diff -Naurd mpfr-3.1.6-a/PATCHES mpfr-3.1.6-b/PATCHES
--- mpfr-3.1.6-a/PATCHES	2017-12-15 12:37:44.074256548 +0000
+++ mpfr-3.1.6-b/PATCHES	2017-12-15 12:37:44.146256304 +0000
@@ -0,0 +1 @@
+root
diff -Naurd mpfr-3.1.6-a/VERSION mpfr-3.1.6-b/VERSION
--- mpfr-3.1.6-a/VERSION	2017-10-26 13:55:51.236013121 +0000
+++ mpfr-3.1.6-b/VERSION	2017-12-15 12:37:44.142256319 +0000
@@ -1 +1 @@
-3.1.6-p1
+3.1.6-p2
diff -Naurd mpfr-3.1.6-a/src/mpfr.h mpfr-3.1.6-b/src/mpfr.h
--- mpfr-3.1.6-a/src/mpfr.h	2017-10-26 13:55:51.232013138 +0000
+++ mpfr-3.1.6-b/src/mpfr.h	2017-12-15 12:37:44.142256319 +0000
@@ -27,7 +27,7 @@
 #define MPFR_VERSION_MAJOR 3
 #define MPFR_VERSION_MINOR 1
 #define MPFR_VERSION_PATCHLEVEL 6
-#define MPFR_VERSION_STRING "3.1.6-p1"
+#define MPFR_VERSION_STRING "3.1.6-p2"
 
 /* Macros dealing with MPFR VERSION */
 #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
diff -Naurd mpfr-3.1.6-a/src/root.c mpfr-3.1.6-b/src/root.c
--- mpfr-3.1.6-a/src/root.c	2017-01-01 01:39:09.000000000 +0000
+++ mpfr-3.1.6-b/src/root.c	2017-12-15 12:37:44.118256398 +0000
@@ -107,6 +107,11 @@
       MPFR_RET_NAN;
     }
 
+  /* Special case |x| = 1. Note that if x = -1, then k is odd
+     (NaN results have already been filtered), so that y = -1. */
+  if (mpfr_cmpabs (x, __gmpfr_one) == 0)
+    return mpfr_set (y, x, rnd_mode);
+
   /* General case */
 
   /* For large k, use exp(log(x)/k). The threshold of 100 seems to be quite
@@ -188,6 +193,14 @@
    Assume all special cases have been eliminated before.
    In the extended exponent range, overflows/underflows are not possible.
    Assume x > 0, or x < 0 and k odd.
+   Also assume |x| <> 1 because log(1) = 0, which does not have an exponent
+   and would yield a failure in the error bound computation. A priori, this
+   constraint is quite artificial because if |x| is close enough to 1, then
+   the exponent of log|x| does not need to be used (in the code, err would
+   be 1 in such a domain). So this constraint |x| <> 1 could be avoided in
+   the code. However, this is an exact case easy to detect, so that such a
+   change would be useless. Values very close to 1 are not an issue, since
+   an underflow is not possible before the MPFR_GET_EXP.
 */
 static int
 mpfr_root_aux (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode)
@@ -219,7 +232,8 @@
       mpfr_log (t, absx, MPFR_RNDN);
       /* t = log|x| * (1 + theta) with |theta| <= 2^(-w) */
       mpfr_div_ui (t, t, k, MPFR_RNDN);
-      expt = MPFR_GET_EXP (t);
+      /* No possible underflow in mpfr_log and mpfr_div_ui. */
+      expt = MPFR_GET_EXP (t);  /* assumes t <> 0 */
       /* t = log|x|/k * (1 + theta) + eps with |theta| <= 2^(-w)
          and |eps| <= 1/2 ulp(t), thus the total error is bounded
          by 1.5 * 2^(expt - w) */
diff -Naurd mpfr-3.1.6-a/src/version.c mpfr-3.1.6-b/src/version.c
--- mpfr-3.1.6-a/src/version.c	2017-10-26 13:55:51.232013138 +0000
+++ mpfr-3.1.6-b/src/version.c	2017-12-15 12:37:44.142256319 +0000
@@ -25,5 +25,5 @@
 const char *
 mpfr_get_version (void)
 {
-  return "3.1.6-p1";
+  return "3.1.6-p2";
 }
diff -Naurd mpfr-3.1.6-a/tests/troot.c mpfr-3.1.6-b/tests/troot.c
--- mpfr-3.1.6-a/tests/troot.c	2017-01-01 01:39:09.000000000 +0000
+++ mpfr-3.1.6-b/tests/troot.c	2017-12-15 12:37:44.118256398 +0000
@@ -405,6 +405,26 @@
   mpfr_clears (x, y1, y2, (mpfr_ptr) 0);
 }
 
+static void
+bug20171214 (void)
+{
+  mpfr_t x, y;
+  int inex;
+
+  mpfr_init2 (x, 805);
+  mpfr_init2 (y, 837);
+  mpfr_set_ui (x, 1, MPFR_RNDN);
+  inex = mpfr_root (y, x, 120, MPFR_RNDN);
+  MPFR_ASSERTN (inex == 0);
+  MPFR_ASSERTN (mpfr_cmp_ui (y, 1) == 0);
+  mpfr_set_si (x, -1, MPFR_RNDN);
+  inex = mpfr_root (y, x, 121, MPFR_RNDN);
+  MPFR_ASSERTN (inex == 0);
+  MPFR_ASSERTN (mpfr_cmp_si (y, -1) == 0);
+  mpfr_clear (x);
+  mpfr_clear (y);
+}
+
 int
 main (void)
 {
@@ -415,6 +435,7 @@
 
   tests_start_mpfr ();
 
+  bug20171214 ();
   exact_powers (3, 1000);
   special ();
   bigint ();