[Python-checkins] r63543 - python/trunk/Lib/test/test_math.py
mark.dickinson
python-checkins at python.org
Fri May 23 04:36:48 CEST 2008
Author: mark.dickinson
Date: Fri May 23 04:36:48 2008
New Revision: 63543
Log:
Add tests for math.sum (Issue #2819)
Modified:
python/trunk/Lib/test/test_math.py
Modified: python/trunk/Lib/test/test_math.py
==============================================================================
--- python/trunk/Lib/test/test_math.py (original)
+++ python/trunk/Lib/test/test_math.py Fri May 23 04:36:48 2008
@@ -630,6 +630,142 @@
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)
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