diff options
Diffstat (limited to 'Lib/test/test_long.py')
| -rw-r--r-- | Lib/test/test_long.py | 143 |
1 files changed, 108 insertions, 35 deletions
diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py index 3ebc1f7..3f9c1e2 100644 --- a/Lib/test/test_long.py +++ b/Lib/test/test_long.py @@ -43,6 +43,53 @@ 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.""" @@ -83,7 +130,7 @@ class LongTest(unittest.TestCase): # The sign of the number is also random. def getran(self, ndigits): - self.assertTrue(ndigits > 0) + self.assertGreater(ndigits, 0) nbits_hi = ndigits * SHIFT nbits_lo = nbits_hi - SHIFT + 1 answer = 0 @@ -275,20 +322,13 @@ class LongTest(unittest.TestCase): "".join("0123456789abcdef"[i] for i in digits) def check_format_1(self, x): - for base, mapper in (8, oct), (10, repr), (16, hex): + for base, mapper in (2, bin), (8, oct), (10, str), (10, repr), (16, hex): got = mapper(x) expected = self.slow_format(x, base) msg = Frm("%s returned %r but expected %r for %r", mapper.__name__, got, expected, x) self.assertEqual(got, expected, msg) self.assertEqual(int(got, 0), x, Frm('int("%s", 0) != %r', got, x)) - # str() has to be checked a little differently since there's no - # trailing "L" - got = str(x) - expected = self.slow_format(x, 10) - msg = Frm("%s returned %r but expected %r for %r", - mapper.__name__, got, expected, x) - self.assertEqual(got, expected, msg) def test_format(self): for x in special: @@ -367,6 +407,23 @@ class LongTest(unittest.TestCase): 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): @@ -421,6 +478,22 @@ class LongTest(unittest.TestCase): 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) @@ -473,11 +546,11 @@ class LongTest(unittest.TestCase): def test_mixed_compares(self): eq = self.assertEqual - # We're mostly concerned with that mixing floats and longs does the - # right stuff, even when longs are too large to fit in a float. + # 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, longs and floats exactly). + # represents all Python ints and floats exactly). class Rat: def __init__(self, value): if isinstance(value, int): @@ -792,21 +865,21 @@ class LongTest(unittest.TestCase): def test_small_ints(self): for i in range(-5, 257): - self.assertTrue(i is i + 0) - self.assertTrue(i is i * 1) - self.assertTrue(i is i - 0) - self.assertTrue(i is i // 1) - self.assertTrue(i is i & -1) - self.assertTrue(i is i | 0) - self.assertTrue(i is i ^ 0) - self.assertTrue(i is ~~i) - self.assertTrue(i is i**1) - self.assertTrue(i is int(str(i))) - self.assertTrue(i is i<<2>>2, str(i)) + 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.assertTrue(i - i is 0) - self.assertTrue(0 * i is 0) + self.assertIs(i - i, 0) + self.assertIs(0 * i, 0) def test_bit_length(self): tiny = 1e-10 @@ -853,7 +926,7 @@ class LongTest(unittest.TestCase): got = round(k+offset, -1) expected = v+offset self.assertEqual(got, expected) - self.assertTrue(type(got) is int) + self.assertIs(type(got), int) # larger second argument self.assertEqual(round(-150, -2), -200) @@ -892,7 +965,7 @@ class LongTest(unittest.TestCase): got = round(10**k + 324678, -3) expect = 10**k + 325000 self.assertEqual(got, expect) - self.assertTrue(type(got) is int) + self.assertIs(type(got), int) # nonnegative second argument: round(x, n) should just return x for n in range(5): @@ -900,7 +973,7 @@ class LongTest(unittest.TestCase): x = random.randrange(-10000, 10000) got = round(x, n) self.assertEqual(got, x) - self.assertTrue(type(got) is int) + 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) @@ -909,7 +982,7 @@ class LongTest(unittest.TestCase): x = random.randrange(-10000, 10000) got = round(x) self.assertEqual(got, x) - self.assertTrue(type(got) is int) + self.assertIs(type(got), int) # bad second argument bad_exponents = ('brian', 2.0, 0j, None) @@ -1114,15 +1187,15 @@ class LongTest(unittest.TestCase): class myint(int): pass - self.assertTrue(type(myint.from_bytes(b'\x00', 'big')) is myint) + self.assertIs(type(myint.from_bytes(b'\x00', 'big')), myint) self.assertEqual(myint.from_bytes(b'\x01', 'big'), 1) - self.assertTrue( - type(myint.from_bytes(b'\x00', 'big', signed=False)) is myint) + self.assertIs( + type(myint.from_bytes(b'\x00', 'big', signed=False)), myint) self.assertEqual(myint.from_bytes(b'\x01', 'big', signed=False), 1) - self.assertTrue(type(myint.from_bytes(b'\x00', 'little')) is myint) + self.assertIs(type(myint.from_bytes(b'\x00', 'little')), myint) self.assertEqual(myint.from_bytes(b'\x01', 'little'), 1) - self.assertTrue(type(myint.from_bytes( - b'\x00', 'little', signed=False)) is myint) + 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) |