Index: Python/dtoa.c
===================================================================
--- Python/dtoa.c	(revision 77383)
+++ Python/dtoa.c	(working copy)
@@ -1138,11 +1138,14 @@
 {
     Bigint *b, *d;
     int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
+    U ulp_rv;
 
+    dval(&ulp_rv) = ulp(rv);
+
     dsign = bc->dsign;
     nd = bc->nd;
     nd0 = bc->nd0;
-    p5 = nd + bc->e0 - 1;
+    p5 = nd + bc->e0;
     speccase = 0;
     if (rv->d == 0.) {  /* special case: value near underflow-to-zero */
         /* threshold was rounded to zero */
@@ -1172,6 +1175,10 @@
     i = P - bbits;
     if (i > (j = P - Emin - 1 + p2)) {
         i = j;
+        if (bc->scale) {
+            word0(&ulp_rv) = (P+2)*Exp_msk1;
+            word1(&ulp_rv) = 0;
+        }
     }
     {
         b = lshift(b, ++i);
@@ -1227,17 +1234,21 @@
         }
     }
 
-    /* Now b/d = exactly half-way between the two floating-point values */
-    /* on either side of the input string.  Compute first digit of b/d. */
+    /* Now 10*b/d = exactly half-way between the two floating-point values */
+    /* on either side of the input string.  If b >= d, round down. */
+    if (cmp(b, d) >= 0) {
+        dd = -1;
+        goto ret;
+    }
 
-    if (!(dig = quorem(b,d))) {
-        b = multadd(b, 10, 0);  /* very unlikely */
-        if (b == NULL) {
-            Bfree(d);
-            return -1;
-        }
-        dig = quorem(b,d);
+    /* Compute first digit of 10*b/d. */
+    b = multadd(b, 10, 0);
+    if (b == NULL) {
+        Bfree(d);
+        return -1;
     }
+    dig = quorem(b, d);
+    assert(dig < 10);
 
     /* Compare b/d with s0 */
 
@@ -1285,12 +1296,12 @@
     else if (dd < 0) {
         if (!dsign)     /* does not happen for round-near */
           retlow1:
-            dval(rv) -= ulp(rv);
+            dval(rv) -= dval(&ulp_rv);
     }
     else if (dd > 0) {
         if (dsign) {
           rethi1:
-            dval(rv) += ulp(rv);
+            dval(rv) += dval(&ulp_rv);
         }
     }
     else {
Index: Lib/test/floating_points.txt
===================================================================
--- Lib/test/floating_points.txt	(revision 77383)
+++ Lib/test/floating_points.txt	(working copy)
@@ -1019,3 +1019,10 @@
 +43723334984997307E-26
 +10182419849537963E-24
 -93501703572661982E-26
+
+# A value that caused a crash in debug builds for Python >= 2.7, 3.1
+# See http://bugs.python.org/issue7632
+2183167012312112312312.23538020374420446192e-370
+
+# Another value designed to test a corner case of Python's strtod code.
+0.99999999999999999999999999999999999999999e+23