diff --git a/var/spack/repos/builtin/packages/mpfr/package.py b/var/spack/repos/builtin/packages/mpfr/package.py
index 01006dd72a..4e69fa1f14 100644
--- a/var/spack/repos/builtin/packages/mpfr/package.py
+++ b/var/spack/repos/builtin/packages/mpfr/package.py
@@ -30,18 +30,33 @@ class Mpfr(AutotoolsPackage):
        floating-point computations with correct rounding."""
 
     homepage = "http://www.mpfr.org"
-    url      = "https://ftp.gnu.org/gnu/mpfr/mpfr-3.1.5.tar.bz2"
+    url      = "https://ftp.gnu.org/gnu/mpfr/mpfr-4.0.1.tar.bz2"
 
+    version('4.0.1', '8c21d8ac7460493b2b9f3ef3cc610454')
+    version('4.0.0', 'ef619f3bb68039e35c4a219e06be72d0')
+    version('3.1.6', '320c28198def956aeacdb240b46b8969')
     version('3.1.5', 'b1d23a55588e3b2a13e3be66bc69fd8d')
     version('3.1.4', 'b8a2f6b0e68bef46e53da2ac439e1cf4')
     version('3.1.3', '5fdfa3cfa5c86514ee4a241a1affa138')
     version('3.1.2', 'ee2c3ac63bf0c2359bf08fc3ee094c19')
 
     # mpir is a drop-in replacement for gmp
-    depends_on('gmp@4.1.0:')  # 4.2.3 or higher is recommended
+    depends_on('gmp@4.1:')  # 4.2.3 or higher is recommended
+    depends_on('gmp@5.0:', when='@4.0.0:')  # http://www.mpfr.org/mpfr-4.0.0/
 
-    patch('vasprintf.patch', when='@3.1.5')
-    patch('strtofr.patch',   when='@3.1.5')
+    # Check the Bugs section of old release pages for patches.
+    # http://www.mpfr.org/mpfr-X.Y.Z/#bugs
+    patches = {
+        '3.1.6': '66a5d58364113a21405fc53f4a48f4e8',
+        '3.1.5': '1dc5fe65feb5607b89fe0f410d53b627',
+        '3.1.4': 'd124381573404fe83654c7d5a79aeabf',
+        '3.1.3': 'ebd1d835e0ae2fd8a9339210ccd1d0a8',
+        '3.1.2': '9f96a5c7cac1d6cd983ed9cf7d997074',
+    }
+
+    for ver, checksum in patches.items():
+        patch('http://www.mpfr.org/mpfr-{0}/allpatches'.format(ver),
+              when='@' + ver, sha256=checksum)
 
     def configure_args(self):
         args = [
diff --git a/var/spack/repos/builtin/packages/mpfr/strtofr.patch b/var/spack/repos/builtin/packages/mpfr/strtofr.patch
deleted file mode 100644
index 01878bf1b0..0000000000
--- a/var/spack/repos/builtin/packages/mpfr/strtofr.patch
+++ /dev/null
@@ -1,92 +0,0 @@
-diff -Naurd mpfr-3.1.5-a/PATCHES mpfr-3.1.5-b/PATCHES
---- mpfr-3.1.5-a/PATCHES	2016-12-19 22:11:17.022676737 +0000
-+++ mpfr-3.1.5-b/PATCHES	2016-12-19 22:11:17.094676820 +0000
-@@ -0,0 +1 @@
-+strtofr
-diff -Naurd mpfr-3.1.5-a/VERSION mpfr-3.1.5-b/VERSION
---- mpfr-3.1.5-a/VERSION	2016-12-15 08:35:46.544430346 +0000
-+++ mpfr-3.1.5-b/VERSION	2016-12-19 22:11:17.094676820 +0000
-@@ -1 +1 @@
--3.1.5-p1
-+3.1.5-p2
-diff -Naurd mpfr-3.1.5-a/src/mpfr.h mpfr-3.1.5-b/src/mpfr.h
---- mpfr-3.1.5-a/src/mpfr.h	2016-12-15 08:35:46.540430340 +0000
-+++ mpfr-3.1.5-b/src/mpfr.h	2016-12-19 22:11:17.090676815 +0000
-@@ -27,7 +27,7 @@
- #define MPFR_VERSION_MAJOR 3
- #define MPFR_VERSION_MINOR 1
- #define MPFR_VERSION_PATCHLEVEL 5
--#define MPFR_VERSION_STRING "3.1.5-p1"
-+#define MPFR_VERSION_STRING "3.1.5-p2"
- 
- /* Macros dealing with MPFR VERSION */
- #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
-diff -Naurd mpfr-3.1.5-a/src/strtofr.c mpfr-3.1.5-b/src/strtofr.c
---- mpfr-3.1.5-a/src/strtofr.c	2016-09-27 07:58:15.000000000 +0000
-+++ mpfr-3.1.5-b/src/strtofr.c	2016-12-19 22:11:17.066676788 +0000
-@@ -743,11 +743,14 @@
-          of the pstr_size most significant digits of pstr->mant, with
-          equality in case exact is non-zero. */
- 
--      /* test if rounding is possible, and if so exit the loop */
--      if (exact || mpfr_can_round_raw (result, ysize,
--                                       (pstr->negative) ? -1 : 1,
--                                       ysize_bits - err - 1,
--                                       MPFR_RNDN, rnd, MPFR_PREC(x)))
-+      /* test if rounding is possible, and if so exit the loop.
-+         Note: we also need to be able to determine the correct ternary value,
-+         thus we use the MPFR_PREC(x) + (rnd == MPFR_RNDN) trick.
-+         For example if result = xxx...xxx111...111 and rnd = RNDN,
-+         then we know the correct rounding is xxx...xx(x+1), but we cannot know
-+         the correct ternary value. */
-+      if (exact || mpfr_round_p (result, ysize, ysize_bits - err - 1,
-+                                 MPFR_PREC(x) + (rnd == MPFR_RNDN)))
-         break;
- 
-     next_loop:
-diff -Naurd mpfr-3.1.5-a/src/version.c mpfr-3.1.5-b/src/version.c
---- mpfr-3.1.5-a/src/version.c	2016-12-15 08:35:46.544430346 +0000
-+++ mpfr-3.1.5-b/src/version.c	2016-12-19 22:11:17.094676820 +0000
-@@ -25,5 +25,5 @@
- const char *
- mpfr_get_version (void)
- {
--  return "3.1.5-p1";
-+  return "3.1.5-p2";
- }
-diff -Naurd mpfr-3.1.5-a/tests/tstrtofr.c mpfr-3.1.5-b/tests/tstrtofr.c
---- mpfr-3.1.5-a/tests/tstrtofr.c	2016-09-27 07:58:14.000000000 +0000
-+++ mpfr-3.1.5-b/tests/tstrtofr.c	2016-12-19 22:11:17.066676788 +0000
-@@ -1191,6 +1191,24 @@
-   mpfr_clears (e, x1, x2, (mpfr_ptr) 0);
- }
- 
-+/* Note: the number is 5^47/2^9. */
-+static void
-+bug20161217 (void)
-+{
-+  mpfr_t fp, z;
-+  static const char * num = "0.1387778780781445675529539585113525390625e31";
-+  int inex;
-+
-+  mpfr_init2 (fp, 110);
-+  mpfr_init2 (z, 110);
-+  inex = mpfr_strtofr (fp, num, NULL, 10, MPFR_RNDN);
-+  MPFR_ASSERTN(inex == 0);
-+  mpfr_set_str_binary (z, "10001100001000010011110110011101101001010000001011011110010001010100010100100110111101000010001011001100001101E-9");
-+  MPFR_ASSERTN(mpfr_equal_p (fp, z));
-+  mpfr_clear (fp);
-+  mpfr_clear (z);
-+}
-+
- int
- main (int argc, char *argv[])
- {
-@@ -1205,6 +1223,7 @@
-   test20100310 ();
-   bug20120814 ();
-   bug20120829 ();
-+  bug20161217 ();
- 
-   tests_end_mpfr ();
-   return 0;
diff --git a/var/spack/repos/builtin/packages/mpfr/vasprintf.patch b/var/spack/repos/builtin/packages/mpfr/vasprintf.patch
deleted file mode 100644
index e1576d5976..0000000000
--- a/var/spack/repos/builtin/packages/mpfr/vasprintf.patch
+++ /dev/null
@@ -1,82 +0,0 @@
-diff -Naurd mpfr-3.1.5-a/PATCHES mpfr-3.1.5-b/PATCHES
---- mpfr-3.1.5-a/PATCHES	2016-12-15 08:35:46.476430238 +0000
-+++ mpfr-3.1.5-b/PATCHES	2016-12-15 08:35:46.544430346 +0000
-@@ -0,0 +1 @@
-+vasprintf
-diff -Naurd mpfr-3.1.5-a/VERSION mpfr-3.1.5-b/VERSION
---- mpfr-3.1.5-a/VERSION	2016-09-27 07:58:14.000000000 +0000
-+++ mpfr-3.1.5-b/VERSION	2016-12-15 08:35:46.544430346 +0000
-@@ -1 +1 @@
--3.1.5
-+3.1.5-p1
-diff -Naurd mpfr-3.1.5-a/src/mpfr.h mpfr-3.1.5-b/src/mpfr.h
---- mpfr-3.1.5-a/src/mpfr.h	2016-09-27 07:58:15.000000000 +0000
-+++ mpfr-3.1.5-b/src/mpfr.h	2016-12-15 08:35:46.540430340 +0000
-@@ -27,7 +27,7 @@
- #define MPFR_VERSION_MAJOR 3
- #define MPFR_VERSION_MINOR 1
- #define MPFR_VERSION_PATCHLEVEL 5
--#define MPFR_VERSION_STRING "3.1.5"
-+#define MPFR_VERSION_STRING "3.1.5-p1"
- 
- /* Macros dealing with MPFR VERSION */
- #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
-diff -Naurd mpfr-3.1.5-a/src/vasprintf.c mpfr-3.1.5-b/src/vasprintf.c
---- mpfr-3.1.5-a/src/vasprintf.c	2016-09-27 07:58:15.000000000 +0000
-+++ mpfr-3.1.5-b/src/vasprintf.c	2016-12-15 08:35:46.520430308 +0000
-@@ -1593,7 +1593,7 @@
-         }
-       else if (spec.spec == 'f' || spec.spec == 'F')
-         {
--          if (spec.prec == -1)
-+          if (spec.prec < 0)
-             spec.prec = 6;
-           if (regular_fg (np, p, spec, NULL) == -1)
-             goto error;
-diff -Naurd mpfr-3.1.5-a/src/version.c mpfr-3.1.5-b/src/version.c
---- mpfr-3.1.5-a/src/version.c	2016-09-27 07:58:15.000000000 +0000
-+++ mpfr-3.1.5-b/src/version.c	2016-12-15 08:35:46.544430346 +0000
-@@ -25,5 +25,5 @@
- const char *
- mpfr_get_version (void)
- {
--  return "3.1.5";
-+  return "3.1.5-p1";
- }
-diff -Naurd mpfr-3.1.5-a/tests/tsprintf.c mpfr-3.1.5-b/tests/tsprintf.c
---- mpfr-3.1.5-a/tests/tsprintf.c	2016-09-27 07:58:14.000000000 +0000
-+++ mpfr-3.1.5-b/tests/tsprintf.c	2016-12-15 08:35:46.520430308 +0000
-@@ -1251,6 +1251,25 @@
-   check_emin_aux (MPFR_EMIN_MIN);
- }
- 
-+static void
-+test20161214 (void)
-+{
-+  mpfr_t x;
-+  char buf[32];
-+  const char s[] = "0x0.fffffffffffff8p+1024";
-+  int r;
-+
-+  mpfr_init2 (x, 64);
-+  mpfr_set_str (x, s, 16, MPFR_RNDN);
-+  r = mpfr_snprintf (buf, 32, "%.*RDf", -2, x);
-+  MPFR_ASSERTN(r == 316);
-+  r = mpfr_snprintf (buf, 32, "%.*RDf", INT_MIN + 1, x);
-+  MPFR_ASSERTN(r == 316);
-+  r = mpfr_snprintf (buf, 32, "%.*RDf", INT_MIN, x);
-+  MPFR_ASSERTN(r == 316);
-+  mpfr_clear (x);
-+}
-+
- int
- main (int argc, char **argv)
- {
-@@ -1271,6 +1290,7 @@
-   mixed ();
-   check_emax ();
-   check_emin ();
-+  test20161214 ();
- 
- #if defined(HAVE_LOCALE_H) && defined(HAVE_SETLOCALE)
- #if MPFR_LCONV_DPTS