import unittest

from test import test_support

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)

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_misc(self):

        import sys

        # 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

        try:

            y = int(x)

        except OverflowError:

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

        self.assert_(isinstance(y, long),

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

        class long2(long):

            pass

        x = long2(1L<<100)

        y = int(x)

        self.assert_(type(y) is long,

            "overflowing int conversion must return long not long subtype")

        # long -> Py_ssize_t conversion

        class X(object):

            def __getslice__(self, i, j):

                return i, j

        self.assertEqual(X()[-5L:7L], (-5, 7))

        # use the clamping effect to test the smallest and largest longs

        # that fit a Py_ssize_t

        slicemin, slicemax = X()[-2L**100:2L**100]

        self.assertEqual(X()[slicemin:slicemax], (slicemin, slicemax))

# ----------------------------------- tests of auto int->long conversion

    def test_auto_overflow(self):

        import math, sys

        special = [0, 1, 2, 3, sys.maxint-1, sys.maxint, sys.maxint+1]

        sqrt = int(math.sqrt(sys.maxint))

        special.extend([sqrt-1, sqrt, sqrt+1])

        special.extend([-i for i in special])

        def checkit(*args):

            # Heavy use of nested scopes here!

            self.assertEqual(got, expected,

                Frm("for %r expected %r got %r", args, expected, got))

        for x in special:

            longx = long(x)

            expected = -longx

            got = -x

            checkit('-', x)

            for y in special:

                longy = long(y)

                expected = longx + longy

                got = x + y

                checkit(x, '+', y)

                expected = longx - longy

                got = x - y

                checkit(x, '-', y)

                expected = longx * longy

                got = x * y

                checkit(x, '*', y)

                if y:

                    expected = longx / longy

                    got = x / y

                    checkit(x, '/', y)

                    expected = longx // longy

                    got = x // y

                    checkit(x, '//', y)

                    expected = divmod(longx, longy)

                    got = divmod(longx, longy)

                    checkit(x, 'divmod', y)

                if abs(y) < 5 and not (x == 0 and y < 0):

                    expected = longx ** longy

                    got = x ** y

                    checkit(x, '**', y)

                    for z in special:

                        if z != 0 :

                            if y >= 0:

                                expected = pow(longx, longy, long(z))

                                got = pow(x, y, z)

                                checkit('pow', x, y, '%', z)

                            else:

                                self.assertRaises(TypeError, pow,longx, longy, long(z))

    def test_float_overflow(self):

        import math

        for x in -2.0, -1.0, 0.0, 1.0, 2.0:

            self.assertEqual(float(long(x)), x)

        shuge = '12345' * 120

        huge = 1L << 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(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):

        import math

        LOG10E = math.log10(math.e)

        for exp in 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 -(1L << 10000), -2L, 0L:

            self.assertRaises(ValueError, math.log, bad)

            self.assertRaises(ValueError, math.log10, bad)

    def test_mixed_compares(self):

        eq = self.assertEqual

        import math

        import sys

        # We're mostly concerned with that mixing floats and longs does the

        # right stuff, even when longs 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, longs and floats exactly).

        class Rat:

            def __init__(self, value):

                if isinstance(value, (int, long)):

                    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" % val)

            def __cmp__(self, other):

                if not isinstance(other, Rat):

                    other = Rat(other)

                return cmp(self.n * other.d, self.d * other.n)

        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,

                          long(t-1), long(t), long(t+1)])

        cases.extend([0, 1, 2, sys.maxint, float(sys.maxint)])

        # 1L<<20000 should exceed all double formats.  long(1e200) is to

        # check that we get equality with 1e200 above.

        t = long(1e200)

        cases.extend([0L, 1L, 2L, 1L << 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 = cmp(Rx, Ry)

                xycmp = cmp(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_main():

    test_support.run_unittest(LongTest)

if __name__ == "__main__":

    test_main()