diff --git a/sysdeps/x86/Makefile b/sysdeps/x86/Makefile
index c369faf00d..081cc72e93 100644
--- a/sysdeps/x86/Makefile
+++ b/sysdeps/x86/Makefile
@@ -11,6 +11,10 @@ tests += tst-get-cpu-features tst-get-cpu-features-static \
 tests-static += tst-get-cpu-features-static
 endif
 
+ifeq ($(subdir),math)
+tests += tst-ldbl-nonnormal-printf
+endif # $(subdir) == math
+
 ifeq ($(subdir),setjmp)
 gen-as-const-headers += jmp_buf-ssp.sym
 sysdep_routines += __longjmp_cancel
diff --git a/sysdeps/x86/ldbl2mpn.c b/sysdeps/x86/ldbl2mpn.c
index ec8464eef7..23afedfb67 100644
--- a/sysdeps/x86/ldbl2mpn.c
+++ b/sysdeps/x86/ldbl2mpn.c
@@ -115,6 +115,14 @@ __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
 	   && res_ptr[N - 1] == 0)
     /* Pseudo zero.  */
     *expt = 0;
+  else
+    /* Unlike other floating point formats, the most significant bit
+       is explicit and expected to be set for normal numbers.  Set it
+       in case it is cleared in the input.  Otherwise, callers will
+       not be able to produce the expected multi-precision integer
+       layout by shifting.  */
+    res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1
+					- ((N - 1) * BITS_PER_MP_LIMB));
 
   return N;
 }
diff --git a/sysdeps/x86/tst-ldbl-nonnormal-printf.c b/sysdeps/x86/tst-ldbl-nonnormal-printf.c
new file mode 100644
index 0000000000..54381ece0b
--- /dev/null
+++ b/sysdeps/x86/tst-ldbl-nonnormal-printf.c
@@ -0,0 +1,52 @@
+/* Test printf with x86-specific non-normal long double value.
+   Copyright (C) 2020 Free Software Foundation, Inc.
+
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <stdio.h>
+#include <string.h>
+#include <support/check.h>
+
+/* Fill the stack with non-zero values.  This makes a crash in
+   snprintf more likely.  */
+static void __attribute__ ((noinline, noclone))
+fill_stack (void)
+{
+  char buffer[65536];
+  memset (buffer, 0xc0, sizeof (buffer));
+  asm ("" ::: "memory");
+}
+
+static int
+do_test (void)
+{
+  fill_stack ();
+
+  long double value;
+  memcpy (&value, "\x00\x04\x00\x00\x00\x00\x00\x00\x00\x04", 10);
+
+  char buf[30];
+  int ret = snprintf (buf, sizeof (buf), "%Lg", value);
+  TEST_COMPARE (ret, strlen (buf));
+  if (strcmp (buf, "nan") != 0)
+    /* If snprintf does not recognize the non-normal number as a NaN,
+       it has added the missing explicit MSB.  */
+    TEST_COMPARE_STRING (buf, "3.02201e-4624");
+  return 0;
+}
+
+#include <support/test-driver.c>