diff --git a/libcxx/benchmarks/CMakeLists.txt b/libcxx/benchmarks/CMakeLists.txt
--- a/libcxx/benchmarks/CMakeLists.txt
+++ b/libcxx/benchmarks/CMakeLists.txt
@@ -166,7 +166,12 @@
     algorithms/min_max_element.bench.cpp
     algorithms/pop_heap.bench.cpp
     algorithms/push_heap.bench.cpp
+    algorithms/ranges_make_heap.bench.cpp
+    algorithms/ranges_make_heap_then_sort_heap.bench.cpp
+    algorithms/ranges_pop_heap.bench.cpp
+    algorithms/ranges_push_heap.bench.cpp
     algorithms/ranges_sort.bench.cpp
+    algorithms/ranges_sort_heap.bench.cpp
     algorithms/ranges_stable_sort.bench.cpp
     algorithms/sort.bench.cpp
     algorithms/sort_heap.bench.cpp
diff --git a/libcxx/benchmarks/algorithms/ranges_make_heap.bench.cpp b/libcxx/benchmarks/algorithms/ranges_make_heap.bench.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/benchmarks/algorithms/ranges_make_heap.bench.cpp
@@ -0,0 +1,37 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+
+#include "common.h"
+
+namespace {
+template <class ValueType, class Order>
+struct RangesMakeHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(
+        state, Quantity, Order(), BatchSize::CountElements,
+        [](auto& Copy) { std::ranges::make_heap(Copy); });
+  }
+
+  std::string name() const {
+    return "BM_RangesMakeHeap" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+  makeCartesianProductBenchmark<RangesMakeHeap, AllValueTypes, AllOrders>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}
diff --git a/libcxx/benchmarks/algorithms/ranges_make_heap_then_sort_heap.bench.cpp b/libcxx/benchmarks/algorithms/ranges_make_heap_then_sort_heap.bench.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/benchmarks/algorithms/ranges_make_heap_then_sort_heap.bench.cpp
@@ -0,0 +1,39 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+
+#include "common.h"
+
+namespace {
+template <class ValueType, class Order>
+struct RangesMakeThenSortHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), BatchSize::CountElements,
+                             [](auto& Copy) {
+                               std::ranges::make_heap(Copy);
+                               std::ranges::sort_heap(Copy);
+                             });
+  }
+
+  std::string name() const {
+    return "BM_RangesMakeThenSortHeap" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+  makeCartesianProductBenchmark<RangesMakeThenSortHeap, AllValueTypes, AllOrders>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}
diff --git a/libcxx/benchmarks/algorithms/ranges_pop_heap.bench.cpp b/libcxx/benchmarks/algorithms/ranges_pop_heap.bench.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/benchmarks/algorithms/ranges_pop_heap.bench.cpp
@@ -0,0 +1,39 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+
+#include "common.h"
+
+namespace {
+template <class ValueType>
+struct RangesPopHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(
+        state, Quantity, Order(), BatchSize::CountElements, [](auto& Copy) {
+          for (auto B = Copy.begin(), I = Copy.end(); I != B; --I) {
+            std::ranges::pop_heap(B, I);
+          }
+        });
+  }
+
+  std::string name() const {
+    return "BM_RangesPopHeap" + ValueType::name() + "_" + std::to_string(Quantity);
+  };
+};
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+  makeCartesianProductBenchmark<RangesPopHeap, AllValueTypes>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}
diff --git a/libcxx/benchmarks/algorithms/ranges_push_heap.bench.cpp b/libcxx/benchmarks/algorithms/ranges_push_heap.bench.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/benchmarks/algorithms/ranges_push_heap.bench.cpp
@@ -0,0 +1,42 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+
+#include "common.h"
+
+namespace {
+template <class ValueType, class Order>
+struct RangesPushHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(
+        state, Quantity, Order(), BatchSize::CountElements, [](auto& Copy) {
+          for (auto I = Copy.begin(), E = Copy.end(); I != E; ++I) {
+            std::ranges::push_heap(Copy.begin(), I + 1);
+          }
+        });
+  }
+
+  bool skip() const { return Order() == ::Order::Heap; }
+
+  std::string name() const {
+    return "BM_RangesPushHeap" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+  makeCartesianProductBenchmark<RangesPushHeap, AllValueTypes, AllOrders>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}
diff --git a/libcxx/benchmarks/algorithms/ranges_sort_heap.bench.cpp b/libcxx/benchmarks/algorithms/ranges_sort_heap.bench.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/benchmarks/algorithms/ranges_sort_heap.bench.cpp
@@ -0,0 +1,36 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+
+#include "common.h"
+
+namespace {
+template <class ValueType>
+struct RangesSortHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(
+        state, Quantity, Order::Heap, BatchSize::CountElements,
+        [](auto& Copy) { std::ranges::sort_heap(Copy); });
+  }
+
+  std::string name() const {
+    return "BM_RangesSortHeap" + ValueType::name() + "_" + std::to_string(Quantity);
+  };
+};
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+  makeCartesianProductBenchmark<RangesSortHeap, AllValueTypes>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}
diff --git a/libcxx/docs/Status/RangesAlgorithms.csv b/libcxx/docs/Status/RangesAlgorithms.csv
--- a/libcxx/docs/Status/RangesAlgorithms.csv
+++ b/libcxx/docs/Status/RangesAlgorithms.csv
@@ -78,10 +78,10 @@
 Permutation,partial_sort,Konstantin Varlamov,n/a,In progress
 Permutation,nth_element,Konstantin Varlamov,`D128149 <https://llvm.org/D128149>`_,✅
 Permutation,inplace_merge,Not assigned,n/a,Not started
-Permutation,make_heap,Not assigned,n/a,Not started
-Permutation,push_heap,Not assigned,n/a,Not started
-Permutation,pop_heap,Not assigned,n/a,Not started
-Permutation,sort_heap,Not assigned,n/a,Not started
+Permutation,make_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
+Permutation,push_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
+Permutation,pop_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
+Permutation,sort_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
 Permutation,prev_permutation,Not assigned,n/a,Not started
 Permutation,next_permutation,Not assigned,n/a,Not started
 Uninitialised memory,uninitialized_copy,Konstantin Varlamov,`D116023 <https://llvm.org/D116023>`_,✅
diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -92,6 +92,7 @@
   __algorithm/ranges_is_sorted_until.h
   __algorithm/ranges_lexicographical_compare.h
   __algorithm/ranges_lower_bound.h
+  __algorithm/ranges_make_heap.h
   __algorithm/ranges_max.h
   __algorithm/ranges_max_element.h
   __algorithm/ranges_merge.h
@@ -104,6 +105,8 @@
   __algorithm/ranges_move_backward.h
   __algorithm/ranges_none_of.h
   __algorithm/ranges_nth_element.h
+  __algorithm/ranges_pop_heap.h
+  __algorithm/ranges_push_heap.h
   __algorithm/ranges_remove.h
   __algorithm/ranges_remove_if.h
   __algorithm/ranges_replace.h
@@ -111,6 +114,7 @@
   __algorithm/ranges_reverse.h
   __algorithm/ranges_set_difference.h
   __algorithm/ranges_sort.h
+  __algorithm/ranges_sort_heap.h
   __algorithm/ranges_stable_sort.h
   __algorithm/ranges_swap_ranges.h
   __algorithm/ranges_transform.h
diff --git a/libcxx/include/__algorithm/make_heap.h b/libcxx/include/__algorithm/make_heap.h
--- a/libcxx/include/__algorithm/make_heap.h
+++ b/libcxx/include/__algorithm/make_heap.h
@@ -14,6 +14,7 @@
 #include <__algorithm/sift_down.h>
 #include <__config>
 #include <__iterator/iterator_traits.h>
+#include <__utility/move.h>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
@@ -22,36 +23,32 @@
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 template <class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 void
-__make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
-    difference_type __n = __last - __first;
-    if (__n > 1)
-    {
-        // start from the first parent, there is no need to consider children
-        for (difference_type __start = (__n - 2) / 2; __start >= 0; --__start)
-        {
-            _VSTD::__sift_down<_Compare>(__first, __comp, __n, __first + __start);
-        }
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+void __make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp) {
+  using _CompRef = typename __comp_ref_type<_Compare>::type;
+  _CompRef __comp_ref = __comp;
+
+  using difference_type = typename iterator_traits<_RandomAccessIterator>::difference_type;
+  difference_type __n = __last - __first;
+  if (__n > 1) {
+    // start from the first parent, there is no need to consider children
+    for (difference_type __start = (__n - 2) / 2; __start >= 0; --__start) {
+        std::__sift_down<_CompRef>(__first, __comp_ref, __n, __first + __start);
     }
+  }
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-    _VSTD::__make_heap<_Comp_ref>(__first, __last, __comp);
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
+  std::__make_heap(std::move(__first), std::move(__last), __comp);
 }
 
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
-{
-    _VSTD::make_heap(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last) {
+  std::make_heap(std::move(__first), std::move(__last),
+      __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/__algorithm/pop_heap.h b/libcxx/include/__algorithm/pop_heap.h
--- a/libcxx/include/__algorithm/pop_heap.h
+++ b/libcxx/include/__algorithm/pop_heap.h
@@ -13,6 +13,7 @@
 #include <__algorithm/comp_ref_type.h>
 #include <__algorithm/push_heap.h>
 #include <__algorithm/sift_down.h>
+#include <__assert>
 #include <__config>
 #include <__iterator/iterator_traits.h>
 #include <__utility/move.h>
@@ -24,44 +25,43 @@
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 template <class _Compare, class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-__pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp,
-           typename iterator_traits<_RandomAccessIterator>::difference_type __len)
-{
-    using value_type = typename iterator_traits<_RandomAccessIterator>::value_type;
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+void __pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp,
+    typename iterator_traits<_RandomAccessIterator>::difference_type __len) {
+  _LIBCPP_ASSERT(__len > 0, "The heap given to pop_heap must be non-empty");
 
-    if (__len > 1)
-    {
-        value_type __top = std::move(*__first);  // create a hole at __first
-        _RandomAccessIterator __hole = std::__floyd_sift_down<_Compare>(__first, __comp, __len);
-        --__last;
-        if (__hole == __last) {
-            *__hole = std::move(__top);
-        } else {
-            *__hole = std::move(*__last);
-            ++__hole;
-            *__last = std::move(__top);
-            std::__sift_up<_Compare>(__first, __hole, __comp, __hole - __first);
-        }
+  using _CompRef = typename __comp_ref_type<_Compare>::type;
+  _CompRef __comp_ref = __comp;
+
+  using value_type = typename iterator_traits<_RandomAccessIterator>::value_type;
+  if (__len > 1) {
+    value_type __top = std::move(*__first);  // create a hole at __first
+    _RandomAccessIterator __hole = std::__floyd_sift_down<_CompRef>(__first, __comp_ref, __len);
+    --__last;
+
+    if (__hole == __last) {
+      *__hole = std::move(__top);
+    } else {
+      *__hole = std::move(*__last);
+      ++__hole;
+      *__last = std::move(__top);
+      std::__sift_up<_CompRef>(__first, __hole, __comp_ref, __hole - __first);
     }
+  }
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-    _VSTD::__pop_heap<_Comp_ref>(__first, __last, __comp, __last - __first);
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
+  typename iterator_traits<_RandomAccessIterator>::difference_type __len = __last - __first;
+  std::__pop_heap(std::move(__first), std::move(__last), __comp, __len);
 }
 
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
-{
-    _VSTD::pop_heap(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last) {
+  std::pop_heap(std::move(__first), std::move(__last),
+      __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/__algorithm/push_heap.h b/libcxx/include/__algorithm/push_heap.h
--- a/libcxx/include/__algorithm/push_heap.h
+++ b/libcxx/include/__algorithm/push_heap.h
@@ -22,47 +22,50 @@
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 template <class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX11 void
-__sift_up(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp,
-          typename iterator_traits<_RandomAccessIterator>::difference_type __len)
-{
-    typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
-    if (__len > 1)
-    {
-        __len = (__len - 2) / 2;
-        _RandomAccessIterator __ptr = __first + __len;
-        if (__comp(*__ptr, *--__last))
-        {
-            value_type __t(_VSTD::move(*__last));
-            do
-            {
-                *__last = _VSTD::move(*__ptr);
-                __last = __ptr;
-                if (__len == 0)
-                    break;
-                __len = (__len - 1) / 2;
-                __ptr = __first + __len;
-            } while (__comp(*__ptr, __t));
-            *__last = _VSTD::move(__t);
-        }
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+void __sift_up(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp,
+        typename iterator_traits<_RandomAccessIterator>::difference_type __len) {
+  using value_type = typename iterator_traits<_RandomAccessIterator>::value_type;
+
+  if (__len > 1) {
+    __len = (__len - 2) / 2;
+    _RandomAccessIterator __ptr = __first + __len;
+
+    if (__comp(*__ptr, *--__last)) {
+      value_type __t(std::move(*__last));
+      do {
+        *__last = std::move(*__ptr);
+        __last = __ptr;
+        if (__len == 0)
+          break;
+        __len = (__len - 1) / 2;
+        __ptr = __first + __len;
+      } while (__comp(*__ptr, __t));
+
+      *__last = std::move(__t);
     }
+  }
+}
+
+template <class _RandomAccessIterator, class _Compare>
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+void __push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp) {
+  using _CompRef = typename __comp_ref_type<_Compare>::type;
+  typename iterator_traits<_RandomAccessIterator>::difference_type __len = __last - __first;
+  std::__sift_up<_CompRef>(std::move(__first), std::move(__last), __comp, __len);
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-    _VSTD::__sift_up<_Comp_ref>(__first, __last, __comp, __last - __first);
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
+  std::__push_heap(std::move(__first), std::move(__last), __comp);
 }
 
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
-{
-    _VSTD::push_heap(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last) {
+  std::push_heap(std::move(__first), std::move(__last),
+      __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/__algorithm/ranges_make_heap.h b/libcxx/include/__algorithm/ranges_make_heap.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_make_heap.h
@@ -0,0 +1,79 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_MAKE_HEAP_H
+#define _LIBCPP___ALGORITHM_RANGES_MAKE_HEAP_H
+
+#include <__algorithm/make_heap.h>
+#include <__algorithm/make_projected.h>
+#include <__concepts/same_as.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__iterator/projected.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __make_heap {
+
+struct __fn {
+  template <class _Iter, class _Sent, class _Comp, class _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Iter __make_heap_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
+    auto __last_iter = ranges::next(__first, __last);
+
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
+    std::__make_heap(std::move(__first), __last_iter, __projected_comp);
+
+    return __last_iter;
+  }
+
+  template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Iter operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __make_heap_fn_impl(std::move(__first), std::move(__last), __comp, __proj);
+  }
+
+  template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Range> operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __make_heap_fn_impl(ranges::begin(__r), ranges::end(__r), __comp, __proj);
+  }
+};
+
+} // namespace __make_heap
+
+inline namespace __cpo {
+  inline constexpr auto make_heap = __make_heap::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_MAKE_HEAP_H
diff --git a/libcxx/include/__algorithm/ranges_pop_heap.h b/libcxx/include/__algorithm/ranges_pop_heap.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_pop_heap.h
@@ -0,0 +1,80 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_POP_HEAP_H
+#define _LIBCPP___ALGORITHM_RANGES_POP_HEAP_H
+
+#include <__algorithm/make_projected.h>
+#include <__algorithm/pop_heap.h>
+#include <__concepts/same_as.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__iterator/projected.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __pop_heap {
+
+struct __fn {
+  template <class _Iter, class _Sent, class _Comp, class _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Iter __pop_heap_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
+    auto __last_iter = ranges::next(__first, __last);
+    auto __len = __last_iter - __first;
+
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
+    std::__pop_heap(std::move(__first), __last_iter, __projected_comp, __len);
+
+    return __last_iter;
+  }
+
+  template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Iter operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __pop_heap_fn_impl(std::move(__first), std::move(__last), __comp, __proj);
+  }
+
+  template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Range> operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __pop_heap_fn_impl(ranges::begin(__r), ranges::end(__r), __comp, __proj);
+  }
+};
+
+} // namespace __pop_heap
+
+inline namespace __cpo {
+  inline constexpr auto pop_heap = __pop_heap::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_POP_HEAP_H
diff --git a/libcxx/include/__algorithm/ranges_push_heap.h b/libcxx/include/__algorithm/ranges_push_heap.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_push_heap.h
@@ -0,0 +1,79 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_PUSH_HEAP_H
+#define _LIBCPP___ALGORITHM_RANGES_PUSH_HEAP_H
+
+#include <__algorithm/make_projected.h>
+#include <__algorithm/push_heap.h>
+#include <__concepts/same_as.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__iterator/projected.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __push_heap {
+
+struct __fn {
+  template <class _Iter, class _Sent, class _Comp, class _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Iter __push_heap_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
+    auto __last_iter = ranges::next(__first, __last);
+
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
+    std::__push_heap(std::move(__first), __last_iter, __projected_comp);
+
+    return __last_iter;
+  }
+
+  template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Iter operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __push_heap_fn_impl(std::move(__first), std::move(__last), __comp, __proj);
+  }
+
+  template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Range> operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __push_heap_fn_impl(ranges::begin(__r), ranges::end(__r), __comp, __proj);
+  }
+};
+
+} // namespace __push_heap
+
+inline namespace __cpo {
+  inline constexpr auto push_heap = __push_heap::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_PUSH_HEAP_H
diff --git a/libcxx/include/__algorithm/ranges_sort_heap.h b/libcxx/include/__algorithm/ranges_sort_heap.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_sort_heap.h
@@ -0,0 +1,79 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_SORT_HEAP_H
+#define _LIBCPP___ALGORITHM_RANGES_SORT_HEAP_H
+
+#include <__algorithm/make_projected.h>
+#include <__algorithm/sort_heap.h>
+#include <__concepts/same_as.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__iterator/projected.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __sort_heap {
+
+struct __fn {
+  template <class _Iter, class _Sent, class _Comp, class _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Iter __sort_heap_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
+    auto __last_iter = ranges::next(__first, __last);
+
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
+    std::__sort_heap(std::move(__first), __last_iter, __projected_comp);
+
+    return __last_iter;
+  }
+
+  template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Iter operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __sort_heap_fn_impl(std::move(__first), std::move(__last), __comp, __proj);
+  }
+
+  template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Range> operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __sort_heap_fn_impl(ranges::begin(__r), ranges::end(__r), __comp, __proj);
+  }
+};
+
+} // namespace __sort_heap
+
+inline namespace __cpo {
+  inline constexpr auto sort_heap = __sort_heap::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_SORT_HEAP_H
diff --git a/libcxx/include/__algorithm/sort_heap.h b/libcxx/include/__algorithm/sort_heap.h
--- a/libcxx/include/__algorithm/sort_heap.h
+++ b/libcxx/include/__algorithm/sort_heap.h
@@ -14,6 +14,7 @@
 #include <__algorithm/pop_heap.h>
 #include <__config>
 #include <__iterator/iterator_traits.h>
+#include <__utility/move.h>
 #include <type_traits> // swap
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
@@ -23,29 +24,27 @@
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 template <class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX17 void
-__sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
-    for (difference_type __n = __last - __first; __n > 1; --__last, (void) --__n)
-        _VSTD::__pop_heap<_Compare>(__first, __last, __comp, __n);
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX11
+void __sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp) {
+  using _CompRef = typename __comp_ref_type<_Compare>::type;
+  _CompRef __comp_ref = __comp;
+
+  using difference_type = typename iterator_traits<_RandomAccessIterator>::difference_type;
+  for (difference_type __n = __last - __first; __n > 1; --__last, (void) --__n)
+    std::__pop_heap<_CompRef>(__first, __last, __comp_ref, __n);
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-    _VSTD::__sort_heap<_Comp_ref>(__first, __last, __comp);
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
+  std::__sort_heap(std::move(__first), std::move(__last), __comp);
 }
 
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
-void
-sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
-{
-    _VSTD::sort_heap(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last) {
+  std::sort_heap(std::move(__first), std::move(__last),
+      __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -287,6 +287,50 @@
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
     constexpr bool ranges::is_partitioned(R&& r, Pred pred, Proj proj = {});                // since C++20
 
+  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+          class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr I
+      ranges::push_heap(I first, S last, Comp comp = {}, Proj proj = {});                   // since C++20
+
+  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr borrowed_iterator_t<R>
+      ranges::push_heap(R&& r, Comp comp = {}, Proj proj = {});                             // since C++20
+
+  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+          class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr I
+      ranges::pop_heap(I first, S last, Comp comp = {}, Proj proj = {});                    // since C++20
+
+  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr borrowed_iterator_t<R>
+      ranges::pop_heap(R&& r, Comp comp = {}, Proj proj = {});                              // since C++20
+
+  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+          class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr I
+      ranges::make_heap(I first, S last, Comp comp = {}, Proj proj = {});                   // since C++20
+
+  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr borrowed_iterator_t<R>
+      ranges::make_heap(R&& r, Comp comp = {}, Proj proj = {});                             // since C++20
+
+  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+          class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr I
+      ranges::sort_heap(I first, S last, Comp comp = {}, Proj proj = {});                   // since C++20
+
+  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr borrowed_iterator_t<R>
+      ranges::sort_heap(R&& r, Comp comp = {}, Proj proj = {});                             // since C++20
+
   template<bidirectional_iterator I, sentinel_for<I> S>
     requires permutable<I>
     constexpr I ranges::reverse(I first, S last);                                           // since C++20
@@ -1313,6 +1357,7 @@
 #include <__algorithm/ranges_is_sorted_until.h>
 #include <__algorithm/ranges_lexicographical_compare.h>
 #include <__algorithm/ranges_lower_bound.h>
+#include <__algorithm/ranges_make_heap.h>
 #include <__algorithm/ranges_max.h>
 #include <__algorithm/ranges_max_element.h>
 #include <__algorithm/ranges_merge.h>
@@ -1325,6 +1370,8 @@
 #include <__algorithm/ranges_move_backward.h>
 #include <__algorithm/ranges_none_of.h>
 #include <__algorithm/ranges_nth_element.h>
+#include <__algorithm/ranges_pop_heap.h>
+#include <__algorithm/ranges_push_heap.h>
 #include <__algorithm/ranges_remove.h>
 #include <__algorithm/ranges_remove_if.h>
 #include <__algorithm/ranges_replace.h>
@@ -1332,6 +1379,7 @@
 #include <__algorithm/ranges_reverse.h>
 #include <__algorithm/ranges_set_difference.h>
 #include <__algorithm/ranges_sort.h>
+#include <__algorithm/ranges_sort_heap.h>
 #include <__algorithm/ranges_stable_sort.h>
 #include <__algorithm/ranges_swap_ranges.h>
 #include <__algorithm/ranges_transform.h>
diff --git a/libcxx/include/module.modulemap.in b/libcxx/include/module.modulemap.in
--- a/libcxx/include/module.modulemap.in
+++ b/libcxx/include/module.modulemap.in
@@ -331,6 +331,7 @@
       module ranges_is_sorted_until          { private header "__algorithm/ranges_is_sorted_until.h" }
       module ranges_lexicographical_compare  { private header "__algorithm/ranges_lexicographical_compare.h" }
       module ranges_lower_bound              { private header "__algorithm/ranges_lower_bound.h" }
+      module ranges_make_heap                { private header "__algorithm/ranges_make_heap.h" }
       module ranges_max                      { private header "__algorithm/ranges_max.h" }
       module ranges_max_element              { private header "__algorithm/ranges_max_element.h" }
       module ranges_merge                    { private header "__algorithm/ranges_merge.h" }
@@ -343,6 +344,8 @@
       module ranges_move_backward            { private header "__algorithm/ranges_move_backward.h" }
       module ranges_none_of                  { private header "__algorithm/ranges_none_of.h" }
       module ranges_nth_element              { private header "__algorithm/ranges_nth_element.h" }
+      module ranges_pop_heap                 { private header "__algorithm/ranges_pop_heap.h" }
+      module ranges_push_heap                { private header "__algorithm/ranges_push_heap.h" }
       module ranges_remove                   { private header "__algorithm/ranges_remove.h" }
       module ranges_remove_if                { private header "__algorithm/ranges_remove_if.h" }
       module ranges_replace                  { private header "__algorithm/ranges_replace.h" }
@@ -350,6 +353,7 @@
       module ranges_reverse                  { private header "__algorithm/ranges_reverse.h" }
       module ranges_set_difference           { private header "__algorithm/ranges_set_difference.h" }
       module ranges_sort                     { private header "__algorithm/ranges_sort.h" }
+      module ranges_sort_heap                { private header "__algorithm/ranges_sort_heap.h" }
       module ranges_stable_sort              { private header "__algorithm/ranges_stable_sort.h" }
       module ranges_swap_ranges              { private header "__algorithm/ranges_swap_ranges.h" }
       module ranges_transform                { private header "__algorithm/ranges_transform.h" }
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
@@ -144,8 +144,8 @@
     (void)std::ranges::lexicographical_compare(a, b, Less(&copies)); assert(copies == 0);
     (void)std::ranges::lower_bound(first, last, value, Less(&copies)); assert(copies == 0);
     (void)std::ranges::lower_bound(a, value, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::make_heap(first, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::make_heap(a, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::make_heap(first, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::make_heap(a, Less(&copies)); assert(copies == 0);
     (void)std::ranges::max(value, value, Less(&copies)); assert(copies == 0);
     (void)std::ranges::max({ value, value }, Less(&copies)); assert(copies == 0);
     (void)std::ranges::max(a, Less(&copies)); assert(copies == 0);
@@ -181,12 +181,12 @@
     //(void)std::ranges::partition_copy(a, first2, last2, UnaryTrue(&copies)); assert(copies == 0);
     //(void)std::ranges::partition_point(first, last, UnaryTrue(&copies)); assert(copies == 0);
     //(void)std::ranges::partition_point(a, UnaryTrue(&copies)); assert(copies == 0);
-    //(void)std::ranges::pop_heap(first, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::pop_heap(a, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::pop_heap(first, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::pop_heap(a, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::prev_permutation(first, last, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::prev_permutation(a, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::push_heap(first, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::push_heap(a, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::push_heap(first, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::push_heap(a, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy_if(first, last, first2, UnaryTrue(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy_if(a, first2, UnaryTrue(&copies)); assert(copies == 0);
     (void)std::ranges::remove_if(first, last, UnaryTrue(&copies)); assert(copies == 0);
@@ -209,8 +209,8 @@
     //(void)std::ranges::set_union(a, b, first2, Less(&copies)); assert(copies == 0);
     (void)std::ranges::sort(first, last, Less(&copies)); assert(copies == 0);
     (void)std::ranges::sort(a, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::sort_heap(first, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::sort_heap(a, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::sort_heap(first, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::sort_heap(a, Less(&copies)); assert(copies == 0);
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(first, last, UnaryTrue(&copies)); assert(copies == 0); }
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(a, UnaryTrue(&copies)); assert(copies == 0); }
     if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(first, last, Less(&copies)); assert(copies == 0); }
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
@@ -127,8 +127,8 @@
     (void)std::ranges::lexicographical_compare(a, b, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::lower_bound(first, last, value, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::lower_bound(a, value, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::make_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::make_heap(a, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::make_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::make_heap(a, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::max(T(), T(), Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::max({ T(), T() }, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::max(a, Less(), Proj(&copies)); assert(copies == 0);
@@ -164,12 +164,12 @@
     //(void)std::ranges::partition_copy(a, first2, last2, UnaryTrue(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partition_point(first, last, UnaryTrue(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partition_point(a, UnaryTrue(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::pop_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::pop_heap(a, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::pop_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::pop_heap(a, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::prev_permutation(first, last, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::prev_permutation(a, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::push_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::push_heap(a, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::push_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::push_heap(a, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy(first, last, first2, value, Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy(a, first2, value, Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy_if(first, last, first2, UnaryTrue(), Proj(&copies)); assert(copies == 0);
@@ -200,8 +200,8 @@
     //(void)std::ranges::set_union(a, b, first2, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::sort(first, last, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::sort(a, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::sort_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::sort_heap(a, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::sort_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::sort_heap(a, Less(), Proj(&copies)); assert(copies == 0);
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(first, last, UnaryTrue(), Proj(&copies)); assert(copies == 0); }
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(a, UnaryTrue(), Proj(&copies)); assert(copies == 0); }
     if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(first, last, Less(), Proj(&copies)); assert(copies == 0); }
diff --git a/libcxx/test/libcxx/private_headers.verify.cpp b/libcxx/test/libcxx/private_headers.verify.cpp
--- a/libcxx/test/libcxx/private_headers.verify.cpp
+++ b/libcxx/test/libcxx/private_headers.verify.cpp
@@ -129,6 +129,7 @@
 #include <__algorithm/ranges_is_sorted_until.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_is_sorted_until.h'}}
 #include <__algorithm/ranges_lexicographical_compare.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_lexicographical_compare.h'}}
 #include <__algorithm/ranges_lower_bound.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_lower_bound.h'}}
+#include <__algorithm/ranges_make_heap.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_make_heap.h'}}
 #include <__algorithm/ranges_max.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_max.h'}}
 #include <__algorithm/ranges_max_element.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_max_element.h'}}
 #include <__algorithm/ranges_merge.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_merge.h'}}
@@ -141,6 +142,8 @@
 #include <__algorithm/ranges_move_backward.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_move_backward.h'}}
 #include <__algorithm/ranges_none_of.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_none_of.h'}}
 #include <__algorithm/ranges_nth_element.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_nth_element.h'}}
+#include <__algorithm/ranges_pop_heap.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_pop_heap.h'}}
+#include <__algorithm/ranges_push_heap.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_push_heap.h'}}
 #include <__algorithm/ranges_remove.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_remove.h'}}
 #include <__algorithm/ranges_remove_if.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_remove_if.h'}}
 #include <__algorithm/ranges_replace.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_replace.h'}}
@@ -148,6 +151,7 @@
 #include <__algorithm/ranges_reverse.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_reverse.h'}}
 #include <__algorithm/ranges_set_difference.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_set_difference.h'}}
 #include <__algorithm/ranges_sort.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_sort.h'}}
+#include <__algorithm/ranges_sort_heap.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_sort_heap.h'}}
 #include <__algorithm/ranges_stable_sort.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_stable_sort.h'}}
 #include <__algorithm/ranges_swap_ranges.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_swap_ranges.h'}}
 #include <__algorithm/ranges_transform.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_transform.h'}}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/make.heap/ranges_make_heap.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/make.heap/ranges_make_heap.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/make.heap/ranges_make_heap.pass.cpp
@@ -0,0 +1,224 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//         class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr I
+//     ranges::make_heap(I first, S last, Comp comp = {}, Proj proj = {});                   // since C++20
+//
+// template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr borrowed_iterator_t<R>
+//     ranges::make_heap(R&& r, Comp comp = {}, Proj proj = {});                             // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasMakeHeapIt = requires(Iter first, Sent last, Comp comp) { std::ranges::make_heap(first, last, comp); };
+
+static_assert(HasMakeHeapIt<int*>);
+static_assert(!HasMakeHeapIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasMakeHeapIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasMakeHeapIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasMakeHeapIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasMakeHeapIt<int*, int*, BadComparator>);
+static_assert(!HasMakeHeapIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasMakeHeapR = requires(Range range, Comp comp) { std::ranges::make_heap(range, comp); };
+
+static_assert(HasMakeHeapR<UncheckedRange<int*>>);
+static_assert(!HasMakeHeapR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasMakeHeapR<RandomAccessRangeBadIndex>);
+static_assert(!HasMakeHeapR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasMakeHeapR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasMakeHeapR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasMakeHeapR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <size_t N, class T, class Iter>
+constexpr void verify_heap(const std::array<T, N>& heapified, Iter last, std::array<T, N> expected) {
+  assert(heapified == expected);
+  assert(base(last) == heapified.data() + heapified.size());
+  assert(std::is_heap(heapified.begin(), heapified.end()));
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_one(const std::array<int, N> input, std::array<int, N> expected) {
+  { // (iterator, sentinel) overload.
+    auto heapified = input;
+    auto b = Iter(heapified.data());
+    auto e = Sent(Iter(heapified.data() + heapified.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::make_heap(b, e);
+    verify_heap(heapified, last, expected);
+  }
+
+  { // (range) overload.
+    auto heapified = input;
+    auto b = Iter(heapified.data());
+    auto e = Sent(Iter(heapified.data() + heapified.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::make_heap(range);
+    verify_heap(heapified, last, expected);
+  }
+}
+
+template <class Iter, class Sent>
+constexpr void test_iterators_2() {
+  // Empty sequence.
+  test_one<Iter, Sent, 0>({}, {});
+  // 1-element sequence.
+  test_one<Iter, Sent, 1>({1}, {1});
+  // 2-element sequence.
+  test_one<Iter, Sent, 2>({2, 1}, {2, 1});
+  // 3-element sequence.
+  test_one<Iter, Sent, 3>({2, 1, 3}, {3, 1, 2});
+  // Longer sequence.
+  test_one<Iter, Sent, 8>({2, 1, 3, 6, 8, 4, 11, 5}, {11, 8, 4, 6, 1, 2, 3, 5});
+  // Longer sequence with duplicates.
+  test_one<Iter, Sent, 7>({2, 1, 3, 6, 2, 8, 6}, {8, 6, 6, 1, 2, 3, 2});
+  // All elements are the same.
+  test_one<Iter, Sent, 3>({1, 1, 1}, {1, 1, 1});
+  // Already heapified.
+  test_one<Iter, Sent, 5>({5, 4, 3, 1, 2}, {5, 4, 3, 1, 2});
+  // Sorted.
+  test_one<Iter, Sent, 5>({1, 2, 3, 4, 5}, {5, 4, 3, 1, 2});
+  // Reverse-sorted.
+  test_one<Iter, Sent, 5>({5, 4, 3, 2, 1}, {5, 4, 3, 2, 1});
+}
+
+template <class Iter>
+constexpr void test_iterators_1() {
+  test_iterators_2<Iter, Iter>();
+  test_iterators_2<Iter, sentinel_wrapper<Iter>>();
+}
+
+constexpr void test_iterators() {
+  test_iterators_1<random_access_iterator<int*>>();
+  test_iterators_1<contiguous_iterator<int*>>();
+  test_iterators_1<int*>();
+}
+
+constexpr bool test() {
+  test_iterators();
+
+  { // A custom comparator works.
+    const std::array input = {5, 4, 3, 2, 1};
+    std::array expected = {1, 2, 3, 5, 4};
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in.begin(), in.end(), std::ranges::greater{});
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in, std::ranges::greater{});
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{2}, A{1}, A{3}};
+    std::array expected = {A{3}, A{1}, A{2}};
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in.begin(), in.end(), {}, &A::a);
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in, {}, &A::a);
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct A {
+      int i;
+      constexpr A(int i_) : i(i_) {}
+
+      constexpr bool comparator(const A& rhs) const { return i < rhs.i; }
+      constexpr const A& projection() const { return *this; }
+
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{2}, A{1}, A{3}};
+    std::array expected = {A{3}, A{1}, A{2}};
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in.begin(), in.end(), &A::comparator, &A::projection);
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in, &A::comparator, &A::projection);
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    const std::array input = {2, 1, 3};
+    std::array expected = {3, 1, 2};
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in.begin(), in.end(), [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::make_heap(in, [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    [[maybe_unused]] std::same_as<std::ranges::dangling> decltype(auto) result =
+        std::ranges::make_heap(std::array{1, 2, 3});
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/assert.pop_heap.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/assert.pop_heap.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/assert.pop_heap.pass.cpp
@@ -0,0 +1,29 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// REQUIRES: has-unix-headers
+// UNSUPPORTED: c++03
+// XFAIL: use_system_cxx_lib && target={{.+}}-apple-macosx{{10.9|10.10|10.11|10.12|10.13|10.14|10.15|11.0|12.0}}
+// ADDITIONAL_COMPILE_FLAGS: -D_LIBCPP_ENABLE_ASSERTIONS=1
+
+// <algorithm>
+
+// Calling `pop_heap` on an empty range is invalid.
+
+#include <algorithm>
+
+#include <array>
+#include "check_assertion.h"
+
+int main(int, char**) {
+  std::array<int, 0> a;
+
+  TEST_LIBCPP_ASSERT_FAILURE(std::pop_heap(a.begin(), a.end()), "The heap given to pop_heap must be non-empty");
+
+  return 0;
+}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/assert.ranges_pop_heap.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/assert.ranges_pop_heap.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/assert.ranges_pop_heap.pass.cpp
@@ -0,0 +1,29 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// REQUIRES: has-unix-headers
+// UNSUPPORTED: c++03, c++11, c++14, c++17, libcpp-has-no-incomplete-ranges
+// ADDITIONAL_COMPILE_FLAGS: -D_LIBCPP_ENABLE_ASSERTIONS=1
+
+// <algorithm>
+
+// Calling `ranges::pop_heap` on an empty range is invalid.
+
+#include <algorithm>
+
+#include <array>
+#include "check_assertion.h"
+
+int main(int, char**) {
+  std::array<int, 0> a;
+
+  TEST_LIBCPP_ASSERT_FAILURE(std::ranges::pop_heap(a.begin(), a.end()), "The heap given to pop_heap must be non-empty");
+  TEST_LIBCPP_ASSERT_FAILURE(std::ranges::pop_heap(a), "The heap given to pop_heap must be non-empty");
+
+  return 0;
+}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/ranges_pop_heap.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/ranges_pop_heap.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/pop.heap/ranges_pop_heap.pass.cpp
@@ -0,0 +1,223 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//         class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr I
+//     ranges::pop_heap(I first, S last, Comp comp = {}, Proj proj = {});                    // since C++20
+//
+// template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr borrowed_iterator_t<R>
+//     ranges::pop_heap(R&& r, Comp comp = {}, Proj proj = {});                              // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasPopHeapIt = requires(Iter first, Sent last, Comp comp) { std::ranges::make_heap(first, last, comp); };
+
+static_assert(HasPopHeapIt<int*>);
+static_assert(!HasPopHeapIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasPopHeapIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasPopHeapIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasPopHeapIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasPopHeapIt<int*, int*, BadComparator>);
+static_assert(!HasPopHeapIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasPopHeapR = requires(Range range, Comp comp) { std::ranges::make_heap(range, comp); };
+
+static_assert(HasPopHeapR<UncheckedRange<int*>>);
+static_assert(!HasPopHeapR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasPopHeapR<RandomAccessRangeBadIndex>);
+static_assert(!HasPopHeapR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasPopHeapR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasPopHeapR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasPopHeapR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <size_t N, class T, class Iter>
+constexpr void verify_heap(const std::array<T, N>& heapified, Iter last, std::array<T, N> expected) {
+  assert(heapified == expected);
+  assert(base(last) == heapified.data() + heapified.size());
+  assert(std::is_heap(heapified.begin(), heapified.end() - 1));
+  assert(*std::max_element(heapified.begin(), heapified.end()) == heapified.back());
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_one(const std::array<int, N> input, std::array<int, N> expected) {
+  assert(!input.empty());
+  assert(std::is_heap(input.begin(), input.end()));
+
+  { // (iterator, sentinel) overload.
+    auto heapified = input;
+    auto b = Iter(heapified.data());
+    auto e = Sent(Iter(heapified.data() + heapified.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::pop_heap(b, e);
+    verify_heap(heapified, last, expected);
+  }
+
+  { // (range) overload.
+    auto heapified = input;
+    auto b = Iter(heapified.data());
+    auto e = Sent(Iter(heapified.data() + heapified.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::pop_heap(range);
+    verify_heap(heapified, last, expected);
+  }
+}
+
+template <class Iter, class Sent>
+constexpr void test_iterators_2() {
+  // 1-element sequence.
+  test_one<Iter, Sent, 1>({1}, {1});
+  // 2-element sequence.
+  test_one<Iter, Sent, 2>({2, 1}, {1, 2});
+  // 3-element sequence.
+  test_one<Iter, Sent, 3>({3, 1, 2}, {2, 1, 3});
+  // Longer sequence.
+  test_one<Iter, Sent, 8>({11, 8, 5, 6, 4, 3, 2, 1}, {8, 6, 5, 1, 4, 3, 2, 11});
+  // Longer sequence with duplicates.
+  test_one<Iter, Sent, 8>({8, 8, 6, 6, 1, 2, 2, 3}, {8, 6, 6, 3, 1, 2, 2, 8});
+  // All elements are the same.
+  test_one<Iter, Sent, 4>({1, 1, 1, 1}, {1, 1, 1, 1});
+}
+
+template <class Iter>
+constexpr void test_iterators_1() {
+  test_iterators_2<Iter, Iter>();
+  test_iterators_2<Iter, sentinel_wrapper<Iter>>();
+}
+
+constexpr void test_iterators() {
+  test_iterators_1<random_access_iterator<int*>>();
+  test_iterators_1<contiguous_iterator<int*>>();
+  test_iterators_1<int*>();
+}
+
+constexpr bool test() {
+  test_iterators();
+
+  { // A custom comparator works.
+    const std::array input = {1, 2, 3, 5, 4};
+    std::array expected = {2, 4, 3, 5, 1};
+    auto comp = std::ranges::greater{};
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in.begin(), in.end(), comp);
+      assert(in == expected);
+      assert(last == in.data() + in.size());
+      assert(std::is_heap(in.begin(), in.end() - 1, comp));
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in, comp);
+      assert(in == expected);
+      assert(last == in.data() + in.size());
+      assert(std::is_heap(in.begin(), in.end() - 1, comp));
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{3}, A{1}, A{2}};
+    std::array expected = {A{2}, A{1}, A{3}};
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in.begin(), in.end(), {}, &A::a);
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in, {}, &A::a);
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct A {
+      int i;
+      constexpr A(int i_) : i(i_) {}
+
+      constexpr bool comparator(const A& rhs) const { return i < rhs.i; }
+      constexpr const A& projection() const { return *this; }
+
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{3}, A{1}, A{2}};
+    std::array expected = {A{2}, A{1}, A{3}};
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in.begin(), in.end(), &A::comparator, &A::projection);
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in, &A::comparator, &A::projection);
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    const std::array input = {3, 1, 2};
+    std::array expected = {2, 1, 3};
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in.begin(), in.end(), [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::pop_heap(in, [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    [[maybe_unused]] std::same_as<std::ranges::dangling> decltype(auto) result =
+        std::ranges::pop_heap(std::array{2, 1, 3});
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/push.heap/ranges_push_heap.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/push.heap/ranges_push_heap.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/push.heap/ranges_push_heap.pass.cpp
@@ -0,0 +1,226 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//         class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr I
+//     ranges::push_heap(I first, S last, Comp comp = {}, Proj proj = {});                   // since C++20
+//
+// template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr borrowed_iterator_t<R>
+//     ranges::push_heap(R&& r, Comp comp = {}, Proj proj = {});                             // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasPushHeapIt = requires(Iter first, Sent last, Comp comp) { std::ranges::make_heap(first, last, comp); };
+
+static_assert(HasPushHeapIt<int*>);
+static_assert(!HasPushHeapIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasPushHeapIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasPushHeapIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasPushHeapIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasPushHeapIt<int*, int*, BadComparator>);
+static_assert(!HasPushHeapIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasPushHeapR = requires(Range range, Comp comp) { std::ranges::make_heap(range, comp); };
+
+static_assert(HasPushHeapR<UncheckedRange<int*>>);
+static_assert(!HasPushHeapR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasPushHeapR<RandomAccessRangeBadIndex>);
+static_assert(!HasPushHeapR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasPushHeapR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasPushHeapR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasPushHeapR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <size_t N, class T, class Iter>
+constexpr void verify_heap(const std::array<T, N>& heapified, Iter last, std::array<T, N> expected) {
+  assert(heapified == expected);
+  assert(base(last) == heapified.data() + heapified.size());
+  assert(std::is_heap(heapified.begin(), heapified.end()));
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_one(const std::array<int, N> input, std::array<int, N> expected) {
+  if (!input.empty()) {
+    assert(std::is_heap(input.begin(), input.end() - 1));
+  }
+
+  { // (iterator, sentinel) overload.
+    auto heapified = input;
+    auto b = Iter(heapified.data());
+    auto e = Sent(Iter(heapified.data() + heapified.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::push_heap(b, e);
+    verify_heap(heapified, last, expected);
+  }
+
+  { // (range) overload.
+    auto heapified = input;
+    auto b = Iter(heapified.data());
+    auto e = Sent(Iter(heapified.data() + heapified.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::push_heap(range);
+    verify_heap(heapified, last, expected);
+  }
+}
+
+template <class Iter, class Sent>
+constexpr void test_iterators_2() {
+  // Empty sequence.
+  test_one<Iter, Sent, 0>({}, {});
+  // 1-element sequence.
+  test_one<Iter, Sent, 1>({1}, {1});
+  // 2-element sequence.
+  test_one<Iter, Sent, 2>({2, 1}, {2, 1});
+  // 3-element sequence.
+  test_one<Iter, Sent, 3>({2, 1, 3}, {3, 1, 2});
+  // Longer sequence.
+  test_one<Iter, Sent, 8>({11, 6, 5, 1, 4, 3, 2, 8}, {11, 8, 5, 6, 4, 3, 2, 1});
+  // Longer sequence with duplicates.
+  test_one<Iter, Sent, 7>({8, 6, 3, 1, 2, 2, 6}, {8, 6, 6, 1, 2, 2, 3});
+  // All elements are the same.
+  test_one<Iter, Sent, 4>({1, 1, 1, 1}, {1, 1, 1, 1});
+  // Already heapified.
+  test_one<Iter, Sent, 5>({5, 4, 3, 1, 2}, {5, 4, 3, 1, 2});
+  // Reverse-sorted.
+  test_one<Iter, Sent, 5>({5, 4, 3, 2, 1}, {5, 4, 3, 2, 1});
+}
+
+template <class Iter>
+constexpr void test_iterators_1() {
+  test_iterators_2<Iter, Iter>();
+  test_iterators_2<Iter, sentinel_wrapper<Iter>>();
+}
+
+constexpr void test_iterators() {
+  test_iterators_1<random_access_iterator<int*>>();
+  test_iterators_1<contiguous_iterator<int*>>();
+  test_iterators_1<int*>();
+}
+
+constexpr bool test() {
+  test_iterators();
+
+  { // A custom comparator works.
+    const std::array input = {5, 4, 3, 2, 1};
+    std::array expected = {1, 5, 3, 2, 4};
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in.begin(), in.end(), std::ranges::greater{});
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in, std::ranges::greater{});
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{2}, A{1}, A{3}};
+    std::array expected = {A{3}, A{1}, A{2}};
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in.begin(), in.end(), {}, &A::a);
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in, {}, &A::a);
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct A {
+      int i;
+      constexpr A(int i_) : i(i_) {}
+
+      constexpr bool comparator(const A& rhs) const { return i < rhs.i; }
+      constexpr const A& projection() const { return *this; }
+
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{2}, A{1}, A{3}};
+    std::array expected = {A{3}, A{1}, A{2}};
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in.begin(), in.end(), &A::comparator, &A::projection);
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in, &A::comparator, &A::projection);
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    const std::array input = {2, 1, 3};
+    std::array expected = {3, 1, 2};
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in.begin(), in.end(), [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_heap(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::push_heap(in, [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_heap(in, last, expected);
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    [[maybe_unused]] std::same_as<std::ranges::dangling> decltype(auto) result =
+        std::ranges::push_heap(std::array{1, 2, 3});
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/sort.heap/ranges_sort_heap.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/sort.heap/ranges_sort_heap.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.heap.operations/sort.heap/ranges_sort_heap.pass.cpp
@@ -0,0 +1,221 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//         class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr I
+//     ranges::sort_heap(I first, S last, Comp comp = {}, Proj proj = {});                   // since C++20
+//
+// template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr borrowed_iterator_t<R>
+//     ranges::sort_heap(R&& r, Comp comp = {}, Proj proj = {});                             // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasSortHeapIt = requires(Iter first, Sent last, Comp comp) { std::ranges::make_heap(first, last, comp); };
+
+static_assert(HasSortHeapIt<int*>);
+static_assert(!HasSortHeapIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasSortHeapIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasSortHeapIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasSortHeapIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasSortHeapIt<int*, int*, BadComparator>);
+static_assert(!HasSortHeapIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasSortHeapR = requires(Range range, Comp comp) { std::ranges::make_heap(range, comp); };
+
+static_assert(HasSortHeapR<UncheckedRange<int*>>);
+static_assert(!HasSortHeapR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasSortHeapR<RandomAccessRangeBadIndex>);
+static_assert(!HasSortHeapR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasSortHeapR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasSortHeapR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasSortHeapR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <size_t N, class T, class Iter>
+constexpr void verify_sorted(const std::array<T, N>& sorted, Iter last, std::array<T, N> expected) {
+  assert(sorted == expected);
+  assert(base(last) == sorted.data() + sorted.size());
+  assert(std::is_sorted(sorted.begin(), sorted.end()));
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_one(const std::array<int, N> input, std::array<int, N> expected) {
+  assert(std::is_heap(input.begin(), input.end()));
+
+  { // (iterator, sentinel) overload.
+    auto sorted = input;
+    auto b = Iter(sorted.data());
+    auto e = Sent(Iter(sorted.data() + sorted.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::sort_heap(b, e);
+    verify_sorted(sorted, last, expected);
+  }
+
+  { // (range) overload.
+    auto sorted = input;
+    auto b = Iter(sorted.data());
+    auto e = Sent(Iter(sorted.data() + sorted.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::sort_heap(range);
+    verify_sorted(sorted, last, expected);
+  }
+}
+
+template <class Iter, class Sent>
+constexpr void test_iterators_2() {
+  // 1-element sequence.
+  test_one<Iter, Sent, 1>({1}, {1});
+  // 2-element sequence.
+  test_one<Iter, Sent, 2>({2, 1}, {1, 2});
+  // 3-element sequence.
+  test_one<Iter, Sent, 3>({3, 1, 2}, {1, 2, 3});
+  // Longer sequence.
+  test_one<Iter, Sent, 8>({11, 8, 4, 6, 1, 2, 3, 5}, {1, 2, 3, 4, 5, 6, 8, 11});
+  // Longer sequence with duplicates.
+  test_one<Iter, Sent, 7>({8, 6, 6, 1, 2, 3, 2}, {1, 2, 2, 3, 6, 6, 8});
+  // All elements are the same.
+  test_one<Iter, Sent, 4>({1, 1, 1, 1}, {1, 1, 1, 1});
+}
+
+template <class Iter>
+constexpr void test_iterators_1() {
+  test_iterators_2<Iter, Iter>();
+  test_iterators_2<Iter, sentinel_wrapper<Iter>>();
+}
+
+constexpr void test_iterators() {
+  test_iterators_1<random_access_iterator<int*>>();
+  test_iterators_1<contiguous_iterator<int*>>();
+  test_iterators_1<int*>();
+}
+
+constexpr bool test() {
+  test_iterators();
+
+  { // A custom comparator works.
+    const std::array input = {1, 2, 3, 5, 4};
+    std::array expected = {5, 4, 3, 2, 1};
+    auto comp = std::ranges::greater{};
+    assert(std::is_heap(input.begin(), input.end(), comp));
+
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in.begin(), in.end(), comp);
+      assert(in == expected);
+      assert(last == in.data() + in.size());
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in, comp);
+      assert(in == expected);
+      assert(last == in.data() + in.size());
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{3}, A{1}, A{2}};
+    std::array expected = {A{1}, A{2}, A{3}};
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in.begin(), in.end(), {}, &A::a);
+      verify_sorted(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in, {}, &A::a);
+      verify_sorted(in, last, expected);
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct A {
+      int i;
+      constexpr A(int i_) : i(i_) {}
+
+      constexpr bool comparator(const A& rhs) const { return i < rhs.i; }
+      constexpr const A& projection() const { return *this; }
+
+      constexpr auto operator<=>(const A&) const = default;
+    };
+
+    const std::array input = {A{3}, A{1}, A{2}};
+    std::array expected = {A{1}, A{2}, A{3}};
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in.begin(), in.end(), &A::comparator, &A::projection);
+      verify_sorted(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in, &A::comparator, &A::projection);
+      verify_sorted(in, last, expected);
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    const std::array input = {3, 1, 2};
+    std::array expected = {1, 2, 3};
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in.begin(), in.end(), [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_sorted(in, last, expected);
+    }
+
+    {
+      auto in = input;
+      auto last = std::ranges::sort_heap(in, [](int i, int j) { return BooleanTestable{i < j}; });
+      verify_sorted(in, last, expected);
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    [[maybe_unused]] std::same_as<std::ranges::dangling> decltype(auto) result =
+        std::ranges::sort_heap(std::array{2, 1, 3});
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
--- a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
+++ b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
@@ -95,7 +95,7 @@
 static_assert(test(std::ranges::is_sorted_until, a));
 static_assert(test(std::ranges::lexicographical_compare, a, a));
 static_assert(test(std::ranges::lower_bound, a, 42));
-//static_assert(test(std::ranges::make_heap, a));
+static_assert(test(std::ranges::make_heap, a));
 static_assert(test(std::ranges::max, a));
 static_assert(test(std::ranges::max_element, a));
 static_assert(test(std::ranges::merge, a, a, a));
@@ -114,9 +114,9 @@
 //static_assert(test(std::ranges::partition, a, odd));
 //static_assert(test(std::ranges::partition_copy, a, a, a, odd));
 //static_assert(test(std::ranges::partition_point, a, odd));
-//static_assert(test(std::ranges::pop_heap, a));
+static_assert(test(std::ranges::pop_heap, a));
 //static_assert(test(std::ranges::prev_permutation, a));
-//static_assert(test(std::ranges::push_heap, a));
+static_assert(test(std::ranges::push_heap, a));
 static_assert(test(std::ranges::remove, a, 42));
 //static_assert(test(std::ranges::remove_copy, a, a, 42));
 //static_assert(test(std::ranges::remove_copy_if, a, a, odd));
@@ -138,7 +138,7 @@
 //static_assert(test(std::ranges::set_union, a, a, a));
 //static_assert(test(std::ranges::shuffle, a, g));
 static_assert(test(std::ranges::sort, a));
-//static_assert(test(std::ranges::sort_heap, a));
+static_assert(test(std::ranges::sort_heap, a));
 //static_assert(test(std::ranges::stable_partition, a, odd));
 static_assert(test(std::ranges::stable_sort, a));
 //static_assert(test(std::ranges::starts_with, a, a));