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std::variant requires default constructor in gcc 8 and 9, and not require in gcc 10/clang

I can not compile the code bellow on Ubuntu 20.04.1 / gcc 9.3.0. According to https://godbolt.org/ it compiles just fine with gcc 10.x, and gcc 7.x, but gives:

In file included from /usr/include/c++/9/variant:36,
                 from test.cpp:1:
/usr/include/c++/9/type_traits: In instantiation of ‘struct std::__is_nt_default_constructible_atom<Foo>’:                                                                                                  
/usr/include/c++/9/type_traits:945:12:   required from ‘struct std::__is_nt_default_constructible_impl<Foo, false>’                                                                                         
/usr/include/c++/9/type_traits:131:12:   required from ‘struct std::__and_<std::is_default_constructible<Foo>, std::__is_nt_default_constructible_impl<Foo, false> >’                                       
/usr/include/c++/9/type_traits:951:12:   required from ‘struct std::is_nothrow_default_constructible<Foo>’                                                                                                  
/usr/include/c++/9/type_traits:2965:25:   required from ‘constexpr const bool std::is_nothrow_default_constructible_v<Foo>’                                                                                 
/usr/include/c++/9/variant:301:4:   [ skipping 2 instantiation contexts, use -ftemplate-backtrace-limit=0 to disable ]                                                                                      
/usr/include/c++/9/type_traits:883:12:   recursively required from ‘constexpr std::variant<_Types>::variant() [with _Types = {Foo, Boo}]’                                                                   
/usr/include/c++/9/type_traits:883:12:   required from ‘struct std::is_constructible<std::variant<Foo, Boo> >’                                                                                              
/usr/include/c++/9/type_traits:889:12:   required from ‘struct std::is_default_constructible<std::variant<Foo, Boo> >’                                                                                      
/usr/include/c++/9/type_traits:2921:25:   required from ‘constexpr const bool std::is_default_constructible_v<std::variant<Foo, Boo> >’                                                                     
/usr/include/c++/9/variant:273:4:   required from ‘constexpr const bool std::__detail::__variant::_Traits<std::variant<Foo, Boo>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<c\
har> > >::_S_default_ctor’                                                                                                                                                                                  
/usr/include/c++/9/variant:1219:11:   required from ‘class std::variant<std::variant<Foo, Boo>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > >’                          
test.cpp:32:53:   required from here                                                                                                                                                                        
/usr/include/c++/9/type_traits:931:47: error: ‘Foo::Foo()’ is private within this context                                                                                                                   
  931 |     : public integral_constant<bool, noexcept(_Tp())>                                                                                                                                               
      |                                               ^~~~~                                                                                                                                                 
test.cpp:10:3: note: declared private here                                                                                                                                                                  
   10 |   Foo() noexcept {}                                                                                                                                                                                 
      |   ^~~                                      

with gcc 8.x and 9.x. Is there some problem with code bellow? Note that if remove template <bool X> in code bellow, all compiles just fine. Or I can remove code in main, and also all compiles fine.

#include <variant>
#include <string>

struct Foo {
public:
  explicit Foo(int) noexcept {}
  Foo(Foo &&) noexcept = default;
  Foo &operator=(Foo &&) = default;
private:
  Foo() noexcept {}
};

struct Boo {
public:
  explicit Boo(int) noexcept {}
  Boo(Boo &&) noexcept = default;
  Boo &operator=(Boo &&) = default;
private:
  Boo() noexcept {}
};


template<bool X>
std::variant<Foo, Boo> g(int v, int x) {
 return  v == 0 ? std::variant<Foo, Boo>{Foo{x}} :
                                 std::variant<Foo, Boo>{Boo{x}};
}


 int main()
{
  std::variant<std::variant<Foo, Boo>, std::string> err{std::string("aaa")};
}

According standard there is no DefaultConstructible requirement in this case.

The variant on itself is allowed to be Non-DefaultConstructible (which is the case in this example for both inner and outer variant).

If Foo() private constructor is removed or deleted, the code works (as expected):

struct Foo {
public:
  explicit Foo(int) noexcept {}
  Foo(Foo &&) noexcept = default;
  Foo &operator=(Foo &&) = default;
private:
//   Foo() noexcept {} -> comment out works
Foo() = deleted; // -> works also.
};

So, this is clearly implementation bug within compiler or standard library.

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