text: import unittest
  from test import support
  
  import sys
  
  import random
  import math
  import array
  
  # Used for lazy formatting of failure messages
  class Frm(object):
      def __init__(self, format, *args):
          self.format = format
          self.args = args
  
      def __str__(self):
          return self.format % self.args
  
  # SHIFT should match the value in longintrepr.h for best testing.
  SHIFT = sys.int_info.bits_per_digit
  BASE = 2 ** SHIFT
  MASK = BASE - 1
  KARATSUBA_CUTOFF = 70   # from longobject.c
  
  # Max number of base BASE digits to use in test cases.  Doubling
  # this will more than double the runtime.
  MAXDIGITS = 15
  
  # build some special values
  special = [0, 1, 2, BASE, BASE >> 1, 0x5555555555555555, 0xaaaaaaaaaaaaaaaa]
  #  some solid strings of one bits
  p2 = 4  # 0 and 1 already added
  for i in range(2*SHIFT):
      special.append(p2 - 1)
      p2 = p2 << 1
  del p2
  # add complements & negations
  special += [~x for x in special] + [-x for x in special]
  
  DBL_MAX = sys.float_info.max
  DBL_MAX_EXP = sys.float_info.max_exp
  DBL_MIN_EXP = sys.float_info.min_exp
  DBL_MANT_DIG = sys.float_info.mant_dig
  DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1)
  
  
  # Pure Python version of correctly-rounded integer-to-float conversion.
  def int_to_float(n):
      """
      Correctly-rounded integer-to-float conversion.
  
      """
      # Constants, depending only on the floating-point format in use.
      # We use an extra 2 bits of precision for rounding purposes.
      PRECISION = sys.float_info.mant_dig + 2
      SHIFT_MAX = sys.float_info.max_exp - PRECISION
      Q_MAX = 1 << PRECISION
      ROUND_HALF_TO_EVEN_CORRECTION = [0, -1, -2, 1, 0, -1, 2, 1]
  
      # Reduce to the case where n is positive.
      if n == 0:
          return 0.0
      elif n < 0:
          return -int_to_float(-n)
  
      # Convert n to a 'floating-point' number q * 2**shift, where q is an
      # integer with 'PRECISION' significant bits.  When shifting n to create q,
      # the least significant bit of q is treated as 'sticky'.  That is, the
      # least significant bit of q is set if either the corresponding bit of n
      # was already set, or any one of the bits of n lost in the shift was set.
      shift = n.bit_length() - PRECISION
      q = n << -shift if shift < 0 else (n >> shift) | bool(n & ~(-1 << shift))
  
      # Round half to even (actually rounds to the nearest multiple of 4,
      # rounding ties to a multiple of 8).
      q += ROUND_HALF_TO_EVEN_CORRECTION[q & 7]
  
      # Detect overflow.
      if shift + (q == Q_MAX) > SHIFT_MAX:
          raise OverflowError("integer too large to convert to float")
  
      # Checks: q is exactly representable, and q**2**shift doesn't overflow.
      assert q % 4 == 0 and q // 4 <= 2**(sys.float_info.mant_dig)
      assert q * 2**shift <= sys.float_info.max
  
      # Some circularity here, since float(q) is doing an int-to-float
      # conversion.  But here q is of bounded size, and is exactly representable
      # as a float.  In a low-level C-like language, this operation would be a
      # simple cast (e.g., from unsigned long long to double).
      return math.ldexp(float(q), shift)
  
  
  # pure Python version of correctly-rounded true division
  def truediv(a, b):
      """Correctly-rounded true division for integers."""
      negative = a^b < 0
      a, b = abs(a), abs(b)
  
      # exceptions:  division by zero, overflow
      if not b:
          raise ZeroDivisionError("division by zero")
      if a >= DBL_MIN_OVERFLOW * b:
          raise OverflowError("int/int too large to represent as a float")
  
     # find integer d satisfying 2**(d - 1) <= a/b < 2**d
      d = a.bit_length() - b.bit_length()
      if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
          d += 1
  
      # compute 2**-exp * a / b for suitable exp
      exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
      a, b = a << max(-exp, 0), b << max(exp, 0)
      q, r = divmod(a, b)
  
      # round-half-to-even: fractional part is r/b, which is > 0.5 iff
      # 2*r > b, and == 0.5 iff 2*r == b.
      if 2*r > b or 2*r == b and q % 2 == 1:
          q += 1
  
      result = math.ldexp(q, exp)
      return -result if negative else result
  
  
  class LongTest(unittest.TestCase):
  
      # Get quasi-random long consisting of ndigits digits (in base BASE).
      # quasi == the most-significant digit will not be 0, and the number
      # is constructed to contain long strings of 0 and 1 bits.  These are
      # more likely than random bits to provoke digit-boundary errors.
      # The sign of the number is also random.
  
      def getran(self, ndigits):
          self.assertGreater(ndigits, 0)
          nbits_hi = ndigits * SHIFT
          nbits_lo = nbits_hi - SHIFT + 1
          answer = 0
          nbits = 0
          r = int(random.random() * (SHIFT * 2)) | 1  # force 1 bits to start
          while nbits < nbits_lo:
              bits = (r >> 1) + 1
              bits = min(bits, nbits_hi - nbits)
              self.assertTrue(1 <= bits <= SHIFT)
              nbits = nbits + bits
              answer = answer << bits
              if r & 1:
                  answer = answer | ((1 << bits) - 1)
              r = int(random.random() * (SHIFT * 2))
          self.assertTrue(nbits_lo <= nbits <= nbits_hi)
          if random.random() < 0.5:
              answer = -answer
          return answer
  
      # Get random long consisting of ndigits random digits (relative to base
      # BASE).  The sign bit is also random.
  
      def getran2(ndigits):
          answer = 0
          for i in range(ndigits):
              answer = (answer << SHIFT) | random.randint(0, MASK)
          if random.random() < 0.5:
              answer = -answer
          return answer
  
      def check_division(self, x, y):
          eq = self.assertEqual
          q, r = divmod(x, y)
          q2, r2 = x//y, x%y
          pab, pba = x*y, y*x
          eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y))
          eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y))
          eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y))
          eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y))
          if y > 0:
              self.assertTrue(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y))
          else:
              self.assertTrue(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y))
  
      def test_division(self):
          digits = list(range(1, MAXDIGITS+1)) + list(range(KARATSUBA_CUTOFF,
                                                        KARATSUBA_CUTOFF + 14))
          digits.append(KARATSUBA_CUTOFF * 3)
          for lenx in digits:
              x = self.getran(lenx)
              for leny in digits:
                  y = self.getran(leny) or 1
                  self.check_division(x, y)
  
          # specific numbers chosen to exercise corner cases of the
          # current long division implementation
  
          # 30-bit cases involving a quotient digit estimate of BASE+1
          self.check_division(1231948412290879395966702881,
                              1147341367131428698)
          self.check_division(815427756481275430342312021515587883,
                         707270836069027745)
          self.check_division(627976073697012820849443363563599041,
                         643588798496057020)
          self.check_division(1115141373653752303710932756325578065,
                         1038556335171453937726882627)
          # 30-bit cases that require the post-subtraction correction step
          self.check_division(922498905405436751940989320930368494,
                         949985870686786135626943396)
          self.check_division(768235853328091167204009652174031844,
                         1091555541180371554426545266)
  
          # 15-bit cases involving a quotient digit estimate of BASE+1
          self.check_division(20172188947443, 615611397)
          self.check_division(1020908530270155025, 950795710)
          self.check_division(128589565723112408, 736393718)
          self.check_division(609919780285761575, 18613274546784)
          # 15-bit cases that require the post-subtraction correction step
          self.check_division(710031681576388032, 26769404391308)
          self.check_division(1933622614268221, 30212853348836)
  
  
  
      def test_karatsuba(self):
          digits = list(range(1, 5)) + list(range(KARATSUBA_CUTOFF,
                                                  KARATSUBA_CUTOFF + 10))
          digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100])
  
          bits = [digit * SHIFT for digit in digits]
  
          # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) ==
          # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check.
          for abits in bits:
              a = (1 << abits) - 1
              for bbits in bits:
                  if bbits < abits:
                      continue
                  b = (1 << bbits) - 1
                  x = a * b
                  y = ((1 << (abits + bbits)) -
                       (1 << abits) -
                       (1 << bbits) +
                       1)
                  self.assertEqual(x, y,
                      Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y))
  
      def check_bitop_identities_1(self, x):
          eq = self.assertEqual
          eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x))
          eq(x | 0, x, Frm("x | 0 != x for x=%r", x))
          eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x))
          eq(x & -1, x, Frm("x & -1 != x for x=%r", x))
          eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x))
          eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x))
          eq(x, ~~x, Frm("x != ~~x for x=%r", x))
          eq(x & x, x, Frm("x & x != x for x=%r", x))
          eq(x | x, x, Frm("x | x != x for x=%r", x))
          eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x))
          eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x))
          eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x))
          eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x))
          eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x))
          eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x))
          for n in range(2*SHIFT):
              p2 = 2 ** n
              eq(x << n >> n, x,
                  Frm("x << n >> n != x for x=%r, n=%r", (x, n)))
              eq(x // p2, x >> n,
                  Frm("x // p2 != x >> n for x=%r n=%r p2=%r", (x, n, p2)))
              eq(x * p2, x << n,
                  Frm("x * p2 != x << n for x=%r n=%r p2=%r", (x, n, p2)))
              eq(x & -p2, x >> n << n,
                  Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", (x, n, p2)))
              eq(x & -p2, x & ~(p2 - 1),
                  Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", (x, n, p2)))
  
      def check_bitop_identities_2(self, x, y):
          eq = self.assertEqual
          eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", (x, y)))
          eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", (x, y)))
          eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", (x, y)))
          eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", (x, y)))
          eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", (x, y)))
          eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", (x, y)))
          eq(x ^ y, (x | y) & ~(x & y),
               Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", (x, y)))
          eq(x ^ y, (x & ~y) | (~x & y),
               Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", (x, y)))
          eq(x ^ y, (x | y) & (~x | ~y),
               Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", (x, y)))
  
      def check_bitop_identities_3(self, x, y, z):
          eq = self.assertEqual
          eq((x & y) & z, x & (y & z),
               Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", (x, y, z)))
          eq((x | y) | z, x | (y | z),
               Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", (x, y, z)))
          eq((x ^ y) ^ z, x ^ (y ^ z),
               Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", (x, y, z)))
          eq(x & (y | z), (x & y) | (x & z),
               Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", (x, y, z)))
          eq(x | (y & z), (x | y) & (x | z),
               Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", (x, y, z)))
  
      def test_bitop_identities(self):
          for x in special:
              self.check_bitop_identities_1(x)
          digits = range(1, MAXDIGITS+1)
          for lenx in digits:
              x = self.getran(lenx)
              self.check_bitop_identities_1(x)
              for leny in digits:
                  y = self.getran(leny)
                  self.check_bitop_identities_2(x, y)
                  self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2))
  
      def slow_format(self, x, base):
          digits = []
          sign = 0
          if x < 0:
              sign, x = 1, -x
          while x:
              x, r = divmod(x, base)
              digits.append(int(r))
          digits.reverse()
          digits = digits or [0]
          return '-'[:sign] + \
                 {2: '0b', 8: '0o', 10: '', 16: '0x'}[base] + \
                 "".join("0123456789abcdef"[i] for i in digits)
  
      def check_format_1(self, x):
          for base, mapper in (2, bin), (8, oct), (10, str), (10, repr), (16, hex):
              got = mapper(x)
              expected = self.slow_format(x, base)
              msg = Frm("%s returned %r but expected %r for %r",
                  mapper.__name__, got, expected, x)
              self.assertEqual(got, expected, msg)
              self.assertEqual(int(got, 0), x, Frm('int("%s", 0) != %r', got, x))
  
      def test_format(self):
          for x in special:
              self.check_format_1(x)
          for i in range(10):
              for lenx in range(1, MAXDIGITS+1):
                  x = self.getran(lenx)
                  self.check_format_1(x)
  
      def test_long(self):
          # Check conversions from string
          LL = [
                  ('1' + '0'*20, 10**20),
                  ('1' + '0'*100, 10**100)
          ]
          for s, v in LL:
              for sign in "", "+", "-":
                  for prefix in "", " ", "\t", "  \t\t  ":
                      ss = prefix + sign + s
                      vv = v
                      if sign == "-" and v is not ValueError:
                          vv = -v
                      try:
                          self.assertEqual(int(ss), vv)
                      except ValueError:
                          pass
  
          # trailing L should no longer be accepted...
          self.assertRaises(ValueError, int, '123L')
          self.assertRaises(ValueError, int, '123l')
          self.assertRaises(ValueError, int, '0L')
          self.assertRaises(ValueError, int, '-37L')
          self.assertRaises(ValueError, int, '0x32L', 16)
          self.assertRaises(ValueError, int, '1L', 21)
          # ... but it's just a normal digit if base >= 22
          self.assertEqual(int('1L', 22), 43)
  
          # tests with base 0
          self.assertEqual(int('000', 0), 0)
          self.assertEqual(int('0o123', 0), 83)
          self.assertEqual(int('0x123', 0), 291)
          self.assertEqual(int('0b100', 0), 4)
          self.assertEqual(int(' 0O123   ', 0), 83)
          self.assertEqual(int(' 0X123  ', 0), 291)
          self.assertEqual(int(' 0B100 ', 0), 4)
          self.assertEqual(int('0', 0), 0)
          self.assertEqual(int('+0', 0), 0)
          self.assertEqual(int('-0', 0), 0)
          self.assertEqual(int('00', 0), 0)
          self.assertRaises(ValueError, int, '08', 0)
          self.assertRaises(ValueError, int, '-012395', 0)
  
          # invalid bases
          invalid_bases = [-909,
                            2**31-1, 2**31, -2**31, -2**31-1,
                            2**63-1, 2**63, -2**63, -2**63-1,
                            2**100, -2**100,
                            ]
          for base in invalid_bases:
              self.assertRaises(ValueError, int, '42', base)
  
  
      def test_conversion(self):
  
          class JustLong:
              # test that __long__ no longer used in 3.x
              def __long__(self):
                  return 42
          self.assertRaises(TypeError, int, JustLong())
  
          class LongTrunc:
              # __long__ should be ignored in 3.x
              def __long__(self):
                  return 42
              def __trunc__(self):
                  return 1729
          self.assertEqual(int(LongTrunc()), 1729)
  
      def check_float_conversion(self, n):
          # Check that int -> float conversion behaviour matches
          # that of the pure Python version above.
          try:
              actual = float(n)
          except OverflowError:
              actual = 'overflow'
  
          try:
              expected = int_to_float(n)
          except OverflowError:
              expected = 'overflow'
  
          msg = ("Error in conversion of integer {} to float.  "
                 "Got {}, expected {}.".format(n, actual, expected))
          self.assertEqual(actual, expected, msg)
  
      @support.requires_IEEE_754
      def test_float_conversion(self):
  
          exact_values = [0, 1, 2,
                           2**53-3,
                           2**53-2,
                           2**53-1,
                           2**53,
                           2**53+2,
                           2**54-4,
                           2**54-2,
                           2**54,
                           2**54+4]
          for x in exact_values:
              self.assertEqual(float(x), x)
              self.assertEqual(float(-x), -x)
  
          # test round-half-even
          for x, y in [(1, 0), (2, 2), (3, 4), (4, 4), (5, 4), (6, 6), (7, 8)]:
              for p in range(15):
                  self.assertEqual(int(float(2**p*(2**53+x))), 2**p*(2**53+y))
  
          for x, y in [(0, 0), (1, 0), (2, 0), (3, 4), (4, 4), (5, 4), (6, 8),
                       (7, 8), (8, 8), (9, 8), (10, 8), (11, 12), (12, 12),
                       (13, 12), (14, 16), (15, 16)]:
              for p in range(15):
                  self.assertEqual(int(float(2**p*(2**54+x))), 2**p*(2**54+y))
  
          # behaviour near extremes of floating-point range
          int_dbl_max = int(DBL_MAX)
          top_power = 2**DBL_MAX_EXP
          halfway = (int_dbl_max + top_power)//2
          self.assertEqual(float(int_dbl_max), DBL_MAX)
          self.assertEqual(float(int_dbl_max+1), DBL_MAX)
          self.assertEqual(float(halfway-1), DBL_MAX)
          self.assertRaises(OverflowError, float, halfway)
          self.assertEqual(float(1-halfway), -DBL_MAX)
          self.assertRaises(OverflowError, float, -halfway)
          self.assertRaises(OverflowError, float, top_power-1)
          self.assertRaises(OverflowError, float, top_power)
          self.assertRaises(OverflowError, float, top_power+1)
          self.assertRaises(OverflowError, float, 2*top_power-1)
          self.assertRaises(OverflowError, float, 2*top_power)
          self.assertRaises(OverflowError, float, top_power*top_power)
  
          for p in range(100):
              x = 2**p * (2**53 + 1) + 1
              y = 2**p * (2**53 + 2)
              self.assertEqual(int(float(x)), y)
  
              x = 2**p * (2**53 + 1)
              y = 2**p * 2**53
              self.assertEqual(int(float(x)), y)
  
          # Compare builtin float conversion with pure Python int_to_float
          # function above.
          test_values = [
              int_dbl_max-1, int_dbl_max, int_dbl_max+1,
              halfway-1, halfway, halfway + 1,
              top_power-1, top_power, top_power+1,
              2*top_power-1, 2*top_power, top_power*top_power,
          ]
          test_values.extend(exact_values)
          for p in range(-4, 8):
              for x in range(-128, 128):
                  test_values.append(2**(p+53) + x)
          for value in test_values:
              self.check_float_conversion(value)
              self.check_float_conversion(-value)
  
      def test_float_overflow(self):
          for x in -2.0, -1.0, 0.0, 1.0, 2.0:
              self.assertEqual(float(int(x)), x)
  
          shuge = '12345' * 120
          huge = 1 << 30000
          mhuge = -huge
          namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math}
          for test in ["float(huge)", "float(mhuge)",
                       "complex(huge)", "complex(mhuge)",
                       "complex(huge, 1)", "complex(mhuge, 1)",
                       "complex(1, huge)", "complex(1, mhuge)",
                       "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.",
                       "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.",
                       "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.",
                       "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.",
                       "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.",
                       "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.",
                       "math.sin(huge)", "math.sin(mhuge)",
                       "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better
                       # math.floor() of an int returns an int now
                       ##"math.floor(huge)", "math.floor(mhuge)",
                       ]:
  
              self.assertRaises(OverflowError, eval, test, namespace)
  
          # XXX Perhaps float(shuge) can raise OverflowError on some box?
          # The comparison should not.
          self.assertNotEqual(float(shuge), int(shuge),
              "float(shuge) should not equal int(shuge)")
  
      def test_logs(self):
          LOG10E = math.log10(math.e)
  
          for exp in list(range(10)) + [100, 1000, 10000]:
              value = 10 ** exp
              log10 = math.log10(value)
              self.assertAlmostEqual(log10, exp)
  
              # log10(value) == exp, so log(value) == log10(value)/log10(e) ==
              # exp/LOG10E
              expected = exp / LOG10E
              log = math.log(value)
              self.assertAlmostEqual(log, expected)
  
          for bad in -(1 << 10000), -2, 0:
              self.assertRaises(ValueError, math.log, bad)
              self.assertRaises(ValueError, math.log10, bad)
  
      def test_mixed_compares(self):
          eq = self.assertEqual
  
          # We're mostly concerned with that mixing floats and ints does the
          # right stuff, even when ints are too large to fit in a float.
          # The safest way to check the results is to use an entirely different
          # method, which we do here via a skeletal rational class (which
          # represents all Python ints and floats exactly).
          class Rat:
              def __init__(self, value):
                  if isinstance(value, int):
                      self.n = value
                      self.d = 1
                  elif isinstance(value, float):
                      # Convert to exact rational equivalent.
                      f, e = math.frexp(abs(value))
                      assert f == 0 or 0.5 <= f < 1.0
                      # |value| = f * 2**e exactly
  
                      # Suck up CHUNK bits at a time; 28 is enough so that we suck
                      # up all bits in 2 iterations for all known binary double-
                      # precision formats, and small enough to fit in an int.
                      CHUNK = 28
                      top = 0
                      # invariant: |value| = (top + f) * 2**e exactly
                      while f:
                          f = math.ldexp(f, CHUNK)
                          digit = int(f)
                          assert digit >> CHUNK == 0
                          top = (top << CHUNK) | digit
                          f -= digit
                          assert 0.0 <= f < 1.0
                          e -= CHUNK
  
                      # Now |value| = top * 2**e exactly.
                      if e >= 0:
                          n = top << e
                          d = 1
                      else:
                          n = top
                          d = 1 << -e
                      if value < 0:
                          n = -n
                      self.n = n
                      self.d = d
                      assert float(n) / float(d) == value
                  else:
                      raise TypeError("can't deal with %r" % value)
  
              def _cmp__(self, other):
                  if not isinstance(other, Rat):
                      other = Rat(other)
                  x, y = self.n * other.d, self.d * other.n
                  return (x > y) - (x < y)
              def __eq__(self, other):
                  return self._cmp__(other) == 0
              def __ge__(self, other):
                  return self._cmp__(other) >= 0
              def __gt__(self, other):
                  return self._cmp__(other) > 0
              def __le__(self, other):
                  return self._cmp__(other) <= 0
              def __lt__(self, other):
                  return self._cmp__(other) < 0
  
          cases = [0, 0.001, 0.99, 1.0, 1.5, 1e20, 1e200]
          # 2**48 is an important boundary in the internals.  2**53 is an
          # important boundary for IEEE double precision.
          for t in 2.0**48, 2.0**50, 2.0**53:
              cases.extend([t - 1.0, t - 0.3, t, t + 0.3, t + 1.0,
                            int(t-1), int(t), int(t+1)])
          cases.extend([0, 1, 2, sys.maxsize, float(sys.maxsize)])
          # 1 << 20000 should exceed all double formats.  int(1e200) is to
          # check that we get equality with 1e200 above.
          t = int(1e200)
          cases.extend([0, 1, 2, 1 << 20000, t-1, t, t+1])
          cases.extend([-x for x in cases])
          for x in cases:
              Rx = Rat(x)
              for y in cases:
                  Ry = Rat(y)
                  Rcmp = (Rx > Ry) - (Rx < Ry)
                  xycmp = (x > y) - (x < y)
                  eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp))
                  eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp))
                  eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp))
                  eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp))
                  eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp))
                  eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp))
                  eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp))
  
      def test__format__(self):
          self.assertEqual(format(123456789, 'd'), '123456789')
          self.assertEqual(format(123456789, 'd'), '123456789')
  
          # sign and aligning are interdependent
          self.assertEqual(format(1, "-"), '1')
          self.assertEqual(format(-1, "-"), '-1')
          self.assertEqual(format(1, "-3"), '  1')
          self.assertEqual(format(-1, "-3"), ' -1')
          self.assertEqual(format(1, "+3"), ' +1')
          self.assertEqual(format(-1, "+3"), ' -1')
          self.assertEqual(format(1, " 3"), '  1')
          self.assertEqual(format(-1, " 3"), ' -1')
          self.assertEqual(format(1, " "), ' 1')
          self.assertEqual(format(-1, " "), '-1')
  
          # hex
          self.assertEqual(format(3, "x"), "3")
          self.assertEqual(format(3, "X"), "3")
          self.assertEqual(format(1234, "x"), "4d2")
          self.assertEqual(format(-1234, "x"), "-4d2")
          self.assertEqual(format(1234, "8x"), "     4d2")
          self.assertEqual(format(-1234, "8x"), "    -4d2")
          self.assertEqual(format(1234, "x"), "4d2")
          self.assertEqual(format(-1234, "x"), "-4d2")
          self.assertEqual(format(-3, "x"), "-3")
          self.assertEqual(format(-3, "X"), "-3")
          self.assertEqual(format(int('be', 16), "x"), "be")
          self.assertEqual(format(int('be', 16), "X"), "BE")
          self.assertEqual(format(-int('be', 16), "x"), "-be")
          self.assertEqual(format(-int('be', 16), "X"), "-BE")
  
          # octal
          self.assertEqual(format(3, "b"), "11")
          self.assertEqual(format(-3, "b"), "-11")
          self.assertEqual(format(1234, "b"), "10011010010")
          self.assertEqual(format(-1234, "b"), "-10011010010")
          self.assertEqual(format(1234, "-b"), "10011010010")
          self.assertEqual(format(-1234, "-b"), "-10011010010")
          self.assertEqual(format(1234, " b"), " 10011010010")
          self.assertEqual(format(-1234, " b"), "-10011010010")
          self.assertEqual(format(1234, "+b"), "+10011010010")
          self.assertEqual(format(-1234, "+b"), "-10011010010")
  
          # make sure these are errors
          self.assertRaises(ValueError, format, 3, "1.3")  # precision disallowed
          self.assertRaises(ValueError, format, 3, "+c")   # sign not allowed
                                                           # with 'c'
  
          # ensure that only int and float type specifiers work
          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 'bcdoxXeEfFgGn%':
                  self.assertRaises(ValueError, format, 0, format_spec)
                  self.assertRaises(ValueError, format, 1, format_spec)
                  self.assertRaises(ValueError, format, -1, format_spec)
                  self.assertRaises(ValueError, format, 2**100, format_spec)
                  self.assertRaises(ValueError, format, -(2**100), format_spec)
  
          # ensure that float type specifiers work; format converts
          #  the int to a float
          for format_spec in 'eEfFgG%':
              for value in [0, 1, -1, 100, -100, 1234567890, -1234567890]:
                  self.assertEqual(format(value, format_spec),
                                   format(float(value), format_spec))
  
      def test_nan_inf(self):
          self.assertRaises(OverflowError, int, float('inf'))
          self.assertRaises(OverflowError, int, float('-inf'))
          self.assertRaises(ValueError, int, float('nan'))
  
      def test_true_division(self):
          huge = 1 << 40000
          mhuge = -huge
          self.assertEqual(huge / huge, 1.0)
          self.assertEqual(mhuge / mhuge, 1.0)
          self.assertEqual(huge / mhuge, -1.0)
          self.assertEqual(mhuge / huge, -1.0)
          self.assertEqual(1 / huge, 0.0)
          self.assertEqual(1 / huge, 0.0)
          self.assertEqual(1 / mhuge, 0.0)
          self.assertEqual(1 / mhuge, 0.0)
          self.assertEqual((666 * huge + (huge >> 1)) / huge, 666.5)
          self.assertEqual((666 * mhuge + (mhuge >> 1)) / mhuge, 666.5)
          self.assertEqual((666 * huge + (huge >> 1)) / mhuge, -666.5)
          self.assertEqual((666 * mhuge + (mhuge >> 1)) / huge, -666.5)
          self.assertEqual(huge / (huge << 1), 0.5)
          self.assertEqual((1000000 * huge) / huge, 1000000)
  
          namespace = {'huge': huge, 'mhuge': mhuge}
  
          for overflow in ["float(huge)", "float(mhuge)",
                           "huge / 1", "huge / 2", "huge / -1", "huge / -2",
                           "mhuge / 100", "mhuge / 200"]:
              self.assertRaises(OverflowError, eval, overflow, namespace)
  
          for underflow in ["1 / huge", "2 / huge", "-1 / huge", "-2 / huge",
                           "100 / mhuge", "200 / mhuge"]:
              result = eval(underflow, namespace)
              self.assertEqual(result, 0.0,
                               "expected underflow to 0 from %r" % underflow)
  
          for zero in ["huge / 0", "mhuge / 0"]:
              self.assertRaises(ZeroDivisionError, eval, zero, namespace)
  
      def check_truediv(self, a, b, skip_small=True):
          """Verify that the result of a/b is correctly rounded, by
          comparing it with a pure Python implementation of correctly
          rounded division.  b should be nonzero."""
  
          # skip check for small a and b: in this case, the current
          # implementation converts the arguments to float directly and
          # then applies a float division.  This can give doubly-rounded
          # results on x87-using machines (particularly 32-bit Linux).
          if skip_small and max(abs(a), abs(b)) < 2**DBL_MANT_DIG:
              return
  
          try:
              # use repr so that we can distinguish between -0.0 and 0.0
              expected = repr(truediv(a, b))
          except OverflowError:
              expected = 'overflow'
          except ZeroDivisionError:
              expected = 'zerodivision'
  
          try:
              got = repr(a / b)
          except OverflowError:
              got = 'overflow'
          except ZeroDivisionError:
              got = 'zerodivision'
  
          self.assertEqual(expected, got, "Incorrectly rounded division {}/{}: "
                           "expected {}, got {}".format(a, b, expected, got))
  
      @support.requires_IEEE_754
      def test_correctly_rounded_true_division(self):
          # more stringent tests than those above, checking that the
          # result of true division of ints is always correctly rounded.
          # This test should probably be considered CPython-specific.
  
          # Exercise all the code paths not involving Gb-sized ints.
          # ... divisions involving zero
          self.check_truediv(123, 0)
          self.check_truediv(-456, 0)
          self.check_truediv(0, 3)
          self.check_truediv(0, -3)
          self.check_truediv(0, 0)
          # ... overflow or underflow by large margin
          self.check_truediv(671 * 12345 * 2**DBL_MAX_EXP, 12345)
          self.check_truediv(12345, 345678 * 2**(DBL_MANT_DIG - DBL_MIN_EXP))
          # ... a much larger or smaller than b
          self.check_truediv(12345*2**100, 98765)
          self.check_truediv(12345*2**30, 98765*7**81)
          # ... a / b near a boundary: one of 1, 2**DBL_MANT_DIG, 2**DBL_MIN_EXP,
          #                 2**DBL_MAX_EXP, 2**(DBL_MIN_EXP-DBL_MANT_DIG)
          bases = (0, DBL_MANT_DIG, DBL_MIN_EXP,
                   DBL_MAX_EXP, DBL_MIN_EXP - DBL_MANT_DIG)
          for base in bases:
              for exp in range(base - 15, base + 15):
                  self.check_truediv(75312*2**max(exp, 0), 69187*2**max(-exp, 0))
                  self.check_truediv(69187*2**max(exp, 0), 75312*2**max(-exp, 0))
  
          # overflow corner case
          for m in [1, 2, 7, 17, 12345, 7**100,
                    -1, -2, -5, -23, -67891, -41**50]:
              for n in range(-10, 10):
                  self.check_truediv(m*DBL_MIN_OVERFLOW + n, m)
                  self.check_truediv(m*DBL_MIN_OVERFLOW + n, -m)
  
          # check detection of inexactness in shifting stage
          for n in range(250):
              # (2**DBL_MANT_DIG+1)/(2**DBL_MANT_DIG) lies halfway
              # between two representable floats, and would usually be
              # rounded down under round-half-to-even.  The tiniest of
              # additions to the numerator should cause it to be rounded
              # up instead.
              self.check_truediv((2**DBL_MANT_DIG + 1)*12345*2**200 + 2**n,
                             2**DBL_MANT_DIG*12345)
  
          # 1/2731 is one of the smallest division cases that's subject
          # to double rounding on IEEE 754 machines working internally with
          # 64-bit precision.  On such machines, the next check would fail,
          # were it not explicitly skipped in check_truediv.
          self.check_truediv(1, 2731)
  
          # a particularly bad case for the old algorithm:  gives an
          # error of close to 3.5 ulps.
          self.check_truediv(295147931372582273023, 295147932265116303360)
          for i in range(1000):
              self.check_truediv(10**(i+1), 10**i)
              self.check_truediv(10**i, 10**(i+1))
  
          # test round-half-to-even behaviour, normal result
          for m in [1, 2, 4, 7, 8, 16, 17, 32, 12345, 7**100,
                    -1, -2, -5, -23, -67891, -41**50]:
              for n in range(-10, 10):
                  self.check_truediv(2**DBL_MANT_DIG*m + n, m)
  
          # test round-half-to-even, subnormal result
          for n in range(-20, 20):
              self.check_truediv(n, 2**1076)
  
          # largeish random divisions: a/b where |a| <= |b| <=
          # 2*|a|; |ans| is between 0.5 and 1.0, so error should
          # always be bounded by 2**-54 with equality possible only
          # if the least significant bit of q=ans*2**53 is zero.
          for M in [10**10, 10**100, 10**1000]:
              for i in range(1000):
                  a = random.randrange(1, M)
                  b = random.randrange(a, 2*a+1)
                  self.check_truediv(a, b)
                  self.check_truediv(-a, b)
                  self.check_truediv(a, -b)
                  self.check_truediv(-a, -b)
  
          # and some (genuinely) random tests
          for _ in range(10000):
              a_bits = random.randrange(1000)
              b_bits = random.randrange(1, 1000)
              x = random.randrange(2**a_bits)
              y = random.randrange(1, 2**b_bits)
              self.check_truediv(x, y)
              self.check_truediv(x, -y)
              self.check_truediv(-x, y)
              self.check_truediv(-x, -y)
  
      def test_small_ints(self):
          for i in range(-5, 257):
              self.assertIs(i, i + 0)
              self.assertIs(i, i * 1)
              self.assertIs(i, i - 0)
              self.assertIs(i, i // 1)
              self.assertIs(i, i & -1)
              self.assertIs(i, i | 0)
              self.assertIs(i, i ^ 0)
              self.assertIs(i, ~~i)
              self.assertIs(i, i**1)
              self.assertIs(i, int(str(i)))
              self.assertIs(i, i<<2>>2, str(i))
          # corner cases
          i = 1 << 70
          self.assertIs(i - i, 0)
          self.assertIs(0 * i, 0)
  
      def test_bit_length(self):
          tiny = 1e-10
          for x in range(-65000, 65000):
              k = x.bit_length()
              # Check equivalence with Python version
              self.assertEqual(k, len(bin(x).lstrip('-0b')))
              # Behaviour as specified in the docs
              if x != 0:
                  self.assertTrue(2**(k-1) <= abs(x) < 2**k)
              else:
                  self.assertEqual(k, 0)
              # Alternative definition: x.bit_length() == 1 + floor(log_2(x))
              if x != 0:
                  # When x is an exact power of 2, numeric errors can
                  # cause floor(log(x)/log(2)) to be one too small; for
                  # small x this can be fixed by adding a small quantity
                  # to the quotient before taking the floor.
                  self.assertEqual(k, 1 + math.floor(
                          math.log(abs(x))/math.log(2) + tiny))
  
          self.assertEqual((0).bit_length(), 0)
          self.assertEqual((1).bit_length(), 1)
          self.assertEqual((-1).bit_length(), 1)
          self.assertEqual((2).bit_length(), 2)
          self.assertEqual((-2).bit_length(), 2)
          for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64, 234]:
              a = 2**i
              self.assertEqual((a-1).bit_length(), i)
              self.assertEqual((1-a).bit_length(), i)
              self.assertEqual((a).bit_length(), i+1)
              self.assertEqual((-a).bit_length(), i+1)
              self.assertEqual((a+1).bit_length(), i+1)
              self.assertEqual((-a-1).bit_length(), i+1)
  
      def test_round(self):
          # check round-half-even algorithm. For round to nearest ten;
          # rounding map is invariant under adding multiples of 20
          test_dict = {0:0, 1:0, 2:0, 3:0, 4:0, 5:0,
                       6:10, 7:10, 8:10, 9:10, 10:10, 11:10, 12:10, 13:10, 14:10,
                       15:20, 16:20, 17:20, 18:20, 19:20}
          for offset in range(-520, 520, 20):
              for k, v in test_dict.items():
                  got = round(k+offset, -1)
                  expected = v+offset
                  self.assertEqual(got, expected)
                  self.assertIs(type(got), int)
  
          # larger second argument
          self.assertEqual(round(-150, -2), -200)
          self.assertEqual(round(-149, -2), -100)
          self.assertEqual(round(-51, -2), -100)
          self.assertEqual(round(-50, -2), 0)
          self.assertEqual(round(-49, -2), 0)
          self.assertEqual(round(-1, -2), 0)
          self.assertEqual(round(0, -2), 0)
          self.assertEqual(round(1, -2), 0)
          self.assertEqual(round(49, -2), 0)
          self.assertEqual(round(50, -2), 0)
          self.assertEqual(round(51, -2), 100)
          self.assertEqual(round(149, -2), 100)
          self.assertEqual(round(150, -2), 200)
          self.assertEqual(round(250, -2), 200)
          self.assertEqual(round(251, -2), 300)
          self.assertEqual(round(172500, -3), 172000)
          self.assertEqual(round(173500, -3), 174000)
          self.assertEqual(round(31415926535, -1), 31415926540)
          self.assertEqual(round(31415926535, -2), 31415926500)
          self.assertEqual(round(31415926535, -3), 31415927000)
          self.assertEqual(round(31415926535, -4), 31415930000)
          self.assertEqual(round(31415926535, -5), 31415900000)
          self.assertEqual(round(31415926535, -6), 31416000000)
          self.assertEqual(round(31415926535, -7), 31420000000)
          self.assertEqual(round(31415926535, -8), 31400000000)
          self.assertEqual(round(31415926535, -9), 31000000000)
          self.assertEqual(round(31415926535, -10), 30000000000)
          self.assertEqual(round(31415926535, -11), 0)
          self.assertEqual(round(31415926535, -12), 0)
          self.assertEqual(round(31415926535, -999), 0)
  
          # should get correct results even for huge inputs
          for k in range(10, 100):
              got = round(10**k + 324678, -3)
              expect = 10**k + 325000
              self.assertEqual(got, expect)
              self.assertIs(type(got), int)
  
          # nonnegative second argument: round(x, n) should just return x
          for n in range(5):
              for i in range(100):
                  x = random.randrange(-10000, 10000)
                  got = round(x, n)
                  self.assertEqual(got, x)
                  self.assertIs(type(got), int)
          for huge_n in 2**31-1, 2**31, 2**63-1, 2**63, 2**100, 10**100:
              self.assertEqual(round(8979323, huge_n), 8979323)
  
          # omitted second argument
          for i in range(100):
              x = random.randrange(-10000, 10000)
              got = round(x)
              self.assertEqual(got, x)
              self.assertIs(type(got), int)
  
          # bad second argument
          bad_exponents = ('brian', 2.0, 0j, None)
          for e in bad_exponents:
              self.assertRaises(TypeError, round, 3, e)
  
      def test_to_bytes(self):
          def check(tests, byteorder, signed=False):
              for test, expected in tests.items():
                  try:
                      self.assertEqual(
                          test.to_bytes(len(expected), byteorder, signed=signed),
                          expected)
                  except Exception as err:
                      raise AssertionError(
                          "failed to convert {0} with byteorder={1} and signed={2}"
                          .format(test, byteorder, signed)) from err
  
          # Convert integers to signed big-endian byte arrays.
          tests1 = {
              0: b'\x00',
              1: b'\x01',
              -1: b'\xff',
              -127: b'\x81',
              -128: b'\x80',
              -129: b'\xff\x7f',
              127: b'\x7f',
              129: b'\x00\x81',
              -255: b'\xff\x01',
              -256: b'\xff\x00',
              255: b'\x00\xff',
              256: b'\x01\x00',
              32767: b'\x7f\xff',
              -32768: b'\xff\x80\x00',
              65535: b'\x00\xff\xff',
              -65536: b'\xff\x00\x00',
              -8388608: b'\x80\x00\x00'
          }
          check(tests1, 'big', signed=True)
  
          # Convert integers to signed little-endian byte arrays.
          tests2 = {
              0: b'\x00',
              1: b'\x01',
              -1: b'\xff',
              -127: b'\x81',
              -128: b'\x80',
              -129: b'\x7f\xff',
              127: b'\x7f',
              129: b'\x81\x00',
              -255: b'\x01\xff',
              -256: b'\x00\xff',
              255: b'\xff\x00',
              256: b'\x00\x01',
              32767: b'\xff\x7f',
              -32768: b'\x00\x80',
              65535: b'\xff\xff\x00',
              -65536: b'\x00\x00\xff',
              -8388608: b'\x00\x00\x80'
          }
          check(tests2, 'little', signed=True)
  
          # Convert integers to unsigned big-endian byte arrays.
          tests3 = {
              0: b'\x00',
              1: b'\x01',
              127: b'\x7f',
              128: b'\x80',
              255: b'\xff',
              256: b'\x01\x00',
              32767: b'\x7f\xff',
              32768: b'\x80\x00',
              65535: b'\xff\xff',
              65536: b'\x01\x00\x00'
          }
          check(tests3, 'big', signed=False)
  
          # Convert integers to unsigned little-endian byte arrays.
          tests4 = {
              0: b'\x00',
              1: b'\x01',
              127: b'\x7f',
              128: b'\x80',
              255: b'\xff',
              256: b'\x00\x01',
              32767: b'\xff\x7f',
              32768: b'\x00\x80',
              65535: b'\xff\xff',
              65536: b'\x00\x00\x01'
          }
          check(tests4, 'little', signed=False)
  
          self.assertRaises(OverflowError, (256).to_bytes, 1, 'big', signed=False)
          self.assertRaises(OverflowError, (256).to_bytes, 1, 'big', signed=True)
          self.assertRaises(OverflowError, (256).to_bytes, 1, 'little', signed=False)
          self.assertRaises(OverflowError, (256).to_bytes, 1, 'little', signed=True)
          self.assertRaises(OverflowError, (-1).to_bytes, 2, 'big', signed=False)
          self.assertRaises(OverflowError, (-1).to_bytes, 2, 'little', signed=False)
          self.assertEqual((0).to_bytes(0, 'big'), b'')
          self.assertEqual((1).to_bytes(5, 'big'), b'\x00\x00\x00\x00\x01')
          self.assertEqual((0).to_bytes(5, 'big'), b'\x00\x00\x00\x00\x00')
          self.assertEqual((-1).to_bytes(5, 'big', signed=True),
                           b'\xff\xff\xff\xff\xff')
          self.assertRaises(OverflowError, (1).to_bytes, 0, 'big')
  
      def test_from_bytes(self):
          def check(tests, byteorder, signed=False):
              for test, expected in tests.items():
                  try:
                      self.assertEqual(
                          int.from_bytes(test, byteorder, signed=signed),
                          expected)
                  except Exception as err:
                      raise AssertionError(
                          "failed to convert {0} with byteorder={1!r} and signed={2}"
                          .format(test, byteorder, signed)) from err
  
          # Convert signed big-endian byte arrays to integers.
          tests1 = {
              b'': 0,
              b'\x00': 0,
              b'\x00\x00': 0,
              b'\x01': 1,
              b'\x00\x01': 1,
              b'\xff': -1,
              b'\xff\xff': -1,
              b'\x81': -127,
              b'\x80': -128,
              b'\xff\x7f': -129,
              b'\x7f': 127,
              b'\x00\x81': 129,
              b'\xff\x01': -255,
              b'\xff\x00': -256,
              b'\x00\xff': 255,
              b'\x01\x00': 256,
              b'\x7f\xff': 32767,
              b'\x80\x00': -32768,
              b'\x00\xff\xff': 65535,
              b'\xff\x00\x00': -65536,
              b'\x80\x00\x00': -8388608
          }
          check(tests1, 'big', signed=True)
  
          # Convert signed little-endian byte arrays to integers.
          tests2 = {
              b'': 0,
              b'\x00': 0,
              b'\x00\x00': 0,
              b'\x01': 1,
              b'\x00\x01': 256,
              b'\xff': -1,
              b'\xff\xff': -1,
              b'\x81': -127,
              b'\x80': -128,
              b'\x7f\xff': -129,
              b'\x7f': 127,
              b'\x81\x00': 129,
              b'\x01\xff': -255,
              b'\x00\xff': -256,
              b'\xff\x00': 255,
              b'\x00\x01': 256,
              b'\xff\x7f': 32767,
              b'\x00\x80': -32768,
              b'\xff\xff\x00': 65535,
              b'\x00\x00\xff': -65536,
              b'\x00\x00\x80': -8388608
          }
          check(tests2, 'little', signed=True)
  
          # Convert unsigned big-endian byte arrays to integers.
          tests3 = {
              b'': 0,
              b'\x00': 0,
              b'\x01': 1,
              b'\x7f': 127,
              b'\x80': 128,
              b'\xff': 255,
              b'\x01\x00': 256,
              b'\x7f\xff': 32767,
              b'\x80\x00': 32768,
              b'\xff\xff': 65535,
              b'\x01\x00\x00': 65536,
          }
          check(tests3, 'big', signed=False)
  
          # Convert integers to unsigned little-endian byte arrays.
          tests4 = {
              b'': 0,
              b'\x00': 0,
              b'\x01': 1,
              b'\x7f': 127,
              b'\x80': 128,
              b'\xff': 255,
              b'\x00\x01': 256,
              b'\xff\x7f': 32767,
              b'\x00\x80': 32768,
              b'\xff\xff': 65535,
              b'\x00\x00\x01': 65536,
          }
          check(tests4, 'little', signed=False)
  
          class myint(int):
              pass
  
          self.assertIs(type(myint.from_bytes(b'\x00', 'big')), myint)
          self.assertEqual(myint.from_bytes(b'\x01', 'big'), 1)
          self.assertIs(
              type(myint.from_bytes(b'\x00', 'big', signed=False)), myint)
          self.assertEqual(myint.from_bytes(b'\x01', 'big', signed=False), 1)
          self.assertIs(type(myint.from_bytes(b'\x00', 'little')), myint)
          self.assertEqual(myint.from_bytes(b'\x01', 'little'), 1)
          self.assertIs(type(myint.from_bytes(
              b'\x00', 'little', signed=False)), myint)
          self.assertEqual(myint.from_bytes(b'\x01', 'little', signed=False), 1)
          self.assertEqual(
              int.from_bytes([255, 0, 0], 'big', signed=True), -65536)
          self.assertEqual(
              int.from_bytes((255, 0, 0), 'big', signed=True), -65536)
          self.assertEqual(int.from_bytes(
              bytearray(b'\xff\x00\x00'), 'big', signed=True), -65536)
          self.assertEqual(int.from_bytes(
              bytearray(b'\xff\x00\x00'), 'big', signed=True), -65536)
          self.assertEqual(int.from_bytes(
              array.array('B', b'\xff\x00\x00'), 'big', signed=True), -65536)
          self.assertEqual(int.from_bytes(
              memoryview(b'\xff\x00\x00'), 'big', signed=True), -65536)
          self.assertRaises(ValueError, int.from_bytes, [256], 'big')
          self.assertRaises(ValueError, int.from_bytes, [0], 'big\x00')
          self.assertRaises(ValueError, int.from_bytes, [0], 'little\x00')
          self.assertRaises(TypeError, int.from_bytes, "", 'big')
          self.assertRaises(TypeError, int.from_bytes, "\x00", 'big')
          self.assertRaises(TypeError, int.from_bytes, 0, 'big')
          self.assertRaises(TypeError, int.from_bytes, 0, 'big', True)
          self.assertRaises(TypeError, myint.from_bytes, "", 'big')
          self.assertRaises(TypeError, myint.from_bytes, "\x00", 'big')
          self.assertRaises(TypeError, myint.from_bytes, 0, 'big')
          self.assertRaises(TypeError, int.from_bytes, 0, 'big', True)
  
      def test_access_to_nonexistent_digit_0(self):
          # http://bugs.python.org/issue14630: A bug in _PyLong_Copy meant that
          # ob_digit[0] was being incorrectly accessed for instances of a
          # subclass of int, with value 0.
          class Integer(int):
              def __new__(cls, value=0):
                  self = int.__new__(cls, value)
                  self.foo = 'foo'
                  return self
  
          integers = [Integer(0) for i in range(1000)]
          for n in map(int, integers):
              self.assertEqual(n, 0)
  
      def test_shift_bool(self):
          # Issue #21422: ensure that bool << int and bool >> int return int
          for value in (True, False):
              for shift in (0, 2):
                  self.assertEqual(type(value << shift), int)
                  self.assertEqual(type(value >> shift), int)
  
  
  def test_main():
      support.run_unittest(LongTest)
  
  if __name__ == "__main__":
      test_main()
  