import unittest
from test import support

import sys

import random
import math
import array

# 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
        with self.subTest(x=x, y=y):
            q, r = divmod(x, y)
            q2, r2 = x//y, x%y
            pab, pba = x*y, y*x
            eq(pab, pba, "multiplication does not commute")
            eq(q, q2, "divmod returns different quotient than /")
            eq(r, r2, "divmod returns different mod than %")
            eq(x, q*y + r, "x != q*y + r after divmod")
            if y > 0:
                self.assertTrue(0 <= r < y, "bad mod from divmod")
            else:
                self.assertTrue(y < r <= 0, "bad mod from divmod")

    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
                with self.subTest(abits=abits, bbits=bbits):
                    b = (1 << bbits) - 1
                    x = a * b
                    y = ((1 << (abits + bbits)) -
                         (1 << abits) -
                         (1 << bbits) +
                         1)
                    self.assertEqual(x, y)

    def check_bitop_identities_1(self, x):
        eq = self.assertEqual
        with self.subTest(x=x):
            eq(x & 0, 0)
            eq(x | 0, x)
            eq(x ^ 0, x)
            eq(x & -1, x)
            eq(x | -1, -1)
            eq(x ^ -1, ~x)
            eq(x, ~~x)
            eq(x & x, x)
            eq(x | x, x)
            eq(x ^ x, 0)
            eq(x & ~x, 0)
            eq(x | ~x, -1)
            eq(x ^ ~x, -1)
            eq(-x, 1 + ~x)
            eq(-x, ~(x-1))
        for n in range(2*SHIFT):
            p2 = 2 ** n
            with self.subTest(x=x, n=n, p2=p2):
                eq(x << n >> n, x)
                eq(x // p2, x >> n)
                eq(x * p2, x << n)
                eq(x & -p2, x >> n << n)
                eq(x & -p2, x & ~(p2 - 1))

    def check_bitop_identities_2(self, x, y):
        eq = self.assertEqual
        with self.subTest(x=x, y=y):
            eq(x & y, y & x)
            eq(x | y, y | x)
            eq(x ^ y, y ^ x)
            eq(x ^ y ^ x, y)
            eq(x & y, ~(~x | ~y))
            eq(x | y, ~(~x & ~y))
            eq(x ^ y, (x | y) & ~(x & y))
            eq(x ^ y, (x & ~y) | (~x & y))
            eq(x ^ y, (x | y) & (~x | ~y))

    def check_bitop_identities_3(self, x, y, z):
        eq = self.assertEqual
        with self.subTest(x=x, y=y, z=z):
            eq((x & y) & z, x & (y & z))
            eq((x | y) | z, x | (y | z))
            eq((x ^ y) ^ z, x ^ (y ^ z))
            eq(x & (y | z), (x & y) | (x & z))
            eq(x | (y & z), (x | y) & (x | 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)
            with self.subTest(x=x, mapper=mapper.__name__):
                expected = self.slow_format(x, base)
                self.assertEqual(got, expected)
            with self.subTest(got=got):
                self.assertEqual(int(got, 0), 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')