Add tests for math.sum (Issue #2819)

This commit is contained in:
Mark Dickinson 2008-05-23 02:36:48 +00:00
parent 99dfe92759
commit c11c3391b0
1 changed files with 136 additions and 0 deletions

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@ -630,6 +630,142 @@ class MathTests(unittest.TestCase):
self.assertRaises(ValueError, math.sqrt, NINF)
self.assert_(math.isnan(math.sqrt(NAN)))
def testSum(self):
# Python version of math.sum algorithm, for comparison
def msum(iterable):
"""Full precision sum of values in iterable. Returns the value of
the sum, rounded to the nearest representable floating-point number
using the round-half-to-even rule.
"""
# Stage 1: accumulate partials
partials = []
for x in iterable:
i = 0
for y in partials:
if abs(x) < abs(y):
x, y = y, x
hi = x + y
lo = y - (hi - x)
if lo:
partials[i] = lo
i += 1
x = hi
partials[i:] = [x] if x else []
# Stage 2: sum partials
if not partials:
return 0.0
# sum from the top, stopping as soon as the sum is inexact.
total = partials.pop()
while partials:
x = partials.pop()
old_total, total = total, total + x
error = x - (total - old_total)
if error != 0.0:
# adjust for correct rounding if necessary
if partials and (partials[-1] > 0.0) == (error > 0.0) and \
total + 2*error - total == 2*error:
total += 2*error
break
return total
from sys import float_info
maxfloat = float_info.max
twopow = 2.**(float_info.max_exp - 1)
test_values = [
([], 0.0),
([0.0], 0.0),
([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
([1e308, 1e308, -1e308], OverflowError),
([-1e308, 1e308, 1e308], 1e308),
([1e308, -1e308, 1e308], 1e308),
([2.0**1023, 2.0**1023, -2.0**1000], OverflowError),
([twopow, twopow, twopow, twopow, -twopow, -twopow, -twopow],
OverflowError),
([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
([2.0**1023-2.0**970, -1.0, 2.0**1023], OverflowError),
([maxfloat, maxfloat*2.**-54], maxfloat),
([maxfloat, maxfloat*2.**-53], OverflowError),
([1./n for n in range(1, 1001)], 7.4854708605503451),
([(-1.)**n/n for n in range(1, 1001)], -0.69264743055982025),
([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),
([INF, -INF, NAN], ValueError),
([NAN, INF, -INF], ValueError),
([INF, NAN, INF], ValueError),
([INF, INF], OverflowError),
([INF, -INF], ValueError),
([-INF, 1e308, 1e308, -INF], OverflowError),
([2.0**1023-2.0**970, 0.0, 2.0**1023], OverflowError),
([2.0**1023-2.0**970, 1.0, 2.0**1023], OverflowError),
([2.0**1023, 2.0**1023], OverflowError),
([2.0**1023, 2.0**1023, -1.0], OverflowError),
([twopow, twopow, twopow, twopow, -twopow, -twopow],
OverflowError),
([twopow, twopow, twopow, twopow, -twopow, twopow], OverflowError),
([-twopow, -twopow, -twopow, -twopow], OverflowError),
([2.**1023, 2.**1023, -2.**971], OverflowError),
([2.**1023, 2.**1023, -2.**970], OverflowError),
([-2.**970, 2.**1023, 2.**1023, -2.**-1074], OverflowError),
([ 2.**1023, 2.**1023, -2.**970, 2.**-1074], OverflowError),
([-2.**1023, 2.**971, -2.**1023], -maxfloat),
([-2.**1023, -2.**1023, 2.**970], OverflowError),
([-2.**1023, -2.**1023, 2.**970, 2.**-1074], OverflowError),
([-2.**-1074, -2.**1023, -2.**1023, 2.**970], OverflowError),
([2.**930, -2.**980, 2.**1023, 2.**1023, twopow, -twopow],
OverflowError),
([2.**1023, 2.**1023, -1e307], OverflowError),
([1e16, 1., 1e-16], 10000000000000002.0),
([1e16-2., 1.-2.**53, -(1e16-2.), -(1.-2.**53)], 0.0),
]
for i, (vals, s) in enumerate(test_values):
if isinstance(s, type) and issubclass(s, Exception):
try:
m = math.sum(vals)
except s:
pass
else:
self.fail("test %d failed: got %r, expected %r "
"for math.sum(%.100r)" %
(i, m, s.__name__, vals))
else:
try:
self.assertEqual(math.sum(vals), s)
except OverflowError:
self.fail("test %d failed: got OverflowError, expected %r "
"for math.sum(%.100r)" % (i, s, vals))
except ValueError:
self.fail("test %d failed: got ValueError, expected %r "
"for math.sum(%.100r)" % (i, s, vals))
# compare with output of msum above, but only when
# result isn't an IEEE special or an exception
if not math.isinf(s) and not math.isnan(s):
self.assertEqual(msum(vals), s)
from random import random, gauss, shuffle
for j in xrange(1000):
vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
s = 0
for i in xrange(200):
v = gauss(0, random()) ** 7 - s
s += v
vals.append(v)
shuffle(vals)
s = msum(vals)
self.assertEqual(msum(vals), math.sum(vals))
def testTan(self):
self.assertRaises(TypeError, math.tan)
self.ftest('tan(0)', math.tan(0), 0)