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//usr/local/lib/python3.9/test/test_long.py
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') 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) # Invalid unicode string # See bpo-34087 self.assertRaises(ValueError, int, '\u3053\u3093\u306b\u3061\u306f') 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) with self.subTest(x=x, y=y, Rcmp=Rcmp): xycmp = (x > y) - (x < y) eq(Rcmp, xycmp) eq(x == y, Rcmp == 0) eq(x != y, Rcmp != 0) eq(x < y, Rcmp < 0) eq(x <= y, Rcmp <= 0) eq(x > y, Rcmp > 0) eq(x >= y, Rcmp >= 0) def test__format__(self): self.assertEqual(format(123456789, 'd'), '123456789') self.assertEqual(format(123456789, 'd'), '123456789') self.assertEqual(format(123456789, ','), '123,456,789') self.assertEqual(format(123456789, '_'), '123_456_789') # 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") self.assertRaises(ValueError, format, 1234567890, ',x') self.assertEqual(format(1234567890, '_x'), '4996_02d2') self.assertEqual(format(1234567890, '_X'), '4996_02D2') # octal self.assertEqual(format(3, "o"), "3") self.assertEqual(format(-3, "o"), "-3") self.assertEqual(format(1234, "o"), "2322") self.assertEqual(format(-1234, "o"), "-2322") self.assertEqual(format(1234, "-o"), "2322") self.assertEqual(format(-1234, "-o"), "-2322") self.assertEqual(format(1234, " o"), " 2322") self.assertEqual(format(-1234, " o"), "-2322") self.assertEqual(format(1234, "+o"), "+2322") self.assertEqual(format(-1234, "+o"), "-2322") self.assertRaises(ValueError, format, 1234567890, ',o') self.assertEqual(format(1234567890, '_o'), '111_4540_1322') # binary 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") self.assertRaises(ValueError, format, 1234567890, ',b') self.assertEqual(format(12345, '_b'), '11_0000_0011_1001') # make sure these are errors self.assertRaises(ValueError, format, 3, "1.3") # precision disallowed self.assertRaises(ValueError, format, 3, "_c") # underscore, self.assertRaises(ValueError, format, 3, ",c") # comma, and self.assertRaises(ValueError, format, 3, "+c") # sign not allowed # with 'c' self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, '_,') self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, ',_') self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, '_,d') self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, ',_d') self.assertRaisesRegex(ValueError, "Cannot specify ',' with 's'", format, 3, ',s') self.assertRaisesRegex(ValueError, "Cannot specify '_' with 's'", format, 3, '_s') # 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_mod_division(self): with self.assertRaises(ZeroDivisionError): _ = 1 % 0 self.assertEqual(13 % 10, 3) self.assertEqual(-13 % 10, 7) self.assertEqual(13 % -10, -7) self.assertEqual(-13 % -10, -3) self.assertEqual(12 % 4, 0) self.assertEqual(-12 % 4, 0) self.assertEqual(12 % -4, 0) self.assertEqual(-12 % -4, 0) 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 test_floordiv(self): with self.assertRaises(ZeroDivisionError): _ = 1 // 0 self.assertEqual(2 // 3, 0) self.assertEqual(2 // -3, -1) self.assertEqual(-2 // 3, -1) self.assertEqual(-2 // -3, 0) self.assertEqual(-11 // -3, 3) self.assertEqual(-11 // 3, -4) self.assertEqual(11 // -3, -4) self.assertEqual(11 // 3, 3) self.assertEqual(-12 // -3, 4) self.assertEqual(-12 // 3, -4) self.assertEqual(12 // -3, -4) self.assertEqual(12 // 3, 4) 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_negative_shift_count(self): with self.assertRaises(ValueError): 42 << -3 with self.assertRaises(ValueError): 42 << -(1 << 1000) with self.assertRaises(ValueError): 42 >> -3 with self.assertRaises(ValueError): 42 >> -(1 << 1000) def test_lshift_of_zero(self): self.assertEqual(0 << 0, 0) self.assertEqual(0 << 10, 0) with self.assertRaises(ValueError): 0 << -1 self.assertEqual(0 << (1 << 1000), 0) with self.assertRaises(ValueError): 0 << -(1 << 1000) @support.cpython_only def test_huge_lshift_of_zero(self): # Shouldn't try to allocate memory for a huge shift. See issue #27870. # Other implementations may have a different boundary for overflow, # or not raise at all. self.assertEqual(0 << sys.maxsize, 0) self.assertEqual(0 << (sys.maxsize + 1), 0) @support.cpython_only @support.bigmemtest(sys.maxsize + 1000, memuse=2/15 * 2, dry_run=False) def test_huge_lshift(self, size): self.assertEqual(1 << (sys.maxsize + 1000), 1 << 1000 << sys.maxsize) def test_huge_rshift(self): self.assertEqual(42 >> (1 << 1000), 0) self.assertEqual((-42) >> (1 << 1000), -1) @support.cpython_only @support.bigmemtest(sys.maxsize + 500, memuse=2/15, dry_run=False) def test_huge_rshift_of_huge(self, size): huge = ((1 << 500) + 11) << sys.maxsize self.assertEqual(huge >> (sys.maxsize + 1), (1 << 499) + 5) self.assertEqual(huge >> (sys.maxsize + 1000), 0) @support.cpython_only def test_small_ints_in_huge_calculation(self): a = 2 ** 100 b = -a + 1 c = a + 1 self.assertIs(a + b, 1) self.assertIs(c - a, 1) 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) 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) class myint2(int): def __new__(cls, value): return int.__new__(cls, value + 1) i = myint2.from_bytes(b'\x01', 'big') self.assertIs(type(i), myint2) self.assertEqual(i, 2) class myint3(int): def __init__(self, value): self.foo = 'bar' i = myint3.from_bytes(b'\x01', 'big') self.assertIs(type(i), myint3) self.assertEqual(i, 1) self.assertEqual(getattr(i, 'foo', 'none'), 'bar') 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_as_integer_ratio(self): class myint(int): pass tests = [10, 0, -10, 1, sys.maxsize + 1, True, False, myint(42)] for value in tests: numerator, denominator = value.as_integer_ratio() self.assertEqual((numerator, denominator), (int(value), 1)) self.assertEqual(type(numerator), int) self.assertEqual(type(denominator), int) if __name__ == "__main__": unittest.main()