diff -Naurd mpfr-3.1.3-a/PATCHES mpfr-3.1.3-b/PATCHES
--- mpfr-3.1.3-a/PATCHES	2015-07-17 08:58:21.094987384 +0000
+++ mpfr-3.1.3-b/PATCHES	2015-07-17 08:58:21.118986898 +0000
@@ -0,0 +1 @@
+frexp
diff -Naurd mpfr-3.1.3-a/VERSION mpfr-3.1.3-b/VERSION
--- mpfr-3.1.3-a/VERSION	2015-07-17 08:54:48.616811495 +0000
+++ mpfr-3.1.3-b/VERSION	2015-07-17 08:58:21.118986898 +0000
@@ -1 +1 @@
-3.1.3-p3
+3.1.3-p4
diff -Naurd mpfr-3.1.3-a/src/frexp.c mpfr-3.1.3-b/src/frexp.c
--- mpfr-3.1.3-a/src/frexp.c	2015-06-19 19:55:09.000000000 +0000
+++ mpfr-3.1.3-b/src/frexp.c	2015-07-17 08:58:21.106987142 +0000
@@ -26,6 +26,13 @@
 mpfr_frexp (mpfr_exp_t *exp, mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
 {
   int inex;
+  unsigned int saved_flags = __gmpfr_flags;
+  MPFR_BLOCK_DECL (flags);
+
+  MPFR_LOG_FUNC
+    (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd),
+     ("y[%Pu]=%.*Rg exp=%" MPFR_EXP_FSPEC "d inex=%d", mpfr_get_prec (y),
+      mpfr_log_prec, y, (mpfr_eexp_t) *exp, inex));
 
   if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
     {
@@ -49,8 +56,32 @@
         }
     }
 
-  inex = mpfr_set (y, x, rnd);
+  MPFR_BLOCK (flags, inex = mpfr_set (y, x, rnd));
+  __gmpfr_flags = saved_flags;
+
+  /* Possible overflow due to the rounding, no possible underflow. */
+
+  if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags)))
+    {
+      int inex2;
+
+      /* An overflow here means that the exponent of y would be larger than
+         the one of x, thus x would be rounded to the next power of 2, and
+         the returned y should be 1/2 in absolute value, rounded (i.e. with
+         possible underflow or overflow). This also implies that x and y are
+         different objects, so that the exponent of x has not been lost. */
+      MPFR_LOG_MSG (("Internal overflow\n", 0));
+      MPFR_ASSERTD (x != y);
+      *exp = MPFR_GET_EXP (x) + 1;
+      inex2 = mpfr_set_si_2exp (y, MPFR_INT_SIGN (x), -1, rnd);
+      MPFR_LOG_MSG (("inex=%d inex2=%d\n", inex, inex2));
+      if (inex2 != 0)
+        inex = inex2;
+      MPFR_RET (inex);
+    }
+
   *exp = MPFR_GET_EXP (y);
-  MPFR_SET_EXP (y, 0);
+  /* Do not use MPFR_SET_EXP because the range has not been checked yet. */
+  MPFR_EXP (y) = 0;
   return mpfr_check_range (y, inex, rnd);
 }
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	2015-07-17 08:54:48.616811495 +0000
+++ mpfr-3.1.3-b/src/mpfr.h	2015-07-17 08:58:21.114986979 +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-p3"
+#define MPFR_VERSION_STRING "3.1.3-p4"
 
 /* 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/version.c mpfr-3.1.3-b/src/version.c
--- mpfr-3.1.3-a/src/version.c	2015-07-17 08:54:48.616811495 +0000
+++ mpfr-3.1.3-b/src/version.c	2015-07-17 08:58:21.118986898 +0000
@@ -25,5 +25,5 @@
 const char *
 mpfr_get_version (void)
 {
-  return "3.1.3-p3";
+  return "3.1.3-p4";
 }
diff -Naurd mpfr-3.1.3-a/tests/tfrexp.c mpfr-3.1.3-b/tests/tfrexp.c
--- mpfr-3.1.3-a/tests/tfrexp.c	2015-06-19 19:55:10.000000000 +0000
+++ mpfr-3.1.3-b/tests/tfrexp.c	2015-07-17 08:58:21.106987142 +0000
@@ -129,12 +129,115 @@
   mpfr_clear (x);
 }
 
+static void check1 (void)
+{
+  mpfr_exp_t emin, emax, e;
+  mpfr_t x, y1, y2;
+  int r, neg, red;
+
+  emin = mpfr_get_emin ();
+  emax = mpfr_get_emax ();
+  set_emin (MPFR_EMIN_MIN);
+  set_emax (MPFR_EMAX_MAX);
+
+  mpfr_init2 (x, 7);
+  mpfr_inits2 (4, y1, y2, (mpfr_ptr) 0);
+
+  mpfr_set_ui_2exp (x, 1, -2, MPFR_RNDN);
+  while (mpfr_regular_p (x))
+    {
+      /* Test the exponents up to 3 and with the maximum exponent
+         (to check potential intermediate overflow). */
+      if (MPFR_GET_EXP (x) == 4)
+        mpfr_set_exp (x, MPFR_EMAX_MAX);
+      e = MPFR_GET_EXP (x);
+      for (neg = 0; neg < 2; neg++)
+        {
+          RND_LOOP (r)
+            {
+              int inex1, inex2;
+              mpfr_exp_t e1, e2;
+              unsigned int flags1, flags2;
+
+              for (red = 0; red < 2; red++)
+                {
+                  if (red)
+                    {
+                      /* e1: exponent of the rounded value of x. */
+                      MPFR_ASSERTN (e1 == e || e1 == e + 1);
+                      set_emin (e);
+                      set_emax (e);
+                      mpfr_clear_flags ();
+                      inex1 = e1 < 0 ?
+                        mpfr_mul_2ui (y1, x, -e1, (mpfr_rnd_t) r) :
+                        mpfr_div_2ui (y1, x, e1, (mpfr_rnd_t) r);
+                      flags1 = __gmpfr_flags;
+                    }
+                  else
+                    {
+                      inex1 = mpfr_set (y1, x, (mpfr_rnd_t) r);
+                      e1 = MPFR_IS_INF (y1) ? e + 1 : MPFR_GET_EXP (y1);
+                      flags1 = inex1 != 0 ? MPFR_FLAGS_INEXACT : 0;
+                    }
+                  mpfr_clear_flags ();
+                  inex2 = mpfr_frexp (&e2, y2, x, (mpfr_rnd_t) r);
+                  flags2 = __gmpfr_flags;
+                  set_emin (MPFR_EMIN_MIN);
+                  set_emax (MPFR_EMAX_MAX);
+                  if ((!red || e == 0) &&
+                      (! mpfr_regular_p (y2) || MPFR_GET_EXP (y2) != 0))
+                    {
+                      printf ("Error in check1 for %s, red = %d, x = ",
+                              mpfr_print_rnd_mode ((mpfr_rnd_t) r), red);
+                      mpfr_dump (x);
+                      printf ("Expected 1/2 <= |y| < 1, got y = ");
+                      mpfr_dump (y2);
+                      exit (1);
+                    }
+                  if (!red)
+                    {
+                      if (e2 > 0)
+                        mpfr_mul_2ui (y2, y2, e2, MPFR_RNDN);
+                      else if (e2 < 0)
+                        mpfr_div_2ui (y2, y2, -e2, MPFR_RNDN);
+                    }
+                  if (! (SAME_SIGN (inex1, inex2) &&
+                         mpfr_equal_p (y1, y2) &&
+                         flags1 == flags2))
+                    {
+                      printf ("Error in check1 for %s, red = %d, x = ",
+                              mpfr_print_rnd_mode ((mpfr_rnd_t) r), red);
+                      mpfr_dump (x);
+                      printf ("Expected y1 = ");
+                      mpfr_dump (y1);
+                      printf ("Got      y2 = ");
+                      mpfr_dump (y2);
+                      printf ("Expected inex ~= %d, got %d\n", inex1, inex2);
+                      printf ("Expected flags:");
+                      flags_out (flags1);
+                      printf ("Got flags:     ");
+                      flags_out (flags2);
+                      exit (1);
+                    }
+                }
+            }
+          mpfr_neg (x, x, MPFR_RNDN);
+        }
+      mpfr_nextabove (x);
+    }
+
+  mpfr_clears (x, y1, y2, (mpfr_ptr) 0);
+  set_emin (emin);
+  set_emax (emax);
+}
+
 int
 main (int argc, char *argv[])
 {
   tests_start_mpfr ();
 
   check_special ();
+  check1 ();
 
   tests_end_mpfr ();
   return 0;