly.
                mask = mask.view()
            mask.flags.writeable = False
            self.cache["mask"] = mask
        return self.cache["mask"]

    @property
    def masked(self):
        return isinstance(self._time.jd1, Masked)

    @property
    def unmasked(self):
        """Get an instance without the mask.

        Note that while one gets a new instance, the underlying data will be shared.

        See Also
        --------
        astropy.time.Time.filled
        """
        # Get a new Time instance that has the unmasked versions of all attributes.
        return self._apply(lambda x: getattr(x, "unmasked", x))

    def filled(self, fill_value):
        """Get a copy of the underlying data, with masked values filled in.

        Parameters
        ----------
        fill_value : object
            Value to replace masked values with.  Note that if this value is masked

        See Also
        --------
        astropy.time.Time.unmasked
        """
        # TODO: once we support Not-a-Time, that can be the default fill_value.
        unmasked = self.unmasked.copy()
        unmasked[self.mask] = fill_value
        return unmasked

    def insert(self, obj, values, axis=0):
        """
        Insert values before the given indices in the column and return
        a new `~astropy.time.Time` or  `~astropy.time.TimeDelta` object.

        The values to be inserted must conform to the rules for in-place setting
        of ``Time`` objects (see ``Get and set values`` in the ``Time``
        documentation).

        The API signature matches the ``np.insert`` API, but is more limited.
        The specification of insert index ``obj`` must be a single integer,
        and the ``axis`` must be ``0`` for simple row insertion before the
        index.

        Parameters
        ----------
        obj : int
            Integer index before which ``values`` is inserted.
        values : array-like
            Value(s) to insert.  If the type of ``values`` is different
            from that of quantity, ``values`` is converted to the matching type.
        axis : int, optional
            Axis along which to insert ``values``.  Default is 0, which is the
            only allowed value and will insert a row.

        Returns
        -------
        out : `~astropy.time.Time` subclass
            New time object with inserted value(s)

        """
        # Validate inputs: obj arg is integer, axis=0, self is not a scalar, and
        # input index is in bounds.
        try:
            idx0 = operator.index(obj)
        except TypeError:
            raise TypeError("obj arg must be an integer")

        if axis != 0:
            raise ValueError("axis must be 0")

        if not self.shape:
            raise TypeError(
                f"cannot insert into scalar {self.__class__.__name__} object"
            )

        if abs(idx0) > len(self):
            raise IndexError(
                f"index {idx0} is out of bounds for axis 0 with size {len(self)}"
            )

        # Turn negative index into positive
        if idx0 < 0:
            idx0 = len(self) + idx0

        # For non-Time object, use numpy to help figure out the length.  (Note annoying
        # case of a string input that has a length which is not the length we want).
        if not isinstance(values, self.__class__):
            values = np.asarray(values)
        n_values = len(values) if values.shape else 1

        # Finally make the new object with the correct length and set values for the
        # three sections, before insert, the insert, and after the insert.
        out = self.__class__.info.new_like(
            [self], len(self) + n_values, name=self.info.name
        )

        out._time.jd1[:idx0] = self._time.jd1[:idx0]
        out._time.jd2[:idx0] = self._time.jd2[:idx0]

        # This uses the Time setting machinery to coerce and validate as necessary.
        out[idx0 : idx0 + n_values] = values

        out._time.jd1[idx0 + n_values :] = self._time.jd1[idx0:]
        out._time.jd2[idx0 + n_values :] = self._time.jd2[idx0:]

        return out

    def __setitem__(self, item, value):
        if not self.writeable:
            if self.shape:
                raise ValueError(
                    f"{self.__class__.__name__} object is read-only. Make a "
                    'copy() or set "writeable" attribute to True.'
                )
            else:
                raise ValueError(
                    f"scalar {self.__class__.__name__} object is read-only."
                )

        # Any use of setitem results in immediate cache invalidation
        del self.cache

        # Setting invalidates transform deltas
        for attr in ("_delta_tdb_tt", "_delta_ut1_utc"):
            if hasattr(self, attr):
                delattr(self, attr)

        if value is np.ma.masked or value is np.nan:
            if not isinstance(self._time.jd2, Masked):
                self._time.jd1 = Masked(self._time.jd1, copy=False)
                self._time.jd2 = Masked(
                    self._time.jd2, mask=self._time.jd1.mask, copy=False
                )
            self._time.jd2.mask[item] = True
            return

        elif value is np.ma.nomask:
            if isinstance(self._time.jd2, Masked):
                self._time.jd2.mask[item] = False
            return

        value = self._make_value_equivalent(item, value)

        # Finally directly set the jd1/2 values.  Locations are known to match.
        if self.scale is not None:
            value = getattr(value, self.scale)
        self._time.jd1[item] = value._time.jd1
        self._time.jd2[item] = value._time.jd2

    def isclose(self, other, atol=None):
        """Returns a boolean or boolean array where two Time objects are
        element-wise equal within a time tolerance.

        This evaluates the expression below::

          abs(self - other) <= atol

        Parameters
        ----------
        other : `~astropy.time.Time`
            Time object for comparison.
        atol : `~astropy.units.Quantity` or `~astropy.time.TimeDelta`
            Absolute tolerance for equality with units of time (e.g. ``u.s`` or
            ``u.day``). Default is two bits in the 128-bit JD time representation,
            equivalent to about 40 picosecs.
        """
        if atol is None:
            # Note: use 2 bits instead of 1 bit based on experience in precision
            # tests, since taking the difference with a UTC time means one has
            # to do a scale change.
            atol = 2 * np.finfo(float).eps * u.day

        if not isinstance(atol, (u.Quantity, TimeDelta)):
            raise TypeError(
                "'atol' argument must be a Quantity or TimeDelta instance, got "
                f"{atol.__class__.__name__} instead"
            )

        try:
            # Separate these out so user sees where the problem is
            dt = self - other
            dt = abs(dt)
            out = dt <= atol
        except Exception as err:
            raise TypeError(
                "'other' argument must support subtraction with Time "
                "and return a value that supports comparison with "
                f"{atol.__class__.__name__}: {err}"
            )

        return out

    def copy(self, format=None):
        """
        Return a fully independent copy the Time object, optionally changing
        the format.

        If ``format`` is supplied then the time format of the returned Time
        object will be set accordingly, otherwise it will be unchanged from the
        original.

        In this method a full copy of the internal time arrays will be made.
        The internal time arrays are normally not changeable by the user so in
        most cases the ``replicate()`` method should be used.

        Parameters
        ----------
        format : str, optional
            Time format of the copy.

        Returns
        -------
        tm : Time object
            Copy of this object
        """
        return self._apply("copy", format=format)

    def replicate(self, format=None, copy=False, cls=None):
        """
        Return a replica of the Time object, optionally changing the format.

        If ``format`` is supplied then the time format of the returned Time
        object will be set accordingly, otherwise it will be unchanged from the
        original.

        If ``copy`` is set to `True` then a full copy of the internal time arrays
        will be made.  By default the replica will use a reference to the
        original arrays when possible to save memory.  The internal time arrays
        are normally not changeable by the user so in most cases it should not
        be necessary to set ``copy`` to `True`.

        The convenience method copy() is available in which ``copy`` is `True`
        by default.

        Parameters
        ----------
        format : str, optional
            Time format of the replica.
        copy : bool, optional
            Return a true copy instead of using references where possible.

        Returns
        -------
        tm : Time object
            Replica of this object
        """
        return self._apply("copy" if copy else "replicate", format=format, cls=cls)

    def _apply(self, method, *args, format=None, cls=None, **kwargs):
        """Create a new time object, possibly applying a method to the arrays.

        Parameters
        ----------
        method : str or callable
            If string, can be 'replicate'  or the name of a relevant
            `~numpy.ndarray` method. In the former case, a new time instance
            with unchanged internal data is created, while in the latter the
            method is applied to the internal ``jd1`` and ``jd2`` arrays, as
            well as to possible ``location``, ``_delta_ut1_utc``, and
            ``_delta_tdb_tt`` arrays.
            If a callable, it is directly applied to the above arrays.
            Examples: 'copy', '__getitem__', 'reshape', `~numpy.broadcast_to`.
        args : tuple
            Any positional arguments for ``method``.
        kwargs : dict
            Any keyword arguments for ``method``.  If the ``format`` keyword
            argument is present, this will be used as the Time format of the
            replica.

        Examples
        --------
        Some ways this is used internally::

            copy : ``_apply('copy')``
            replicate : ``_apply('replicate')``
            reshape : ``_apply('reshape', new_shape)``
            index or slice : ``_apply('__getitem__', item)``
            broadcast : ``_apply(np.broadcast, shape=new_shape)``
        """
        new_format = self.format if format is None else format

        if callable(method):
            apply_method = lambda array: method(array, *args, **kwargs)

        else:
            if method == "replicate":
                apply_method = None
            else:
                apply_method = operator.methodcaller(method, *args, **kwargs)

        jd1, jd2 = self._time.jd1, self._time.jd2
        if apply_method:
            jd1 = apply_method(jd1)
            jd2 = apply_method(jd2)

        # Get a new instance of our class and set its attributes directly.
        tm = super().__new__(cls or self.__class__)
        tm._time = TimeJD(
            jd1,
            jd2,
            self.scale,
            precision=None,
            in_subfmt="*",
            out_subfmt="*",
            from_jd=True,
        )

        # Optional ndarray attributes.
        for attr in ("_delta_ut1_utc", "_delta_tdb_tt", "_location"):
            try:
                val = getattr(self, attr)
            except AttributeError:
                continue

            if apply_method:
                # Apply the method to any value arrays (though skip if there is
                # only an array scalar and the method would return a view,
                # since in that case nothing would change).
                if getattr(val, "shape", ()):
                    val = apply_method(val)
                elif method == "copy" or method == "flatten":
                    # flatten should copy also for a single element array, but
                    # we cannot use it directly for array scalars, since it
                    # always returns a one-dimensional array. So, just copy.
                    val = copy.copy(val)

            setattr(tm, attr, val)

        # Copy other 'info' attr only if it has actually been defined and the
        # time object is not a scalar (issue #10688).
        # See PR #3898 for further explanation and justification, along
        # with Quantity.__array_finalize__
        if "info" in self.__dict__:
            tm.info = self.info

        # Make the new internal _time object corresponding to the format
        # in the copy.  If the format is unchanged this process is lightweight
        # and does not create any new arrays.
        if new_format not in tm.FORMATS:
            raise ValueError(f"format must be one of {list(tm.FORMATS)}")

        NewFormat = tm.FORMATS[new_format]

        tm._time = NewFormat(
            tm._time.jd1,
            tm._time.jd2,
            tm._time._scale,
            precision=self.precision,
            in_subfmt=NewFormat._get_allowed_subfmt(self.in_subfmt),
            out_subfmt=NewFormat._get_allowed_subfmt(self.out_subfmt),
            from_jd=True,
        )
        tm._format = new_format
        tm.SCALES = self.SCALES

        # Finally, if we do not own our data, we link caches, so that
        # those can be cleared as needed if any instance is written to.
        if not (tm._time.jd1.base if tm.masked else tm._time.jd1).flags["OWNDATA"]:
            tm._id_cache = self._id_cache

        return tm

    def __copy__(self):
        """
        Overrides the default behavior of the `copy.copy` function in
        the python stdlib to behave like `Time.copy`. Does *not* make a
        copy of the JD arrays - only copies by reference.
        """
        return self.replicate()

    def __deepcopy__(self, memo):
        """
        Overrides the default behavior of the `copy.deepcopy` function
        in the python stdlib to behave like `Time.copy`. Does make a
        copy of the JD arrays.
        """
        return self.copy()

    def _advanced_index(self, indices, axis=None, keepdims=False):
        """Turn argmin, argmax output into an advanced index.

        Argmin, argmax output contains indices along a given axis in an array
        shaped like the other dimensions.  To use this to get values at the
        correct location, a list is constructed in which the other axes are
        indexed sequentially.  For ``keepdims`` is ``True``, the net result is
        the same as constructing an index grid with ``np.ogrid`` and then
        replacing the ``axis`` item with ``indices`` with its shaped expanded
        at ``axis``. For ``keepdims`` is ``False``, the result is the same but
        with the ``axis`` dimension removed from all list entries.

        For ``axis`` is ``None``, this calls :func:`~numpy.unravel_index`.

        Parameters
        ----------
        indices : array
            Output of argmin or argmax.
        axis : int or None
            axis along which argmin or argmax was used.
        keepdims : bool
            Whether to construct indices that keep or remove the axis along
            which argmin or argmax was used.  Default: ``False``.

        Returns
        -------
        advanced_index : list of arrays
            Suitable for use as an advanced index.
        """
        if axis is None:
            return np.unravel_index(indices, self.shape)

        ndim = self.ndim
        if axis < 0:
            axis = axis + ndim

        if keepdims and indices.ndim < self.ndim:
            indices = np.expand_dims(indices, axis)

        index = [
            indices
            if i == axis
            else np.arange(s).reshape(
                (1,) * (i if keepdims or i < axis else i - 1)
                + (s,)
                + (1,) * (ndim - i - (1 if keepdims or i > axis else 2))
            )
            for i, s in enumerate(self.shape)
        ]

        return tuple(index)

    def argmin(self, axis=None, out=None):
        """Return indices of the minimum values along the given axis.

        This is similar to :meth:`~numpy.ndarray.argmin`, but adapted to ensure
        that the full precision given by the two doubles ``jd1`` and ``jd2``
        is used.  See :func:`~numpy.argmin` for detailed documentation.
        """
        # First get the minimum at normal precision.
        jd1, jd2 = self._time.jd1, self._time.jd2
        approx = np.min(jd1 + jd2, axis, keepdims=True)

        # Approx is very close to the true minimum, and by subtracting it at
        # full precision, all numbers near 0 can be represented correctly,
        # so we can be sure we get the true minimum.
        # The below is effectively what would be done for
        # dt = (self - self.__class__(approx, format='jd')).jd
        # which translates to:
        # approx_jd1, approx_jd2 = day_frac(approx, 0.)
        # dt = (self.jd1 - approx_jd1) + (self.jd2 - approx_jd2)
        dt = (jd1 - approx) + jd2

        return dt.argmin(axis, out)

    def argmax(self, axis=None, out=None):
        """Return indices of the maximum values along the given axis.

        This is similar to :meth:`~numpy.ndarray.argmax`, but adapted to ensure
        that the full precision given by the two doubles ``jd1`` and ``jd2``
        is used.  See :func:`~numpy.argmax` for detailed documentation.
        """
        # For procedure, see comment on argmin.
        jd1, jd2 = self._time.jd1, self._time.jd2
        approx = np.max(jd1 + jd2, axis, keepdims=True)

        dt = (jd1 - approx) + jd2

        return dt.argmax(axis, out)

    def argsort(self, axis=-1, kind="stable"):
        """Returns the indices that would sort the time array.

        This is similar to :meth:`~numpy.ndarray.argsort`, but adapted to ensure that
        the full precision given by the two doubles ``jd1`` and ``jd2`` is used, and
        that corresponding attributes are copied.  Internally, it uses
        :func:`~numpy.lexsort`, and hence no sort method can be chosen.

        Parameters
        ----------
        axis : int, optional
            Axis along which to sort. Default is -1, which means sort along the last
            axis.
        kind : 'stable', optional
            Sorting is done with :func:`~numpy.lexsort` so this argument is ignored, but
            kept for compatibility with :func:`~numpy.argsort`. The sorting is stable,
            meaning that the order of equal elements is preserved.

        Returns
        -------
        indices : ndarray
            An array of indices that sort the time array.
        """
        # For procedure, see comment on argmin.
        jd1, jd2 = self._time.jd1, self._time.jd2
        approx = jd1 + jd2
        remainder = (jd1 - approx) + jd2

        if axis is None:
            return np.lexsort((remainder.ravel(), approx.ravel()))
        else:
            return np.lexsort(keys=(remainder, approx), axis=axis)

    def min(self, axis=None, out=None, keepdims=False):
        """Minimum along a given axis.

        This is similar to :meth:`~numpy.ndarray.min`, but adapted to ensure
        that the full precision given by the two doubles ``jd1`` and ``jd2``
        is used, and that corresponding attributes are copied.

        Note that the ``out`` argument is present only for compatibility with
        ``np.min``; since `Time` instances are immutable, it is not possible
        to have an actual ``out`` to store the result in.
        """
        if out is not None:
            raise ValueError(
                "Since `Time` instances are immutable, ``out`` "
                "cannot be set to anything but ``None``."
            )
        return self[self._advanced_index(self.argmin(axis), axis, keepdims)]

    def max(self, axis=None, out=None, keepdims=False):
        """Maximum along a given axis.

        This is similar to :meth:`~numpy.ndarray.max`, but adapted to ensure
        that the full precision given by the two doubles ``jd1`` and ``jd2``
        is used, and that corresponding attributes are copied.

        Note that the ``out`` argument is present only for compatibility with
        ``np.max``; since `Time` instances are immutable, it is not possible
        to have an actual ``out`` to store the result in.
        """
        if out is not None:
            raise ValueError(
                "Since `Time` instances are immutable, ``out`` "
                "cannot be set to anything but ``None``."
            )
        return self[self._advanced_index(self.argmax(axis), axis, keepdims)]

    def ptp(self, axis=None, out=None, keepdims=False):
        """Peak to peak (maximum - minimum) along a given axis.

        This is similar to :meth:`~numpy.ndarray.ptp`, but adapted to ensure
        that the full precision given by the two doubles ``jd1`` and ``jd2``
        is used.

        Note that the ``out`` argument is present only for compatibility with
        `~numpy.ptp`; since `Time` instances are immutable, it is not possible
        to have an actual ``out`` to store the result in.
        """
        if out is not None:
            raise ValueError(
                "Since `Time` instances are immutable, ``out`` "
                "cannot be set to anything but ``None``."
            )
        return self.max(axis, keepdims=keepdims) - self.min(axis, keepdims=keepdims)

    def sort(self, axis=-1):
        """Return a copy sorted along the specified axis.

        This is similar to :meth:`~numpy.ndarray.sort`, but internally uses
        indexing with :func:`~numpy.lexsort` to ensure that the full precision
        given by the two doubles ``jd1`` and ``jd2`` is kept, and that
        corresponding attributes are properly sorted and copied as well.

        Parameters
        ----------
        axis : int or None
            Axis to be sorted.  If ``None``, the flattened array is sorted.
            By default, sort over the last axis.
        """
        return self[self._advanced_index(self.argsort(axis), axis, keepdims=True)]

    def mean(self, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
        """Mean along a given axis.

        This is similar to :meth:`~numpy.ndarray.mean`, but adapted to ensure
        that the full precision given by the two doubles ``jd1`` and ``jd2`` is
        used, and that corresponding attributes are copied.

        Note that the ``out`` argument is present only for compatibility with
        ``np.mean``; since `Time` instances are immutable, it is not possible
        to have an actual ``out`` to store the result in.

        Similarly, the ``dtype`` argument is also present for compatibility
        only; it has no meaning for `Time`.

        Parameters
        ----------
        axis : None or int or tuple of ints, optional
            Axis or axes along which the means are computed. The default is to
            compute the mean of the flattened array.
        dtype : None
            Only present for compatibility with :meth:`~numpy.ndarray.mean`,
            must be `None`.
        out : None
            Only present for compatibility with :meth:`~numpy.ndarray.mean`,
            must be `None`.
        keepdims : bool, optional
            If this is set to True, the axes which are reduced are left
            in the result as dimensions with size one. With this option,
            the result will broadcast correctly against the input array.
        where : array_like of bool, optional
            Elements to include in the mean. See `~numpy.ufunc.reduce` for
            details.

        Returns
        -------
        m : Time
            A new Time instance containing the mean values
        """
        if dtype is not None:
            raise ValueError("Cannot set ``dtype`` on `Time` instances")
        if out is not None:
            raise ValueError(
                "Since `Time` instances are immutable, ``out`` "
                "cannot be set to anything but ``None``."
            )

        where = where & ~self.mask
        where_broadcasted = np.broadcast_to(where, self.shape)

        kwargs = dict(
            axis=axis,
            keepdims=keepdims,
            where=where,
        )

        divisor = np.sum(where_broadcasted, axis=axis, keepdims=keepdims)
        if np.any(divisor == 0):
            raise ValueError(
                "Mean over zero elements is not supported as it would give an undefined"
                " time;see issue https://github.com/astropy/astropy/issues/6509"
            )

        jd1, jd2 = day_frac(
            val1=np.sum(np.ma.getdata(self.jd1), **kwargs),
            val2=np.sum(np.ma.getdata(self.jd2), **kwargs),
            divisor=divisor,
        )

        result = type(self)(
            val=jd1,
            val2=jd2,
            format="jd",
            scale=self.scale,
            copy=False,
        )
        result.format = self.format
        return result

    @lazyproperty
    def _id_cache(self):
        """Cache of all instances that share underlying data.

        Helps to ensure all cached data can be deleted if the
        underlying data is changed.
        """
        return WeakValueDictionary({id(self): self})

    @_id_cache.setter
    def _id_cache(self, _id_cache):
        _id_cache[id(self)] = self
        # lazyproperty will do the actual storing of the result.

    @lazyproperty
    def cache(self):
        """
        Return the cache associated with this instance.
        """
        return defaultdict(dict)

    @cache.deleter
    def cache(self):
        for instance in self._id_cache.values():
            instance.cache.clear()

    def __getattr__(self, attr):
        """
        Get dynamic attributes to output format or do timescale conversion.
        """
        if attr in self.SCALES and self.scale is not None:
            cache = self.cache["scale"]
            if attr not in cache:
                if attr == self.scale:
                    tm = self
                else:
                    tm = self.replicate()
                    tm._set_scale(attr)
                    if tm.shape:
                        # Prevent future modification of cached array-like object
                        tm.writeable = False
                cache[attr] = tm
            return cache[attr]

        elif attr in self.FORMATS:
            return self.to_value(attr, subfmt=None)

        elif attr in TIME_SCALES:  # allowed ones done above (self.SCALES)
            if self.scale is None:
                raise ScaleValueError(
                    "Cannot convert TimeDelta with "
                    "undefined scale to any defined scale."
                )
            else:
                raise ScaleValueError(
                    f"Cannot convert {self.__class__.__name__} with scale "
                    f"'{self.scale}' to scale '{attr}'"
                )

        else:
            # Should raise AttributeError
            return self.__getattribute__(attr)

    def __dir__(self):
        return sorted(set(super().__dir__()) | set(self.SCALES) | set(self.FORMATS))

    def _match_shape(self, val):
        """
        Ensure that `val` is matched to length of self.  If val has length 1
        then broadcast, otherwise cast to double and make sure shape matches.
        """
        val = _make_array(val, copy=True)  # be conservative and copy
        if val.size > 1 and val.shape != self.shape:
            try:
                # check the value can be broadcast to the shape of self.
                val = np.broadcast_to(val, self.shape, subok=True)
            except Exception:
                raise ValueError(
                    "Attribute shape must match or be broadcastable to that of "
                    "Time object. Typically, give either a single value or "
                    "one for each time."
                )

        return val

    def _time_comparison(self, other, op):
        """If other is of same class as self, compare difference in self.scale.
        Otherwise, return NotImplemented.
        """
        if other.__class__ is not self.__class__:
            try:
                other = self.__class__(other, scale=self.scale)
            except Exception:
                # Let other have a go.
                return NotImplemented

        if (
            self.scale is not None
            and self.scale not in other.SCALES
            or other.scale is not None
            and other.scale not in self.SCALES
        ):
            # Other will also not be able to do it, so raise a TypeError
            # immediately, allowing us to explain why it doesn't work.
            raise TypeError(
                f"Cannot compare {self.__class__.__name__} instances with "
                f"scales '{self.scale}' and '{other.scale}'"
            )

        if self.scale is not None and other.scale is not None:
            other = getattr(other, self.scale)

        return op((self.jd1 - other.jd1) + (self.jd2 - other.jd2), 0.0)

    def __lt__(self, other):
        return self._time_comparison(other, operator.lt)

    def __le__(self, other):
        return self._time_comparison(other, operator.le)

    def __eq__(self, other):
        """
        If other is an incompatible object for comparison, return `False`.
        Otherwise, return `True` if the time difference between self and
        other is zero.
        """
        return self._time_comparison(other, operator.eq)

    def __ne__(self, other):
        """
        If other is an incompatible object for comparison, return `True`.
        Otherwise, return `False` if the time difference between self and
        other is zero.
        """
        return self._time_comparison(other, operator.ne)

    def __gt__(self, other):
        return self._time_comparison(other, operator.gt)

    def __ge__(self, other):
        return self._time_comparison(other, operator.ge)


class Time(TimeBase):
    """
    Represent and manipulate times and dates for astronomy.

    A `Time` object is initialized with one or more times in the ``val``
    argument.  The input times in ``val`` must conform to the specified
    ``format`` and must correspond to the specified time ``scale``.  The
    optional ``val2`` time input should be supplied only for numeric input
    formats (e.g. JD) where very high precision (better than 64-bit precision)
    is required.

    The allowed values for ``format`` can be listed with::

      >>> list(Time.FORMATS)
      ['jd', 'mjd', 'decimalyear', 'unix', 'unix_tai', 'cxcsec', 'gps', 'plot_date',
       'stardate', 'datetime', 'ymdhms', 'iso', 'isot', 'yday', 'datetime64',
       'fits', 'byear', 'jyear', 'byear_str', 'jyear_str']

    See also: http://docs.astropy.org/en/stable/time/

    Parameters
    ----------
    val : sequence, ndarray, number, str, bytes, or `~astropy.time.Time` object
        Value(s) to initialize the time or times.  Bytes are decoded as ascii.
    val2 : sequence, ndarray, or number; optional
        Value(s) to initialize the time or times.  Only used for numerical
        input, to help preserve precision.
    format : str, optional
        Format of input value(s), specifying how to interpret them (e.g., ISO, JD, or
        Unix time). By default, the same format will be used for output representation.
    scale : str, optional
        Time scale of input value(s), must be one of the following:
        ('tai', 'tcb', 'tcg', 'tdb', 'tt', 'ut1', 'utc')
    precision : int, optional
        Digits of precision in string representation of time
    in_subfmt : str, optional
        Unix glob to select subformats for parsing input times
    out_subfmt : str, optional
        Unix glob to select subformat for outputting times
    location : `~astropy.coordinates.EarthLocation` or tuple, optional
        If given as an tuple, it should be able to initialize an
        an EarthLocation instance, i.e., either contain 3 items with units of
        length for geocentric coordinates, or contain a longitude, latitude,
        and an optional height for geodetic coordinates.
        Can be a single location, or one for each input time.
        If not given, assumed to be the center of the Earth for time scale
        transformations to and from the solar-system barycenter.
    copy : bool, optional
        Make a copy of the input values
    """

    SCALES = TIME_SCALES
    """List of time scales"""

    FORMATS = TIME_FORMATS
    """Dict of time formats"""

    def __new__(
        cls,
        val,
        val2=None,
        format=None,
        scale=None,
        precision=None,
        in_subfmt=None,
        out_subfmt=None,
        location=None,
        copy=False,
    ):
        if isinstance(val, Time):
            self = val.replicate(format=format, copy=copy, cls=cls)
        else:
            self = super().__new__(cls)

        return self

    def __init__(
        self,
        val,
        val2=None,
        format=None,
        scale=None,
        precision=None,
        in_subfmt=None,
        out_subfmt=None,
        location=None,
        copy=False,
    ):
        if location is not None:
            from astropy.coordinates import EarthLocation

            if isinstance(location, EarthLocation):
                self._location = location
            else:
                self._location = EarthLocation(*location)
            if self._location.size == 1:
                self._location = self._location.squeeze()
        elif not hasattr(self, "_location"):
            self._location = None

        if isinstance(val, Time):
            # Update _time formatting parameters if explicitly specified
            if precision is not None:
                self._time.precision = precision
            if in_subfmt is not None:
                self._time.in_subfmt = in_subfmt
            if out_subfmt is not None:
                self._time.out_subfmt = out_subfmt
            self.SCALES = TIME_TYPES[self.scale]
            if scale is not None:
                self._set_scale(scale)
        else:
            self._init_from_vals(
                val, val2, format, scale, copy, precision, in_subfmt, out_subfmt
            )
            self.SCALES = TIME_TYPES[self.scale]

        if self.location is not None and (
            self.location.size > 1 and self.location.shape != self.shape
        ):
            try:
                # check the location can be broadcast to self's shape.
                self._location = np.broadcast_to(self._location, self.shape, subok=True)
            except Exception as err:
                raise ValueError(
                    f"The location with shape {self.location.shape} cannot be "
                    f"broadcast against time with shape {self.shape}. "
                    "Typically, either give a single location or one for each time."
                ) from err

    def _make_value_equivalent(self, item, value):
        """Coerce setitem value into an equivalent Time object."""
        # If there is a vector location then broadcast to the Time shape
        # and then select with ``item``
        if self.location is not None and self.location.shape:
            self_location = np.broadcast_to(self.location, self.shape, subok=True)[item]
        else:
            self_location = self.location

        if isinstance(value, Time):
            # Make sure locations are compatible.  Location can be either None or
            # a Location object.
            if self_location is None and value.location is None:
                match = True
            elif (self_location is None and value.location is not None) or (
                self_location is not None and value.location is None
            ):
                match = False
            else:
                match = np.all(self_location == value.location)
            if not match:
                raise ValueError(
                    "cannot set to Time with different location: expected "
                    f"location={self_location} and got location={value.location}"
                )
        else:
            try:
                value = self.__class__(value, scale=self.scale, location=self_location)
            except Exception:
                try:
                    value = self.__class__(
                        value,
                        scale=self.scale,
                        format=self.format,
                        location=self_location,
                    )
                except Exception as err:
                    raise ValueError(
                        f"cannot convert value to a compatible Time object: {err}"
                    )
        return value

    @classmethod
    def now(cls):
        """
        Creates a new object corresponding to the instant in time this
        method is called.

        .. note::
            "Now" is determined using the `~datetime.datetime.now`
            function, so its accuracy and precision is determined by that
            function.  Generally that means it is set by the accuracy of
            your system clock. The timezone is set to UTC.

        Returns
        -------
        nowtime : :class:`~astropy.time.Time`
            A new `Time` object (or a subclass of `Time` if this is called from
            such a subclass) at the current time.
        """
        # call `now` immediately to be sure it's ASAP
        dtnow = datetime.now(tz=timezone.utc)
        return cls(val=dtnow, format="datetime", scale="utc")

    info = TimeInfo()

    @classmethod
    def strptime(cls, time_string, format_string, **kwargs):
        """
        Parse a string to a Time according to a format specification.
        See `time.strptime` documentation for format specification.

        >>> Time.strptime('2012-Jun-30 23:59:60', '%Y-%b-%d %H:%M:%S')
        <Time object: scale='utc' format='isot' value=2012-06-30T23:59:60.000>

        Parameters
        ----------
        time_string : str, sequence, or ndarray
            Objects containing time data of type string
        format_string : str
            String specifying format of time_string.
        kwargs : dict
            Any keyword arguments for ``Time``.  If the ``format`` keyword
            argument is present, this will be used as the Time format.

        Returns
        -------
        time_obj : `~astropy.time.Time`
            A new `~astropy.time.Time` object corresponding to the input
            ``time_string``.

        """
        time_array = np.asarray(time_string)

        if time_array.dtype.kind not in ("U", "S"):
            raise TypeError(
                "Expected type is string, a bytes-like object or a sequence "
                f"of these. Got dtype '{time_array.dtype.kind}'"
            )

        to_string = (
            str
            if time_array.dtype.kind == "U"
            else lambda x: str(x.item(), encoding="ascii")
        )
        iterator = np.nditer([time_array, None], op_dtypes=[time_array.dtype, "U30"])

        for time, formatted in iterator:
            tt, fraction = _strptime._strptime(to_string(time), format_string)
            time_tuple = tt[:6] + (fraction,)
            formatted[...] = "{:04}-{:02}-{:02}T{:02}:{:02}:{:02}.{:06}".format(
                *time_tuple
            )

        format = kwargs.pop("format", None)
        out = cls(*iterator.operands[1:], format="isot", **kwargs)
        if format is not None:
            out.format = format

        return out

    def strftime(self, format_spec):
        """
        Convert Time to a string or a numpy.array of strings according to a
        format specification.
        See `time.strftime` documentation for format specification.

        Parameters
        ----------
        format_spec : str
            Format definition of return string.

        Returns
        -------
        formatted : str or numpy.array
            String or numpy.array of strings formatted according to the given
            format string.

        """
        formatted_strings = []
        for sk in self.replicate("iso")._time.str_kwargs():
            date_tuple = date(sk["year"], sk["mon"], sk["day"]).timetuple()
            datetime_tuple = (
                sk["year"],
                sk["mon"],
                sk["day"],
                sk["hour"],
                sk["min"],
                sk["sec"],
                date_tuple[6],
                date_tuple[7],
                -1,
            )
            fmtd_str = format_spec
            if "%f" in fmtd_str:
                fmtd_str = fmtd_str.replace(
                    "%f",
                    "{frac:0{precision}}".format(
                        frac=sk["fracsec"], precision=self.precision
                    ),
                )
            fmtd_str = strftime(fmtd_str, datetime_tuple)
            formatted_strings.append(fmtd_str)

        if self.isscalar:
            return formatted_strings[0]
        else:
            return np.array(formatted_strings).reshape(self.shape)

    def light_travel_time(
        self, skycoord, kind="barycentric", location=None, ephemeris=None
    ):
        """Light travel time correction to the barycentre or heliocentre.

        The frame transformations used to calculate the location of the solar
        system barycentre and the heliocentre rely on the erfa routine epv00,
        which is consistent with the JPL DE405 ephemeris to an accuracy of
        11.2 km, corresponding to a light travel time of 4 microseconds.

        The routine assumes the source(s) are at large distance, i.e., neglects
        finite-distance effects.

        Parameters
        ----------
        skycoord : `~astropy.coordinates.SkyCoord`
            The sky location to calculate the correction for.
        kind : str, optional
            ``'barycentric'`` (default) or ``'heliocentric'``
        location : `~astropy.coordinates.EarthLocation`, optional
            The location of the observatory to calculate the correction for.
            If no location is given, the ``location`` attribute of the Time
            object is used
        ephemeris : str, optional
            Solar system ephemeris to use (e.g., 'builtin', 'jpl'). By default,
            use the one set with ``astropy.coordinates.solar_system_ephemeris.set``.
            For more information, see `~astropy.coordinates.solar_system_ephemeris`.

        Returns
        -------
        time_offset : `~astropy.time.TimeDelta`
            The time offset between the barycentre or Heliocentre and Earth,
            in TDB seconds.  Should be added to the original time to get the
            time in the Solar system barycentre or the Heliocentre.
            Also, the time conversion to BJD will then include the relativistic correction as well.
        """
        if kind.lower() not in ("barycentric", "heliocentric"):
            raise ValueError(
                "'kind' parameter must be one of 'heliocentric' or 'barycentric'"
            )

        if location is None:
            if self.location is None:
                raise ValueError(
                    "An EarthLocation needs to be set or passed in to calculate bary- "
                    "or heliocentric corrections"
                )
            location = self.location

        from astropy.coordinates import (
            GCRS,
            HCRS,
            ICRS,
            CartesianRepresentation,
            UnitSphericalRepresentation,
            solar_system_ephemeris,
        )

        # ensure sky location is ICRS compatible
        if not skycoord.is_transformable_to(ICRS()):
            raise ValueError("Given skycoord is not transformable to the ICRS")

        # get location of observatory in ITRS coordinates at this Time
        try:
            itrs = location.get_itrs(obstime=self)
        except Exception:
            raise ValueError(
                "Supplied location does not have a valid `get_itrs` method"
            )

        with solar_system_ephemeris.set(ephemeris):
            if kind.lower() == "heliocentric":
                # convert to heliocentric coordinates, aligned with ICRS
                cpos = itrs.transform_to(HCRS(obstime=self)).cartesian.xyz
            else:
                # first we need to convert to GCRS coordinates with the correct
                # obstime, since ICRS coordinates have no frame time
                gcrs_coo = itrs.transform_to(GCRS(obstime=self))
                # convert to barycentric (BCRS) coordinates, aligned with ICRS
                cpos = gcrs_coo.transform_to(ICRS()).cartesian.xyz

        # get unit ICRS vector to star
        spos = (
            skycoord.icrs.represent_as(UnitSphericalRepresentation)
            .represent_as(CartesianRepresentation)
            .xyz
        )

        # Move X,Y,Z to last dimension, to enable possible broadcasting below.
        cpos = np.rollaxis(cpos, 0, cpos.ndim)
        spos = np.rollaxis(spos, 0, spos.ndim)

        # calculate light travel time correction
        tcor_val = (spos * cpos).sum(axis=-1) / const.c
        return TimeDelta(tcor_val, scale="tdb")

    def earth_rotation_angle(self, longitude=None):
        """Calculate local Earth rotation angle.

        Parameters
        ----------
        longitude : `~astropy.units.Quantity`, `~astropy.coordinates.EarthLocation`, str, or None; optional
            The longitude on the Earth at which to compute the Earth rotation
            angle (taken from a location as needed).  If `None` (default), taken
            from the ``location`` attribute of the Time instance. If the special
            string 'tio', the result will be relative to the Terrestrial
            Intermediate Origin (TIO) (i.e., the output of `~erfa.era00`).

        Returns
        -------
        `~astropy.coordinates.Longitude`
            Local Earth rotation angle with units of hourangle.

        See Also
        --------
        astropy.time.Time.sidereal_time

        References
        ----------
        IAU 2006 NFA Glossary
        (currently located at: https://syrte.obspm.fr/iauWGnfa/NFA_Glossary.html)

        Notes
        -----
        The difference between apparent sidereal time and Earth rotation angle
        is the equation of the origins, which is the angle between the Celestial
        Intermediate Origin (CIO) and the equinox. Applying apparent sidereal
        time to the hour angle yields the true apparent Right Ascension with
        respect to the equinox, while applying the Earth rotation angle yields
        the intermediate (CIRS) Right Ascension with respect to the CIO.

        The result includes the TIO locator (s'), which positions the Terrestrial
        Intermediate Origin on the equator of the Celestial Intermediate Pole (CIP)
        and is rigorously corrected for polar motion.
        (except when ``longitude='tio'``).

        """
        if isinstance(longitude, str) and longitude == "tio":
            longitude = 0
            include_tio = False
        else:
            include_tio = True

        return self._sid_time_or_earth_rot_ang(
            longitude=longitude,
            function=erfa.era00,
            scales=("ut1",),
            include_tio=include_tio,
        )

    def sidereal_time(self, kind, longitude=None, model=None):
        """Calculate sidereal time.

        Parameters
        ----------
        kind : str
            ``'mean'`` or ``'apparent'``, i.e., accounting for precession
            only, or also for nutation.
        longitude : `~astropy.units.Quantity`, `~astropy.coordinates.EarthLocation`, str, or None; optional
            The longitude on the Earth at which to compute the Earth rotation
            angle (taken from a location as needed).  If `None` (default), taken
            from the ``location`` attribute of the Time instance. If the special
            string  'greenwich' or 'tio', the result will be relative to longitude
            0 for models before 2000, and relative to the Terrestrial Intermediate
            Origin (TIO) for later ones (i.e., the output of the relevant ERFA
            function that calculates greenwich sidereal time).
        model : str or None; optional
            Precession (and nutation) model to use.  The available ones are:
            - {0}: {1}
            - {2}: {3}
            If `None` (default), the last (most recent) one from the appropriate
            list above is used.

        Returns
        -------
        `~astropy.coordinates.Longitude`
            Local sidereal time, with units of hourangle.

        See Also
        --------
        astropy.time.Time.earth_rotation_angle

        References
        ----------
        IAU 2006 NFA Glossary
        (currently located at: https://syrte.obspm.fr/iauWGnfa/NFA_Glossary.html)

        Notes
        -----
        The difference between apparent sidereal time and Earth rotation angle
        is the equation of the origins, which is the angle between the Celestial
        Intermediate Origin (CIO) and the equinox. Applying apparent sidereal
        time to the hour angle yields the true apparent Right Ascension with
        respect to the equinox, while applying the Earth rotation angle yields
        the intermediate (CIRS) Right Ascension with respect to the CIO.

        For the IAU precession models from 2000 onwards, the result includes the
        TIO locator (s'), which positions the Terrestrial Intermediate Origin on
        the equator of the Celestial Intermediate Pole (CIP) and is rigorously
        corrected for polar motion (except when ``longitude='tio'`` or ``'greenwich'``).

        """  # (docstring is formatted below)
        if kind.lower() not in SIDEREAL_TIME_MODELS:
            raise ValueError(
                "The kind of sidereal time has to be "
                + " or ".join(sorted(SIDEREAL_TIME_MODELS))
            )

        available_models = SIDEREAL_TIME_MODELS[kind.lower()]

        if model is None:
            model = sorted(available_models)[-1]
        elif model.upper() not in available_models:
            raise ValueError(
                f"Model {model} not implemented for {kind} sidereal time; "
                f"available models are {sorted(available_models)}"
            )

        model_kwargs = available_models[model.upper()]

        if isinstance(longitude, str) and longitude in ("tio", "greenwich"):
            longitude = 0
            model_kwargs = model_kwargs.copy()
            model_kwargs["include_tio"] = False

        return self._sid_time_or_earth_rot_ang(longitude=longitude, **model_kwargs)

    if isinstance(sidereal_time.__doc__, str):
        sidereal_time.__doc__ = sidereal_time.__doc__.format(
            "apparent",
            sorted(SIDEREAL_TIME_MODELS["apparent"]),
            "mean",
            sorted(SIDEREAL_TIME_MODELS["mean"]),
        )

    def _sid_time_or_earth_rot_ang(self, longitude, function, scales, include_tio=True):
        """Calculate a local sidereal time or Earth rotation angle.

        Parameters
        ----------
        longitude : `~astropy.units.Quantity`, `~astropy.coordinates.EarthLocation`, str, or None; optional
            The longitude on the Earth at which to compute the Earth rotation
            angle (taken from a location as needed).  If `None` (default), taken
            from the ``location`` attribute of the Time instance.
        function : callable
            The ERFA function to use.
        scales : tuple of str
            The time scales that the function requires on input.
        include_tio : bool, optional
            Whether to includes the TIO locator corrected for polar motion.
            Should be `False` for pre-2000 IAU models.  Default: `True`.

        Returns
        -------
        `~astropy.coordinates.Longitude`
            Local sidereal time or Earth rotation angle, with units of hourangle.

        """
        from astropy.coordinates import EarthLocation, Longitude
        from astropy.coordinates.builtin_frames.utils import get_polar_motion
        from astropy.coordinates.matrix_utilities import rotation_matrix

        if longitude is None:
            if self.location is None:
                raise ValueError(
                    "No longitude is given but the location for "
                    "the Time object is not set."
                )
            longitude = self.location.lon
        elif isinstance(longitude, EarthLocation):
            longitude = longitude.lon
        else:
            # Sanity check on input; default unit is degree.
            longitude = Longitude(longitude, u.degree, copy=False)

        theta = self._call_erfa(function, scales)

        if include_tio:
            # TODO: this duplicates part of coordinates.erfa_astrom.ErfaAstrom.apio;
            # maybe posisble to factor out to one or the other.
            sp = self._call_erfa(erfa.sp00, ("tt",))
            xp, yp = get_polar_motion(self)
            # Form the rotation matrix, CIRS to apparent [HA,Dec].
            r = (
                rotation_matrix(longitude, "z")
                @ rotation_matrix(-yp, "x", unit=u.radian)
                @ rotation_matrix(-xp, "y", unit=u.radian)
                @ rotation_matrix(theta + sp, "z", unit=u.radian)
            )
            # Solve for angle.
            angle = np.arctan2(r[..., 0, 1], r[..., 0, 0]) << u.radian

        else:
            angle = longitude + (theta << u.radian)

        return Longitude(angle, u.hourangle)

    def _call_erfa(self, function, scales):
        # TODO: allow erfa functions to be used on Time with __array_ufunc__.
        erfa_parameters = [
            getattr(getattr(self, scale)._time, jd_part)
            for scale in scales
            for jd_part in ("jd1", "jd2")
        ]

        result = function(*erfa_parameters)

        if self.masked:
            result[self.mask] = np.nan

        return result

    def get_delta_ut1_utc(self, iers_table=None, return_status=False):
        """Find UT1 - UTC differences by interpolating in IERS Table.

        Parameters
        ----------
        iers_table : `~astropy.utils.iers.IERS`, optional
            Table containing UT1-UTC differences from IERS Bulletins A
            and/or B.  Default: `~astropy.utils.iers.earth_orientation_table`
            (which in turn defaults to the combined version provided by
            `~astropy.utils.iers.IERS_Auto`).
        return_status : bool
            Whether to return status values.  If `False` (default), iers
            raises `IndexError` if any time is out of the range
            covered by the IERS table.

        Returns
        -------
        ut1_utc : float or float array
            UT1-UTC, interpolated in IERS Table
        status : int or int array
            Status values (if ``return_status=`True```)::
            ``astropy.utils.iers.FROM_IERS_B``
            ``astropy.utils.iers.FROM_IERS_A``
            ``astropy.utils.iers.FROM_IERS_A_PREDICTION``
            ``astropy.utils.iers.TIME_BEFORE_IERS_RANGE``
            ``astropy.utils.iers.TIME_BEYOND_IERS_RANGE``

        Notes
        -----
        In normal usage, UT1-UTC differences are calculated automatically
        on the first instance ut1 is needed.

        Examples
        --------
        To check in code whether any times are before the IERS table range::

            >>> from astropy.utils.iers import TIME_BEFORE_IERS_RANGE
            >>> t = Time(['1961-01-01', '2000-01-01'], scale='utc')
            >>> delta, status = t.get_delta_ut1_utc(return_status=True)  # doctest: +REMOTE_DATA
            >>> status == TIME_BEFORE_IERS_RANGE  # doctest: +REMOTE_DATA
            array([ True, False]...)
        """
        if iers_table is None:
            from astropy.utils.iers import earth_orientation_table

            iers_table = earth_orientation_table.get()

        return iers_table.ut1_utc(self.utc, return_status=return_status)

    # Property for ERFA DUT arg = UT1 - UTC
    def _get_delta_ut1_utc(self, jd1=None, jd2=None):
        """
        Get ERFA DUT arg = UT1 - UTC.  This getter takes optional jd1 and
        jd2 args because it gets called that way when converting time scales.
        If delta_ut1_utc is not yet set, this will interpolate them from the
        the IERS table.
        """
        # Sec. 4.3.1: the arg DUT is the quantity delta_UT1 = UT1 - UTC in
        # seconds. It is obtained from tables published by the IERS.
        if not hasattr(self, "_delta_ut1_utc"):
            from astropy.utils.iers import earth_orientation_table

            iers_table = earth_orientation_table.get()
            # jd1, jd2 are normally set (see above), except if delta_ut1_utc
            # is access directly; ensure we behave as expected for that case
            if jd1 is None:
                self_utc = self.utc
                jd1, jd2 = self_utc._time.jd1, self_utc._time.jd2
                scale = "utc"
            else:
                scale = self.scale
            # interpolate UT1-UTC in IERS table
            delta = iers_table.ut1_utc(jd1, jd2)
            # if we interpolated using UT1 jds, we may be off by one
            # second near leap seconds (and very slightly off elsewhere)
            if scale == "ut1":
                # calculate UTC using the offset we got; the ERFA routine
                # is tolerant of leap seconds, so will do this right
                jd1_utc, jd2_utc = erfa.ut1utc(jd1, jd2, delta.to_value(u.s))
                # calculate a better estimate using the nearly correct UTC
                delta = iers_table.ut1_utc(jd1_utc, jd2_utc)

            self._set_delta_ut1_utc(delta)

        return self._delta_ut1_utc

    def _set_delta_ut1_utc(self, val):
        del self.cache
        if hasattr(val, "to"):  # Matches Quantity but also TimeDelta.
            val = val.to(u.second).value
        val = self._match_shape(val)
        self._delta_ut1_utc = val

    # Note can't use @property because _get_delta_tdb_tt is explicitly
    # called with the optional jd1 and jd2 args.
    delta_ut1_utc = property(_get_delta_ut1_utc, _set_delta_ut1_utc)
    """UT1 - UTC time scale offset"""

    # Property for ERFA DTR arg = TDB - TT
    def _get_delta_tdb_tt(self, jd1=None, jd2=None):
        if not hasattr(self, "_delta_tdb_tt"):
            # If jd1 and jd2 are not provided (which is the case for property
            # attribute access) then require that the time scale is TT or TDB.
            # Otherwise the computations here are not correct.
            if jd1 is None or jd2 is None:
                if self.scale not in ("tt", "tdb"):
                    raise ValueError(
                        "Accessing the delta_tdb_tt attribute is only "
                        "possible for TT or TDB time scales"
                    )
                else:
                    jd1 = self._time.jd1
                    jd2 = self._time.jd2

            # First go from the current input time (which is either
            # TDB or TT) to an approximate UT1.  Since TT and TDB are
            # pretty close (few msec?), assume TT.  Similarly, since the
            # UT1 terms are very small, use UTC instead of UT1.
            njd1, njd2 = erfa.tttai(jd1, jd2)
            njd1, njd2 = erfa.taiutc(njd1, njd2)
            # subtract 0.5, so UT is fraction of the day from midnight
            ut = day_frac(njd1 - 0.5, njd2)[1]

            if self.location is None:
                # Assume geocentric.
                self._delta_tdb_tt = erfa.dtdb(jd1, jd2, ut, 0.0, 0.0, 0.0)
            else:
                location = self.location
                # Geodetic params needed for d_tdb_tt()
                lon = location.lon
                rxy = np.hypot(location.x, location.y)
                z = location.z
                self._delta_tdb_tt = erfa.dtdb(
                    jd1,
                    jd2,
                    ut,
                    lon.to_value(u.radian),
                    rxy.to_value(u.km),
                    z.to_value(u.km),
                )

        return self._delta_tdb_tt

    def _set_delta_tdb_tt(self, val):
        del self.cache
        if hasattr(val, "to"):  # Matches Quantity but also TimeDelta.
            val = val.to(u.second).value
        val = self._match_shape(val)
        self._delta_tdb_tt = val

    # Note can't use @property because _get_delta_tdb_tt is explicitly
    # called with the optional jd1 and jd2 args.
    delta_tdb_tt = property(_get_delta_tdb_tt, _set_delta_tdb_tt)
    """TDB - TT time scale offset"""

    def __sub__(self, other):
        # T      - Tdelta = T
        # T      - T      = Tdelta
        other_is_delta = not isinstance(other, Time)
        if other_is_delta:  # T - Tdelta
            # Check other is really a TimeDelta or something that can initialize.
            if not isinstance(other, TimeDelta):
                try:
                    other = TimeDelta(other)
                except Exception:
                    return NotImplemented

            # we need a constant scale to calculate, which is guaranteed for
            # TimeDelta, but not for Time (which can be UTC)
            out = self.replicate()
            if self.scale in other.SCALES:
                if other.scale not in (out.scale, None):
                    other = getattr(other, out.scale)
            else:
                if other.scale is None:
                    out._set_scale("tai")
                else:
                    if self.scale not in TIME_TYPES[other.scale]:
                        raise TypeError(
                            "Cannot subtract Time and TimeDelta instances "
                            f"with scales '{self.scale}' and '{other.scale}'"
                        )
                    out._set_scale(other.scale)
            # remove attributes that are invalidated by changing time
            for attr in ("_delta_ut1_utc", "_delta_tdb_tt"):
                if hasattr(out, attr):
                    delattr(out, attr)

        else:  # T - T
            # the scales should be compatible (e.g., cannot convert TDB to LOCAL)
            if other.scale not in self.SCALES:
                raise TypeError(
                    "Cannot subtract Time instances "
                    f"with scales '{self.scale}' and '{other.scale}'"
                )
            self_time = (
                self._time if self.scale in TIME_DELTA_SCALES else self.tai._time
            )
            # set up TimeDelta, subtraction to be done shortly
            out = TimeDelta(
                self_time.jd1, self_time.jd2, format="jd", scale=self_time.scale
            )

            if other.scale != out.scale:
                other = getattr(other, out.scale)

        jd1 = out._time.jd1 - other._time.jd1
        jd2 = out._time.jd2 - other._time.jd2

        out._time.jd1, out._time.jd2 = day_frac(jd1, jd2)

        if other_is_delta:
            # Go back to left-side scale if needed
            out._set_scale(self.scale)

        return out

    def __add__(self, other):
        # T      + Tdelta = T
        # T      + T      = error
        if isinstance(other, Time):
            raise OperandTypeError(self, other, "+")

        # Check other is really a TimeDelta or something that can initialize.
        if not isinstance(other, TimeDelta):
            try:
                other = TimeDelta(other)
            except Exception:
                return NotImplemented

        # ideally, we calculate in the scale of the Time item, since that is
        # what we want the output in, but this may not be possible, since
        # TimeDelta cannot be converted arbitrarily
        out = self.replicate()
        if self.scale in other.SCALES:
            if other.scale not in (out.scale, None):
                other = getattr(other, out.scale)
        else:
            if other.scale is None:
                out._set_scale("tai")
            else:
                if self.scale not in TIME_TYPES[other.scale]:
                    raise TypeError(
                        "Cannot add Time and TimeDelta instances "
                        f"with scales '{self.scale}' and '{other.scale}'"
                    )
                out._set_scale(other.scale)
        # remove attributes that are invalidated by changing time
        for attr in ("_delta_ut1_utc", "_delta_tdb_tt"):
            if hasattr(out, attr):
                delattr(out, attr)

        jd1 = out._time.jd1 + other._time.jd1
        jd2 = out._time.jd2 + other._time.jd2

        out._time.jd1, out._time.jd2 = day_frac(jd1, jd2)

        # Go back to left-side scale if needed
        out._set_scale(self.scale)

        return out

    # Reverse addition is possible: <something-Tdelta-ish> + T
    # but there is no case of <something> - T, so no __rsub__.
    def __radd__(self, other):
        return self.__add__(other)

    def mean(self, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
        scale = self.scale
        if scale == "utc":
            self = self.tai
        result = super().mean(
            axis=axis, dtype=dtype, out=out, keepdims=keepdims, where=where
        )
        if scale == "utc":
            result = result.utc

        result.out_subfmt = self.out_subfmt

        location = self.location
        if self.location is not None:
            if self.location.shape:
                if axis is None:
                    axis_normalized = tuple(range(self.ndim))
                elif isinstance(axis, int):
                    axis_normalized = (axis,)
                else:
                    axis_normalized = axis

                sl = [slice(None)] * self.location.ndim
                for a in axis_normalized:
                    sl[a] = slice(0, 1)

                if np.any(self.location != self.location[tuple(sl)]):
                    raise ValueError(
                        "`location` must be constant over the reduction axes."
                    )

                if not keepdims:
                    for a in axis_normalized:
                        sl[a] = 0

                location = self.location[tuple(sl)]

        result._location = location
        return result

    def __array_function__(self, function, types, args, kwargs):
        """
        Wrap numpy functions.

        Parameters
        ----------
        function : callable
            Numpy function to wrap
        types : iterable of classes
            Classes that provide an ``__array_function__`` override. Can
            in principle be used to interact with other classes. Below,
            mostly passed on to `~numpy.ndarray`, which can only interact
            with subclasses.
        args : tuple
            Positional arguments provided in the function call.
        kwargs : dict
            Keyword arguments provided in the function call.
        """
        if function in CUSTOM_FUNCTIONS:
            f = CUSTOM_FUNCTIONS[function]
            return f(*args, **kwargs)
        elif function in UNSUPPORTED_FUNCTIONS:
            return NotImplemented
        else:
            return super().__array_function__(function, types, args, kwargs)

    def to_datetime(self, timezone=None, leap_second_strict="raise"):
        # TODO: this could likely go through to_value, as long as that
        # had an **kwargs part that was just passed on to _time.
        tm = self.replicate(format="datetime")
        return tm._shaped_like_input(
            tm._time.to_value(timezone, leap_second_strict=leap_second_strict)
        )

    to_datetime.__doc__ = TimeDatetime.to_value.__doc__


class TimeDeltaMissingUnitWarning(AstropyDeprecationWarning):
    """Warning for missing unit or format in TimeDelta."""


class TimeDelta(TimeBase):
    """
    Represent the time difference between two times.

    A TimeDelta object is initialized with one or more times in the ``val``
    argument.  The input times in ``val`` must conform to the specified
    ``format``.  The optional ``val2`` time input should be supplied only for
    numeric input formats (e.g. JD) where very high precision (better than
    64-bit precision) is required.

    The allowed values for ``format`` can be listed with::

      >>> list(TimeDelta.FORMATS)
      ['sec', 'jd', 'datetime', 'quantity_str']

    Note that for time differences, the scale can be among three groups:
    geocentric ('tai', 'tt', 'tcg'), barycentric ('tcb', 'tdb'), and rotational
    ('ut1'). Within each of these, the scales for time differences are the
    same. Conversion between geocentric and barycentric is possible, as there
    is only a scale factor change, but one cannot convert to or from 'ut1', as
    this requires knowledge of the actual times, not just their difference. For
    a similar reason, 'utc' is not a valid scale for a time difference: a UTC
    day is not always 86400 seconds.

    For more information see:

    - https://docs.astropy.org/en/stable/time/
    - https://docs.astropy.org/en/stable/time/index.html#time-deltas

    Parameters
    ----------
    val : sequence, ndarray, number, `~astropy.units.Quantity` or `~astropy.time.TimeDelta` object
        Value(s) to initialize the time difference(s). Any quantities will
        be converted appropriately (with care taken to avoid rounding
        errors for regular time units).
    val2 : sequence, ndarray, number, or `~astropy.units.Quantity`; optional
        Additional values, as needed to preserve precision.
    format : str, optional
        Format of input value(s). For numerical inputs without units,
        "jd" is assumed and values are interpreted as days.
        A deprecation warning is raised in this case. To avoid the warning,
        either specify the format or add units to the input values.
    scale : str, optional
        Time scale of input value(s), must be one of the following values:
        ('tdb', 'tt', 'ut1', 'tcg', 'tcb', 'tai'). If not given (or
        ``None``), the scale is arbitrary; when added or subtracted from a
        ``Time`` instance, it will be used without conversion.
    precision : int, optional
        Digits of precision in string representation of time
    in_subfmt : str, optional
        Unix glob to select subformats for parsing input times
    out_subfmt : str, optional
        Unix glob to select subformat for outputting times
    copy : bool, optional
        Make a copy of the input values
    """

    SCALES = TIME_DELTA_SCALES
    """List of time delta scales."""

    FORMATS = TIME_DELTA_FORMATS
    """Dict of time delta formats."""

    info = TimeDeltaInfo()

    def __new__(
        cls,
        val,
        val2=None,
        format=None,
        scale=None,
        precision=None,
        in_subfmt=None,
        out_subfmt=None,
        location=None,
        copy=False,
    ):
        if isinstance(val, TimeDelta):
            self = val.replicate(format=format, copy=copy, cls=cls)
        else:
            self = super().__new__(cls)

        return self

    def __init__(
        self,
        val,
        val2=None,
        format=None,
        scale=None,
        *,
        precision=None,
        in_subfmt=None,
        out_subfmt=None,
        copy=False,
    ):
        if isinstance(val, TimeDelta):
            if scale is not None:
                self._set_scale(scale)
        else:
            self._init_from_vals(
                val,
                val2,
                format,
                scale,
                copy,
                precision=precision,
                in_subfmt=in_subfmt,
                out_subfmt=out_subfmt,
            )
            self._check_numeric_no_unit(val, format)

            if scale is not None:
                self.SCALES = TIME_DELTA_TYPES[scale]

    def _check_numeric_no_unit(self, val, format):
        if (
            isinstance(self._time, TimeDeltaNumeric)
            and getattr(val, "unit", None) is None
            and format is None
        ):
            warn(
                "Numerical value without unit or explicit format passed to"
                " TimeDelta, assuming days",
                TimeDeltaMissingUnitWarning,
            )

    def replicate(self, *args, **kwargs):
        out = super().replicate(*args, **kwargs)
        out.SCALES = self.SCALES
        return out

    def to_datetime(self):
        """
        Convert to ``datetime.timedelta`` object.
        """
        tm = self.replicate(format="datetime")
        return tm._shaped_like_input(tm._time.value)

    def _set_scale(self, scale):
        """
        This is the key routine that actually does time scale conversions.
        This is not public and not connected to the read-only scale property.
        """
        if scale == self.scale:
            return
        if scale not in self.SCALES:
            raise ValueError(
                "Scale {scale!r} is not in the allowed scales {sorted(self.SCALES)}"
            )

        # For TimeDelta, there can only be a change in scale factor,
        # which is written as time2 - time1 = scale_offset * time1
        scale_offset = SCALE_OFFSETS[(self.scale, scale)]
        if scale_offset is None:
            self._time.scale = scale
        else:
            jd1, jd2 = self._time.jd1, self._time.jd2
            offset1, offset2 = day_frac(jd1, jd2, factor=scale_offset)
            self._time = self.FORMATS[self.format](
                jd1 + offset1,
                jd2 + offset2,
                scale,
                self.precision,
                self.in_subfmt,
                self.out_subfmt,
                from_jd=True,
            )

    def _add_sub(self, other, op):
        """Perform common elements of addition / subtraction for two delta times."""
        # If not a TimeDelta then see if it can be turned into a TimeDelta.
        if not isinstance(other, TimeDelta):
            try:
                other = TimeDelta(other)
            except Exception:
                return NotImplemented

        # the scales should be compatible (e.g., cannot convert TDB to TAI)
        if (
            self.scale is not None
            and self.scale not in other.SCALES
            or other.scale is not None
            and other.scale not in self.SCALES
        ):
            raise TypeError(
                "Cannot add TimeDelta instances with scales '{}' and '{}'".format(
                    self.scale, other.scale
                )
            )

        # adjust the scale of other if the scale of self is set (or no scales)
        if self.scale is not None or other.scale is None:
            out = self.replicate()
            if other.scale is not None:
                other = getattr(other, self.scale)
        else:
            out = other.replicate()

        jd1 = op(self._time.jd1, other._time.jd1)
        jd2 = op(self._time.jd2, other._time.jd2)

        out._time.jd1, out._time.jd2 = day_frac(jd1, jd2)

        return out

    def __add__(self, other):
        # If other is a Time then use Time.__add__ to do the calculation.
        if isinstance(other, Time):
            return other.__add__(self)

        return self._add_sub(other, operator.add)

    def __sub__(self, other):
        # TimeDelta - Time is an error
        if isinstance(other, Time):
            raise OperandTypeError(self, other, "-")

        return self._add_sub(other, operator.sub)

    def __radd__(self, other):
        return self.__add__(other)

    def __rsub__(self, other):
        out = self.__sub__(other)
        return -out

    def __neg__(self):
        """Negation of a `TimeDelta` object."""
        new = self.copy()
        new._time.jd1 = -self._time.jd1
        new._time.jd2 = -self._time.jd2
        return new

    def __abs__(self):
        """Absolute value of a `TimeDelta` object."""
        jd1, jd2 = self._time.jd1, self._time.jd2
        negative = jd1 + jd2 < 0
        new = self.copy()
        new._time.jd1 = np.where(negative, -jd1, jd1)
        new._time.jd2 = np.where(negative, -jd2, jd2)
        return new

    def __mul__(self, other):
        """Multiplication of `TimeDelta` objects by numbers/arrays."""
        # Check needed since otherwise the self.jd1 * other multiplication
        # would enter here again (via __rmul__)
        if isinstance(other, Time):
            raise OperandTypeError(self, other, "*")
        elif (isinstance(other, u.UnitBase) and other == u.dimensionless_unscaled) or (
            isinstance(other, str) and other == ""
        ):
            return self.copy()

        # If other is something consistent with a dimensionless quantity
        # (could just be a float or an array), then we can just multiple in.
        try:
            other = u.Quantity(other, u.dimensionless_unscaled, copy=False)
        except Exception:
            # If not consistent with a dimensionless quantity, try downgrading
            # self to a quantity and see if things work.
            try:
                return self.to(u.day) * other
            except Exception:
                # The various ways we could multiply all failed;
                # returning NotImplemented to give other a final chance.
                return NotImplemented

        jd1, jd2 = day_frac(self.jd1, self.jd2, factor=other.value)
        out = TimeDelta(jd1, jd2, format="jd", scale=self.scale)

        if self.format != "jd":
            out = out.replicate(format=self.format)
        return out

    def __rmul__(self, other):
        """Multiplication of numbers/arrays with `TimeDelta` objects."""
        return self.__mul__(other)

    def __truediv__(self, other):
        """Division of `TimeDelta` objects by numbers/arrays."""
        # Cannot do __mul__(1./other) as that looses precision
        if (isinstance(other, u.UnitBase) and other == u.dimensionless_unscaled) or (
            isinstance(other, str) and other == ""
        ):
            return self.copy()

        # If other is something consistent with a dimensionless quantity
        # (could just be a float or an array), then we can just divide in.
        try:
            other = u.Quantity(other, u.dimensionless_unscaled, copy=False)
        except Exception:
            # If not consistent with a dimensionless quantity, try downgrading
            # self to a quantity and see if things work.
            try:
                return self.to(u.day) / other
            except Exception:
                # The various ways we could divide all failed;
                # returning NotImplemented to give other a final chance.
                return NotImplemented

        jd1, jd2 = day_frac(self.jd1, self.jd2, divisor=other.value)
        out = TimeDelta(jd1, jd2, format="jd", scale=self.scale)

        if self.format != "jd":
            out = out.replicate(format=self.format)
        return out

    def __rtruediv__(self, other):
        """Division by `TimeDelta` objects of numbers/arrays."""
        # Here, we do not have to worry about returning NotImplemented,
        # since other has already had a chance to look at us.
        return other / self.to(u.day)

    def to(self, unit, equivalencies=[]):
        """
        Convert to a quantity in the specified unit.

        Parameters
        ----------
        unit : unit-like
            The unit to convert to.
        equivalencies : list of tuple
            A list of equivalence pairs to try if the units are not directly
            convertible (see :ref:`astropy:unit_equivalencies`). If `None`, no
            equivalencies will be applied at all, not even any set globallyq
            or within a context.

        Returns
        -------
        quantity : `~astropy.units.Quantity`
            The quantity in the units specified.

        See Also
        --------
        to_value : get the numerical value in a given unit.
        """
        return u.Quantity(self._time.jd1 + self._time.jd2, u.day).to(
            unit, equivalencies=equivalencies
        )

    def to_value(self, *args, **kwargs):
        """Get time delta values expressed in specified output format or unit.

        This method is flexible and handles both conversion to a specified
        ``TimeDelta`` format / sub-format AND conversion to a specified unit.
        If positional argument(s) are provided then the first one is checked
        to see if it is a valid ``TimeDelta`` format, and next it is checked
        to see if it is a valid unit or unit string.

        To convert to a ``TimeDelta`` format and optional sub-format the options
        are::

          tm = TimeDelta(1.0 * u.s)
          tm.to_value('jd')  # equivalent of tm.jd
          tm.to_value('jd', 'decimal')  # convert to 'jd' as a Decimal object
          tm.to_value('jd', subfmt='decimal')
          tm.to_value(format='jd', subfmt='decimal')

        To convert to a unit with optional equivalencies, the options are::

          tm.to_value('hr')  # convert to u.hr (hours)
          tm.to_value('hr', equivalencies=[])
          tm.to_value(unit='hr', equivalencies=[])

        The built-in `~astropy.time.TimeDelta` options for ``format`` are shown below::

          >>> list(TimeDelta.FORMATS)
          ['sec', 'jd', 'datetime', 'quantity_str']

        For the two numerical formats 'jd' and 'sec', the available ``subfmt``
        options are: {'float', 'long', 'decimal', 'str', 'bytes'}. Here, 'long'
        uses ``numpy.longdouble`` for somewhat enhanced precision (with the
        enhancement depending on platform), and 'decimal' instances of
        :class:`decimal.Decimal` for full precision.  For the 'str' and 'bytes'
        sub-formats, the number of digits is also chosen such that time values
        are represented accurately.  Default: as set by ``out_subfmt`` (which by
        default picks the first available for a given format, i.e., 'float').

        Parameters
        ----------
        format : str, optional
            The format in which one wants the `~astropy.time.TimeDelta` values.
            Default: the current format.
        subfmt : str, optional
            Possible sub-format in which the values should be given. Default: as
            set by ``out_subfmt`` (which by default picks the first available
            for a given format, i.e., 'float' or 'date_hms').
        unit : `~astropy.units.UnitBase` instance or str, optional
            The unit in which the value should be given.
        equivalencies : list of tuple
            A list of equivalence pairs to try if the units are not directly
            convertible (see :ref:`astropy:unit_equivalencies`). If `None`, no
            equivalencies will be applied at all, not even any set globally or
            within a context.

        Returns
        -------
        value : ndarray or scalar
            The value in the format or units specified.

        See Also
        --------
        to : Convert to a `~astropy.units.Quantity` instance in a given unit.
        value : The time value in the current format.

        """
        if not (args or kwargs):
            raise TypeError("to_value() missing required format or unit argument")

        # Validate keyword arguments.
        if kwargs:
            allowed_kwargs = {"format", "subfmt", "unit", "equivalencies"}
            if not set(kwargs).issubset(allowed_kwargs):
                bad = (set(kwargs) - allowed_kwargs).pop()
                raise TypeError(
                    f"{self.to_value.__qualname__}() got an unexpected keyword argument"
                    f" '{bad}'"
                )

        # Handle a valid format as first positional argument or keyword. This will also
        # accept a subfmt keyword if supplied.
        if "format" in kwargs or (
            args != () and (args[0] is None or args[0] in self.FORMATS)
        ):
            # Super-class will error with duplicate arguments, etc.
            return super().to_value(*args, **kwargs)

        # Handle subfmt keyword with no format and no args.
        if "subfmt" in kwargs:
            if args:
                raise ValueError(
                    "cannot specify 'subfmt' and positional argument that is not a "
                    "valid format"
                )
            return super().to_value(self.format, **kwargs)

        # At this point any positional argument must be a unit so try parsing as such.
        # If it fails then give an informative exception.
        # TODO: deprecate providing equivalencies as a positional argument. This is
        # quite non-obvious in this context.
        if args:
            try:
                unit = u.Unit(args[0])
            except ValueError as exc:
                raise ValueError(
                    "first argument is not one of the known "
                    f"formats ({list(self.FORMATS)}) and failed to parse as a unit."
                ) from exc
            args = (unit,) + args[1:]

        return u.Quantity(self._time.jd1 + self._time.jd2, u.day).to_value(
            *args, **kwargs
        )

    def _make_value_equivalent(self, item, value):
        """Coerce setitem value into an equivalent TimeDelta object."""
        if not isinstance(value, TimeDelta):
            try:
                value = self.__class__(value, scale=self.scale, format=self.format)
            except Exception as err:
                raise ValueError(
                    f"cannot convert value to a compatible TimeDelta object: {err}"
                )
        return value

    def isclose(self, other, atol=None, rtol=0.0):
        """Returns a boolean or boolean array where two TimeDelta objects are
        element-wise equal within a time tolerance.

        This effectively evaluates the expression below::

          abs(self - other) <= atol + rtol * abs(other)

        Parameters
        ----------
        other : `~astropy.units.Quantity` or `~astropy.time.TimeDelta`
            Quantity or TimeDelta object for comparison.
        atol : `~astropy.units.Quantity` or `~astropy.time.TimeDelta`
            Absolute tolerance for equality with units of time (e.g. ``u.s`` or
            ``u.day``). Default is one bit in the 128-bit JD time representation,
            equivalent to about 20 picosecs.
        rtol : float
            Relative tolerance for equality
        """
        try:
            other_day = other.to_value(u.day)
        except Exception as err:
            raise TypeError(f"'other' argument must support conversion to days: {err}")

        if atol is None:
            atol = np.finfo(float).eps * u.day

        if not isinstance(atol, (u.Quantity, TimeDelta)):
            raise TypeError(
                "'atol' argument must be a Quantity or TimeDelta instance, got "
                f"{atol.__class__.__name__} instead"
            )

        return np.isclose(
            self.to_value(u.day), other_day, rtol=rtol, atol=atol.to_value(u.day)
        )


class ScaleValueError(Exception):
    pass


def _make_array(val, copy=False):
    """
    Take ``val`` and convert/reshape to an array.  If ``copy`` is `True`
    then copy input values.

    Returns
    -------
    val : ndarray
        Array version of ``val``.
    """
    if isinstance(val, (tuple, list)) and len(val) > 0 and isinstance(val[0], Time):
        dtype = object
    else:
        dtype = None

    val = np.array(val, copy=copy, subok=True, dtype=dtype)

    # Allow only float64, string or object arrays as input
    # (object is for datetime, maybe add more specific test later?)
    # This also ensures the right byteorder for float64 (closes #2942).
    if val.dtype.kind == "f" and val.dtype.itemsize >= np.dtype(np.float64).itemsize:
        pass
    elif val.dtype.kind in "OSUMaV":
        pass
    else:
        val = np.asanyarray(val, dtype=np.float64)

    return val


def get_mask_and_data(mask, val):
    """
    Update ``mask`` in place and return unmasked ``val`` data.

    If ``val`` is not masked then ``mask`` and ``val`` are returned
    unchanged.

    Parameters
    ----------
    mask : bool, ndarray(bool)
        Mask to update
    val: ndarray, np.ma.MaskedArray, Masked
        Input val

    Returns
    -------
    mask, val: bool, ndarray
        Updated mask, unmasked data
    """
    if not isinstance(val, (np.ma.MaskedArray, Masked)):
        return mask, val

    if isinstance(val, np.ma.MaskedArray):
        data = val.data
    else:
        data = val.unmasked

    # For structured dtype, the mask is structured too.  We consider an
    # array element masked if any field of the structure is masked.
    if val.dtype.names:
        val_mask = val.mask != np.zeros_like(val.mask, shape=())
    else:
        val_mask = val.mask
    if np.any(val_mask):
        # Final mask is the logical-or of inputs
        mask = mask | val_mask

    return mask, data


class OperandTypeError(TypeError):
    def __init__(self, left, right, op=None):
        op_string = "" if op is None else f" for {op}"
        super().__init__(
            "Unsupported operand type(s){}: '{}' and '{}'".format(
                op_string, left.__class__.__name__, right.__class__.__name__
            )
        )


def _check_leapsec():
    global _LEAP_SECONDS_CHECK
    if _LEAP_SECONDS_CHECK != _LeapSecondsCheck.DONE:
        with _LEAP_SECONDS_LOCK:
            # There are three ways we can get here:
            # 1. First call (NOT_STARTED).
            # 2. Re-entrant call (RUNNING). We skip the initialisation
            #    and don't worry about leap second errors.
            # 3. Another thread which raced with the first call
            #    (RUNNING). The first thread has relinquished the
            #    lock to us, so initialization is complete.
            if _LEAP_SECONDS_CHECK == _LeapSecondsCheck.NOT_STARTED:
                _LEAP_SECONDS_CHECK = _LeapSecondsCheck.RUNNING
                update_leap_seconds()
                _LEAP_SECONDS_CHECK = _LeapSecondsCheck.DONE


def update_leap_seconds(files=None):
    """If the current ERFA leap second table is out of date, try to update it.

    Uses `astropy.utils.iers.LeapSeconds.auto_open` to try to find an
    up-to-date table.  See that routine for the definition of "out of date".

    In order to make it safe to call this any time, all exceptions are turned
    into warnings,

    Parameters
    ----------
    files : list of path-like, optional
        List of files/URLs to attempt to open.  By default, uses defined by
        `astropy.utils.iers.LeapSeconds.auto_open`, which includes the table
        used by ERFA itself, so if that is up to date, nothing will happen.

    Returns
    -------
    n_update : int
        Number of items updated.

    """
    try:
        from astropy.utils import iers

        table = iers.LeapSeconds.auto_open(files)
        return erfa.leap_seconds.update(table)

    except Exception as exc:
        warn(
            f"leap-second auto-update failed due to the following exception: {exc!r}",
            AstropyWarning,
        )
        return 0