# Django 2.2.9.dev20191202104323 文档

# django.db.models.functions.math 源代码

    import math

    from django.db.models.expressions import Func
    from django.db.models.fields import FloatField, IntegerField
    from django.db.models.functions import Cast
    from django.db.models.functions.mixins import (
        FixDecimalInputMixin, NumericOutputFieldMixin,
    )
    from django.db.models.lookups import Transform

    class Abs(Transform):
        function = 'ABS'
        lookup_name = 'abs'

    class ACos(NumericOutputFieldMixin, Transform):
        function = 'ACOS'
        lookup_name = 'acos'

    class ASin(NumericOutputFieldMixin, Transform):
        function = 'ASIN'
        lookup_name = 'asin'

    class ATan(NumericOutputFieldMixin, Transform):
        function = 'ATAN'
        lookup_name = 'atan'

    class ATan2(NumericOutputFieldMixin, Func):
        function = 'ATAN2'
        arity = 2

        def as_sqlite(self, compiler, connection, **extra_context):
            if not getattr(connection.ops, 'spatialite', False) or not (
                (4, 3, 0) <= connection.ops.spatial_version < (5, 0, 0)
            ):
                return self.as_sql(compiler, connection)
            # This function is usually ATan2(y, x), returning the inverse tangent
            # of y / x, but it's ATan2(x, y) on SpatiaLite >= 4.3.0, < 5.0.0.
            # Cast integers to float to avoid inconsistent/buggy behavior if the
            # arguments are mixed between integer and float or decimal.
            # https://www.gaia-gis.it/fossil/libspatialite/tktview?name=0f72cca3a2
            clone = self.copy()
            clone.set_source_expressions([
                Cast(expression, FloatField()) if isinstance(expression.output_field, IntegerField)
                else expression for expression in self.get_source_expressions()[::-1]
            ])
            return clone.as_sql(compiler, connection, **extra_context)

    class Ceil(Transform):
        function = 'CEILING'
        lookup_name = 'ceil'

        def as_oracle(self, compiler, connection, **extra_context):
            return super().as_sql(compiler, connection, function='CEIL', **extra_context)

    class Cos(NumericOutputFieldMixin, Transform):
        function = 'COS'
        lookup_name = 'cos'

    class Cot(NumericOutputFieldMixin, Transform):
        function = 'COT'
        lookup_name = 'cot'

        def as_oracle(self, compiler, connection, **extra_context):
            return super().as_sql(compiler, connection, template='(1 / TAN(%(expressions)s))', **extra_context)

    class Degrees(NumericOutputFieldMixin, Transform):
        function = 'DEGREES'
        lookup_name = 'degrees'

        def as_oracle(self, compiler, connection, **extra_context):
            return super().as_sql(
                compiler, connection,
                template='((%%(expressions)s) * 180 / %s)' % math.pi,
                **extra_context
            )

    class Exp(NumericOutputFieldMixin, Transform):
        function = 'EXP'
        lookup_name = 'exp'

    class Floor(Transform):
        function = 'FLOOR'
        lookup_name = 'floor'

    class Ln(NumericOutputFieldMixin, Transform):
        function = 'LN'
        lookup_name = 'ln'

    class Log(FixDecimalInputMixin, NumericOutputFieldMixin, Func):
        function = 'LOG'
        arity = 2

        def as_sqlite(self, compiler, connection, **extra_context):
            if not getattr(connection.ops, 'spatialite', False):
                return self.as_sql(compiler, connection)
            # This function is usually Log(b, x) returning the logarithm of x to
            # the base b, but on SpatiaLite it's Log(x, b).
            clone = self.copy()
            clone.set_source_expressions(self.get_source_expressions()[::-1])
            return clone.as_sql(compiler, connection, **extra_context)

    class Mod(FixDecimalInputMixin, NumericOutputFieldMixin, Func):
        function = 'MOD'
        arity = 2

    class Pi(NumericOutputFieldMixin, Func):
        function = 'PI'
        arity = 0

        def as_oracle(self, compiler, connection, **extra_context):
            return super().as_sql(compiler, connection, template=str(math.pi), **extra_context)

    class Power(NumericOutputFieldMixin, Func):
        function = 'POWER'
        arity = 2

    class Radians(NumericOutputFieldMixin, Transform):
        function = 'RADIANS'
        lookup_name = 'radians'

        def as_oracle(self, compiler, connection, **extra_context):
            return super().as_sql(
                compiler, connection,
                template='((%%(expressions)s) * %s / 180)' % math.pi,
                **extra_context
            )

    class Round(Transform):
        function = 'ROUND'
        lookup_name = 'round'

    class Sin(NumericOutputFieldMixin, Transform):
        function = 'SIN'
        lookup_name = 'sin'

    class Sqrt(NumericOutputFieldMixin, Transform):
        function = 'SQRT'
        lookup_name = 'sqrt'

    class Tan(NumericOutputFieldMixin, Transform):
        function = 'TAN'
        lookup_name = 'tan'