diff -Naurd mpfr-3.1.3-a/PATCHES mpfr-3.1.3-b/PATCHES
--- mpfr-3.1.3-a/PATCHES	2016-02-23 07:55:54.028346753 +0000
+++ mpfr-3.1.3-b/PATCHES	2016-02-23 07:55:54.052346433 +0000
@@ -0,0 +1 @@
+sum
diff -Naurd mpfr-3.1.3-a/VERSION mpfr-3.1.3-b/VERSION
--- mpfr-3.1.3-a/VERSION	2016-02-23 07:55:17.232592762 +0000
+++ mpfr-3.1.3-b/VERSION	2016-02-23 07:55:54.052346433 +0000
@@ -1 +1 @@
-3.1.3-p15
+3.1.3-p16
diff -Naurd mpfr-3.1.3-a/src/mpfr-impl.h mpfr-3.1.3-b/src/mpfr-impl.h
--- mpfr-3.1.3-a/src/mpfr-impl.h	2015-06-19 19:55:09.000000000 +0000
+++ mpfr-3.1.3-b/src/mpfr-impl.h	2016-02-23 07:55:54.040346593 +0000
@@ -1876,7 +1876,8 @@
 __MPFR_DECLSPEC int mpfr_check _MPFR_PROTO ((mpfr_srcptr));
 
 __MPFR_DECLSPEC int mpfr_sum_sort _MPFR_PROTO ((mpfr_srcptr *const,
-                                                unsigned long, mpfr_srcptr *));
+                                                unsigned long, mpfr_srcptr *,
+                                                mpfr_prec_t *));
 
 __MPFR_DECLSPEC int mpfr_get_cputime _MPFR_PROTO ((void));
 
diff -Naurd mpfr-3.1.3-a/src/mpfr.h mpfr-3.1.3-b/src/mpfr.h
--- mpfr-3.1.3-a/src/mpfr.h	2016-02-23 07:55:17.232592762 +0000
+++ mpfr-3.1.3-b/src/mpfr.h	2016-02-23 07:55:54.052346433 +0000
@@ -27,7 +27,7 @@
 #define MPFR_VERSION_MAJOR 3
 #define MPFR_VERSION_MINOR 1
 #define MPFR_VERSION_PATCHLEVEL 3
-#define MPFR_VERSION_STRING "3.1.3-p15"
+#define MPFR_VERSION_STRING "3.1.3-p16"
 
 /* Macros dealing with MPFR VERSION */
 #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
diff -Naurd mpfr-3.1.3-a/src/sum.c mpfr-3.1.3-b/src/sum.c
--- mpfr-3.1.3-a/src/sum.c	2015-06-19 19:55:09.000000000 +0000
+++ mpfr-3.1.3-b/src/sum.c	2016-02-23 07:55:54.040346593 +0000
@@ -45,9 +45,13 @@
                         mpfr_exp_t, mpfr_uexp_t);
 
 /* Either sort the tab in perm and returns 0
-   Or returns 1 for +INF, -1 for -INF and 2 for NAN */
+   Or returns 1 for +INF, -1 for -INF and 2 for NAN.
+   Also set *maxprec to the maximal precision of tab[0..n-1] and of the
+   initial value of *maxprec.
+*/
 int
-mpfr_sum_sort (mpfr_srcptr *const tab, unsigned long n, mpfr_srcptr *perm)
+mpfr_sum_sort (mpfr_srcptr *const tab, unsigned long n, mpfr_srcptr *perm,
+               mpfr_prec_t *maxprec)
 {
   mpfr_exp_t min, max;
   mpfr_uexp_t exp_num;
@@ -79,6 +83,8 @@
           if (MPFR_GET_EXP (tab[i]) > max)
             max = MPFR_GET_EXP(tab[i]);
         }
+      if (MPFR_PREC (tab[i]) > *maxprec)
+        *maxprec = MPFR_PREC (tab[i]);
     }
   if (MPFR_UNLIKELY (sign_inf != 0))
     return sign_inf;
@@ -213,7 +219,8 @@
 
 
 /* Sum a list of float with order given by permutation perm,
- * intermediate size set to F.
+ * intermediate size set to F. Return non-zero if at least one of
+ * the operations is inexact (thus 0 implies that the sum is exact).
  * Internal use function.
  */
 static int
@@ -230,16 +237,19 @@
   for (i = 1; i < n - 1; i++)
     {
       MPFR_ASSERTD (!MPFR_IS_NAN (sum) && !MPFR_IS_INF (sum));
-      error_trap |= mpfr_add (sum, sum, tab[i], MPFR_RNDN);
+      if (mpfr_add (sum, sum, tab[i], MPFR_RNDN))
+        error_trap = 1;
     }
-  error_trap |= mpfr_add (ret, sum, tab[n - 1], MPFR_RNDN);
+  if (mpfr_add (ret, sum, tab[n - 1], MPFR_RNDN))
+    error_trap = 1;
   mpfr_clear (sum);
   return error_trap;
 }
 
 /* Sum a list of floating-point numbers.
+ * If the return value is 0, then the sum is exact.
+ * Otherwise the return value gives no information.
  */
-
 int
 mpfr_sum (mpfr_ptr ret, mpfr_ptr *const tab_p, unsigned long n, mpfr_rnd_t rnd)
 {
@@ -266,7 +276,8 @@
   /* Sort and treat special cases */
   MPFR_TMP_MARK (marker);
   perm = (mpfr_srcptr *) MPFR_TMP_ALLOC (n * sizeof *perm);
-  error_trap = mpfr_sum_sort (tab, n, perm);
+  prec = MPFR_PREC (ret);
+  error_trap = mpfr_sum_sort (tab, n, perm, &prec);
   /* Check if there was a NAN or a INF */
   if (MPFR_UNLIKELY (error_trap != 0))
     {
@@ -281,8 +292,7 @@
       MPFR_RET (0);
     }
 
-  /* Initial precision */
-  prec = MAX (MPFR_PREC (tab[0]), MPFR_PREC (ret));
+  /* Initial precision is max(prec(ret),prec(tab[0]),...,prec(tab[n-1])) */
   k = MPFR_INT_CEIL_LOG2 (n) + 1;
   prec += k + 2;
   mpfr_init2 (cur_sum, prec);
@@ -295,8 +305,7 @@
       error_trap = sum_once (cur_sum, perm, n, prec + k);
       if (MPFR_LIKELY (error_trap == 0 ||
                        (!MPFR_IS_ZERO (cur_sum) &&
-                        mpfr_can_round (cur_sum,
-                                        MPFR_GET_EXP (cur_sum) - prec + 2,
+                        mpfr_can_round (cur_sum, prec - 2,
                                         MPFR_RNDN, rnd, MPFR_PREC (ret)))))
         break;
       MPFR_ZIV_NEXT (loop, prec);
@@ -305,11 +314,13 @@
   MPFR_ZIV_FREE (loop);
   MPFR_TMP_FREE (marker);
 
-  error_trap |= mpfr_set (ret, cur_sum, rnd);
+  if (mpfr_set (ret, cur_sum, rnd))
+    error_trap = 1;
   mpfr_clear (cur_sum);
 
   MPFR_SAVE_EXPO_FREE (expo);
-  error_trap |= mpfr_check_range (ret, 0, rnd);
+  if (mpfr_check_range (ret, 0, rnd))
+    error_trap = 1;
   return error_trap; /* It doesn't return the ternary value */
 }
 
diff -Naurd mpfr-3.1.3-a/src/version.c mpfr-3.1.3-b/src/version.c
--- mpfr-3.1.3-a/src/version.c	2016-02-23 07:55:17.232592762 +0000
+++ mpfr-3.1.3-b/src/version.c	2016-02-23 07:55:54.052346433 +0000
@@ -25,5 +25,5 @@
 const char *
 mpfr_get_version (void)
 {
-  return "3.1.3-p15";
+  return "3.1.3-p16";
 }
diff -Naurd mpfr-3.1.3-a/tests/tsum.c mpfr-3.1.3-b/tests/tsum.c
--- mpfr-3.1.3-a/tests/tsum.c	2015-06-19 19:55:10.000000000 +0000
+++ mpfr-3.1.3-b/tests/tsum.c	2016-02-23 07:55:54.040346593 +0000
@@ -126,6 +126,7 @@
   mpfr_ptr *tabtmp;
   mpfr_srcptr *perm;
   unsigned long i;
+  mpfr_prec_t prec = MPFR_PREC_MIN;
 
   /* Init stuff */
   tab = (mpfr_t *) (*__gmp_allocate_func) (n * sizeof (mpfr_t));
@@ -140,7 +141,7 @@
       tabtmp[i] = tab[i];
     }
 
-  mpfr_sum_sort ((mpfr_srcptr *)tabtmp, n, perm);
+  mpfr_sum_sort ((mpfr_srcptr *)tabtmp, n, perm, &prec);
 
   if (check_is_sorted (n, perm) == 0)
     {
@@ -300,6 +301,41 @@
   mpfr_clears (tab[0], tab[1], tab[2], r, (mpfr_ptr) 0);
 }
 
+/* bug reported by Joseph S. Myers on 2013-10-27
+   https://sympa.inria.fr/sympa/arc/mpfr/2013-10/msg00015.html */
+static void
+bug20131027 (void)
+{
+  mpfr_t r, t[4];
+  mpfr_ptr p[4];
+  char *s[4] = {
+    "0x1p1000",
+    "-0x0.fffffffffffff80000000000000001p1000",
+    "-0x1p947",
+    "0x1p880"
+  };
+  int i;
+
+  mpfr_init2 (r, 53);
+  for (i = 0; i < 4; i++)
+    {
+      mpfr_init2 (t[i], i == 0 ? 53 : 1000);
+      mpfr_set_str (t[i], s[i], 0, MPFR_RNDN);
+      p[i] = t[i];
+    }
+  mpfr_sum (r, p, 4, MPFR_RNDN);
+
+  if (MPFR_NOTZERO (r))
+    {
+      printf ("mpfr_sum incorrect in bug20131027: expected 0, got\n");
+      mpfr_dump (r);
+      exit (1);
+    }
+
+  for (i = 0; i < 4; i++)
+    mpfr_clear (t[i]);
+  mpfr_clear (r);
+}
 
 int
 main (void)
@@ -310,6 +346,7 @@
   tests_start_mpfr ();
 
   check_special ();
+  bug20131027 ();
   test_sort (1764, 1026);
   for (p = 2 ; p < 444 ; p += 17)
     for (n = 2 ; n < 1026 ; n += 42 + p)