text: 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(ValueError, 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)
          # Invalid unicode string
          # See bpo-34087
          self.assertRaises(ValueError, float, '\u3053\u3093\u306b\u3061\u306f')
  
      def test_noargs(self):
          self.assertEqual(float(), 0.0)
  
      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)
  
          class MyIndex:
              def __init__(self, value):
                  self.value = value
              def __index__(self):
                  return self.value
  
          self.assertEqual(float(MyIndex(42)), 42.0)
          self.assertRaises(OverflowError, float, MyIndex(2**2000))
  
          class MyInt:
              def __int__(self):
                  return 42
  
          self.assertRaises(TypeError, float, MyInt())
  
      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)
  
      @support.requires_IEEE_754
      def test_serialized_float_rounding(self):
          from _testcapi import FLT_MAX
          self.assertEqual(struct.pack("<f", 3.40282356e38), struct.pack("<f", FLT_MAX))
          self.assertEqual(struct.pack("<f", -3.40282356e38), struct.pack("<f", -FLT_MAX))
  
  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')
  
      def test_issue35560(self):
          self.assertEqual(format(123.0, '00'), '123.0')
          self.assertEqual(format(123.34, '00f'), '123.340000')
          self.assertEqual(format(123.34, '00e'), '1.233400e+02')
          self.assertEqual(format(123.34, '00g'), '123.34')
          self.assertEqual(format(123.34, '00.10f'), '123.3400000000')
          self.assertEqual(format(123.34, '00.10e'), '1.2334000000e+02')
          self.assertEqual(format(123.34, '00.10g'), '123.34')
          self.assertEqual(format(123.34, '01f'), '123.340000')
  
          self.assertEqual(format(-123.0, '00'), '-123.0')
          self.assertEqual(format(-123.34, '00f'), '-123.340000')
          self.assertEqual(format(-123.34, '00e'), '-1.233400e+02')
          self.assertEqual(format(-123.34, '00g'), '-123.34')
          self.assertEqual(format(-123.34, '00.10f'), '-123.3400000000')
          self.assertEqual(format(-123.34, '00.10f'), '-123.3400000000')
          self.assertEqual(format(-123.34, '00.10e'), '-1.2334000000e+02')
          self.assertEqual(format(-123.34, '00.10g'), '-123.34')
  
  class ReprTestCase(unittest.TestCase):
      def test_repr(self):
          with open(os.path.join(os.path.split(__file__)[0],
                    'floating_points.txt')) as floats_file:
              for line in floats_file:
                  line = line.strip()
                  if not line or line.startswith('#'):
                      continue
                  v = eval(line)
                  self.assertEqual(v, eval(repr(v)))
  
      @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()
  