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1387 lines
54 KiB
1387 lines
54 KiB
3 years ago
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import unittest
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from test import support
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import sys
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import random
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import math
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import array
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# SHIFT should match the value in longintrepr.h for best testing.
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SHIFT = sys.int_info.bits_per_digit
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BASE = 2 ** SHIFT
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MASK = BASE - 1
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KARATSUBA_CUTOFF = 70 # from longobject.c
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# Max number of base BASE digits to use in test cases. Doubling
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# this will more than double the runtime.
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MAXDIGITS = 15
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# build some special values
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special = [0, 1, 2, BASE, BASE >> 1, 0x5555555555555555, 0xaaaaaaaaaaaaaaaa]
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# some solid strings of one bits
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p2 = 4 # 0 and 1 already added
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for i in range(2*SHIFT):
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special.append(p2 - 1)
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p2 = p2 << 1
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del p2
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# add complements & negations
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special += [~x for x in special] + [-x for x in special]
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DBL_MAX = sys.float_info.max
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DBL_MAX_EXP = sys.float_info.max_exp
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DBL_MIN_EXP = sys.float_info.min_exp
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DBL_MANT_DIG = sys.float_info.mant_dig
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DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1)
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# Pure Python version of correctly-rounded integer-to-float conversion.
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def int_to_float(n):
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"""
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Correctly-rounded integer-to-float conversion.
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"""
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# Constants, depending only on the floating-point format in use.
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# We use an extra 2 bits of precision for rounding purposes.
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PRECISION = sys.float_info.mant_dig + 2
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SHIFT_MAX = sys.float_info.max_exp - PRECISION
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Q_MAX = 1 << PRECISION
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ROUND_HALF_TO_EVEN_CORRECTION = [0, -1, -2, 1, 0, -1, 2, 1]
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# Reduce to the case where n is positive.
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if n == 0:
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return 0.0
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elif n < 0:
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return -int_to_float(-n)
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# Convert n to a 'floating-point' number q * 2**shift, where q is an
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# integer with 'PRECISION' significant bits. When shifting n to create q,
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# the least significant bit of q is treated as 'sticky'. That is, the
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# least significant bit of q is set if either the corresponding bit of n
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# was already set, or any one of the bits of n lost in the shift was set.
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shift = n.bit_length() - PRECISION
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q = n << -shift if shift < 0 else (n >> shift) | bool(n & ~(-1 << shift))
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# Round half to even (actually rounds to the nearest multiple of 4,
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# rounding ties to a multiple of 8).
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q += ROUND_HALF_TO_EVEN_CORRECTION[q & 7]
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# Detect overflow.
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if shift + (q == Q_MAX) > SHIFT_MAX:
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raise OverflowError("integer too large to convert to float")
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# Checks: q is exactly representable, and q**2**shift doesn't overflow.
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assert q % 4 == 0 and q // 4 <= 2**(sys.float_info.mant_dig)
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assert q * 2**shift <= sys.float_info.max
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# Some circularity here, since float(q) is doing an int-to-float
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# conversion. But here q is of bounded size, and is exactly representable
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# as a float. In a low-level C-like language, this operation would be a
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# simple cast (e.g., from unsigned long long to double).
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return math.ldexp(float(q), shift)
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# pure Python version of correctly-rounded true division
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def truediv(a, b):
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"""Correctly-rounded true division for integers."""
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negative = a^b < 0
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a, b = abs(a), abs(b)
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# exceptions: division by zero, overflow
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if not b:
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raise ZeroDivisionError("division by zero")
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if a >= DBL_MIN_OVERFLOW * b:
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raise OverflowError("int/int too large to represent as a float")
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# find integer d satisfying 2**(d - 1) <= a/b < 2**d
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d = a.bit_length() - b.bit_length()
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if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
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d += 1
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# compute 2**-exp * a / b for suitable exp
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exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
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a, b = a << max(-exp, 0), b << max(exp, 0)
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q, r = divmod(a, b)
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# round-half-to-even: fractional part is r/b, which is > 0.5 iff
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# 2*r > b, and == 0.5 iff 2*r == b.
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if 2*r > b or 2*r == b and q % 2 == 1:
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q += 1
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result = math.ldexp(q, exp)
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return -result if negative else result
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class LongTest(unittest.TestCase):
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# Get quasi-random long consisting of ndigits digits (in base BASE).
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# quasi == the most-significant digit will not be 0, and the number
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# is constructed to contain long strings of 0 and 1 bits. These are
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# more likely than random bits to provoke digit-boundary errors.
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# The sign of the number is also random.
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def getran(self, ndigits):
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self.assertGreater(ndigits, 0)
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nbits_hi = ndigits * SHIFT
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nbits_lo = nbits_hi - SHIFT + 1
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answer = 0
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nbits = 0
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r = int(random.random() * (SHIFT * 2)) | 1 # force 1 bits to start
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while nbits < nbits_lo:
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bits = (r >> 1) + 1
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bits = min(bits, nbits_hi - nbits)
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self.assertTrue(1 <= bits <= SHIFT)
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nbits = nbits + bits
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answer = answer << bits
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if r & 1:
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answer = answer | ((1 << bits) - 1)
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r = int(random.random() * (SHIFT * 2))
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self.assertTrue(nbits_lo <= nbits <= nbits_hi)
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if random.random() < 0.5:
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answer = -answer
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return answer
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# Get random long consisting of ndigits random digits (relative to base
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# BASE). The sign bit is also random.
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def getran2(ndigits):
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answer = 0
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for i in range(ndigits):
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answer = (answer << SHIFT) | random.randint(0, MASK)
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if random.random() < 0.5:
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answer = -answer
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return answer
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def check_division(self, x, y):
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eq = self.assertEqual
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with self.subTest(x=x, y=y):
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q, r = divmod(x, y)
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q2, r2 = x//y, x%y
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pab, pba = x*y, y*x
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eq(pab, pba, "multiplication does not commute")
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eq(q, q2, "divmod returns different quotient than /")
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eq(r, r2, "divmod returns different mod than %")
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eq(x, q*y + r, "x != q*y + r after divmod")
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if y > 0:
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self.assertTrue(0 <= r < y, "bad mod from divmod")
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else:
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self.assertTrue(y < r <= 0, "bad mod from divmod")
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def test_division(self):
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digits = list(range(1, MAXDIGITS+1)) + list(range(KARATSUBA_CUTOFF,
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KARATSUBA_CUTOFF + 14))
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digits.append(KARATSUBA_CUTOFF * 3)
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for lenx in digits:
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x = self.getran(lenx)
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for leny in digits:
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y = self.getran(leny) or 1
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self.check_division(x, y)
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# specific numbers chosen to exercise corner cases of the
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# current long division implementation
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# 30-bit cases involving a quotient digit estimate of BASE+1
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self.check_division(1231948412290879395966702881,
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1147341367131428698)
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self.check_division(815427756481275430342312021515587883,
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707270836069027745)
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self.check_division(627976073697012820849443363563599041,
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643588798496057020)
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self.check_division(1115141373653752303710932756325578065,
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1038556335171453937726882627)
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# 30-bit cases that require the post-subtraction correction step
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self.check_division(922498905405436751940989320930368494,
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949985870686786135626943396)
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self.check_division(768235853328091167204009652174031844,
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1091555541180371554426545266)
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# 15-bit cases involving a quotient digit estimate of BASE+1
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self.check_division(20172188947443, 615611397)
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self.check_division(1020908530270155025, 950795710)
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self.check_division(128589565723112408, 736393718)
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self.check_division(609919780285761575, 18613274546784)
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# 15-bit cases that require the post-subtraction correction step
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self.check_division(710031681576388032, 26769404391308)
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self.check_division(1933622614268221, 30212853348836)
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def test_karatsuba(self):
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digits = list(range(1, 5)) + list(range(KARATSUBA_CUTOFF,
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KARATSUBA_CUTOFF + 10))
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digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100])
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bits = [digit * SHIFT for digit in digits]
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# Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) ==
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# 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check.
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for abits in bits:
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a = (1 << abits) - 1
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for bbits in bits:
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if bbits < abits:
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continue
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with self.subTest(abits=abits, bbits=bbits):
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b = (1 << bbits) - 1
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x = a * b
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y = ((1 << (abits + bbits)) -
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(1 << abits) -
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(1 << bbits) +
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1)
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self.assertEqual(x, y)
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def check_bitop_identities_1(self, x):
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eq = self.assertEqual
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with self.subTest(x=x):
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eq(x & 0, 0)
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eq(x | 0, x)
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eq(x ^ 0, x)
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eq(x & -1, x)
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eq(x | -1, -1)
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eq(x ^ -1, ~x)
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eq(x, ~~x)
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eq(x & x, x)
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eq(x | x, x)
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eq(x ^ x, 0)
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eq(x & ~x, 0)
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eq(x | ~x, -1)
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eq(x ^ ~x, -1)
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eq(-x, 1 + ~x)
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eq(-x, ~(x-1))
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for n in range(2*SHIFT):
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p2 = 2 ** n
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with self.subTest(x=x, n=n, p2=p2):
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eq(x << n >> n, x)
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eq(x // p2, x >> n)
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eq(x * p2, x << n)
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eq(x & -p2, x >> n << n)
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eq(x & -p2, x & ~(p2 - 1))
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def check_bitop_identities_2(self, x, y):
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eq = self.assertEqual
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with self.subTest(x=x, y=y):
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eq(x & y, y & x)
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eq(x | y, y | x)
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eq(x ^ y, y ^ x)
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eq(x ^ y ^ x, y)
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eq(x & y, ~(~x | ~y))
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eq(x | y, ~(~x & ~y))
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eq(x ^ y, (x | y) & ~(x & y))
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eq(x ^ y, (x & ~y) | (~x & y))
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eq(x ^ y, (x | y) & (~x | ~y))
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def check_bitop_identities_3(self, x, y, z):
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eq = self.assertEqual
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with self.subTest(x=x, y=y, z=z):
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eq((x & y) & z, x & (y & z))
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eq((x | y) | z, x | (y | z))
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eq((x ^ y) ^ z, x ^ (y ^ z))
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eq(x & (y | z), (x & y) | (x & z))
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eq(x | (y & z), (x | y) & (x | z))
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def test_bitop_identities(self):
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for x in special:
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self.check_bitop_identities_1(x)
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digits = range(1, MAXDIGITS+1)
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for lenx in digits:
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x = self.getran(lenx)
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self.check_bitop_identities_1(x)
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for leny in digits:
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y = self.getran(leny)
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self.check_bitop_identities_2(x, y)
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self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2))
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def slow_format(self, x, base):
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digits = []
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sign = 0
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if x < 0:
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sign, x = 1, -x
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while x:
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x, r = divmod(x, base)
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digits.append(int(r))
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digits.reverse()
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digits = digits or [0]
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return '-'[:sign] + \
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{2: '0b', 8: '0o', 10: '', 16: '0x'}[base] + \
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"".join("0123456789abcdef"[i] for i in digits)
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def check_format_1(self, x):
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for base, mapper in (2, bin), (8, oct), (10, str), (10, repr), (16, hex):
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got = mapper(x)
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with self.subTest(x=x, mapper=mapper.__name__):
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expected = self.slow_format(x, base)
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self.assertEqual(got, expected)
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with self.subTest(got=got):
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self.assertEqual(int(got, 0), x)
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def test_format(self):
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for x in special:
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self.check_format_1(x)
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for i in range(10):
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for lenx in range(1, MAXDIGITS+1):
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x = self.getran(lenx)
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self.check_format_1(x)
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def test_long(self):
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# Check conversions from string
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LL = [
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('1' + '0'*20, 10**20),
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('1' + '0'*100, 10**100)
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]
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for s, v in LL:
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for sign in "", "+", "-":
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for prefix in "", " ", "\t", " \t\t ":
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ss = prefix + sign + s
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vv = v
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if sign == "-" and v is not ValueError:
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vv = -v
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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_bit_count(self):
|
||
|
|
for a in range(-1000, 1000):
|
||
|
|
self.assertEqual(a.bit_count(), bin(a).count("1"))
|
||
|
|
|
||
|
|
for exp in [10, 17, 63, 64, 65, 1009, 70234, 1234567]:
|
||
|
|
a = 2**exp
|
||
|
|
self.assertEqual(a.bit_count(), 1)
|
||
|
|
self.assertEqual((a - 1).bit_count(), exp)
|
||
|
|
self.assertEqual((a ^ 63).bit_count(), 7)
|
||
|
|
self.assertEqual(((a - 1) ^ 510).bit_count(), exp - 8)
|
||
|
|
|
||
|
|
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()
|