testbed/django__django/django/db/models/expressions.py

import copy
import datetime
import functools
import inspect
from collections import defaultdict
from decimal import Decimal
from types import NoneType
from uuid import UUID

from django.core.exceptions import EmptyResultSet, FieldError, FullResultSet
from django.db import DatabaseError, NotSupportedError, connection
from django.db.models import fields
from django.db.models.constants import LOOKUP_SEP
from django.db.models.query_utils import Q
from django.utils.deconstruct import deconstructible
from django.utils.functional import cached_property
from django.utils.hashable import make_hashable


class SQLiteNumericMixin:
    """
    Some expressions with output_field=DecimalField() must be cast to
    numeric to be properly filtered.
    """

    def as_sqlite(self, compiler, connection, **extra_context):
        sql, params = self.as_sql(compiler, connection, **extra_context)
        try:
            if self.output_field.get_internal_type() == "DecimalField":
                sql = "CAST(%s AS NUMERIC)" % sql
        except FieldError:
            pass
        return sql, params


class Combinable:
    """
    Provide the ability to combine one or two objects with
    some connector. For example F('foo') + F('bar').
    """

    # Arithmetic connectors
    ADD = "+"
    SUB = "-"
    MUL = "*"
    DIV = "/"
    POW = "^"
    # The following is a quoted % operator - it is quoted because it can be
    # used in strings that also have parameter substitution.
    MOD = "%%"

    # Bitwise operators - note that these are generated by .bitand()
    # and .bitor(), the '&' and '|' are reserved for boolean operator
    # usage.
    BITAND = "&"
    BITOR = "|"
    BITLEFTSHIFT = "<<"
    BITRIGHTSHIFT = ">>"
    BITXOR = "#"

    def _combine(self, other, connector, reversed):
        if not hasattr(other, "resolve_expression"):
            # everything must be resolvable to an expression
            other = Value(other)

        if reversed:
            return CombinedExpression(other, connector, self)
        return CombinedExpression(self, connector, other)

    #############
    # OPERATORS #
    #############

    def __neg__(self):
        return self._combine(-1, self.MUL, False)

    def __add__(self, other):
        return self._combine(other, self.ADD, False)

    def __sub__(self, other):
        return self._combine(other, self.SUB, False)

    def __mul__(self, other):
        return self._combine(other, self.MUL, False)

    def __truediv__(self, other):
        return self._combine(other, self.DIV, False)

    def __mod__(self, other):
        return self._combine(other, self.MOD, False)

    def __pow__(self, other):
        return self._combine(other, self.POW, False)

    def __and__(self, other):
        if getattr(self, "conditional", False) and getattr(other, "conditional", False):
            return Q(self) & Q(other)
        raise NotImplementedError(
            "Use .bitand(), .bitor(), and .bitxor() for bitwise logical operations."
        )

    def bitand(self, other):
        return self._combine(other, self.BITAND, False)

    def bitleftshift(self, other):
        return self._combine(other, self.BITLEFTSHIFT, False)

    def bitrightshift(self, other):
        return self._combine(other, self.BITRIGHTSHIFT, False)

    def __xor__(self, other):
        if getattr(self, "conditional", False) and getattr(other, "conditional", False):
            return Q(self) ^ Q(other)
        raise NotImplementedError(
            "Use .bitand(), .bitor(), and .bitxor() for bitwise logical operations."
        )

    def bitxor(self, other):
        return self._combine(other, self.BITXOR, False)

    def __or__(self, other):
        if getattr(self, "conditional", False) and getattr(other, "conditional", False):
            return Q(self) | Q(other)
        raise NotImplementedError(
            "Use .bitand(), .bitor(), and .bitxor() for bitwise logical operations."
        )

    def bitor(self, other):
        return self._combine(other, self.BITOR, False)

    def __radd__(self, other):
        return self._combine(other, self.ADD, True)

    def __rsub__(self, other):
        return self._combine(other, self.SUB, True)

    def __rmul__(self, other):
        return self._combine(other, self.MUL, True)

    def __rtruediv__(self, other):
        return self._combine(other, self.DIV, True)

    def __rmod__(self, other):
        return self._combine(other, self.MOD, True)

    def __rpow__(self, other):
        return self._combine(other, self.POW, True)

    def __rand__(self, other):
        raise NotImplementedError(
            "Use .bitand(), .bitor(), and .bitxor() for bitwise logical operations."
        )

    def __ror__(self, other):
        raise NotImplementedError(
            "Use .bitand(), .bitor(), and .bitxor() for bitwise logical operations."
        )

    def __rxor__(self, other):
        raise NotImplementedError(
            "Use .bitand(), .bitor(), and .bitxor() for bitwise logical operations."
        )

    def __invert__(self):
        return NegatedExpression(self)


class BaseExpression:
    """Base class for all query expressions."""

    empty_result_set_value = NotImplemented
    # aggregate specific fields
    is_summary = False
    _output_field_resolved_to_none = False
    # Can the expression be used in a WHERE clause?
    filterable = True
    # Can the expression can be used as a source expression in Window?
    window_compatible = False
    # Can the expression be used as a database default value?
    allowed_default = False

    def __init__(self, output_field=None):
        if output_field is not None:
            self.output_field = output_field

    def __getstate__(self):
        state = self.__dict__.copy()
        state.pop("convert_value", None)
        return state

    def get_db_converters(self, connection):
        return (
            []
            if self.convert_value is self._convert_value_noop
            else [self.convert_value]
        ) + self.output_field.get_db_converters(connection)

    def get_source_expressions(self):
        return []

    def set_source_expressions(self, exprs):
        assert not exprs

    def _parse_expressions(self, *expressions):
        return [
            arg
            if hasattr(arg, "resolve_expression")
            else (F(arg) if isinstance(arg, str) else Value(arg))
            for arg in expressions
        ]

    def as_sql(self, compiler, connection):
        """
        Responsible for returning a (sql, [params]) tuple to be included
        in the current query.

        Different backends can provide their own implementation, by
        providing an `as_{vendor}` method and patching the Expression:

        ```
        def override_as_sql(self, compiler, connection):
            # custom logic
            return super().as_sql(compiler, connection)
        setattr(Expression, 'as_' + connection.vendor, override_as_sql)
        ```

        Arguments:
         * compiler: the query compiler responsible for generating the query.
           Must have a compile method, returning a (sql, [params]) tuple.
           Calling compiler(value) will return a quoted `value`.

         * connection: the database connection used for the current query.

        Return: (sql, params)
          Where `sql` is a string containing ordered sql parameters to be
          replaced with the elements of the list `params`.
        """
        raise NotImplementedError("Subclasses must implement as_sql()")

    @cached_property
    def contains_aggregate(self):
        return any(
            expr and expr.contains_aggregate for expr in self.get_source_expressions()
        )

    @cached_property
    def contains_over_clause(self):
        return any(
            expr and expr.contains_over_clause for expr in self.get_source_expressions()
        )

    @cached_property
    def contains_column_references(self):
        return any(
            expr and expr.contains_column_references
            for expr in self.get_source_expressions()
        )

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        """
        Provide the chance to do any preprocessing or validation before being
        added to the query.

        Arguments:
         * query: the backend query implementation
         * allow_joins: boolean allowing or denying use of joins
           in this query
         * reuse: a set of reusable joins for multijoins
         * summarize: a terminal aggregate clause
         * for_save: whether this expression about to be used in a save or update

        Return: an Expression to be added to the query.
        """
        c = self.copy()
        c.is_summary = summarize
        c.set_source_expressions(
            [
                expr.resolve_expression(query, allow_joins, reuse, summarize)
                if expr
                else None
                for expr in c.get_source_expressions()
            ]
        )
        return c

    @property
    def conditional(self):
        return isinstance(self.output_field, fields.BooleanField)

    @property
    def field(self):
        return self.output_field

    @cached_property
    def output_field(self):
        """Return the output type of this expressions."""
        output_field = self._resolve_output_field()
        if output_field is None:
            self._output_field_resolved_to_none = True
            raise FieldError("Cannot resolve expression type, unknown output_field")
        return output_field

    @cached_property
    def _output_field_or_none(self):
        """
        Return the output field of this expression, or None if
        _resolve_output_field() didn't return an output type.
        """
        try:
            return self.output_field
        except FieldError:
            if not self._output_field_resolved_to_none:
                raise

    def _resolve_output_field(self):
        """
        Attempt to infer the output type of the expression.

        As a guess, if the output fields of all source fields match then simply
        infer the same type here.

        If a source's output field resolves to None, exclude it from this check.
        If all sources are None, then an error is raised higher up the stack in
        the output_field property.
        """
        # This guess is mostly a bad idea, but there is quite a lot of code
        # (especially 3rd party Func subclasses) that depend on it, we'd need a
        # deprecation path to fix it.
        sources_iter = (
            source for source in self.get_source_fields() if source is not None
        )
        for output_field in sources_iter:
            for source in sources_iter:
                if not isinstance(output_field, source.__class__):
                    raise FieldError(
                        "Expression contains mixed types: %s, %s. You must "
                        "set output_field."
                        % (
                            output_field.__class__.__name__,
                            source.__class__.__name__,
                        )
                    )
            return output_field

    @staticmethod
    def _convert_value_noop(value, expression, connection):
        return value

    @cached_property
    def convert_value(self):
        """
        Expressions provide their own converters because users have the option
        of manually specifying the output_field which may be a different type
        from the one the database returns.
        """
        field = self.output_field
        internal_type = field.get_internal_type()
        if internal_type == "FloatField":
            return (
                lambda value, expression, connection: None
                if value is None
                else float(value)
            )
        elif internal_type.endswith("IntegerField"):
            return (
                lambda value, expression, connection: None
                if value is None
                else int(value)
            )
        elif internal_type == "DecimalField":
            return (
                lambda value, expression, connection: None
                if value is None
                else Decimal(value)
            )
        return self._convert_value_noop

    def get_lookup(self, lookup):
        return self.output_field.get_lookup(lookup)

    def get_transform(self, name):
        return self.output_field.get_transform(name)

    def relabeled_clone(self, change_map):
        clone = self.copy()
        clone.set_source_expressions(
            [
                e.relabeled_clone(change_map) if e is not None else None
                for e in self.get_source_expressions()
            ]
        )
        return clone

    def replace_expressions(self, replacements):
        if replacement := replacements.get(self):
            return replacement
        clone = self.copy()
        source_expressions = clone.get_source_expressions()
        clone.set_source_expressions(
            [
                expr.replace_expressions(replacements) if expr else None
                for expr in source_expressions
            ]
        )
        return clone

    def get_refs(self):
        refs = set()
        for expr in self.get_source_expressions():
            refs |= expr.get_refs()
        return refs

    def copy(self):
        return copy.copy(self)

    def prefix_references(self, prefix):
        clone = self.copy()
        clone.set_source_expressions(
            [
                F(f"{prefix}{expr.name}")
                if isinstance(expr, F)
                else expr.prefix_references(prefix)
                for expr in self.get_source_expressions()
            ]
        )
        return clone

    def get_group_by_cols(self):
        if not self.contains_aggregate:
            return [self]
        cols = []
        for source in self.get_source_expressions():
            cols.extend(source.get_group_by_cols())
        return cols

    def get_source_fields(self):
        """Return the underlying field types used by this aggregate."""
        return [e._output_field_or_none for e in self.get_source_expressions()]

    def asc(self, **kwargs):
        return OrderBy(self, **kwargs)

    def desc(self, **kwargs):
        return OrderBy(self, descending=True, **kwargs)

    def reverse_ordering(self):
        return self

    def flatten(self):
        """
        Recursively yield this expression and all subexpressions, in
        depth-first order.
        """
        yield self
        for expr in self.get_source_expressions():
            if expr:
                if hasattr(expr, "flatten"):
                    yield from expr.flatten()
                else:
                    yield expr

    def select_format(self, compiler, sql, params):
        """
        Custom format for select clauses. For example, EXISTS expressions need
        to be wrapped in CASE WHEN on Oracle.
        """
        if hasattr(self.output_field, "select_format"):
            return self.output_field.select_format(compiler, sql, params)
        return sql, params


@deconstructible
class Expression(BaseExpression, Combinable):
    """An expression that can be combined with other expressions."""

    @cached_property
    def identity(self):
        constructor_signature = inspect.signature(self.__init__)
        args, kwargs = self._constructor_args
        signature = constructor_signature.bind_partial(*args, **kwargs)
        signature.apply_defaults()
        arguments = signature.arguments.items()
        identity = [self.__class__]
        for arg, value in arguments:
            if isinstance(value, fields.Field):
                if value.name and value.model:
                    value = (value.model._meta.label, value.name)
                else:
                    value = type(value)
            else:
                value = make_hashable(value)
            identity.append((arg, value))
        return tuple(identity)

    def __eq__(self, other):
        if not isinstance(other, Expression):
            return NotImplemented
        return other.identity == self.identity

    def __hash__(self):
        return hash(self.identity)


# Type inference for CombinedExpression.output_field.
# Missing items will result in FieldError, by design.
#
# The current approach for NULL is based on lowest common denominator behavior
# i.e. if one of the supported databases is raising an error (rather than
# return NULL) for `val <op> NULL`, then Django raises FieldError.

_connector_combinations = [
    # Numeric operations - operands of same type.
    {
        connector: [
            (fields.IntegerField, fields.IntegerField, fields.IntegerField),
            (fields.FloatField, fields.FloatField, fields.FloatField),
            (fields.DecimalField, fields.DecimalField, fields.DecimalField),
        ]
        for connector in (
            Combinable.ADD,
            Combinable.SUB,
            Combinable.MUL,
            # Behavior for DIV with integer arguments follows Postgres/SQLite,
            # not MySQL/Oracle.
            Combinable.DIV,
            Combinable.MOD,
            Combinable.POW,
        )
    },
    # Numeric operations - operands of different type.
    {
        connector: [
            (fields.IntegerField, fields.DecimalField, fields.DecimalField),
            (fields.DecimalField, fields.IntegerField, fields.DecimalField),
            (fields.IntegerField, fields.FloatField, fields.FloatField),
            (fields.FloatField, fields.IntegerField, fields.FloatField),
        ]
        for connector in (
            Combinable.ADD,
            Combinable.SUB,
            Combinable.MUL,
            Combinable.DIV,
            Combinable.MOD,
        )
    },
    # Bitwise operators.
    {
        connector: [
            (fields.IntegerField, fields.IntegerField, fields.IntegerField),
        ]
        for connector in (
            Combinable.BITAND,
            Combinable.BITOR,
            Combinable.BITLEFTSHIFT,
            Combinable.BITRIGHTSHIFT,
            Combinable.BITXOR,
        )
    },
    # Numeric with NULL.
    {
        connector: [
            (field_type, NoneType, field_type),
            (NoneType, field_type, field_type),
        ]
        for connector in (
            Combinable.ADD,
            Combinable.SUB,
            Combinable.MUL,
            Combinable.DIV,
            Combinable.MOD,
            Combinable.POW,
        )
        for field_type in (fields.IntegerField, fields.DecimalField, fields.FloatField)
    },
    # Date/DateTimeField/DurationField/TimeField.
    {
        Combinable.ADD: [
            # Date/DateTimeField.
            (fields.DateField, fields.DurationField, fields.DateTimeField),
            (fields.DateTimeField, fields.DurationField, fields.DateTimeField),
            (fields.DurationField, fields.DateField, fields.DateTimeField),
            (fields.DurationField, fields.DateTimeField, fields.DateTimeField),
            # DurationField.
            (fields.DurationField, fields.DurationField, fields.DurationField),
            # TimeField.
            (fields.TimeField, fields.DurationField, fields.TimeField),
            (fields.DurationField, fields.TimeField, fields.TimeField),
        ],
    },
    {
        Combinable.SUB: [
            # Date/DateTimeField.
            (fields.DateField, fields.DurationField, fields.DateTimeField),
            (fields.DateTimeField, fields.DurationField, fields.DateTimeField),
            (fields.DateField, fields.DateField, fields.DurationField),
            (fields.DateField, fields.DateTimeField, fields.DurationField),
            (fields.DateTimeField, fields.DateField, fields.DurationField),
            (fields.DateTimeField, fields.DateTimeField, fields.DurationField),
            # DurationField.
            (fields.DurationField, fields.DurationField, fields.DurationField),
            # TimeField.
            (fields.TimeField, fields.DurationField, fields.TimeField),
            (fields.TimeField, fields.TimeField, fields.DurationField),
        ],
    },
]

_connector_combinators = defaultdict(list)


def register_combinable_fields(lhs, connector, rhs, result):
    """
    Register combinable types:
        lhs <connector> rhs -> result
    e.g.
        register_combinable_fields(
            IntegerField, Combinable.ADD, FloatField, FloatField
        )
    """
    _connector_combinators[connector].append((lhs, rhs, result))


for d in _connector_combinations:
    for connector, field_types in d.items():
        for lhs, rhs, result in field_types:
            register_combinable_fields(lhs, connector, rhs, result)


@functools.lru_cache(maxsize=128)
def _resolve_combined_type(connector, lhs_type, rhs_type):
    combinators = _connector_combinators.get(connector, ())
    for combinator_lhs_type, combinator_rhs_type, combined_type in combinators:
        if issubclass(lhs_type, combinator_lhs_type) and issubclass(
            rhs_type, combinator_rhs_type
        ):
            return combined_type


class CombinedExpression(SQLiteNumericMixin, Expression):
    def __init__(self, lhs, connector, rhs, output_field=None):
        super().__init__(output_field=output_field)
        self.connector = connector
        self.lhs = lhs
        self.rhs = rhs

    def __repr__(self):
        return "<{}: {}>".format(self.__class__.__name__, self)

    def __str__(self):
        return "{} {} {}".format(self.lhs, self.connector, self.rhs)

    def get_source_expressions(self):
        return [self.lhs, self.rhs]

    def set_source_expressions(self, exprs):
        self.lhs, self.rhs = exprs

    def _resolve_output_field(self):
        # We avoid using super() here for reasons given in
        # Expression._resolve_output_field()
        combined_type = _resolve_combined_type(
            self.connector,
            type(self.lhs._output_field_or_none),
            type(self.rhs._output_field_or_none),
        )
        if combined_type is None:
            raise FieldError(
                f"Cannot infer type of {self.connector!r} expression involving these "
                f"types: {self.lhs.output_field.__class__.__name__}, "
                f"{self.rhs.output_field.__class__.__name__}. You must set "
                f"output_field."
            )
        return combined_type()

    def as_sql(self, compiler, connection):
        expressions = []
        expression_params = []
        sql, params = compiler.compile(self.lhs)
        expressions.append(sql)
        expression_params.extend(params)
        sql, params = compiler.compile(self.rhs)
        expressions.append(sql)
        expression_params.extend(params)
        # order of precedence
        expression_wrapper = "(%s)"
        sql = connection.ops.combine_expression(self.connector, expressions)
        return expression_wrapper % sql, expression_params

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        lhs = self.lhs.resolve_expression(
            query, allow_joins, reuse, summarize, for_save
        )
        rhs = self.rhs.resolve_expression(
            query, allow_joins, reuse, summarize, for_save
        )
        if not isinstance(self, (DurationExpression, TemporalSubtraction)):
            try:
                lhs_type = lhs.output_field.get_internal_type()
            except (AttributeError, FieldError):
                lhs_type = None
            try:
                rhs_type = rhs.output_field.get_internal_type()
            except (AttributeError, FieldError):
                rhs_type = None
            if "DurationField" in {lhs_type, rhs_type} and lhs_type != rhs_type:
                return DurationExpression(
                    self.lhs, self.connector, self.rhs
                ).resolve_expression(
                    query,
                    allow_joins,
                    reuse,
                    summarize,
                    for_save,
                )
            datetime_fields = {"DateField", "DateTimeField", "TimeField"}
            if (
                self.connector == self.SUB
                and lhs_type in datetime_fields
                and lhs_type == rhs_type
            ):
                return TemporalSubtraction(self.lhs, self.rhs).resolve_expression(
                    query,
                    allow_joins,
                    reuse,
                    summarize,
                    for_save,
                )
        c = self.copy()
        c.is_summary = summarize
        c.lhs = lhs
        c.rhs = rhs
        return c

    @cached_property
    def allowed_default(self):
        return self.lhs.allowed_default and self.rhs.allowed_default


class DurationExpression(CombinedExpression):
    def compile(self, side, compiler, connection):
        try:
            output = side.output_field
        except FieldError:
            pass
        else:
            if output.get_internal_type() == "DurationField":
                sql, params = compiler.compile(side)
                return connection.ops.format_for_duration_arithmetic(sql), params
        return compiler.compile(side)

    def as_sql(self, compiler, connection):
        if connection.features.has_native_duration_field:
            return super().as_sql(compiler, connection)
        connection.ops.check_expression_support(self)
        expressions = []
        expression_params = []
        sql, params = self.compile(self.lhs, compiler, connection)
        expressions.append(sql)
        expression_params.extend(params)
        sql, params = self.compile(self.rhs, compiler, connection)
        expressions.append(sql)
        expression_params.extend(params)
        # order of precedence
        expression_wrapper = "(%s)"
        sql = connection.ops.combine_duration_expression(self.connector, expressions)
        return expression_wrapper % sql, expression_params

    def as_sqlite(self, compiler, connection, **extra_context):
        sql, params = self.as_sql(compiler, connection, **extra_context)
        if self.connector in {Combinable.MUL, Combinable.DIV}:
            try:
                lhs_type = self.lhs.output_field.get_internal_type()
                rhs_type = self.rhs.output_field.get_internal_type()
            except (AttributeError, FieldError):
                pass
            else:
                allowed_fields = {
                    "DecimalField",
                    "DurationField",
                    "FloatField",
                    "IntegerField",
                }
                if lhs_type not in allowed_fields or rhs_type not in allowed_fields:
                    raise DatabaseError(
                        f"Invalid arguments for operator {self.connector}."
                    )
        return sql, params


class TemporalSubtraction(CombinedExpression):
    output_field = fields.DurationField()

    def __init__(self, lhs, rhs):
        super().__init__(lhs, self.SUB, rhs)

    def as_sql(self, compiler, connection):
        connection.ops.check_expression_support(self)
        lhs = compiler.compile(self.lhs)
        rhs = compiler.compile(self.rhs)
        return connection.ops.subtract_temporals(
            self.lhs.output_field.get_internal_type(), lhs, rhs
        )


@deconstructible(path="django.db.models.F")
class F(Combinable):
    """An object capable of resolving references to existing query objects."""

    allowed_default = False

    def __init__(self, name):
        """
        Arguments:
         * name: the name of the field this expression references
        """
        self.name = name

    def __repr__(self):
        return "{}({})".format(self.__class__.__name__, self.name)

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        return query.resolve_ref(self.name, allow_joins, reuse, summarize)

    def replace_expressions(self, replacements):
        return replacements.get(self, self)

    def asc(self, **kwargs):
        return OrderBy(self, **kwargs)

    def desc(self, **kwargs):
        return OrderBy(self, descending=True, **kwargs)

    def __eq__(self, other):
        return self.__class__ == other.__class__ and self.name == other.name

    def __hash__(self):
        return hash(self.name)

    def copy(self):
        return copy.copy(self)


class ResolvedOuterRef(F):
    """
    An object that contains a reference to an outer query.

    In this case, the reference to the outer query has been resolved because
    the inner query has been used as a subquery.
    """

    contains_aggregate = False
    contains_over_clause = False

    def as_sql(self, *args, **kwargs):
        raise ValueError(
            "This queryset contains a reference to an outer query and may "
            "only be used in a subquery."
        )

    def resolve_expression(self, *args, **kwargs):
        col = super().resolve_expression(*args, **kwargs)
        if col.contains_over_clause:
            raise NotSupportedError(
                f"Referencing outer query window expression is not supported: "
                f"{self.name}."
            )
        # FIXME: Rename possibly_multivalued to multivalued and fix detection
        # for non-multivalued JOINs (e.g. foreign key fields). This should take
        # into account only many-to-many and one-to-many relationships.
        col.possibly_multivalued = LOOKUP_SEP in self.name
        return col

    def relabeled_clone(self, relabels):
        return self

    def get_group_by_cols(self):
        return []


class OuterRef(F):
    contains_aggregate = False

    def resolve_expression(self, *args, **kwargs):
        if isinstance(self.name, self.__class__):
            return self.name
        return ResolvedOuterRef(self.name)

    def relabeled_clone(self, relabels):
        return self


@deconstructible(path="django.db.models.Func")
class Func(SQLiteNumericMixin, Expression):
    """An SQL function call."""

    function = None
    template = "%(function)s(%(expressions)s)"
    arg_joiner = ", "
    arity = None  # The number of arguments the function accepts.

    def __init__(self, *expressions, output_field=None, **extra):
        if self.arity is not None and len(expressions) != self.arity:
            raise TypeError(
                "'%s' takes exactly %s %s (%s given)"
                % (
                    self.__class__.__name__,
                    self.arity,
                    "argument" if self.arity == 1 else "arguments",
                    len(expressions),
                )
            )
        super().__init__(output_field=output_field)
        self.source_expressions = self._parse_expressions(*expressions)
        self.extra = extra

    def __repr__(self):
        args = self.arg_joiner.join(str(arg) for arg in self.source_expressions)
        extra = {**self.extra, **self._get_repr_options()}
        if extra:
            extra = ", ".join(
                str(key) + "=" + str(val) for key, val in sorted(extra.items())
            )
            return "{}({}, {})".format(self.__class__.__name__, args, extra)
        return "{}({})".format(self.__class__.__name__, args)

    def _get_repr_options(self):
        """Return a dict of extra __init__() options to include in the repr."""
        return {}

    def get_source_expressions(self):
        return self.source_expressions

    def set_source_expressions(self, exprs):
        self.source_expressions = exprs

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        c = self.copy()
        c.is_summary = summarize
        for pos, arg in enumerate(c.source_expressions):
            c.source_expressions[pos] = arg.resolve_expression(
                query, allow_joins, reuse, summarize, for_save
            )
        return c

    def as_sql(
        self,
        compiler,
        connection,
        function=None,
        template=None,
        arg_joiner=None,
        **extra_context,
    ):
        connection.ops.check_expression_support(self)
        sql_parts = []
        params = []
        for arg in self.source_expressions:
            try:
                arg_sql, arg_params = compiler.compile(arg)
            except EmptyResultSet:
                empty_result_set_value = getattr(
                    arg, "empty_result_set_value", NotImplemented
                )
                if empty_result_set_value is NotImplemented:
                    raise
                arg_sql, arg_params = compiler.compile(Value(empty_result_set_value))
            except FullResultSet:
                arg_sql, arg_params = compiler.compile(Value(True))
            sql_parts.append(arg_sql)
            params.extend(arg_params)
        data = {**self.extra, **extra_context}
        # Use the first supplied value in this order: the parameter to this
        # method, a value supplied in __init__()'s **extra (the value in
        # `data`), or the value defined on the class.
        if function is not None:
            data["function"] = function
        else:
            data.setdefault("function", self.function)
        template = template or data.get("template", self.template)
        arg_joiner = arg_joiner or data.get("arg_joiner", self.arg_joiner)
        data["expressions"] = data["field"] = arg_joiner.join(sql_parts)
        return template % data, params

    def copy(self):
        copy = super().copy()
        copy.source_expressions = self.source_expressions[:]
        copy.extra = self.extra.copy()
        return copy

    @cached_property
    def allowed_default(self):
        return all(expression.allowed_default for expression in self.source_expressions)


@deconstructible(path="django.db.models.Value")
class Value(SQLiteNumericMixin, Expression):
    """Represent a wrapped value as a node within an expression."""

    # Provide a default value for `for_save` in order to allow unresolved
    # instances to be compiled until a decision is taken in #25425.
    for_save = False
    allowed_default = True

    def __init__(self, value, output_field=None):
        """
        Arguments:
         * value: the value this expression represents. The value will be
           added into the sql parameter list and properly quoted.

         * output_field: an instance of the model field type that this
           expression will return, such as IntegerField() or CharField().
        """
        super().__init__(output_field=output_field)
        self.value = value

    def __repr__(self):
        return f"{self.__class__.__name__}({self.value!r})"

    def as_sql(self, compiler, connection):
        connection.ops.check_expression_support(self)
        val = self.value
        output_field = self._output_field_or_none
        if output_field is not None:
            if self.for_save:
                val = output_field.get_db_prep_save(val, connection=connection)
            else:
                val = output_field.get_db_prep_value(val, connection=connection)
            if hasattr(output_field, "get_placeholder"):
                return output_field.get_placeholder(val, compiler, connection), [val]
        if val is None:
            # cx_Oracle does not always convert None to the appropriate
            # NULL type (like in case expressions using numbers), so we
            # use a literal SQL NULL
            return "NULL", []
        return "%s", [val]

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        c = super().resolve_expression(query, allow_joins, reuse, summarize, for_save)
        c.for_save = for_save
        return c

    def get_group_by_cols(self):
        return []

    def _resolve_output_field(self):
        if isinstance(self.value, str):
            return fields.CharField()
        if isinstance(self.value, bool):
            return fields.BooleanField()
        if isinstance(self.value, int):
            return fields.IntegerField()
        if isinstance(self.value, float):
            return fields.FloatField()
        if isinstance(self.value, datetime.datetime):
            return fields.DateTimeField()
        if isinstance(self.value, datetime.date):
            return fields.DateField()
        if isinstance(self.value, datetime.time):
            return fields.TimeField()
        if isinstance(self.value, datetime.timedelta):
            return fields.DurationField()
        if isinstance(self.value, Decimal):
            return fields.DecimalField()
        if isinstance(self.value, bytes):
            return fields.BinaryField()
        if isinstance(self.value, UUID):
            return fields.UUIDField()

    @property
    def empty_result_set_value(self):
        return self.value


class RawSQL(Expression):
    allowed_default = True

    def __init__(self, sql, params, output_field=None):
        if output_field is None:
            output_field = fields.Field()
        self.sql, self.params = sql, params
        super().__init__(output_field=output_field)

    def __repr__(self):
        return "{}({}, {})".format(self.__class__.__name__, self.sql, self.params)

    def as_sql(self, compiler, connection):
        return "(%s)" % self.sql, self.params

    def get_group_by_cols(self):
        return [self]

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        # Resolve parents fields used in raw SQL.
        if query.model:
            for parent in query.model._meta.get_parent_list():
                for parent_field in parent._meta.local_fields:
                    _, column_name = parent_field.get_attname_column()
                    if column_name.lower() in self.sql.lower():
                        query.resolve_ref(
                            parent_field.name, allow_joins, reuse, summarize
                        )
                        break
        return super().resolve_expression(
            query, allow_joins, reuse, summarize, for_save
        )


class Star(Expression):
    def __repr__(self):
        return "'*'"

    def as_sql(self, compiler, connection):
        return "*", []


class DatabaseDefault(Expression):
    """Placeholder expression for the database default in an insert query."""

    def as_sql(self, compiler, connection):
        return "DEFAULT", []


class Col(Expression):
    contains_column_references = True
    possibly_multivalued = False

    def __init__(self, alias, target, output_field=None):
        if output_field is None:
            output_field = target
        super().__init__(output_field=output_field)
        self.alias, self.target = alias, target

    def __repr__(self):
        alias, target = self.alias, self.target
        identifiers = (alias, str(target)) if alias else (str(target),)
        return "{}({})".format(self.__class__.__name__, ", ".join(identifiers))

    def as_sql(self, compiler, connection):
        alias, column = self.alias, self.target.column
        identifiers = (alias, column) if alias else (column,)
        sql = ".".join(map(compiler.quote_name_unless_alias, identifiers))
        return sql, []

    def relabeled_clone(self, relabels):
        if self.alias is None:
            return self
        return self.__class__(
            relabels.get(self.alias, self.alias), self.target, self.output_field
        )

    def get_group_by_cols(self):
        return [self]

    def get_db_converters(self, connection):
        if self.target == self.output_field:
            return self.output_field.get_db_converters(connection)
        return self.output_field.get_db_converters(
            connection
        ) + self.target.get_db_converters(connection)


class Ref(Expression):
    """
    Reference to column alias of the query. For example, Ref('sum_cost') in
    qs.annotate(sum_cost=Sum('cost')) query.
    """

    def __init__(self, refs, source):
        super().__init__()
        self.refs, self.source = refs, source

    def __repr__(self):
        return "{}({}, {})".format(self.__class__.__name__, self.refs, self.source)

    def get_source_expressions(self):
        return [self.source]

    def set_source_expressions(self, exprs):
        (self.source,) = exprs

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        # The sub-expression `source` has already been resolved, as this is
        # just a reference to the name of `source`.
        return self

    def get_refs(self):
        return {self.refs}

    def relabeled_clone(self, relabels):
        return self

    def as_sql(self, compiler, connection):
        return connection.ops.quote_name(self.refs), []

    def get_group_by_cols(self):
        return [self]


class ExpressionList(Func):
    """
    An expression containing multiple expressions. Can be used to provide a
    list of expressions as an argument to another expression, like a partition
    clause.
    """

    template = "%(expressions)s"

    def __init__(self, *expressions, **extra):
        if not expressions:
            raise ValueError(
                "%s requires at least one expression." % self.__class__.__name__
            )
        super().__init__(*expressions, **extra)

    def __str__(self):
        return self.arg_joiner.join(str(arg) for arg in self.source_expressions)

    def as_sqlite(self, compiler, connection, **extra_context):
        # Casting to numeric is unnecessary.
        return self.as_sql(compiler, connection, **extra_context)


class OrderByList(Func):
    allowed_default = False
    template = "ORDER BY %(expressions)s"

    def __init__(self, *expressions, **extra):
        expressions = (
            (
                OrderBy(F(expr[1:]), descending=True)
                if isinstance(expr, str) and expr[0] == "-"
                else expr
            )
            for expr in expressions
        )
        super().__init__(*expressions, **extra)

    def as_sql(self, *args, **kwargs):
        if not self.source_expressions:
            return "", ()
        return super().as_sql(*args, **kwargs)

    def get_group_by_cols(self):
        group_by_cols = []
        for order_by in self.get_source_expressions():
            group_by_cols.extend(order_by.get_group_by_cols())
        return group_by_cols


@deconstructible(path="django.db.models.ExpressionWrapper")
class ExpressionWrapper(SQLiteNumericMixin, Expression):
    """
    An expression that can wrap another expression so that it can provide
    extra context to the inner expression, such as the output_field.
    """

    def __init__(self, expression, output_field):
        super().__init__(output_field=output_field)
        self.expression = expression

    def set_source_expressions(self, exprs):
        self.expression = exprs[0]

    def get_source_expressions(self):
        return [self.expression]

    def get_group_by_cols(self):
        if isinstance(self.expression, Expression):
            expression = self.expression.copy()
            expression.output_field = self.output_field
            return expression.get_group_by_cols()
        # For non-expressions e.g. an SQL WHERE clause, the entire
        # `expression` must be included in the GROUP BY clause.
        return super().get_group_by_cols()

    def as_sql(self, compiler, connection):
        return compiler.compile(self.expression)

    def __repr__(self):
        return "{}({})".format(self.__class__.__name__, self.expression)

    @property
    def allowed_default(self):
        return self.expression.allowed_default


class NegatedExpression(ExpressionWrapper):
    """The logical negation of a conditional expression."""

    def __init__(self, expression):
        super().__init__(expression, output_field=fields.BooleanField())

    def __invert__(self):
        return self.expression.copy()

    def as_sql(self, compiler, connection):
        try:
            sql, params = super().as_sql(compiler, connection)
        except EmptyResultSet:
            features = compiler.connection.features
            if not features.supports_boolean_expr_in_select_clause:
                return "1=1", ()
            return compiler.compile(Value(True))
        ops = compiler.connection.ops
        # Some database backends (e.g. Oracle) don't allow EXISTS() and filters
        # to be compared to another expression unless they're wrapped in a CASE
        # WHEN.
        if not ops.conditional_expression_supported_in_where_clause(self.expression):
            return f"CASE WHEN {sql} = 0 THEN 1 ELSE 0 END", params
        return f"NOT {sql}", params

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        resolved = super().resolve_expression(
            query, allow_joins, reuse, summarize, for_save
        )
        if not getattr(resolved.expression, "conditional", False):
            raise TypeError("Cannot negate non-conditional expressions.")
        return resolved

    def select_format(self, compiler, sql, params):
        # Wrap boolean expressions with a CASE WHEN expression if a database
        # backend (e.g. Oracle) doesn't support boolean expression in SELECT or
        # GROUP BY list.
        expression_supported_in_where_clause = (
            compiler.connection.ops.conditional_expression_supported_in_where_clause
        )
        if (
            not compiler.connection.features.supports_boolean_expr_in_select_clause
            # Avoid double wrapping.
            and expression_supported_in_where_clause(self.expression)
        ):
            sql = "CASE WHEN {} THEN 1 ELSE 0 END".format(sql)
        return sql, params


@deconstructible(path="django.db.models.When")
class When(Expression):
    template = "WHEN %(condition)s THEN %(result)s"
    # This isn't a complete conditional expression, must be used in Case().
    conditional = False

    def __init__(self, condition=None, then=None, **lookups):
        if lookups:
            if condition is None:
                condition, lookups = Q(**lookups), None
            elif getattr(condition, "conditional", False):
                condition, lookups = Q(condition, **lookups), None
        if condition is None or not getattr(condition, "conditional", False) or lookups:
            raise TypeError(
                "When() supports a Q object, a boolean expression, or lookups "
                "as a condition."
            )
        if isinstance(condition, Q) and not condition:
            raise ValueError("An empty Q() can't be used as a When() condition.")
        super().__init__(output_field=None)
        self.condition = condition
        self.result = self._parse_expressions(then)[0]

    def __str__(self):
        return "WHEN %r THEN %r" % (self.condition, self.result)

    def __repr__(self):
        return "<%s: %s>" % (self.__class__.__name__, self)

    def get_source_expressions(self):
        return [self.condition, self.result]

    def set_source_expressions(self, exprs):
        self.condition, self.result = exprs

    def get_source_fields(self):
        # We're only interested in the fields of the result expressions.
        return [self.result._output_field_or_none]

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        c = self.copy()
        c.is_summary = summarize
        if hasattr(c.condition, "resolve_expression"):
            c.condition = c.condition.resolve_expression(
                query, allow_joins, reuse, summarize, False
            )
        c.result = c.result.resolve_expression(
            query, allow_joins, reuse, summarize, for_save
        )
        return c

    def as_sql(self, compiler, connection, template=None, **extra_context):
        connection.ops.check_expression_support(self)
        template_params = extra_context
        sql_params = []
        condition_sql, condition_params = compiler.compile(self.condition)
        template_params["condition"] = condition_sql
        result_sql, result_params = compiler.compile(self.result)
        template_params["result"] = result_sql
        template = template or self.template
        return template % template_params, (
            *sql_params,
            *condition_params,
            *result_params,
        )

    def get_group_by_cols(self):
        # This is not a complete expression and cannot be used in GROUP BY.
        cols = []
        for source in self.get_source_expressions():
            cols.extend(source.get_group_by_cols())
        return cols

    @cached_property
    def allowed_default(self):
        return self.condition.allowed_default and self.result.allowed_default


@deconstructible(path="django.db.models.Case")
class Case(SQLiteNumericMixin, Expression):
    """
    An SQL searched CASE expression:

        CASE
            WHEN n > 0
                THEN 'positive'
            WHEN n < 0
                THEN 'negative'
            ELSE 'zero'
        END
    """

    template = "CASE %(cases)s ELSE %(default)s END"
    case_joiner = " "

    def __init__(self, *cases, default=None, output_field=None, **extra):
        if not all(isinstance(case, When) for case in cases):
            raise TypeError("Positional arguments must all be When objects.")
        super().__init__(output_field)
        self.cases = list(cases)
        self.default = self._parse_expressions(default)[0]
        self.extra = extra

    def __str__(self):
        return "CASE %s, ELSE %r" % (
            ", ".join(str(c) for c in self.cases),
            self.default,
        )

    def __repr__(self):
        return "<%s: %s>" % (self.__class__.__name__, self)

    def get_source_expressions(self):
        return self.cases + [self.default]

    def set_source_expressions(self, exprs):
        *self.cases, self.default = exprs

    def resolve_expression(
        self, query=None, allow_joins=True, reuse=None, summarize=False, for_save=False
    ):
        c = self.copy()
        c.is_summary = summarize
        for pos, case in enumerate(c.cases):
            c.cases[pos] = case.resolve_expression(
                query, allow_joins, reuse, summarize, for_save
            )
        c.default = c.default.resolve_expression(
            query, allow_joins, reuse, summarize, for_save
        )
        return c

    def copy(self):
        c = super().copy()
        c.cases = c.cases[:]
        return c

    def as_sql(
        self, compiler, connection, template=None, case_joiner=None, **extra_context
    ):
        connection.ops.check_expression_support(self)
        if not self.cases:
            return compiler.compile(self.default)
        template_params = {**self.extra, **extra_context}
        case_parts = []
        sql_params = []
        default_sql, default_params = compiler.compile(self.default)
        for case in self.cases:
            try:
                case_sql, case_params = compiler.compile(case)
            except EmptyResultSet:
                continue
            except FullResultSet:
                default_sql, default_params = compiler.compile(case.result)
                break
            case_parts.append(case_sql)
            sql_params.extend(case_params)
        if not case_parts:
            return default_sql, default_params
        case_joiner = case_joiner or self.case_joiner
        template_params["cases"] = case_joiner.join(case_parts)
        template_params["default"] = default_sql
        sql_params.extend(default_params)
        template = template or template_params.get("template", self.template)
        sql = template % template_params
        if self._output_field_or_none is not None:
            sql = connection.ops.unification_cast_sql(self.output_field) % sql
        return sql, sql_params

    def get_group_by_cols(self):
        if not self.cases:
            return self.default.get_group_by_cols()
        return super().get_group_by_cols()

    @cached_property
    def allowed_default(self):
        return self.default.allowed_default and all(
            case_.allowed_default for case_ in self.cases
        )


class Subquery(BaseExpression, Combinable):
    """
    An explicit subquery. It may contain OuterRef() references to the outer
    query which will be resolved when it is applied to that query.
    """

    template = "(%(subquery)s)"
    contains_aggregate = False
    empty_result_set_value = None
    subquery = True

    def __init__(self, queryset, output_field=None, **extra):
        # Allow the usage of both QuerySet and sql.Query objects.
        self.query = getattr(queryset, "query", queryset).clone()
        self.query.subquery = True
        self.extra = extra
        super().__init__(output_field)

    def get_source_expressions(self):
        return [self.query]

    def set_source_expressions(self, exprs):
        self.query = exprs[0]

    def _resolve_output_field(self):
        return self.query.output_field

    def copy(self):
        clone = super().copy()
        clone.query = clone.query.clone()
        return clone

    @property
    def external_aliases(self):
        return self.query.external_aliases

    def get_external_cols(self):
        return self.query.get_external_cols()

    def as_sql(self, compiler, connection, template=None, **extra_context):
        connection.ops.check_expression_support(self)
        template_params = {**self.extra, **extra_context}
        subquery_sql, sql_params = self.query.as_sql(compiler, connection)
        template_params["subquery"] = subquery_sql[1:-1]

        template = template or template_params.get("template", self.template)
        sql = template % template_params
        return sql, sql_params

    def get_group_by_cols(self):
        return self.query.get_group_by_cols(wrapper=self)


class Exists(Subquery):
    template = "EXISTS(%(subquery)s)"
    output_field = fields.BooleanField()
    empty_result_set_value = False

    def __init__(self, queryset, **kwargs):
        super().__init__(queryset, **kwargs)
        self.query = self.query.exists()

    def select_format(self, compiler, sql, params):
        # Wrap EXISTS() with a CASE WHEN expression if a database backend
        # (e.g. Oracle) doesn't support boolean expression in SELECT or GROUP
        # BY list.
        if not compiler.connection.features.supports_boolean_expr_in_select_clause:
            sql = "CASE WHEN {} THEN 1 ELSE 0 END".format(sql)
        return sql, params


@deconstructible(path="django.db.models.OrderBy")
class OrderBy(Expression):
    template = "%(expression)s %(ordering)s"
    conditional = False

    def __init__(self, expression, descending=False, nulls_first=None, nulls_last=None):
        if nulls_first and nulls_last:
            raise ValueError("nulls_first and nulls_last are mutually exclusive")
        if nulls_first is False or nulls_last is False:
            raise ValueError("nulls_first and nulls_last values must be True or None.")
        self.nulls_first = nulls_first
        self.nulls_last = nulls_last
        self.descending = descending
        if not hasattr(expression, "resolve_expression"):
            raise ValueError("expression must be an expression type")
        self.expression = expression

    def __repr__(self):
        return "{}({}, descending={})".format(
            self.__class__.__name__, self.expression, self.descending
        )

    def set_source_expressions(self, exprs):
        self.expression = exprs[0]

    def get_source_expressions(self):
        return [self.expression]

    def as_sql(self, compiler, connection, template=None, **extra_context):
        template = template or self.template
        if connection.features.supports_order_by_nulls_modifier:
            if self.nulls_last:
                template = "%s NULLS LAST" % template
            elif self.nulls_first:
                template = "%s NULLS FIRST" % template
        else:
            if self.nulls_last and not (
                self.descending and connection.features.order_by_nulls_first
            ):
                template = "%%(expression)s IS NULL, %s" % template
            elif self.nulls_first and not (
                not self.descending and connection.features.order_by_nulls_first
            ):
                template = "%%(expression)s IS NOT NULL, %s" % template
        connection.ops.check_expression_support(self)
        expression_sql, params = compiler.compile(self.expression)
        placeholders = {
            "expression": expression_sql,
            "ordering": "DESC" if self.descending else "ASC",
            **extra_context,
        }
        params *= template.count("%(expression)s")
        return (template % placeholders).rstrip(), params

    def as_oracle(self, compiler, connection):
        # Oracle doesn't allow ORDER BY EXISTS() or filters unless it's wrapped
        # in a CASE WHEN.
        if connection.ops.conditional_expression_supported_in_where_clause(
            self.expression
        ):
            copy = self.copy()
            copy.expression = Case(
                When(self.expression, then=True),
                default=False,
            )
            return copy.as_sql(compiler, connection)
        return self.as_sql(compiler, connection)

    def get_group_by_cols(self):
        cols = []
        for source in self.get_source_expressions():
            cols.extend(source.get_group_by_cols())
        return cols

    def reverse_ordering(self):
        self.descending = not self.descending
        if self.nulls_first:
            self.nulls_last = True
            self.nulls_first = None
        elif self.nulls_last:
            self.nulls_first = True
            self.nulls_last = None
        return self

    def asc(self):
        self.descending = False

    def desc(self):
        self.descending = True


class Window(SQLiteNumericMixin, Expression):
    template = "%(expression)s OVER (%(window)s)"
    # Although the main expression may either be an aggregate or an
    # expression with an aggregate function, the GROUP BY that will
    # be introduced in the query as a result is not desired.
    contains_aggregate = False
    contains_over_clause = True

    def __init__(
        self,
        expression,
        partition_by=None,
        order_by=None,
        frame=None,
        output_field=None,
    ):
        self.partition_by = partition_by
        self.order_by = order_by
        self.frame = frame

        if not getattr(expression, "window_compatible", False):
            raise ValueError(
                "Expression '%s' isn't compatible with OVER clauses."
                % expression.__class__.__name__
            )

        if self.partition_by is not None:
            if not isinstance(self.partition_by, (tuple, list)):
                self.partition_by = (self.partition_by,)
            self.partition_by = ExpressionList(*self.partition_by)

        if self.order_by is not None:
            if isinstance(self.order_by, (list, tuple)):
                self.order_by = OrderByList(*self.order_by)
            elif isinstance(self.order_by, (BaseExpression, str)):
                self.order_by = OrderByList(self.order_by)
            else:
                raise ValueError(
                    "Window.order_by must be either a string reference to a "
                    "field, an expression, or a list or tuple of them."
                )
        super().__init__(output_field=output_field)
        self.source_expression = self._parse_expressions(expression)[0]

    def _resolve_output_field(self):
        return self.source_expression.output_field

    def get_source_expressions(self):
        return [self.source_expression, self.partition_by, self.order_by, self.frame]

    def set_source_expressions(self, exprs):
        self.source_expression, self.partition_by, self.order_by, self.frame = exprs

    def as_sql(self, compiler, connection, template=None):
        connection.ops.check_expression_support(self)
        if not connection.features.supports_over_clause:
            raise NotSupportedError("This backend does not support window expressions.")
        expr_sql, params = compiler.compile(self.source_expression)
        window_sql, window_params = [], ()

        if self.partition_by is not None:
            sql_expr, sql_params = self.partition_by.as_sql(
                compiler=compiler,
                connection=connection,
                template="PARTITION BY %(expressions)s",
            )
            window_sql.append(sql_expr)
            window_params += tuple(sql_params)

        if self.order_by is not None:
            order_sql, order_params = compiler.compile(self.order_by)
            window_sql.append(order_sql)
            window_params += tuple(order_params)

        if self.frame:
            frame_sql, frame_params = compiler.compile(self.frame)
            window_sql.append(frame_sql)
            window_params += tuple(frame_params)

        template = template or self.template

        return (
            template % {"expression": expr_sql, "window": " ".join(window_sql).strip()},
            (*params, *window_params),
        )

    def as_sqlite(self, compiler, connection):
        if isinstance(self.output_field, fields.DecimalField):
            # Casting to numeric must be outside of the window expression.
            copy = self.copy()
            source_expressions = copy.get_source_expressions()
            source_expressions[0].output_field = fields.FloatField()
            copy.set_source_expressions(source_expressions)
            return super(Window, copy).as_sqlite(compiler, connection)
        return self.as_sql(compiler, connection)

    def __str__(self):
        return "{} OVER ({}{}{})".format(
            str(self.source_expression),
            "PARTITION BY " + str(self.partition_by) if self.partition_by else "",
            str(self.order_by or ""),
            str(self.frame or ""),
        )

    def __repr__(self):
        return "<%s: %s>" % (self.__class__.__name__, self)

    def get_group_by_cols(self):
        group_by_cols = []
        if self.partition_by:
            group_by_cols.extend(self.partition_by.get_group_by_cols())
        if self.order_by is not None:
            group_by_cols.extend(self.order_by.get_group_by_cols())
        return group_by_cols


class WindowFrame(Expression):
    """
    Model the frame clause in window expressions. There are two types of frame
    clauses which are subclasses, however, all processing and validation (by no
    means intended to be complete) is done here. Thus, providing an end for a
    frame is optional (the default is UNBOUNDED FOLLOWING, which is the last
    row in the frame).
    """

    template = "%(frame_type)s BETWEEN %(start)s AND %(end)s"

    def __init__(self, start=None, end=None):
        self.start = Value(start)
        self.end = Value(end)

    def set_source_expressions(self, exprs):
        self.start, self.end = exprs

    def get_source_expressions(self):
        return [self.start, self.end]

    def as_sql(self, compiler, connection):
        connection.ops.check_expression_support(self)
        start, end = self.window_frame_start_end(
            connection, self.start.value, self.end.value
        )
        return (
            self.template
            % {
                "frame_type": self.frame_type,
                "start": start,
                "end": end,
            },
            [],
        )

    def __repr__(self):
        return "<%s: %s>" % (self.__class__.__name__, self)

    def get_group_by_cols(self):
        return []

    def __str__(self):
        if self.start.value is not None and self.start.value < 0:
            start = "%d %s" % (abs(self.start.value), connection.ops.PRECEDING)
        elif self.start.value is not None and self.start.value == 0:
            start = connection.ops.CURRENT_ROW
        else:
            start = connection.ops.UNBOUNDED_PRECEDING

        if self.end.value is not None and self.end.value > 0:
            end = "%d %s" % (self.end.value, connection.ops.FOLLOWING)
        elif self.end.value is not None and self.end.value == 0:
            end = connection.ops.CURRENT_ROW
        else:
            end = connection.ops.UNBOUNDED_FOLLOWING
        return self.template % {
            "frame_type": self.frame_type,
            "start": start,
            "end": end,
        }

    def window_frame_start_end(self, connection, start, end):
        raise NotImplementedError("Subclasses must implement window_frame_start_end().")


class RowRange(WindowFrame):
    frame_type = "ROWS"

    def window_frame_start_end(self, connection, start, end):
        return connection.ops.window_frame_rows_start_end(start, end)


class ValueRange(WindowFrame):
    frame_type = "RANGE"

    def window_frame_start_end(self, connection, start, end):
        return connection.ops.window_frame_range_start_end(start, end)