import unittest

from test import test_support

import sys

import random

# 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 = 15

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 = map(long, [0, 1, 2, BASE, BASE >> 1])

special.append(0x5555555555555555L)

special.append(0xaaaaaaaaaaaaaaaaL)

#  some solid strings of one bits

p2 = 4L  # 0 and 1 already added

for i in range(2*SHIFT):

    special.append(p2 - 1)

    p2 = p2 << 1

del p2

# add complements & negations

special = special + map(lambda x: ~x, special) + \

                    map(lambda x: -x, special)

L = [

        ('0', 0),

        ('1', 1),

        ('9', 9),

        ('10', 10),

        ('99', 99),

        ('100', 100),

        ('314', 314),

        (' 314', 314),

        ('314 ', 314),

        ('  \t\t  314  \t\t  ', 314),

        (repr(sys.maxint), sys.maxint),

        ('  1x', ValueError),

        ('  1  ', 1),

        ('  1\02  ', ValueError),

        ('', ValueError),

        (' ', ValueError),

        ('  \t\t  ', ValueError)

]

if test_support.have_unicode:

    L += [

        (unicode('0'), 0),

        (unicode('1'), 1),

        (unicode('9'), 9),

        (unicode('10'), 10),

        (unicode('99'), 99),

        (unicode('100'), 100),

        (unicode('314'), 314),

        (unicode(' 314'), 314),

        (unicode('\u0663\u0661\u0664 ','raw-unicode-escape'), 314),

        (unicode('  \t\t  314  \t\t  '), 314),

        (unicode('  1x'), ValueError),

        (unicode('  1  '), 1),

        (unicode('  1\02  '), ValueError),

        (unicode(''), ValueError),

        (unicode(' '), ValueError),

        (unicode('  \t\t  '), ValueError),

        (unichr(0x200), ValueError),

]

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.assert_(ndigits > 0)

        nbits_hi = ndigits * SHIFT

        nbits_lo = nbits_hi - SHIFT + 1

        answer = 0L

        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.assert_(1 <= bits <= SHIFT)

            nbits = nbits + bits

            answer = answer << bits

            if r & 1:

                answer = answer | ((1 << bits) - 1)

            r = int(random.random() * (SHIFT * 2))

        self.assert_(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 = 0L

        for i in xrange(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.assert_(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y))

        else:

            self.assert_(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y))

    def test_division(self):

        digits = range(1, MAXDIGITS+1) + 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 1L

                self.check_division(x, y)

    def test_karatsuba(self):

        digits = range(1, 5) + 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 = (1L << abits) - 1

            for bbits in bits:

                if bbits < abits:

                    continue

                b = (1L << bbits) - 1

                x = a * b

                y = ((1L << (abits + bbits)) -

                     (1L << abits) -

                     (1L << 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 xrange(2*SHIFT):

            p2 = 2L ** 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 = xrange(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):

        if (x, base) == (0, 8):

            # this is an oddball!

            return "0L"

        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] + \

               {8: '0', 10: '', 16: '0x'}[base] + \

               "".join(map(lambda i: "0123456789abcdef"[i], digits)) + "L"

    def check_format_1(self, x):

        for base, mapper in (8, oct), (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(long(got, 0), x, Frm('long("%s", 0) != %r', got, x))

        # str() has to be checked a little differently since there's no

        # trailing "L"

        got = str(x)

        expected = self.slow_format(x, 10)[:-1]

        msg = Frm("%s returned %r but expected %r for %r",

            mapper.__name__, got, expected, x)

        self.assertEqual(got, expected, msg)

    def test_format(self):

        for x in special:

            self.check_format_1(x)

        for i in xrange(10):

            for lenx in xrange(1, MAXDIGITS+1):

                x = self.getran(lenx)

                self.check_format_1(x)

    def test_long(self):

        self.assertEqual(long(314), 314L)

        self.assertEqual(long(3.14), 3L)

        self.assertEqual(long(314L), 314L)

        # Check that long() of basic types actually returns a long

        self.assertEqual(type(long(314)), long)

        self.assertEqual(type(long(3.14)), long)

        self.assertEqual(type(long(314L)), long)

        # Check that conversion from float truncates towards zero

        self.assertEqual(long(-3.14), -3L)

        self.assertEqual(long(3.9), 3L)

        self.assertEqual(long(-3.9), -3L)

        self.assertEqual(long(3.5), 3L)

        self.assertEqual(long(-3.5), -3L)

        self.assertEqual(long("-3"), -3L)

        if test_support.have_unicode:

            self.assertEqual(long(unicode("-3")), -3L)

        # Different base:

        self.assertEqual(long("10",16), 16L)

        if test_support.have_unicode:

            self.assertEqual(long(unicode("10"),16), 16L)

        # Check conversions from string (same test set as for int(), and then some)

        LL = [

                ('1' + '0'*20, 10L**20),

                ('1' + '0'*100, 10L**100)

        ]

        L2 = L[:]

        if test_support.have_unicode:

            L2 += [

                (unicode('1') + unicode('0')*20, 10L**20),

                (unicode('1') + unicode('0')*100, 10L**100),

        ]

        for s, v in L2 + 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(long(ss), long(vv))

                    except v:

                        pass

        self.assertRaises(ValueError, long, '123\0')

        self.assertRaises(ValueError, long, '53', 40)

        self.assertRaises(TypeError, long, 1, 12)

        # SF patch #1638879: embedded NULs were not detected with

        # explicit base

        self.assertRaises(ValueError, long, '123\0', 10)

        self.assertRaises(ValueError, long, '123\x00 245', 20)

        self.assertEqual(long('100000000000000000000000000000000', 2),

                         4294967296)

        self.assertEqual(long('102002022201221111211', 3), 4294967296)

        self.assertEqual(long('10000000000000000', 4), 4294967296)

        self.assertEqual(long('32244002423141', 5), 4294967296)

        self.assertEqual(long('1550104015504', 6), 4294967296)

        self.assertEqual(long('211301422354', 7), 4294967296)

        self.assertEqual(long('40000000000', 8), 4294967296)

        self.assertEqual(long('12068657454', 9), 4294967296)

        self.assertEqual(long('4294967296', 10), 4294967296)

        self.assertEqual(long('1904440554', 11), 4294967296)

        self.assertEqual(long('9ba461594', 12), 4294967296)

        self.assertEqual(long('535a79889', 13), 4294967296)

        self.assertEqual(long('2ca5b7464', 14), 4294967296)

        self.assertEqual(long('1a20dcd81', 15), 4294967296)

        self.assertEqual(long('100000000', 16), 4294967296)

        self.assertEqual(long('a7ffda91', 17), 4294967296)

        self.assertEqual(long('704he7g4', 18), 4294967296)

        self.assertEqual(long('4f5aff66', 19), 4294967296)

        self.assertEqual(long('3723ai4g', 20), 4294967296)

        self.assertEqual(long('281d55i4', 21), 4294967296)

        self.assertEqual(long('1fj8b184', 22), 4294967296)

        self.assertEqual(long('1606k7ic', 23), 4294967296)

        self.assertEqual(long('mb994ag', 24), 4294967296)

        self.assertEqual(long('hek2mgl', 25), 4294967296)

        self.assertEqual(long('dnchbnm', 26), 4294967296)

        self.assertEqual(long('b28jpdm', 27), 4294967296)

        self.assertEqual(long('8pfgih4', 28), 4294967296)

        self.assertEqual(long('76beigg', 29), 4294967296)

        self.assertEqual(long('5qmcpqg', 30), 4294967296)

        self.assertEqual(long('4q0jto4', 31), 4294967296)

        self.assertEqual(long('4000000', 32), 4294967296)

        self.assertEqual(long('3aokq94', 33), 4294967296)

        self.assertEqual(long('2qhxjli', 34), 4294967296)

        self.assertEqual(long('2br45qb', 35), 4294967296)

        self.assertEqual(long('1z141z4', 36), 4294967296)

        self.assertEqual(long('100000000000000000000000000000001', 2),

                         4294967297)

        self.assertEqual(long('102002022201221111212', 3), 4294967297)

        self.assertEqual(long('10000000000000001', 4), 4294967297)

        self.assertEqual(long('32244002423142', 5), 4294967297)

        self.assertEqual(long('1550104015505', 6), 4294967297)

        self.assertEqual(long('211301422355', 7), 4294967297)

        self.assertEqual(long('40000000001', 8), 4294967297)

        self.assertEqual(long('12068657455', 9), 4294967297)

        self.assertEqual(long('4294967297', 10), 4294967297)

        self.assertEqual(long('1904440555', 11), 4294967297)

        self.assertEqual(long('9ba461595', 12), 4294967297)

        self.assertEqual(long('535a7988a', 13), 4294967297)

        self.assertEqual(long('2ca5b7465', 14), 4294967297)

        self.assertEqual(long('1a20dcd82', 15), 4294967297)

        self.assertEqual(long('100000001', 16), 4294967297)

        self.assertEqual(long('a7ffda92', 17), 4294967297)

        self.assertEqual(long('704he7g5', 18), 4294967297)

        self.assertEqual(long('4f5aff67', 19), 4294967297)

        self.assertEqual(long('3723ai4h', 20), 4294967297)

        self.assertEqual(long('281d55i5', 21), 4294967297)

        self.assertEqual(long('1fj8b185', 22), 4294967297)

        self.assertEqual(long('1606k7id', 23), 4294967297)

        self.assertEqual(long('mb994ah', 24), 4294967297)

        self.assertEqual(long('hek2mgm', 25), 4294967297)

        self.assertEqual(long('dnchbnn', 26), 4294967297)

        self.assertEqual(long('b28jpdn', 27), 4294967297)

        self.assertEqual(long('8pfgih5', 28), 4294967297)

        self.assertEqual(long('76beigh', 29), 4294967297)

        self.assertEqual(long('5qmcpqh', 30), 4294967297)

        self.assertEqual(long('4q0jto5', 31), 4294967297)

        self.assertEqual(long('4000001', 32), 4294967297)

        self.assertEqual(long('3aokq95', 33), 4294967297)

        self.assertEqual(long('2qhxjlj', 34), 4294967297)

        self.assertEqual(long('2br45qc', 35), 4294967297)

        self.assertEqual(long('1z141z5', 36), 4294967297)

    def test_conversion(self):

        # Test __long__()

        class ClassicMissingMethods:

            pass

        self.assertRaises(AttributeError, long, ClassicMissingMethods())

        class MissingMethods(object):

            pass

        self.assertRaises(TypeError, long, MissingMethods())

        class Foo0:

            def __long__(self):

                return 42L

        class Foo1(object):

            def __long__(self):

                return 42L

        class Foo2(long):

            def __long__(self):

                return 42L

        class Foo3(long):

            def __long__(self):

                return self

        class Foo4(long):

            def __long__(self):

                return 42

        class Foo5(long):

            def __long__(self):

                return 42.

        self.assertEqual(long(Foo0()), 42L)

        self.assertEqual(long(Foo1()), 42L)

        self.assertEqual(long(Foo2()), 42L)

        self.assertEqual(long(Foo3()), 0)

        self.assertEqual(long(Foo4()), 42)

        self.assertRaises(TypeError, long, Foo5())

        class Classic:

            pass

        for base in (object, Classic):

            class LongOverridesTrunc(base):

                def __long__(self):

                    return 42

                def __trunc__(self):

                    return -12

            self.assertEqual(long(LongOverridesTrunc()), 42)

            class JustTrunc(base):

                def __trunc__(self):

                    return 42

            self.assertEqual(long(JustTrunc()), 42)

            for trunc_result_base in (object, Classic):

                class Integral(trunc_result_base):

                    def __int__(self):

                        return 42

                class TruncReturnsNonLong(base):

                    def __trunc__(self):

                        return Integral()

                self.assertEqual(long(TruncReturnsNonLong()), 42)

                class NonIntegral(trunc_result_base):

                    def __trunc__(self):

                        # Check that we avoid infinite recursion.

                        return NonIntegral()

                class TruncReturnsNonIntegral(base):

                    def __trunc__(self):

                        return NonIntegral()

                try:

                    long(TruncReturnsNonIntegral())

                except TypeError as e:

                    self.assertEquals(str(e),

                                      "__trunc__ returned non-Integral"

                                      " (type NonIntegral)")

                else:

                    self.fail("Failed to raise TypeError with %s" %

                              ((base, trunc_result_base),))

    def test_misc(self):

        # check the extremes in int<->long conversion

        hugepos = sys.maxint

        hugeneg = -hugepos - 1

        hugepos_aslong = long(hugepos)

        hugeneg_aslong = long(hugeneg)

        self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxint) != sys.maxint")

        self.assertEqual(hugeneg, hugeneg_aslong,

            "long(-sys.maxint-1) != -sys.maxint-1")

        # long -> int should not fail for hugepos_aslong or hugeneg_aslong

        x = int(hugepos_aslong)

        try:

            self.assertEqual(x, hugepos,

                  "converting sys.maxint to long and back to int fails")

        except OverflowError:

            self.fail("int(long(sys.maxint)) overflowed!")

        if not isinstance(x, int):

            raise TestFailed("int(long(sys.maxint)) should have returned int")

        x = int(hugeneg_aslong)

        try:

            self.assertEqual(x, hugeneg,

                  "converting -sys.maxint-1 to long and back to int fails")

        except OverflowError:

            self.fail("int(long(-sys.maxint-1)) overflowed!")

        if not isinstance(x, int):

            raise TestFailed("int(long(-sys.maxint-1)) should have "

                             "returned int")

        # but long -> int should overflow for hugepos+1 and hugeneg-1

        x = hugepos_aslong + 1

        try:

            y = int(x)

        except OverflowError:

            self.fail("int(long(sys.maxint) + 1) mustn't overflow")

        self.assert_(isinstance(y, long),

            "int(long(sys.maxint) + 1) should have returned long")

        x = hugeneg_aslong - 1