Lib/test/test_long.py

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(int, [0, 1, 2, BASE, BASE >> 1])
special.append(0x5555555555555555)
special.append(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 = 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 = 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.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 = 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.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 = 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)

    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):
        if (x, base) == (0, 8):
            # this is an oddball!
            return "0"
        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))

    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(int(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)
        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 range(10):
            for lenx in range(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 = int(hugepos)
        hugeneg_aslong = int(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, int),
            "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, int),
               "int(long(-sys.maxint-1) - 1) should have returned long")

        class long2(int):
            pass
        x = long2(1<<100)
        y = int(x)
        self.assert_(type(y) is int,
            "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()[-5:7], (-5, 7))
        # use the clamping effect to test the smallest and largest longs
        # that fit a Py_ssize_t
        slicemin, slicemax = X()[-2**100:2**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 = int(x)

            expected = -longx
            got = -x
            checkit('-', x)

            for y in special:
                longy = int(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, int(z))
                                got = pow(x, y, z)
                                checkit('pow', x, y, '%', z)
                            else:
                                self.assertRaises(TypeError, pow,longx, longy, int(z))

    def test_float_overflow(self):
        import math

        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(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 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
        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):
                    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,
                          int(t-1), int(t), int(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 = 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 = 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()