diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -341,11 +341,11 @@
     is_sorted_until(ForwardIterator first, ForwardIterator last, Compare comp);
 
 template <class RandomAccessIterator>
-    void
+    constexpr void               // constexpr in C++20
     sort(RandomAccessIterator first, RandomAccessIterator last);
 
 template <class RandomAccessIterator, class Compare>
-    void
+    constexpr void               // constexpr in C++20
     sort(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
 
 template <class RandomAccessIterator>
@@ -3950,7 +3950,6 @@
 void
 __sort(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
 {
-    // _Compare is known to be a reference type
     typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
     typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
     const difference_type __limit = is_trivially_copy_constructible<value_type>::value &&
@@ -4139,47 +4138,13 @@
     }
 }
 
-// This forwarder keeps the top call and the recursive calls using the same instantiation, forcing a reference _Compare
-template <class _RandomAccessIterator, class _Compare>
+template <class _Compare, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 void
-sort(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
+__sort(_Tp** __first, _Tp** __last, __less<_Tp*>&)
 {
-    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-    _VSTD::__sort<_Comp_ref>(__first, __last, _Comp_ref(__comp));
-}
-
-template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY
-void
-sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
-{
-    _VSTD::sort(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-void
-sort(_Tp** __first, _Tp** __last)
-{
-    _VSTD::sort((uintptr_t*)__first, (uintptr_t*)__last, __less<uintptr_t>());
-}
-
-template <class _Tp>
-inline _LIBCPP_INLINE_VISIBILITY
-void
-sort(__wrap_iter<_Tp*> __first, __wrap_iter<_Tp*> __last)
-{
-    _VSTD::sort(__first.base(), __last.base());
-}
-
-template <class _Tp, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY
-void
-sort(__wrap_iter<_Tp*> __first, __wrap_iter<_Tp*> __last, _Compare __comp)
-{
-    typedef typename add_lvalue_reference<_Compare>::type _Comp_ref;
-    _VSTD::sort<_Tp*, _Comp_ref>(__first.base(), __last.base(), __comp);
+    __less<uintptr_t> __comp;
+    _VSTD::__sort<__less<uintptr_t>&, uintptr_t*>((uintptr_t*)__first, (uintptr_t*)__last, __comp);
 }
 
 _LIBCPP_EXTERN_TEMPLATE(_LIBCPP_FUNC_VIS void __sort<__less<char>&, char*>(char*, char*, __less<char>&))
@@ -5153,6 +5118,11 @@
                                    __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
+template <class _Compare, class _RandomAccessIterator>
+_LIBCPP_CONSTEXPR_AFTER_CXX17 void
+__partial_sort(_RandomAccessIterator __first, _RandomAccessIterator __middle, _RandomAccessIterator __last,
+             _Compare __comp);
+
 // nth_element
 
 template<class _Compare, class _RandomAccessIterator>
@@ -5380,6 +5350,45 @@
     _VSTD::nth_element(__first, __nth, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
+// sort
+
+template <class _Compare, class _RandomAccessIterator>
+_LIBCPP_CONSTEXPR_AFTER_CXX17 void
+__sort_constexpr(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
+{
+    if (__libcpp_is_constant_evaluated()) {
+        _VSTD::__partial_sort<_Compare>(__first, __last, __last, __comp);
+    } else {
+        _VSTD::__sort<_Compare>(__first, __last, __comp);
+    }
+}
+
+template <class _RandomAccessIterator, class _Compare>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
+void
+sort(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
+{
+    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
+    _VSTD::__sort_constexpr<_Comp_ref>(__first, __last, _Comp_ref(__comp));
+}
+
+template <class _Tp, class _Compare>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
+void
+sort(__wrap_iter<_Tp*> __first, __wrap_iter<_Tp*> __last, _Compare __comp)
+{
+    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
+    _VSTD::__sort_constexpr<_Comp_ref>(__first.base(), __last.base(), _Comp_ref(__comp));
+}
+
+template <class _RandomAccessIterator>
+inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
+void
+sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
+{
+    _VSTD::sort(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+}
+
 // includes
 
 template <class _Compare, class _InputIterator1, class _InputIterator2>
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.sort/sort/sort_constexpr.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.sort/sort/sort_constexpr.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.sort/sort/sort_constexpr.pass.cpp
@@ -0,0 +1,101 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// <algorithm>
+
+// template<RandomAccessIterator Iter>
+//   requires ShuffleIterator<Iter>
+//         && LessThanComparable<Iter::value_type>
+//   void
+//   sort(Iter first, Iter last);
+
+#include <algorithm>
+#include <cassert>
+
+#include "test_macros.h"
+#include "test_iterators.h"
+#include "MoveOnly.h"
+
+template<int N, class T, class Iter>
+TEST_CONSTEXPR_CXX20 bool test()
+{
+    int orig[N] = {};
+    unsigned x = 1;
+    for (int i=0; i < N; ++i) {
+        x = (x * 1664525) + 1013904223;
+        orig[i] = x % 1000;
+    }
+    T work[N] = {};
+    std::copy(orig, orig+N, work);
+    std::sort(Iter(work), Iter(work+N));
+    assert(std::is_sorted(work, work+N));
+    assert(std::is_permutation(work, work+N, orig));
+
+    return true;
+}
+
+template<int N, class T, class Iter>
+TEST_CONSTEXPR_CXX20 bool test_pointers()
+{
+    T data[N] = {};
+    T *orig[N] = {};
+    unsigned x = 1;
+    for (int i=0; i < N; ++i) {
+        orig[i] = &data[x % 258];
+    }
+    T *work[N] = {};
+    std::copy(orig, orig+N, work);
+    std::sort(Iter(work), Iter(work+N));
+    assert(std::is_sorted(work, work+N));
+    assert(std::is_permutation(work, work+N, orig));
+
+    return true;
+}
+
+int main(int, char**)
+{
+    test<7, int, int*>();
+    test<7, int, random_access_iterator<int*> >();
+    test<257, int, int*>();
+    test<257, int, random_access_iterator<int*> >();
+
+#if TEST_STD_VER >= 11
+    test<7, MoveOnly, MoveOnly*>();
+    test<7, MoveOnly, random_access_iterator<MoveOnly*> >();
+    test<257, MoveOnly, MoveOnly*>();
+    test<257, MoveOnly, random_access_iterator<MoveOnly*> >();
+#endif
+
+    test_pointers<17, char, char**>();
+    test_pointers<17, char, random_access_iterator<char**> >();
+    test_pointers<17, const char, const char**>();
+    test_pointers<17, const char, random_access_iterator<const char**> >();
+    test_pointers<17, int, int**>();
+    test_pointers<17, int, random_access_iterator<int**> >();
+
+#if TEST_STD_VER >= 20
+    static_assert(test<7, int, int*>());
+    static_assert(test<7, int, random_access_iterator<int*>>());
+    static_assert(test<257, int, int*>());
+    static_assert(test<257, int, random_access_iterator<int*>>());
+
+    static_assert(test<7, MoveOnly, MoveOnly*>());
+    static_assert(test<7, MoveOnly, random_access_iterator<MoveOnly*>>());
+    static_assert(test<257, MoveOnly, MoveOnly*>());
+    static_assert(test<257, MoveOnly, random_access_iterator<MoveOnly*>>());
+
+    static_assert(test_pointers<17, char, char**>());
+    static_assert(test_pointers<17, char, random_access_iterator<char**>>());
+    static_assert(test_pointers<17, const char, const char**>());
+    static_assert(test_pointers<17, const char, random_access_iterator<const char**>>());
+    static_assert(test_pointers<17, int, int**>());
+    static_assert(test_pointers<17, int, random_access_iterator<int**>>());
+#endif
+
+    return 0;
+}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.sort/sort/sort_constexpr_comp.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.sort/sort/sort_constexpr_comp.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.sort/sort/sort_constexpr_comp.pass.cpp
@@ -0,0 +1,102 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// <algorithm>
+
+// template<RandomAccessIterator Iter, StrictWeakOrder<auto, Iter::value_type> Compare>
+//   requires ShuffleIterator<Iter>
+//         && CopyConstructible<Compare>
+//   void
+//   sort(Iter first, Iter last, Compare comp);
+
+#include <algorithm>
+#include <cassert>
+#include <functional>
+
+#include "test_macros.h"
+#include "test_iterators.h"
+#include "MoveOnly.h"
+
+template<int N, class T, class Iter>
+TEST_CONSTEXPR_CXX20 bool test()
+{
+    int orig[N] = {};
+    unsigned x = 1;
+    for (int i=0; i < N; ++i) {
+        x = (x * 1664525) + 1013904223;
+        orig[i] = x % 1000;
+    }
+    T work[N] = {};
+    std::copy(orig, orig+N, work);
+    std::sort(Iter(work), Iter(work+N), std::greater<T>());
+    assert(std::is_sorted(work, work+N, std::greater<T>()));
+    assert(std::is_permutation(work, work+N, orig));
+
+    return true;
+}
+
+template<int N, class T, class Iter>
+TEST_CONSTEXPR_CXX20 bool test_pointers()
+{
+    T data[N] = {};
+    T *orig[N] = {};
+    unsigned x = 1;
+    for (int i=0; i < N; ++i) {
+        orig[i] = &data[x % 258];
+    }
+    T *work[N] = {};
+    std::copy(orig, orig+N, work);
+    std::sort(Iter(work), Iter(work+N), std::greater<T*>());
+    assert(std::is_sorted(work, work+N, std::greater<T*>()));
+    assert(std::is_permutation(work, work+N, orig));
+
+    return true;
+}
+
+int main(int, char**)
+{
+    test<7, int, int*>();
+    test<7, int, random_access_iterator<int*> >();
+    test<257, int, int*>();
+    test<257, int, random_access_iterator<int*> >();
+
+#if TEST_STD_VER >= 11
+    test<7, MoveOnly, MoveOnly*>();
+    test<7, MoveOnly, random_access_iterator<MoveOnly*> >();
+    test<257, MoveOnly, MoveOnly*>();
+    test<257, MoveOnly, random_access_iterator<MoveOnly*> >();
+#endif
+
+    test_pointers<17, char, char**>();
+    test_pointers<17, char, random_access_iterator<char**> >();
+    test_pointers<17, const char, const char**>();
+    test_pointers<17, const char, random_access_iterator<const char**> >();
+    test_pointers<17, int, int**>();
+    test_pointers<17, int, random_access_iterator<int**> >();
+
+#if TEST_STD_VER >= 20
+    static_assert(test<7, int, int*>());
+    static_assert(test<7, int, random_access_iterator<int*>>());
+    static_assert(test<257, int, int*>());
+    static_assert(test<257, int, random_access_iterator<int*>>());
+
+    static_assert(test<7, MoveOnly, MoveOnly*>());
+    static_assert(test<7, MoveOnly, random_access_iterator<MoveOnly*>>());
+    static_assert(test<257, MoveOnly, MoveOnly*>());
+    static_assert(test<257, MoveOnly, random_access_iterator<MoveOnly*>>());
+
+    static_assert(test_pointers<17, char, char**>());
+    static_assert(test_pointers<17, char, random_access_iterator<char**>>());
+    static_assert(test_pointers<17, const char, const char**>());
+    static_assert(test_pointers<17, const char, random_access_iterator<const char**>>());
+    static_assert(test_pointers<17, int, int**>());
+    static_assert(test_pointers<17, int, random_access_iterator<int**>>());
+#endif
+
+    return 0;
+}