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"""Manage shelves of pickled objects.

A "shelf" is a persistent, dictionary-like object.  The difference
with dbm databases is that the values (not the keys!) in a shelf can
be essentially arbitrary Python objects -- anything that the "pickle"
module can handle.  This includes most class instances, recursive data
types, and objects containing lots of shared sub-objects.  The keys
are ordinary strings.

To summarize the interface (key is a string, data is an arbitrary
object):

        import shelve
        d = shelve.open(filename) # open, with (g)dbm filename -- no suffix

        d[key] = data   # store data at key (overwrites old data if
                        # using an existing key)
        data = d[key]   # retrieve a COPY of the data at key (raise
                        # KeyError if no such key) -- NOTE that this
                        # access returns a *copy* of the entry!
        del d[key]      # delete data stored at key (raises KeyError
                        # if no such key)
        flag = d.has_key(key)   # true if the key exists; same as "key in d"
        list = d.keys() # a list of all existing keys (slow!)

        d.close()       # close it

Dependent on the implementation, closing a persistent dictionary may
or may not be necessary to flush changes to disk.

Normally, d[key] returns a COPY of the entry.  This needs care when
mutable entries are mutated: for example, if d[key] is a list,
        d[key].append(anitem)
does NOT modify the entry d[key] itself, as stored in the persistent
mapping -- it only modifies the copy, which is then immediately
discarded, so that the append has NO effect whatsoever.  To append an
item to d[key] in a way that will affect the persistent mapping, use:
        data = d[key]
        data.append(anitem)
        d[key] = data

To avoid the problem with mutable entries, you may pass the keyword
argument writeback=True in the call to shelve.open.  When you use:
        d = shelve.open(filename, writeback=True)
then d keeps a cache of all entries you access, and writes them all back
to the persistent mapping when you call d.close().  This ensures that
such usage as d[key].append(anitem) works as intended.

However, using keyword argument writeback=True may consume vast amount
of memory for the cache, and it may make d.close() very slow, if you
access many of d's entries after opening it in this way: d has no way to
check which of the entries you access are mutable and/or which ones you
actually mutate, so it must cache, and write back at close, all of the
entries that you access.  You can call d.sync() to write back all the
entries in the cache, and empty the cache (d.sync() also synchronizes
the persistent dictionary on disk, if feasible).
"""

# Try using cPickle and cStringIO if available.

try:
    from cPickle import Pickler, Unpickler
except ImportError:
    from pickle import Pickler, Unpickler

try:
    from cStringIO import StringIO
except ImportError:
    from StringIO import StringIO

import UserDict
import warnings

__all__ = ["Shelf","BsdDbShelf","DbfilenameShelf","open"]

class Shelf(UserDict.DictMixin):
    """Base class for shelf implementations.

    This is initialized with a dictionary-like object.
    See the module's __doc__ string for an overview of the interface.
    """

    def __init__(self, dict, protocol=None, writeback=False):
        self.dict = dict
        if protocol is None:
            protocol = 0
        self._protocol = protocol
        self.writeback = writeback
        self.cache = {}

    def keys(self):
        return self.dict.keys()

    def __len__(self):
        return len(self.dict)

    def has_key(self, key):
        return self.dict.has_key(key)

    def __contains__(self, key):
        return self.dict.has_key(key)

    def get(self, key, default=None):
        if self.dict.has_key(key):
            return self[key]
        return default

    def __getitem__(self, key):
        try:
            value = self.cache[key]
        except KeyError:
            f = StringIO(self.dict[key])
            value = Unpickler(f).load()
            if self.writeback:
                self.cache[key] = value
        return value

    def __setitem__(self, key, value):
        if self.writeback:
            self.cache[key] = value
        f = StringIO()
        p = Pickler(f, self._protocol)
        p.dump(value)
        self.dict[key] = f.getvalue()

    def __delitem__(self, key):
        del self.dict[key]
        try:
            del self.cache[key]
        except KeyError:
            pass

    def close(self):
        self.sync()
        try:
            self.dict.close()
        except AttributeError:
            pass
        self.dict = 0

    def __del__(self):
        if not hasattr(self, 'writeback'):
            # __init__ didn't succeed, so don't bother closing
            return
        self.close()

    def sync(self):
        if self.writeback and self.cache:
            self.writeback = False
            for key, entry in self.cache.iteritems():
                self[key] = entry
            self.writeback = True
            self.cache = {}
        if hasattr(self.dict, 'sync'):
            self.dict.sync()


class BsdDbShelf(Shelf):
    """Shelf implementation using the "BSD" db interface.

    This adds methods first(), next(), previous(), last() and
    set_location() that have no counterpart in [g]dbm databases.

    The actual database must be opened using one of the "bsddb"
    modules "open" routines (i.e. bsddb.hashopen, bsddb.btopen or
    bsddb.rnopen) and passed to the constructor.

    See the module's __doc__ string for an overview of the interface.
    """

    def __init__(self, dict, protocol=None, writeback=False):
        Shelf.__init__(self, dict, protocol, writeback)

    def set_location(self, key):
        (key, value) = self.dict.set_location(key)
        f = StringIO(value)
        return (key, Unpickler(f).load())

    def next(self):
        (key, value) = self.dict.next()
        f = StringIO(value)
        return (key, Unpickler(f).load())

    def previous(self):
        (key, value) = self.dict.previous()
        f = StringIO(value)
        return (key, Unpickler(f).load())

    def first(self):
        (key, value) = self.dict.first()
        f = StringIO(value)
        return (key, Unpickler(f).load())

    def last(self):
        (key, value) = self.dict.last()
        f = StringIO(value)
        return (key, Unpickler(f).load())


class DbfilenameShelf(Shelf):
    """Shelf implementation using the "anydbm" generic dbm interface.

    This is initialized with the filename for the dbm database.
    See the module's __doc__ string for an overview of the interface.
    """

    def __init__(self, filename, flag='c', protocol=None, writeback=False):
        import anydbm
        Shelf.__init__(self, anydbm.open(filename, flag), protocol, writeback)


def open(filename, flag='c', protocol=None, writeback=False):
    """Open a persistent dictionary for reading and writing.

    The filename parameter is the base filename for the underlying
    database.  As a side-effect, an extension may be added to the
    filename and more than one file may be created.  The optional flag
    parameter has the same interpretation as the flag parameter of
    anydbm.open(). The optional protocol parameter specifies the
    version of the pickle protocol (0, 1, or 2).

    See the module's __doc__ string for an overview of the interface.
    """

    return DbfilenameShelf(filename, flag, protocol, writeback)
>930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420
import fractions
import operator
import os
import random
import sys
import struct
import time
import unittest

from test import support
from test.test_grammar import (VALID_UNDERSCORE_LITERALS,
                               INVALID_UNDERSCORE_LITERALS)
from math import isinf, isnan, copysign, ldexp

INF = float("inf")
NAN = float("nan")

have_getformat = hasattr(float, "__getformat__")
requires_getformat = unittest.skipUnless(have_getformat,
                                         "requires __getformat__")
requires_setformat = unittest.skipUnless(hasattr(float, "__setformat__"),
                                         "requires __setformat__")

#locate file with float format test values
test_dir = os.path.dirname(__file__) or os.curdir
format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt')

class FloatSubclass(float):
    pass

class OtherFloatSubclass(float):
    pass

class GeneralFloatCases(unittest.TestCase):

    def test_float(self):
        self.assertEqual(float(3.14), 3.14)
        self.assertEqual(float(314), 314.0)
        self.assertEqual(float("  3.14  "), 3.14)
        self.assertRaises(ValueError, float, "  0x3.1  ")
        self.assertRaises(ValueError, float, "  -0x3.p-1  ")
        self.assertRaises(ValueError, float, "  +0x3.p-1  ")
        self.assertRaises(ValueError, float, "++3.14")
        self.assertRaises(ValueError, float, "+-3.14")
        self.assertRaises(ValueError, float, "-+3.14")
        self.assertRaises(ValueError, float, "--3.14")
        self.assertRaises(ValueError, float, ".nan")
        self.assertRaises(ValueError, float, "+.inf")
        self.assertRaises(ValueError, float, ".")
        self.assertRaises(ValueError, float, "-.")
        self.assertRaises(TypeError, float, {})
        self.assertRaisesRegex(TypeError, "not 'dict'", float, {})
        # Lone surrogate
        self.assertRaises(UnicodeEncodeError, float, '\uD8F0')
        # check that we don't accept alternate exponent markers
        self.assertRaises(ValueError, float, "-1.7d29")
        self.assertRaises(ValueError, float, "3D-14")
        self.assertEqual(float("  \u0663.\u0661\u0664  "), 3.14)
        self.assertEqual(float("\N{EM SPACE}3.14\N{EN SPACE}"), 3.14)
        # extra long strings should not be a problem
        float(b'.' + b'1'*1000)
        float('.' + '1'*1000)

    def test_underscores(self):
        for lit in VALID_UNDERSCORE_LITERALS:
            if not any(ch in lit for ch in 'jJxXoObB'):
                self.assertEqual(float(lit), eval(lit))
                self.assertEqual(float(lit), float(lit.replace('_', '')))
        for lit in INVALID_UNDERSCORE_LITERALS:
            if lit in ('0_7', '09_99'):  # octals are not recognized here
                continue
            if not any(ch in lit for ch in 'jJxXoObB'):
                self.assertRaises(ValueError, float, lit)
        # Additional test cases; nan and inf are never valid as literals,
        # only in the float() constructor, but we don't allow underscores
        # in or around them.
        self.assertRaises(ValueError, float, '_NaN')
        self.assertRaises(ValueError, float, 'Na_N')
        self.assertRaises(ValueError, float, 'IN_F')
        self.assertRaises(ValueError, float, '-_INF')
        self.assertRaises(ValueError, float, '-INF_')
        # Check that we handle bytes values correctly.
        self.assertRaises(ValueError, float, b'0_.\xff9')

    def test_non_numeric_input_types(self):
        # Test possible non-numeric types for the argument x, including
        # subclasses of the explicitly documented accepted types.
        class CustomStr(str): pass
        class CustomBytes(bytes): pass
        class CustomByteArray(bytearray): pass

        factories = [
            bytes,
            bytearray,
            lambda b: CustomStr(b.decode()),
            CustomBytes,
            CustomByteArray,
            memoryview,
        ]
        try:
            from array import array
        except ImportError:
            pass
        else:
            factories.append(lambda b: array('B', b))

        for f in factories:
            x = f(b" 3.14  ")
            with self.subTest(type(x)):
                self.assertEqual(float(x), 3.14)
                with self.assertRaisesRegex(ValueError, "could not convert"):
                    float(f(b'A' * 0x10))

    def test_float_memoryview(self):
        self.assertEqual(float(memoryview(b'12.3')[1:4]), 2.3)
        self.assertEqual(float(memoryview(b'12.3\x00')[1:4]), 2.3)
        self.assertEqual(float(memoryview(b'12.3 ')[1:4]), 2.3)
        self.assertEqual(float(memoryview(b'12.3A')[1:4]), 2.3)
        self.assertEqual(float(memoryview(b'12.34')[1:4]), 2.3)

    def test_error_message(self):
        def check(s):
            with self.assertRaises(ValueError, msg='float(%r)' % (s,)) as cm:
                float(s)
            self.assertEqual(str(cm.exception),
                'could not convert string to float: %r' % (s,))

        check('\xbd')
        check('123\xbd')
        check('  123 456  ')
        check(b'  123 456  ')

        # non-ascii digits (error came from non-digit '!')
        check('\u0663\u0661\u0664!')
        # embedded NUL
        check('123\x00')
        check('123\x00 245')
        check('123\x00245')
        # byte string with embedded NUL
        check(b'123\x00')
        # non-UTF-8 byte string
        check(b'123\xa0')

    @support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE')
    def test_float_with_comma(self):
        # set locale to something that doesn't use '.' for the decimal point
        # float must not accept the locale specific decimal point but
        # it still has to accept the normal python syntax
        import locale
        if not locale.localeconv()['decimal_point'] == ',':
            self.skipTest('decimal_point is not ","')

        self.assertEqual(float("  3.14  "), 3.14)
        self.assertEqual(float("+3.14  "), 3.14)
        self.assertEqual(float("-3.14  "), -3.14)
        self.assertEqual(float(".14  "), .14)
        self.assertEqual(float("3.  "), 3.0)
        self.assertEqual(float("3.e3  "), 3000.0)
        self.assertEqual(float("3.2e3  "), 3200.0)
        self.assertEqual(float("2.5e-1  "), 0.25)
        self.assertEqual(float("5e-1"), 0.5)
        self.assertRaises(ValueError, float, "  3,14  ")
        self.assertRaises(ValueError, float, "  +3,14  ")
        self.assertRaises(ValueError, float, "  -3,14  ")
        self.assertRaises(ValueError, float, "  0x3.1  ")
        self.assertRaises(ValueError, float, "  -0x3.p-1  ")
        self.assertRaises(ValueError, float, "  +0x3.p-1  ")
        self.assertEqual(float("  25.e-1  "), 2.5)
        self.assertAlmostEqual(float("  .25e-1  "), .025)

    def test_floatconversion(self):
        # Make sure that calls to __float__() work properly
        class Foo1(object):
            def __float__(self):
                return 42.

        class Foo2(float):
            def __float__(self):
                return 42.

        class Foo3(float):
            def __new__(cls, value=0.):
                return float.__new__(cls, 2*value)

            def __float__(self):
                return self

        class Foo4(float):
            def __float__(self):
                return 42

        # Issue 5759: __float__ not called on str subclasses (though it is on
        # unicode subclasses).
        class FooStr(str):
            def __float__(self):
                return float(str(self)) + 1

        self.assertEqual(float(Foo1()), 42.)
        self.assertEqual(float(Foo2()), 42.)
        with self.assertWarns(DeprecationWarning):
            self.assertEqual(float(Foo3(21)), 42.)
        self.assertRaises(TypeError, float, Foo4(42))
        self.assertEqual(float(FooStr('8')), 9.)

        class Foo5:
            def __float__(self):
                return ""
        self.assertRaises(TypeError, time.sleep, Foo5())

        # Issue #24731
        class F:
            def __float__(self):
                return OtherFloatSubclass(42.)
        with self.assertWarns(DeprecationWarning):
            self.assertEqual(float(F()), 42.)
        with self.assertWarns(DeprecationWarning):
            self.assertIs(type(float(F())), float)
        with self.assertWarns(DeprecationWarning):
            self.assertEqual(FloatSubclass(F()), 42.)
        with self.assertWarns(DeprecationWarning):
            self.assertIs(type(FloatSubclass(F())), FloatSubclass)

    def test_keyword_args(self):
        with self.assertRaisesRegex(TypeError, 'keyword argument'):
            float(x='3.14')

    def test_is_integer(self):
        self.assertFalse((1.1).is_integer())
        self.assertTrue((1.).is_integer())
        self.assertFalse(float("nan").is_integer())
        self.assertFalse(float("inf").is_integer())

    def test_floatasratio(self):
        for f, ratio in [
                (0.875, (7, 8)),
                (-0.875, (-7, 8)),
                (0.0, (0, 1)),
                (11.5, (23, 2)),
            ]:
            self.assertEqual(f.as_integer_ratio(), ratio)

        for i in range(10000):
            f = random.random()
            f *= 10 ** random.randint(-100, 100)
            n, d = f.as_integer_ratio()
            self.assertEqual(float(n).__truediv__(d), f)

        R = fractions.Fraction
        self.assertEqual(R(0, 1),
                         R(*float(0.0).as_integer_ratio()))
        self.assertEqual(R(5, 2),
                         R(*float(2.5).as_integer_ratio()))
        self.assertEqual(R(1, 2),
                         R(*float(0.5).as_integer_ratio()))
        self.assertEqual(R(4728779608739021, 2251799813685248),
                         R(*float(2.1).as_integer_ratio()))
        self.assertEqual(R(-4728779608739021, 2251799813685248),
                         R(*float(-2.1).as_integer_ratio()))
        self.assertEqual(R(-2100, 1),
                         R(*float(-2100.0).as_integer_ratio()))

        self.assertRaises(OverflowError, float('inf').as_integer_ratio)
        self.assertRaises(OverflowError, float('-inf').as_integer_ratio)
        self.assertRaises(ValueError, float('nan').as_integer_ratio)

    def test_float_containment(self):
        floats = (INF, -INF, 0.0, 1.0, NAN)
        for f in floats:
            self.assertIn(f, [f])
            self.assertIn(f, (f,))
            self.assertIn(f, {f})
            self.assertIn(f, {f: None})
            self.assertEqual([f].count(f), 1, "[].count('%r') != 1" % f)
            self.assertIn(f, floats)

        for f in floats:
            # nonidentical containers, same type, same contents
            self.assertTrue([f] == [f], "[%r] != [%r]" % (f, f))
            self.assertTrue((f,) == (f,), "(%r,) != (%r,)" % (f, f))
            self.assertTrue({f} == {f}, "{%r} != {%r}" % (f, f))
            self.assertTrue({f : None} == {f: None}, "{%r : None} != "
                                                   "{%r : None}" % (f, f))

            # identical containers
            l, t, s, d = [f], (f,), {f}, {f: None}
            self.assertTrue(l == l, "[%r] not equal to itself" % f)
            self.assertTrue(t == t, "(%r,) not equal to itself" % f)
            self.assertTrue(s == s, "{%r} not equal to itself" % f)
            self.assertTrue(d == d, "{%r : None} not equal to itself" % f)

    def assertEqualAndEqualSign(self, a, b):
        # fail unless a == b and a and b have the same sign bit;
        # the only difference from assertEqual is that this test
        # distinguishes -0.0 and 0.0.
        self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b)))

    @support.requires_IEEE_754
    def test_float_mod(self):
        # Check behaviour of % operator for IEEE 754 special cases.
        # In particular, check signs of zeros.
        mod = operator.mod

        self.assertEqualAndEqualSign(mod(-1.0, 1.0), 0.0)
        self.assertEqualAndEqualSign(mod(-1e-100, 1.0), 1.0)
        self.assertEqualAndEqualSign(mod(-0.0, 1.0), 0.0)
        self.assertEqualAndEqualSign(mod(0.0, 1.0), 0.0)
        self.assertEqualAndEqualSign(mod(1e-100, 1.0), 1e-100)
        self.assertEqualAndEqualSign(mod(1.0, 1.0), 0.0)

        self.assertEqualAndEqualSign(mod(-1.0, -1.0), -0.0)
        self.assertEqualAndEqualSign(mod(-1e-100, -1.0), -1e-100)
        self.assertEqualAndEqualSign(mod(-0.0, -1.0), -0.0)
        self.assertEqualAndEqualSign(mod(0.0, -1.0), -0.0)
        self.assertEqualAndEqualSign(mod(1e-100, -1.0), -1.0)
        self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0)

    @support.requires_IEEE_754
    def test_float_pow(self):
        # test builtin pow and ** operator for IEEE 754 special cases.
        # Special cases taken from section F.9.4.4 of the C99 specification

        for pow_op in pow, operator.pow:
            # x**NAN is NAN for any x except 1
            self.assertTrue(isnan(pow_op(-INF, NAN)))
            self.assertTrue(isnan(pow_op(-2.0, NAN)))
            self.assertTrue(isnan(pow_op(-1.0, NAN)))
            self.assertTrue(isnan(pow_op(-0.5, NAN)))
            self.assertTrue(isnan(pow_op(-0.0, NAN)))
            self.assertTrue(isnan(pow_op(0.0, NAN)))
            self.assertTrue(isnan(pow_op(0.5, NAN)))
            self.assertTrue(isnan(pow_op(2.0, NAN)))
            self.assertTrue(isnan(pow_op(INF, NAN)))
            self.assertTrue(isnan(pow_op(NAN, NAN)))

            # NAN**y is NAN for any y except +-0
            self.assertTrue(isnan(pow_op(NAN, -INF)))
            self.assertTrue(isnan(pow_op(NAN, -2.0)))
            self.assertTrue(isnan(pow_op(NAN, -1.0)))
            self.assertTrue(isnan(pow_op(NAN, -0.5)))
            self.assertTrue(isnan(pow_op(NAN, 0.5)))
            self.assertTrue(isnan(pow_op(NAN, 1.0)))
            self.assertTrue(isnan(pow_op(NAN, 2.0)))
            self.assertTrue(isnan(pow_op(NAN, INF)))

            # (+-0)**y raises ZeroDivisionError for y a negative odd integer
            self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0)
            self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0)

            # (+-0)**y raises ZeroDivisionError for y finite and negative
            # but not an odd integer
            self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0)
            self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5)
            self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0)
            self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5)

            # (+-0)**y is +-0 for y a positive odd integer
            self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0)
            self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0)

            # (+-0)**y is 0 for y finite and positive but not an odd integer
            self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0)
            self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0)
            self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0)
            self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0)

            # (-1)**+-inf is 1
            self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0)

            # 1**y is 1 for any y, even if y is an infinity or nan
            self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0)

            # x**+-0 is 1 for any x, even if x is a zero, infinity, or nan
            self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0)

            # x**y defers to complex pow for finite negative x and
            # non-integral y.
            self.assertEqual(type(pow_op(-2.0, -0.5)), complex)
            self.assertEqual(type(pow_op(-2.0, 0.5)), complex)
            self.assertEqual(type(pow_op(-1.0, -0.5)), complex)
            self.assertEqual(type(pow_op(-1.0, 0.5)), complex)
            self.assertEqual(type(pow_op(-0.5, -0.5)), complex)
            self.assertEqual(type(pow_op(-0.5, 0.5)), complex)

            # x**-INF is INF for abs(x) < 1
            self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF)
            self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF)
            self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF)
            self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF)

            # x**-INF is 0 for abs(x) > 1
            self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0)
            self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0)
            self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0)
            self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0)

            # x**INF is 0 for abs(x) < 1
            self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0)
            self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0)
            self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0)
            self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0)

            # x**INF is INF for abs(x) > 1
            self.assertEqualAndEqualSign(pow_op(-INF, INF), INF)
            self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF)
            self.assertEqualAndEqualSign(pow_op(2.0, INF), INF)
            self.assertEqualAndEqualSign(pow_op(INF, INF), INF)

            # (-INF)**y is -0.0 for y a negative odd integer
            self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0)

            # (-INF)**y is 0.0 for y negative but not an odd integer
            self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0)
            self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0)

            # (-INF)**y is -INF for y a positive odd integer
            self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF)

            # (-INF)**y is INF for y positive but not an odd integer
            self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF)
            self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF)

            # INF**y is INF for y positive
            self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF)
            self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF)
            self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF)

            # INF**y is 0.0 for y negative
            self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0)
            self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0)
            self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0)

            # basic checks not covered by the special cases above
            self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25)
            self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5)
            self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0)
            self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25)
            self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5)
            self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0)
            self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0)
            self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0)

            # 1 ** large and -1 ** large; some libms apparently
            # have problems with these
            self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0)
            self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0)
            self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0)

            # check sign for results that underflow to 0
            self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0)
            self.assertEqual(type(pow_op(-2.0, -2000.5)), complex)
            self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0)
            self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0)
            self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0)
            self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0)
            self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0)
            self.assertEqual(type(pow_op(-0.5, 2000.5)), complex)
            self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0)
            self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0)
            self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0)
            self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0)

            # check we don't raise an exception for subnormal results,
            # and validate signs.  Tests currently disabled, since
            # they fail on systems where a subnormal result from pow
            # is flushed to zero (e.g. Debian/ia64.)
            #self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315)
            #self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315)
            #self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315)
            #self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315)
            #self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315)
            #self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315)
            #self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315)
            #self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315)


@requires_setformat
class FormatFunctionsTestCase(unittest.TestCase):

    def setUp(self):
        self.save_formats = {'double':float.__getformat__('double'),
                             'float':float.__getformat__('float')}

    def tearDown(self):
        float.__setformat__('double', self.save_formats['double'])
        float.__setformat__('float', self.save_formats['float'])

    def test_getformat(self):
        self.assertIn(float.__getformat__('double'),
                      ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
        self.assertIn(float.__getformat__('float'),
                      ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
        self.assertRaises(ValueError, float.__getformat__, 'chicken')
        self.assertRaises(TypeError, float.__getformat__, 1)

    def test_setformat(self):
        for t in 'double', 'float':
            float.__setformat__(t, 'unknown')
            if self.save_formats[t] == 'IEEE, big-endian':
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, little-endian')
            elif self.save_formats[t] == 'IEEE, little-endian':
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, big-endian')
            else:
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, big-endian')
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, little-endian')
            self.assertRaises(ValueError, float.__setformat__,
                              t, 'chicken')
        self.assertRaises(ValueError, float.__setformat__,
                          'chicken', 'unknown')

BE_DOUBLE_INF = b'\x7f\xf0\x00\x00\x00\x00\x00\x00'
LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF))
BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00'
LE_DOUBLE_NAN = bytes(reversed(BE_DOUBLE_NAN))

BE_FLOAT_INF = b'\x7f\x80\x00\x00'
LE_FLOAT_INF = bytes(reversed(BE_FLOAT_INF))
BE_FLOAT_NAN = b'\x7f\xc0\x00\x00'
LE_FLOAT_NAN = bytes(reversed(BE_FLOAT_NAN))

# on non-IEEE platforms, attempting to unpack a bit pattern
# representing an infinity or a NaN should raise an exception.

@requires_setformat
class UnknownFormatTestCase(unittest.TestCase):
    def setUp(self):
        self.save_formats = {'double':float.__getformat__('double'),
                             'float':float.__getformat__('float')}
        float.__setformat__('double', 'unknown')
        float.__setformat__('float', 'unknown')

    def tearDown(self):
        float.__setformat__('double', self.save_formats['double'])
        float.__setformat__('float', self.save_formats['float'])

    def test_double_specials_dont_unpack(self):
        for fmt, data in [('>d', BE_DOUBLE_INF),
                          ('>d', BE_DOUBLE_NAN),
                          ('<d', LE_DOUBLE_INF),
                          ('<d', LE_DOUBLE_NAN)]:
            self.assertRaises(ValueError, struct.unpack, fmt, data)

    def test_float_specials_dont_unpack(self):
        for fmt, data in [('>f', BE_FLOAT_INF),
                          ('>f', BE_FLOAT_NAN),
                          ('<f', LE_FLOAT_INF),
                          ('<f', LE_FLOAT_NAN)]:
            self.assertRaises(ValueError, struct.unpack, fmt, data)


# on an IEEE platform, all we guarantee is that bit patterns
# representing infinities or NaNs do not raise an exception; all else
# is accident (today).
# let's also try to guarantee that -0.0 and 0.0 don't get confused.

class IEEEFormatTestCase(unittest.TestCase):

    @support.requires_IEEE_754
    def test_double_specials_do_unpack(self):
        for fmt, data in [('>d', BE_DOUBLE_INF),
                          ('>d', BE_DOUBLE_NAN),
                          ('<d', LE_DOUBLE_INF),
                          ('<d', LE_DOUBLE_NAN)]:
            struct.unpack(fmt, data)

    @support.requires_IEEE_754
    def test_float_specials_do_unpack(self):
        for fmt, data in [('>f', BE_FLOAT_INF),
                          ('>f', BE_FLOAT_NAN),
                          ('<f', LE_FLOAT_INF),
                          ('<f', LE_FLOAT_NAN)]:
            struct.unpack(fmt, data)

class FormatTestCase(unittest.TestCase):

    def test_format(self):
        # these should be rewritten to use both format(x, spec) and
        # x.__format__(spec)

        self.assertEqual(format(0.0, 'f'), '0.000000')

        # the default is 'g', except for empty format spec
        self.assertEqual(format(0.0, ''), '0.0')
        self.assertEqual(format(0.01, ''), '0.01')
        self.assertEqual(format(0.01, 'g'), '0.01')

        # empty presentation type should format in the same way as str
        # (issue 5920)
        x = 100/7.
        self.assertEqual(format(x, ''), str(x))
        self.assertEqual(format(x, '-'), str(x))
        self.assertEqual(format(x, '>'), str(x))
        self.assertEqual(format(x, '2'), str(x))

        self.assertEqual(format(1.0, 'f'), '1.000000')

        self.assertEqual(format(-1.0, 'f'), '-1.000000')

        self.assertEqual(format( 1.0, ' f'), ' 1.000000')
        self.assertEqual(format(-1.0, ' f'), '-1.000000')
        self.assertEqual(format( 1.0, '+f'), '+1.000000')
        self.assertEqual(format(-1.0, '+f'), '-1.000000')

        # % formatting
        self.assertEqual(format(-1.0, '%'), '-100.000000%')

        # conversion to string should fail
        self.assertRaises(ValueError, format, 3.0, "s")

        # other format specifiers shouldn't work on floats,
        #  in particular int specifiers
        for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] +
                            [chr(x) for x in range(ord('A'), ord('Z')+1)]):
            if not format_spec in 'eEfFgGn%':
                self.assertRaises(ValueError, format, 0.0, format_spec)
                self.assertRaises(ValueError, format, 1.0, format_spec)
                self.assertRaises(ValueError, format, -1.0, format_spec)
                self.assertRaises(ValueError, format, 1e100, format_spec)
                self.assertRaises(ValueError, format, -1e100, format_spec)
                self.assertRaises(ValueError, format, 1e-100, format_spec)
                self.assertRaises(ValueError, format, -1e-100, format_spec)

        # issue 3382
        self.assertEqual(format(NAN, 'f'), 'nan')
        self.assertEqual(format(NAN, 'F'), 'NAN')
        self.assertEqual(format(INF, 'f'), 'inf')
        self.assertEqual(format(INF, 'F'), 'INF')

    @support.requires_IEEE_754
    def test_format_testfile(self):
        with open(format_testfile) as testfile:
            for line in testfile:
                if line.startswith('--'):
                    continue
                line = line.strip()
                if not line:
                    continue

                lhs, rhs = map(str.strip, line.split('->'))
                fmt, arg = lhs.split()
                self.assertEqual(fmt % float(arg), rhs)
                self.assertEqual(fmt % -float(arg), '-' + rhs)

    def test_issue5864(self):
        self.assertEqual(format(123.456, '.4'), '123.5')
        self.assertEqual(format(1234.56, '.4'), '1.235e+03')
        self.assertEqual(format(12345.6, '.4'), '1.235e+04')

class ReprTestCase(unittest.TestCase):
    def test_repr(self):
        floats_file = open(os.path.join(os.path.split(__file__)[0],
                           'floating_points.txt'))
        for line in floats_file:
            line = line.strip()
            if not line or line.startswith('#'):
                continue
            v = eval(line)
            self.assertEqual(v, eval(repr(v)))
        floats_file.close()

    @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
                         "applies only when using short float repr style")
    def test_short_repr(self):
        # test short float repr introduced in Python 3.1.  One aspect
        # of this repr is that we get some degree of str -> float ->
        # str roundtripping.  In particular, for any numeric string
        # containing 15 or fewer significant digits, those exact same
        # digits (modulo trailing zeros) should appear in the output.
        # No more repr(0.03) -> "0.029999999999999999"!

        test_strings = [
            # output always includes *either* a decimal point and at
            # least one digit after that point, or an exponent.
            '0.0',
            '1.0',
            '0.01',
            '0.02',
            '0.03',
            '0.04',
            '0.05',
            '1.23456789',
            '10.0',
            '100.0',
            # values >= 1e16 get an exponent...
            '1000000000000000.0',
            '9999999999999990.0',
            '1e+16',
            '1e+17',
            # ... and so do values < 1e-4
            '0.001',
            '0.001001',
            '0.00010000000000001',
            '0.0001',
            '9.999999999999e-05',
            '1e-05',
            # values designed to provoke failure if the FPU rounding
            # precision isn't set correctly
            '8.72293771110361e+25',
            '7.47005307342313e+26',
            '2.86438000439698e+28',
            '8.89142905246179e+28',
            '3.08578087079232e+35',
            ]

        for s in test_strings:
            negs = '-'+s
            self.assertEqual(s, repr(float(s)))
            self.assertEqual(negs, repr(float(negs)))
            # Since Python 3.2, repr and str are identical
            self.assertEqual(repr(float(s)), str(float(s)))
            self.assertEqual(repr(float(negs)), str(float(negs)))

@support.requires_IEEE_754
class RoundTestCase(unittest.TestCase):

    def test_inf_nan(self):
        self.assertRaises(OverflowError, round, INF)
        self.assertRaises(OverflowError, round, -INF)
        self.assertRaises(ValueError, round, NAN)
        self.assertRaises(TypeError, round, INF, 0.0)
        self.assertRaises(TypeError, round, -INF, 1.0)
        self.assertRaises(TypeError, round, NAN, "ceci n'est pas un integer")
        self.assertRaises(TypeError, round, -0.0, 1j)

    def test_large_n(self):
        for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]:
            self.assertEqual(round(123.456, n), 123.456)
            self.assertEqual(round(-123.456, n), -123.456)
            self.assertEqual(round(1e300, n), 1e300)
            self.assertEqual(round(1e-320, n), 1e-320)
        self.assertEqual(round(1e150, 300), 1e150)
        self.assertEqual(round(1e300, 307), 1e300)
        self.assertEqual(round(-3.1415, 308), -3.1415)
        self.assertEqual(round(1e150, 309), 1e150)
        self.assertEqual(round(1.4e-315, 315), 1e-315)

    def test_small_n(self):
        for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]:
            self.assertEqual(round(123.456, n), 0.0)
            self.assertEqual(round(-123.456, n), -0.0)
            self.assertEqual(round(1e300, n), 0.0)
            self.assertEqual(round(1e-320, n), 0.0)

    def test_overflow(self):
        self.assertRaises(OverflowError, round, 1.6e308, -308)
        self.assertRaises(OverflowError, round, -1.7e308, -308)

    @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
                         "applies only when using short float repr style")
    def test_previous_round_bugs(self):
        # particular cases that have occurred in bug reports
        self.assertEqual(round(562949953421312.5, 1),
                          562949953421312.5)
        self.assertEqual(round(56294995342131.5, 3),
                         56294995342131.5)
        # round-half-even
        self.assertEqual(round(25.0, -1), 20.0)
        self.assertEqual(round(35.0, -1), 40.0)
        self.assertEqual(round(45.0, -1), 40.0)
        self.assertEqual(round(55.0, -1), 60.0)
        self.assertEqual(round(65.0, -1), 60.0)
        self.assertEqual(round(75.0, -1), 80.0)
        self.assertEqual(round(85.0, -1), 80.0)
        self.assertEqual(round(95.0, -1), 100.0)

    @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
                         "applies only when using short float repr style")
    def test_matches_float_format(self):
        # round should give the same results as float formatting
        for i in range(500):
            x = i/1000.
            self.assertEqual(float(format(x, '.0f')), round(x, 0))
            self.assertEqual(float(format(x, '.1f')), round(x, 1))
            self.assertEqual(float(format(x, '.2f')), round(x, 2))
            self.assertEqual(float(format(x, '.3f')), round(x, 3))

        for i in range(5, 5000, 10):
            x = i/1000.
            self.assertEqual(float(format(x, '.0f')), round(x, 0))
            self.assertEqual(float(format(x, '.1f')), round(x, 1))
            self.assertEqual(float(format(x, '.2f')), round(x, 2))
            self.assertEqual(float(format(x, '.3f')), round(x, 3))

        for i in range(500):
            x = random.random()
            self.assertEqual(float(format(x, '.0f')), round(x, 0))
            self.assertEqual(float(format(x, '.1f')), round(x, 1))
            self.assertEqual(float(format(x, '.2f')), round(x, 2))
            self.assertEqual(float(format(x, '.3f')), round(x, 3))

    def test_format_specials(self):
        # Test formatting of nans and infs.

        def test(fmt, value, expected):
            # Test with both % and format().
            self.assertEqual(fmt % value, expected, fmt)
            fmt = fmt[1:] # strip off the %
            self.assertEqual(format(value, fmt), expected, fmt)

        for fmt in ['%e', '%f', '%g', '%.0e', '%.6f', '%.20g',
                    '%#e', '%#f', '%#g', '%#.20e', '%#.15f', '%#.3g']:
            pfmt = '%+' + fmt[1:]
            sfmt = '% ' + fmt[1:]
            test(fmt, INF, 'inf')
            test(fmt, -INF, '-inf')
            test(fmt, NAN, 'nan')
            test(fmt, -NAN, 'nan')
            # When asking for a sign, it's always provided. nans are
            #  always positive.
            test(pfmt, INF, '+inf')
            test(pfmt, -INF, '-inf')
            test(pfmt, NAN, '+nan')
            test(pfmt, -NAN, '+nan')
            # When using ' ' for a sign code, only infs can be negative.
            #  Others have a space.
            test(sfmt, INF, ' inf')
            test(sfmt, -INF, '-inf')
            test(sfmt, NAN, ' nan')
            test(sfmt, -NAN, ' nan')

    def test_None_ndigits(self):
        for x in round(1.23), round(1.23, None), round(1.23, ndigits=None):
            self.assertEqual(x, 1)
            self.assertIsInstance(x, int)
        for x in round(1.78), round(1.78, None), round(1.78, ndigits=None):
            self.assertEqual(x, 2)
            self.assertIsInstance(x, int)


# Beginning with Python 2.6 float has cross platform compatible
# ways to create and represent inf and nan
class InfNanTest(unittest.TestCase):
    def test_inf_from_str(self):
        self.assertTrue(isinf(float("inf")))
        self.assertTrue(isinf(float("+inf")))
        self.assertTrue(isinf(float("-inf")))
        self.assertTrue(isinf(float("infinity")))
        self.assertTrue(isinf(float("+infinity")))
        self.assertTrue(isinf(float("-infinity")))

        self.assertEqual(repr(float("inf")), "inf")
        self.assertEqual(repr(float("+inf")), "inf")
        self.assertEqual(repr(float("-inf")), "-inf")
        self.assertEqual(repr(float("infinity")), "inf")
        self.assertEqual(repr(float("+infinity")), "inf")
        self.assertEqual(repr(float("-infinity")), "-inf")

        self.assertEqual(repr(float("INF")), "inf")
        self.assertEqual(repr(float("+Inf")), "inf")
        self.assertEqual(repr(float("-iNF")), "-inf")
        self.assertEqual(repr(float("Infinity")), "inf")
        self.assertEqual(repr(float("+iNfInItY")), "inf")
        self.assertEqual(repr(float("-INFINITY")), "-inf")

        self.assertEqual(str(float("inf")), "inf")
        self.assertEqual(str(float("+inf")), "inf")
        self.assertEqual(str(float("-inf")), "-inf")
        self.assertEqual(str(float("infinity")), "inf")
        self.assertEqual(str(float("+infinity")), "inf")
        self.assertEqual(str(float("-infinity")), "-inf")

        self.assertRaises(ValueError, float, "info")
        self.assertRaises(ValueError, float, "+info")
        self.assertRaises(ValueError, float, "-info")
        self.assertRaises(ValueError, float, "in")
        self.assertRaises(ValueError, float, "+in")
        self.assertRaises(ValueError, float, "-in")
        self.assertRaises(ValueError, float, "infinit")
        self.assertRaises(ValueError, float, "+Infin")
        self.assertRaises(ValueError, float, "-INFI")
        self.assertRaises(ValueError, float, "infinitys")

        self.assertRaises(ValueError, float, "++Inf")
        self.assertRaises(ValueError, float, "-+inf")
        self.assertRaises(ValueError, float, "+-infinity")
        self.assertRaises(ValueError, float, "--Infinity")

    def test_inf_as_str(self):
        self.assertEqual(repr(1e300 * 1e300), "inf")
        self.assertEqual(repr(-1e300 * 1e300), "-inf")

        self.assertEqual(str(1e300 * 1e300), "inf")
        self.assertEqual(str(-1e300 * 1e300), "-inf")

    def test_nan_from_str(self):
        self.assertTrue(isnan(float("nan")))
        self.assertTrue(isnan(float("+nan")))
        self.assertTrue(isnan(float("-nan")))

        self.assertEqual(repr(float("nan")), "nan")
        self.assertEqual(repr(float("+nan")), "nan")
        self.assertEqual(repr(float("-nan")), "nan")

        self.assertEqual(repr(float("NAN")), "nan")
        self.assertEqual(repr(float("+NAn")), "nan")
        self.assertEqual(repr(float("-NaN")), "nan")

        self.assertEqual(str(float("nan")), "nan")
        self.assertEqual(str(float("+nan")), "nan")
        self.assertEqual(str(float("-nan")), "nan")

        self.assertRaises(ValueError, float, "nana")
        self.assertRaises(ValueError, float, "+nana")
        self.assertRaises(ValueError, float, "-nana")
        self.assertRaises(ValueError, float, "na")
        self.assertRaises(ValueError, float, "+na")
        self.assertRaises(ValueError, float, "-na")

        self.assertRaises(ValueError, float, "++nan")
        self.assertRaises(ValueError, float, "-+NAN")
        self.assertRaises(ValueError, float, "+-NaN")
        self.assertRaises(ValueError, float, "--nAn")

    def test_nan_as_str(self):
        self.assertEqual(repr(1e300 * 1e300 * 0), "nan")
        self.assertEqual(repr(-1e300 * 1e300 * 0), "nan")

        self.assertEqual(str(1e300 * 1e300 * 0), "nan")
        self.assertEqual(str(-1e300 * 1e300 * 0), "nan")

    def test_inf_signs(self):
        self.assertEqual(copysign(1.0, float('inf')), 1.0)
        self.assertEqual(copysign(1.0, float('-inf')), -1.0)

    @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
                         "applies only when using short float repr style")
    def test_nan_signs(self):
        # When using the dtoa.c code, the sign of float('nan') should
        # be predictable.
        self.assertEqual(copysign(1.0, float('nan')), 1.0)
        self.assertEqual(copysign(1.0, float('-nan')), -1.0)


fromHex = float.fromhex
toHex = float.hex
class HexFloatTestCase(unittest.TestCase):
    MAX = fromHex('0x.fffffffffffff8p+1024')  # max normal
    MIN = fromHex('0x1p-1022')                # min normal
    TINY = fromHex('0x0.0000000000001p-1022') # min subnormal
    EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up

    def identical(self, x, y):
        # check that floats x and y are identical, or that both
        # are NaNs
        if isnan(x) or isnan(y):
            if isnan(x) == isnan(y):
                return
        elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)):
            return
        self.fail('%r not identical to %r' % (x, y))

    def test_ends(self):
        self.identical(self.MIN, ldexp(1.0, -1022))
        self.identical(self.TINY, ldexp(1.0, -1074))
        self.identical(self.EPS, ldexp(1.0, -52))
        self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970)))

    def test_invalid_inputs(self):
        invalid_inputs = [
            'infi',   # misspelt infinities and nans
            '-Infinit',
            '++inf',
            '-+Inf',
            '--nan',
            '+-NaN',
            'snan',
            'NaNs',
            'nna',
            'an',
            'nf',
            'nfinity',
            'inity',
            'iinity',
            '0xnan',
            '',
            ' ',
            'x1.0p0',
            '0xX1.0p0',
            '+ 0x1.0p0', # internal whitespace
            '- 0x1.0p0',
            '0 x1.0p0',
            '0x 1.0p0',
            '0x1 2.0p0',
            '+0x1 .0p0',
            '0x1. 0p0',
            '-0x1.0 1p0',
            '-0x1.0 p0',
            '+0x1.0p +0',
            '0x1.0p -0',
            '0x1.0p 0',
            '+0x1.0p+ 0',
            '-0x1.0p- 0',
            '++0x1.0p-0', # double signs
            '--0x1.0p0',
            '+-0x1.0p+0',
            '-+0x1.0p0',
            '0x1.0p++0',
            '+0x1.0p+-0',
            '-0x1.0p-+0',
            '0x1.0p--0',
            '0x1.0.p0',
            '0x.p0', # no hex digits before or after point
            '0x1,p0', # wrong decimal point character
            '0x1pa',
            '0x1p\uff10',  # fullwidth Unicode digits
            '\uff10x1p0',
            '0x\uff11p0',
            '0x1.\uff10p0',
            '0x1p0 \n 0x2p0',
            '0x1p0\0 0x1p0',  # embedded null byte is not end of string
            ]
        for x in invalid_inputs:
            try:
                result = fromHex(x)
            except ValueError:
                pass
            else:
                self.fail('Expected float.fromhex(%r) to raise ValueError; '
                          'got %r instead' % (x, result))


    def test_whitespace(self):
        value_pairs = [
            ('inf', INF),
            ('-Infinity', -INF),
            ('nan', NAN),
            ('1.0', 1.0),
            ('-0x.2', -0.125),
            ('-0.0', -0.0)
            ]
        whitespace = [
            '',
            ' ',
            '\t',
            '\n',
            '\n \t',
            '\f',
            '\v',
            '\r'
            ]
        for inp, expected in value_pairs:
            for lead in whitespace:
                for trail in whitespace:
                    got = fromHex(lead + inp + trail)
                    self.identical(got, expected)


    def test_from_hex(self):
        MIN = self.MIN;
        MAX = self.MAX;
        TINY = self.TINY;
        EPS = self.EPS;

        # two spellings of infinity, with optional signs; case-insensitive
        self.identical(fromHex('inf'), INF)
        self.identical(fromHex('+Inf'), INF)
        self.identical(fromHex('-INF'), -INF)
        self.identical(fromHex('iNf'), INF)
        self.identical(fromHex('Infinity'), INF)
        self.identical(fromHex('+INFINITY'), INF)
        self.identical(fromHex('-infinity'), -INF)
        self.identical(fromHex('-iNFiNitY'), -INF)

        # nans with optional sign; case insensitive
        self.identical(fromHex('nan'), NAN)
        self.identical(fromHex('+NaN'), NAN)
        self.identical(fromHex('-NaN'), NAN)
        self.identical(fromHex('-nAN'), NAN)

        # variations in input format
        self.identical(fromHex('1'), 1.0)
        self.identical(fromHex('+1'), 1.0)
        self.identical(fromHex('1.'), 1.0)
        self.identical(fromHex('1.0'), 1.0)
        self.identical(fromHex('1.0p0'), 1.0)
        self.identical(fromHex('01'), 1.0)
        self.identical(fromHex('01.'), 1.0)
        self.identical(fromHex('0x1'), 1.0)
        self.identical(fromHex('0x1.'), 1.0)
        self.identical(fromHex('0x1.0'), 1.0)
        self.identical(fromHex('+0x1.0'), 1.0)
        self.identical(fromHex('0x1p0'), 1.0)
        self.identical(fromHex('0X1p0'), 1.0)
        self.identical(fromHex('0X1P0'), 1.0)
        self.identical(fromHex('0x1P0'), 1.0)
        self.identical(fromHex('0x1.p0'), 1.0)
        self.identical(fromHex('0x1.0p0'), 1.0)
        self.identical(fromHex('0x.1p4'), 1.0)
        self.identical(fromHex('0x.1p04'), 1.0)
        self.identical(fromHex('0x.1p004'), 1.0)
        self.identical(fromHex('0x1p+0'), 1.0)
        self.identical(fromHex('0x1P-0'), 1.0)
        self.identical(fromHex('+0x1p0'), 1.0)
        self.identical(fromHex('0x01p0'), 1.0)
        self.identical(fromHex('0x1p00'), 1.0)
        self.identical(fromHex(' 0x1p0 '), 1.0)
        self.identical(fromHex('\n 0x1p0'), 1.0)
        self.identical(fromHex('0x1p0 \t'), 1.0)
        self.identical(fromHex('0xap0'), 10.0)
        self.identical(fromHex('0xAp0'), 10.0)
        self.identical(fromHex('0xaP0'), 10.0)
        self.identical(fromHex('0xAP0'), 10.0)
        self.identical(fromHex('0xbep0'), 190.0)
        self.identical(fromHex('0xBep0'), 190.0)
        self.identical(fromHex('0xbEp0'), 190.0)
        self.identical(fromHex('0XBE0P-4'), 190.0)
        self.identical(fromHex('0xBEp0'), 190.0)
        self.identical(fromHex('0xB.Ep4'), 190.0)
        self.identical(fromHex('0x.BEp8'), 190.0)
        self.identical(fromHex('0x.0BEp12'), 190.0)

        # moving the point around
        pi = fromHex('0x1.921fb54442d18p1')
        self.identical(fromHex('0x.006487ed5110b46p11'), pi)
        self.identical(fromHex('0x.00c90fdaa22168cp10'), pi)
        self.identical(fromHex('0x.01921fb54442d18p9'), pi)
        self.identical(fromHex('0x.03243f6a8885a3p8'), pi)
        self.identical(fromHex('0x.06487ed5110b46p7'), pi)
        self.identical(fromHex('0x.0c90fdaa22168cp6'), pi)
        self.identical(fromHex('0x.1921fb54442d18p5'), pi)
        self.identical(fromHex('0x.3243f6a8885a3p4'), pi)
        self.identical(fromHex('0x.6487ed5110b46p3'), pi)
        self.identical(fromHex('0x.c90fdaa22168cp2'), pi)
        self.identical(fromHex('0x1.921fb54442d18p1'), pi)
        self.identical(fromHex('0x3.243f6a8885a3p0'), pi)
        self.identical(fromHex('0x6.487ed5110b46p-1'), pi)
        self.identical(fromHex('0xc.90fdaa22168cp-2'), pi)
        self.identical(fromHex('0x19.21fb54442d18p-3'), pi)
        self.identical(fromHex('0x32.43f6a8885a3p-4'), pi)
        self.identical(fromHex('0x64.87ed5110b46p-5'), pi)
        self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi)
        self.identical(fromHex('0x192.1fb54442d18p-7'), pi)
        self.identical(fromHex('0x324.3f6a8885a3p-8'), pi)
        self.identical(fromHex('0x648.7ed5110b46p-9'), pi)
        self.identical(fromHex('0xc90.fdaa22168cp-10'), pi)
        self.identical(fromHex('0x1921.fb54442d18p-11'), pi)
        # ...
        self.identical(fromHex('0x1921fb54442d1.8p-47'), pi)
        self.identical(fromHex('0x3243f6a8885a3p-48'), pi)
        self.identical(fromHex('0x6487ed5110b46p-49'), pi)
        self.identical(fromHex('0xc90fdaa22168cp-50'), pi)
        self.identical(fromHex('0x1921fb54442d18p-51'), pi)
        self.identical(fromHex('0x3243f6a8885a30p-52'), pi)
        self.identical(fromHex('0x6487ed5110b460p-53'), pi)
        self.identical(fromHex('0xc90fdaa22168c0p-54'), pi)
        self.identical(fromHex('0x1921fb54442d180p-55'), pi)


        # results that should overflow...
        self.assertRaises(OverflowError, fromHex, '-0x1p1024')
        self.assertRaises(OverflowError, fromHex, '0x1p+1025')
        self.assertRaises(OverflowError, fromHex, '+0X1p1030')
        self.assertRaises(OverflowError, fromHex, '-0x1p+1100')
        self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789')
        self.assertRaises(OverflowError, fromHex, '+0X.8p+1025')
        self.assertRaises(OverflowError, fromHex, '+0x0.8p1025')
        self.assertRaises(OverflowError, fromHex, '-0x0.4p1026')
        self.assertRaises(OverflowError, fromHex, '0X2p+1023')
        self.assertRaises(OverflowError, fromHex, '0x2.p1023')
        self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023')
        self.assertRaises(OverflowError, fromHex, '+0X4p+1022')
        self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023')
        self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023')
        self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023')
        self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022')
        self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970')
        self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960')
        self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960')

        # ...and those that round to +-max float
        self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX)
        self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX)
        self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX)

        # zeros
        self.identical(fromHex('0x0p0'), 0.0)
        self.identical(fromHex('0x0p1000'), 0.0)
        self.identical(fromHex('-0x0p1023'), -0.0)
        self.identical(fromHex('0X0p1024'), 0.0)
        self.identical(fromHex('-0x0p1025'), -0.0)
        self.identical(fromHex('0X0p2000'), 0.0)
        self.identical(fromHex('0x0p123456789123456789'), 0.0)
        self.identical(fromHex('-0X0p-0'), -0.0)
        self.identical(fromHex('-0X0p-1000'), -0.0)
        self.identical(fromHex('0x0p-1023'), 0.0)
        self.identical(fromHex('-0X0p-1024'), -0.0)
        self.identical(fromHex('-0x0p-1025'), -0.0)
        self.identical(fromHex('-0x0p-1072'), -0.0)
        self.identical(fromHex('0X0p-1073'), 0.0)
        self.identical(fromHex('-0x0p-1074'), -0.0)
        self.identical(fromHex('0x0p-1075'), 0.0)
        self.identical(fromHex('0X0p-1076'), 0.0)
        self.identical(fromHex('-0X0p-2000'), -0.0)
        self.identical(fromHex('-0x0p-123456789123456789'), -0.0)

        # values that should underflow to 0
        self.identical(fromHex('0X1p-1075'), 0.0)
        self.identical(fromHex('-0X1p-1075'), -0.0)
        self.identical(fromHex('-0x1p-123456789123456789'), -0.0)
        self.identical(fromHex('0x1.00000000000000001p-1075'), TINY)
        self.identical(fromHex('-0x1.1p-1075'), -TINY)
        self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY)

        # check round-half-even is working correctly near 0 ...
        self.identical(fromHex('0x1p-1076'), 0.0)
        self.identical(fromHex('0X2p-1076'), 0.0)
        self.identical(fromHex('0X3p-1076'), TINY)
        self.identical(fromHex('0x4p-1076'), TINY)
        self.identical(fromHex('0X5p-1076'), TINY)
        self.identical(fromHex('0X6p-1076'), 2*TINY)
        self.identical(fromHex('0x7p-1076'), 2*TINY)
        self.identical(fromHex('0X8p-1076'), 2*TINY)
        self.identical(fromHex('0X9p-1076'), 2*TINY)
        self.identical(fromHex('0xap-1076'), 2*TINY)
        self.identical(fromHex('0Xbp-1076'), 3*TINY)
        self.identical(fromHex('0xcp-1076'), 3*TINY)
        self.identical(fromHex('0Xdp-1076'), 3*TINY)
        self.identical(fromHex('0Xep-1076'), 4*TINY)
        self.identical(fromHex('0xfp-1076'), 4*TINY)
        self.identical(fromHex('0x10p-1076'), 4*TINY)
        self.identical(fromHex('-0x1p-1076'), -0.0)
        self.identical(fromHex('-0X2p-1076'), -0.0)
        self.identical(fromHex('-0x3p-1076'), -TINY)
        self.identical(fromHex('-0X4p-1076'), -TINY)
        self.identical(fromHex('-0x5p-1076'), -TINY)
        self.identical(fromHex('-0x6p-1076'), -2*TINY)
        self.identical(fromHex('-0X7p-1076'), -2*TINY)
        self.identical(fromHex('-0X8p-1076'), -2*TINY)
        self.identical(fromHex('-0X9p-1076'), -2*TINY)
        self.identical(fromHex('-0Xap-1076'), -2*TINY)
        self.identical(fromHex('-0xbp-1076'), -3*TINY)
        self.identical(fromHex('-0xcp-1076'), -3*TINY)
        self.identical(fromHex('-0Xdp-1076'), -3*TINY)
        self.identical(fromHex('-0xep-1076'), -4*TINY)
        self.identical(fromHex('-0Xfp-1076'), -4*TINY)
        self.identical(fromHex('-0X10p-1076'), -4*TINY)

        # ... and near MIN ...
        self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY)
        self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY)
        self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY)
        self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY)
        self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY)
        self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY)
        self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY)
        self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY)
        self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY)
        self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN)
        self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN)
        self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN)
        self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN)
        self.identical(fromHex('0x1.00000000000000p-1022'), MIN)
        self.identical(fromHex('0x1.00000000000002p-1022'), MIN)
        self.identical(fromHex('0x1.00000000000004p-1022'), MIN)
        self.identical(fromHex('0x1.00000000000006p-1022'), MIN)
        self.identical(fromHex('0x1.00000000000008p-1022'), MIN)
        self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY)
        self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY)
        self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY)
        self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY)
        self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY)
        self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY)
        self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY)
        self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY)

        # ... and near 1.0.
        self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS)
        self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS)
        self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS)
        self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS)
        self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS)
        self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2)
        self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2)
        self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2)
        self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2)
        self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2)
        self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2)
        self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2)
        self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0)
        self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0)
        self.identical(fromHex('0X0.fffffffffffffep0'), 1.0)
        self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0)
        self.identical(fromHex('0X1.00000000000000p0'), 1.0)
        self.identical(fromHex('0X1.00000000000001p0'), 1.0)
        self.identical(fromHex('0x1.00000000000002p0'), 1.0)
        self.identical(fromHex('0X1.00000000000003p0'), 1.0)
        self.identical(fromHex('0x1.00000000000004p0'), 1.0)
        self.identical(fromHex('0X1.00000000000005p0'), 1.0)
        self.identical(fromHex('0X1.00000000000006p0'), 1.0)
        self.identical(fromHex('0X1.00000000000007p0'), 1.0)
        self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'),
                       1.0)
        self.identical(fromHex('0x1.00000000000008p0'), 1.0)
        self.identical(fromHex('0x1.00000000000008000000000000000001p0'),
                       1+EPS)
        self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS)
        self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS)
        self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS)
        self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS)
        self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS)
        self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS)
        self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS)
        self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS)
        self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS)
        self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS)
        self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS)
        self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS)
        self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS)
        self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS)
        self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS)
        self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'),
                       1.0+EPS)
        self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS)
        self.identical(fromHex('0X1.00000000000018000000000000000001p0'),
                       1.0+2*EPS)
        self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS)
        self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS)
        self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS)
        self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS)
        self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS)
        self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS)
        self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS)
        self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS)

    def test_roundtrip(self):
        def roundtrip(x):
            return fromHex(toHex(x))

        for x in [NAN, INF, self.MAX, self.MIN, self.MIN-self.TINY, self.TINY, 0.0]:
            self.identical(x, roundtrip(x))
            self.identical(-x, roundtrip(-x))

        # fromHex(toHex(x)) should exactly recover x, for any non-NaN float x.
        import random
        for i in range(10000):
            e = random.randrange(-1200, 1200)
            m = random.random()
            s = random.choice([1.0, -1.0])
            try:
                x = s*ldexp(m, e)
            except OverflowError:
                pass
            else:
                self.identical(x, fromHex(toHex(x)))

    def test_subclass(self):
        class F(float):
            def __new__(cls, value):
                return float.__new__(cls, value + 1)

        f = F.fromhex((1.5).hex())
        self.assertIs(type(f), F)
        self.assertEqual(f, 2.5)

        class F2(float):
            def __init__(self, value):
                self.foo = 'bar'

        f = F2.fromhex((1.5).hex())
        self.assertIs(type(f), F2)
        self.assertEqual(f, 1.5)
        self.assertEqual(getattr(f, 'foo', 'none'), 'bar')


if __name__ == '__main__':
    unittest.main()