[libc++][format] Add __format_arg_store.

This implements the struct `__format_arg_store` and its dependencies:
* the class basic_format_arg,
* the class basic_format_args,
* the class basic_format_context,
* the function make_format_args,
* the function wmake_format_args,
* the function visit_format_arg,
* several Standard required typedefs.

The following parts will be implemented in a later patch:

* the child class `basic_format_arg::handle`,
* the function `basic_format_arg::basic_format_arg(const T* p)`.

The following extension has been implemented:
* the class basic_format_arg supports `__[u]int128_t` on platform where libc++ supports 128 bit integrals.

Implements parts of:
* P0645 Text Formatting

Completes:
* LWG3371 visit_format_arg and make_format_args are not hidden friends
* LWG3542 basic_format_arg mishandles basic_string_view with custom traits

Note https://mordante.github.io/blog/2021/06/05/format.html gives a bit more information about the goals and non-goals of this initial patch series.

Reviewed By: #libc, ldionne, vitaut

Differential Revision: https://reviews.llvm.org/D103357

NOKEYCHECK=True
GitOrigin-RevId: 0922ce56f4f04fbcacead6cdf0416341fe44e4bb
diff --git a/include/CMakeLists.txt b/include/CMakeLists.txt
index 07faed9..33bc1ec 100644
--- a/include/CMakeLists.txt
+++ b/include/CMakeLists.txt
@@ -128,7 +128,11 @@
   __config
   __debug
   __errc
+  __format/format_arg.h
+  __format/format_args.h
+  __format/format_context.h
   __format/format_error.h
+  __format/format_fwd.h
   __format/format_parse_context.h
   __function_like.h
   __functional_base
diff --git a/include/__availability b/include/__availability
index 13d1195..87d43ed 100644
--- a/include/__availability
+++ b/include/__availability
@@ -139,9 +139,9 @@
 // #   define _LIBCPP_AVAILABILITY_DISABLE_FTM___cpp_lib_semaphore
 
     // This controls the availability of the C++20 format library.
-    // The library is in development and not ABI stable yet. Currently
-    // P2216 is aiming to be retroactively accepted in C++20. This paper
-    // contains ABI breaking changes.
+    // The library is in development and not ABI stable yet. P2216 is
+    // retroactively accepted in C++20. This paper contains ABI breaking
+    // changes.
 #   define _LIBCPP_AVAILABILITY_FORMAT
 // #   define _LIBCPP_AVAILABILITY_DISABLE_FTM___cpp_lib_format
 
@@ -238,9 +238,9 @@
 #   endif
 
     // This controls the availability of the C++20 format library.
-    // The library is in development and not ABI stable yet. Currently
-    // P2216 is aiming to be retroactively accepted in C++20. This paper
-    // contains ABI breaking changes.
+    // The library is in development and not ABI stable yet. P2216 is
+    // retroactively accepted in C++20. This paper contains ABI breaking
+    // changes.
 #   define _LIBCPP_AVAILABILITY_FORMAT                                          \
         __attribute__((unavailable))
 #   define _LIBCPP_AVAILABILITY_DISABLE_FTM___cpp_lib_format
diff --git a/include/__format/format_arg.h b/include/__format/format_arg.h
new file mode 100644
index 0000000..dd8ef48
--- /dev/null
+++ b/include/__format/format_arg.h
@@ -0,0 +1,256 @@
+// -*- 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___FORMAT_FORMAT_ARG_H
+#define _LIBCPP___FORMAT_FORMAT_ARG_H
+
+#include <__config>
+#include <__format/format_error.h>
+#include <__format/format_fwd.h>
+#include <__functional_base>
+#include <__variant/monostate.h>
+#include <concepts>
+#include <string>
+#include <string_view>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17
+
+// TODO FMT Remove this once we require compilers with proper C++20 support.
+// If the compiler has no concepts support, the format header will be disabled.
+// Without concepts support enable_if needs to be used and that too much effort
+// to support compilers with partial C++20 support.
+#if !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+namespace __format {
+/** The type stored in @ref basic_format_arg. */
+enum class _LIBCPP_ENUM_VIS __arg_t : uint8_t {
+  __none,
+  __bool,
+  __char_type,
+  __int,
+  __long_long,
+#ifndef _LIBCPP_HAS_NO_INT128
+  __i128,
+#endif
+  __unsigned,
+  __unsigned_long_long,
+#ifndef _LIBCPP_HAS_NO_INT128
+  __u128,
+#endif
+  __float,
+  __double,
+  __long_double,
+  __const_char_type_ptr,
+  __string_view,
+  __ptr
+};
+} // namespace __format
+
+template <class _Visitor, class _Context>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_AVAILABILITY_FORMAT decltype(auto)
+visit_format_arg(_Visitor&& __vis, basic_format_arg<_Context> __arg) {
+  switch (__arg.__type_) {
+  case __format::__arg_t::__none:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), monostate{});
+  case __format::__arg_t::__bool:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__bool);
+  case __format::__arg_t::__char_type:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__char_type);
+  case __format::__arg_t::__int:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__int);
+  case __format::__arg_t::__long_long:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__long_long);
+#ifndef _LIBCPP_HAS_NO_INT128
+  case __format::__arg_t::__i128:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__i128);
+#endif
+  case __format::__arg_t::__unsigned:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__unsigned);
+  case __format::__arg_t::__unsigned_long_long:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis),
+                         __arg.__unsigned_long_long);
+#ifndef _LIBCPP_HAS_NO_INT128
+  case __format::__arg_t::__u128:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__u128);
+#endif
+  case __format::__arg_t::__float:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__float);
+  case __format::__arg_t::__double:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__double);
+  case __format::__arg_t::__long_double:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__long_double);
+  case __format::__arg_t::__const_char_type_ptr:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis),
+                         __arg.__const_char_type_ptr);
+  case __format::__arg_t::__string_view:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__string_view);
+  case __format::__arg_t::__ptr:
+    return _VSTD::invoke(_VSTD::forward<_Visitor>(__vis), __arg.__ptr);
+  }
+  _LIBCPP_UNREACHABLE();
+}
+
+template <class _Context>
+class _LIBCPP_TEMPLATE_VIS _LIBCPP_AVAILABILITY_FORMAT basic_format_arg {
+public:
+  // TODO FMT Define the handle class.
+  class handle;
+
+  _LIBCPP_HIDE_FROM_ABI basic_format_arg() noexcept
+      : __type_{__format::__arg_t::__none} {}
+
+  _LIBCPP_HIDE_FROM_ABI explicit operator bool() const noexcept {
+    return __type_ != __format::__arg_t::__none;
+  }
+
+private:
+  using char_type = typename _Context::char_type;
+
+  // TODO FMT Implement constrain [format.arg]/4
+  // Constraints: The template specialization
+  //   typename Context::template formatter_type<T>
+  // meets the Formatter requirements ([formatter.requirements]).  The extent
+  // to which an implementation determines that the specialization meets the
+  // Formatter requirements is unspecified, except that as a minimum the
+  // expression
+  //   typename Context::template formatter_type<T>()
+  //    .format(declval<const T&>(), declval<Context&>())
+  // shall be well-formed when treated as an unevaluated operand.
+
+  template <class _Ctx, class... _Args>
+  _LIBCPP_HIDE_FROM_ABI
+      _LIBCPP_AVAILABILITY_FORMAT friend __format_arg_store<_Ctx, _Args...>
+      _VSTD::make_format_args(const _Args&...);
+
+  template <class _Visitor, class _Ctx>
+  _LIBCPP_HIDE_FROM_ABI _LIBCPP_AVAILABILITY_FORMAT friend decltype(auto)
+  _VSTD::visit_format_arg(_Visitor&& __vis, basic_format_arg<_Ctx> __arg);
+
+  union {
+    bool __bool;
+    char_type __char_type;
+    int __int;
+    unsigned __unsigned;
+    long long __long_long;
+    unsigned long long __unsigned_long_long;
+#ifndef _LIBCPP_HAS_NO_INT128
+    __int128_t __i128;
+    __uint128_t __u128;
+#endif
+    float __float;
+    double __double;
+    long double __long_double;
+    const char_type* __const_char_type_ptr;
+    basic_string_view<char_type> __string_view;
+    const void* __ptr;
+    // TODO FMT Add the handle.
+  };
+  __format::__arg_t __type_;
+
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(bool __v) noexcept
+      : __bool(__v), __type_(__format::__arg_t::__bool) {}
+
+  template <class _Tp>
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(_Tp __v) noexcept
+      requires(same_as<_Tp, char_type> ||
+               (same_as<_Tp, char> && same_as<char_type, wchar_t>))
+      : __char_type(__v), __type_(__format::__arg_t::__char_type) {}
+
+  template <__libcpp_signed_integer _Tp>
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(_Tp __v) noexcept {
+    if constexpr (sizeof(_Tp) <= sizeof(int)) {
+      __int = static_cast<int>(__v);
+      __type_ = __format::__arg_t::__int;
+    } else if constexpr (sizeof(_Tp) <= sizeof(long long)) {
+      __long_long = static_cast<long long>(__v);
+      __type_ = __format::__arg_t::__long_long;
+    }
+#ifndef _LIBCPP_HAS_NO_INT128
+    else if constexpr (sizeof(_Tp) == sizeof(__int128_t)) {
+      __i128 = __v;
+      __type_ = __format::__arg_t::__i128;
+    }
+#endif
+    else
+      static_assert(sizeof(_Tp) == 0, "An unsupported signed integer was used");
+  }
+
+  template <__libcpp_unsigned_integer _Tp>
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(_Tp __v) noexcept {
+    if constexpr (sizeof(_Tp) <= sizeof(unsigned)) {
+      __unsigned = static_cast<unsigned>(__v);
+      __type_ = __format::__arg_t::__unsigned;
+    } else if constexpr (sizeof(_Tp) <= sizeof(unsigned long long)) {
+      __unsigned_long_long = static_cast<unsigned long long>(__v);
+      __type_ = __format::__arg_t::__unsigned_long_long;
+    }
+#ifndef _LIBCPP_HAS_NO_INT128
+    else if constexpr (sizeof(_Tp) == sizeof(__int128_t)) {
+      __u128 = __v;
+      __type_ = __format::__arg_t::__u128;
+    }
+#endif
+    else
+      static_assert(sizeof(_Tp) == 0,
+                    "An unsupported unsigned integer was used");
+  }
+
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(float __v) noexcept
+      : __float(__v), __type_(__format::__arg_t::__float) {}
+
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(double __v) noexcept
+      : __double(__v), __type_(__format::__arg_t::__double) {}
+
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(long double __v) noexcept
+      : __long_double(__v), __type_(__format::__arg_t::__long_double) {}
+
+  // Note not a 'noexcept' function.
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(const char_type* __s)
+      : __const_char_type_ptr(__s),
+        __type_(__format::__arg_t::__const_char_type_ptr) {
+    _LIBCPP_ASSERT(__s, "Used a nullptr argument to initialize a C-string");
+  }
+
+  template <class _Traits>
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(
+      basic_string_view<char_type, _Traits> __s) noexcept
+      : __string_view{__s.data(), __s.size()},
+        __type_(__format::__arg_t::__string_view) {}
+
+  template <class _Traits, class _Allocator>
+  _LIBCPP_HIDE_FROM_ABI explicit basic_format_arg(
+      const basic_string<char_type, _Traits, _Allocator>& __s) noexcept
+      : __string_view{__s.data(), __s.size()},
+        __type_(__format::__arg_t::__string_view) {}
+
+  _LIBCPP_HIDE_FROM_ABI
+  explicit basic_format_arg(nullptr_t) noexcept
+      : __ptr(nullptr), __type_(__format::__arg_t::__ptr) {}
+
+  // TODO FMT Implement the _Tp* constructor.
+};
+
+#endif // !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+#endif //_LIBCPP_STD_VER > 17
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___FORMAT_FORMAT_ARG_H
diff --git a/include/__format/format_args.h b/include/__format/format_args.h
new file mode 100644
index 0000000..0a26b95
--- /dev/null
+++ b/include/__format/format_args.h
@@ -0,0 +1,71 @@
+// -*- 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___FORMAT_FORMAT_ARGS_H
+#define _LIBCPP___FORMAT_FORMAT_ARGS_H
+
+#include <__availability>
+#include <__config>
+#include <__format/format_fwd.h>
+#include <cstddef>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17
+
+// TODO FMT Remove this once we require compilers with proper C++20 support.
+// If the compiler has no concepts support, the format header will be disabled.
+// Without concepts support enable_if needs to be used and that too much effort
+// to support compilers with partial C++20 support.
+#if !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+template <class _Context>
+class _LIBCPP_TEMPLATE_VIS _LIBCPP_AVAILABILITY_FORMAT basic_format_args {
+public:
+  // TODO FMT Implement [format.args]/5
+  // [Note 1: Implementations are encouraged to optimize the representation of
+  // basic_format_args for small number of formatting arguments by storing
+  // indices of type alternatives separately from values and packing the
+  // former. - end note]
+  // Note: Change  __format_arg_store to use a built-in array.
+  _LIBCPP_HIDE_FROM_ABI basic_format_args() noexcept = default;
+
+  template <class... _Args>
+  _LIBCPP_HIDE_FROM_ABI basic_format_args(
+      const __format_arg_store<_Context, _Args...>& __store) noexcept
+      : __size_(sizeof...(_Args)), __data_(__store.__args.data()) {}
+
+  _LIBCPP_HIDE_FROM_ABI
+  basic_format_arg<_Context> get(size_t __id) const noexcept {
+    return __id < __size_ ? __data_[__id] : basic_format_arg<_Context>{};
+  }
+
+  _LIBCPP_HIDE_FROM_ABI size_t __size() const noexcept { return __size_; }
+
+private:
+  size_t __size_{0};
+  const basic_format_arg<_Context>* __data_{nullptr};
+};
+
+#endif // !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+#endif //_LIBCPP_STD_VER > 17
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___FORMAT_FORMAT_ARGS_H
diff --git a/include/__format/format_context.h b/include/__format/format_context.h
new file mode 100644
index 0000000..e277aa0
--- /dev/null
+++ b/include/__format/format_context.h
@@ -0,0 +1,160 @@
+// -*- 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___FORMAT_FORMAT_CONTEXT_H
+#define _LIBCPP___FORMAT_FORMAT_CONTEXT_H
+
+#include <__availability>
+#include <__config>
+#include <__format/format_args.h>
+#include <__format/format_fwd.h>
+#include <__iterator/concepts.h>
+#include <concepts>
+#include <iterator>
+#include <string>
+
+#ifndef _LIBCPP_HAS_NO_LOCALIZATION
+#include <locale>
+#include <optional>
+#endif
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17
+
+// TODO FMT Remove this once we require compilers with proper C++20 support.
+// If the compiler has no concepts support, the format header will be disabled.
+// Without concepts support enable_if needs to be used and that too much effort
+// to support compilers with partial C++20 support.
+#if !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+template <class _OutIt, class _CharT>
+requires output_iterator<_OutIt, const _CharT&>
+class _LIBCPP_TEMPLATE_VIS _LIBCPP_AVAILABILITY_FORMAT basic_format_context;
+
+#ifndef _LIBCPP_HAS_NO_LOCALIZATION
+/**
+ * Helper to create a basic_format_context.
+ *
+ * This is needed since the constructor is private.
+ */
+template <class _OutIt, class _CharT>
+_LIBCPP_HIDE_FROM_ABI basic_format_context<_OutIt, _CharT>
+__format_context_create(
+    _OutIt __out_it,
+    basic_format_args<basic_format_context<_OutIt, _CharT>> __args,
+    optional<_VSTD::locale>&& __loc = nullopt) {
+  return _VSTD::basic_format_context(_VSTD::move(__out_it), __args,
+                                     _VSTD::move(__loc));
+}
+#else
+template <class _OutIt, class _CharT>
+_LIBCPP_HIDE_FROM_ABI basic_format_context<_OutIt, _CharT>
+__format_context_create(
+    _OutIt __out_it,
+    basic_format_args<basic_format_context<_OutIt, _CharT>> __args) {
+  return _VSTD::basic_format_context(_VSTD::move(__out_it), __args);
+}
+#endif
+
+template <class _OutIt, class _CharT>
+requires output_iterator<_OutIt, const _CharT&>
+class _LIBCPP_TEMPLATE_VIS _LIBCPP_AVAILABILITY_FORMAT basic_format_context {
+public:
+  using iterator = _OutIt;
+  using char_type = _CharT;
+  template <class _Tp>
+  using formatter_type = formatter<_Tp, _CharT>;
+
+  basic_format_context(const basic_format_context&) = delete;
+  basic_format_context& operator=(const basic_format_context&) = delete;
+
+  _LIBCPP_HIDE_FROM_ABI basic_format_arg<basic_format_context>
+  arg(size_t __id) const {
+    return __args_.get(__id);
+  }
+#ifndef _LIBCPP_HAS_NO_LOCALIZATION
+  _LIBCPP_HIDE_FROM_ABI _VSTD::locale locale() {
+    if (!__loc_)
+      __loc_ = _VSTD::locale{};
+    return *__loc_;
+  }
+#endif
+  _LIBCPP_HIDE_FROM_ABI iterator out() { return __out_it_; }
+  _LIBCPP_HIDE_FROM_ABI void advance_to(iterator __it) { __out_it_ = __it; }
+
+private:
+  iterator __out_it_;
+  basic_format_args<basic_format_context> __args_;
+#ifndef _LIBCPP_HAS_NO_LOCALIZATION
+
+  // The Standard doesn't specify how the locale is stored.
+  // [format.context]/6
+  // std::locale locale();
+  //   Returns: The locale passed to the formatting function if the latter
+  //   takes one, and std::locale() otherwise.
+  // This is done by storing the locale of the constructor in this optional. If
+  // locale() is called and the optional has no value the value will be created.
+  // This allows the implementation to lazily create the locale.
+  // TODO FMT Validate whether lazy creation is the best solution.
+  optional<_VSTD::locale> __loc_;
+
+  template <class __OutIt, class __CharT>
+  friend _LIBCPP_HIDE_FROM_ABI basic_format_context<__OutIt, __CharT>
+  _VSTD::__format_context_create(
+      __OutIt, basic_format_args<basic_format_context<__OutIt, __CharT>>,
+      optional<_VSTD::locale>&&);
+
+  // Note: the Standard doesn't specify the required constructors.
+  _LIBCPP_HIDE_FROM_ABI
+  explicit basic_format_context(_OutIt __out_it,
+                                basic_format_args<basic_format_context> __args,
+                                optional<_VSTD::locale>&& __loc)
+      : __out_it_(_VSTD::move(__out_it)), __args_(__args),
+        __loc_(_VSTD::move(__loc)) {}
+#else
+  template <class __OutIt, class __CharT>
+  friend _LIBCPP_HIDE_FROM_ABI basic_format_context<__OutIt, __CharT>
+      _VSTD::__format_context_create(
+          __OutIt, basic_format_args<basic_format_context<__OutIt, __CharT>>);
+
+  _LIBCPP_HIDE_FROM_ABI
+  explicit basic_format_context(_OutIt __out_it,
+                                basic_format_args<basic_format_context> __args)
+      : __out_it_(_VSTD::move(__out_it)), __args_(__args) {}
+#endif
+};
+
+// TODO FMT Implement [format.context]/4
+// [Note 1: For a given type charT, implementations are encouraged to provide a
+// single instantiation of basic_format_context for appending to
+// basic_string<charT>, vector<charT>, or any other container with contiguous
+// storage by wrapping those in temporary objects with a uniform interface
+// (such as a span<charT>) and polymorphic reallocation. - end note]
+
+using format_context = basic_format_context<back_insert_iterator<string>, char>;
+using wformat_context =
+    basic_format_context<back_insert_iterator<wstring>, wchar_t>;
+
+#endif // !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+#endif //_LIBCPP_STD_VER > 17
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___FORMAT_FORMAT_CONTEXT_H
diff --git a/include/__format/format_fwd.h b/include/__format/format_fwd.h
new file mode 100644
index 0000000..7da30ae
--- /dev/null
+++ b/include/__format/format_fwd.h
@@ -0,0 +1,56 @@
+// -*- 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___FORMAT_FORMAT_FWD_H
+#define _LIBCPP___FORMAT_FORMAT_FWD_H
+
+#include <__availability>
+#include <__config>
+#include <__iterator/concepts.h>
+#include <__utility/forward.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17
+
+// TODO FMT Remove this once we require compilers with proper C++20 support.
+// If the compiler has no concepts support, the format header will be disabled.
+// Without concepts support enable_if needs to be used and that too much effort
+// to support compilers with partial C++20 support.
+#if !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+template <class _Context>
+class _LIBCPP_TEMPLATE_VIS _LIBCPP_AVAILABILITY_FORMAT basic_format_arg;
+
+template <class _Context, class... _Args>
+struct _LIBCPP_TEMPLATE_VIS __format_arg_store;
+
+template <class _Ctx, class... _Args>
+_LIBCPP_HIDE_FROM_ABI __format_arg_store<_Ctx, _Args...>
+make_format_args(const _Args&...);
+
+template <class _Tp, class _CharT = char>
+struct _LIBCPP_TEMPLATE_VIS _LIBCPP_AVAILABILITY_FORMAT formatter;
+
+#endif // !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+#endif //_LIBCPP_STD_VER > 17
+
+_LIBCPP_END_NAMESPACE_STD
+
+_LIBCPP_POP_MACROS
+
+#endif // _LIBCPP___FORMAT_FORMAT_FWD_H
diff --git a/include/concepts b/include/concepts
index bfa27dd..99dd85c 100644
--- a/include/concepts
+++ b/include/concepts
@@ -152,10 +152,28 @@
 #include <__concepts/swappable.h>
 #include <__concepts/totally_ordered.h>
 #include <__config>
+#include <type_traits>
 #include <version>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif
 
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+// Concept helpers for the internal type traits for the fundamental types.
+
+template <class _Tp>
+concept __libcpp_unsigned_integer = __libcpp_is_unsigned_integer<_Tp>::value;
+template <class _Tp>
+concept __libcpp_signed_integer = __libcpp_is_signed_integer<_Tp>::value;
+template <class _Tp>
+concept __libcpp_floating_point = __libcpp_is_floating_point<_Tp>::value;
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+_LIBCPP_END_NAMESPACE_STD
+
 #endif // _LIBCPP_CONCEPTS
diff --git a/include/format b/include/format
index 0f5f842..b320b75 100644
--- a/include/format
+++ b/include/format
@@ -13,6 +13,136 @@
 /*
 
 namespace std {
+  // [format.context], class template basic_format_context
+  template<class Out, class charT>
+  class basic_format_context {
+    basic_format_args<basic_format_context> args_;      // exposition only
+    Out out_;                                           // exposition only
+
+  public:
+    using iterator = Out;
+    using char_type = charT;
+    template<class T> using formatter_type = formatter<T, charT>;
+
+    basic_format_arg<basic_format_context> arg(size_t id) const;
+    std::locale locale();
+
+    iterator out();
+    void advance_to(iterator it);
+  };
+  using format_context = basic_format_context<unspecified, char>;
+  using wformat_context = basic_format_context<unspecified, wchar_t>;
+
+  // [format.args], class template basic_format_args
+  template<class Context>
+  class basic_format_args {
+    size_t size_;                               // exposition only
+    const basic_format_arg<Context>* data_;     // exposition only
+
+  public:
+    basic_format_args() noexcept;
+
+    template<class... Args>
+      basic_format_args(const format-arg-store<Context, Args...>& store) noexcept;
+
+    basic_format_arg<Context> get(size_t i) const noexcept;
+  };
+  using format_args = basic_format_args<format_context>;
+  using wformat_args = basic_format_args<wformat_context>;
+
+
+  template<class Out, class charT>
+    using format_args_t = basic_format_args<basic_format_context<Out, charT>>;
+
+  // [format.parse.ctx], class template basic_format_parse_context
+  template<class charT>
+  class basic_format_parse_context {
+  public:
+    using char_type = charT;
+    using const_iterator = typename basic_string_view<charT>::const_iterator;
+    using iterator = const_iterator;
+
+  private:
+    iterator begin_;                                    // exposition only
+    iterator end_;                                      // exposition only
+    enum indexing { unknown, manual, automatic };       // exposition only
+    indexing indexing_;                                 // exposition only
+    size_t next_arg_id_;                                // exposition only
+    size_t num_args_;                                   // exposition only
+
+  public:
+    constexpr explicit basic_format_parse_context(basic_string_view<charT> fmt,
+                                                  size_t num_args = 0) noexcept;
+    basic_format_parse_context(const basic_format_parse_context&) = delete;
+    basic_format_parse_context& operator=(const basic_format_parse_context&) = delete;
+
+    constexpr const_iterator begin() const noexcept;
+    constexpr const_iterator end() const noexcept;
+    constexpr void advance_to(const_iterator it);
+
+    constexpr size_t next_arg_id();
+    constexpr void check_arg_id(size_t id);
+  };
+  using format_parse_context = basic_format_parse_context<char>;
+  using wformat_parse_context = basic_format_parse_context<wchar_t>;
+
+  // [format.arguments], arguments
+  // [format.arg], class template basic_format_arg
+  template<class Context>
+  class basic_format_arg {
+  public:
+    class handle;
+
+  private:
+    using char_type = typename Context::char_type;                              // exposition only
+
+    variant<monostate, bool, char_type,
+            int, unsigned int, long long int, unsigned long long int,
+            float, double, long double,
+            const char_type*, basic_string_view<char_type>,
+            const void*, handle> value;                                         // exposition only
+
+    template<class T> explicit basic_format_arg(const T& v) noexcept;           // exposition only
+    explicit basic_format_arg(float n) noexcept;                                // exposition only
+    explicit basic_format_arg(double n) noexcept;                               // exposition only
+    explicit basic_format_arg(long double n) noexcept;                          // exposition only
+    explicit basic_format_arg(const char_type* s);                              // exposition only
+
+    template<class traits>
+      explicit basic_format_arg(
+        basic_string_view<char_type, traits> s) noexcept;                       // exposition only
+
+    template<class traits, class Allocator>
+      explicit basic_format_arg(
+        const basic_string<char_type, traits, Allocator>& s) noexcept;          // exposition only
+
+    explicit basic_format_arg(nullptr_t) noexcept;                              // exposition only
+
+    template<class T>
+      explicit basic_format_arg(const T* p) noexcept;                           // exposition only
+
+  public:
+    basic_format_arg() noexcept;
+
+    explicit operator bool() const noexcept;
+  };
+
+  template<class Visitor, class Context>
+    see below visit_format_arg(Visitor&& vis, basic_format_arg<Context> arg);
+
+  // [format.arg.store], class template format-arg-store
+  template<class Context, class... Args>
+  struct format-arg-store {      // exposition only
+    array<basic_format_arg<Context>, sizeof...(Args)> args;
+  };
+
+  template<class Context = format_context, class... Args>
+    format-arg-store<Context, Args...>
+      make_format_args(const Args&... args);
+  template<class... Args>
+    format-arg-store<wformat_context, Args...>
+      make_wformat_args(const Args&... args);
+
   // [format.error], class format_error
   class format_error : public runtime_error {
   public:
@@ -61,13 +191,61 @@
 #if !defined(_LIBCPP_HAS_NO_INCOMPLETE_FORMAT)
 
 #include <__config>
+#include <__format/format_arg.h>
+#include <__format/format_args.h>
+#include <__format/format_context.h>
 #include <__format/format_error.h>
 #include <__format/format_parse_context.h>
+#include <array>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
-#  pragma GCC system_header
+#pragma GCC system_header
 #endif
 
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17
+
+// TODO FMT Remove this once we require compilers with proper C++20 support.
+// If the compiler has no concepts support, the format header will be disabled.
+// Without concepts support enable_if needs to be used and that too much effort
+// to support compilers with partial C++20 support.
+#if !defined(_LIBCPP_HAS_NO_CONCEPTS)
+
+// TODO FMT Evaluate which templates should be external templates. This
+// improves the efficiency of the header. However since the header is still
+// under heavy development and not all classes are stable it makes no sense
+// to do this optimization now.
+
+using format_args = basic_format_args<format_context>;
+using wformat_args = basic_format_args<wformat_context>;
+
+template <class _OutIt, class _CharT>
+using format_args_t = basic_format_args<basic_format_context<_OutIt, _CharT>>;
+
+template <class _Context, class... _Args>
+struct _LIBCPP_TEMPLATE_VIS __format_arg_store {
+  // TODO FMT Use a built-in array.
+  array<basic_format_arg<_Context>, sizeof...(_Args)> __args;
+};
+
+template <class _Context = format_context, class... _Args>
+_LIBCPP_HIDE_FROM_ABI __format_arg_store<_Context, _Args...>
+make_format_args(const _Args&... __args) {
+  return {basic_format_arg<_Context>(__args)...};
+}
+
+template <class... _Args>
+_LIBCPP_HIDE_FROM_ABI __format_arg_store<wformat_context, _Args...>
+make_wformat_args(const _Args&... __args) {
+  return _VSTD::make_format_args<wformat_context>(__args...);
+}
+
+#endif // !defined(_LIBCPP_HAS_NO_CONCEPTS)
+#endif //_LIBCPP_STD_VER > 17
+
+_LIBCPP_END_NAMESPACE_STD
+
 #endif // !defined(_LIBCPP_HAS_NO_INCOMPLETE_FORMAT)
 
 #endif // _LIBCPP_FORMAT
diff --git a/include/module.modulemap b/include/module.modulemap
index f0d6023..5ef0f9a 100644
--- a/include/module.modulemap
+++ b/include/module.modulemap
@@ -431,7 +431,15 @@
     export *
 
     module __format {
+      module format_arg           { private header "__format/format_arg.h"           }
+      module format_args          { private header "__format/format_args.h"          }
+      module format_context {
+        private header "__format/format_context.h"
+        export optional
+        export locale
+      }
       module format_error         { private header "__format/format_error.h"         }
+      module format_fwd           { private header "__format/format_fwd.h"           }
       module format_parse_context { private header "__format/format_parse_context.h" }
     }
   }
diff --git a/include/type_traits b/include/type_traits
index a1d1640..63f2d3a 100644
--- a/include/type_traits
+++ b/include/type_traits
@@ -790,6 +790,7 @@
 #endif // __has_keyword(__is_integral)
 
 // __libcpp_is_signed_integer, __libcpp_is_unsigned_integer
+// <concepts> implements __libcpp_signed_integer, __libcpp_unsigned_integer
 
 // [basic.fundamental] defines five standard signed integer types;
 // __int128_t is an extended signed integer type.
@@ -817,6 +818,7 @@
 #endif
 
 // is_floating_point
+// <concepts> implements __libcpp_floating_point
 
 template <class _Tp> struct __libcpp_is_floating_point              : public false_type {};
 template <>          struct __libcpp_is_floating_point<float>       : public true_type {};