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bpo-20499: Rounding error in statistics.pvariance #28230

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Merged
rhettinger merged 12 commits into from
Sep 9, 2021
Merged

bpo-20499: Rounding error in statistics.pvariance #28230

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0a1d350
Incorrect first draft
rhettinger Sep 8, 2021
d8714cc
Exact ss
rhettinger Sep 8, 2021
2108d4d
Add test
rhettinger Sep 8, 2021
da6c6cb
Add blurb
rhettinger Sep 8, 2021
69387c6
Remove superfluous comment
rhettinger Sep 8, 2021
39973fd
Add another test
rhettinger Sep 8, 2021
829d5ec
Improve clairity
rhettinger Sep 8, 2021
cc78aaf
Beautify the order of terms
rhettinger Sep 8, 2021
c0b1560
Removed unused "start" argument from internal function
rhettinger Sep 8, 2021
c746482
Modernize and speed-up _exact_ratio() internal function
rhettinger Sep 8, 2021
e7c46fa
Remove unnecessary sort
rhettinger Sep 8, 2021
117ad6b
Add accuracy comments to stdev() and pstdev().
rhettinger Sep 8, 2021
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Removed unused "start" argument from internal function
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@rhettinger
rhettinger committed Sep 8, 2021
commit c0b156043308baef9f3115e6031444defcce1895
17 changes: 6 additions & 11 deletions Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -147,21 +147,17 @@ class StatisticsError(ValueError):

# === Private utilities ===

def _sum(data, start=0):
"""_sum(data [, start]) -> (type, sum, count)
def _sum(data):
"""_sum(data) -> (type, sum, count)

Return a high-precision sum of the given numeric data as a fraction,
together with the type to be converted to and the count of items.

If optional argument ``start`` is given, it is added to the total.
If ``data`` is empty, ``start`` (defaulting to 0) is returned.


Examples
--------

>>> _sum([3, 2.25, 4.5, -0.5, 1.0], 0.75)
(<class 'float'>, Fraction(11, 1), 5)
>>> _sum([3, 2.25, 4.5, -0.5, 0.25])
(<class 'float'>, Fraction(19, 2), 5)

Some sources of round-off error will be avoided:

Expand All @@ -184,10 +180,9 @@ def _sum(data, start=0):
allowed.
"""
count = 0
n, d = _exact_ratio(start)
partials = {d: n}
partials = {}
partials_get = partials.get
T = _coerce(int, type(start))
T = int
for typ, values in groupby(data, type):
T = _coerce(T, typ) # or raise TypeError
for n, d in map(_exact_ratio, values):
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14 changes: 0 additions & 14 deletions Lib/test/test_statistics.py
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Expand Up @@ -1250,20 +1250,14 @@ def test_empty_data(self):
# Override test for empty data.
for data in ([], (), iter([])):
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]),
(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),
(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):
self.assertEqual(self.func([Fraction(1, 1000)]*500),
Expand All @@ -1284,14 +1278,6 @@ def test_compare_with_math_fsum(self):
data = [random.uniform(-100, 1000) for _ in range(1000)]
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)[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.
self.assertRaises(TypeError, self.func, [1, 2, 3], '999')
Expand Down