import unittest, struct

import os

from test import test_support

import math

from math import isinf, isnan, copysign, ldexp

import operator

import random, fractions

INF = float("inf")

NAN = float("nan")

class GeneralFloatCases(unittest.TestCase):

    def test_float(self):

        self.assertEqual(float(3.14), 3.14)

        self.assertEqual(float(314), 314.0)

        self.assertEqual(float(314L), 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")

        if test_support.have_unicode:

            self.assertEqual(float(unicode("  3.14  ")), 3.14)

            self.assertEqual(float(unicode("  \u0663.\u0661\u0664  ",'raw-unicode-escape')), 3.14)

            # Implementation limitation in PyFloat_FromString()

            self.assertRaises(ValueError, float, unicode("1"*10000))

    @test_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 syntac

        import locale

        if not locale.localeconv()['decimal_point'] == ',':

            return

        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.assertEqual(test_support.fcmp(float("  .25e-1  "), .025), 0)

    def test_floatconversion(self):

        # Make sure that calls to __float__() work properly

        class Foo0:

            def __float__(self):

                return 42.

        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

        self.assertAlmostEqual(float(Foo0()), 42.)

        self.assertAlmostEqual(float(Foo1()), 42.)

        self.assertAlmostEqual(float(Foo2()), 42.)

        self.assertAlmostEqual(float(Foo3(21)), 42.)

        self.assertRaises(TypeError, float, Foo4(42))

    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)

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.assert_(float.__getformat__('double') in

                     ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])

        self.assert_(float.__getformat__('float') in

                     ['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 = '\x7f\xf0\x00\x00\x00\x00\x00\x00'

LE_DOUBLE_INF = ''.join(reversed(BE_DOUBLE_INF))

BE_DOUBLE_NAN = '\x7f\xf8\x00\x00\x00\x00\x00\x00'

LE_DOUBLE_NAN = ''.join(reversed(BE_DOUBLE_NAN))

BE_FLOAT_INF = '\x7f\x80\x00\x00'

LE_FLOAT_INF = ''.join(reversed(BE_FLOAT_INF))

BE_FLOAT_NAN = '\x7f\xc0\x00\x00'

LE_FLOAT_NAN = ''.join(reversed(BE_FLOAT_NAN))

# on non-IEEE platforms, attempting to unpack a bit pattern

# representing an infinity or a NaN should raise an exception.

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):

    if float.__getformat__("double").startswith("IEEE"):

        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)

    if float.__getformat__("float").startswith("IEEE"):

        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)

    if float.__getformat__("double").startswith("IEEE"):

        def test_negative_zero(self):

            import math

            def pos_pos():

                return 0.0, math.atan2(0.0, -1)

            def pos_neg():

                return 0.0, math.atan2(-0.0, -1)

            def neg_pos():

                return -0.0, math.atan2(0.0, -1)

            def neg_neg():

                return -0.0, math.atan2(-0.0, -1)

            self.assertEquals(pos_pos(), neg_pos())

            self.assertEquals(pos_neg(), neg_neg())

    if float.__getformat__("double").startswith("IEEE"):

        def test_underflow_sign(self):

            import math

            # check that -1e-1000 gives -0.0, not 0.0

            self.assertEquals(math.atan2(-1e-1000, -1), math.atan2(-0.0, -1))

            self.assertEquals(math.atan2(float('-1e-1000'), -1),

                              math.atan2(-0.0, -1))

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()

# 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.assert_(isinf(float("inf")))

        self.assert_(isinf(float("+inf")))

        self.assert_(isinf(float("-inf")))

        self.assert_(isinf(float("infinity")))

        self.assert_(isinf(float("+infinity")))

        self.assert_(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")

    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.assert_(isnan(float("nan")))

        self.assert_(isnan(float("+nan")))

        self.assert_(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")

    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 notest_float_nan(self):

        self.assert_(NAN.is_nan())

        self.failIf(INF.is_nan())

        self.failIf((0.).is_nan())

    def notest_float_inf(self):

        self.assert_(INF.is_inf())

        self.failIf(NAN.is_inf())

        self.failIf((0.).is_inf())

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',

            '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',

            u'0x1p\uff10',  # fullwidth Unicode digits

            u'\uff10x1p0',

            u'0x\uff11p0',

            u'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_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(u'0x1p0'), 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)