[libc++] Split out `<__functional_{ops,search}>` from `<functional>`. NFCI

[• Quuxplusone]

Summary

This comes out of my comments on D99041. The general strategy is:

• Split out __search into <__functional_search>, so <algorithm> can include <__functional_search> instead of <functional>
• Split out the lifted operators into <__functional_ops>, so many headers (notably <valarray>, <numeric>, and <set>) can include <__functional_ops> instead of <functional>

[cjdb]

LGTM except for the change to <concepts>. I think we should merge both, and then take a discussion to the mailing list for broader consideration.

libcxx/include/concepts

393

I'm against this change, per my reason in D99041.

[zoecarver]

This mostly LGTM. Thanks for the cleanup. It will be great to rely less on <functional>.

This change shouldn't have any observable effect so it might make sense to say "NFC" in the title.

libcxx/include/__functional_search

11

Does it make sense to combine these two headers?

libcxx/include/concepts

393

You can keep using forward that comes from utility/type_traits.

[• Quuxplusone]

libcxx/include/concepts

393

Yeah, and I know libc++ style is generally to use forward over static_cast; I was just testing the waters here. 😛 (The advantage would be avoiding a couple of function template instantiations every time this concept is used. OTOH maybe that matters only if __invoke is also changed to avoid forward.)
I'm not sure if @cjdb's comment refers to worrying about "changes to invoke that aren't done through __invoke, and so we're blind to the changes", which by now I think Tim Song has put to rest; but anyway I think my path of least resistance here is to eliminate the diffs in <concepts> and try that part again separately, maybe after more of @cjdb's patches have landed.

[• Quuxplusone]

Revert diffs in <concepts>

[zoecarver]

libcxx/include/concepts

393

Maybe this isn't the case with static_cast vs forward because they're so synonymous, but I think the added confusion to someone reading this isn't worth the absolutely minimal gain of one template instantiation (which will likely actually be cached for the use in __invoke anyway).

[ldionne]

I would rather we use __functional/XYZ.h instead. Or if you convince me that __functional_XYZ is better instead, then we should make other headers consistent with that choice.

Also, just to clarify, you didn't modify any code at all, only moved it around, right? Your modifications to __invoke have been reverted from the patch. I checked, but I want to make double-sure that's your intent, since I'd push back on a change to the definition of the concept to use __invoke.

[• Quuxplusone]

@ldionne wrote:

I would rather we use functional/XYZ.h instead. Or if you convince me that functional_XYZ is better instead, then we should make other headers consistent with that choice.

The other headers have been consistent with __functional_XYZ forever. Let's take this to Slack.

Also, just to clarify, you didn't modify any code at all, only moved it around, right?

That's right. (Now that the <concepts> change has been deleted, that is, that's right.)

[cjdb]

In D99044#2641551, @Quuxplusone wrote:

@ldionne wrote:

I would rather we use functional/XYZ.h instead. Or if you convince me that functional_XYZ is better instead, then we should make other headers consistent with that choice.

The other headers have been consistent with __functional_XYZ forever. Let's take this to Slack.

There's a dedicated LLVM Discord server. Can we have this conversation there please?

[• Quuxplusone]

Use __invoke instead of invoke, as a global preference. (__invoke comes from <type_traits>, which means we don't need to include <functional>. After this patch, git grep '::invoke(' returns no results, and I think we can easily keep it that way.)

Old dependency graph: https://i.imgur.com/o5Tu2Yc.png
New dependency graph: https://i.imgur.com/P6D8hEH.png

(Btw, I looked at what it would take to move all the invoke/__invoke stuff into its own header, and that turned out to be pretty icky, because result_of depends on __invoke_result_t, and result_of is mandated to be in <type_traits>. So in order to put invoke in the same header as __invoke, we'd need to either put invoke in <type_traits>, or split out __invoke into a header that's even lower-level than <type_traits>, e.g. "<type_traits> includes <__functional_invoke> includes <__type_traits_base>." That's too Byzantine for me.)

[curdeius]

libcxx/include/numeric

151

Why not this?

[• Quuxplusone]

Unfortunately we can't use __invoke in bind_front and not_fn
without major surgery, because that causes some kind of problem
with their noexcept clauses. I think using is_nothrow_invocable<...>
is somehow strictly SFINAE-safer than using noexcept(invoke(...)).

But we can't use is_nothrow_invocable for not_fn, because what we care about there is that neither invoke nor operator! throw exceptions.

And we can't use is_nothrow_invocable for bind_front without further surgery, because apparently is_nothrow_invocable<Args...> is ill-formed! Clang wants us to pass parameter-pack expansions only to template parameters that themselves are packs, and is_nothrow_invocable<Fn, Args...> wants a non-pack as its first template parameter. Either this is really awful of C++, or I've misdiagnosed the problem.

[• Quuxplusone]

libcxx/include/numeric

151

I don't know! Updated the diff to find out. ;)

[ldionne]

FWIW, I love this patch in spirit, however it'll have to use __functional/search.h and __functional/ops.h to make any progress. I think it's worth doing.

libcxx/include/CMakeLists.txt

 set(files
   __availability
   __bit_reference
   __bits
   __bsd_locale_defaults.h
   __bsd_locale_fallbacks.h
   __config
   __debug
   __errc
   __functional_03
   __functional_base
   __functional_base_03
+  __functional_ops
+  __functional_search
   __hash_table
   __libcpp_version
   __locale
   __memory/allocator_traits.h
   __memory/base.h
   __memory/pointer_traits.h
   __memory/utilities.h
   __mutex_base

libcxx/include/__functional_base

 private:
     struct __two {char __lx; char __lxx;};
     template <class _Up> static __two __test(...);
     template <class _Up> static char __test(typename _Up::result_type* = 0);
 public:
     static const bool value = sizeof(__test<_Tp>(0)) == 1;
 };
 
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS less : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x < __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS less<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) < _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) < _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) < _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
 // __weak_result_type
 
 template <class _Tp>
 struct __derives_from_unary_function
 {
 private:
     struct __two {char __lx; char __lxx;};
     static __two __test(...);

libcxx/include/__functional_ops

+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// 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_FUNCTIONAL_OPS
+#define _LIBCPP_FUNCTIONAL_OPS
+
+#include <__config>
+#include <__functional_base> // unary_function, binary_function
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS plus : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x + __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS plus<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) + _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) + _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) + _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS minus : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x - __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS minus<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) - _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) - _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) - _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS multiplies : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x * __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS multiplies<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) * _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) * _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) * _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS divides : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x / __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS divides<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) / _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) / _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) / _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS modulus : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x % __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS modulus<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) % _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) % _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) % _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS negate : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return -__x;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS negate<void>
+{
+    template <class _Tp>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_Tp&& __x) const
+    _NOEXCEPT_(noexcept(- _VSTD::forward<_Tp>(__x)))
+    -> decltype        (- _VSTD::forward<_Tp>(__x))
+        { return        - _VSTD::forward<_Tp>(__x); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS equal_to : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x == __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS equal_to<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) == _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) == _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) == _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS not_equal_to : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x != __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS not_equal_to<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) != _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) != _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) != _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS greater : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x > __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS greater<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) > _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) > _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) > _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS less : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x < __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS less<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) < _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) < _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) < _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS greater_equal : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x >= __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS greater_equal<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) >= _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) >= _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) >= _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS less_equal : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x <= __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS less_equal<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) <= _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) <= _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) <= _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS logical_and : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x && __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS logical_and<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) && _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) && _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) && _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS logical_or : binary_function<_Tp, _Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x || __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS logical_or<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) || _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) || _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) || _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS logical_not : unary_function<_Tp, bool>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    bool operator()(const _Tp& __x) const
+        {return !__x;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS logical_not<void>
+{
+    template <class _Tp>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_Tp&& __x) const
+    _NOEXCEPT_(noexcept(!_VSTD::forward<_Tp>(__x)))
+    -> decltype        (!_VSTD::forward<_Tp>(__x))
+        { return        !_VSTD::forward<_Tp>(__x); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS bit_and : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x & __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS bit_and<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) & _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) & _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) & _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS bit_or : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x | __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS bit_or<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) | _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) | _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) | _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+#else
+template <class _Tp>
+#endif
+struct _LIBCPP_TEMPLATE_VIS bit_xor : binary_function<_Tp, _Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x, const _Tp& __y) const
+        {return __x ^ __y;}
+};
+
+#if _LIBCPP_STD_VER > 11
+template <>
+struct _LIBCPP_TEMPLATE_VIS bit_xor<void>
+{
+    template <class _T1, class _T2>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_T1&& __t, _T2&& __u) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) ^ _VSTD::forward<_T2>(__u)))
+    -> decltype        (_VSTD::forward<_T1>(__t) ^ _VSTD::forward<_T2>(__u))
+        { return        _VSTD::forward<_T1>(__t) ^ _VSTD::forward<_T2>(__u); }
+    typedef void is_transparent;
+};
+#endif
+
+
+#if _LIBCPP_STD_VER > 11
+template <class _Tp = void>
+struct _LIBCPP_TEMPLATE_VIS bit_not : unary_function<_Tp, _Tp>
+{
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    _Tp operator()(const _Tp& __x) const
+        {return ~__x;}
+};
+
+template <>
+struct _LIBCPP_TEMPLATE_VIS bit_not<void>
+{
+    template <class _Tp>
+    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
+    auto operator()(_Tp&& __x) const
+    _NOEXCEPT_(noexcept(~_VSTD::forward<_Tp>(__x)))
+    -> decltype        (~_VSTD::forward<_Tp>(__x))
+        { return        ~_VSTD::forward<_Tp>(__x); }
+    typedef void is_transparent;
+};
+#endif
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif  // _LIBCPP_FUNCTIONAL_OPS

libcxx/include/__functional_search

+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// 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_FUNCTIONAL_SEARCH
+#define _LIBCPP_FUNCTIONAL_SEARCH
+
+#include <__config>
+#include <iterator>
+#include <utility> // make_pair
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+template <class _BinaryPredicate, class _ForwardIterator1, class _ForwardIterator2>
+pair<_ForwardIterator1, _ForwardIterator1> _LIBCPP_CONSTEXPR_AFTER_CXX11
+__search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
+         _ForwardIterator2 __first2, _ForwardIterator2 __last2, _BinaryPredicate __pred,
+         forward_iterator_tag, forward_iterator_tag)
+{
+    if (__first2 == __last2)
+        return _VSTD::make_pair(__first1, __first1);  // Everything matches an empty sequence
+    while (true)
+    {
+        // Find first element in sequence 1 that matchs *__first2, with a mininum of loop checks
+        while (true)
+        {
+            if (__first1 == __last1)  // return __last1 if no element matches *__first2
+                return _VSTD::make_pair(__last1, __last1);
+            if (__pred(*__first1, *__first2))
+                break;
+            ++__first1;
+        }
+        // *__first1 matches *__first2, now match elements after here
+        _ForwardIterator1 __m1 = __first1;
+        _ForwardIterator2 __m2 = __first2;
+        while (true)
+        {
+            if (++__m2 == __last2)  // If pattern exhausted, __first1 is the answer (works for 1 element pattern)
+                return _VSTD::make_pair(__first1, __m1);
+            if (++__m1 == __last1)  // Otherwise if source exhaused, pattern not found
+                return _VSTD::make_pair(__last1, __last1);
+            if (!__pred(*__m1, *__m2))  // if there is a mismatch, restart with a new __first1
+            {
+                ++__first1;
+                break;
+            }  // else there is a match, check next elements
+        }
+    }
+}
+
+template <class _BinaryPredicate, class _RandomAccessIterator1, class _RandomAccessIterator2>
+_LIBCPP_CONSTEXPR_AFTER_CXX11
+pair<_RandomAccessIterator1, _RandomAccessIterator1>
+__search(_RandomAccessIterator1 __first1, _RandomAccessIterator1 __last1,
+         _RandomAccessIterator2 __first2, _RandomAccessIterator2 __last2, _BinaryPredicate __pred,
+           random_access_iterator_tag, random_access_iterator_tag)
+{
+    typedef typename iterator_traits<_RandomAccessIterator1>::difference_type _D1;
+    typedef typename iterator_traits<_RandomAccessIterator2>::difference_type _D2;
+    // Take advantage of knowing source and pattern lengths.  Stop short when source is smaller than pattern
+    const _D2 __len2 = __last2 - __first2;
+    if (__len2 == 0)
+        return _VSTD::make_pair(__first1, __first1);
+    const _D1 __len1 = __last1 - __first1;
+    if (__len1 < __len2)
+        return _VSTD::make_pair(__last1, __last1);
+    const _RandomAccessIterator1 __s = __last1 - (__len2 - 1);  // Start of pattern match can't go beyond here
+
+    while (true)
+    {
+        while (true)
+        {
+            if (__first1 == __s)
+                return _VSTD::make_pair(__last1, __last1);
+            if (__pred(*__first1, *__first2))
+                break;
+            ++__first1;
+        }
+
+        _RandomAccessIterator1 __m1 = __first1;
+        _RandomAccessIterator2 __m2 = __first2;
+         while (true)
+         {
+             if (++__m2 == __last2)
+                 return _VSTD::make_pair(__first1, __first1 + __len2);
+             ++__m1;          // no need to check range on __m1 because __s guarantees we have enough source
+             if (!__pred(*__m1, *__m2))
+             {
+                 ++__first1;
+                 break;
+             }
+         }
+    }
+}
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif  // _LIBCPP_FUNCTIONAL_SEARCH

libcxx/include/algorithm

template <class BidirectionalIterator, class Compare>
     constexpr bool     // constexpr in C++20
     prev_permutation(BidirectionalIterator first, BidirectionalIterator last, Compare comp);
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_search> // __search
 #include <initializer_list>
 #include <type_traits>
 #include <cstring>
-#include <utility> // needed to provide swap_ranges.
+#include <utility> // pair
 #include <memory>
-#include <functional>
 #include <iterator>
 #include <cstddef>
 #include <bit>
 #include <version>
 
 #include <__debug>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

libcxx/include/concepts

namespace std {
   // [concept.strictweakorder], concept strict_weak_order
   template<class R, class T, class U>
     concept strict_weak_order = see below;
 }
 
 */
 
 #include <__config>
-#include <functional>
-#include <type_traits>
+#include <type_traits> // __invoke
 #include <utility>
 #include <version>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_PUSH_MACROS

 concept semiregular = copyable<_Tp> && default_initializable<_Tp>;
 
 template<class _Tp>
 concept regular = semiregular<_Tp> && equality_comparable<_Tp>;
 
 // [concept.invocable]
 template<class _Fn, class... _Args>
 concept invocable = requires(_Fn&& __fn, _Args&&... __args) {
-  _VSTD::invoke(_VSTD::forward<_Fn>(__fn), _VSTD::forward<_Args>(__args)...); // not required to be equality preserving
+  _VSTD::__invoke(_VSTD::forward<_Fn>(__fn), _VSTD::forward<_Args>(__args)...); // not required to be equality preserving
 };
 
 // [concept.regular.invocable]
 template<class _Fn, class... _Args>
 concept regular_invocable = invocable<_Fn, _Args...>;
 
 #endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_CONCEPTS)
 
 _LIBCPP_END_NAMESPACE_STD
 
 _LIBCPP_POP_MACROS
 
 #endif // _LIBCPP_CONCEPTS

libcxx/include/experimental/coroutine

 
 } // namespace coroutines_v1
 } // namespace experimental
 } // namespace std
 
  */
 
 #include <experimental/__config>
+#include <__functional_ops> // less
 #include <new>
 #include <type_traits>
-#include <functional>
-#include <memory> // for hash<T*>
+#include <utility> // hash
 #include <cstddef>
 #include <__debug>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 #ifdef _LIBCPP_HAS_NO_COROUTINES

libcxx/include/experimental/propagate_const

 
 #include <experimental/__config>
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 #if _LIBCPP_STD_VER > 11
 
+#include <__functional_ops> // less, greater, equal_to
 #include <type_traits>
-#include <utility>
-#include <functional>
+#include <utility> // hash
 
 _LIBCPP_BEGIN_NAMESPACE_LFTS_V2
 
 
 template <class _Tp>
 class propagate_const;
 
 template <class _Up>

libcxx/include/experimental/simd

 };
 
 } // parallelism_v2
 } // std::experimental
 
 */
 
 #include <experimental/__config>
+#include <__functional_ops> // plus, multiplies, bit_and, bit_or, bit_xor
 #include <algorithm>
 #include <array>
 #include <cstddef>
-#include <functional>
+#include <utility> // pair
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_PUSH_MACROS
 #include <__undef_macros>
 

libcxx/include/ext/hash_map

template <class Key, class T, class Hash, class Pred, class Alloc>
     operator!=(const hash_multimap<Key, T, Hash, Pred, Alloc>& x,
                const hash_multimap<Key, T, Hash, Pred, Alloc>& y);
 
 }  // __gnu_cxx
 
 */
 
 #include <__config>
+#include <__functional_ops> // equal_to
 #include <__hash_table>
-#include <functional>
 #include <stdexcept>
 #include <type_traits>
 #include <ext/__hash>
 
 #if defined(__DEPRECATED) && __DEPRECATED
 #if defined(_LIBCPP_WARNING)
     _LIBCPP_WARNING("Use of the header <ext/hash_map> is deprecated.  Migrate to <unordered_map>")
 #else

libcxx/include/ext/hash_set

template <class Value, class Hash, class Pred, class Alloc>
     bool
     operator!=(const hash_multiset<Value, Hash, Pred, Alloc>& x,
                const hash_multiset<Value, Hash, Pred, Alloc>& y);
 }  // __gnu_cxx
 
 */
 
 #include <__config>
+#include <__functional_ops> // equal_to
 #include <__hash_table>
-#include <functional>
 #include <ext/__hash>
 
 #if defined(__DEPRECATED) && __DEPRECATED
 #if defined(_LIBCPP_WARNING)
     _LIBCPP_WARNING("Use of the header <ext/hash_set> is deprecated.  Migrate to <unordered_set>")
 #else
 #   warning Use of the header <ext/hash_set> is deprecated.  Migrate to <unordered_set>
 #endif

libcxx/include/functional

          will be minimal.
 
 */
 
 #include <__config>
 #include <type_traits>
 #include <typeinfo>
 #include <exception>
+#include <iterator>
 #include <memory>
 #include <tuple>
 #include <utility>
 #include <version>
 
 #include <__functional_base>
+#include <__functional_ops>
+#include <__functional_search>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS plus : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x + __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS plus<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) + _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) + _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) + _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS minus : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x - __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS minus<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) - _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) - _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) - _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS multiplies : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x * __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS multiplies<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) * _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) * _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) * _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS divides : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x / __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS divides<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) / _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) / _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) / _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS modulus : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x % __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS modulus<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) % _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) % _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) % _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS negate : unary_function<_Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x) const
-        {return -__x;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS negate<void>
-{
-    template <class _Tp>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_Tp&& __x) const
-    _NOEXCEPT_(noexcept(- _VSTD::forward<_Tp>(__x)))
-    -> decltype        (- _VSTD::forward<_Tp>(__x))
-        { return        - _VSTD::forward<_Tp>(__x); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS equal_to : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x == __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS equal_to<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) == _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) == _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) == _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS not_equal_to : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x != __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS not_equal_to<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) != _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) != _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) != _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS greater : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x > __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS greater<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) > _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) > _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) > _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-// less in <__functional_base>
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS greater_equal : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x >= __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS greater_equal<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) >= _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) >= _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) >= _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS less_equal : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x <= __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS less_equal<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) <= _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) <= _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) <= _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS logical_and : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x && __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS logical_and<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) && _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) && _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) && _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS logical_or : binary_function<_Tp, _Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x || __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS logical_or<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) || _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) || _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) || _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS logical_not : unary_function<_Tp, bool>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    bool operator()(const _Tp& __x) const
-        {return !__x;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS logical_not<void>
-{
-    template <class _Tp>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_Tp&& __x) const
-    _NOEXCEPT_(noexcept(!_VSTD::forward<_Tp>(__x)))
-    -> decltype        (!_VSTD::forward<_Tp>(__x))
-        { return        !_VSTD::forward<_Tp>(__x); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS bit_and : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x & __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS bit_and<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) & _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) & _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) & _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS bit_or : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x | __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS bit_or<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) | _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) | _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) | _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-#else
-template <class _Tp>
-#endif
-struct _LIBCPP_TEMPLATE_VIS bit_xor : binary_function<_Tp, _Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x, const _Tp& __y) const
-        {return __x ^ __y;}
-};
-
-#if _LIBCPP_STD_VER > 11
-template <>
-struct _LIBCPP_TEMPLATE_VIS bit_xor<void>
-{
-    template <class _T1, class _T2>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_T1&& __t, _T2&& __u) const
-    _NOEXCEPT_(noexcept(_VSTD::forward<_T1>(__t) ^ _VSTD::forward<_T2>(__u)))
-    -> decltype        (_VSTD::forward<_T1>(__t) ^ _VSTD::forward<_T2>(__u))
-        { return        _VSTD::forward<_T1>(__t) ^ _VSTD::forward<_T2>(__u); }
-    typedef void is_transparent;
-};
-#endif
-
-
-#if _LIBCPP_STD_VER > 11
-template <class _Tp = void>
-struct _LIBCPP_TEMPLATE_VIS bit_not : unary_function<_Tp, _Tp>
-{
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    _Tp operator()(const _Tp& __x) const
-        {return ~__x;}
-};
-
-template <>
-struct _LIBCPP_TEMPLATE_VIS bit_not<void>
-{
-    template <class _Tp>
-    _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
-    auto operator()(_Tp&& __x) const
-    _NOEXCEPT_(noexcept(~_VSTD::forward<_Tp>(__x)))
-    -> decltype        (~_VSTD::forward<_Tp>(__x))
-        { return        ~_VSTD::forward<_Tp>(__x); }
-    typedef void is_transparent;
-};
-#endif
-
 template <class _Predicate>
 class _LIBCPP_TEMPLATE_VIS _LIBCPP_DEPRECATED_IN_CXX17 unary_negate
     : public unary_function<typename _Predicate::argument_type, bool>
 {
     _Predicate __pred_;
 public:
     _LIBCPP_CONSTEXPR_AFTER_CXX11 _LIBCPP_INLINE_VISIBILITY
     explicit unary_negate(const _Predicate& __pred)

 constexpr auto bind_front(_Fn&& __f, _Args&&... __args)
 {
     return __perfect_forward<__bind_front_op, _Fn, _Args...>(_VSTD::forward<_Fn>(__f),
                                                              _VSTD::forward<_Args>(__args)...);
 }
 
 #endif // _LIBCPP_STD_VER > 17
 
-// struct hash<T*> in <memory>
-
-template <class _BinaryPredicate, class _ForwardIterator1, class _ForwardIterator2>
-pair<_ForwardIterator1, _ForwardIterator1> _LIBCPP_CONSTEXPR_AFTER_CXX11
-__search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
-         _ForwardIterator2 __first2, _ForwardIterator2 __last2, _BinaryPredicate __pred,
-         forward_iterator_tag, forward_iterator_tag)
-{
-    if (__first2 == __last2)
-        return _VSTD::make_pair(__first1, __first1);  // Everything matches an empty sequence
-    while (true)
-    {
-        // Find first element in sequence 1 that matchs *__first2, with a mininum of loop checks
-        while (true)
-        {
-            if (__first1 == __last1)  // return __last1 if no element matches *__first2
-                return _VSTD::make_pair(__last1, __last1);
-            if (__pred(*__first1, *__first2))
-                break;
-            ++__first1;
-        }
-        // *__first1 matches *__first2, now match elements after here
-        _ForwardIterator1 __m1 = __first1;
-        _ForwardIterator2 __m2 = __first2;
-        while (true)
-        {
-            if (++__m2 == __last2)  // If pattern exhausted, __first1 is the answer (works for 1 element pattern)
-                return _VSTD::make_pair(__first1, __m1);
-            if (++__m1 == __last1)  // Otherwise if source exhaused, pattern not found
-                return _VSTD::make_pair(__last1, __last1);
-            if (!__pred(*__m1, *__m2))  // if there is a mismatch, restart with a new __first1
-            {
-                ++__first1;
-                break;
-            }  // else there is a match, check next elements
-        }
-    }
-}
-
-template <class _BinaryPredicate, class _RandomAccessIterator1, class _RandomAccessIterator2>
-_LIBCPP_CONSTEXPR_AFTER_CXX11
-pair<_RandomAccessIterator1, _RandomAccessIterator1>
-__search(_RandomAccessIterator1 __first1, _RandomAccessIterator1 __last1,
-         _RandomAccessIterator2 __first2, _RandomAccessIterator2 __last2, _BinaryPredicate __pred,
-           random_access_iterator_tag, random_access_iterator_tag)
-{
-    typedef typename iterator_traits<_RandomAccessIterator1>::difference_type _D1;
-    typedef typename iterator_traits<_RandomAccessIterator2>::difference_type _D2;
-    // Take advantage of knowing source and pattern lengths.  Stop short when source is smaller than pattern
-    const _D2 __len2 = __last2 - __first2;
-    if (__len2 == 0)
-        return _VSTD::make_pair(__first1, __first1);
-    const _D1 __len1 = __last1 - __first1;
-    if (__len1 < __len2)
-        return _VSTD::make_pair(__last1, __last1);
-    const _RandomAccessIterator1 __s = __last1 - (__len2 - 1);  // Start of pattern match can't go beyond here
-
-    while (true)
-    {
-        while (true)
-        {
-            if (__first1 == __s)
-                return _VSTD::make_pair(__last1, __last1);
-            if (__pred(*__first1, *__first2))
-                break;
-            ++__first1;
-        }
-
-        _RandomAccessIterator1 __m1 = __first1;
-        _RandomAccessIterator2 __m2 = __first2;
-         while (true)
-         {
-             if (++__m2 == __last2)
-                 return _VSTD::make_pair(__first1, __first1 + __len2);
-             ++__m1;          // no need to check range on __m1 because __s guarantees we have enough source
-             if (!__pred(*__m1, *__m2))
-             {
-                 ++__first1;
-                 break;
-             }
-         }
-    }
-}
-
 #if _LIBCPP_STD_VER > 14
-
 // default searcher
 template<class _ForwardIterator, class _BinaryPredicate = equal_to<>>
 class _LIBCPP_TYPE_VIS default_searcher {
 public:
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
     default_searcher(_ForwardIterator __f, _ForwardIterator __l,
                        _BinaryPredicate __p = _BinaryPredicate())
         : __first_(__f), __last_(__l), __pred_(__p) {}
 
     template <typename _ForwardIterator2>
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17
     pair<_ForwardIterator2, _ForwardIterator2>
     operator () (_ForwardIterator2 __f, _ForwardIterator2 __l) const
     {
         return _VSTD::__search(__f, __l, __first_, __last_, __pred_,
             typename _VSTD::iterator_traits<_ForwardIterator>::iterator_category(),
             typename _VSTD::iterator_traits<_ForwardIterator2>::iterator_category());
     }
 
 private:
     _ForwardIterator __first_;
     _ForwardIterator __last_;
     _BinaryPredicate __pred_;
-    };
-
 #endif // _LIBCPP_STD_VER > 14
 
 #if _LIBCPP_STD_VER > 17
 template <class _Tp>
 using unwrap_reference_t = typename unwrap_reference<_Tp>::type;
 
 template <class _Tp>
 using unwrap_ref_decay_t = typename unwrap_ref_decay<_Tp>::type;

libcxx/include/map

 typename multimap<Key, T, Compare, Allocator>::size_type
 erase_if(multimap<Key, T, Compare, Allocator>& c, Predicate pred);  // C++20
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_ops> // less
 #include <__tree>
 #include <__node_handle>
 #include <iterator> // __libcpp_erase_if_container
 #include <memory>
 #include <utility>
-#include <functional>
 #include <initializer_list>
 #include <type_traits>
 #include <version>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 

libcxx/include/memory

 #include <typeinfo>
 #include <cstddef>
 #include <cstdint>
 #include <new>
 #include <utility>
 #include <limits>
 #include <iterator>
 #include <__functional_base>
+#include <__functional_ops> // less
 #include <iosfwd>
 #include <tuple>
 #include <stdexcept>
 #include <cstring>
 #include <__memory/allocator_traits.h>
 #include <__memory/base.h>
 #include <__memory/pointer_traits.h>
 #include <__memory/utilities.h>

libcxx/include/module.modulemap

module std [system] {
   }
 
   // FIXME: These should be private.
   module __bits { header "__bits" export * }
   module __bit_reference { header "__bit_reference" export * }
   module __debug { header "__debug" export * }
   module __errc { header "__errc" export * }
   module __functional_base { header "__functional_base" export * }
+  module __functional_ops { header "__functional_ops" export * }
+  module __functional_search { header "__functional_search" export * }
   module __hash_table { header "__hash_table" export * }
   module __locale { header "__locale" export * }
   module __mutex_base { header "__mutex_base" export * }
+  module __node_handle { header "__node_handle" export * }
   module __split_buffer { header "__split_buffer" export * }
   module __sso_allocator { header "__sso_allocator" export * }
   module __std_stream { header "__std_stream" export * }
   module __string { header "__string" export * }
   module __tree { header "__tree" export * }
   module __tuple { header "__tuple" export * }
   module __undef_macros { header "__undef_macros" export * }
-  module __node_handle { header "__node_handle" export * }
 
   module experimental {
     requires cplusplus11
 
     module algorithm {
       header "experimental/algorithm"
       export *
     }

libcxx/include/mutex

 template<class Callable, class ...Args>
   void call_once(once_flag& flag, Callable&& func, Args&&... args);
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_base>
 #include <__mutex_base>
 #include <cstdint>
-#include <functional>
 #include <memory>
 #ifndef _LIBCPP_CXX03_LANG
 #include <tuple>
 #endif
 #include <version>
 #include <__threading_support>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

libcxx/include/numeric

 template<class T>
     constexpr T* midpoint(T* a, T* b);        // C++20
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_ops> // plus, multiplies
 #include <iterator>
-#include <limits> // for numeric_limits
-#include <functional>
-#include <cmath> // for isnormal
+#include <limits> // numeric_limits
 #include <version>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_PUSH_MACROS
 #include <__undef_macros>
 

libcxx/include/optional

 
 } // namespace std
 
 */
 
 #include <__config>
 #include <__availability>
 #include <__debug>
-#include <__functional_base>
-#include <functional>
 #include <initializer_list>
 #include <new>
 #include <stdexcept>
 #include <type_traits>
 #include <utility>
 #include <version>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

libcxx/include/queue

void swap(priority_queue<T, Container, Compare>& x,
             priority_queue<T, Container, Compare>& y)
             noexcept(noexcept(x.swap(y)));
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_ops> // less
 #include <deque>
 #include <vector>
-#include <functional>
 #include <algorithm>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 

libcxx/include/set

 typename multiset<Key, Compare, Allocator>::size_type
 erase_if(multiset<Key, Compare, Allocator>& c, Predicate pred);  // C++20
 
 }  // std
 
 */
 
 #include <__config>
-#include <__tree>
+#include <__functional_ops> // less
 #include <__node_handle>
-#include <functional>
+#include <__tree>
 #include <iterator> // __libcpp_erase_if_container
 #include <version>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_BEGIN_NAMESPACE_STD

libcxx/include/thread

 
 */
 
 #include <__config>
 #include <iosfwd>
 #include <__functional_base>
 #include <type_traits>
 #include <cstddef>
-#include <functional>
 #include <memory>
 #include <system_error>
 #include <chrono>
 #include <__mutex_base>
 #ifndef _LIBCPP_CXX03_LANG
 #include <tuple>
 #endif
 #include <__threading_support>

libcxx/include/unordered_map

template <class Key, class T, class Hash, class Pred, class Alloc>
     operator!=(const unordered_multimap<Key, T, Hash, Pred, Alloc>& x,
                const unordered_multimap<Key, T, Hash, Pred, Alloc>& y);
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_ops> // equal_to
 #include <__hash_table>
 #include <__node_handle>
-#include <functional>
 #include <iterator> // __libcpp_erase_if_container
 #include <stdexcept>
 #include <tuple>
 #include <version>
 
 #include <__debug>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)

libcxx/include/unordered_set

template <class Value, class Hash, class Pred, class Alloc>
     bool
     operator!=(const unordered_multiset<Value, Hash, Pred, Alloc>& x,
                const unordered_multiset<Value, Hash, Pred, Alloc>& y);
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_ops> // equal_to
 #include <__hash_table>
 #include <__node_handle>
-#include <functional>
 #include <iterator> // __libcpp_erase_if_container
 #include <version>
 
 #include <__debug>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif

libcxx/include/valarray

 template <class T> unspecified1 end(valarray<T>& v);
 template <class T> unspecified2 end(const valarray<T>& v);
 
 }  // std
 
 */
 
 #include <__config>
+#include <__functional_ops> // negate, logical_not, less
 #include <cstddef>
 #include <cmath>
 #include <initializer_list>
 #include <algorithm>
-#include <functional>
 #include <new>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
 _LIBCPP_PUSH_MACROS
 #include <__undef_macros>

libcxx/include/variant

namespace std {
   template <> struct hash<monostate>;
 
 } // namespace std
 
 */
 
 #include <__config>
 #include <__availability>
+#include <__functional_ops> // less, greater
 #include <__tuple>
 #include <array>
 #include <exception>
-#include <functional>
 #include <initializer_list>
 #include <new>
 #include <tuple>
 #include <type_traits>
 #include <utility>
 #include <limits>
 #include <version>