diff -Naurd mpfr-3.1.3-a/PATCHES mpfr-3.1.3-b/PATCHES
--- mpfr-3.1.3-a/PATCHES	2016-02-15 15:11:00.898156344 +0000
+++ mpfr-3.1.3-b/PATCHES	2016-02-15 15:11:00.966156445 +0000
@@ -0,0 +1 @@
+zeta
diff -Naurd mpfr-3.1.3-a/VERSION mpfr-3.1.3-b/VERSION
--- mpfr-3.1.3-a/VERSION	2016-02-15 15:10:03.414066216 +0000
+++ mpfr-3.1.3-b/VERSION	2016-02-15 15:11:00.966156445 +0000
@@ -1 +1 @@
-3.1.3-p6
+3.1.3-p7
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	2016-02-15 15:10:03.410066210 +0000
+++ mpfr-3.1.3-b/src/mpfr.h	2016-02-15 15:11:00.962156439 +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-p6"
+#define MPFR_VERSION_STRING "3.1.3-p7"
 
 /* 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	2016-02-15 15:10:03.414066216 +0000
+++ mpfr-3.1.3-b/src/version.c	2016-02-15 15:11:00.966156445 +0000
@@ -25,5 +25,5 @@
 const char *
 mpfr_get_version (void)
 {
-  return "3.1.3-p6";
+  return "3.1.3-p7";
 }
diff -Naurd mpfr-3.1.3-a/src/zeta.c mpfr-3.1.3-b/src/zeta.c
--- mpfr-3.1.3-a/src/zeta.c	2015-06-19 19:55:10.000000000 +0000
+++ mpfr-3.1.3-b/src/zeta.c	2016-02-15 15:11:00.942156410 +0000
@@ -377,8 +377,8 @@
         }
     }
 
-  /* Check for case s= 1 before changing the exponent range */
-  if (mpfr_cmp (s, __gmpfr_one) ==0)
+  /* Check for case s=1 before changing the exponent range */
+  if (mpfr_cmp (s, __gmpfr_one) == 0)
     {
       MPFR_SET_INF (z);
       MPFR_SET_POS (z);
@@ -420,7 +420,7 @@
       MPFR_ZIV_INIT (loop, prec1);
       for (;;)
         {
-          mpfr_sub (s1, __gmpfr_one, s, MPFR_RNDN);/* s1 = 1-s */
+          mpfr_sub (s1, __gmpfr_one, s, MPFR_RNDN); /* s1 = 1-s */
           mpfr_zeta_pos (z_pre, s1, MPFR_RNDN);   /* zeta(1-s)  */
           mpfr_gamma (y, s1, MPFR_RNDN);          /* gamma(1-s) */
           if (MPFR_IS_INF (y)) /* Zeta(s) < 0 for -4k-2 < s < -4k,
@@ -432,17 +432,32 @@
               break;
             }
           mpfr_mul (z_pre, z_pre, y, MPFR_RNDN);  /* gamma(1-s)*zeta(1-s) */
-          mpfr_const_pi (p, MPFR_RNDD);
-          mpfr_mul (y, s, p, MPFR_RNDN);
-          mpfr_div_2ui (y, y, 1, MPFR_RNDN);      /* s*Pi/2 */
-          mpfr_sin (y, y, MPFR_RNDN);             /* sin(Pi*s/2) */
-          mpfr_mul (z_pre, z_pre, y, MPFR_RNDN);
+
+          mpfr_const_pi (p, MPFR_RNDD); /* p is Pi */
+
+          /* multiply z_pre by 2^s*Pi^(s-1) where p=Pi, s1=1-s */
           mpfr_mul_2ui (y, p, 1, MPFR_RNDN);      /* 2*Pi */
           mpfr_neg (s1, s1, MPFR_RNDN);           /* s-1 */
           mpfr_pow (y, y, s1, MPFR_RNDN);         /* (2*Pi)^(s-1) */
           mpfr_mul (z_pre, z_pre, y, MPFR_RNDN);
           mpfr_mul_2ui (z_pre, z_pre, 1, MPFR_RNDN);
 
+          /* multiply z_pre by sin(Pi*s/2) */
+          mpfr_mul (y, s, p, MPFR_RNDN);
+          mpfr_div_2ui (p, y, 1, MPFR_RNDN);      /* p = s*Pi/2 */
+          mpfr_sin (y, p, MPFR_RNDN);             /* y = sin(Pi*s/2) */
+          if (MPFR_GET_EXP(y) < 0) /* take account of cancellation in sin(p) */
+            {
+              mpfr_t t;
+              mpfr_init2 (t, prec1 - MPFR_GET_EXP(y));
+              mpfr_const_pi (t, MPFR_RNDD);
+              mpfr_mul (t, s, t, MPFR_RNDN);
+              mpfr_div_2ui (t, t, 1, MPFR_RNDN);
+              mpfr_sin (y, t, MPFR_RNDN);
+              mpfr_clear (t);
+            }
+          mpfr_mul (z_pre, z_pre, y, MPFR_RNDN);
+
           if (MPFR_LIKELY (MPFR_CAN_ROUND (z_pre, prec1 - add, precz,
                                            rnd_mode)))
             break;
diff -Naurd mpfr-3.1.3-a/tests/tzeta.c mpfr-3.1.3-b/tests/tzeta.c
--- mpfr-3.1.3-a/tests/tzeta.c	2015-06-19 19:55:10.000000000 +0000
+++ mpfr-3.1.3-b/tests/tzeta.c	2016-02-15 15:11:00.942156410 +0000
@@ -394,6 +394,27 @@
   mpfr_nextabove (s);
   MPFR_ASSERTN (mpfr_equal_p (z, s) && inex > 0);
 
+  /* bug reported by Fredrik Johansson on 19 Jan 2016 */
+  mpfr_set_prec (s, 536);
+  mpfr_set_ui_2exp (s, 1, -424, MPFR_RNDN);
+  mpfr_sub_ui (s, s, 128, MPFR_RNDN);  /* -128 + 2^(-424) */
+  for (prec = 6; prec <= 536; prec += 8) /* should go through 318 */
+    {
+      mpfr_set_prec (z, prec);
+      mpfr_zeta (z, s, MPFR_RNDD);
+      mpfr_set_prec (y, prec + 10);
+      mpfr_zeta (y, s, MPFR_RNDD);
+      mpfr_prec_round (y, prec, MPFR_RNDD);
+      if (! mpfr_equal_p (z, y))
+        {
+          printf ("mpfr_zeta fails near -128 for inprec=%lu outprec=%lu\n",
+                  (unsigned long) mpfr_get_prec (s), (unsigned long) prec);
+          printf ("expected "); mpfr_dump (y);
+          printf ("got      "); mpfr_dump (z);
+          exit (1);
+        }
+    }
+
   mpfr_clear (s);
   mpfr_clear (y);
   mpfr_clear (z);