cpython/Lib/test/test_decimal.py

# Copyright (c) 2004 Python Software Foundation.
# All rights reserved.

# Written by Eric Price <eprice at tjhsst.edu>
#    and Facundo Batista <facundo at taniquetil.com.ar>
#    and Raymond Hettinger <python at rcn.com>
#    and Aahz (aahz at pobox.com)
#    and Tim Peters

"""
These are the test cases for the Decimal module.

There are two groups of tests, Arithmetic and Behaviour. The former test
the Decimal arithmetic using the tests provided by Mike Cowlishaw. The latter
test the pythonic behaviour according to PEP 327.

Cowlishaw's tests can be downloaded from:

   http://speleotrove.com/decimal/dectest.zip

This test module can be called from command line with one parameter (Arithmetic
or Behaviour) to test each part, or without parameter to test both parts. If
you're working through IDLE, you can import this test module and call test()
with the corresponding argument.
"""

import math
import os, sys
import operator
import warnings
import pickle, copy
import unittest
import numbers
import locale
from test.support import (is_resource_enabled,
                          requires_IEEE_754, requires_docstrings,
                          check_disallow_instantiation)
from test.support import (TestFailed,
                          run_with_locale, cpython_only,
                          darwin_malloc_err_warning)
from test.support.import_helper import import_fresh_module
from test.support import threading_helper
from test.support import warnings_helper
import random
import inspect
import threading


if sys.platform == 'darwin':
    darwin_malloc_err_warning('test_decimal')


C = import_fresh_module('decimal', fresh=['_decimal'])
P = import_fresh_module('decimal', blocked=['_decimal'])
import decimal as orig_sys_decimal

# fractions module must import the correct decimal module.
cfractions = import_fresh_module('fractions', fresh=['fractions'])
sys.modules['decimal'] = P
pfractions = import_fresh_module('fractions', fresh=['fractions'])
sys.modules['decimal'] = C
fractions = {C:cfractions, P:pfractions}
sys.modules['decimal'] = orig_sys_decimal

requires_cdecimal = unittest.skipUnless(C, "test requires C version")

# Useful Test Constant
Signals = {
  C: tuple(C.getcontext().flags.keys()) if C else None,
  P: tuple(P.getcontext().flags.keys())
}
# Signals ordered with respect to precedence: when an operation
# produces multiple signals, signals occurring later in the list
# should be handled before those occurring earlier in the list.
OrderedSignals = {
  C: [C.Clamped, C.Rounded, C.Inexact, C.Subnormal, C.Underflow,
      C.Overflow, C.DivisionByZero, C.InvalidOperation,
      C.FloatOperation] if C else None,
  P: [P.Clamped, P.Rounded, P.Inexact, P.Subnormal, P.Underflow,
      P.Overflow, P.DivisionByZero, P.InvalidOperation,
      P.FloatOperation]
}
def assert_signals(cls, context, attr, expected):
    d = getattr(context, attr)
    cls.assertTrue(all(d[s] if s in expected else not d[s] for s in d))

ROUND_UP = P.ROUND_UP
ROUND_DOWN = P.ROUND_DOWN
ROUND_CEILING = P.ROUND_CEILING
ROUND_FLOOR = P.ROUND_FLOOR
ROUND_HALF_UP = P.ROUND_HALF_UP
ROUND_HALF_DOWN = P.ROUND_HALF_DOWN
ROUND_HALF_EVEN = P.ROUND_HALF_EVEN
ROUND_05UP = P.ROUND_05UP

RoundingModes = [
  ROUND_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR,
  ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_HALF_EVEN,
  ROUND_05UP
]

# Tests are built around these assumed context defaults.
# test() restores the original context.
ORIGINAL_CONTEXT = {
  C: C.getcontext().copy() if C else None,
  P: P.getcontext().copy()
}
def init(m):
    if not m: return
    DefaultTestContext = m.Context(
       prec=9, rounding=ROUND_HALF_EVEN, traps=dict.fromkeys(Signals[m], 0)
    )
    m.setcontext(DefaultTestContext)

TESTDATADIR = 'decimaltestdata'
if __name__ == '__main__':
    file = sys.argv[0]
else:
    file = __file__
testdir = os.path.dirname(file) or os.curdir
directory = testdir + os.sep + TESTDATADIR + os.sep

skip_expected = not os.path.isdir(directory)

# Make sure it actually raises errors when not expected and caught in flags
# Slower, since it runs some things several times.
EXTENDEDERRORTEST = False

# Test extra functionality in the C version (-DEXTRA_FUNCTIONALITY).
EXTRA_FUNCTIONALITY = True if hasattr(C, 'DecClamped') else False
requires_extra_functionality = unittest.skipUnless(
  EXTRA_FUNCTIONALITY, "test requires build with -DEXTRA_FUNCTIONALITY")
skip_if_extra_functionality = unittest.skipIf(
  EXTRA_FUNCTIONALITY, "test requires regular build")


class IBMTestCases:
    """Class which tests the Decimal class against the IBM test cases."""

    def setUp(self):
        self.context = self.decimal.Context()
        self.readcontext = self.decimal.Context()
        self.ignore_list = ['#']

        # List of individual .decTest test ids that correspond to tests that
        # we're skipping for one reason or another.
        self.skipped_test_ids = set([
            # Skip implementation-specific scaleb tests.
            'scbx164',
            'scbx165',

            # For some operations (currently exp, ln, log10, power), the decNumber
            # reference implementation imposes additional restrictions on the context
            # and operands.  These restrictions are not part of the specification;
            # however, the effect of these restrictions does show up in some of the
            # testcases.  We skip testcases that violate these restrictions, since
            # Decimal behaves differently from decNumber for these testcases so these
            # testcases would otherwise fail.
            'expx901',
            'expx902',
            'expx903',
            'expx905',
            'lnx901',
            'lnx902',
            'lnx903',
            'lnx905',
            'logx901',
            'logx902',
            'logx903',
            'logx905',
            'powx1183',
            'powx1184',
            'powx4001',
            'powx4002',
            'powx4003',
            'powx4005',
            'powx4008',
            'powx4010',
            'powx4012',
            'powx4014',
            ])

        if self.decimal == C:
            # status has additional Subnormal, Underflow
            self.skipped_test_ids.add('pwsx803')
            self.skipped_test_ids.add('pwsx805')
            # Correct rounding (skipped for decNumber, too)
            self.skipped_test_ids.add('powx4302')
            self.skipped_test_ids.add('powx4303')
            self.skipped_test_ids.add('powx4342')
            self.skipped_test_ids.add('powx4343')
            # http://bugs.python.org/issue7049
            self.skipped_test_ids.add('pwmx325')
            self.skipped_test_ids.add('pwmx326')

        # Map test directives to setter functions.
        self.ChangeDict = {'precision' : self.change_precision,
                           'rounding' : self.change_rounding_method,
                           'maxexponent' : self.change_max_exponent,
                           'minexponent' : self.change_min_exponent,
                           'clamp' : self.change_clamp}

        # Name adapter to be able to change the Decimal and Context
        # interface without changing the test files from Cowlishaw.
        self.NameAdapter = {'and':'logical_and',
                            'apply':'_apply',
                            'class':'number_class',
                            'comparesig':'compare_signal',
                            'comparetotal':'compare_total',
                            'comparetotmag':'compare_total_mag',
                            'copy':'copy_decimal',
                            'copyabs':'copy_abs',
                            'copynegate':'copy_negate',
                            'copysign':'copy_sign',
                            'divideint':'divide_int',
                            'invert':'logical_invert',
                            'iscanonical':'is_canonical',
                            'isfinite':'is_finite',
                            'isinfinite':'is_infinite',
                            'isnan':'is_nan',
                            'isnormal':'is_normal',
                            'isqnan':'is_qnan',
                            'issigned':'is_signed',
                            'issnan':'is_snan',
                            'issubnormal':'is_subnormal',
                            'iszero':'is_zero',
                            'maxmag':'max_mag',
                            'minmag':'min_mag',
                            'nextminus':'next_minus',
                            'nextplus':'next_plus',
                            'nexttoward':'next_toward',
                            'or':'logical_or',
                            'reduce':'normalize',
                            'remaindernear':'remainder_near',
                            'samequantum':'same_quantum',
                            'squareroot':'sqrt',
                            'toeng':'to_eng_string',
                            'tointegral':'to_integral_value',
                            'tointegralx':'to_integral_exact',
                            'tosci':'to_sci_string',
                            'xor':'logical_xor'}

        # Map test-case names to roundings.
        self.RoundingDict = {'ceiling' : ROUND_CEILING,
                             'down' : ROUND_DOWN,
                             'floor' : ROUND_FLOOR,
                             'half_down' : ROUND_HALF_DOWN,
                             'half_even' : ROUND_HALF_EVEN,
                             'half_up' : ROUND_HALF_UP,
                             'up' : ROUND_UP,
                             '05up' : ROUND_05UP}

        # Map the test cases' error names to the actual errors.
        self.ErrorNames = {'clamped' : self.decimal.Clamped,
                           'conversion_syntax' : self.decimal.InvalidOperation,
                           'division_by_zero' : self.decimal.DivisionByZero,
                           'division_impossible' : self.decimal.InvalidOperation,
                           'division_undefined' : self.decimal.InvalidOperation,
                           'inexact' : self.decimal.Inexact,
                           'invalid_context' : self.decimal.InvalidOperation,
                           'invalid_operation' : self.decimal.InvalidOperation,
                           'overflow' : self.decimal.Overflow,
                           'rounded' : self.decimal.Rounded,
                           'subnormal' : self.decimal.Subnormal,
                           'underflow' : self.decimal.Underflow}

        # The following functions return True/False rather than a
        # Decimal instance.
        self.LogicalFunctions = ('is_canonical',
                                 'is_finite',
                                 'is_infinite',
                                 'is_nan',
                                 'is_normal',
                                 'is_qnan',
                                 'is_signed',
                                 'is_snan',
                                 'is_subnormal',
                                 'is_zero',
                                 'same_quantum')

    def read_unlimited(self, v, context):
        """Work around the limitations of the 32-bit _decimal version. The
           guaranteed maximum values for prec, Emax etc. are 425000000,
           but higher values usually work, except for rare corner cases.
           In particular, all of the IBM tests pass with maximum values
           of 1070000000."""
        if self.decimal == C and self.decimal.MAX_EMAX == 425000000:
            self.readcontext._unsafe_setprec(1070000000)
            self.readcontext._unsafe_setemax(1070000000)
            self.readcontext._unsafe_setemin(-1070000000)
            return self.readcontext.create_decimal(v)
        else:
            return self.decimal.Decimal(v, context)

    def eval_file(self, file):
        global skip_expected
        if skip_expected:
            raise unittest.SkipTest
        with open(file, encoding="utf-8") as f:
            for line in f:
                line = line.replace('\r\n', '').replace('\n', '')
                #print line
                try:
                    t = self.eval_line(line)
                except self.decimal.DecimalException as exception:
                    #Exception raised where there shouldn't have been one.
                    self.fail('Exception "'+exception.__class__.__name__ + '" raised on line '+line)


    def eval_line(self, s):
        if s.find(' -> ') >= 0 and s[:2] != '--' and not s.startswith('  --'):
            s = (s.split('->')[0] + '->' +
                 s.split('->')[1].split('--')[0]).strip()
        else:
            s = s.split('--')[0].strip()

        for ignore in self.ignore_list:
            if s.find(ignore) >= 0:
                #print s.split()[0], 'NotImplemented--', ignore
                return
        if not s:
            return
        elif ':' in s:
            return self.eval_directive(s)
        else:
            return self.eval_equation(s)

    def eval_directive(self, s):
        funct, value = (x.strip().lower() for x in s.split(':'))
        if funct == 'rounding':
            value = self.RoundingDict[value]
        else:
            try:
                value = int(value)
            except ValueError:
                pass

        funct = self.ChangeDict.get(funct, (lambda *args: None))
        funct(value)

    def eval_equation(self, s):

        if not TEST_ALL and random.random() < 0.90:
            return

        self.context.clear_flags()

        try:
            Sides = s.split('->')
            L = Sides[0].strip().split()
            id = L[0]
            if DEBUG:
                print("Test ", id, end=" ")
            funct = L[1].lower()
            valstemp = L[2:]
            L = Sides[1].strip().split()
            ans = L[0]
            exceptions = L[1:]
        except (TypeError, AttributeError, IndexError):
            raise self.decimal.InvalidOperation
        def FixQuotes(val):
            val = val.replace("''", 'SingleQuote').replace('""', 'DoubleQuote')
            val = val.replace("'", '').replace('"', '')
            val = val.replace('SingleQuote', "'").replace('DoubleQuote', '"')
            return val

        if id in self.skipped_test_ids:
            return

        fname = self.NameAdapter.get(funct, funct)
        if fname == 'rescale':
            return
        funct = getattr(self.context, fname)
        vals = []
        conglomerate = ''
        quote = 0
        theirexceptions = [self.ErrorNames[x.lower()] for x in exceptions]

        for exception in Signals[self.decimal]:
            self.context.traps[exception] = 1 #Catch these bugs...
        for exception in theirexceptions:
            self.context.traps[exception] = 0
        for i, val in enumerate(valstemp):
            if val.count("'") % 2 == 1:
                quote = 1 - quote
            if quote:
                conglomerate = conglomerate + ' ' + val
                continue
            else:
                val = conglomerate + val
                conglomerate = ''
            v = FixQuotes(val)
            if fname in ('to_sci_string', 'to_eng_string'):
                if EXTENDEDERRORTEST:
                    for error in theirexceptions:
                        self.context.traps[error] = 1
                        try:
                            funct(self.context.create_decimal(v))
                        except error:
                            pass
                        except Signals[self.decimal] as e:
                            self.fail("Raised %s in %s when %s disabled" % \
                                      (e, s, error))
                        else:
                            self.fail("Did not raise %s in %s" % (error, s))
                        self.context.traps[error] = 0
                v = self.context.create_decimal(v)
            else:
                v = self.read_unlimited(v, self.context)
            vals.append(v)

        ans = FixQuotes(ans)

        if EXTENDEDERRORTEST and fname not in ('to_sci_string', 'to_eng_string'):
            for error in theirexceptions:
                self.context.traps[error] = 1
                try:
                    funct(*vals)
                except error:
                    pass
                except Signals[self.decimal] as e:
                    self.fail("Raised %s in %s when %s disabled" % \
                              (e, s, error))
                else:
                    self.fail("Did not raise %s in %s" % (error, s))
                self.context.traps[error] = 0

            # as above, but add traps cumulatively, to check precedence
            ordered_errors = [e for e in OrderedSignals[self.decimal] if e in theirexceptions]
            for error in ordered_errors:
                self.context.traps[error] = 1
                try:
                    funct(*vals)
                except error:
                    pass
                except Signals[self.decimal] as e:
                    self.fail("Raised %s in %s; expected %s" %
                              (type(e), s, error))
                else:
                    self.fail("Did not raise %s in %s" % (error, s))
            # reset traps
            for error in ordered_errors:
                self.context.traps[error] = 0


        if DEBUG:
            print("--", self.context)
        try:
            result = str(funct(*vals))
            if fname in self.LogicalFunctions:
                result = str(int(eval(result))) # 'True', 'False' -> '1', '0'
        except Signals[self.decimal] as error:
            self.fail("Raised %s in %s" % (error, s))
        except: #Catch any error long enough to state the test case.
            print("ERROR:", s)
            raise

        myexceptions = self.getexceptions()

        myexceptions.sort(key=repr)
        theirexceptions.sort(key=repr)

        self.assertEqual(result, ans,
                         'Incorrect answer for ' + s + ' -- got ' + result)

        self.assertEqual(myexceptions, theirexceptions,
              'Incorrect flags set in ' + s + ' -- got ' + str(myexceptions))

    def getexceptions(self):
        return [e for e in Signals[self.decimal] if self.context.flags[e]]

    def change_precision(self, prec):
        if self.decimal == C and self.decimal.MAX_PREC == 425000000:
            self.context._unsafe_setprec(prec)
        else:
            self.context.prec = prec
    def change_rounding_method(self, rounding):
        self.context.rounding = rounding
    def change_min_exponent(self, exp):
        if self.decimal == C and self.decimal.MAX_PREC == 425000000:
            self.context._unsafe_setemin(exp)
        else:
            self.context.Emin = exp
    def change_max_exponent(self, exp):
        if self.decimal == C and self.decimal.MAX_PREC == 425000000:
            self.context._unsafe_setemax(exp)
        else:
            self.context.Emax = exp
    def change_clamp(self, clamp):
        self.context.clamp = clamp


# The following classes test the behaviour of Decimal according to PEP 327

class ExplicitConstructionTest:
    '''Unit tests for Explicit Construction cases of Decimal.'''

    def test_explicit_empty(self):
        Decimal = self.decimal.Decimal
        self.assertEqual(Decimal(), Decimal("0"))

    def test_explicit_from_None(self):
        Decimal = self.decimal.Decimal
        self.assertRaises(TypeError, Decimal, None)

    def test_explicit_from_int(self):
        Decimal = self.decimal.Decimal

        #positive
        d = Decimal(45)
        self.assertEqual(str(d), '45')

        #very large positive
        d = Decimal(500000123)
        self.assertEqual(str(d), '500000123')

        #negative
        d = Decimal(-45)
        self.assertEqual(str(d), '-45')

        #zero
        d = Decimal(0)
        self.assertEqual(str(d), '0')

        # single word longs
        for n in range(0, 32):
            for sign in (-1, 1):
                for x in range(-5, 5):
                    i = sign * (2**n + x)
                    d = Decimal(i)
                    self.assertEqual(str(d), str(i))

    def test_explicit_from_string(self):
        Decimal = self.decimal.Decimal
        InvalidOperation = self.decimal.InvalidOperation
        localcontext = self.decimal.localcontext

        #empty
        self.assertEqual(str(Decimal('')), 'NaN')

        #int
        self.assertEqual(str(Decimal('45')), '45')

        #float
        self.assertEqual(str(Decimal('45.34')), '45.34')

        #engineer notation
        self.assertEqual(str(Decimal('45e2')), '4.5E+3')

        #just not a number
        self.assertEqual(str(Decimal('ugly')), 'NaN')

        #leading and trailing whitespace permitted
        self.assertEqual(str(Decimal('1.3E4 \n')), '1.3E+4')
        self.assertEqual(str(Decimal('  -7.89')), '-7.89')
        self.assertEqual(str(Decimal("  3.45679  ")), '3.45679')

        # underscores
        self.assertEqual(str(Decimal('1_3.3e4_0')), '1.33E+41')
        self.assertEqual(str(Decimal('1_0_0_0')), '1000')

        # unicode whitespace
        for lead in ["", ' ', '\u00a0', '\u205f']:
            for trail in ["", ' ', '\u00a0', '\u205f']:
                self.assertEqual(str(Decimal(lead + '9.311E+28' + trail)),
                                 '9.311E+28')

        with localcontext() as c:
            c.traps[InvalidOperation] = True
            # Invalid string
            self.assertRaises(InvalidOperation, Decimal, "xyz")
            # Two arguments max
            self.assertRaises(TypeError, Decimal, "1234", "x", "y")

            # space within the numeric part
            self.assertRaises(InvalidOperation, Decimal, "1\u00a02\u00a03")
            self.assertRaises(InvalidOperation, Decimal, "\u00a01\u00a02\u00a0")

            # unicode whitespace
            self.assertRaises(InvalidOperation, Decimal, "\u00a0")
            self.assertRaises(InvalidOperation, Decimal, "\u00a0\u00a0")

            # embedded NUL
            self.assertRaises(InvalidOperation, Decimal, "12\u00003")

            # underscores don't prevent errors
            self.assertRaises(InvalidOperation, Decimal, "1_2_\u00003")

    def test_explicit_from_tuples(self):
        Decimal = self.decimal.Decimal

        #zero
        d = Decimal( (0, (0,), 0) )
        self.assertEqual(str(d), '0')

        #int
        d = Decimal( (1, (4, 5), 0) )
        self.assertEqual(str(d), '-45')

        #float
        d = Decimal( (0, (4, 5, 3, 4), -2) )
        self.assertEqual(str(d), '45.34')

        #weird
        d = Decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) )
        self.assertEqual(str(d), '-4.34913534E-17')

        #inf
        d = Decimal( (0, (), "F") )
        self.assertEqual(str(d), 'Infinity')

        #wrong number of items
        self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 9, 1)) )

        #bad sign
        self.assertRaises(ValueError, Decimal, (8, (4, 3, 4, 9, 1), 2) )
        self.assertRaises(ValueError, Decimal, (0., (4, 3, 4, 9, 1), 2) )
        self.assertRaises(ValueError, Decimal, (Decimal(1), (4, 3, 4, 9, 1), 2))

        #bad exp
        self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 9, 1), 'wrong!') )
        self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 9, 1), 0.) )
        self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 9, 1), '1') )

        #bad coefficients
        self.assertRaises(ValueError, Decimal, (1, "xyz", 2) )
        self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, None, 1), 2) )
        self.assertRaises(ValueError, Decimal, (1, (4, -3, 4, 9, 1), 2) )
        self.assertRaises(ValueError, Decimal, (1, (4, 10, 4, 9, 1), 2) )
        self.assertRaises(ValueError, Decimal, (1, (4, 3, 4, 'a', 1), 2) )

    def test_explicit_from_list(self):
        Decimal = self.decimal.Decimal

        d = Decimal([0, [0], 0])
        self.assertEqual(str(d), '0')

        d = Decimal([1, [4, 3, 4, 9, 1, 3, 5, 3, 4], -25])
        self.assertEqual(str(d), '-4.34913534E-17')

        d = Decimal([1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25])
        self.assertEqual(str(d), '-4.34913534E-17')

        d = Decimal((1, [4, 3, 4, 9, 1, 3, 5, 3, 4], -25))
        self.assertEqual(str(d), '-4.34913534E-17')

    def test_explicit_from_bool(self):
        Decimal = self.decimal.Decimal

        self.assertIs(bool(Decimal(0)), False)
        self.assertIs(bool(Decimal(1)), True)
        self.assertEqual(Decimal(False), Decimal(0))
        self.assertEqual(Decimal(True), Decimal(1))

    def test_explicit_from_Decimal(self):
        Decimal = self.decimal.Decimal

        #positive
        d = Decimal(45)
        e = Decimal(d)
        self.assertEqual(str(e), '45')

        #very large positive
        d = Decimal(500000123)
        e = Decimal(d)
        self.assertEqual(str(e), '500000123')

        #negative
        d = Decimal(-45)
        e = Decimal(d)
        self.assertEqual(str(e), '-45')

        #zero
        d = Decimal(0)
        e = Decimal(d)
        self.assertEqual(str(e), '0')

    @requires_IEEE_754
    def test_explicit_from_float(self):

        Decimal = self.decimal.Decimal

        r = Decimal(0.1)
        self.assertEqual(type(r), Decimal)
        self.assertEqual(str(r),
                '0.1000000000000000055511151231257827021181583404541015625')
        self.assertTrue(Decimal(float('nan')).is_qnan())
        self.assertTrue(Decimal(float('inf')).is_infinite())
        self.assertTrue(Decimal(float('-inf')).is_infinite())
        self.assertEqual(str(Decimal(float('nan'))),
                         str(Decimal('NaN')))
        self.assertEqual(str(Decimal(float('inf'))),
                         str(Decimal('Infinity')))
        self.assertEqual(str(Decimal(float('-inf'))),
                         str(Decimal('-Infinity')))
        self.assertEqual(str(Decimal(float('-0.0'))),
                         str(Decimal('-0')))
        for i in range(200):
            x = random.expovariate(0.01) * (random.random() * 2.0 - 1.0)
            self.assertEqual(x, float(Decimal(x))) # roundtrip

    def test_explicit_context_create_decimal(self):
        Decimal = self.decimal.Decimal
        InvalidOperation = self.decimal.InvalidOperation
        Rounded = self.decimal.Rounded

        nc = copy.copy(self.decimal.getcontext())
        nc.prec = 3

        # empty
        d = Decimal()
        self.assertEqual(str(d), '0')
        d = nc.create_decimal()
        self.assertEqual(str(d), '0')

        # from None
        self.assertRaises(TypeError, nc.create_decimal, None)

        # from int
        d = nc.create_decimal(456)
        self.assertIsInstance(d, Decimal)
        self.assertEqual(nc.create_decimal(45678),
                         nc.create_decimal('457E+2'))

        # from string
        d = Decimal('456789')
        self.assertEqual(str(d), '456789')
        d = nc.create_decimal('456789')
        self.assertEqual(str(d), '4.57E+5')
        # leading and trailing whitespace should result in a NaN;
        # spaces are already checked in Cowlishaw's test-suite, so
        # here we just check that a trailing newline results in a NaN
        self.assertEqual(str(nc.create_decimal('3.14\n')), 'NaN')

        # from tuples
        d = Decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) )
        self.assertEqual(str(d), '-4.34913534E-17')
        d = nc.create_decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) )
        self.assertEqual(str(d), '-4.35E-17')

        # from Decimal
        prevdec = Decimal(500000123)
        d = Decimal(prevdec)
        self.assertEqual(str(d), '500000123')
        d = nc.create_decimal(prevdec)
        self.assertEqual(str(d), '5.00E+8')

        # more integers
        nc.prec = 28
        nc.traps[InvalidOperation] = True

        for v in [-2**63-1, -2**63, -2**31-1, -2**31, 0,
                   2**31-1, 2**31, 2**63-1, 2**63]:
            d = nc.create_decimal(v)
            self.assertTrue(isinstance(d, Decimal))
            self.assertEqual(int(d), v)

        nc.prec = 3
        nc.traps[Rounded] = True
        self.assertRaises(Rounded, nc.create_decimal, 1234)

        # from string
        nc.prec = 28
        self.assertEqual(str(nc.create_decimal('0E-017')), '0E-17')
        self.assertEqual(str(nc.create_decimal('45')), '45')
        self.assertEqual(str(nc.create_decimal('-Inf')), '-Infinity')
        self.assertEqual(str(nc.create_decimal('NaN123')), 'NaN123')

        # invalid arguments
        self.assertRaises(InvalidOperation, nc.create_decimal, "xyz")
        self.assertRaises(ValueError, nc.create_decimal, (1, "xyz", -25))
        self.assertRaises(TypeError, nc.create_decimal, "1234", "5678")
        # no whitespace and underscore stripping is done with this method
        self.assertRaises(InvalidOperation, nc.create_decimal, " 1234")
        self.assertRaises(InvalidOperation, nc.create_decimal, "12_34")

        # too many NaN payload digits
        nc.prec = 3
        self.assertRaises(InvalidOperation, nc.create_decimal, 'NaN12345')
        self.assertRaises(InvalidOperation, nc.create_decimal,
                          Decimal('NaN12345'))

        nc.traps[InvalidOperation] = False
        self.assertEqual(str(nc.create_decimal('NaN12345')), 'NaN')
        self.assertTrue(nc.flags[InvalidOperation])

        nc.flags[InvalidOperation] = False
        self.assertEqual(str(nc.create_decimal(Decimal('NaN12345'))), 'NaN')
        self.assertTrue(nc.flags[InvalidOperation])

    def test_explicit_context_create_from_float(self):

        Decimal = self.decimal.Decimal

        nc = self.decimal.Context()
        r = nc.create_decimal(0.1)
        self.assertEqual(type(r), Decimal)
        self.assertEqual(str(r), '0.1000000000000000055511151231')
        self.assertTrue(nc.create_decimal(float('nan')).is_qnan())
        self.assertTrue(nc.create_decimal(float('inf')).is_infinite())
        self.assertTrue(nc.create_decimal(float('-inf')).is_infinite())
        self.assertEqual(str(nc.create_decimal(float('nan'))),
                         str(nc.create_decimal('NaN')))
        self.assertEqual(str(nc.create_decimal(float('inf'))),
                         str(nc.create_decimal('Infinity')))
        self.assertEqual(str(nc.create_decimal(float('-inf'))),
                         str(nc.create_decimal('-Infinity')))
        self.assertEqual(str(nc.create_decimal(float('-0.0'))),
                         str(nc.create_decimal('-0')))
        nc.prec = 100
        for i in range(200):
            x = random.expovariate(0.01) * (random.random() * 2.0 - 1.0)
            self.assertEqual(x, float(nc.create_decimal(x))) # roundtrip

    def test_unicode_digits(self):
        Decimal = self.decimal.Decimal

        test_values = {
            '\uff11': '1',
            '\u0660.\u0660\u0663\u0667\u0662e-\u0663' : '0.0000372',
            '-nan\u0c68\u0c6a\u0c66\u0c66' : '-NaN2400',
            }
        for input, expected in test_values.items():
            self.assertEqual(str(Decimal(input)), expected)

@requires_cdecimal
class CExplicitConstructionTest(ExplicitConstructionTest, unittest.TestCase):
    decimal = C
class PyExplicitConstructionTest(ExplicitConstructionTest, unittest.TestCase):
    decimal = P

class ImplicitConstructionTest:
    '''Unit tests for Implicit Construction cases of Decimal.'''

    def test_implicit_from_None(self):
        Decimal = self.decimal.Decimal
        self.assertRaises(TypeError, eval, 'Decimal(5) + None', locals())

    def test_implicit_from_int(self):
        Decimal = self.decimal.Decimal

        #normal
        self.assertEqual(str(Decimal(5) + 45), '50')
        #exceeding precision
        self.assertEqual(Decimal(5) + 123456789000, Decimal(123456789000))

    def test_implicit_from_string(self):
        Decimal = self.decimal.Decimal
        self.assertRaises(TypeError, eval, 'Decimal(5) + "3"', locals())

    def test_implicit_from_float(self):
        Decimal = self.decimal.Decimal
        self.assertRaises(TypeError, eval, 'Decimal(5) + 2.2', locals())

    def test_implicit_from_Decimal(self):
        Decimal = self.decimal.Decimal
        self.assertEqual(Decimal(5) + Decimal(45), Decimal(50))

    def test_rop(self):
        Decimal = self.decimal.Decimal

        # Allow other classes to be trained to interact with Decimals
        class E:
            def __divmod__(self, other):
                return 'divmod ' + str(other)
            def __rdivmod__(self, other):
                return str(other) + ' rdivmod'
            def __lt__(self, other):
                return 'lt ' + str(other)
            def __gt__(self, other):
                return 'gt ' + str(other)
            def __le__(self, other):
                return 'le ' + str(other)
            def __ge__(self, other):
                return 'ge ' + str(other)
            def __eq__(self, other):
                return 'eq ' + str(other)
            def __ne__(self, other):
                return 'ne ' + str(other)

        self.assertEqual(divmod(E(), Decimal(10)), 'divmod 10')
        self.assertEqual(divmod(Decimal(10), E()), '10 rdivmod')
        self.assertEqual(eval('Decimal(10) < E()'), 'gt 10')
        self.assertEqual(eval('Decimal(10) > E()'), 'lt 10')
        self.assertEqual(eval('Decimal(10) <= E()'), 'ge 10')
        self.assertEqual(eval('Decimal(10) >= E()'), 'le 10')
        self.assertEqual(eval('Decimal(10) == E()'), 'eq 10')
        self.assertEqual(eval('Decimal(10) != E()'), 'ne 10')

        # insert operator methods and then exercise them
        oplist = [
            ('+', '__add__', '__radd__'),
            ('-', '__sub__', '__rsub__'),
            ('*', '__mul__', '__rmul__'),
            ('/', '__truediv__', '__rtruediv__'),
            ('%', '__mod__', '__rmod__'),
            ('//', '__floordiv__', '__rfloordiv__'),
            ('**', '__pow__', '__rpow__')
        ]

        for sym, lop, rop in oplist:
            setattr(E, lop, lambda self, other: 'str' + lop + str(other))
            setattr(E, rop, lambda self, other: str(other) + rop + 'str')
            self.assertEqual(eval('E()' + sym + 'Decimal(10)'),
                             'str' + lop + '10')
            self.assertEqual(eval('Decimal(10)' + sym + 'E()'),
                             '10' + rop + 'str')

@requires_cdecimal
class CImplicitConstructionTest(ImplicitConstructionTest, unittest.TestCase):
    decimal = C
class PyImplicitConstructionTest(ImplicitConstructionTest, unittest.TestCase):
    decimal = P

class FormatTest:
    '''Unit tests for the format function.'''
    def test_formatting(self):
        Decimal = self.decimal.Decimal

        # triples giving a format, a Decimal, and the expected result
        test_values = [
            ('e', '0E-15', '0e-15'),
            ('e', '2.3E-15', '2.3e-15'),
            ('e', '2.30E+2', '2.30e+2'), # preserve significant zeros
            ('e', '2.30000E-15', '2.30000e-15'),
            ('e', '1.23456789123456789e40', '1.23456789123456789e+40'),
            ('e', '1.5', '1.5e+0'),
            ('e', '0.15', '1.5e-1'),
            ('e', '0.015', '1.5e-2'),
            ('e', '0.0000000000015', '1.5e-12'),
            ('e', '15.0', '1.50e+1'),
            ('e', '-15', '-1.5e+1'),
            ('e', '0', '0e+0'),
            ('e', '0E1', '0e+1'),
            ('e', '0.0', '0e-1'),
            ('e', '0.00', '0e-2'),
            ('.6e', '0E-15', '0.000000e-9'),
            ('.6e', '0', '0.000000e+6'),
            ('.6e', '9.999999', '9.999999e+0'),
            ('.6e', '9.9999999', '1.000000e+1'),
            ('.6e', '-1.23e5', '-1.230000e+5'),
            ('.6e', '1.23456789e-3', '1.234568e-3'),
            ('f', '0', '0'),
            ('f', '0.0', '0.0'),
            ('f', '0E-2', '0.00'),
            ('f', '0.00E-8', '0.0000000000'),
            ('f', '0E1', '0'), # loses exponent information
            ('f', '3.2E1', '32'),
            ('f', '3.2E2', '320'),
            ('f', '3.20E2', '320'),
            ('f', '3.200E2', '320.0'),
            ('f', '3.2E-6', '0.0000032'),
            ('.6f', '0E-15', '0.000000'), # all zeros treated equally
            ('.6f', '0E1', '0.000000'),
            ('.6f', '0', '0.000000'),
            ('.0f', '0', '0'), # no decimal point
            ('.0f', '0e-2', '0'),
            ('.0f', '3.14159265', '3'),
            ('.1f', '3.14159265', '3.1'),
            ('.4f', '3.14159265', '3.1416'),
            ('.6f', '3.14159265', '3.141593'),
            ('.7f', '3.14159265', '3.1415926'), # round-half-even!
            ('.8f', '3.14159265', '3.14159265'),
            ('.9f', '3.14159265', '3.141592650'),

            ('g', '0', '0'),
            ('g', '0.0', '0.0'),
            ('g', '0E1', '0e+1'),
            ('G', '0E1', '0E+1'),
            ('g', '0E-5', '0.00000'),
            ('g', '0E-6', '0.000000'),
            ('g', '0E-7', '0e-7'),
            ('g', '-0E2', '-0e+2'),
            ('.0g', '3.14159265', '3'),  # 0 sig fig -> 1 sig fig
            ('.0n', '3.14159265', '3'),  # same for 'n'
            ('.1g', '3.14159265', '3'),
            ('.2g', '3.14159265', '3.1'),
            ('.5g', '3.14159265', '3.1416'),
            ('.7g', '3.14159265', '3.141593'),
            ('.8g', '3.14159265', '3.1415926'), # round-half-even!
            ('.9g', '3.14159265', '3.14159265'),
            ('.10g', '3.14159265', '3.14159265'), # don't pad

            ('%', '0E1', '0%'),
            ('%', '0E0', '0%'),
            ('%', '0E-1', '0%'),
            ('%', '0E-2', '0%'),
            ('%', '0E-3', '0.0%'),
            ('%', '0E-4', '0.00%'),

            ('.3%', '0', '0.000%'), # all zeros treated equally
            ('.3%', '0E10', '0.000%'),
            ('.3%', '0E-10', '0.000%'),
            ('.3%', '2.34', '234.000%'),
            ('.3%', '1.234567', '123.457%'),
            ('.0%', '1.23', '123%'),

            ('e', 'NaN', 'NaN'),
            ('f', '-NaN123', '-NaN123'),
            ('+g', 'NaN456', '+NaN456'),
            ('.3e', 'Inf', 'Infinity'),
            ('.16f', '-Inf', '-Infinity'),
            ('.0g', '-sNaN', '-sNaN'),

            ('', '1.00', '1.00'),

            # test alignment and padding
            ('6', '123', '   123'),
            ('<6', '123', '123   '),
            ('>6', '123', '   123'),
            ('^6', '123', ' 123  '),
            ('=+6', '123', '+  123'),
            ('#<10', 'NaN', 'NaN#######'),
            ('#<10', '-4.3', '-4.3######'),
            ('#<+10', '0.0130', '+0.0130###'),
            ('#< 10', '0.0130', ' 0.0130###'),
            ('@>10', '-Inf', '@-Infinity'),
            ('#>5', '-Inf', '-Infinity'),
            ('?^5', '123', '?123?'),
            ('%^6', '123', '%123%%'),
            (' ^6', '-45.6', '-45.6 '),
            ('/=10', '-45.6', '-/////45.6'),
            ('/=+10', '45.6', '+/////45.6'),
            ('/= 10', '45.6', ' /////45.6'),
            ('\x00=10', '-inf', '-\x00Infinity'),
            ('\x00^16', '-inf', '\x00\x00\x00-Infinity\x00\x00\x00\x00'),
            ('\x00>10', '1.2345', '\x00\x00\x00\x001.2345'),
            ('\x00<10', '1.2345', '1.2345\x00\x00\x00\x00'),

            # thousands separator
            (',', '1234567', '1,234,567'),
            (',', '123456', '123,456'),
            (',', '12345', '12,345'),
            (',', '1234', '1,234'),
            (',', '123', '123'),
            (',', '12', '12'),
            (',', '1', '1'),
            (',', '0', '0'),
            (',', '-1234567', '-1,234,567'),
            (',', '-123456', '-123,456'),
            ('7,', '123456', '123,456'),
            ('8,', '123456', ' 123,456'),
            ('08,', '123456', '0,123,456'), # special case: extra 0 needed
            ('+08,', '123456', '+123,456'), # but not if there's a sign
            (' 08,', '123456', ' 123,456'),
            ('08,', '-123456', '-123,456'),
            ('+09,', '123456', '+0,123,456'),
            # ... with fractional part...
            ('07,', '1234.56', '1,234.56'),
            ('08,', '1234.56', '1,234.56'),
            ('09,', '1234.56', '01,234.56'),
            ('010,', '1234.56', '001,234.56'),
            ('011,', '1234.56', '0,001,234.56'),
            ('012,', '1234.56', '0,001,234.56'),
            ('08,.1f', '1234.5', '01,234.5'),
            # no thousands separators in fraction part
            (',', '1.23456789', '1.23456789'),
            (',%', '123.456789', '12,345.6789%'),
            (',e', '123456', '1.23456e+5'),
            (',E', '123456', '1.23456E+5'),

            # negative zero: default behavior
            ('.1f', '-0', '-0.0'),
            ('.1f', '-.0', '-0.0'),
            ('.1f', '-.01', '-0.0'),

            # negative zero: z option
            ('z.1f', '0.', '0.0'),
            ('z6.1f', '0.', '   0.0'),
            ('z6.1f', '-1.', '  -1.0'),
            ('z.1f', '-0.', '0.0'),
            ('z.1f', '.01', '0.0'),
            ('z.1f', '-.01', '0.0'),
            ('z.2f', '0.', '0.00'),
            ('z.2f', '-0.', '0.00'),
            ('z.2f', '.001', '0.00'),
            ('z.2f', '-.001', '0.00'),

            ('z.1e', '0.', '0.0e+1'),
            ('z.1e', '-0.', '0.0e+1'),
            ('z.1E', '0.', '0.0E+1'),
            ('z.1E', '-0.', '0.0E+1'),

            ('z.2e', '-0.001', '-1.00e-3'),  # tests for mishandled rounding
            ('z.2g', '-0.001', '-0.001'),
            ('z.2%', '-0.001', '-0.10%'),

            ('zf', '-0.0000', '0.0000'),  # non-normalized form is preserved

            ('z.1f', '-00000.000001', '0.0'),
            ('z.1f', '-00000.', '0.0'),
            ('z.1f', '-.0000000000', '0.0'),

            ('z.2f', '-00000.000001', '0.00'),
            ('z.2f', '-00000.', '0.00'),
            ('z.2f', '-.0000000000', '0.00'),

            ('z.1f', '.09', '0.1'),
            ('z.1f', '-.09', '-0.1'),

            (' z.0f', '-0.', ' 0'),
            ('+z.0f', '-0.', '+0'),
            ('-z.0f', '-0.', '0'),
            (' z.0f', '-1.', '-1'),
            ('+z.0f', '-1.', '-1'),
            ('-z.0f', '-1.', '-1'),

            ('z>6.1f', '-0.', 'zz-0.0'),
            ('z>z6.1f', '-0.', 'zzz0.0'),
            ('x>z6.1f', '-0.', 'xxx0.0'),
            ('🖤>z6.1f', '-0.', '🖤🖤🖤0.0'),  # multi-byte fill char
            ('\x00>z6.1f', '-0.', '\x00\x00\x000.0'),  # null fill char

            # issue 114563 ('z' format on F type in cdecimal)
            ('z3,.10F', '-6.24E-323', '0.0000000000'),

            # issue 91060 ('#' format in cdecimal)
            ('#', '0', '0.'),

            # issue 6850
            ('a=-7.0', '0.12345', 'aaaa0.1'),

            # issue 22090
            ('<^+15.20%', 'inf', '<<+Infinity%<<<'),
            ('\x07>,%', 'sNaN1234567', 'sNaN1234567%'),
            ('=10.10%', 'NaN123', '   NaN123%'),
            ]
        for fmt, d, result in test_values:
            self.assertEqual(format(Decimal(d), fmt), result)

        # bytes format argument
        self.assertRaises(TypeError, Decimal(1).__format__, b'-020')

    def test_negative_zero_format_directed_rounding(self):
        with self.decimal.localcontext() as ctx:
            ctx.rounding = ROUND_CEILING
            self.assertEqual(format(self.decimal.Decimal('-0.001'), 'z.2f'),
                            '0.00')

    def test_negative_zero_bad_format(self):
        self.assertRaises(ValueError, format, self.decimal.Decimal('1.23'), 'fz')

    def test_n_format(self):
        Decimal = self.decimal.Decimal

        try:
            from locale import CHAR_MAX
        except ImportError:
            self.skipTest('locale.CHAR_MAX not available')

        def make_grouping(lst):
            return ''.join([chr(x) for x in lst]) if self.decimal == C else lst

        def get_fmt(x, override=None, fmt='n'):
            if self.decimal == C:
                return Decimal(x).__format__(fmt, override)
            else:
                return Decimal(x).__format__(fmt, _localeconv=override)

        # Set up some localeconv-like dictionaries
        en_US = {
            'decimal_point' : '.',
            'grouping' : make_grouping([3, 3, 0]),
            'thousands_sep' : ','
            }

        fr_FR = {
            'decimal_point' : ',',
            'grouping' : make_grouping([CHAR_MAX]),
            'thousands_sep' : ''
            }

        ru_RU = {
            'decimal_point' : ',',
            'grouping': make_grouping([3, 3, 0]),
            'thousands_sep' : ' '
            }

        crazy = {
            'decimal_point' : '&',
            'grouping': make_grouping([1, 4, 2, CHAR_MAX]),
            'thousands_sep' : '-'
            }

        dotsep_wide = {
            'decimal_point' : b'\xc2\xbf'.decode('utf-8'),
            'grouping': make_grouping([3, 3, 0]),
            'thousands_sep' : b'\xc2\xb4'.decode('utf-8')
            }

        self.assertEqual(get_fmt(Decimal('12.7'), en_US), '12.7')
        self.assertEqual(get_fmt(Decimal('12.7'), fr_FR), '12,7')
        self.assertEqual(get_fmt(Decimal('12.7'), ru_RU), '12,7')
        self.assertEqual(get_fmt(Decimal('12.7'), crazy), '1-2&7')

        self.assertEqual(get_fmt(123456789, en_US), '123,456,789')
        self.assertEqual(get_fmt(123456789, fr_FR), '123456789')
        self.assertEqual(get_fmt(123456789, ru_RU), '123 456 789')
        self.assertEqual(get_fmt(1234567890123, crazy), '123456-78-9012-3')

        self.assertEqual(get_fmt(123456789, en_US, '.6n'), '1.23457e+8')
        self.assertEqual(get_fmt(123456789, fr_FR, '.6n'), '1,23457e+8')
        self.assertEqual(get_fmt(123456789, ru_RU, '.6n'), '1,23457e+8')
        self.assertEqual(get_fmt(123456789, crazy, '.6n'), '1&23457e+8')

        # zero padding
        self.assertEqual(get_fmt(1234, fr_FR, '03n'), '1234')
        self.assertEqual(get_fmt(1234, fr_FR, '04n'), '1234')
        self.assertEqual(get_fmt(1234, fr_FR, '05n'), '01234')
        self.assertEqual(get_fmt(1234, fr_FR, '06n'), '001234')

        self.assertEqual(get_fmt(12345, en_US, '05n'), '12,345')
        self.assertEqual(get_fmt(12345, en_US, '06n'), '12,345')
        self.assertEqual(get_fmt(12345, en_US, '07n'), '012,345')
        self.assertEqual(get_fmt(12345, en_US, '08n'), '0,012,345')
        self.assertEqual(get_fmt(12345, en_US, '09n'), '0,012,345')
        self.assertEqual(get_fmt(12345, en_US, '010n'), '00,012,345')

        self.assertEqual(get_fmt(123456, crazy, '06n'), '1-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '07n'), '1-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '08n'), '1-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '09n'), '01-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '010n'), '0-01-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '011n'), '0-01-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '012n'), '00-01-2345-6')
        self.assertEqual(get_fmt(123456, crazy, '013n'), '000-01-2345-6')

        # wide char separator and decimal point
        self.assertEqual(get_fmt(Decimal('-1.5'), dotsep_wide, '020n'),
                         '-0\u00b4000\u00b4000\u00b4000\u00b4001\u00bf5')

    def test_deprecated_N_format(self):
        Decimal = self.decimal.Decimal
        h = Decimal('6.62607015e-34')
        if self.decimal == C:
            with self.assertWarns(DeprecationWarning) as cm:
                r = format(h, 'N')
            self.assertEqual(cm.filename, __file__)
            self.assertEqual(r, format(h, 'n').upper())
            with self.assertWarns(DeprecationWarning) as cm:
                r = format(h, '010.3N')
            self.assertEqual(cm.filename, __file__)
            self.assertEqual(r, format(h, '010.3n').upper())
        else:
            self.assertRaises(ValueError, format, h, 'N')
            self.assertRaises(ValueError, format, h, '010.3N')
        with warnings_helper.check_no_warnings(self):
            self.assertEqual(format(h, 'N>10.3'), 'NN6.63E-34')
            self.assertEqual(format(h, 'N>10.3n'), 'NN6.63e-34')
            self.assertEqual(format(h, 'N>10.3e'), 'N6.626e-34')
            self.assertEqual(format(h, 'N>10.3f'), 'NNNNN0.000')
            self.assertRaises(ValueError, format, h, '>Nf')
            self.assertRaises(ValueError, format, h, '10Nf')
            self.assertRaises(ValueError, format, h, 'Nx')

    @run_with_locale('LC_ALL', 'ps_AF', '')
    def test_wide_char_separator_decimal_point(self):
        # locale with wide char separator and decimal point
        Decimal = self.decimal.Decimal

        decimal_point = locale.localeconv()['decimal_point']
        thousands_sep = locale.localeconv()['thousands_sep']
        if decimal_point != '\u066b':
            self.skipTest('inappropriate decimal point separator '
                          '({!a} not {!a})'.format(decimal_point, '\u066b'))
        if thousands_sep != '\u066c':
            self.skipTest('inappropriate thousands separator '
                          '({!a} not {!a})'.format(thousands_sep, '\u066c'))

        self.assertEqual(format(Decimal('100000000.123'), 'n'),
                         '100\u066c000\u066c000\u066b123')

    def test_decimal_from_float_argument_type(self):
        class A(self.decimal.Decimal):
            def __init__(self, a):
                self.a_type = type(a)
        a = A.from_float(42.5)
        self.assertEqual(self.decimal.Decimal, a.a_type)

        a = A.from_float(42)
        self.assertEqual(self.decimal.Decimal, a.a_type)

@requires_cdecimal
class CFormatTest(FormatTest, unittest.TestCase):
    decimal = C
class PyFormatTest(FormatTest, unittest.TestCase):
    decimal = P

class ArithmeticOperatorsTest:
    '''Unit tests for all arithmetic operators, binary and unary.'''

    def test_addition(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('-11.1')
        d2 = Decimal('22.2')

        #two Decimals
        self.assertEqual(d1+d2, Decimal('11.1'))
        self.assertEqual(d2+d1, Decimal('11.1'))

        #with other type, left
        c = d1 + 5
        self.assertEqual(c, Decimal('-6.1'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 5 + d1
        self.assertEqual(c, Decimal('-6.1'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 += d2
        self.assertEqual(d1, Decimal('11.1'))

        #inline with other type
        d1 += 5
        self.assertEqual(d1, Decimal('16.1'))

    def test_subtraction(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('-11.1')
        d2 = Decimal('22.2')

        #two Decimals
        self.assertEqual(d1-d2, Decimal('-33.3'))
        self.assertEqual(d2-d1, Decimal('33.3'))

        #with other type, left
        c = d1 - 5
        self.assertEqual(c, Decimal('-16.1'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 5 - d1
        self.assertEqual(c, Decimal('16.1'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 -= d2
        self.assertEqual(d1, Decimal('-33.3'))

        #inline with other type
        d1 -= 5
        self.assertEqual(d1, Decimal('-38.3'))

    def test_multiplication(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('-5')
        d2 = Decimal('3')

        #two Decimals
        self.assertEqual(d1*d2, Decimal('-15'))
        self.assertEqual(d2*d1, Decimal('-15'))

        #with other type, left
        c = d1 * 5
        self.assertEqual(c, Decimal('-25'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 5 * d1
        self.assertEqual(c, Decimal('-25'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 *= d2
        self.assertEqual(d1, Decimal('-15'))

        #inline with other type
        d1 *= 5
        self.assertEqual(d1, Decimal('-75'))

    def test_division(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('-5')
        d2 = Decimal('2')

        #two Decimals
        self.assertEqual(d1/d2, Decimal('-2.5'))
        self.assertEqual(d2/d1, Decimal('-0.4'))

        #with other type, left
        c = d1 / 4
        self.assertEqual(c, Decimal('-1.25'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 4 / d1
        self.assertEqual(c, Decimal('-0.8'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 /= d2
        self.assertEqual(d1, Decimal('-2.5'))

        #inline with other type
        d1 /= 4
        self.assertEqual(d1, Decimal('-0.625'))

    def test_floor_division(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('5')
        d2 = Decimal('2')

        #two Decimals
        self.assertEqual(d1//d2, Decimal('2'))
        self.assertEqual(d2//d1, Decimal('0'))

        #with other type, left
        c = d1 // 4
        self.assertEqual(c, Decimal('1'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 7 // d1
        self.assertEqual(c, Decimal('1'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 //= d2
        self.assertEqual(d1, Decimal('2'))

        #inline with other type
        d1 //= 2
        self.assertEqual(d1, Decimal('1'))

    def test_powering(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('5')
        d2 = Decimal('2')

        #two Decimals
        self.assertEqual(d1**d2, Decimal('25'))
        self.assertEqual(d2**d1, Decimal('32'))

        #with other type, left
        c = d1 ** 4
        self.assertEqual(c, Decimal('625'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 7 ** d1
        self.assertEqual(c, Decimal('16807'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 **= d2
        self.assertEqual(d1, Decimal('25'))

        #inline with other type
        d1 **= 4
        self.assertEqual(d1, Decimal('390625'))

    def test_module(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('5')
        d2 = Decimal('2')

        #two Decimals
        self.assertEqual(d1%d2, Decimal('1'))
        self.assertEqual(d2%d1, Decimal('2'))

        #with other type, left
        c = d1 % 4
        self.assertEqual(c, Decimal('1'))
        self.assertEqual(type(c), type(d1))

        #with other type, right
        c = 7 % d1
        self.assertEqual(c, Decimal('2'))
        self.assertEqual(type(c), type(d1))

        #inline with decimal
        d1 %= d2
        self.assertEqual(d1, Decimal('1'))

        #inline with other type
        d1 %= 4
        self.assertEqual(d1, Decimal('1'))

    def test_floor_div_module(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('5')
        d2 = Decimal('2')

        #two Decimals
        (p, q) = divmod(d1, d2)
        self.assertEqual(p, Decimal('2'))
        self.assertEqual(q, Decimal('1'))
        self.assertEqual(type(p), type(d1))
        self.assertEqual(type(q), type(d1))

        #with other type, left
        (p, q) = divmod(d1, 4)
        self.assertEqual(p, Decimal('1'))
        self.assertEqual(q, Decimal('1'))
        self.assertEqual(type(p), type(d1))
        self.assertEqual(type(q), type(d1))

        #with other type, right
        (p, q) = divmod(7, d1)
        self.assertEqual(p, Decimal('1'))
        self.assertEqual(q, Decimal('2'))
        self.assertEqual(type(p), type(d1))
        self.assertEqual(type(q), type(d1))

    def test_unary_operators(self):
        Decimal = self.decimal.Decimal

        self.assertEqual(+Decimal(45), Decimal(+45))           #  +
        self.assertEqual(-Decimal(45), Decimal(-45))           #  -
        self.assertEqual(abs(Decimal(45)), abs(Decimal(-45)))  # abs

    def test_nan_comparisons(self):
        # comparisons involving signaling nans signal InvalidOperation

        # order comparisons (<, <=, >, >=) involving only quiet nans
        # also signal InvalidOperation

        # equality comparisons (==, !=) involving only quiet nans
        # don't signal, but return False or True respectively.
        Decimal = self.decimal.Decimal
        InvalidOperation = self.decimal.InvalidOperation
        localcontext = self.decimal.localcontext

        n = Decimal('NaN')
        s = Decimal('sNaN')
        i = Decimal('Inf')
        f = Decimal('2')

        qnan_pairs = (n, n), (n, i), (i, n), (n, f), (f, n)
        snan_pairs = (s, n), (n, s), (s, i), (i, s), (s, f), (f, s), (s, s)
        order_ops = operator.lt, operator.le, operator.gt, operator.ge
        equality_ops = operator.eq, operator.ne

        # results when InvalidOperation is not trapped
        with localcontext() as ctx:
            ctx.traps[InvalidOperation] = 0

            for x, y in qnan_pairs + snan_pairs:
                for op in order_ops + equality_ops:
                    got = op(x, y)
                    expected = True if op is operator.ne else False
                    self.assertIs(expected, got,
                                "expected {0!r} for operator.{1}({2!r}, {3!r}); "
                                "got {4!r}".format(
                            expected, op.__name__, x, y, got))

        # repeat the above, but this time trap the InvalidOperation
        with localcontext() as ctx:
            ctx.traps[InvalidOperation] = 1

            for x, y in qnan_pairs:
                for op in equality_ops:
                    got = op(x, y)
                    expected = True if op is operator.ne else False
                    self.assertIs(expected, got,
                                  "expected {0!r} for "
                                  "operator.{1}({2!r}, {3!r}); "
                                  "got {4!r}".format(
                            expected, op.__name__, x, y, got))

            for x, y in snan_pairs:
                for op in equality_ops:
                    self.assertRaises(InvalidOperation, operator.eq, x, y)
                    self.assertRaises(InvalidOperation, operator.ne, x, y)

            for x, y in qnan_pairs + snan_pairs:
                for op in order_ops:
                    self.assertRaises(InvalidOperation, op, x, y)

    def test_copy_sign(self):
        Decimal = self.decimal.Decimal

        d = Decimal(1).copy_sign(Decimal(-2))
        self.assertEqual(Decimal(1).copy_sign(-2), d)
        self.assertRaises(TypeError, Decimal(1).copy_sign, '-2')

@requires_cdecimal
class CArithmeticOperatorsTest(ArithmeticOperatorsTest, unittest.TestCase):
    decimal = C
class PyArithmeticOperatorsTest(ArithmeticOperatorsTest, unittest.TestCase):
    decimal = P

# The following are two functions used to test threading in the next class

def thfunc1(cls):
    Decimal = cls.decimal.Decimal
    InvalidOperation = cls.decimal.InvalidOperation
    DivisionByZero = cls.decimal.DivisionByZero
    Overflow = cls.decimal.Overflow
    Underflow = cls.decimal.Underflow
    Inexact = cls.decimal.Inexact
    getcontext = cls.decimal.getcontext
    localcontext = cls.decimal.localcontext

    d1 = Decimal(1)
    d3 = Decimal(3)
    test1 = d1/d3

    cls.finish1.set()
    cls.synchro.wait()

    test2 = d1/d3
    with localcontext() as c2:
        cls.assertTrue(c2.flags[Inexact])
        cls.assertRaises(DivisionByZero, c2.divide, d1, 0)
        cls.assertTrue(c2.flags[DivisionByZero])
        with localcontext() as c3:
            cls.assertTrue(c3.flags[Inexact])
            cls.assertTrue(c3.flags[DivisionByZero])
            cls.assertRaises(InvalidOperation, c3.compare, d1, Decimal('sNaN'))
            cls.assertTrue(c3.flags[InvalidOperation])
            del c3
        cls.assertFalse(c2.flags[InvalidOperation])
        del c2

    cls.assertEqual(test1, Decimal('0.333333333333333333333333'))
    cls.assertEqual(test2, Decimal('0.333333333333333333333333'))

    c1 = getcontext()
    cls.assertTrue(c1.flags[Inexact])
    for sig in Overflow, Underflow, DivisionByZero, InvalidOperation:
        cls.assertFalse(c1.flags[sig])

def thfunc2(cls):
    Decimal = cls.decimal.Decimal
    InvalidOperation = cls.decimal.InvalidOperation
    DivisionByZero = cls.decimal.DivisionByZero
    Overflow = cls.decimal.Overflow
    Underflow = cls.decimal.Underflow
    Inexact = cls.decimal.Inexact
    getcontext = cls.decimal.getcontext
    localcontext = cls.decimal.localcontext

    d1 = Decimal(1)
    d3 = Decimal(3)
    test1 = d1/d3

    thiscontext = getcontext()
    thiscontext.prec = 18
    test2 = d1/d3

    with localcontext() as c2:
        cls.assertTrue(c2.flags[Inexact])
        cls.assertRaises(Overflow, c2.multiply, Decimal('1e425000000'), 999)
        cls.assertTrue(c2.flags[Overflow])
        with localcontext(thiscontext) as c3:
            cls.assertTrue(c3.flags[Inexact])
            cls.assertFalse(c3.flags[Overflow])
            c3.traps[Underflow] = True
            cls.assertRaises(Underflow, c3.divide, Decimal('1e-425000000'), 999)
            cls.assertTrue(c3.flags[Underflow])
            del c3
        cls.assertFalse(c2.flags[Underflow])
        cls.assertFalse(c2.traps[Underflow])
        del c2

    cls.synchro.set()
    cls.finish2.set()

    cls.assertEqual(test1, Decimal('0.333333333333333333333333'))
    cls.assertEqual(test2, Decimal('0.333333333333333333'))

    cls.assertFalse(thiscontext.traps[Underflow])
    cls.assertTrue(thiscontext.flags[Inexact])
    for sig in Overflow, Underflow, DivisionByZero, InvalidOperation:
        cls.assertFalse(thiscontext.flags[sig])


@threading_helper.requires_working_threading()
class ThreadingTest:
    '''Unit tests for thread local contexts in Decimal.'''

    # Take care executing this test from IDLE, there's an issue in threading
    # that hangs IDLE and I couldn't find it

    def test_threading(self):
        DefaultContext = self.decimal.DefaultContext

        if self.decimal == C and not self.decimal.HAVE_THREADS:
            self.skipTest("compiled without threading")
        # Test the "threading isolation" of a Context. Also test changing
        # the DefaultContext, which acts as a template for the thread-local
        # contexts.
        save_prec = DefaultContext.prec
        save_emax = DefaultContext.Emax
        save_emin = DefaultContext.Emin
        DefaultContext.prec = 24
        DefaultContext.Emax = 425000000
        DefaultContext.Emin = -425000000

        self.synchro = threading.Event()
        self.finish1 = threading.Event()
        self.finish2 = threading.Event()

        th1 = threading.Thread(target=thfunc1, args=(self,))
        th2 = threading.Thread(target=thfunc2, args=(self,))

        th1.start()
        th2.start()

        self.finish1.wait()
        self.finish2.wait()

        for sig in Signals[self.decimal]:
            self.assertFalse(DefaultContext.flags[sig])

        th1.join()
        th2.join()

        DefaultContext.prec = save_prec
        DefaultContext.Emax = save_emax
        DefaultContext.Emin = save_emin


@requires_cdecimal
class CThreadingTest(ThreadingTest, unittest.TestCase):
    decimal = C

class PyThreadingTest(ThreadingTest, unittest.TestCase):
    decimal = P

class UsabilityTest:
    '''Unit tests for Usability cases of Decimal.'''

    def test_comparison_operators(self):

        Decimal = self.decimal.Decimal

        da = Decimal('23.42')
        db = Decimal('23.42')
        dc = Decimal('45')

        #two Decimals
        self.assertGreater(dc, da)
        self.assertGreaterEqual(dc, da)
        self.assertLess(da, dc)
        self.assertLessEqual(da, dc)
        self.assertEqual(da, db)
        self.assertNotEqual(da, dc)
        self.assertLessEqual(da, db)
        self.assertGreaterEqual(da, db)

        #a Decimal and an int
        self.assertGreater(dc, 23)
        self.assertLess(23, dc)
        self.assertEqual(dc, 45)

        #a Decimal and uncomparable
        self.assertNotEqual(da, 'ugly')
        self.assertNotEqual(da, 32.7)
        self.assertNotEqual(da, object())
        self.assertNotEqual(da, object)

        # sortable
        a = list(map(Decimal, range(100)))
        b =  a[:]
        random.shuffle(a)
        a.sort()
        self.assertEqual(a, b)

    def test_decimal_float_comparison(self):
        Decimal = self.decimal.Decimal

        da = Decimal('0.25')
        db = Decimal('3.0')
        self.assertLess(da, 3.0)
        self.assertLessEqual(da, 3.0)
        self.assertGreater(db, 0.25)
        self.assertGreaterEqual(db, 0.25)
        self.assertNotEqual(da, 1.5)
        self.assertEqual(da, 0.25)
        self.assertGreater(3.0, da)
        self.assertGreaterEqual(3.0, da)
        self.assertLess(0.25, db)
        self.assertLessEqual(0.25, db)
        self.assertNotEqual(0.25, db)
        self.assertEqual(3.0, db)
        self.assertNotEqual(0.1, Decimal('0.1'))

    def test_decimal_complex_comparison(self):
        Decimal = self.decimal.Decimal

        da = Decimal('0.25')
        db = Decimal('3.0')
        self.assertNotEqual(da, (1.5+0j))
        self.assertNotEqual((1.5+0j), da)
        self.assertEqual(da, (0.25+0j))
        self.assertEqual((0.25+0j), da)
        self.assertEqual((3.0+0j), db)
        self.assertEqual(db, (3.0+0j))

        self.assertNotEqual(db, (3.0+1j))
        self.assertNotEqual((3.0+1j), db)

        self.assertIs(db.__lt__(3.0+0j), NotImplemented)
        self.assertIs(db.__le__(3.0+0j), NotImplemented)
        self.assertIs(db.__gt__(3.0+0j), NotImplemented)
        self.assertIs(db.__le__(3.0+0j), NotImplemented)

    def test_decimal_fraction_comparison(self):
        D = self.decimal.Decimal
        F = fractions[self.decimal].Fraction
        Context = self.decimal.Context
        localcontext = self.decimal.localcontext
        InvalidOperation = self.decimal.InvalidOperation


        emax = C.MAX_EMAX if C else 999999999
        emin = C.MIN_EMIN if C else -999999999
        etiny = C.MIN_ETINY if C else -1999999997
        c = Context(Emax=emax, Emin=emin)

        with localcontext(c):
            c.prec = emax
            self.assertLess(D(0), F(1,9999999999999999999999999999999999999))
            self.assertLess(F(-1,9999999999999999999999999999999999999), D(0))
            self.assertLess(F(0,1), D("1e" + str(etiny)))
            self.assertLess(D("-1e" + str(etiny)), F(0,1))
            self.assertLess(F(0,9999999999999999999999999), D("1e" + str(etiny)))
            self.assertLess(D("-1e" + str(etiny)), F(0,9999999999999999999999999))

            self.assertEqual(D("0.1"), F(1,10))
            self.assertEqual(F(1,10), D("0.1"))

            c.prec = 300
            self.assertNotEqual(D(1)/3, F(1,3))
            self.assertNotEqual(F(1,3), D(1)/3)

            self.assertLessEqual(F(120984237, 9999999999), D("9e" + str(emax)))
            self.assertGreaterEqual(D("9e" + str(emax)), F(120984237, 9999999999))

            self.assertGreater(D('inf'), F(99999999999,123))
            self.assertGreater(D('inf'), F(-99999999999,123))
            self.assertLess(D('-inf'), F(99999999999,123))
            self.assertLess(D('-inf'), F(-99999999999,123))

            self.assertRaises(InvalidOperation, D('nan').__gt__, F(-9,123))
            self.assertIs(NotImplemented, F(-9,123).__lt__(D('nan')))
            self.assertNotEqual(D('nan'), F(-9,123))
            self.assertNotEqual(F(-9,123), D('nan'))

    def test_copy_and_deepcopy_methods(self):
        Decimal = self.decimal.Decimal

        d = Decimal('43.24')
        c = copy.copy(d)
        self.assertEqual(id(c), id(d))
        dc = copy.deepcopy(d)
        self.assertEqual(id(dc), id(d))

    def test_hash_method(self):

        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext

        def hashit(d):
            a = hash(d)
            b = d.__hash__()
            self.assertEqual(a, b)
            return a

        #just that it's hashable
        hashit(Decimal(23))
        hashit(Decimal('Infinity'))
        hashit(Decimal('-Infinity'))
        hashit(Decimal('nan123'))
        hashit(Decimal('-NaN'))

        test_values = [Decimal(sign*(2**m + n))
                       for m in [0, 14, 15, 16, 17, 30, 31,
                                 32, 33, 61, 62, 63, 64, 65, 66]
                       for n in range(-10, 10)
                       for sign in [-1, 1]]
        test_values.extend([
                Decimal("-1"), # ==> -2
                Decimal("-0"), # zeros
                Decimal("0.00"),
                Decimal("-0.000"),
                Decimal("0E10"),
                Decimal("-0E12"),
                Decimal("10.0"), # negative exponent
                Decimal("-23.00000"),
                Decimal("1230E100"), # positive exponent
                Decimal("-4.5678E50"),
                # a value for which hash(n) != hash(n % (2**64-1))
                # in Python pre-2.6
                Decimal(2**64 + 2**32 - 1),
                # selection of values which fail with the old (before
                # version 2.6) long.__hash__
                Decimal("1.634E100"),
                Decimal("90.697E100"),
                Decimal("188.83E100"),
                Decimal("1652.9E100"),
                Decimal("56531E100"),
                ])

        # check that hash(d) == hash(int(d)) for integral values
        for value in test_values:
            self.assertEqual(hashit(value), hash(int(value)))

        # check that the hashes of a Decimal float match when they
        # represent exactly the same values
        test_strings = ['inf', '-Inf', '0.0', '-.0e1',
                        '34.0', '2.5', '112390.625', '-0.515625']
        for s in test_strings:
            f = float(s)
            d = Decimal(s)
            self.assertEqual(hashit(d), hash(f))

        with localcontext() as c:
            # check that the value of the hash doesn't depend on the
            # current context (issue #1757)
            x = Decimal("123456789.1")

            c.prec = 6
            h1 = hashit(x)
            c.prec = 10
            h2 = hashit(x)
            c.prec = 16
            h3 = hashit(x)

            self.assertEqual(h1, h2)
            self.assertEqual(h1, h3)

            c.prec = 10000
            x = 1100 ** 1248
            self.assertEqual(hashit(Decimal(x)), hashit(x))

    def test_hash_method_nan(self):
        Decimal = self.decimal.Decimal
        self.assertRaises(TypeError, hash, Decimal('sNaN'))
        value = Decimal('NaN')
        self.assertEqual(hash(value), object.__hash__(value))
        class H:
            def __hash__(self):
                return 42
        class D(Decimal, H):
            pass
        value = D('NaN')
        self.assertEqual(hash(value), object.__hash__(value))

    def test_min_and_max_methods(self):
        Decimal = self.decimal.Decimal

        d1 = Decimal('15.32')
        d2 = Decimal('28.5')
        l1 = 15
        l2 = 28

        #between Decimals
        self.assertIs(min(d1,d2), d1)
        self.assertIs(min(d2,d1), d1)
        self.assertIs(max(d1,d2), d2)
        self.assertIs(max(d2,d1), d2)

        #between Decimal and int
        self.assertIs(min(d1,l2), d1)
        self.assertIs(min(l2,d1), d1)
        self.assertIs(max(l1,d2), d2)
        self.assertIs(max(d2,l1), d2)

    def test_as_nonzero(self):
        Decimal = self.decimal.Decimal

        #as false
        self.assertFalse(Decimal(0))
        #as true
        self.assertTrue(Decimal('0.372'))

    def test_tostring_methods(self):
        #Test str and repr methods.
        Decimal = self.decimal.Decimal

        d = Decimal('15.32')
        self.assertEqual(str(d), '15.32')               # str
        self.assertEqual(repr(d), "Decimal('15.32')")   # repr

    def test_tonum_methods(self):
        #Test float and int methods.
        Decimal = self.decimal.Decimal

        d1 = Decimal('66')
        d2 = Decimal('15.32')

        #int
        self.assertEqual(int(d1), 66)
        self.assertEqual(int(d2), 15)

        #float
        self.assertEqual(float(d1), 66)
        self.assertEqual(float(d2), 15.32)

        #floor
        test_pairs = [
            ('123.00', 123),
            ('3.2', 3),
            ('3.54', 3),
            ('3.899', 3),
            ('-2.3', -3),
            ('-11.0', -11),
            ('0.0', 0),
            ('-0E3', 0),
            ('89891211712379812736.1', 89891211712379812736),
            ]
        for d, i in test_pairs:
            self.assertEqual(math.floor(Decimal(d)), i)
        self.assertRaises(ValueError, math.floor, Decimal('-NaN'))
        self.assertRaises(ValueError, math.floor, Decimal('sNaN'))
        self.assertRaises(ValueError, math.floor, Decimal('NaN123'))
        self.assertRaises(OverflowError, math.floor, Decimal('Inf'))
        self.assertRaises(OverflowError, math.floor, Decimal('-Inf'))

        #ceiling
        test_pairs = [
            ('123.00', 123),
            ('3.2', 4),
            ('3.54', 4),
            ('3.899', 4),
            ('-2.3', -2),
            ('-11.0', -11),
            ('0.0', 0),
            ('-0E3', 0),
            ('89891211712379812736.1', 89891211712379812737),
            ]
        for d, i in test_pairs:
            self.assertEqual(math.ceil(Decimal(d)), i)
        self.assertRaises(ValueError, math.ceil, Decimal('-NaN'))
        self.assertRaises(ValueError, math.ceil, Decimal('sNaN'))
        self.assertRaises(ValueError, math.ceil, Decimal('NaN123'))
        self.assertRaises(OverflowError, math.ceil, Decimal('Inf'))
        self.assertRaises(OverflowError, math.ceil, Decimal('-Inf'))

        #round, single argument
        test_pairs = [
            ('123.00', 123),
            ('3.2', 3),
            ('3.54', 4),
            ('3.899', 4),
            ('-2.3', -2),
            ('-11.0', -11),
            ('0.0', 0),
            ('-0E3', 0),
            ('-3.5', -4),
            ('-2.5', -2),
            ('-1.5', -2),
            ('-0.5', 0),
            ('0.5', 0),
            ('1.5', 2),
            ('2.5', 2),
            ('3.5', 4),
            ]
        for d, i in test_pairs:
            self.assertEqual(round(Decimal(d)), i)
        self.assertRaises(ValueError, round, Decimal('-NaN'))
        self.assertRaises(ValueError, round, Decimal('sNaN'))
        self.assertRaises(ValueError, round, Decimal('NaN123'))
        self.assertRaises(OverflowError, round, Decimal('Inf'))
        self.assertRaises(OverflowError, round, Decimal('-Inf'))

        #round, two arguments;  this is essentially equivalent
        #to quantize, which is already extensively tested
        test_triples = [
            ('123.456', -4, '0E+4'),
            ('-123.456', -4, '-0E+4'),
            ('123.456', -3, '0E+3'),
            ('-123.456', -3, '-0E+3'),
            ('123.456', -2, '1E+2'),
            ('123.456', -1, '1.2E+2'),
            ('123.456', 0, '123'),
            ('123.456', 1, '123.5'),
            ('123.456', 2, '123.46'),
            ('123.456', 3, '123.456'),
            ('123.456', 4, '123.4560'),
            ('123.455', 2, '123.46'),
            ('123.445', 2, '123.44'),
            ('Inf', 4, 'NaN'),
            ('-Inf', -23, 'NaN'),
            ('sNaN314', 3, 'NaN314'),
            ]
        for d, n, r in test_triples:
            self.assertEqual(str(round(Decimal(d), n)), r)

    def test_nan_to_float(self):
        # Test conversions of decimal NANs to float.
        # See http://bugs.python.org/issue15544
        Decimal = self.decimal.Decimal
        for s in ('nan', 'nan1234', '-nan', '-nan2468'):
            f = float(Decimal(s))
            self.assertTrue(math.isnan(f))
            sign = math.copysign(1.0, f)
            self.assertEqual(sign, -1.0 if s.startswith('-') else 1.0)

    def test_snan_to_float(self):
        Decimal = self.decimal.Decimal
        for s in ('snan', '-snan', 'snan1357', '-snan1234'):
            d = Decimal(s)
            self.assertRaises(ValueError, float, d)

    def test_eval_round_trip(self):
        Decimal = self.decimal.Decimal

        #with zero
        d = Decimal( (0, (0,), 0) )
        self.assertEqual(d, eval(repr(d)))

        #int
        d = Decimal( (1, (4, 5), 0) )
        self.assertEqual(d, eval(repr(d)))

        #float
        d = Decimal( (0, (4, 5, 3, 4), -2) )
        self.assertEqual(d, eval(repr(d)))

        #weird
        d = Decimal( (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) )
        self.assertEqual(d, eval(repr(d)))

    def test_as_tuple(self):
        Decimal = self.decimal.Decimal

        #with zero
        d = Decimal(0)
        self.assertEqual(d.as_tuple(), (0, (0,), 0) )

        #int
        d = Decimal(-45)
        self.assertEqual(d.as_tuple(), (1, (4, 5), 0) )

        #complicated string
        d = Decimal("-4.34913534E-17")
        self.assertEqual(d.as_tuple(), (1, (4, 3, 4, 9, 1, 3, 5, 3, 4), -25) )

        # The '0' coefficient is implementation specific to decimal.py.
        # It has no meaning in the C-version and is ignored there.
        d = Decimal("Infinity")
        self.assertEqual(d.as_tuple(), (0, (0,), 'F') )

        #leading zeros in coefficient should be stripped
        d = Decimal( (0, (0, 0, 4, 0, 5, 3, 4), -2) )
        self.assertEqual(d.as_tuple(), (0, (4, 0, 5, 3, 4), -2) )
        d = Decimal( (1, (0, 0, 0), 37) )
        self.assertEqual(d.as_tuple(), (1, (0,), 37))
        d = Decimal( (1, (), 37) )
        self.assertEqual(d.as_tuple(), (1, (0,), 37))

        #leading zeros in NaN diagnostic info should be stripped
        d = Decimal( (0, (0, 0, 4, 0, 5, 3, 4), 'n') )
        self.assertEqual(d.as_tuple(), (0, (4, 0, 5, 3, 4), 'n') )
        d = Decimal( (1, (0, 0, 0), 'N') )
        self.assertEqual(d.as_tuple(), (1, (), 'N') )
        d = Decimal( (1, (), 'n') )
        self.assertEqual(d.as_tuple(), (1, (), 'n') )

        # For infinities, decimal.py has always silently accepted any
        # coefficient tuple.
        d = Decimal( (0, (0,), 'F') )
        self.assertEqual(d.as_tuple(), (0, (0,), 'F'))
        d = Decimal( (0, (4, 5, 3, 4), 'F') )
        self.assertEqual(d.as_tuple(), (0, (0,), 'F'))
        d = Decimal( (1, (0, 2, 7, 1), 'F') )
        self.assertEqual(d.as_tuple(), (1, (0,), 'F'))

    def test_as_integer_ratio(self):
        Decimal = self.decimal.Decimal

        # exceptional cases
        self.assertRaises(OverflowError,
                          Decimal.as_integer_ratio, Decimal('inf'))
        self.assertRaises(OverflowError,
                          Decimal.as_integer_ratio, Decimal('-inf'))
        self.assertRaises(ValueError,
                          Decimal.as_integer_ratio, Decimal('-nan'))
        self.assertRaises(ValueError,
                          Decimal.as_integer_ratio, Decimal('snan123'))

        for exp in range(-4, 2):
            for coeff in range(1000):
                for sign in '+', '-':
                    d = Decimal('%s%dE%d' % (sign, coeff, exp))
                    pq = d.as_integer_ratio()
                    p, q = pq

                    # check return type
                    self.assertIsInstance(pq, tuple)
                    self.assertIsInstance(p, int)
                    self.assertIsInstance(q, int)

                    # check normalization:  q should be positive;
                    # p should be relatively prime to q.
                    self.assertGreater(q, 0)
                    self.assertEqual(math.gcd(p, q), 1)

                    # check that p/q actually gives the correct value
                    self.assertEqual(Decimal(p) / Decimal(q), d)

    def test_subclassing(self):
        # Different behaviours when subclassing Decimal
        Decimal = self.decimal.Decimal

        class MyDecimal(Decimal):
            y = None

        d1 = MyDecimal(1)
        d2 = MyDecimal(2)
        d = d1 + d2
        self.assertIs(type(d), Decimal)

        d = d1.max(d2)
        self.assertIs(type(d), Decimal)

        d = copy.copy(d1)
        self.assertIs(type(d), MyDecimal)
        self.assertEqual(d, d1)

        d = copy.deepcopy(d1)
        self.assertIs(type(d), MyDecimal)
        self.assertEqual(d, d1)

        # Decimal(Decimal)
        d = Decimal('1.0')
        x = Decimal(d)
        self.assertIs(type(x), Decimal)
        self.assertEqual(x, d)

        # MyDecimal(Decimal)
        m = MyDecimal(d)
        self.assertIs(type(m), MyDecimal)
        self.assertEqual(m, d)
        self.assertIs(m.y, None)

        # Decimal(MyDecimal)
        x = Decimal(m)
        self.assertIs(type(x), Decimal)
        self.assertEqual(x, d)

        # MyDecimal(MyDecimal)
        m.y = 9
        x = MyDecimal(m)
        self.assertIs(type(x), MyDecimal)
        self.assertEqual(x, d)
        self.assertIs(x.y, None)

    def test_implicit_context(self):
        Decimal = self.decimal.Decimal
        getcontext = self.decimal.getcontext

        # Check results when context given implicitly.  (Issue 2478)
        c = getcontext()
        self.assertEqual(str(Decimal(0).sqrt()),
                         str(c.sqrt(Decimal(0))))

    def test_none_args(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        localcontext = self.decimal.localcontext
        InvalidOperation = self.decimal.InvalidOperation
        DivisionByZero = self.decimal.DivisionByZero
        Overflow = self.decimal.Overflow
        Underflow = self.decimal.Underflow
        Subnormal = self.decimal.Subnormal
        Inexact = self.decimal.Inexact
        Rounded = self.decimal.Rounded
        Clamped = self.decimal.Clamped

        with localcontext(Context()) as c:
            c.prec = 7
            c.Emax = 999
            c.Emin = -999

            x = Decimal("111")
            y = Decimal("1e9999")
            z = Decimal("1e-9999")

            ##### Unary functions
            c.clear_flags()
            self.assertEqual(str(x.exp(context=None)), '1.609487E+48')
            self.assertTrue(c.flags[Inexact])
            self.assertTrue(c.flags[Rounded])
            c.clear_flags()
            self.assertRaises(Overflow, y.exp, context=None)
            self.assertTrue(c.flags[Overflow])

            self.assertIs(z.is_normal(context=None), False)
            self.assertIs(z.is_subnormal(context=None), True)

            c.clear_flags()
            self.assertEqual(str(x.ln(context=None)), '4.709530')
            self.assertTrue(c.flags[Inexact])
            self.assertTrue(c.flags[Rounded])
            c.clear_flags()
            self.assertRaises(InvalidOperation, Decimal(-1).ln, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            self.assertEqual(str(x.log10(context=None)), '2.045323')
            self.assertTrue(c.flags[Inexact])
            self.assertTrue(c.flags[Rounded])
            c.clear_flags()
            self.assertRaises(InvalidOperation, Decimal(-1).log10, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            self.assertEqual(str(x.logb(context=None)), '2')
            self.assertRaises(DivisionByZero, Decimal(0).logb, context=None)
            self.assertTrue(c.flags[DivisionByZero])

            c.clear_flags()
            self.assertEqual(str(x.logical_invert(context=None)), '1111000')
            self.assertRaises(InvalidOperation, y.logical_invert, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            self.assertEqual(str(y.next_minus(context=None)), '9.999999E+999')
            self.assertRaises(InvalidOperation, Decimal('sNaN').next_minus, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            self.assertEqual(str(y.next_plus(context=None)), 'Infinity')
            self.assertRaises(InvalidOperation, Decimal('sNaN').next_plus, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            self.assertEqual(str(z.normalize(context=None)), '0')
            self.assertRaises(Overflow, y.normalize, context=None)
            self.assertTrue(c.flags[Overflow])

            self.assertEqual(str(z.number_class(context=None)), '+Subnormal')

            c.clear_flags()
            self.assertEqual(str(z.sqrt(context=None)), '0E-1005')
            self.assertTrue(c.flags[Clamped])
            self.assertTrue(c.flags[Inexact])
            self.assertTrue(c.flags[Rounded])
            self.assertTrue(c.flags[Subnormal])
            self.assertTrue(c.flags[Underflow])
            c.clear_flags()
            self.assertRaises(Overflow, y.sqrt, context=None)
            self.assertTrue(c.flags[Overflow])

            c.capitals = 0
            self.assertEqual(str(z.to_eng_string(context=None)), '1e-9999')
            c.capitals = 1


            ##### Binary functions
            c.clear_flags()
            ans = str(x.compare(Decimal('Nan891287828'), context=None))
            self.assertEqual(ans, 'NaN1287828')
            self.assertRaises(InvalidOperation, x.compare, Decimal('sNaN'), context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.compare_signal(8224, context=None))
            self.assertEqual(ans, '-1')
            self.assertRaises(InvalidOperation, x.compare_signal, Decimal('NaN'), context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.logical_and(101, context=None))
            self.assertEqual(ans, '101')
            self.assertRaises(InvalidOperation, x.logical_and, 123, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.logical_or(101, context=None))
            self.assertEqual(ans, '111')
            self.assertRaises(InvalidOperation, x.logical_or, 123, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.logical_xor(101, context=None))
            self.assertEqual(ans, '10')
            self.assertRaises(InvalidOperation, x.logical_xor, 123, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.max(101, context=None))
            self.assertEqual(ans, '111')
            self.assertRaises(InvalidOperation, x.max, Decimal('sNaN'), context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.max_mag(101, context=None))
            self.assertEqual(ans, '111')
            self.assertRaises(InvalidOperation, x.max_mag, Decimal('sNaN'), context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.min(101, context=None))
            self.assertEqual(ans, '101')
            self.assertRaises(InvalidOperation, x.min, Decimal('sNaN'), context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.min_mag(101, context=None))
            self.assertEqual(ans, '101')
            self.assertRaises(InvalidOperation, x.min_mag, Decimal('sNaN'), context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.remainder_near(101, context=None))
            self.assertEqual(ans, '10')
            self.assertRaises(InvalidOperation, y.remainder_near, 101, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.rotate(2, context=None))
            self.assertEqual(ans, '11100')
            self.assertRaises(InvalidOperation, x.rotate, 101, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.scaleb(7, context=None))
            self.assertEqual(ans, '1.11E+9')
            self.assertRaises(InvalidOperation, x.scaleb, 10000, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            ans = str(x.shift(2, context=None))
            self.assertEqual(ans, '11100')
            self.assertRaises(InvalidOperation, x.shift, 10000, context=None)
            self.assertTrue(c.flags[InvalidOperation])


            ##### Ternary functions
            c.clear_flags()
            ans = str(x.fma(2, 3, context=None))
            self.assertEqual(ans, '225')
            self.assertRaises(Overflow, x.fma, Decimal('1e9999'), 3, context=None)
            self.assertTrue(c.flags[Overflow])


            ##### Special cases
            c.rounding = ROUND_HALF_EVEN
            ans = str(Decimal('1.5').to_integral(rounding=None, context=None))
            self.assertEqual(ans, '2')
            c.rounding = ROUND_DOWN
            ans = str(Decimal('1.5').to_integral(rounding=None, context=None))
            self.assertEqual(ans, '1')
            ans = str(Decimal('1.5').to_integral(rounding=ROUND_UP, context=None))
            self.assertEqual(ans, '2')
            c.clear_flags()
            self.assertRaises(InvalidOperation, Decimal('sNaN').to_integral, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.rounding = ROUND_HALF_EVEN
            ans = str(Decimal('1.5').to_integral_value(rounding=None, context=None))
            self.assertEqual(ans, '2')
            c.rounding = ROUND_DOWN
            ans = str(Decimal('1.5').to_integral_value(rounding=None, context=None))
            self.assertEqual(ans, '1')
            ans = str(Decimal('1.5').to_integral_value(rounding=ROUND_UP, context=None))
            self.assertEqual(ans, '2')
            c.clear_flags()
            self.assertRaises(InvalidOperation, Decimal('sNaN').to_integral_value, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.rounding = ROUND_HALF_EVEN
            ans = str(Decimal('1.5').to_integral_exact(rounding=None, context=None))
            self.assertEqual(ans, '2')
            c.rounding = ROUND_DOWN
            ans = str(Decimal('1.5').to_integral_exact(rounding=None, context=None))
            self.assertEqual(ans, '1')
            ans = str(Decimal('1.5').to_integral_exact(rounding=ROUND_UP, context=None))
            self.assertEqual(ans, '2')
            c.clear_flags()
            self.assertRaises(InvalidOperation, Decimal('sNaN').to_integral_exact, context=None)
            self.assertTrue(c.flags[InvalidOperation])

            c.rounding = ROUND_UP
            ans = str(Decimal('1.50001').quantize(exp=Decimal('1e-3'), rounding=None, context=None))
            self.assertEqual(ans, '1.501')
            c.rounding = ROUND_DOWN
            ans = str(Decimal('1.50001').quantize(exp=Decimal('1e-3'), rounding=None, context=None))
            self.assertEqual(ans, '1.500')
            ans = str(Decimal('1.50001').quantize(exp=Decimal('1e-3'), rounding=ROUND_UP, context=None))
            self.assertEqual(ans, '1.501')
            c.clear_flags()
            self.assertRaises(InvalidOperation, y.quantize, Decimal('1e-10'), rounding=ROUND_UP, context=None)
            self.assertTrue(c.flags[InvalidOperation])

        with localcontext(Context()) as context:
            context.prec = 7
            context.Emax = 999
            context.Emin = -999
            with localcontext(ctx=None) as c:
                self.assertEqual(c.prec, 7)
                self.assertEqual(c.Emax, 999)
                self.assertEqual(c.Emin, -999)

    def test_conversions_from_int(self):
        # Check that methods taking a second Decimal argument will
        # always accept an integer in place of a Decimal.
        Decimal = self.decimal.Decimal

        self.assertEqual(Decimal(4).compare(3),
                         Decimal(4).compare(Decimal(3)))
        self.assertEqual(Decimal(4).compare_signal(3),
                         Decimal(4).compare_signal(Decimal(3)))
        self.assertEqual(Decimal(4).compare_total(3),
                         Decimal(4).compare_total(Decimal(3)))
        self.assertEqual(Decimal(4).compare_total_mag(3),
                         Decimal(4).compare_total_mag(Decimal(3)))
        self.assertEqual(Decimal(10101).logical_and(1001),
                         Decimal(10101).logical_and(Decimal(1001)))
        self.assertEqual(Decimal(10101).logical_or(1001),
                         Decimal(10101).logical_or(Decimal(1001)))
        self.assertEqual(Decimal(10101).logical_xor(1001),
                         Decimal(10101).logical_xor(Decimal(1001)))
        self.assertEqual(Decimal(567).max(123),
                         Decimal(567).max(Decimal(123)))
        self.assertEqual(Decimal(567).max_mag(123),
                         Decimal(567).max_mag(Decimal(123)))
        self.assertEqual(Decimal(567).min(123),
                         Decimal(567).min(Decimal(123)))
        self.assertEqual(Decimal(567).min_mag(123),
                         Decimal(567).min_mag(Decimal(123)))
        self.assertEqual(Decimal(567).next_toward(123),
                         Decimal(567).next_toward(Decimal(123)))
        self.assertEqual(Decimal(1234).quantize(100),
                         Decimal(1234).quantize(Decimal(100)))
        self.assertEqual(Decimal(768).remainder_near(1234),
                         Decimal(768).remainder_near(Decimal(1234)))
        self.assertEqual(Decimal(123).rotate(1),
                         Decimal(123).rotate(Decimal(1)))
        self.assertEqual(Decimal(1234).same_quantum(1000),
                         Decimal(1234).same_quantum(Decimal(1000)))
        self.assertEqual(Decimal('9.123').scaleb(-100),
                         Decimal('9.123').scaleb(Decimal(-100)))
        self.assertEqual(Decimal(456).shift(-1),
                         Decimal(456).shift(Decimal(-1)))

        self.assertEqual(Decimal(-12).fma(Decimal(45), 67),
                         Decimal(-12).fma(Decimal(45), Decimal(67)))
        self.assertEqual(Decimal(-12).fma(45, 67),
                         Decimal(-12).fma(Decimal(45), Decimal(67)))
        self.assertEqual(Decimal(-12).fma(45, Decimal(67)),
                         Decimal(-12).fma(Decimal(45), Decimal(67)))

@requires_cdecimal
class CUsabilityTest(UsabilityTest, unittest.TestCase):
    decimal = C
class PyUsabilityTest(UsabilityTest, unittest.TestCase):
    decimal = P

    def setUp(self):
        super().setUp()
        self._previous_int_limit = sys.get_int_max_str_digits()
        sys.set_int_max_str_digits(7000)

    def tearDown(self):
        sys.set_int_max_str_digits(self._previous_int_limit)
        super().tearDown()

class PythonAPItests:

    def test_abc(self):
        Decimal = self.decimal.Decimal

        self.assertTrue(issubclass(Decimal, numbers.Number))
        self.assertFalse(issubclass(Decimal, numbers.Real))
        self.assertIsInstance(Decimal(0), numbers.Number)
        self.assertNotIsInstance(Decimal(0), numbers.Real)

    def test_pickle(self):
        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
            Decimal = self.decimal.Decimal

            savedecimal = sys.modules['decimal']

            # Round trip
            sys.modules['decimal'] = self.decimal
            d = Decimal('-3.141590000')
            p = pickle.dumps(d, proto)
            e = pickle.loads(p)
            self.assertEqual(d, e)

            if C:
                # Test interchangeability
                x = C.Decimal('-3.123e81723')
                y = P.Decimal('-3.123e81723')

                sys.modules['decimal'] = C
                sx = pickle.dumps(x, proto)
                sys.modules['decimal'] = P
                r = pickle.loads(sx)
                self.assertIsInstance(r, P.Decimal)
                self.assertEqual(r, y)

                sys.modules['decimal'] = P
                sy = pickle.dumps(y, proto)
                sys.modules['decimal'] = C
                r = pickle.loads(sy)
                self.assertIsInstance(r, C.Decimal)
                self.assertEqual(r, x)

                x = C.Decimal('-3.123e81723').as_tuple()
                y = P.Decimal('-3.123e81723').as_tuple()

                sys.modules['decimal'] = C
                sx = pickle.dumps(x, proto)
                sys.modules['decimal'] = P
                r = pickle.loads(sx)
                self.assertIsInstance(r, P.DecimalTuple)
                self.assertEqual(r, y)

                sys.modules['decimal'] = P
                sy = pickle.dumps(y, proto)
                sys.modules['decimal'] = C
                r = pickle.loads(sy)
                self.assertIsInstance(r, C.DecimalTuple)
                self.assertEqual(r, x)

            sys.modules['decimal'] = savedecimal

    def test_int(self):
        Decimal = self.decimal.Decimal

        for x in range(-250, 250):
            s = '%0.2f' % (x / 100.0)
            # should work the same as for floats
            self.assertEqual(int(Decimal(s)), int(float(s)))
            # should work the same as to_integral in the ROUND_DOWN mode
            d = Decimal(s)
            r = d.to_integral(ROUND_DOWN)
            self.assertEqual(Decimal(int(d)), r)

        self.assertRaises(ValueError, int, Decimal('-nan'))
        self.assertRaises(ValueError, int, Decimal('snan'))
        self.assertRaises(OverflowError, int, Decimal('inf'))
        self.assertRaises(OverflowError, int, Decimal('-inf'))

    @cpython_only
    def test_small_ints(self):
        Decimal = self.decimal.Decimal
        # bpo-46361
        for x in range(-5, 257):
            self.assertIs(int(Decimal(x)), x)

    def test_trunc(self):
        Decimal = self.decimal.Decimal

        for x in range(-250, 250):
            s = '%0.2f' % (x / 100.0)
            # should work the same as for floats
            self.assertEqual(int(Decimal(s)), int(float(s)))
            # should work the same as to_integral in the ROUND_DOWN mode
            d = Decimal(s)
            r = d.to_integral(ROUND_DOWN)
            self.assertEqual(Decimal(math.trunc(d)), r)

    def test_from_float(self):

        Decimal = self.decimal.Decimal

        class MyDecimal(Decimal):
            def __init__(self, _):
                self.x = 'y'

        self.assertTrue(issubclass(MyDecimal, Decimal))

        r = MyDecimal.from_float(0.1)
        self.assertEqual(type(r), MyDecimal)
        self.assertEqual(str(r),
                '0.1000000000000000055511151231257827021181583404541015625')
        self.assertEqual(r.x, 'y')

        bigint = 12345678901234567890123456789
        self.assertEqual(MyDecimal.from_float(bigint), MyDecimal(bigint))
        self.assertTrue(MyDecimal.from_float(float('nan')).is_qnan())
        self.assertTrue(MyDecimal.from_float(float('inf')).is_infinite())
        self.assertTrue(MyDecimal.from_float(float('-inf')).is_infinite())
        self.assertEqual(str(MyDecimal.from_float(float('nan'))),
                         str(Decimal('NaN')))
        self.assertEqual(str(MyDecimal.from_float(float('inf'))),
                         str(Decimal('Infinity')))
        self.assertEqual(str(MyDecimal.from_float(float('-inf'))),
                         str(Decimal('-Infinity')))
        self.assertRaises(TypeError, MyDecimal.from_float, 'abc')
        for i in range(200):
            x = random.expovariate(0.01) * (random.random() * 2.0 - 1.0)
            self.assertEqual(x, float(MyDecimal.from_float(x))) # roundtrip

    def test_create_decimal_from_float(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        Inexact = self.decimal.Inexact

        context = Context(prec=5, rounding=ROUND_DOWN)
        self.assertEqual(
            context.create_decimal_from_float(math.pi),
            Decimal('3.1415')
        )
        context = Context(prec=5, rounding=ROUND_UP)
        self.assertEqual(
            context.create_decimal_from_float(math.pi),
            Decimal('3.1416')
        )
        context = Context(prec=5, traps=[Inexact])
        self.assertRaises(
            Inexact,
            context.create_decimal_from_float,
            math.pi
        )
        self.assertEqual(repr(context.create_decimal_from_float(-0.0)),
                         "Decimal('-0')")
        self.assertEqual(repr(context.create_decimal_from_float(1.0)),
                         "Decimal('1')")
        self.assertEqual(repr(context.create_decimal_from_float(10)),
                         "Decimal('10')")

    def test_quantize(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        InvalidOperation = self.decimal.InvalidOperation

        c = Context(Emax=99999, Emin=-99999)
        self.assertEqual(
            Decimal('7.335').quantize(Decimal('.01')),
            Decimal('7.34')
        )
        self.assertEqual(
            Decimal('7.335').quantize(Decimal('.01'), rounding=ROUND_DOWN),
            Decimal('7.33')
        )
        self.assertRaises(
            InvalidOperation,
            Decimal("10e99999").quantize, Decimal('1e100000'), context=c
        )

        c = Context()
        d = Decimal("0.871831e800")
        x = d.quantize(context=c, exp=Decimal("1e797"), rounding=ROUND_DOWN)
        self.assertEqual(x, Decimal('8.71E+799'))

    def test_complex(self):
        Decimal = self.decimal.Decimal

        x = Decimal("9.8182731e181273")
        self.assertEqual(x.real, x)
        self.assertEqual(x.imag, 0)
        self.assertEqual(x.conjugate(), x)

        x = Decimal("1")
        self.assertEqual(complex(x), complex(float(1)))

        self.assertRaises(AttributeError, setattr, x, 'real', 100)
        self.assertRaises(AttributeError, setattr, x, 'imag', 100)
        self.assertRaises(AttributeError, setattr, x, 'conjugate', 100)
        self.assertRaises(AttributeError, setattr, x, '__complex__', 100)

    def test_named_parameters(self):
        D = self.decimal.Decimal
        Context = self.decimal.Context
        localcontext = self.decimal.localcontext
        InvalidOperation = self.decimal.InvalidOperation
        Overflow = self.decimal.Overflow

        xc = Context()
        xc.prec = 1
        xc.Emax = 1
        xc.Emin = -1

        with localcontext() as c:
            c.clear_flags()

            self.assertEqual(D(9, xc), 9)
            self.assertEqual(D(9, context=xc), 9)
            self.assertEqual(D(context=xc, value=9), 9)
            self.assertEqual(D(context=xc), 0)
            xc.clear_flags()
            self.assertRaises(InvalidOperation, D, "xyz", context=xc)
            self.assertTrue(xc.flags[InvalidOperation])
            self.assertFalse(c.flags[InvalidOperation])

            xc.clear_flags()
            self.assertEqual(D(2).exp(context=xc), 7)
            self.assertRaises(Overflow, D(8).exp, context=xc)
            self.assertTrue(xc.flags[Overflow])
            self.assertFalse(c.flags[Overflow])

            xc.clear_flags()
            self.assertEqual(D(2).ln(context=xc), D('0.7'))
            self.assertRaises(InvalidOperation, D(-1).ln, context=xc)
            self.assertTrue(xc.flags[InvalidOperation])
            self.assertFalse(c.flags[InvalidOperation])

            self.assertEqual(D(0).log10(context=xc), D('-inf'))
            self.assertEqual(D(-1).next_minus(context=xc), -2)
            self.assertEqual(D(-1).next_plus(context=xc), D('-0.9'))
            self.assertEqual(D("9.73").normalize(context=xc), D('1E+1'))
            self.assertEqual(D("9999").to_integral(context=xc), 9999)
            self.assertEqual(D("-2000").to_integral_exact(context=xc), -2000)
            self.assertEqual(D("123").to_integral_value(context=xc), 123)
            self.assertEqual(D("0.0625").sqrt(context=xc), D('0.2'))

            self.assertEqual(D("0.0625").compare(context=xc, other=3), -1)
            xc.clear_flags()
            self.assertRaises(InvalidOperation,
                              D("0").compare_signal, D('nan'), context=xc)
            self.assertTrue(xc.flags[InvalidOperation])
            self.assertFalse(c.flags[InvalidOperation])
            self.assertEqual(D("0.01").max(D('0.0101'), context=xc), D('0.0'))
            self.assertEqual(D("0.01").max(D('0.0101'), context=xc), D('0.0'))
            self.assertEqual(D("0.2").max_mag(D('-0.3'), context=xc),
                             D('-0.3'))
            self.assertEqual(D("0.02").min(D('-0.03'), context=xc), D('-0.0'))
            self.assertEqual(D("0.02").min_mag(D('-0.03'), context=xc),
                             D('0.0'))
            self.assertEqual(D("0.2").next_toward(D('-1'), context=xc), D('0.1'))
            xc.clear_flags()
            self.assertRaises(InvalidOperation,
                              D("0.2").quantize, D('1e10'), context=xc)
            self.assertTrue(xc.flags[InvalidOperation])
            self.assertFalse(c.flags[InvalidOperation])
            self.assertEqual(D("9.99").remainder_near(D('1.5'), context=xc),
                             D('-0.5'))

            self.assertEqual(D("9.9").fma(third=D('0.9'), context=xc, other=7),
                             D('7E+1'))

            self.assertRaises(TypeError, D(1).is_canonical, context=xc)
            self.assertRaises(TypeError, D(1).is_finite, context=xc)
            self.assertRaises(TypeError, D(1).is_infinite, context=xc)
            self.assertRaises(TypeError, D(1).is_nan, context=xc)
            self.assertRaises(TypeError, D(1).is_qnan, context=xc)
            self.assertRaises(TypeError, D(1).is_snan, context=xc)
            self.assertRaises(TypeError, D(1).is_signed, context=xc)
            self.assertRaises(TypeError, D(1).is_zero, context=xc)

            self.assertFalse(D("0.01").is_normal(context=xc))
            self.assertTrue(D("0.01").is_subnormal(context=xc))

            self.assertRaises(TypeError, D(1).adjusted, context=xc)
            self.assertRaises(TypeError, D(1).conjugate, context=xc)
            self.assertRaises(TypeError, D(1).radix, context=xc)

            self.assertEqual(D(-111).logb(context=xc), 2)
            self.assertEqual(D(0).logical_invert(context=xc), 1)
            self.assertEqual(D('0.01').number_class(context=xc), '+Subnormal')
            self.assertEqual(D('0.21').to_eng_string(context=xc), '0.21')

            self.assertEqual(D('11').logical_and(D('10'), context=xc), 0)
            self.assertEqual(D('11').logical_or(D('10'), context=xc), 1)
            self.assertEqual(D('01').logical_xor(D('10'), context=xc), 1)
            self.assertEqual(D('23').rotate(1, context=xc), 3)
            self.assertEqual(D('23').rotate(1, context=xc), 3)
            xc.clear_flags()
            self.assertRaises(Overflow,
                              D('23').scaleb, 1, context=xc)
            self.assertTrue(xc.flags[Overflow])
            self.assertFalse(c.flags[Overflow])
            self.assertEqual(D('23').shift(-1, context=xc), 0)

            self.assertRaises(TypeError, D.from_float, 1.1, context=xc)
            self.assertRaises(TypeError, D(0).as_tuple, context=xc)

            self.assertEqual(D(1).canonical(), 1)
            self.assertRaises(TypeError, D("-1").copy_abs, context=xc)
            self.assertRaises(TypeError, D("-1").copy_negate, context=xc)
            self.assertRaises(TypeError, D(1).canonical, context="x")
            self.assertRaises(TypeError, D(1).canonical, xyz="x")

    def test_exception_hierarchy(self):

        decimal = self.decimal
        DecimalException = decimal.DecimalException
        InvalidOperation = decimal.InvalidOperation
        FloatOperation = decimal.FloatOperation
        DivisionByZero = decimal.DivisionByZero
        Overflow = decimal.Overflow
        Underflow = decimal.Underflow
        Subnormal = decimal.Subnormal
        Inexact = decimal.Inexact
        Rounded = decimal.Rounded
        Clamped = decimal.Clamped

        self.assertTrue(issubclass(DecimalException, ArithmeticError))

        self.assertTrue(issubclass(InvalidOperation, DecimalException))
        self.assertTrue(issubclass(FloatOperation, DecimalException))
        self.assertTrue(issubclass(FloatOperation, TypeError))
        self.assertTrue(issubclass(DivisionByZero, DecimalException))
        self.assertTrue(issubclass(DivisionByZero, ZeroDivisionError))
        self.assertTrue(issubclass(Overflow, Rounded))
        self.assertTrue(issubclass(Overflow, Inexact))
        self.assertTrue(issubclass(Overflow, DecimalException))
        self.assertTrue(issubclass(Underflow, Inexact))
        self.assertTrue(issubclass(Underflow, Rounded))
        self.assertTrue(issubclass(Underflow, Subnormal))
        self.assertTrue(issubclass(Underflow, DecimalException))

        self.assertTrue(issubclass(Subnormal, DecimalException))
        self.assertTrue(issubclass(Inexact, DecimalException))
        self.assertTrue(issubclass(Rounded, DecimalException))
        self.assertTrue(issubclass(Clamped, DecimalException))

        self.assertTrue(issubclass(decimal.ConversionSyntax, InvalidOperation))
        self.assertTrue(issubclass(decimal.DivisionImpossible, InvalidOperation))
        self.assertTrue(issubclass(decimal.DivisionUndefined, InvalidOperation))
        self.assertTrue(issubclass(decimal.DivisionUndefined, ZeroDivisionError))
        self.assertTrue(issubclass(decimal.InvalidContext, InvalidOperation))

@requires_cdecimal
class CPythonAPItests(PythonAPItests, unittest.TestCase):
    decimal = C
class PyPythonAPItests(PythonAPItests, unittest.TestCase):
    decimal = P

class ContextAPItests:

    def test_none_args(self):
        Context = self.decimal.Context
        InvalidOperation = self.decimal.InvalidOperation
        DivisionByZero = self.decimal.DivisionByZero
        Overflow = self.decimal.Overflow

        c1 = Context()
        c2 = Context(prec=None, rounding=None, Emax=None, Emin=None,
                     capitals=None, clamp=None, flags=None, traps=None)
        for c in [c1, c2]:
            self.assertEqual(c.prec, 28)
            self.assertEqual(c.rounding, ROUND_HALF_EVEN)
            self.assertEqual(c.Emax, 999999)
            self.assertEqual(c.Emin, -999999)
            self.assertEqual(c.capitals, 1)
            self.assertEqual(c.clamp, 0)
            assert_signals(self, c, 'flags', [])
            assert_signals(self, c, 'traps', [InvalidOperation, DivisionByZero,
                                              Overflow])

    def test_pickle(self):

        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
            Context = self.decimal.Context

            savedecimal = sys.modules['decimal']

            # Round trip
            sys.modules['decimal'] = self.decimal
            c = Context()
            e = pickle.loads(pickle.dumps(c, proto))

            self.assertEqual(c.prec, e.prec)
            self.assertEqual(c.Emin, e.Emin)
            self.assertEqual(c.Emax, e.Emax)
            self.assertEqual(c.rounding, e.rounding)
            self.assertEqual(c.capitals, e.capitals)
            self.assertEqual(c.clamp, e.clamp)
            self.assertEqual(c.flags, e.flags)
            self.assertEqual(c.traps, e.traps)

            # Test interchangeability
            combinations = [(C, P), (P, C)] if C else [(P, P)]
            for dumper, loader in combinations:
                for ri, _ in enumerate(RoundingModes):
                    for fi, _ in enumerate(OrderedSignals[dumper]):
                        for ti, _ in enumerate(OrderedSignals[dumper]):

                            prec = random.randrange(1, 100)
                            emin = random.randrange(-100, 0)
                            emax = random.randrange(1, 100)
                            caps = random.randrange(2)
                            clamp = random.randrange(2)

                            # One module dumps
                            sys.modules['decimal'] = dumper
                            c = dumper.Context(
                                  prec=prec, Emin=emin, Emax=emax,
                                  rounding=RoundingModes[ri],
                                  capitals=caps, clamp=clamp,
                                  flags=OrderedSignals[dumper][:fi],
                                  traps=OrderedSignals[dumper][:ti]
                            )
                            s = pickle.dumps(c, proto)

                            # The other module loads
                            sys.modules['decimal'] = loader
                            d = pickle.loads(s)
                            self.assertIsInstance(d, loader.Context)

                            self.assertEqual(d.prec, prec)
                            self.assertEqual(d.Emin, emin)
                            self.assertEqual(d.Emax, emax)
                            self.assertEqual(d.rounding, RoundingModes[ri])
                            self.assertEqual(d.capitals, caps)
                            self.assertEqual(d.clamp, clamp)
                            assert_signals(self, d, 'flags', OrderedSignals[loader][:fi])
                            assert_signals(self, d, 'traps', OrderedSignals[loader][:ti])

            sys.modules['decimal'] = savedecimal

    def test_equality_with_other_types(self):
        Decimal = self.decimal.Decimal

        self.assertIn(Decimal(10), ['a', 1.0, Decimal(10), (1,2), {}])
        self.assertNotIn(Decimal(10), ['a', 1.0, (1,2), {}])

    def test_copy(self):
        # All copies should be deep
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.copy()
        self.assertNotEqual(id(c), id(d))
        self.assertNotEqual(id(c.flags), id(d.flags))
        self.assertNotEqual(id(c.traps), id(d.traps))
        k1 = set(c.flags.keys())
        k2 = set(d.flags.keys())
        self.assertEqual(k1, k2)
        self.assertEqual(c.flags, d.flags)

    def test__clamp(self):
        # In Python 3.2, the private attribute `_clamp` was made
        # public (issue 8540), with the old `_clamp` becoming a
        # property wrapping `clamp`.  For the duration of Python 3.2
        # only, the attribute should be gettable/settable via both
        # `clamp` and `_clamp`; in Python 3.3, `_clamp` should be
        # removed.
        Context = self.decimal.Context
        c = Context()
        self.assertRaises(AttributeError, getattr, c, '_clamp')

    def test_abs(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.abs(Decimal(-1))
        self.assertEqual(c.abs(-1), d)
        self.assertRaises(TypeError, c.abs, '-1')

    def test_add(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.add(Decimal(1), Decimal(1))
        self.assertEqual(c.add(1, 1), d)
        self.assertEqual(c.add(Decimal(1), 1), d)
        self.assertEqual(c.add(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.add, '1', 1)
        self.assertRaises(TypeError, c.add, 1, '1')

    def test_compare(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.compare(Decimal(1), Decimal(1))
        self.assertEqual(c.compare(1, 1), d)
        self.assertEqual(c.compare(Decimal(1), 1), d)
        self.assertEqual(c.compare(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.compare, '1', 1)
        self.assertRaises(TypeError, c.compare, 1, '1')

    def test_compare_signal(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.compare_signal(Decimal(1), Decimal(1))
        self.assertEqual(c.compare_signal(1, 1), d)
        self.assertEqual(c.compare_signal(Decimal(1), 1), d)
        self.assertEqual(c.compare_signal(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.compare_signal, '1', 1)
        self.assertRaises(TypeError, c.compare_signal, 1, '1')

    def test_compare_total(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.compare_total(Decimal(1), Decimal(1))
        self.assertEqual(c.compare_total(1, 1), d)
        self.assertEqual(c.compare_total(Decimal(1), 1), d)
        self.assertEqual(c.compare_total(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.compare_total, '1', 1)
        self.assertRaises(TypeError, c.compare_total, 1, '1')

    def test_compare_total_mag(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.compare_total_mag(Decimal(1), Decimal(1))
        self.assertEqual(c.compare_total_mag(1, 1), d)
        self.assertEqual(c.compare_total_mag(Decimal(1), 1), d)
        self.assertEqual(c.compare_total_mag(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.compare_total_mag, '1', 1)
        self.assertRaises(TypeError, c.compare_total_mag, 1, '1')

    def test_copy_abs(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.copy_abs(Decimal(-1))
        self.assertEqual(c.copy_abs(-1), d)
        self.assertRaises(TypeError, c.copy_abs, '-1')

    def test_copy_decimal(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.copy_decimal(Decimal(-1))
        self.assertEqual(c.copy_decimal(-1), d)
        self.assertRaises(TypeError, c.copy_decimal, '-1')

    def test_copy_negate(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.copy_negate(Decimal(-1))
        self.assertEqual(c.copy_negate(-1), d)
        self.assertRaises(TypeError, c.copy_negate, '-1')

    def test_copy_sign(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.copy_sign(Decimal(1), Decimal(-2))
        self.assertEqual(c.copy_sign(1, -2), d)
        self.assertEqual(c.copy_sign(Decimal(1), -2), d)
        self.assertEqual(c.copy_sign(1, Decimal(-2)), d)
        self.assertRaises(TypeError, c.copy_sign, '1', -2)
        self.assertRaises(TypeError, c.copy_sign, 1, '-2')

    def test_divide(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.divide(Decimal(1), Decimal(2))
        self.assertEqual(c.divide(1, 2), d)
        self.assertEqual(c.divide(Decimal(1), 2), d)
        self.assertEqual(c.divide(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.divide, '1', 2)
        self.assertRaises(TypeError, c.divide, 1, '2')

    def test_divide_int(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.divide_int(Decimal(1), Decimal(2))
        self.assertEqual(c.divide_int(1, 2), d)
        self.assertEqual(c.divide_int(Decimal(1), 2), d)
        self.assertEqual(c.divide_int(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.divide_int, '1', 2)
        self.assertRaises(TypeError, c.divide_int, 1, '2')

    def test_divmod(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.divmod(Decimal(1), Decimal(2))
        self.assertEqual(c.divmod(1, 2), d)
        self.assertEqual(c.divmod(Decimal(1), 2), d)
        self.assertEqual(c.divmod(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.divmod, '1', 2)
        self.assertRaises(TypeError, c.divmod, 1, '2')

    def test_exp(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.exp(Decimal(10))
        self.assertEqual(c.exp(10), d)
        self.assertRaises(TypeError, c.exp, '10')

    def test_fma(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.fma(Decimal(2), Decimal(3), Decimal(4))
        self.assertEqual(c.fma(2, 3, 4), d)
        self.assertEqual(c.fma(Decimal(2), 3, 4), d)
        self.assertEqual(c.fma(2, Decimal(3), 4), d)
        self.assertEqual(c.fma(2, 3, Decimal(4)), d)
        self.assertEqual(c.fma(Decimal(2), Decimal(3), 4), d)
        self.assertRaises(TypeError, c.fma, '2', 3, 4)
        self.assertRaises(TypeError, c.fma, 2, '3', 4)
        self.assertRaises(TypeError, c.fma, 2, 3, '4')

        # Issue 12079 for Context.fma ...
        self.assertRaises(TypeError, c.fma,
                          Decimal('Infinity'), Decimal(0), "not a decimal")
        self.assertRaises(TypeError, c.fma,
                          Decimal(1), Decimal('snan'), 1.222)
        # ... and for Decimal.fma.
        self.assertRaises(TypeError, Decimal('Infinity').fma,
                          Decimal(0), "not a decimal")
        self.assertRaises(TypeError, Decimal(1).fma,
                          Decimal('snan'), 1.222)

    def test_is_finite(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_finite(Decimal(10))
        self.assertEqual(c.is_finite(10), d)
        self.assertRaises(TypeError, c.is_finite, '10')

    def test_is_infinite(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_infinite(Decimal(10))
        self.assertEqual(c.is_infinite(10), d)
        self.assertRaises(TypeError, c.is_infinite, '10')

    def test_is_nan(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_nan(Decimal(10))
        self.assertEqual(c.is_nan(10), d)
        self.assertRaises(TypeError, c.is_nan, '10')

    def test_is_normal(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_normal(Decimal(10))
        self.assertEqual(c.is_normal(10), d)
        self.assertRaises(TypeError, c.is_normal, '10')

    def test_is_qnan(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_qnan(Decimal(10))
        self.assertEqual(c.is_qnan(10), d)
        self.assertRaises(TypeError, c.is_qnan, '10')

    def test_is_signed(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_signed(Decimal(10))
        self.assertEqual(c.is_signed(10), d)
        self.assertRaises(TypeError, c.is_signed, '10')

    def test_is_snan(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_snan(Decimal(10))
        self.assertEqual(c.is_snan(10), d)
        self.assertRaises(TypeError, c.is_snan, '10')

    def test_is_subnormal(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_subnormal(Decimal(10))
        self.assertEqual(c.is_subnormal(10), d)
        self.assertRaises(TypeError, c.is_subnormal, '10')

    def test_is_zero(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.is_zero(Decimal(10))
        self.assertEqual(c.is_zero(10), d)
        self.assertRaises(TypeError, c.is_zero, '10')

    def test_ln(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.ln(Decimal(10))
        self.assertEqual(c.ln(10), d)
        self.assertRaises(TypeError, c.ln, '10')

    def test_log10(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.log10(Decimal(10))
        self.assertEqual(c.log10(10), d)
        self.assertRaises(TypeError, c.log10, '10')

    def test_logb(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.logb(Decimal(10))
        self.assertEqual(c.logb(10), d)
        self.assertRaises(TypeError, c.logb, '10')

    def test_logical_and(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.logical_and(Decimal(1), Decimal(1))
        self.assertEqual(c.logical_and(1, 1), d)
        self.assertEqual(c.logical_and(Decimal(1), 1), d)
        self.assertEqual(c.logical_and(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.logical_and, '1', 1)
        self.assertRaises(TypeError, c.logical_and, 1, '1')

    def test_logical_invert(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.logical_invert(Decimal(1000))
        self.assertEqual(c.logical_invert(1000), d)
        self.assertRaises(TypeError, c.logical_invert, '1000')

    def test_logical_or(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.logical_or(Decimal(1), Decimal(1))
        self.assertEqual(c.logical_or(1, 1), d)
        self.assertEqual(c.logical_or(Decimal(1), 1), d)
        self.assertEqual(c.logical_or(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.logical_or, '1', 1)
        self.assertRaises(TypeError, c.logical_or, 1, '1')

    def test_logical_xor(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.logical_xor(Decimal(1), Decimal(1))
        self.assertEqual(c.logical_xor(1, 1), d)
        self.assertEqual(c.logical_xor(Decimal(1), 1), d)
        self.assertEqual(c.logical_xor(1, Decimal(1)), d)
        self.assertRaises(TypeError, c.logical_xor, '1', 1)
        self.assertRaises(TypeError, c.logical_xor, 1, '1')

    def test_max(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.max(Decimal(1), Decimal(2))
        self.assertEqual(c.max(1, 2), d)
        self.assertEqual(c.max(Decimal(1), 2), d)
        self.assertEqual(c.max(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.max, '1', 2)
        self.assertRaises(TypeError, c.max, 1, '2')

    def test_max_mag(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.max_mag(Decimal(1), Decimal(2))
        self.assertEqual(c.max_mag(1, 2), d)
        self.assertEqual(c.max_mag(Decimal(1), 2), d)
        self.assertEqual(c.max_mag(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.max_mag, '1', 2)
        self.assertRaises(TypeError, c.max_mag, 1, '2')

    def test_min(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.min(Decimal(1), Decimal(2))
        self.assertEqual(c.min(1, 2), d)
        self.assertEqual(c.min(Decimal(1), 2), d)
        self.assertEqual(c.min(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.min, '1', 2)
        self.assertRaises(TypeError, c.min, 1, '2')

    def test_min_mag(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.min_mag(Decimal(1), Decimal(2))
        self.assertEqual(c.min_mag(1, 2), d)
        self.assertEqual(c.min_mag(Decimal(1), 2), d)
        self.assertEqual(c.min_mag(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.min_mag, '1', 2)
        self.assertRaises(TypeError, c.min_mag, 1, '2')

    def test_minus(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.minus(Decimal(10))
        self.assertEqual(c.minus(10), d)
        self.assertRaises(TypeError, c.minus, '10')

    def test_multiply(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.multiply(Decimal(1), Decimal(2))
        self.assertEqual(c.multiply(1, 2), d)
        self.assertEqual(c.multiply(Decimal(1), 2), d)
        self.assertEqual(c.multiply(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.multiply, '1', 2)
        self.assertRaises(TypeError, c.multiply, 1, '2')

    def test_next_minus(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.next_minus(Decimal(10))
        self.assertEqual(c.next_minus(10), d)
        self.assertRaises(TypeError, c.next_minus, '10')

    def test_next_plus(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.next_plus(Decimal(10))
        self.assertEqual(c.next_plus(10), d)
        self.assertRaises(TypeError, c.next_plus, '10')

    def test_next_toward(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.next_toward(Decimal(1), Decimal(2))
        self.assertEqual(c.next_toward(1, 2), d)
        self.assertEqual(c.next_toward(Decimal(1), 2), d)
        self.assertEqual(c.next_toward(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.next_toward, '1', 2)
        self.assertRaises(TypeError, c.next_toward, 1, '2')

    def test_normalize(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.normalize(Decimal(10))
        self.assertEqual(c.normalize(10), d)
        self.assertRaises(TypeError, c.normalize, '10')

    def test_number_class(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        self.assertEqual(c.number_class(123), c.number_class(Decimal(123)))
        self.assertEqual(c.number_class(0), c.number_class(Decimal(0)))
        self.assertEqual(c.number_class(-45), c.number_class(Decimal(-45)))

    def test_plus(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.plus(Decimal(10))
        self.assertEqual(c.plus(10), d)
        self.assertRaises(TypeError, c.plus, '10')

    def test_power(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.power(Decimal(1), Decimal(4))
        self.assertEqual(c.power(1, 4), d)
        self.assertEqual(c.power(Decimal(1), 4), d)
        self.assertEqual(c.power(1, Decimal(4)), d)
        self.assertEqual(c.power(Decimal(1), Decimal(4)), d)
        self.assertRaises(TypeError, c.power, '1', 4)
        self.assertRaises(TypeError, c.power, 1, '4')
        self.assertEqual(c.power(modulo=5, b=8, a=2), 1)

    def test_quantize(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.quantize(Decimal(1), Decimal(2))
        self.assertEqual(c.quantize(1, 2), d)
        self.assertEqual(c.quantize(Decimal(1), 2), d)
        self.assertEqual(c.quantize(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.quantize, '1', 2)
        self.assertRaises(TypeError, c.quantize, 1, '2')

    def test_remainder(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.remainder(Decimal(1), Decimal(2))
        self.assertEqual(c.remainder(1, 2), d)
        self.assertEqual(c.remainder(Decimal(1), 2), d)
        self.assertEqual(c.remainder(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.remainder, '1', 2)
        self.assertRaises(TypeError, c.remainder, 1, '2')

    def test_remainder_near(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.remainder_near(Decimal(1), Decimal(2))
        self.assertEqual(c.remainder_near(1, 2), d)
        self.assertEqual(c.remainder_near(Decimal(1), 2), d)
        self.assertEqual(c.remainder_near(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.remainder_near, '1', 2)
        self.assertRaises(TypeError, c.remainder_near, 1, '2')

    def test_rotate(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.rotate(Decimal(1), Decimal(2))
        self.assertEqual(c.rotate(1, 2), d)
        self.assertEqual(c.rotate(Decimal(1), 2), d)
        self.assertEqual(c.rotate(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.rotate, '1', 2)
        self.assertRaises(TypeError, c.rotate, 1, '2')

    def test_sqrt(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.sqrt(Decimal(10))
        self.assertEqual(c.sqrt(10), d)
        self.assertRaises(TypeError, c.sqrt, '10')

    def test_same_quantum(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.same_quantum(Decimal(1), Decimal(2))
        self.assertEqual(c.same_quantum(1, 2), d)
        self.assertEqual(c.same_quantum(Decimal(1), 2), d)
        self.assertEqual(c.same_quantum(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.same_quantum, '1', 2)
        self.assertRaises(TypeError, c.same_quantum, 1, '2')

    def test_scaleb(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.scaleb(Decimal(1), Decimal(2))
        self.assertEqual(c.scaleb(1, 2), d)
        self.assertEqual(c.scaleb(Decimal(1), 2), d)
        self.assertEqual(c.scaleb(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.scaleb, '1', 2)
        self.assertRaises(TypeError, c.scaleb, 1, '2')

    def test_shift(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.shift(Decimal(1), Decimal(2))
        self.assertEqual(c.shift(1, 2), d)
        self.assertEqual(c.shift(Decimal(1), 2), d)
        self.assertEqual(c.shift(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.shift, '1', 2)
        self.assertRaises(TypeError, c.shift, 1, '2')

    def test_subtract(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.subtract(Decimal(1), Decimal(2))
        self.assertEqual(c.subtract(1, 2), d)
        self.assertEqual(c.subtract(Decimal(1), 2), d)
        self.assertEqual(c.subtract(1, Decimal(2)), d)
        self.assertRaises(TypeError, c.subtract, '1', 2)
        self.assertRaises(TypeError, c.subtract, 1, '2')

    def test_to_eng_string(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.to_eng_string(Decimal(10))
        self.assertEqual(c.to_eng_string(10), d)
        self.assertRaises(TypeError, c.to_eng_string, '10')

    def test_to_sci_string(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.to_sci_string(Decimal(10))
        self.assertEqual(c.to_sci_string(10), d)
        self.assertRaises(TypeError, c.to_sci_string, '10')

    def test_to_integral_exact(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.to_integral_exact(Decimal(10))
        self.assertEqual(c.to_integral_exact(10), d)
        self.assertRaises(TypeError, c.to_integral_exact, '10')

    def test_to_integral_value(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context

        c = Context()
        d = c.to_integral_value(Decimal(10))
        self.assertEqual(c.to_integral_value(10), d)
        self.assertRaises(TypeError, c.to_integral_value, '10')
        self.assertRaises(TypeError, c.to_integral_value, 10, 'x')

@requires_cdecimal
class CContextAPItests(ContextAPItests, unittest.TestCase):
    decimal = C
class PyContextAPItests(ContextAPItests, unittest.TestCase):
    decimal = P

class ContextWithStatement:
    # Can't do these as docstrings until Python 2.6
    # as doctest can't handle __future__ statements

    def test_localcontext(self):
        # Use a copy of the current context in the block
        getcontext = self.decimal.getcontext
        localcontext = self.decimal.localcontext

        orig_ctx = getcontext()
        with localcontext() as enter_ctx:
            set_ctx = getcontext()
        final_ctx = getcontext()
        self.assertIs(orig_ctx, final_ctx, 'did not restore context correctly')
        self.assertIsNot(orig_ctx, set_ctx, 'did not copy the context')
        self.assertIs(set_ctx, enter_ctx, '__enter__ returned wrong context')

    def test_localcontextarg(self):
        # Use a copy of the supplied context in the block
        Context = self.decimal.Context
        getcontext = self.decimal.getcontext
        localcontext = self.decimal.localcontext

        localcontext = self.decimal.localcontext
        orig_ctx = getcontext()
        new_ctx = Context(prec=42)
        with localcontext(new_ctx) as enter_ctx:
            set_ctx = getcontext()
        final_ctx = getcontext()
        self.assertIs(orig_ctx, final_ctx, 'did not restore context correctly')
        self.assertEqual(set_ctx.prec, new_ctx.prec, 'did not set correct context')
        self.assertIsNot(new_ctx, set_ctx, 'did not copy the context')
        self.assertIs(set_ctx, enter_ctx, '__enter__ returned wrong context')

    def test_localcontext_kwargs(self):
        with self.decimal.localcontext(
            prec=10, rounding=ROUND_HALF_DOWN,
            Emin=-20, Emax=20, capitals=0,
            clamp=1
        ) as ctx:
            self.assertEqual(ctx.prec, 10)
            self.assertEqual(ctx.rounding, self.decimal.ROUND_HALF_DOWN)
            self.assertEqual(ctx.Emin, -20)
            self.assertEqual(ctx.Emax, 20)
            self.assertEqual(ctx.capitals, 0)
            self.assertEqual(ctx.clamp, 1)

        self.assertRaises(TypeError, self.decimal.localcontext, precision=10)

        self.assertRaises(ValueError, self.decimal.localcontext, Emin=1)
        self.assertRaises(ValueError, self.decimal.localcontext, Emax=-1)
        self.assertRaises(ValueError, self.decimal.localcontext, capitals=2)
        self.assertRaises(ValueError, self.decimal.localcontext, clamp=2)

        self.assertRaises(TypeError, self.decimal.localcontext, rounding="")
        self.assertRaises(TypeError, self.decimal.localcontext, rounding=1)

        self.assertRaises(TypeError, self.decimal.localcontext, flags="")
        self.assertRaises(TypeError, self.decimal.localcontext, traps="")
        self.assertRaises(TypeError, self.decimal.localcontext, Emin="")
        self.assertRaises(TypeError, self.decimal.localcontext, Emax="")

    def test_local_context_kwargs_does_not_overwrite_existing_argument(self):
        ctx = self.decimal.getcontext()
        orig_prec = ctx.prec
        with self.decimal.localcontext(prec=10) as ctx2:
            self.assertEqual(ctx2.prec, 10)
            self.assertEqual(ctx.prec, orig_prec)
        with self.decimal.localcontext(prec=20) as ctx2:
            self.assertEqual(ctx2.prec, 20)
            self.assertEqual(ctx.prec, orig_prec)

    def test_nested_with_statements(self):
        # Use a copy of the supplied context in the block
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        getcontext = self.decimal.getcontext
        localcontext = self.decimal.localcontext
        Clamped = self.decimal.Clamped
        Overflow = self.decimal.Overflow

        orig_ctx = getcontext()
        orig_ctx.clear_flags()
        new_ctx = Context(Emax=384)
        with localcontext() as c1:
            self.assertEqual(c1.flags, orig_ctx.flags)
            self.assertEqual(c1.traps, orig_ctx.traps)
            c1.traps[Clamped] = True
            c1.Emin = -383
            self.assertNotEqual(orig_ctx.Emin, -383)
            self.assertRaises(Clamped, c1.create_decimal, '0e-999')
            self.assertTrue(c1.flags[Clamped])
            with localcontext(new_ctx) as c2:
                self.assertEqual(c2.flags, new_ctx.flags)
                self.assertEqual(c2.traps, new_ctx.traps)
                self.assertRaises(Overflow, c2.power, Decimal('3.4e200'), 2)
                self.assertFalse(c2.flags[Clamped])
                self.assertTrue(c2.flags[Overflow])
                del c2
            self.assertFalse(c1.flags[Overflow])
            del c1
        self.assertNotEqual(orig_ctx.Emin, -383)
        self.assertFalse(orig_ctx.flags[Clamped])
        self.assertFalse(orig_ctx.flags[Overflow])
        self.assertFalse(new_ctx.flags[Clamped])
        self.assertFalse(new_ctx.flags[Overflow])

    def test_with_statements_gc1(self):
        localcontext = self.decimal.localcontext

        with localcontext() as c1:
            del c1
            with localcontext() as c2:
                del c2
                with localcontext() as c3:
                    del c3
                    with localcontext() as c4:
                        del c4

    def test_with_statements_gc2(self):
        localcontext = self.decimal.localcontext

        with localcontext() as c1:
            with localcontext(c1) as c2:
                del c1
                with localcontext(c2) as c3:
                    del c2
                    with localcontext(c3) as c4:
                        del c3
                        del c4

    def test_with_statements_gc3(self):
        Context = self.decimal.Context
        localcontext = self.decimal.localcontext
        getcontext = self.decimal.getcontext
        setcontext = self.decimal.setcontext

        with localcontext() as c1:
            del c1
            n1 = Context(prec=1)
            setcontext(n1)
            with localcontext(n1) as c2:
                del n1
                self.assertEqual(c2.prec, 1)
                del c2
                n2 = Context(prec=2)
                setcontext(n2)
                del n2
                self.assertEqual(getcontext().prec, 2)
                n3 = Context(prec=3)
                setcontext(n3)
                self.assertEqual(getcontext().prec, 3)
                with localcontext(n3) as c3:
                    del n3
                    self.assertEqual(c3.prec, 3)
                    del c3
                    n4 = Context(prec=4)
                    setcontext(n4)
                    del n4
                    self.assertEqual(getcontext().prec, 4)
                    with localcontext() as c4:
                        self.assertEqual(c4.prec, 4)
                        del c4

@requires_cdecimal
class CContextWithStatement(ContextWithStatement, unittest.TestCase):
    decimal = C
class PyContextWithStatement(ContextWithStatement, unittest.TestCase):
    decimal = P

class ContextFlags:

    def test_flags_irrelevant(self):
        # check that the result (numeric result + flags raised) of an
        # arithmetic operation doesn't depend on the current flags
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        Inexact = self.decimal.Inexact
        Rounded = self.decimal.Rounded
        Underflow = self.decimal.Underflow
        Clamped = self.decimal.Clamped
        Subnormal = self.decimal.Subnormal

        def raise_error(context, flag):
            if self.decimal == C:
                context.flags[flag] = True
                if context.traps[flag]:
                    raise flag
            else:
                context._raise_error(flag)

        context = Context(prec=9, Emin = -425000000, Emax = 425000000,
                          rounding=ROUND_HALF_EVEN, traps=[], flags=[])

        # operations that raise various flags, in the form (function, arglist)
        operations = [
            (context._apply, [Decimal("100E-425000010")]),
            (context.sqrt, [Decimal(2)]),
            (context.add, [Decimal("1.23456789"), Decimal("9.87654321")]),
            (context.multiply, [Decimal("1.23456789"), Decimal("9.87654321")]),
            (context.subtract, [Decimal("1.23456789"), Decimal("9.87654321")]),
            ]

        # try various flags individually, then a whole lot at once
        flagsets = [[Inexact], [Rounded], [Underflow], [Clamped], [Subnormal],
                    [Inexact, Rounded, Underflow, Clamped, Subnormal]]

        for fn, args in operations:
            # find answer and flags raised using a clean context
            context.clear_flags()
            ans = fn(*args)
            flags = [k for k, v in context.flags.items() if v]

            for extra_flags in flagsets:
                # set flags, before calling operation
                context.clear_flags()
                for flag in extra_flags:
                    raise_error(context, flag)
                new_ans = fn(*args)

                # flags that we expect to be set after the operation
                expected_flags = list(flags)
                for flag in extra_flags:
                    if flag not in expected_flags:
                        expected_flags.append(flag)
                expected_flags.sort(key=id)

                # flags we actually got
                new_flags = [k for k,v in context.flags.items() if v]
                new_flags.sort(key=id)

                self.assertEqual(ans, new_ans,
                                 "operation produces different answers depending on flags set: " +
                                 "expected %s, got %s." % (ans, new_ans))
                self.assertEqual(new_flags, expected_flags,
                                  "operation raises different flags depending on flags set: " +
                                  "expected %s, got %s" % (expected_flags, new_flags))

    def test_flag_comparisons(self):
        Context = self.decimal.Context
        Inexact = self.decimal.Inexact
        Rounded = self.decimal.Rounded

        c = Context()

        # Valid SignalDict
        self.assertNotEqual(c.flags, c.traps)
        self.assertNotEqual(c.traps, c.flags)

        c.flags = c.traps
        self.assertEqual(c.flags, c.traps)
        self.assertEqual(c.traps, c.flags)

        c.flags[Rounded] = True
        c.traps = c.flags
        self.assertEqual(c.flags, c.traps)
        self.assertEqual(c.traps, c.flags)

        d = {}
        d.update(c.flags)
        self.assertEqual(d, c.flags)
        self.assertEqual(c.flags, d)

        d[Inexact] = True
        self.assertNotEqual(d, c.flags)
        self.assertNotEqual(c.flags, d)

        # Invalid SignalDict
        d = {Inexact:False}
        self.assertNotEqual(d, c.flags)
        self.assertNotEqual(c.flags, d)

        d = ["xyz"]
        self.assertNotEqual(d, c.flags)
        self.assertNotEqual(c.flags, d)

    @requires_IEEE_754
    def test_float_operation(self):
        Decimal = self.decimal.Decimal
        FloatOperation = self.decimal.FloatOperation
        localcontext = self.decimal.localcontext

        with localcontext() as c:
            ##### trap is off by default
            self.assertFalse(c.traps[FloatOperation])

            # implicit conversion sets the flag
            c.clear_flags()
            self.assertEqual(Decimal(7.5), 7.5)
            self.assertTrue(c.flags[FloatOperation])

            c.clear_flags()
            self.assertEqual(c.create_decimal(7.5), 7.5)
            self.assertTrue(c.flags[FloatOperation])

            # explicit conversion does not set the flag
            c.clear_flags()
            x = Decimal.from_float(7.5)
            self.assertFalse(c.flags[FloatOperation])
            # comparison sets the flag
            self.assertEqual(x, 7.5)
            self.assertTrue(c.flags[FloatOperation])

            c.clear_flags()
            x = c.create_decimal_from_float(7.5)
            self.assertFalse(c.flags[FloatOperation])
            self.assertEqual(x, 7.5)
            self.assertTrue(c.flags[FloatOperation])

            ##### set the trap
            c.traps[FloatOperation] = True

            # implicit conversion raises
            c.clear_flags()
            self.assertRaises(FloatOperation, Decimal, 7.5)
            self.assertTrue(c.flags[FloatOperation])

            c.clear_flags()
            self.assertRaises(FloatOperation, c.create_decimal, 7.5)
            self.assertTrue(c.flags[FloatOperation])

            # explicit conversion is silent
            c.clear_flags()
            x = Decimal.from_float(7.5)
            self.assertFalse(c.flags[FloatOperation])

            c.clear_flags()
            x = c.create_decimal_from_float(7.5)
            self.assertFalse(c.flags[FloatOperation])

    def test_float_comparison(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        FloatOperation = self.decimal.FloatOperation
        localcontext = self.decimal.localcontext

        def assert_attr(a, b, attr, context, signal=None):
            context.clear_flags()
            f = getattr(a, attr)
            if signal == FloatOperation:
                self.assertRaises(signal, f, b)
            else:
                self.assertIs(f(b), True)
            self.assertTrue(context.flags[FloatOperation])

        small_d = Decimal('0.25')
        big_d = Decimal('3.0')
        small_f = 0.25
        big_f = 3.0

        zero_d = Decimal('0.0')
        neg_zero_d = Decimal('-0.0')
        zero_f = 0.0
        neg_zero_f = -0.0

        inf_d = Decimal('Infinity')
        neg_inf_d = Decimal('-Infinity')
        inf_f = float('inf')
        neg_inf_f = float('-inf')

        def doit(c, signal=None):
            # Order
            for attr in '__lt__', '__le__':
                assert_attr(small_d, big_f, attr, c, signal)

            for attr in '__gt__', '__ge__':
                assert_attr(big_d, small_f, attr, c, signal)

            # Equality
            assert_attr(small_d, small_f, '__eq__', c, None)

            assert_attr(neg_zero_d, neg_zero_f, '__eq__', c, None)
            assert_attr(neg_zero_d, zero_f, '__eq__', c, None)

            assert_attr(zero_d, neg_zero_f, '__eq__', c, None)
            assert_attr(zero_d, zero_f, '__eq__', c, None)

            assert_attr(neg_inf_d, neg_inf_f, '__eq__', c, None)
            assert_attr(inf_d, inf_f, '__eq__', c, None)

            # Inequality
            assert_attr(small_d, big_f, '__ne__', c, None)

            assert_attr(Decimal('0.1'), 0.1, '__ne__', c, None)

            assert_attr(neg_inf_d, inf_f, '__ne__', c, None)
            assert_attr(inf_d, neg_inf_f, '__ne__', c, None)

            assert_attr(Decimal('NaN'), float('nan'), '__ne__', c, None)

        def test_containers(c, signal=None):
            c.clear_flags()
            s = set([100.0, Decimal('100.0')])
            self.assertEqual(len(s), 1)
            self.assertTrue(c.flags[FloatOperation])

            c.clear_flags()
            if signal:
                self.assertRaises(signal, sorted, [1.0, Decimal('10.0')])
            else:
                s = sorted([10.0, Decimal('10.0')])
            self.assertTrue(c.flags[FloatOperation])

            c.clear_flags()
            b = 10.0 in [Decimal('10.0'), 1.0]
            self.assertTrue(c.flags[FloatOperation])

            c.clear_flags()
            b = 10.0 in {Decimal('10.0'):'a', 1.0:'b'}
            self.assertTrue(c.flags[FloatOperation])

        nc = Context()
        with localcontext(nc) as c:
            self.assertFalse(c.traps[FloatOperation])
            doit(c, signal=None)
            test_containers(c, signal=None)

            c.traps[FloatOperation] = True
            doit(c, signal=FloatOperation)
            test_containers(c, signal=FloatOperation)

    def test_float_operation_default(self):
        Decimal = self.decimal.Decimal
        Context = self.decimal.Context
        Inexact = self.decimal.Inexact
        FloatOperation= self.decimal.FloatOperation

        context = Context()
        self.assertFalse(context.flags[FloatOperation])
        self.assertFalse(context.traps[FloatOperation])

        context.clear_traps()
        context.traps[Inexact] = True
        context.traps[FloatOperation] = True
        self.assertTrue(context.traps[FloatOperation])
        self.assertTrue(context.traps[Inexact])

@requires_cdecimal
class CContextFlags(ContextFlags, unittest.TestCase):
    decimal = C
class PyContextFlags(ContextFlags, unittest.TestCase):
    decimal = P

class SpecialContexts:
    """Test the context templates."""

    def test_context_templates(self):
        BasicContext = self.decimal.BasicContext
        ExtendedContext = self.decimal.ExtendedContext
        getcontext = self.decimal.getcontext
        setcontext = self.decimal.setcontext
        InvalidOperation = self.decimal.InvalidOperation
        DivisionByZero = self.decimal.DivisionByZero
        Overflow = self.decimal.Overflow
        Underflow = self.decimal.Underflow
        Clamped = self.decimal.Clamped

        assert_signals(self, BasicContext, 'traps',
            [InvalidOperation, DivisionByZero, Overflow, Underflow, Clamped]
        )

        savecontext = getcontext().copy()
        basic_context_prec = BasicContext.prec
        extended_context_prec = ExtendedContext.prec

        ex = None
        try:
            BasicContext.prec = ExtendedContext.prec = 441
            for template in BasicContext, ExtendedContext:
                setcontext(template)
                c = getcontext()
                self.assertIsNot(c, template)
                self.assertEqual(c.prec, 441)
        except Exception as e:
            ex = e.__class__
        finally:
            BasicContext.prec = basic_context_prec
            ExtendedContext.prec = extended_context_prec
            setcontext(savecontext)
            if ex:
                raise ex

    def test_default_context(self):
        DefaultContext = self.decimal.DefaultContext
        BasicContext = self.decimal.BasicContext
        ExtendedContext = self.decimal.ExtendedContext
        getcontext = self.decimal.getcontext
        setcontext = self.decimal.setcontext
        InvalidOperation = self.decimal.InvalidOperation
        DivisionByZero = self.decimal.DivisionByZero
        Overflow = self.decimal.Overflow

        self.assertEqual(BasicContext.prec, 9)
        self.assertEqual(ExtendedContext.prec, 9)

        assert_signals(self, DefaultContext, 'traps',
            [InvalidOperation, DivisionByZero, Overflow]
        )

        savecontext = getcontext().copy()
        default_context_prec = DefaultContext.prec

        ex = None
        try:
            c = getcontext()
            saveprec = c.prec

            DefaultContext.prec = 961
            c = getcontext()
            self.assertEqual(c.prec, saveprec)

            setcontext(DefaultContext)
            c = getcontext()
            self.assertIsNot(c, DefaultContext)
            self.assertEqual(c.prec, 961)
        except Exception as e:
            ex = e.__class__
        finally:
            DefaultContext.prec = default_context_prec
            setcontext(savecontext)
            if ex:
                raise ex

@requires_cdecimal
class CSpecialContexts(SpecialContexts, unittest.TestCase):
    decimal = C
class PySpecialContexts(SpecialContexts, unittest.TestCase):
    decimal = P

class ContextInputValidation:

    def test_invalid_context(self):
        Context = self.decimal.Context
        DefaultContext = self.decimal.DefaultContext

        c = DefaultContext.copy()

        # prec, Emax
        for attr in ['prec', 'Emax']:
            setattr(c, attr, 999999)
            self.assertEqual(getattr(c, attr), 999999)
            self.assertRaises(ValueError, setattr, c, attr, -1)
            self.assertRaises(TypeError, setattr, c, attr, 'xyz')

        # Emin
        setattr(c, 'Emin', -999999)
        self.assertEqual(getattr(c, 'Emin'), -999999)
        self.assertRaises(ValueError, setattr, c, 'Emin', 1)
        self.assertRaises(TypeError, setattr, c, 'Emin', (1,2,3))

        self.assertRaises(TypeError, setattr, c, 'rounding', -1)
        self.assertRaises(TypeError, setattr, c, 'rounding', 9)
        self.assertRaises(TypeError, setattr, c, 'rounding', 1.0)
        self.assertRaises(TypeError, setattr, c, 'rounding', 'xyz')

        # capitals, clamp
        for attr in ['capitals', 'clamp']:
            self.assertRaises(ValueError, setattr, c, attr, -1)
            self.assertRaises(ValueError, setattr, c, attr, 2)
            self.assertRaises(TypeError, setattr, c, attr, [1,2,3])

        # Invalid attribute
        self.assertRaises(AttributeError, setattr, c, 'emax', 100)

        # Invalid signal dict
        self.assertRaises(TypeError, setattr, c, 'flags', [])
        self.assertRaises(KeyError, setattr, c, 'flags', {})
        self.assertRaises(KeyError, setattr, c, 'traps',
                          {'InvalidOperation':0})

        # Attributes cannot be deleted
        for attr in ['prec', 'Emax', 'Emin', 'rounding', 'capitals', 'clamp',
                     'flags', 'traps']:
            self.assertRaises(AttributeError, c.__delattr__, attr)

        # Invalid attributes
        self.assertRaises(TypeError, getattr, c, 9)
        self.assertRaises(TypeError, setattr, c, 9)

        # Invalid values in constructor
        self.assertRaises(TypeError, Context, rounding=999999)
        self.assertRaises(TypeError, Context, rounding='xyz')
        self.assertRaises(ValueError, Context, clamp=2)
        self.assertRaises(ValueError, Context, capitals=-1)
        self.assertRaises(KeyError, Context, flags=["P"])
        self.assertRaises(KeyError, Context, traps=["Q"])

        # Type error in conversion
        self.assertRaises(TypeError, Context, flags=(0,1))
        self.assertRaises(TypeError, Context, traps=(1,0))

@requires_cdecimal
class CContextInputValidation(ContextInputValidation, unittest.TestCase):
    decimal = C
class PyContextInputValidation(ContextInputValidation, unittest.TestCase):
    decimal = P

class ContextSubclassing:

    def test_context_subclassing(self):
        decimal = self.decimal
        Decimal = decimal.Decimal
        Context = decimal.Context
        Clamped = decimal.Clamped
        DivisionByZero = decimal.DivisionByZero
        Inexact = decimal.Inexact
        Overflow = decimal.Overflow
        Rounded = decimal.Rounded
        Subnormal = decimal.Subnormal
        Underflow = decimal.Underflow
        InvalidOperation = decimal.InvalidOperation

        class MyContext(Context):
            def __init__(self, prec=None, rounding=None, Emin=None, Emax=None,
                               capitals=None, clamp=None, flags=None,
                               traps=None):
                Context.__init__(self)
                if prec is not None:
                    self.prec = prec
                if rounding is not None:
                    self.rounding = rounding
                if Emin is not None:
                    self.Emin = Emin
                if Emax is not None:
                    self.Emax = Emax
                if capitals is not None:
                    self.capitals = capitals
                if clamp is not None:
                    self.clamp = clamp
                if flags is not None:
                    if isinstance(flags, list):
                        flags = {v:(v in flags) for v in OrderedSignals[decimal] + flags}
                    self.flags = flags
                if traps is not None:
                    if isinstance(traps, list):
                        traps = {v:(v in traps) for v in OrderedSignals[decimal] + traps}
                    self.traps = traps

        c = Context()
        d = MyContext()
        for attr in ('prec', 'rounding', 'Emin', 'Emax', 'capitals', 'clamp',
                     'flags', 'traps'):
            self.assertEqual(getattr(c, attr), getattr(d, attr))

        # prec
        self.assertRaises(ValueError, MyContext, **{'prec':-1})
        c = MyContext(prec=1)
        self.assertEqual(c.prec, 1)
        self.assertRaises(InvalidOperation, c.quantize, Decimal('9e2'), 0)

        # rounding
        self.assertRaises(TypeError, MyContext, **{'rounding':'XYZ'})
        c = MyContext(rounding=ROUND_DOWN, prec=1)
        self.assertEqual(c.rounding, ROUND_DOWN)
        self.assertEqual(c.plus(Decimal('9.9')), 9)

        # Emin
        self.assertRaises(ValueError, MyContext, **{'Emin':5})
        c = MyContext(Emin=-1, prec=1)
        self.assertEqual(c.Emin, -1)
        x = c.add(Decimal('1e-99'), Decimal('2.234e-2000'))
        self.assertEqual(x, Decimal('0.0'))
        for signal in (Inexact, Underflow, Subnormal, Rounded, Clamped):
            self.assertTrue(c.flags[signal])

        # Emax
        self.assertRaises(ValueError, MyContext, **{'Emax':-1})
        c = MyContext(Emax=1, prec=1)
        self.assertEqual(c.Emax, 1)
        self.assertRaises(Overflow, c.add, Decimal('1e99'), Decimal('2.234e2000'))
        if self.decimal == C:
            for signal in (Inexact, Overflow, Rounded):
                self.assertTrue(c.flags[signal])

        # capitals
        self.assertRaises(ValueError, MyContext, **{'capitals':-1})
        c = MyContext(capitals=0)
        self.assertEqual(c.capitals, 0)
        x = c.create_decimal('1E222')
        self.assertEqual(c.to_sci_string(x), '1e+222')

        # clamp
        self.assertRaises(ValueError, MyContext, **{'clamp':2})
        c = MyContext(clamp=1, Emax=99)
        self.assertEqual(c.clamp, 1)
        x = c.plus(Decimal('1e99'))
        self.assertEqual(str(x), '1.000000000000000000000000000E+99')

        # flags
        self.assertRaises(TypeError, MyContext, **{'flags':'XYZ'})
        c = MyContext(flags=[Rounded, DivisionByZero])
        for signal in (Rounded, DivisionByZero):
            self.assertTrue(c.flags[signal])
        c.clear_flags()
        for signal in OrderedSignals[decimal]:
            self.assertFalse(c.flags[signal])

        # traps
        self.assertRaises(TypeError, MyContext, **{'traps':'XYZ'})
        c = MyContext(traps=[Rounded, DivisionByZero])
        for signal in (Rounded, DivisionByZero):
            self.assertTrue(c.traps[signal])
        c.clear_traps()
        for signal in OrderedSignals[decimal]:
            self.assertFalse(c.traps[signal])

@requires_cdecimal
class CContextSubclassing(ContextSubclassing, unittest.TestCase):
    decimal = C
class PyContextSubclassing(ContextSubclassing, unittest.TestCase):
    decimal = P

@skip_if_extra_functionality
@requires_cdecimal
class CheckAttributes(unittest.TestCase):

    def test_module_attributes(self):

        # Architecture dependent context limits
        self.assertEqual(C.MAX_PREC, P.MAX_PREC)
        self.assertEqual(C.MAX_EMAX, P.MAX_EMAX)
        self.assertEqual(C.MIN_EMIN, P.MIN_EMIN)
        self.assertEqual(C.MIN_ETINY, P.MIN_ETINY)

        self.assertTrue(C.HAVE_THREADS is True or C.HAVE_THREADS is False)
        self.assertTrue(P.HAVE_THREADS is True or P.HAVE_THREADS is False)

        self.assertEqual(C.__version__, P.__version__)

        self.assertLessEqual(set(dir(C)), set(dir(P)))
        self.assertEqual([n for n in dir(C) if n[:2] != '__'], sorted(P.__all__))

    def test_context_attributes(self):

        x = [s for s in dir(C.Context()) if '__' in s or not s.startswith('_')]
        y = [s for s in dir(P.Context()) if '__' in s or not s.startswith('_')]
        self.assertEqual(set(x) - set(y), set())

    def test_decimal_attributes(self):

        x = [s for s in dir(C.Decimal(9)) if '__' in s or not s.startswith('_')]
        y = [s for s in dir(C.Decimal(9)) if '__' in s or not s.startswith('_')]
        self.assertEqual(set(x) - set(y), set())

class Coverage:

    def test_adjusted(self):
        Decimal = self.decimal.Decimal

        self.assertEqual(Decimal('1234e9999').adjusted(), 10002)
        # XXX raise?
        self.assertEqual(Decimal('nan').adjusted(), 0)
        self.assertEqual(Decimal('inf').adjusted(), 0)

    def test_canonical(self):
        Decimal = self.decimal.Decimal
        getcontext = self.decimal.getcontext

        x = Decimal(9).canonical()
        self.assertEqual(x, 9)

        c = getcontext()
        x = c.canonical(Decimal(9))
        self.assertEqual(x, 9)

    def test_context_repr(self):
        c = self.decimal.DefaultContext.copy()

        c.prec = 425000000
        c.Emax = 425000000
        c.Emin = -425000000
        c.rounding = ROUND_HALF_DOWN
        c.capitals = 0
        c.clamp = 1
        for sig in OrderedSignals[self.decimal]:
            c.flags[sig] = False
            c.traps[sig] = False

        s = c.__repr__()
        t = "Context(prec=425000000, rounding=ROUND_HALF_DOWN, " \
            "Emin=-425000000, Emax=425000000, capitals=0, clamp=1, " \
            "flags=[], traps=[])"
        self.assertEqual(s, t)

    def test_implicit_context(self):
        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext

        with localcontext() as c:
            c.prec = 1
            c.Emax = 1
            c.Emin = -1

            # abs
            self.assertEqual(abs(Decimal("-10")), 10)
            # add
            self.assertEqual(Decimal("7") + 1, 8)
            # divide
            self.assertEqual(Decimal("10") / 5, 2)
            # divide_int
            self.assertEqual(Decimal("10") // 7, 1)
            # fma
            self.assertEqual(Decimal("1.2").fma(Decimal("0.01"), 1), 1)
            self.assertIs(Decimal("NaN").fma(7, 1).is_nan(), True)
            # three arg power
            self.assertEqual(pow(Decimal(10), 2, 7), 2)
            if self.decimal == C:
                self.assertEqual(pow(10, Decimal(2), 7), 2)
                self.assertEqual(pow(10, 2, Decimal(7)), 2)
            else:
                # XXX: Three-arg power doesn't use __rpow__.
                self.assertRaises(TypeError, pow, 10, Decimal(2), 7)
                # XXX: There is no special method to dispatch on the
                # third arg of three-arg power.
                self.assertRaises(TypeError, pow, 10, 2, Decimal(7))
            # exp
            self.assertEqual(Decimal("1.01").exp(), 3)
            # is_normal
            self.assertIs(Decimal("0.01").is_normal(), False)
            # is_subnormal
            self.assertIs(Decimal("0.01").is_subnormal(), True)
            # ln
            self.assertEqual(Decimal("20").ln(), 3)
            # log10
            self.assertEqual(Decimal("20").log10(), 1)
            # logb
            self.assertEqual(Decimal("580").logb(), 2)
            # logical_invert
            self.assertEqual(Decimal("10").logical_invert(), 1)
            # minus
            self.assertEqual(-Decimal("-10"), 10)
            # multiply
            self.assertEqual(Decimal("2") * 4, 8)
            # next_minus
            self.assertEqual(Decimal("10").next_minus(), 9)
            # next_plus
            self.assertEqual(Decimal("10").next_plus(), Decimal('2E+1'))
            # normalize
            self.assertEqual(Decimal("-10").normalize(), Decimal('-1E+1'))
            # number_class
            self.assertEqual(Decimal("10").number_class(), '+Normal')
            # plus
            self.assertEqual(+Decimal("-1"), -1)
            # remainder
            self.assertEqual(Decimal("10") % 7, 3)
            # subtract
            self.assertEqual(Decimal("10") - 7, 3)
            # to_integral_exact
            self.assertEqual(Decimal("1.12345").to_integral_exact(), 1)

            # Boolean functions
            self.assertTrue(Decimal("1").is_canonical())
            self.assertTrue(Decimal("1").is_finite())
            self.assertTrue(Decimal("1").is_finite())
            self.assertTrue(Decimal("snan").is_snan())
            self.assertTrue(Decimal("-1").is_signed())
            self.assertTrue(Decimal("0").is_zero())
            self.assertTrue(Decimal("0").is_zero())

        # Copy
        with localcontext() as c:
            c.prec = 10000
            x = 1228 ** 1523
            y = -Decimal(x)

            z = y.copy_abs()
            self.assertEqual(z, x)

            z = y.copy_negate()
            self.assertEqual(z, x)

            z = y.copy_sign(Decimal(1))
            self.assertEqual(z, x)

    def test_divmod(self):
        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext
        InvalidOperation = self.decimal.InvalidOperation
        DivisionByZero = self.decimal.DivisionByZero

        with localcontext() as c:
            q, r = divmod(Decimal("10912837129"), 1001)
            self.assertEqual(q, Decimal('10901935'))
            self.assertEqual(r, Decimal('194'))

            q, r = divmod(Decimal("NaN"), 7)
            self.assertTrue(q.is_nan() and r.is_nan())

            c.traps[InvalidOperation] = False
            q, r = divmod(Decimal("NaN"), 7)
            self.assertTrue(q.is_nan() and r.is_nan())

            c.traps[InvalidOperation] = False
            c.clear_flags()
            q, r = divmod(Decimal("inf"), Decimal("inf"))
            self.assertTrue(q.is_nan() and r.is_nan())
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            q, r = divmod(Decimal("inf"), 101)
            self.assertTrue(q.is_infinite() and r.is_nan())
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            q, r = divmod(Decimal(0), 0)
            self.assertTrue(q.is_nan() and r.is_nan())
            self.assertTrue(c.flags[InvalidOperation])

            c.traps[DivisionByZero] = False
            c.clear_flags()
            q, r = divmod(Decimal(11), 0)
            self.assertTrue(q.is_infinite() and r.is_nan())
            self.assertTrue(c.flags[InvalidOperation] and
                            c.flags[DivisionByZero])

    def test_power(self):
        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext
        Overflow = self.decimal.Overflow
        Rounded = self.decimal.Rounded

        with localcontext() as c:
            c.prec = 3
            c.clear_flags()
            self.assertEqual(Decimal("1.0") ** 100, Decimal('1.00'))
            self.assertTrue(c.flags[Rounded])

            c.prec = 1
            c.Emax = 1
            c.Emin = -1
            c.clear_flags()
            c.traps[Overflow] = False
            self.assertEqual(Decimal(10000) ** Decimal("0.5"), Decimal('inf'))
            self.assertTrue(c.flags[Overflow])

    def test_quantize(self):
        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext
        InvalidOperation = self.decimal.InvalidOperation

        with localcontext() as c:
            c.prec = 1
            c.Emax = 1
            c.Emin = -1
            c.traps[InvalidOperation] = False
            x = Decimal(99).quantize(Decimal("1e1"))
            self.assertTrue(x.is_nan())

    def test_radix(self):
        Decimal = self.decimal.Decimal
        getcontext = self.decimal.getcontext

        c = getcontext()
        self.assertEqual(Decimal("1").radix(), 10)
        self.assertEqual(c.radix(), 10)

    def test_rop(self):
        Decimal = self.decimal.Decimal

        for attr in ('__radd__', '__rsub__', '__rmul__', '__rtruediv__',
                     '__rdivmod__', '__rmod__', '__rfloordiv__', '__rpow__'):
            self.assertIs(getattr(Decimal("1"), attr)("xyz"), NotImplemented)

    def test_round(self):
        # Python3 behavior: round() returns Decimal
        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext

        with localcontext() as c:
            c.prec = 28

            self.assertEqual(str(Decimal("9.99").__round__()), "10")
            self.assertEqual(str(Decimal("9.99e-5").__round__()), "0")
            self.assertEqual(str(Decimal("1.23456789").__round__(5)), "1.23457")
            self.assertEqual(str(Decimal("1.2345").__round__(10)), "1.2345000000")
            self.assertEqual(str(Decimal("1.2345").__round__(-10)), "0E+10")

            self.assertRaises(TypeError, Decimal("1.23").__round__, "5")
            self.assertRaises(TypeError, Decimal("1.23").__round__, 5, 8)

    def test_create_decimal(self):
        c = self.decimal.Context()
        self.assertRaises(ValueError, c.create_decimal, ["%"])

    def test_int(self):
        Decimal = self.decimal.Decimal
        localcontext = self.decimal.localcontext

        with localcontext() as c:
            c.prec = 9999
            x = Decimal(1221**1271) / 10**3923
            self.assertEqual(int(x), 1)
            self.assertEqual(x.to_integral(), 2)

    def test_copy(self):
        Context = self.decimal.Context

        c = Context()
        c.prec = 10000
        x = -(1172 ** 1712)

        y = c.copy_abs(x)
        self.assertEqual(y, -x)

        y = c.copy_negate(x)
        self.assertEqual(y, -x)

        y = c.copy_sign(x, 1)
        self.assertEqual(y, -x)

@requires_cdecimal
class CCoverage(Coverage, unittest.TestCase):
    decimal = C
class PyCoverage(Coverage, unittest.TestCase):
    decimal = P

    def setUp(self):
        super().setUp()
        self._previous_int_limit = sys.get_int_max_str_digits()
        sys.set_int_max_str_digits(7000)

    def tearDown(self):
        sys.set_int_max_str_digits(self._previous_int_limit)
        super().tearDown()

class PyFunctionality(unittest.TestCase):
    """Extra functionality in decimal.py"""

    def test_py_alternate_formatting(self):
        # triples giving a format, a Decimal, and the expected result
        Decimal = P.Decimal
        localcontext = P.localcontext

        test_values = [
            # Issue 7094: Alternate formatting (specified by #)
            ('.0e', '1.0', '1e+0'),
            ('#.0e', '1.0', '1.e+0'),
            ('.0f', '1.0', '1'),
            ('#.0f', '1.0', '1.'),
            ('g', '1.1', '1.1'),
            ('#g', '1.1', '1.1'),
            ('.0g', '1', '1'),
            ('#.0g', '1', '1.'),
            ('.0%', '1.0', '100%'),
            ('#.0%', '1.0', '100.%'),
            ]
        for fmt, d, result in test_values:
            self.assertEqual(format(Decimal(d), fmt), result)

class PyWhitebox(unittest.TestCase):
    """White box testing for decimal.py"""

    def test_py_exact_power(self):
        # Rarely exercised lines in _power_exact.
        Decimal = P.Decimal
        localcontext = P.localcontext

        with localcontext() as c:
            c.prec = 8
            x = Decimal(2**16) ** Decimal("-0.5")
            self.assertEqual(x, Decimal('0.00390625'))

            x = Decimal(2**16) ** Decimal("-0.6")
            self.assertEqual(x, Decimal('0.0012885819'))

            x = Decimal("256e7") ** Decimal("-0.5")

            x = Decimal(152587890625) ** Decimal('-0.0625')
            self.assertEqual(x, Decimal("0.2"))

            x = Decimal("152587890625e7") ** Decimal('-0.0625')

            x = Decimal(5**2659) ** Decimal('-0.0625')

            c.prec = 1
            x = Decimal("152587890625") ** Decimal('-0.5')
            self.assertEqual(x, Decimal('3e-6'))
            c.prec = 2
            x = Decimal("152587890625") ** Decimal('-0.5')
            self.assertEqual(x, Decimal('2.6e-6'))
            c.prec = 3
            x = Decimal("152587890625") ** Decimal('-0.5')
            self.assertEqual(x, Decimal('2.56e-6'))
            c.prec = 28
            x = Decimal("152587890625") ** Decimal('-0.5')
            self.assertEqual(x, Decimal('2.56e-6'))

            c.prec = 201
            x = Decimal(2**578) ** Decimal("-0.5")

            # See https://github.com/python/cpython/issues/118027
            # Testing for an exact power could appear to hang, in the Python
            # version, as it attempted to compute 10**(MAX_EMAX + 1).
            # Fixed via https://github.com/python/cpython/pull/118503.
            c.prec = P.MAX_PREC
            c.Emax = P.MAX_EMAX
            c.Emin = P.MIN_EMIN
            c.traps[P.Inexact] = 1
            D2 = Decimal(2)
            # If the bug is still present, the next statement won't complete.
            res = D2 ** 117
            self.assertEqual(res, 1 << 117)

    def test_py_immutability_operations(self):
        # Do operations and check that it didn't change internal objects.
        Decimal = P.Decimal
        DefaultContext = P.DefaultContext
        setcontext = P.setcontext

        c = DefaultContext.copy()
        c.traps = dict((s, 0) for s in OrderedSignals[P])
        setcontext(c)

        d1 = Decimal('-25e55')
        b1 = Decimal('-25e55')
        d2 = Decimal('33e+33')
        b2 = Decimal('33e+33')

        def checkSameDec(operation, useOther=False):
            if useOther:
                eval("d1." + operation + "(d2)")
                self.assertEqual(d1._sign, b1._sign)
                self.assertEqual(d1._int, b1._int)
                self.assertEqual(d1._exp, b1._exp)
                self.assertEqual(d2._sign, b2._sign)
                self.assertEqual(d2._int, b2._int)
                self.assertEqual(d2._exp, b2._exp)
            else:
                eval("d1." + operation + "()")
                self.assertEqual(d1._sign, b1._sign)
                self.assertEqual(d1._int, b1._int)
                self.assertEqual(d1._exp, b1._exp)

        Decimal(d1)
        self.assertEqual(d1._sign, b1._sign)
        self.assertEqual(d1._int, b1._int)
        self.assertEqual(d1._exp, b1._exp)

        checkSameDec("__abs__")
        checkSameDec("__add__", True)
        checkSameDec("__divmod__", True)
        checkSameDec("__eq__", True)
        checkSameDec("__ne__", True)
        checkSameDec("__le__", True)
        checkSameDec("__lt__", True)
        checkSameDec("__ge__", True)
        checkSameDec("__gt__", True)
        checkSameDec("__float__")
        checkSameDec("__floordiv__", True)
        checkSameDec("__hash__")
        checkSameDec("__int__")
        checkSameDec("__trunc__")
        checkSameDec("__mod__", True)
        checkSameDec("__mul__", True)
        checkSameDec("__neg__")
        checkSameDec("__bool__")
        checkSameDec("__pos__")
        checkSameDec("__pow__", True)
        checkSameDec("__radd__", True)
        checkSameDec("__rdivmod__", True)
        checkSameDec("__repr__")
        checkSameDec("__rfloordiv__", True)
        checkSameDec("__rmod__", True)
        checkSameDec("__rmul__", True)
        checkSameDec("__rpow__", True)
        checkSameDec("__rsub__", True)
        checkSameDec("__str__")
        checkSameDec("__sub__", True)
        checkSameDec("__truediv__", True)
        checkSameDec("adjusted")
        checkSameDec("as_tuple")
        checkSameDec("compare", True)
        checkSameDec("max", True)
        checkSameDec("min", True)
        checkSameDec("normalize")
        checkSameDec("quantize", True)
        checkSameDec("remainder_near", True)
        checkSameDec("same_quantum", True)
        checkSameDec("sqrt")
        checkSameDec("to_eng_string")
        checkSameDec("to_integral")

    def test_py_decimal_id(self):
        Decimal = P.Decimal

        d = Decimal(45)
        e = Decimal(d)
        self.assertEqual(str(e), '45')
        self.assertNotEqual(id(d), id(e))

    def test_py_rescale(self):
        # Coverage
        Decimal = P.Decimal
        localcontext = P.localcontext

        with localcontext() as c:
            x = Decimal("NaN")._rescale(3, ROUND_UP)
            self.assertTrue(x.is_nan())

    def test_py__round(self):
        # Coverage
        Decimal = P.Decimal

        self.assertRaises(ValueError, Decimal("3.1234")._round, 0, ROUND_UP)

class CFunctionality(unittest.TestCase):
    """Extra functionality in _decimal"""

    @requires_extra_functionality
    def test_c_ieee_context(self):
        # issue 8786: Add support for IEEE 754 contexts to decimal module.
        IEEEContext = C.IEEEContext
        DECIMAL32 = C.DECIMAL32
        DECIMAL64 = C.DECIMAL64
        DECIMAL128 = C.DECIMAL128

        def assert_rest(self, context):
            self.assertEqual(context.clamp, 1)
            assert_signals(self, context, 'traps', [])
            assert_signals(self, context, 'flags', [])

        c = IEEEContext(DECIMAL32)
        self.assertEqual(c.prec, 7)
        self.assertEqual(c.Emax, 96)
        self.assertEqual(c.Emin, -95)
        assert_rest(self, c)

        c = IEEEContext(DECIMAL64)
        self.assertEqual(c.prec, 16)
        self.assertEqual(c.Emax, 384)
        self.assertEqual(c.Emin, -383)
        assert_rest(self, c)

        c = IEEEContext(DECIMAL128)
        self.assertEqual(c.prec, 34)
        self.assertEqual(c.Emax, 6144)
        self.assertEqual(c.Emin, -6143)
        assert_rest(self, c)

        # Invalid values
        self.assertRaises(OverflowError, IEEEContext, 2**63)
        self.assertRaises(ValueError, IEEEContext, -1)
        self.assertRaises(ValueError, IEEEContext, 1024)

    @requires_extra_functionality
    def test_c_context(self):
        Context = C.Context

        c = Context(flags=C.DecClamped, traps=C.DecRounded)
        self.assertEqual(c._flags, C.DecClamped)
        self.assertEqual(c._traps, C.DecRounded)

    @requires_extra_functionality
    def test_constants(self):
        # Condition flags
        cond = (
            C.DecClamped, C.DecConversionSyntax, C.DecDivisionByZero,
            C.DecDivisionImpossible, C.DecDivisionUndefined,
            C.DecFpuError, C.DecInexact, C.DecInvalidContext,
            C.DecInvalidOperation, C.DecMallocError,
            C.DecFloatOperation, C.DecOverflow, C.DecRounded,
            C.DecSubnormal, C.DecUnderflow
        )

        # IEEEContext
        self.assertEqual(C.DECIMAL32, 32)
        self.assertEqual(C.DECIMAL64, 64)
        self.assertEqual(C.DECIMAL128, 128)
        self.assertEqual(C.IEEE_CONTEXT_MAX_BITS, 512)

        # Conditions
        for i, v in enumerate(cond):
            self.assertEqual(v, 1<<i)

        self.assertEqual(C.DecIEEEInvalidOperation,
                         C.DecConversionSyntax|
                         C.DecDivisionImpossible|
                         C.DecDivisionUndefined|
                         C.DecFpuError|
                         C.DecInvalidContext|
                         C.DecInvalidOperation|
                         C.DecMallocError)

        self.assertEqual(C.DecErrors,
                         C.DecIEEEInvalidOperation|
                         C.DecDivisionByZero)

        self.assertEqual(C.DecTraps,
                         C.DecErrors|C.DecOverflow|C.DecUnderflow)

@requires_cdecimal
class CWhitebox(unittest.TestCase):
    """Whitebox testing for _decimal"""

    def test_bignum(self):
        # Not exactly whitebox, but too slow with pydecimal.

        Decimal = C.Decimal
        localcontext = C.localcontext

        b1 = 10**35
        b2 = 10**36
        with localcontext() as c:
            c.prec = 1000000
            for i in range(5):
                a = random.randrange(b1, b2)
                b = random.randrange(1000, 1200)
                x = a ** b
                y = Decimal(a) ** Decimal(b)
                self.assertEqual(x, y)

    def test_invalid_construction(self):
        self.assertRaises(TypeError, C.Decimal, 9, "xyz")

    def test_c_input_restriction(self):
        # Too large for _decimal to be converted exactly
        Decimal = C.Decimal
        InvalidOperation = C.InvalidOperation
        Context = C.Context
        localcontext = C.localcontext

        with localcontext(Context()):
            self.assertRaises(InvalidOperation, Decimal,
                              "1e9999999999999999999")

    def test_c_context_repr(self):
        # This test is _decimal-only because flags are not printed
        # in the same order.
        DefaultContext = C.DefaultContext
        FloatOperation = C.FloatOperation

        c = DefaultContext.copy()

        c.prec = 425000000
        c.Emax = 425000000
        c.Emin = -425000000
        c.rounding = ROUND_HALF_DOWN
        c.capitals = 0
        c.clamp = 1
        for sig in OrderedSignals[C]:
            c.flags[sig] = True
            c.traps[sig] = True
        c.flags[FloatOperation] = True
        c.traps[FloatOperation] = True

        s = c.__repr__()
        t = "Context(prec=425000000, rounding=ROUND_HALF_DOWN, " \
            "Emin=-425000000, Emax=425000000, capitals=0, clamp=1, " \
            "flags=[Clamped, InvalidOperation, DivisionByZero, Inexact, " \
                   "FloatOperation, Overflow, Rounded, Subnormal, Underflow], " \
            "traps=[Clamped, InvalidOperation, DivisionByZero, Inexact, " \
                   "FloatOperation, Overflow, Rounded, Subnormal, Underflow])"
        self.assertEqual(s, t)

    def test_c_context_errors(self):
        Context = C.Context
        InvalidOperation = C.InvalidOperation
        Overflow = C.Overflow
        FloatOperation = C.FloatOperation
        localcontext = C.localcontext
        getcontext = C.getcontext
        setcontext = C.setcontext
        HAVE_CONFIG_64 = (C.MAX_PREC > 425000000)

        c = Context()

        # SignalDict: input validation
        self.assertRaises(KeyError, c.flags.__setitem__, 801, 0)
        self.assertRaises(KeyError, c.traps.__setitem__, 801, 0)
        self.assertRaises(ValueError, c.flags.__delitem__, Overflow)
        self.assertRaises(ValueError, c.traps.__delitem__, InvalidOperation)
        self.assertRaises(TypeError, setattr, c, 'flags', ['x'])
        self.assertRaises(TypeError, setattr, c,'traps', ['y'])
        self.assertRaises(KeyError, setattr, c, 'flags', {0:1})
        self.assertRaises(KeyError, setattr, c, 'traps', {0:1})

        # Test assignment from a signal dict with the correct length but
        # one invalid key.
        d = c.flags.copy()
        del d[FloatOperation]
        d["XYZ"] = 91283719
        self.assertRaises(KeyError, setattr, c, 'flags', d)
        self.assertRaises(KeyError, setattr, c, 'traps', d)

        # Input corner cases
        int_max = 2**63-1 if HAVE_CONFIG_64 else 2**31-1
        gt_max_emax = 10**18 if HAVE_CONFIG_64 else 10**9

        # prec, Emax, Emin
        for attr in ['prec', 'Emax']:
            self.assertRaises(ValueError, setattr, c, attr, gt_max_emax)
        self.assertRaises(ValueError, setattr, c, 'Emin', -gt_max_emax)

        # prec, Emax, Emin in context constructor
        self.assertRaises(ValueError, Context, prec=gt_max_emax)
        self.assertRaises(ValueError, Context, Emax=gt_max_emax)
        self.assertRaises(ValueError, Context, Emin=-gt_max_emax)

        # Overflow in conversion
        self.assertRaises(OverflowError, Context, prec=int_max+1)
        self.assertRaises(OverflowError, Context, Emax=int_max+1)
        self.assertRaises(OverflowError, Context, Emin=-int_max-2)
        self.assertRaises(OverflowError, Context, clamp=int_max+1)
        self.assertRaises(OverflowError, Context, capitals=int_max+1)

        # OverflowError, general ValueError
        for attr in ('prec', 'Emin', 'Emax', 'capitals', 'clamp'):
            self.assertRaises(OverflowError, setattr, c, attr, int_max+1)
            self.assertRaises(OverflowError, setattr, c, attr, -int_max-2)
            if sys.platform != 'win32':
                self.assertRaises(ValueError, setattr, c, attr, int_max)
                self.assertRaises(ValueError, setattr, c, attr, -int_max-1)

        # OverflowError: _unsafe_setprec, _unsafe_setemin, _unsafe_setemax
        if C.MAX_PREC == 425000000:
            self.assertRaises(OverflowError, getattr(c, '_unsafe_setprec'),
                              int_max+1)
            self.assertRaises(OverflowError, getattr(c, '_unsafe_setemax'),
                              int_max+1)
            self.assertRaises(OverflowError, getattr(c, '_unsafe_setemin'),
                              -int_max-2)

        # ValueError: _unsafe_setprec, _unsafe_setemin, _unsafe_setemax
        if C.MAX_PREC == 425000000:
            self.assertRaises(ValueError, getattr(c, '_unsafe_setprec'), 0)
            self.assertRaises(ValueError, getattr(c, '_unsafe_setprec'),
                              1070000001)
            self.assertRaises(ValueError, getattr(c, '_unsafe_setemax'), -1)
            self.assertRaises(ValueError, getattr(c, '_unsafe_setemax'),
                              1070000001)
            self.assertRaises(ValueError, getattr(c, '_unsafe_setemin'),
                              -1070000001)
            self.assertRaises(ValueError, getattr(c, '_unsafe_setemin'), 1)

        # capitals, clamp
        for attr in ['capitals', 'clamp']:
            self.assertRaises(ValueError, setattr, c, attr, -1)
            self.assertRaises(ValueError, setattr, c, attr, 2)
            self.assertRaises(TypeError, setattr, c, attr, [1,2,3])
            if HAVE_CONFIG_64:
                self.assertRaises(ValueError, setattr, c, attr, 2**32)
                self.assertRaises(ValueError, setattr, c, attr, 2**32+1)

        # Invalid local context
        self.assertRaises(TypeError, exec, 'with localcontext("xyz"): pass',
                          locals())
        self.assertRaises(TypeError, exec,
                          'with localcontext(context=getcontext()): pass',
                          locals())

        # setcontext
        saved_context = getcontext()
        self.assertRaises(TypeError, setcontext, "xyz")
        setcontext(saved_context)

    def test_rounding_strings_interned(self):

        self.assertIs(C.ROUND_UP, P.ROUND_UP)
        self.assertIs(C.ROUND_DOWN, P.ROUND_DOWN)
        self.assertIs(C.ROUND_CEILING, P.ROUND_CEILING)
        self.assertIs(C.ROUND_FLOOR, P.ROUND_FLOOR)
        self.assertIs(C.ROUND_HALF_UP, P.ROUND_HALF_UP)
        self.assertIs(C.ROUND_HALF_DOWN, P.ROUND_HALF_DOWN)
        self.assertIs(C.ROUND_HALF_EVEN, P.ROUND_HALF_EVEN)
        self.assertIs(C.ROUND_05UP, P.ROUND_05UP)

    @requires_extra_functionality
    def test_c_context_errors_extra(self):
        Context = C.Context
        InvalidOperation = C.InvalidOperation
        Overflow = C.Overflow
        localcontext = C.localcontext
        getcontext = C.getcontext
        setcontext = C.setcontext
        HAVE_CONFIG_64 = (C.MAX_PREC > 425000000)

        c = Context()

        # Input corner cases
        int_max = 2**63-1 if HAVE_CONFIG_64 else 2**31-1

        # OverflowError, general ValueError
        self.assertRaises(OverflowError, setattr, c, '_allcr', int_max+1)
        self.assertRaises(OverflowError, setattr, c, '_allcr', -int_max-2)
        if sys.platform != 'win32':
            self.assertRaises(ValueError, setattr, c, '_allcr', int_max)
            self.assertRaises(ValueError, setattr, c, '_allcr', -int_max-1)

        # OverflowError, general TypeError
        for attr in ('_flags', '_traps'):
            self.assertRaises(OverflowError, setattr, c, attr, int_max+1)
            self.assertRaises(OverflowError, setattr, c, attr, -int_max-2)
            if sys.platform != 'win32':
                self.assertRaises(TypeError, setattr, c, attr, int_max)
                self.assertRaises(TypeError, setattr, c, attr, -int_max-1)

        # _allcr
        self.assertRaises(ValueError, setattr, c, '_allcr', -1)
        self.assertRaises(ValueError, setattr, c, '_allcr', 2)
        self.assertRaises(TypeError, setattr, c, '_allcr', [1,2,3])
        if HAVE_CONFIG_64:
            self.assertRaises(ValueError, setattr, c, '_allcr', 2**32)
            self.assertRaises(ValueError, setattr, c, '_allcr', 2**32+1)

        # _flags, _traps
        for attr in ['_flags', '_traps']:
            self.assertRaises(TypeError, setattr, c, attr, 999999)
            self.assertRaises(TypeError, setattr, c, attr, 'x')

    def test_c_valid_context(self):
        # These tests are for code coverage in _decimal.
        DefaultContext = C.DefaultContext
        Clamped = C.Clamped
        Underflow = C.Underflow
        Inexact = C.Inexact
        Rounded = C.Rounded
        Subnormal = C.Subnormal

        c = DefaultContext.copy()

        # Exercise all getters and setters
        c.prec = 34
        c.rounding = ROUND_HALF_UP
        c.Emax = 3000
        c.Emin = -3000
        c.capitals = 1
        c.clamp = 0

        self.assertEqual(c.prec, 34)
        self.assertEqual(c.rounding, ROUND_HALF_UP)
        self.assertEqual(c.Emin, -3000)
        self.assertEqual(c.Emax, 3000)
        self.assertEqual(c.capitals, 1)
        self.assertEqual(c.clamp, 0)

        self.assertEqual(c.Etiny(), -3033)
        self.assertEqual(c.Etop(), 2967)

        # Exercise all unsafe setters
        if C.MAX_PREC == 425000000:
            c._unsafe_setprec(999999999)
            c._unsafe_setemax(999999999)
            c._unsafe_setemin(-999999999)
            self.assertEqual(c.prec, 999999999)
            self.assertEqual(c.Emax, 999999999)
            self.assertEqual(c.Emin, -999999999)

    @requires_extra_functionality
    def test_c_valid_context_extra(self):
        DefaultContext = C.DefaultContext

        c = DefaultContext.copy()
        self.assertEqual(c._allcr, 1)
        c._allcr = 0
        self.assertEqual(c._allcr, 0)

    def test_c_round(self):
        # Restricted input.
        Decimal = C.Decimal
        InvalidOperation = C.InvalidOperation
        localcontext = C.localcontext
        MAX_EMAX = C.MAX_EMAX
        MIN_ETINY = C.MIN_ETINY
        int_max = 2**63-1 if C.MAX_PREC > 425000000 else 2**31-1

        with localcontext() as c:
            c.traps[InvalidOperation] = True
            self.assertRaises(InvalidOperation, Decimal("1.23").__round__,
                              -int_max-1)
            self.assertRaises(InvalidOperation, Decimal("1.23").__round__,
                              int_max)
            self.assertRaises(InvalidOperation, Decimal("1").__round__,
                              int(MAX_EMAX+1))
            self.assertRaises(C.InvalidOperation, Decimal("1").__round__,
                              -int(MIN_ETINY-1))
            self.assertRaises(OverflowError, Decimal("1.23").__round__,
                              -int_max-2)
            self.assertRaises(OverflowError, Decimal("1.23").__round__,
                              int_max+1)

    def test_c_format(self):
        # Restricted input
        Decimal = C.Decimal
        HAVE_CONFIG_64 = (C.MAX_PREC > 425000000)

        self.assertRaises(TypeError, Decimal(1).__format__, "=10.10", [], 9)
        self.assertRaises(TypeError, Decimal(1).__format__, "=10.10", 9)
        self.assertRaises(TypeError, Decimal(1).__format__, [])

        self.assertRaises(ValueError, Decimal(1).__format__, "<>=10.10")
        maxsize = 2**63-1 if HAVE_CONFIG_64 else 2**31-1
        self.assertRaises(ValueError, Decimal("1.23456789").__format__,
                          "=%d.1" % maxsize)

    def test_c_integral(self):
        Decimal = C.Decimal
        Inexact = C.Inexact
        localcontext = C.localcontext

        x = Decimal(10)
        self.assertEqual(x.to_integral(), 10)
        self.assertRaises(TypeError, x.to_integral, '10')
        self.assertRaises(TypeError, x.to_integral, 10, 'x')
        self.assertRaises(TypeError, x.to_integral, 10)

        self.assertEqual(x.to_integral_value(), 10)
        self.assertRaises(TypeError, x.to_integral_value, '10')
        self.assertRaises(TypeError, x.to_integral_value, 10, 'x')
        self.assertRaises(TypeError, x.to_integral_value, 10)

        self.assertEqual(x.to_integral_exact(), 10)
        self.assertRaises(TypeError, x.to_integral_exact, '10')
        self.assertRaises(TypeError, x.to_integral_exact, 10, 'x')
        self.assertRaises(TypeError, x.to_integral_exact, 10)

        with localcontext() as c:
            x = Decimal("99999999999999999999999999.9").to_integral_value(ROUND_UP)
            self.assertEqual(x, Decimal('100000000000000000000000000'))

            x = Decimal("99999999999999999999999999.9").to_integral_exact(ROUND_UP)
            self.assertEqual(x, Decimal('100000000000000000000000000'))

            c.traps[Inexact] = True
            self.assertRaises(Inexact, Decimal("999.9").to_integral_exact, ROUND_UP)

    def test_c_funcs(self):
        # Invalid arguments
        Decimal = C.Decimal
        InvalidOperation = C.InvalidOperation
        DivisionByZero = C.DivisionByZero
        getcontext = C.getcontext
        localcontext = C.localcontext

        self.assertEqual(Decimal('9.99e10').to_eng_string(), '99.9E+9')

        self.assertRaises(TypeError, pow, Decimal(1), 2, "3")
        self.assertRaises(TypeError, Decimal(9).number_class, "x", "y")
        self.assertRaises(TypeError, Decimal(9).same_quantum, 3, "x", "y")

        self.assertRaises(
            TypeError,
            Decimal("1.23456789").quantize, Decimal('1e-100000'), []
        )
        self.assertRaises(
            TypeError,
            Decimal("1.23456789").quantize, Decimal('1e-100000'), getcontext()
        )
        self.assertRaises(
            TypeError,
            Decimal("1.23456789").quantize, Decimal('1e-100000'), 10
        )
        self.assertRaises(
            TypeError,
            Decimal("1.23456789").quantize, Decimal('1e-100000'), ROUND_UP, 1000
        )

        with localcontext() as c:
            c.clear_traps()

            # Invalid arguments
            self.assertRaises(TypeError, c.copy_sign, Decimal(1), "x", "y")
            self.assertRaises(TypeError, c.canonical, 200)
            self.assertRaises(TypeError, c.is_canonical, 200)
            self.assertRaises(TypeError, c.divmod, 9, 8, "x", "y")
            self.assertRaises(TypeError, c.same_quantum, 9, 3, "x", "y")

            self.assertEqual(str(c.canonical(Decimal(200))), '200')
            self.assertEqual(c.radix(), 10)

            c.traps[DivisionByZero] = True
            self.assertRaises(DivisionByZero, Decimal(9).__divmod__, 0)
            self.assertRaises(DivisionByZero, c.divmod, 9, 0)
            self.assertTrue(c.flags[InvalidOperation])

            c.clear_flags()
            c.traps[InvalidOperation] = True
            self.assertRaises(InvalidOperation, Decimal(9).__divmod__, 0)
            self.assertRaises(InvalidOperation, c.divmod, 9, 0)
            self.assertTrue(c.flags[DivisionByZero])

            c.traps[InvalidOperation] = True
            c.prec = 2
            self.assertRaises(InvalidOperation, pow, Decimal(1000), 1, 501)

    def test_va_args_exceptions(self):
        Decimal = C.Decimal
        Context = C.Context

        x = Decimal("10001111111")

        for attr in ['exp', 'is_normal', 'is_subnormal', 'ln', 'log10',
                     'logb', 'logical_invert', 'next_minus', 'next_plus',
                     'normalize', 'number_class', 'sqrt', 'to_eng_string']:
            func = getattr(x, attr)
            self.assertRaises(TypeError, func, context="x")
            self.assertRaises(TypeError, func, "x", context=None)

        for attr in ['compare', 'compare_signal', 'logical_and',
                     'logical_or', 'max', 'max_mag', 'min', 'min_mag',
                     'remainder_near', 'rotate', 'scaleb', 'shift']:
            func = getattr(x, attr)
            self.assertRaises(TypeError, func, context="x")
            self.assertRaises(TypeError, func, "x", context=None)

        self.assertRaises(TypeError, x.to_integral, rounding=None, context=[])
        self.assertRaises(TypeError, x.to_integral, rounding={}, context=[])
        self.assertRaises(TypeError, x.to_integral, [], [])

        self.assertRaises(TypeError, x.to_integral_value, rounding=None, context=[])
        self.assertRaises(TypeError, x.to_integral_value, rounding={}, context=[])
        self.assertRaises(TypeError, x.to_integral_value, [], [])

        self.assertRaises(TypeError, x.to_integral_exact, rounding=None, context=[])
        self.assertRaises(TypeError, x.to_integral_exact, rounding={}, context=[])
        self.assertRaises(TypeError, x.to_integral_exact, [], [])

        self.assertRaises(TypeError, x.fma, 1, 2, context="x")
        self.assertRaises(TypeError, x.fma, 1, 2, "x", context=None)

        self.assertRaises(TypeError, x.quantize, 1, [], context=None)
        self.assertRaises(TypeError, x.quantize, 1, [], rounding=None)
        self.assertRaises(TypeError, x.quantize, 1, [], [])

        c = Context()
        self.assertRaises(TypeError, c.power, 1, 2, mod="x")
        self.assertRaises(TypeError, c.power, 1, "x", mod=None)
        self.assertRaises(TypeError, c.power, "x", 2, mod=None)

    @requires_extra_functionality
    def test_c_context_templates(self):
        self.assertEqual(
            C.BasicContext._traps,
            C.DecIEEEInvalidOperation|C.DecDivisionByZero|C.DecOverflow|
            C.DecUnderflow|C.DecClamped
        )
        self.assertEqual(
            C.DefaultContext._traps,
            C.DecIEEEInvalidOperation|C.DecDivisionByZero|C.DecOverflow
        )

    @requires_extra_functionality
    def test_c_signal_dict(self):

        # SignalDict coverage
        Context = C.Context
        DefaultContext = C.DefaultContext

        InvalidOperation = C.InvalidOperation
        FloatOperation = C.FloatOperation
        DivisionByZero = C.DivisionByZero
        Overflow = C.Overflow
        Subnormal = C.Subnormal
        Underflow = C.Underflow
        Rounded = C.Rounded
        Inexact = C.Inexact
        Clamped = C.Clamped

        DecClamped = C.DecClamped
        DecInvalidOperation = C.DecInvalidOperation
        DecIEEEInvalidOperation = C.DecIEEEInvalidOperation

        def assertIsExclusivelySet(signal, signal_dict):
            for sig in signal_dict:
                if sig == signal:
                    self.assertTrue(signal_dict[sig])
                else:
                    self.assertFalse(signal_dict[sig])

        c = DefaultContext.copy()

        # Signal dict methods
        self.assertTrue(Overflow in c.traps)
        c.clear_traps()
        for k in c.traps.keys():
            c.traps[k] = True
        for v in c.traps.values():
            self.assertTrue(v)
        c.clear_traps()
        for k, v in c.traps.items():
            self.assertFalse(v)

        self.assertFalse(c.flags.get(Overflow))
        self.assertIs(c.flags.get("x"), None)
        self.assertEqual(c.flags.get("x", "y"), "y")
        self.assertRaises(TypeError, c.flags.get, "x", "y", "z")

        self.assertEqual(len(c.flags), len(c.traps))
        s = sys.getsizeof(c.flags)
        s = sys.getsizeof(c.traps)
        s = c.flags.__repr__()

        # Set flags/traps.
        c.clear_flags()
        c._flags = DecClamped
        self.assertTrue(c.flags[Clamped])

        c.clear_traps()
        c._traps = DecInvalidOperation
        self.assertTrue(c.traps[InvalidOperation])

        # Set flags/traps from dictionary.
        c.clear_flags()
        d = c.flags.copy()
        d[DivisionByZero] = True
        c.flags = d
        assertIsExclusivelySet(DivisionByZero, c.flags)

        c.clear_traps()
        d = c.traps.copy()
        d[Underflow] = True
        c.traps = d
        assertIsExclusivelySet(Underflow, c.traps)

        # Random constructors
        IntSignals = {
          Clamped: C.DecClamped,
          Rounded: C.DecRounded,
          Inexact: C.DecInexact,
          Subnormal: C.DecSubnormal,
          Underflow: C.DecUnderflow,
          Overflow: C.DecOverflow,
          DivisionByZero: C.DecDivisionByZero,
          FloatOperation: C.DecFloatOperation,
          InvalidOperation: C.DecIEEEInvalidOperation
        }
        IntCond = [
          C.DecDivisionImpossible, C.DecDivisionUndefined, C.DecFpuError,
          C.DecInvalidContext, C.DecInvalidOperation, C.DecMallocError,
          C.DecConversionSyntax,
        ]

        lim = len(OrderedSignals[C])
        for r in range(lim):
            for t in range(lim):
                for round in RoundingModes:
                    flags = random.sample(OrderedSignals[C], r)
                    traps = random.sample(OrderedSignals[C], t)
                    prec = random.randrange(1, 10000)
                    emin = random.randrange(-10000, 0)
                    emax = random.randrange(0, 10000)
                    clamp = random.randrange(0, 2)
                    caps = random.randrange(0, 2)
                    cr = random.randrange(0, 2)
                    c = Context(prec=prec, rounding=round, Emin=emin, Emax=emax,
                                capitals=caps, clamp=clamp, flags=list(flags),
                                traps=list(traps))

                    self.assertEqual(c.prec, prec)
                    self.assertEqual(c.rounding, round)
                    self.assertEqual(c.Emin, emin)
                    self.assertEqual(c.Emax, emax)
                    self.assertEqual(c.capitals, caps)
                    self.assertEqual(c.clamp, clamp)

                    f = 0
                    for x in flags:
                        f |= IntSignals[x]
                    self.assertEqual(c._flags, f)

                    f = 0
                    for x in traps:
                        f |= IntSignals[x]
                    self.assertEqual(c._traps, f)

        for cond in IntCond:
            c._flags = cond
            self.assertTrue(c._flags&DecIEEEInvalidOperation)
            assertIsExclusivelySet(InvalidOperation, c.flags)

        for cond in IntCond:
            c._traps = cond
            self.assertTrue(c._traps&DecIEEEInvalidOperation)
            assertIsExclusivelySet(InvalidOperation, c.traps)

    def test_invalid_override(self):
        Decimal = C.Decimal

        try:
            from locale import CHAR_MAX
        except ImportError:
            self.skipTest('locale.CHAR_MAX not available')

        def make_grouping(lst):
            return ''.join([chr(x) for x in lst])

        def get_fmt(x, override=None, fmt='n'):
            return Decimal(x).__format__(fmt, override)

        invalid_grouping = {
            'decimal_point' : ',',
            'grouping' : make_grouping([255, 255, 0]),
            'thousands_sep' : ','
        }
        invalid_dot = {
            'decimal_point' : 'xxxxx',
            'grouping' : make_grouping([3, 3, 0]),
            'thousands_sep' : ','
        }
        invalid_sep = {
            'decimal_point' : '.',
            'grouping' : make_grouping([3, 3, 0]),
            'thousands_sep' : 'yyyyy'
        }

        if CHAR_MAX == 127: # negative grouping in override
            self.assertRaises(ValueError, get_fmt, 12345,
                              invalid_grouping, 'g')

        self.assertRaises(ValueError, get_fmt, 12345, invalid_dot, 'g')
        self.assertRaises(ValueError, get_fmt, 12345, invalid_sep, 'g')

    def test_exact_conversion(self):
        Decimal = C.Decimal
        localcontext = C.localcontext
        InvalidOperation = C.InvalidOperation

        with localcontext() as c:

            c.traps[InvalidOperation] = True

            # Clamped
            x = "0e%d" % sys.maxsize
            self.assertRaises(InvalidOperation, Decimal, x)

            x = "0e%d" % (-sys.maxsize-1)
            self.assertRaises(InvalidOperation, Decimal, x)

            # Overflow
            x = "1e%d" % sys.maxsize
            self.assertRaises(InvalidOperation, Decimal, x)

            # Underflow
            x = "1e%d" % (-sys.maxsize-1)
            self.assertRaises(InvalidOperation, Decimal, x)

    def test_from_tuple(self):
        Decimal = C.Decimal
        localcontext = C.localcontext
        InvalidOperation = C.InvalidOperation
        Overflow = C.Overflow
        Underflow = C.Underflow

        with localcontext() as c:

            c.prec = 9
            c.traps[InvalidOperation] = True
            c.traps[Overflow] = True
            c.traps[Underflow] = True

            # SSIZE_MAX
            x = (1, (), sys.maxsize)
            self.assertEqual(str(c.create_decimal(x)), '-0E+999999')
            self.assertRaises(InvalidOperation, Decimal, x)

            x = (1, (0, 1, 2), sys.maxsize)
            self.assertRaises(Overflow, c.create_decimal, x)
            self.assertRaises(InvalidOperation, Decimal, x)

            # SSIZE_MIN
            x = (1, (), -sys.maxsize-1)
            self.assertEqual(str(c.create_decimal(x)), '-0E-1000007')
            self.assertRaises(InvalidOperation, Decimal, x)

            x = (1, (0, 1, 2), -sys.maxsize-1)
            self.assertRaises(Underflow, c.create_decimal, x)
            self.assertRaises(InvalidOperation, Decimal, x)

            # OverflowError
            x = (1, (), sys.maxsize+1)
            self.assertRaises(OverflowError, c.create_decimal, x)
            self.assertRaises(OverflowError, Decimal, x)

            x = (1, (), -sys.maxsize-2)
            self.assertRaises(OverflowError, c.create_decimal, x)
            self.assertRaises(OverflowError, Decimal, x)

            # Specials
            x = (1, (), "N")
            self.assertEqual(str(Decimal(x)), '-sNaN')
            x = (1, (0,), "N")
            self.assertEqual(str(Decimal(x)), '-sNaN')
            x = (1, (0, 1), "N")
            self.assertEqual(str(Decimal(x)), '-sNaN1')

    def test_sizeof(self):
        Decimal = C.Decimal
        HAVE_CONFIG_64 = (C.MAX_PREC > 425000000)

        self.assertGreater(Decimal(0).__sizeof__(), 0)
        if HAVE_CONFIG_64:
            x = Decimal(10**(19*24)).__sizeof__()
            y = Decimal(10**(19*25)).__sizeof__()
            self.assertEqual(y, x+8)
        else:
            x = Decimal(10**(9*24)).__sizeof__()
            y = Decimal(10**(9*25)).__sizeof__()
            self.assertEqual(y, x+4)

    def test_internal_use_of_overridden_methods(self):
        Decimal = C.Decimal

        # Unsound subtyping
        class X(float):
            def as_integer_ratio(self):
                return 1
            def __abs__(self):
                return self

        class Y(float):
            def __abs__(self):
                return [1]*200

        class I(int):
            def bit_length(self):
                return [1]*200

        class Z(float):
            def as_integer_ratio(self):
                return (I(1), I(1))
            def __abs__(self):
                return self

        for cls in X, Y, Z:
            self.assertEqual(Decimal.from_float(cls(101.1)),
                             Decimal.from_float(101.1))

    def test_c_immutable_types(self):
        SignalDict = type(C.Context().flags)
        SignalDictMixin = SignalDict.__bases__[0]
        ContextManager = type(C.localcontext())
        types = (
            SignalDictMixin,
            ContextManager,
            C.Decimal,
            C.Context,
        )
        for tp in types:
            with self.subTest(tp=tp):
                with self.assertRaisesRegex(TypeError, "immutable"):
                    tp.foo = 1

    def test_c_disallow_instantiation(self):
        ContextManager = type(C.localcontext())
        check_disallow_instantiation(self, ContextManager)

    def test_c_signaldict_segfault(self):
        # See gh-106263 for details.
        SignalDict = type(C.Context().flags)
        sd = SignalDict()
        err_msg = "invalid signal dict"

        with self.assertRaisesRegex(ValueError, err_msg):
            len(sd)

        with self.assertRaisesRegex(ValueError, err_msg):
            iter(sd)

        with self.assertRaisesRegex(ValueError, err_msg):
            repr(sd)

        with self.assertRaisesRegex(ValueError, err_msg):
            sd[C.InvalidOperation] = True

        with self.assertRaisesRegex(ValueError, err_msg):
            sd[C.InvalidOperation]

        with self.assertRaisesRegex(ValueError, err_msg):
            sd == C.Context().flags

        with self.assertRaisesRegex(ValueError, err_msg):
            C.Context().flags == sd

        with self.assertRaisesRegex(ValueError, err_msg):
            sd.copy()

    def test_format_fallback_capitals(self):
        # Fallback to _pydecimal formatting (triggered by `#` format which
        # is unsupported by mpdecimal) should honor the current context.
        x = C.Decimal('6.09e+23')
        self.assertEqual(format(x, '#'), '6.09E+23')
        with C.localcontext(capitals=0):
            self.assertEqual(format(x, '#'), '6.09e+23')

    def test_format_fallback_rounding(self):
        y = C.Decimal('6.09')
        self.assertEqual(format(y, '#.1f'), '6.1')
        with C.localcontext(rounding=C.ROUND_DOWN):
            self.assertEqual(format(y, '#.1f'), '6.0')

@requires_docstrings
@requires_cdecimal
class SignatureTest(unittest.TestCase):
    """Function signatures"""

    def test_inspect_module(self):
        for attr in dir(P):
            if attr.startswith('_'):
                continue
            p_func = getattr(P, attr)
            c_func = getattr(C, attr)
            if (attr == 'Decimal' or attr == 'Context' or
                inspect.isfunction(p_func)):
                p_sig = inspect.signature(p_func)
                c_sig = inspect.signature(c_func)

                # parameter names:
                c_names = list(c_sig.parameters.keys())
                p_names = [x for x in p_sig.parameters.keys() if not
                           x.startswith('_')]

                self.assertEqual(c_names, p_names,
                                 msg="parameter name mismatch in %s" % p_func)

                c_kind = [x.kind for x in c_sig.parameters.values()]
                p_kind = [x[1].kind for x in p_sig.parameters.items() if not
                          x[0].startswith('_')]

                # parameters:
                if attr != 'setcontext':
                    self.assertEqual(c_kind, p_kind,
                                     msg="parameter kind mismatch in %s" % p_func)

    def test_inspect_types(self):

        POS = inspect._ParameterKind.POSITIONAL_ONLY
        POS_KWD = inspect._ParameterKind.POSITIONAL_OR_KEYWORD

        # Type heuristic (type annotations would help!):
        pdict = {C: {'other': C.Decimal(1),
                     'third': C.Decimal(1),
                     'x': C.Decimal(1),
                     'y': C.Decimal(1),
                     'z': C.Decimal(1),
                     'a': C.Decimal(1),
                     'b': C.Decimal(1),
                     'c': C.Decimal(1),
                     'exp': C.Decimal(1),
                     'modulo': C.Decimal(1),
                     'num': "1",
                     'f': 1.0,
                     'rounding': C.ROUND_HALF_UP,
                     'context': C.getcontext()},
                 P: {'other': P.Decimal(1),
                     'third': P.Decimal(1),
                     'a': P.Decimal(1),
                     'b': P.Decimal(1),
                     'c': P.Decimal(1),
                     'exp': P.Decimal(1),
                     'modulo': P.Decimal(1),
                     'num': "1",
                     'f': 1.0,
                     'rounding': P.ROUND_HALF_UP,
                     'context': P.getcontext()}}

        def mkargs(module, sig):
            args = []
            kwargs = {}
            for name, param in sig.parameters.items():
                if name == 'self': continue
                if param.kind == POS:
                    args.append(pdict[module][name])
                elif param.kind == POS_KWD:
                    kwargs[name] = pdict[module][name]
                else:
                    raise TestFailed("unexpected parameter kind")
            return args, kwargs

        def tr(s):
            """The C Context docstrings use 'x' in order to prevent confusion
               with the article 'a' in the descriptions."""
            if s == 'x': return 'a'
            if s == 'y': return 'b'
            if s == 'z': return 'c'
            return s

        def doit(ty):
            p_type = getattr(P, ty)
            c_type = getattr(C, ty)
            for attr in dir(p_type):
                if attr.startswith('_'):
                    continue
                p_func = getattr(p_type, attr)
                c_func = getattr(c_type, attr)
                if inspect.isfunction(p_func):
                    p_sig = inspect.signature(p_func)
                    c_sig = inspect.signature(c_func)

                    # parameter names:
                    p_names = list(p_sig.parameters.keys())
                    c_names = [tr(x) for x in c_sig.parameters.keys()]

                    self.assertEqual(c_names, p_names,
                                     msg="parameter name mismatch in %s" % p_func)

                    p_kind = [x.kind for x in p_sig.parameters.values()]
                    c_kind = [x.kind for x in c_sig.parameters.values()]

                    # 'self' parameter:
                    self.assertIs(p_kind[0], POS_KWD)
                    self.assertIs(c_kind[0], POS)

                    # remaining parameters:
                    if ty == 'Decimal':
                        self.assertEqual(c_kind[1:], p_kind[1:],
                                         msg="parameter kind mismatch in %s" % p_func)
                    else: # Context methods are positional only in the C version.
                        self.assertEqual(len(c_kind), len(p_kind),
                                         msg="parameter kind mismatch in %s" % p_func)

                    # Run the function:
                    args, kwds = mkargs(C, c_sig)
                    try:
                        getattr(c_type(9), attr)(*args, **kwds)
                    except Exception:
                        raise TestFailed("invalid signature for %s: %s %s" % (c_func, args, kwds))

                    args, kwds = mkargs(P, p_sig)
                    try:
                        getattr(p_type(9), attr)(*args, **kwds)
                    except Exception:
                        raise TestFailed("invalid signature for %s: %s %s" % (p_func, args, kwds))

        doit('Decimal')
        doit('Context')


def load_tests(loader, tests, pattern):
    if TODO_TESTS is not None:
        # Run only Arithmetic tests
        tests = loader.suiteClass()
    # Dynamically build custom test definition for each file in the test
    # directory and add the definitions to the DecimalTest class.  This
    # procedure insures that new files do not get skipped.
    for filename in os.listdir(directory):
        if '.decTest' not in filename or filename.startswith("."):
            continue
        head, tail = filename.split('.')
        if TODO_TESTS is not None and head not in TODO_TESTS:
            continue
        tester = lambda self, f=filename: self.eval_file(directory + f)
        setattr(IBMTestCases, 'test_' + head, tester)
        del filename, head, tail, tester
    for prefix, mod in ('C', C), ('Py', P):
        if not mod:
            continue
        test_class = type(prefix + 'IBMTestCases',
                          (IBMTestCases, unittest.TestCase),
                          {'decimal': mod})
        tests.addTest(loader.loadTestsFromTestCase(test_class))

    if TODO_TESTS is None:
        from doctest import DocTestSuite, IGNORE_EXCEPTION_DETAIL
        orig_context = orig_sys_decimal.getcontext().copy()
        for mod in C, P:
            if not mod:
                continue
            def setUp(slf, mod=mod):
                sys.modules['decimal'] = mod
                init(mod)
            def tearDown(slf, mod=mod):
                sys.modules['decimal'] = orig_sys_decimal
                mod.setcontext(ORIGINAL_CONTEXT[mod].copy())
                orig_sys_decimal.setcontext(orig_context.copy())
            optionflags = IGNORE_EXCEPTION_DETAIL if mod is C else 0
            sys.modules['decimal'] = mod
            tests.addTest(DocTestSuite(mod, setUp=setUp, tearDown=tearDown,
                                   optionflags=optionflags))
            sys.modules['decimal'] = orig_sys_decimal
    return tests

def setUpModule():
    init(C)
    init(P)
    global TEST_ALL
    TEST_ALL = ARITH if ARITH is not None else is_resource_enabled('decimal')

def tearDownModule():
    if C: C.setcontext(ORIGINAL_CONTEXT[C].copy())
    P.setcontext(ORIGINAL_CONTEXT[P].copy())
    if not C:
        warnings.warn('C tests skipped: no module named _decimal.',
                      UserWarning)
    if not orig_sys_decimal is sys.modules['decimal']:
        raise TestFailed("Internal error: unbalanced number of changes to "
                         "sys.modules['decimal'].")


ARITH = None
TEST_ALL = True
TODO_TESTS = None
DEBUG = False

def test(arith=None, verbose=None, todo_tests=None, debug=None):
    """ Execute the tests.

    Runs all arithmetic tests if arith is True or if the "decimal" resource
    is enabled in regrtest.py
    """

    global ARITH, TODO_TESTS, DEBUG
    ARITH = arith
    TODO_TESTS = todo_tests
    DEBUG = debug
    unittest.main(__name__, verbosity=2 if verbose else 1, exit=False, argv=[__name__])


if __name__ == '__main__':
    import optparse
    p = optparse.OptionParser("test_decimal.py [--debug] [{--skip | test1 [test2 [...]]}]")
    p.add_option('--debug', '-d', action='store_true', help='shows the test number and context before each test')
    p.add_option('--skip',  '-s', action='store_true', help='skip over 90% of the arithmetic tests')
    (opt, args) = p.parse_args()

    if opt.skip:
        test(arith=False, verbose=True)
    elif args:
        test(arith=True, verbose=True, todo_tests=args, debug=opt.debug)
    else:
        test(arith=True, verbose=True)