diff --git a/libstdc++-v3/include/ext/numeric_traits.h b/libstdc++-v3/include/ext/numeric_traits.h
index 69f286d7be7..585ecc0ba9f 100644
--- a/libstdc++-v3/include/ext/numeric_traits.h
+++ b/libstdc++-v3/include/ext/numeric_traits.h
@@ -51,11 +51,25 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
   (__glibcxx_signed(_Tp) ? \
    (((((_Tp)1 << (__glibcxx_digits(_Tp) - 1)) - 1) << 1) + 1) : ~(_Tp)0)
 
+  template<typename _Tp>
+    struct __is_integer_nonstrict
+    : public std::__is_integer<_Tp>
+    { };
+
+#if defined __STRICT_ANSI__ && defined __SIZEOF_INT128__
+  // __is_integer<__int128> is false, but we still want to allow it here.
+  template<> struct __is_integer_nonstrict<__int128>
+  { enum { __value = 1 }; typedef std::__true_type __type; };
+
+  template<> struct __is_integer_nonstrict<unsigned __int128>
+  { enum { __value = 1 }; typedef std::__true_type __type; };
+#endif
+
   template<typename _Value>
     struct __numeric_traits_integer
     {
 #if __cplusplus >= 201103L
-      static_assert(std::__is_integer<_Value>::__value,
+      static_assert(__is_integer_nonstrict<_Value>::__value,
 		    "invalid specialization");
 #endif
 
@@ -132,7 +146,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 
   template<typename _Value>
     struct __numeric_traits
-    : public __conditional_type<std::__is_integer<_Value>::__value,
+    : public __conditional_type<__is_integer_nonstrict<_Value>::__value,
 				__numeric_traits_integer<_Value>,
 				__numeric_traits_floating<_Value> >::__type
     { };
diff --git a/libstdc++-v3/include/std/limits b/libstdc++-v3/include/std/limits
index f5e403be727..20883ba6403 100644
--- a/libstdc++-v3/include/std/limits
+++ b/libstdc++-v3/include/std/limits
@@ -1477,8 +1477,6 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
        = round_toward_zero;
     };
 
-#if !defined(__STRICT_ANSI__)
-
 #define __INT_N(TYPE, BITSIZE, EXT, UEXT)				\
   template<>								\
     struct numeric_limits<TYPE>						\
@@ -1632,6 +1630,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 #define __INT_N_U201103(TYPE)
 #endif
 
+#if !defined(__STRICT_ANSI__)
 #ifdef __GLIBCXX_TYPE_INT_N_0
   __INT_N(__GLIBCXX_TYPE_INT_N_0, __GLIBCXX_BITSIZE_INT_N_0,
 	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_0),
@@ -1653,11 +1652,16 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 	  __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_3))
 #endif
 
+#elif defined __STRICT_ANSI__ && defined __SIZEOF_INT128__
+  __INT_N(__int128, 128,
+	  __INT_N_201103 (__int128),
+	  __INT_N_U201103 (__int128))
+#endif
+
 #undef __INT_N
 #undef __INT_N_201103
 #undef __INT_N_U201103
 
-#endif
 
   /// numeric_limits<float> specialization.
   template<>
diff --git a/libstdc++-v3/testsuite/std/ranges/iota/96042.cc b/libstdc++-v3/testsuite/std/ranges/iota/96042.cc
new file mode 100644
index 00000000000..6f5c8f61fd2
--- /dev/null
+++ b/libstdc++-v3/testsuite/std/ranges/iota/96042.cc
@@ -0,0 +1,39 @@
+// Copyright (C) 2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This 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 General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-options "-std=c++2a" }
+// { dg-do compile { target c++2a } }
+
+#include <ranges>
+
+void
+test01()
+{
+  // PR libstdc++/96042
+  using V = std::ranges::iota_view<long long, int>;
+  using D = std::ranges::range_difference_t<V>;
+  using L = std::numeric_limits<D>;
+  static_assert( L::is_specialized );
+  static_assert( L::is_signed );
+  static_assert( L::is_integer );
+  static_assert( L::is_exact );
+  static_assert( L::digits > std::numeric_limits<long long>::digits );
+  static_assert( L::digits10 == static_cast<int>(L::digits * 0.30103) );
+  static_assert( L::min() == (D(1) << L::digits) );
+  static_assert( L::max() == ~L::min() );
+  static_assert( L::lowest() == L::min() );
+}