diff --git a/sysdeps/generic/nan-pseudo-number.h b/sysdeps/generic/nan-pseudo-number.h
new file mode 100644
index 0000000000..1562e06e4b
--- /dev/null
+++ b/sysdeps/generic/nan-pseudo-number.h
@@ -0,0 +1,32 @@
+/* Pseudo-normal number handling.  Generic version.
+   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/>.  */
+
+#ifndef NAN_PSEUDO_NUMBER_H
+#define NAN_PSEUDO_NUMBER_H	1
+
+/* Set this macro and override the definition of IS_PSEUDO_SIGNALING if pseudo
+   numbers need special handling.  */
+#define HANDLE_PSEUDO_NUMBERS 0
+static inline int
+is_pseudo_signaling (uint32_t exi __attribute__ ((unused)),
+		     uint32_t hxi __attribute__ ((unused)))
+{
+  return 0;
+}
+
+#endif /* nan-pseudo-number.h */
diff --git a/sysdeps/ieee754/ldbl-96/s_issignalingl.c b/sysdeps/ieee754/ldbl-96/s_issignalingl.c
index ec542ad468..37e05aa259 100644
--- a/sysdeps/ieee754/ldbl-96/s_issignalingl.c
+++ b/sysdeps/ieee754/ldbl-96/s_issignalingl.c
@@ -19,12 +19,19 @@
 #include <math.h>
 #include <math_private.h>
 #include <nan-high-order-bit.h>
+#include <nan-pseudo-number.h>
 
 int
 __issignalingl (long double x)
 {
   uint32_t exi, hxi, lxi;
   GET_LDOUBLE_WORDS (exi, hxi, lxi, x);
+
+  /* By default we do not recognize a pseudo NaN as sNaN.  However on 80387 and
+     later all pseudo numbers including pseudo NaNs result in a signal and are
+     hence recognized as signaling.  */
+  int ret = is_pseudo_signaling (exi, hxi);
+
 #if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
 # error not implemented
 #else
@@ -34,11 +41,9 @@ __issignalingl (long double x)
   hxi ^= 0x40000000;
   /* If lxi != 0, then set any suitable bit of the significand in hxi.  */
   hxi |= (lxi | -lxi) >> 31;
-  /* We do not recognize a pseudo NaN as sNaN; they're invalid on 80387 and
-     later.  */
   /* We have to compare for greater (instead of greater or equal), because x's
      significand being all-zero designates infinity not NaN.  */
-  return ((exi & 0x7fff) == 0x7fff) && (hxi > 0xc0000000);
+  return ret || (((exi & 0x7fff) == 0x7fff) && (hxi > 0xc0000000));
 #endif
 }
 libm_hidden_def (__issignalingl)
diff --git a/sysdeps/x86/fpu/nan-pseudo-number.h b/sysdeps/x86/fpu/nan-pseudo-number.h
new file mode 100644
index 0000000000..ea43b175a1
--- /dev/null
+++ b/sysdeps/x86/fpu/nan-pseudo-number.h
@@ -0,0 +1,30 @@
+/* Pseudo-normal number handling.  x86 version.
+   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/>.  */
+
+#ifndef NAN_PSEUDO_NUMBER_H
+#define NAN_PSEUDO_NUMBER_H	1
+
+#define HANDLE_PSEUDO_NUMBERS 1
+/* Pseudo numbers on x86 are always signaling.  */
+static inline int
+is_pseudo_signaling (uint32_t exi, uint32_t hxi)
+{
+  return ((exi & 0x7fff) && ((hxi & 0x80000000) == 0));
+}
+
+#endif /* nan-pseudo-number.h */
