Merged revisions 63562,63570,63728,63734,63784,63788,63802,63817,63827,63839,63887,63975,63998 via svnmerge from

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

........
  r63562 | martin.v.loewis | 2008-05-23 17:06:50 +0200 (Fri, 23 May 2008) | 2 lines

  Patch #1722225: Support QNX 6.
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  r63570 | trent.nelson | 2008-05-23 22:33:14 +0200 (Fri, 23 May 2008) | 1 line

  Introduce a user macro named $(externalsDir), which should point to the root directory of where all the external sources should live.  Developers can change this value if their external sources live elsewhere.  The default of '..\..' matches the current status quo.
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  r63728 | gregory.p.smith | 2008-05-26 23:16:34 +0200 (Mon, 26 May 2008) | 4 lines

  Fix issue2589: there was a potential integer overflow leading to
  memory corruption on esoteric platforms and incorrect behavior on
  normal platforms.
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  r63734 | gregory.p.smith | 2008-05-27 00:07:28 +0200 (Tue, 27 May 2008) | 3 lines

  Fix issue2588: Do not execute str[size-1] = '\0' when a 0 size is
  passed in.  (The assert won't prevent this in non-debug builds).
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  r63784 | raymond.hettinger | 2008-05-29 10:38:23 +0200 (Thu, 29 May 2008) | 1 line

  Fix two typos.
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  r63788 | facundo.batista | 2008-05-29 18:39:26 +0200 (Thu, 29 May 2008) | 6 lines


  Fixed the semantic of timeout for socket.create_connection and
  all the upper level libraries that use it, including urllib2.
  Added and fixed some tests, and changed docs correspondingly.
  Thanks to John J Lee for the patch and the pusing, :)
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  r63802 | mark.dickinson | 2008-05-30 04:46:53 +0200 (Fri, 30 May 2008) | 2 lines

  Fix typo in testSum
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  r63817 | raymond.hettinger | 2008-05-30 20:20:50 +0200 (Fri, 30 May 2008) | 8 lines

  * Mark intermedidate computes values (hi, lo, yr) as volatile.
  * Expand comments.
  * Swap variable names in the sum_exact code so that x and y
    are consistently chosen as the larger and smaller magnitude
    values respectively.
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  r63827 | raymond.hettinger | 2008-05-31 05:24:31 +0200 (Sat, 31 May 2008) | 1 line

  Implement heapq in terms of less-than (to match list.sort()).
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  r63839 | gerhard.haering | 2008-05-31 23:33:27 +0200 (Sat, 31 May 2008) | 2 lines

  Fixed rowcount for SELECT statements. They're -1 now (again), for better DB-API 2.0 compliance.
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  r63887 | gregory.p.smith | 2008-06-02 06:05:52 +0200 (Mon, 02 Jun 2008) | 4 lines

  Fix issue 2782: be less strict about the format string type in strftime.
  Accept unicode and anything else ParseTuple "s#" can deal with.  This
  matches the time.strftime behavior.
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  r63975 | neal.norwitz | 2008-06-06 06:47:01 +0200 (Fri, 06 Jun 2008) | 3 lines

  Aldo Cortesi confirmed this is still needed for OpenBSD 4.2 and 4.3.
  (I didn't regen configure, since I don't have a working autoconf.)
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  r63998 | raymond.hettinger | 2008-06-06 23:47:51 +0200 (Fri, 06 Jun 2008) | 1 line

  Issue 3501: Make heapq support both __le__ and __lt__.
........

1 files changed, 32 insertions, 20 deletions

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 5c5def2..16c829a 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -373,14 +373,20 @@ FUNC1(tanh, tanh, 0,
    value semantics across iterations (i.e. handling -Inf + Inf).
 
    Note 2:  No provision is made for intermediate overflow handling;
-   therefore, sum([1e+308, 1e-308, 1e+308]) returns result 1e+308 while
+   therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
    sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
    overflow of the first partial sum.
 
-   Note 3: Aggressively optimizing compilers can potentially eliminate the
-   residual values needed for accurate summation. For instance, the statements
-   "hi = x + y; lo = y - (hi - x);" could be mis-transformed to
-   "hi = x + y; lo = 0.0;" which defeats the computation of residuals.
+   Note 3: The itermediate values lo, yr, and hi are declared volatile so
+   aggressive compilers won't algebraicly reduce lo to always be exactly 0.0.
+   Also, the volatile declaration forces the values to be stored in memory as
+   regular doubles instead of extended long precision (80-bit) values.  This
+   prevents double rounding because any addition or substraction of two doubles
+   can be resolved exactly into double-sized hi and lo values.  As long as the 
+   hi value gets forced into a double before yr and lo are computed, the extra
+   bits in downstream extended precision operations (x87 for example) will be
+   exactly zero and therefore can be losslessly stored back into a double,
+   thereby preventing double rounding.
 
    Note 4: A similar implementation is in Modules/cmathmodule.c.
    Be sure to update both when making changes.
@@ -457,7 +463,8 @@ math_sum(PyObject *self, PyObject *seq)
 {
 	PyObject *item, *iter, *sum = NULL;
 	Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
-	double x, y, hi, lo=0.0, ps[NUM_PARTIALS], *p = ps;
+	double x, y, t, ps[NUM_PARTIALS], *p = ps;
+	volatile double hi, yr, lo;
 
 	iter = PyObject_GetIter(seq);
 	if (iter == NULL)
@@ -483,10 +490,12 @@ math_sum(PyObject *self, PyObject *seq)
 
 		for (i = j = 0; j < n; j++) {       /* for y in partials */
 			y = p[j];
+			if (fabs(x) < fabs(y)) {
+					t = x; x = y; y = t;
+			}
 			hi = x + y;
-			lo = fabs(x) < fabs(y)
-			   ? x - (hi - y)
-			   : y - (hi - x);
+			yr = hi - x;
+			lo = y - yr;
 			if (lo != 0.0)
 				p[i++] = lo;
 			x = hi;
@@ -506,38 +515,41 @@ math_sum(PyObject *self, PyObject *seq)
 		}
 	}
 
+	hi = 0.0;
 	if (n > 0) {
 		hi = p[--n];
 		if (Py_IS_FINITE(hi)) {
 			/* sum_exact(ps, hi) from the top, stop when the sum becomes inexact. */
 			while (n > 0) {
-				x = p[--n];
-				y = hi;
+				x = hi;
+				y = p[--n];
+				assert(fabs(y) < fabs(x));
 				hi = x + y;
-				assert(fabs(x) < fabs(y));
-				lo = x - (hi - y);
+				yr = hi - x;
+				lo = y - yr;
 				if (lo != 0.0)
 					break;
 			}
-			/* Little dance to allow half-even rounding across multiple partials.
-                           Needed so that sum([1e-16, 1, 1e16]) will round-up to two instead
-                           of down to zero (the 1e16 makes the 1 slightly closer to two). */
+			/* Make half-even rounding work across multiple partials.  Needed 
+			   so that sum([1e-16, 1, 1e16]) will round-up the last digit to 
+			   two instead of down to zero (the 1e-16 makes the 1 slightly 
+			   closer to two).  With a potential 1 ULP rounding error fixed-up,
+			   math.sum() can guarantee commutativity. */
 			if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
 			              (lo > 0.0 && p[n-1] > 0.0))) {
 				y = lo * 2.0;
 				x = hi + y;
-				if (y == (x - hi))
+				yr = x - hi;
+				if (y == yr)
 					hi = x;
 			}
 		}
-		else {  /* raise corresponding error */
+		else {  /* raise exception corresponding to a special value */
 			errno = Py_IS_NAN(hi) ? EDOM : ERANGE;
 			if (is_error(hi))
 				goto _sum_error;
 		}
 	}
-	else  /* default */
-		hi = 0.0;
 	sum = PyFloat_FromDouble(hi);
 
 _sum_error: