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Fixed issue #25177, problems with the mean of very small and very large numbers.

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Steven D'Aprano 2015-12-01 17:04:32 +11:00
parent ee1a0e4b8c
commit 40a841bcb9
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363
Lib/test/test_statistics.py
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@ -21,6 +21,37 @@ import statistics
# === Helper functions and class ===
def _nan_equal(a, b):
"""Return True if a and b are both the same kind of NAN.
>>> _nan_equal(Decimal('NAN'), Decimal('NAN'))
True
>>> _nan_equal(Decimal('sNAN'), Decimal('sNAN'))
True
>>> _nan_equal(Decimal('NAN'), Decimal('sNAN'))
False
>>> _nan_equal(Decimal(42), Decimal('NAN'))
False
>>> _nan_equal(float('NAN'), float('NAN'))
True
>>> _nan_equal(float('NAN'), 0.5)
False
>>> _nan_equal(float('NAN'), Decimal('NAN'))
False
NAN payloads are not compared.
"""
if type(a) is not type(b):
return False
if isinstance(a, float):
return math.isnan(a) and math.isnan(b)
aexp = a.as_tuple()[2]
bexp = b.as_tuple()[2]
return (aexp == bexp) and (aexp in ('n', 'N')) # Both NAN or both sNAN.
def _calc_errors(actual, expected):
"""Return the absolute and relative errors between two numbers.
@ -675,15 +706,60 @@ class ExactRatioTest(unittest.TestCase):
self.assertEqual(_exact_ratio(D("12.345")), (12345, 1000))
self.assertEqual(_exact_ratio(D("-1.98")), (-198, 100))
def test_inf(self):
INF = float("INF")
class MyFloat(float):
pass
class MyDecimal(Decimal):
pass
for inf in (INF, -INF):
for type_ in (float, MyFloat, Decimal, MyDecimal):
x = type_(inf)
ratio = statistics._exact_ratio(x)
self.assertEqual(ratio, (x, None))
self.assertEqual(type(ratio[0]), type_)
self.assertTrue(math.isinf(ratio[0]))
def test_float_nan(self):
NAN = float("NAN")
class MyFloat(float):
pass
for nan in (NAN, MyFloat(NAN)):
ratio = statistics._exact_ratio(nan)
self.assertTrue(math.isnan(ratio[0]))
self.assertIs(ratio[1], None)
self.assertEqual(type(ratio[0]), type(nan))
def test_decimal_nan(self):
NAN = Decimal("NAN")
sNAN = Decimal("sNAN")
class MyDecimal(Decimal):
pass
for nan in (NAN, MyDecimal(NAN), sNAN, MyDecimal(sNAN)):
ratio = statistics._exact_ratio(nan)
self.assertTrue(_nan_equal(ratio[0], nan))
self.assertIs(ratio[1], None)
self.assertEqual(type(ratio[0]), type(nan))
class DecimalToRatioTest(unittest.TestCase):
# Test _decimal_to_ratio private function.
def testSpecialsRaise(self):
# Test that NANs and INFs raise ValueError.
# Non-special values are covered by _exact_ratio above.
for d in (Decimal('NAN'), Decimal('sNAN'), Decimal('INF')):
self.assertRaises(ValueError, statistics._decimal_to_ratio, d)
def test_infinity(self):
# Test that INFs are handled correctly.
inf = Decimal('INF')
self.assertEqual(statistics._decimal_to_ratio(inf), (inf, None))
self.assertEqual(statistics._decimal_to_ratio(-inf), (-inf, None))
def test_nan(self):
# Test that NANs are handled correctly.
for nan in (Decimal('NAN'), Decimal('sNAN')):
num, den = statistics._decimal_to_ratio(nan)
# Because NANs always compare non-equal, we cannot use assertEqual.
# Nor can we use an identity test, as we don't guarantee anything
# about the object identity.
self.assertTrue(_nan_equal(num, nan))
self.assertIs(den, None)
def test_sign(self):
# Test sign is calculated correctly.
@ -718,25 +794,181 @@ class DecimalToRatioTest(unittest.TestCase):
self.assertEqual(t, (147000, 1))
class CheckTypeTest(unittest.TestCase):
# Test _check_type private function.
class IsFiniteTest(unittest.TestCase):
# Test _isfinite private function.
def test_allowed(self):
# Test that a type which should be allowed is allowed.
allowed = set([int, float])
statistics._check_type(int, allowed)
statistics._check_type(float, allowed)
def test_finite(self):
# Test that finite numbers are recognised as finite.
for x in (5, Fraction(1, 3), 2.5, Decimal("5.5")):
self.assertTrue(statistics._isfinite(x))
def test_not_allowed(self):
# Test that a type which should not be allowed raises.
allowed = set([int, float])
self.assertRaises(TypeError, statistics._check_type, Decimal, allowed)
def test_infinity(self):
# Test that INFs are not recognised as finite.
for x in (float("inf"), Decimal("inf")):
self.assertFalse(statistics._isfinite(x))
def test_add_to_allowed(self):
# Test that a second type will be added to the allowed set.
allowed = set([int])
statistics._check_type(float, allowed)
self.assertEqual(allowed, set([int, float]))
def test_nan(self):
# Test that NANs are not recognised as finite.
for x in (float("nan"), Decimal("NAN"), Decimal("sNAN")):
self.assertFalse(statistics._isfinite(x))
class CoerceTest(unittest.TestCase):
# Test that private function _coerce correctly deals with types.
# The coercion rules are currently an implementation detail, although at
# some point that should change. The tests and comments here define the
# correct implementation.
# Pre-conditions of _coerce:
#
# - The first time _sum calls _coerce, the
# - coerce(T, S) will never be called with bool as the first argument;
# this is a pre-condition, guarded with an assertion.
#
# - coerce(T, T) will always return T; we assume T is a valid numeric
# type. Violate this assumption at your own risk.
#
# - Apart from as above, bool is treated as if it were actually int.
#
# - coerce(int, X) and coerce(X, int) return X.
# -
def test_bool(self):
# bool is somewhat special, due to the pre-condition that it is
# never given as the first argument to _coerce, and that it cannot
# be subclassed. So we test it specially.
for T in (int, float, Fraction, Decimal):
self.assertIs(statistics._coerce(T, bool), T)
class MyClass(T): pass
self.assertIs(statistics._coerce(MyClass, bool), MyClass)
def assertCoerceTo(self, A, B):
"""Assert that type A coerces to B."""
self.assertIs(statistics._coerce(A, B), B)
self.assertIs(statistics._coerce(B, A), B)
def check_coerce_to(self, A, B):
"""Checks that type A coerces to B, including subclasses."""
# Assert that type A is coerced to B.
self.assertCoerceTo(A, B)
# Subclasses of A are also coerced to B.
class SubclassOfA(A): pass
self.assertCoerceTo(SubclassOfA, B)
# A, and subclasses of A, are coerced to subclasses of B.
class SubclassOfB(B): pass
self.assertCoerceTo(A, SubclassOfB)
self.assertCoerceTo(SubclassOfA, SubclassOfB)
def assertCoerceRaises(self, A, B):
"""Assert that coercing A to B, or vice versa, raises TypeError."""
self.assertRaises(TypeError, statistics._coerce, (A, B))
self.assertRaises(TypeError, statistics._coerce, (B, A))
def check_type_coercions(self, T):
"""Check that type T coerces correctly with subclasses of itself."""
assert T is not bool
# Coercing a type with itself returns the same type.
self.assertIs(statistics._coerce(T, T), T)
# Coercing a type with a subclass of itself returns the subclass.
class U(T): pass
class V(T): pass
class W(U): pass
for typ in (U, V, W):
self.assertCoerceTo(T, typ)
self.assertCoerceTo(U, W)
# Coercing two subclasses that aren't parent/child is an error.
self.assertCoerceRaises(U, V)
self.assertCoerceRaises(V, W)
def test_int(self):
# Check that int coerces correctly.
self.check_type_coercions(int)
for typ in (float, Fraction, Decimal):
self.check_coerce_to(int, typ)
def test_fraction(self):
# Check that Fraction coerces correctly.
self.check_type_coercions(Fraction)
self.check_coerce_to(Fraction, float)
def test_decimal(self):
# Check that Decimal coerces correctly.
self.check_type_coercions(Decimal)
def test_float(self):
# Check that float coerces correctly.
self.check_type_coercions(float)
def test_non_numeric_types(self):
for bad_type in (str, list, type(None), tuple, dict):
for good_type in (int, float, Fraction, Decimal):
self.assertCoerceRaises(good_type, bad_type)
def test_incompatible_types(self):
# Test that incompatible types raise.
for T in (float, Fraction):
class MySubclass(T): pass
self.assertCoerceRaises(T, Decimal)
self.assertCoerceRaises(MySubclass, Decimal)
class ConvertTest(unittest.TestCase):
# Test private _convert function.
def check_exact_equal(self, x, y):
"""Check that x equals y, and has the same type as well."""
self.assertEqual(x, y)
self.assertIs(type(x), type(y))
def test_int(self):
# Test conversions to int.
x = statistics._convert(Fraction(71), int)
self.check_exact_equal(x, 71)
class MyInt(int): pass
x = statistics._convert(Fraction(17), MyInt)
self.check_exact_equal(x, MyInt(17))
def test_fraction(self):
# Test conversions to Fraction.
x = statistics._convert(Fraction(95, 99), Fraction)
self.check_exact_equal(x, Fraction(95, 99))
class MyFraction(Fraction):
def __truediv__(self, other):
return self.__class__(super().__truediv__(other))
x = statistics._convert(Fraction(71, 13), MyFraction)
self.check_exact_equal(x, MyFraction(71, 13))
def test_float(self):
# Test conversions to float.
x = statistics._convert(Fraction(-1, 2), float)
self.check_exact_equal(x, -0.5)
class MyFloat(float):
def __truediv__(self, other):
return self.__class__(super().__truediv__(other))
x = statistics._convert(Fraction(9, 8), MyFloat)
self.check_exact_equal(x, MyFloat(1.125))
def test_decimal(self):
# Test conversions to Decimal.
x = statistics._convert(Fraction(1, 40), Decimal)
self.check_exact_equal(x, Decimal("0.025"))
class MyDecimal(Decimal):
def __truediv__(self, other):
return self.__class__(super().__truediv__(other))
x = statistics._convert(Fraction(-15, 16), MyDecimal)
self.check_exact_equal(x, MyDecimal("-0.9375"))
def test_inf(self):
for INF in (float('inf'), Decimal('inf')):
for inf in (INF, -INF):
x = statistics._convert(inf, type(inf))
self.check_exact_equal(x, inf)
def test_nan(self):
for nan in (float('nan'), Decimal('NAN'), Decimal('sNAN')):
x = statistics._convert(nan, type(nan))
self.assertTrue(_nan_equal(x, nan))
# === Tests for public functions ===
@ -874,52 +1106,71 @@ class UnivariateTypeMixin:
self.assertIs(type(result), kind)
class TestSum(NumericTestCase, UnivariateCommonMixin, UnivariateTypeMixin):
class TestSumCommon(UnivariateCommonMixin, UnivariateTypeMixin):
# Common test cases for statistics._sum() function.
# This test suite looks only at the numeric value returned by _sum,
# after conversion to the appropriate type.
def setUp(self):
def simplified_sum(*args):
T, value, n = statistics._sum(*args)
return statistics._coerce(value, T)
self.func = simplified_sum
class TestSum(NumericTestCase):
# Test cases for statistics._sum() function.
# These tests look at the entire three value tuple returned by _sum.
def setUp(self):
self.func = statistics._sum
def test_empty_data(self):
# Override test for empty data.
for data in ([], (), iter([])):
self.assertEqual(self.func(data), 0)
self.assertEqual(self.func(data, 23), 23)
self.assertEqual(self.func(data, 2.3), 2.3)
self.assertEqual(self.func(data), (int, Fraction(0), 0))
self.assertEqual(self.func(data, 23), (int, Fraction(23), 0))
self.assertEqual(self.func(data, 2.3), (float, Fraction(2.3), 0))
def test_ints(self):
self.assertEqual(self.func([1, 5, 3, -4, -8, 20, 42, 1]), 60)
self.assertEqual(self.func([4, 2, 3, -8, 7], 1000), 1008)
self.assertEqual(self.func([1, 5, 3, -4, -8, 20, 42, 1]),
(int, Fraction(60), 8))
self.assertEqual(self.func([4, 2, 3, -8, 7], 1000),
(int, Fraction(1008), 5))
def test_floats(self):
self.assertEqual(self.func([0.25]*20), 5.0)
self.assertEqual(self.func([0.125, 0.25, 0.5, 0.75], 1.5), 3.125)
self.assertEqual(self.func([0.25]*20),
(float, Fraction(5.0), 20))
self.assertEqual(self.func([0.125, 0.25, 0.5, 0.75], 1.5),
(float, Fraction(3.125), 4))
def test_fractions(self):
F = Fraction
self.assertEqual(self.func([Fraction(1, 1000)]*500), Fraction(1, 2))
self.assertEqual(self.func([Fraction(1, 1000)]*500),
(Fraction, Fraction(1, 2), 500))
def test_decimals(self):
D = Decimal
data = [D("0.001"), D("5.246"), D("1.702"), D("-0.025"),
D("3.974"), D("2.328"), D("4.617"), D("2.843"),
]
self.assertEqual(self.func(data), Decimal("20.686"))
self.assertEqual(self.func(data),
(Decimal, Decimal("20.686"), 8))
def test_compare_with_math_fsum(self):
# Compare with the math.fsum function.
# Ideally we ought to get the exact same result, but sometimes
# we differ by a very slight amount :-(
data = [random.uniform(-100, 1000) for _ in range(1000)]
self.assertApproxEqual(self.func(data), math.fsum(data), rel=2e-16)
self.assertApproxEqual(float(self.func(data)[1]), math.fsum(data), rel=2e-16)
def test_start_argument(self):
# Test that the optional start argument works correctly.
data = [random.uniform(1, 1000) for _ in range(100)]
t = self.func(data)
self.assertEqual(t+42, self.func(data, 42))
self.assertEqual(t-23, self.func(data, -23))
self.assertEqual(t+1e20, self.func(data, 1e20))
t = self.func(data)[1]
self.assertEqual(t+42, self.func(data, 42)[1])
self.assertEqual(t-23, self.func(data, -23)[1])
self.assertEqual(t+Fraction(1e20), self.func(data, 1e20)[1])
def test_strings_fail(self):
# Sum of strings should fail.
@ -934,7 +1185,7 @@ class TestSum(NumericTestCase, UnivariateCommonMixin, UnivariateTypeMixin):
def test_mixed_sum(self):
# Mixed input types are not (currently) allowed.
# Check that mixed data types fail.
self.assertRaises(TypeError, self.func, [1, 2.0, Fraction(1, 2)])
self.assertRaises(TypeError, self.func, [1, 2.0, Decimal(1)])
# And so does mixed start argument.
self.assertRaises(TypeError, self.func, [1, 2.0], Decimal(1))
@ -942,11 +1193,14 @@ class TestSum(NumericTestCase, UnivariateCommonMixin, UnivariateTypeMixin):
class SumTortureTest(NumericTestCase):
def test_torture(self):
# Tim Peters' torture test for sum, and variants of same.
self.assertEqual(statistics._sum([1, 1e100, 1, -1e100]*10000), 20000.0)
self.assertEqual(statistics._sum([1e100, 1, 1, -1e100]*10000), 20000.0)
self.assertApproxEqual(
statistics._sum([1e-100, 1, 1e-100, -1]*10000), 2.0e-96, rel=5e-16
)
self.assertEqual(statistics._sum([1, 1e100, 1, -1e100]*10000),
(float, Fraction(20000.0), 40000))
self.assertEqual(statistics._sum([1e100, 1, 1, -1e100]*10000),
(float, Fraction(20000.0), 40000))
T, num, count = statistics._sum([1e-100, 1, 1e-100, -1]*10000)
self.assertIs(T, float)
self.assertEqual(count, 40000)
self.assertApproxEqual(float(num), 2.0e-96, rel=5e-16)
class SumSpecialValues(NumericTestCase):
@ -955,7 +1209,7 @@ class SumSpecialValues(NumericTestCase):
def test_nan(self):
for type_ in (float, Decimal):
nan = type_('nan')
result = statistics._sum([1, nan, 2])
result = statistics._sum([1, nan, 2])[1]
self.assertIs(type(result), type_)
self.assertTrue(math.isnan(result))
@ -968,10 +1222,10 @@ class SumSpecialValues(NumericTestCase):
def do_test_inf(self, inf):
# Adding a single infinity gives infinity.
result = statistics._sum([1, 2, inf, 3])
result = statistics._sum([1, 2, inf, 3])[1]
self.check_infinity(result, inf)
# Adding two infinities of the same sign also gives infinity.
result = statistics._sum([1, 2, inf, 3, inf, 4])
result = statistics._sum([1, 2, inf, 3, inf, 4])[1]
self.check_infinity(result, inf)
def test_float_inf(self):
@ -987,7 +1241,7 @@ class SumSpecialValues(NumericTestCase):
def test_float_mismatched_infs(self):
# Test that adding two infinities of opposite sign gives a NAN.
inf = float('inf')
result = statistics._sum([1, 2, inf, 3, -inf, 4])
result = statistics._sum([1, 2, inf, 3, -inf, 4])[1]
self.assertTrue(math.isnan(result))
def test_decimal_extendedcontext_mismatched_infs_to_nan(self):
@ -995,7 +1249,7 @@ class SumSpecialValues(NumericTestCase):
inf = Decimal('inf')
data = [1, 2, inf, 3, -inf, 4]
with decimal.localcontext(decimal.ExtendedContext):
self.assertTrue(math.isnan(statistics._sum(data)))
self.assertTrue(math.isnan(statistics._sum(data)[1]))
def test_decimal_basiccontext_mismatched_infs_to_nan(self):
# Test adding Decimal INFs with opposite sign raises InvalidOperation.
@ -1111,6 +1365,19 @@ class TestMean(NumericTestCase, AverageMixin, UnivariateTypeMixin):
d = Decimal('1e4')
self.assertEqual(statistics.mean([d]), d)
def test_regression_25177(self):
# Regression test for issue 25177.
# Ensure very big and very small floats don't overflow.
# See http://bugs.python.org/issue25177.
self.assertEqual(statistics.mean(
[8.988465674311579e+307, 8.98846567431158e+307]),
8.98846567431158e+307)
big = 8.98846567431158e+307
tiny = 5e-324
for n in (2, 3, 5, 200):
self.assertEqual(statistics.mean([big]*n), big)
self.assertEqual(statistics.mean([tiny]*n), tiny)
class TestMedian(NumericTestCase, AverageMixin):
# Common tests for median and all median.* functions.