diff --git a/include/__bit_reference b/include/__bit_reference
index 21ce11f5..b91532db 100644
--- a/include/__bit_reference
+++ b/include/__bit_reference
@@ -131,13 +131,14 @@ public:
     __bit_const_reference(const __bit_reference<_Cp>& __x) _NOEXCEPT
         : __seg_(__x.__seg_), __mask_(__x.__mask_) {}
 
-    _LIBCPP_INLINE_VISIBILITY operator bool() const _NOEXCEPT
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR operator bool() const _NOEXCEPT
         {return static_cast<bool>(*__seg_ & __mask_);}
 
     _LIBCPP_INLINE_VISIBILITY __bit_iterator<_Cp, true> operator&() const _NOEXCEPT
         {return __bit_iterator<_Cp, true>(__seg_, static_cast<unsigned>(__ctz(__mask_)));}
 private:
     _LIBCPP_INLINE_VISIBILITY
+    _LIBCPP_CONSTEXPR
     __bit_const_reference(__storage_pointer __s, __storage_type __m) _NOEXCEPT
         : __seg_(__s), __mask_(__m) {}
 
diff --git a/include/bitset b/include/bitset
index b3a58673..55b55759 100644
--- a/include/bitset
+++ b/include/bitset
@@ -168,12 +168,12 @@ protected:
     typedef __bit_iterator<__bitset, false>            iterator;
     typedef __bit_iterator<__bitset, true>             const_iterator;
 
-    __bitset() _NOEXCEPT;
-    explicit __bitset(unsigned long long __v) _NOEXCEPT;
+    _LIBCPP_CONSTEXPR __bitset() _NOEXCEPT;
+    explicit _LIBCPP_CONSTEXPR __bitset(unsigned long long __v) _NOEXCEPT;
 
     _LIBCPP_INLINE_VISIBILITY reference __make_ref(size_t __pos) _NOEXCEPT
         {return reference(__first_ + __pos / __bits_per_word, __storage_type(1) << __pos % __bits_per_word);}
-    _LIBCPP_INLINE_VISIBILITY const_reference __make_ref(size_t __pos) const _NOEXCEPT
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR const_reference __make_ref(size_t __pos) const _NOEXCEPT
         {return const_reference(__first_ + __pos / __bits_per_word, __storage_type(1) << __pos % __bits_per_word);}
     _LIBCPP_INLINE_VISIBILITY iterator __make_iter(size_t __pos) _NOEXCEPT
         {return iterator(__first_ + __pos / __bits_per_word, __pos % __bits_per_word);}
@@ -194,8 +194,10 @@ protected:
     bool any() const _NOEXCEPT;
     size_t __hash_code() const _NOEXCEPT;
 private:
+#ifdef _LIBCPP_HAS_NO_CONSTEXPR
     void __init(unsigned long long __v, false_type) _NOEXCEPT;
     void __init(unsigned long long __v, true_type) _NOEXCEPT;
+#endif  // _LIBCPP_HAS_NO_CONSTEXPR
     unsigned long to_ulong(false_type) const;
     unsigned long to_ulong(true_type) const;
     unsigned long long to_ullong(false_type) const;
@@ -206,11 +208,19 @@ private:
 
 template <size_t _N_words, size_t _Size>
 inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
 __bitset<_N_words, _Size>::__bitset() _NOEXCEPT
+#ifndef _LIBCPP_HAS_NO_CONSTEXPR
+    : __first_{0}
+#endif
 {
+#ifdef _LIBCPP_HAS_NO_CONSTEXPR
     _VSTD::fill_n(__first_, _N_words, __storage_type(0));
+#endif
 }
 
+#ifdef _LIBCPP_HAS_NO_CONSTEXPR
+
 template <size_t _N_words, size_t _Size>
 void
 __bitset<_N_words, _Size>::__init(unsigned long long __v, false_type) _NOEXCEPT
@@ -232,11 +242,19 @@ __bitset<_N_words, _Size>::__init(unsigned long long __v, true_type) _NOEXCEPT
     _VSTD::fill(__first_ + 1, __first_ + sizeof(__first_)/sizeof(__first_[0]), __storage_type(0));
 }
 
+#endif  // _LIBCPP_HAS_NO_CONSTEXPR
+
 template <size_t _N_words, size_t _Size>
 inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
 __bitset<_N_words, _Size>::__bitset(unsigned long long __v) _NOEXCEPT
+#ifndef _LIBCPP_HAS_NO_CONSTEXPR
+    : __first_{__v}
+#endif
 {
+#ifdef _LIBCPP_HAS_NO_CONSTEXPR
     __init(__v, integral_constant<bool, sizeof(unsigned long long) == sizeof(__storage_type)>());
+#endif
 }
 
 template <size_t _N_words, size_t _Size>
@@ -426,12 +444,12 @@ protected:
     typedef __bit_iterator<__bitset, false>            iterator;
     typedef __bit_iterator<__bitset, true>             const_iterator;
 
-    __bitset() _NOEXCEPT;
-    explicit __bitset(unsigned long long __v) _NOEXCEPT;
+    _LIBCPP_CONSTEXPR __bitset() _NOEXCEPT;
+    explicit _LIBCPP_CONSTEXPR __bitset(unsigned long long __v) _NOEXCEPT;
 
     _LIBCPP_INLINE_VISIBILITY reference __make_ref(size_t __pos) _NOEXCEPT
         {return reference(&__first_, __storage_type(1) << __pos);}
-    _LIBCPP_INLINE_VISIBILITY const_reference __make_ref(size_t __pos) const _NOEXCEPT
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR const_reference __make_ref(size_t __pos) const _NOEXCEPT
         {return const_reference(&__first_, __storage_type(1) << __pos);}
     _LIBCPP_INLINE_VISIBILITY iterator __make_iter(size_t __pos) _NOEXCEPT
         {return iterator(&__first_ + __pos / __bits_per_word, __pos % __bits_per_word);}
@@ -455,6 +473,7 @@ protected:
 
 template <size_t _Size>
 inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
 __bitset<1, _Size>::__bitset() _NOEXCEPT
     : __first_(0)
 {
@@ -462,6 +481,7 @@ __bitset<1, _Size>::__bitset() _NOEXCEPT
 
 template <size_t _Size>
 inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
 __bitset<1, _Size>::__bitset(unsigned long long __v) _NOEXCEPT
     : __first_(static_cast<__storage_type>(__v))
 {
@@ -567,12 +587,12 @@ protected:
     typedef __bit_iterator<__bitset, false>            iterator;
     typedef __bit_iterator<__bitset, true>             const_iterator;
 
-    __bitset() _NOEXCEPT;
-    explicit __bitset(unsigned long long) _NOEXCEPT;
+    _LIBCPP_CONSTEXPR __bitset() _NOEXCEPT;
+    explicit _LIBCPP_CONSTEXPR __bitset(unsigned long long) _NOEXCEPT;
 
     _LIBCPP_INLINE_VISIBILITY reference __make_ref(size_t) _NOEXCEPT
         {return reference(0, 1);}
-    _LIBCPP_INLINE_VISIBILITY const_reference __make_ref(size_t) const _NOEXCEPT
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR const_reference __make_ref(size_t) const _NOEXCEPT
         {return const_reference(0, 1);}
     _LIBCPP_INLINE_VISIBILITY iterator __make_iter(size_t) _NOEXCEPT
         {return iterator(0, 0);}
@@ -595,11 +615,13 @@ protected:
 };
 
 inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
 __bitset<0, 0>::__bitset() _NOEXCEPT
 {
 }
 
 inline _LIBCPP_INLINE_VISIBILITY
+_LIBCPP_CONSTEXPR
 __bitset<0, 0>::__bitset(unsigned long long) _NOEXCEPT
 {
 }
@@ -619,8 +641,9 @@ public:
     typedef typename base::const_reference const_reference;
 
     // 23.3.5.1 constructors:
-    /*constexpr*/ _LIBCPP_INLINE_VISIBILITY bitset() _NOEXCEPT {}
-    /*constexpr*/ _LIBCPP_INLINE_VISIBILITY bitset(unsigned long long __v) _NOEXCEPT : base(__v) {}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR bitset() _NOEXCEPT {}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
+        bitset(unsigned long long __v) _NOEXCEPT : base(__v) {}
     template<class _CharT>
         explicit bitset(const _CharT* __str,
                         typename basic_string<_CharT>::size_type __n = basic_string<_CharT>::npos,
@@ -647,7 +670,8 @@ public:
     bitset& flip(size_t __pos);
 
     // element access:
-    _LIBCPP_INLINE_VISIBILITY const_reference operator[](size_t __p) const {return base::__make_ref(__p);}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
+                              const_reference operator[](size_t __p) const {return base::__make_ref(__p);}
     _LIBCPP_INLINE_VISIBILITY       reference operator[](size_t __p)       {return base::__make_ref(__p);}
     unsigned long to_ulong() const;
     unsigned long long to_ullong() const;
@@ -663,7 +687,7 @@ public:
     basic_string<char, char_traits<char>, allocator<char> > to_string(char __zero = '0',
                                                                       char __one = '1') const;
     size_t count() const _NOEXCEPT;
-    /*constexpr*/ _LIBCPP_INLINE_VISIBILITY size_t size() const _NOEXCEPT {return _Size;}
+    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR size_t size() const _NOEXCEPT {return _Size;}
     bool operator==(const bitset& __rhs) const _NOEXCEPT;
     bool operator!=(const bitset& __rhs) const _NOEXCEPT;
     bool test(size_t __pos) const;
diff --git a/test/utilities/template.bitset/bitset.cons/default.pass.cpp b/test/utilities/template.bitset/bitset.cons/default.pass.cpp
index 5d743c6b..bd5ca7e0 100644
--- a/test/utilities/template.bitset/bitset.cons/default.pass.cpp
+++ b/test/utilities/template.bitset/bitset.cons/default.pass.cpp
@@ -18,7 +18,7 @@ template <std::size_t N>
 void test_default_ctor()
 {
     {
-    std::bitset<N> v1;
+    _LIBCPP_CONSTEXPR std::bitset<N> v1;
     assert(v1.size() == N);
     for (std::size_t i = 0; i < N; ++i)
         assert(v1[i] == false);
diff --git a/test/utilities/template.bitset/bitset.cons/ull_ctor.pass.cpp b/test/utilities/template.bitset/bitset.cons/ull_ctor.pass.cpp
index c849937d..023fedc2 100644
--- a/test/utilities/template.bitset/bitset.cons/ull_ctor.pass.cpp
+++ b/test/utilities/template.bitset/bitset.cons/ull_ctor.pass.cpp
@@ -18,7 +18,7 @@ template <std::size_t N>
 void test_val_ctor()
 {
     {
-    std::bitset<N> v(0xAAAAAAAAAAAAAAAAULL);
+    _LIBCPP_CONSTEXPR std::bitset<N> v(0xAAAAAAAAAAAAAAAAULL);
     assert(v.size() == N);
     unsigned M = std::min<std::size_t>(N, 64);
     for (std::size_t i = 0; i < M; ++i)
diff --git a/test/utilities/template.bitset/bitset.members/reset_one.pass.cpp b/test/utilities/template.bitset/bitset.members/reset_one.pass.cpp
index 2b9b097f..ebaa9e7a 100644
--- a/test/utilities/template.bitset/bitset.members/reset_one.pass.cpp
+++ b/test/utilities/template.bitset/bitset.members/reset_one.pass.cpp
@@ -12,6 +12,9 @@
 #include <bitset>
 #include <cassert>
 
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wtautological-compare"
+
 template <std::size_t N>
 void test_reset_one()
 {