Merged revisions 65258,65292,65299,65308-65309,65315,65326 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r65258 | mark.dickinson | 2008-07-27 08:15:29 +0100 (Sun, 27 Jul 2008) | 4 lines

  Remove math.sum tests related to overflow, special values, and behaviour
  near the extremes of the floating-point range.  (The behaviour of math.sum
  should be regarded as undefined in these cases.)
........
  r65292 | mark.dickinson | 2008-07-29 19:45:38 +0100 (Tue, 29 Jul 2008) | 4 lines

  More modifications to tests for math.sum:  replace the Python
  version of msum by a version using a different algorithm, and
  use the new float.fromhex method to specify test results exactly.
........
  r65299 | mark.dickinson | 2008-07-30 13:01:41 +0100 (Wed, 30 Jul 2008) | 5 lines

  Fix special-value handling for math.sum.
  Also minor cleanups to the code: fix tabbing, remove
  trailing whitespace, and reformat to fit into 80
  columns.
........
  r65308 | mark.dickinson | 2008-07-30 17:20:10 +0100 (Wed, 30 Jul 2008) | 2 lines

  Rename math.sum to math.fsum
........
  r65309 | mark.dickinson | 2008-07-30 17:25:16 +0100 (Wed, 30 Jul 2008) | 3 lines

  Replace math.sum with math.fsum in a couple of comments
  that were missed by r65308
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  r65315 | mark.dickinson | 2008-07-30 21:23:15 +0100 (Wed, 30 Jul 2008) | 2 lines

  Add note about problems with math.fsum on x86 hardware.
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  r65326 | mark.dickinson | 2008-07-31 15:48:32 +0100 (Thu, 31 Jul 2008) | 2 lines

  Rename testSum to testFsum and move it to proper place in test_math.py
........

2 files changed, 97 insertions, 153 deletions

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 1eafeba..9e646ac 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -359,6 +359,102 @@ class MathTests(unittest.TestCase):
         self.assertEquals(math.frexp(NINF)[0], NINF)
         self.assert_(math.isnan(math.frexp(NAN)[0]))
 
+    def testFsum(self):
+        # math.fsum relies on exact rounding for correct operation.
+        # There's a known problem with IA32 floating-point that causes
+        # inexact rounding in some situations, and will cause the
+        # math.fsum tests below to fail; see issue #2937.  On non IEEE
+        # 754 platforms, and on IEEE 754 platforms that exhibit the
+        # problem described in issue #2937, we simply skip the whole
+        # test.
+
+        if not float.__getformat__("double").startswith("IEEE"):
+            return
+
+        # on IEEE 754 compliant machines, both of the expressions
+        # below should round to 10000000000000002.0.
+        if 1e16+2.0 != 1e16+2.9999:
+            return
+
+        # Python version of math.fsum, for comparison.  Uses a
+        # different algorithm based on frexp, ldexp and integer
+        # arithmetic.
+        from sys import float_info
+        mant_dig = float_info.mant_dig
+        etiny = float_info.min_exp - mant_dig
+
+        def msum(iterable):
+            """Full precision summation.  Compute sum(iterable) without any
+            intermediate accumulation of error.  Based on the 'lsum' function
+            at http://code.activestate.com/recipes/393090/
+
+            """
+            tmant, texp = 0, 0
+            for x in iterable:
+                mant, exp = math.frexp(x)
+                mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
+                if texp > exp:
+                    tmant <<= texp-exp
+                    texp = exp
+                else:
+                    mant <<= exp-texp
+                tmant += mant
+            # Round tmant * 2**texp to a float.  The original recipe
+            # used float(str(tmant)) * 2.0**texp for this, but that's
+            # a little unsafe because str -> float conversion can't be
+            # relied upon to do correct rounding on all platforms.
+            tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
+            if tail > 0:
+                h = 1 << (tail-1)
+                tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
+                texp += tail
+            return math.ldexp(tmant, texp)
+
+        test_values = [
+            ([], 0.0),
+            ([0.0], 0.0),
+            ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
+            ([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),
+            ([1./n for n in range(1, 1001)],
+             float.fromhex('0x1.df11f45f4e61ap+2')),
+            ([(-1.)**n/n for n in range(1, 1001)],
+             float.fromhex('-0x1.62a2af1bd3624p-1')),
+            ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),
+            ([1e16, 1., 1e-16], 10000000000000002.0),
+            ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),
+            # exercise code for resizing partials array
+            ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
+             [-2.**1022],
+             float.fromhex('0x1.5555555555555p+970')),
+            ]
+
+        for i, (vals, expected) in enumerate(test_values):
+            try:
+                actual = math.fsum(vals)
+            except OverflowError:
+                self.fail("test %d failed: got OverflowError, expected %r "
+                          "for math.fsum(%.100r)" % (i, expected, vals))
+            except ValueError:
+                self.fail("test %d failed: got ValueError, expected %r "
+                          "for math.fsum(%.100r)" % (i, expected, vals))
+            self.assertEqual(actual, expected)
+
+        from random import random, gauss, shuffle
+        for j in range(1000):
+            vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
+            s = 0
+            for i in range(200):
+                v = gauss(0, random()) ** 7 - s
+                s += v
+                vals.append(v)
+            shuffle(vals)
+
+            s = msum(vals)
+            self.assertEqual(msum(vals), math.fsum(vals))
+
     def testHypot(self):
         self.assertRaises(TypeError, math.hypot)
         self.ftest('hypot(0,0)', math.hypot(0,0), 0)
@@ -641,158 +737,6 @@ class MathTests(unittest.TestCase):
         self.assertRaises(ValueError, math.sqrt, NINF)
         self.assert_(math.isnan(math.sqrt(NAN)))
 
-    def testSum(self):
-        # math.sum relies on exact rounding for correct operation.
-        # There's a known problem with IA32 floating-point that causes
-        # inexact rounding in some situations, and will cause the
-        # math.sum tests below to fail; see issue #2937.  On non IEEE
-        # 754 platforms, and on IEEE 754 platforms that exhibit the
-        # problem described in issue #2937, we simply skip the whole
-        # test.
-
-        if not float.__getformat__("double").startswith("IEEE"):
-            return
-
-        # on IEEE 754 compliant machines, both of the expressions
-        # below should round to 10000000000000002.0.
-        if 1e16+2.999 != 1e16+2.9999:
-            return
-
-        # 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 range(1000):
-            vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
-            s = 0
-            for i in range(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)
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index da62a4f..14e9fca 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -5,7 +5,7 @@ import random
 import time
 import pickle
 import warnings
-from math import log, exp, sqrt, pi, sum as msum
+from math import log, exp, sqrt, pi, fsum as msum
 from test import support
 
 class TestBasicOps(unittest.TestCase):