How is `std::cout` implemented?

how std::cout is created?

First things first, from https://en.cppreference.com/w/cpp/io/ios_base/Init :

std::ios_base::Init

This class is used to ensure that the default C++ streams (std::cin,
std::cout, etc.) are properly initialized and destructed. […]

The header <iostream> behaves as if it defines (directly or
indirectly) an instance of std::ios_base::Init with static storage
duration: […]

Meh, let’s do a real code example. I will be using GCC C++ library. From https://github.com/gcc-mirror/gcc/blob/master/libstdc%2B%2B-v3/include/std/iostream#L73 , this is the important part:

 // For construction of filebuffers for cout, cin, cerr, clog et. al.
 static ios_base::Init __ioinit;

Now we jump to the constructor of ios_base::Init class, in https://github.com/gcc-mirror/gcc/blob/master/libstdc%2B%2B-v3/src/c%2B%2B98/ios_init.cc#L85 :

ios_base::Init::Init()
  {
    if (__gnu_cxx::__exchange_and_add_dispatch(&_S_refcount, 1) == 0)
      {
    // Standard streams default to synced with "C" operations.
    _S_synced_with_stdio = true;

    new (&buf_cout_sync) stdio_sync_filebuf<char>(stdout);
    new (&buf_cin_sync) stdio_sync_filebuf<char>(stdin);
    new (&buf_cerr_sync) stdio_sync_filebuf<char>(stderr);

    // The standard streams are constructed once only and never
    // destroyed.
    new (&cout) ostream(&buf_cout_sync);
    new (&cin) istream(&buf_cin_sync);
    new (&cerr) ostream(&buf_cerr_sync);
    new (&clog) ostream(&buf_cerr_sync);
    cin.tie(&cout);
    cerr.setf(ios_base::unitbuf);
    // _GLIBCXX_RESOLVE_LIB_DEFECTS
    // 455. cerr::tie() and wcerr::tie() are overspecified.
    cerr.tie(&cout);

The _S_refcount is there for when you would call ios_base::Init::Init(); manually from a constructor of a static class, it protects against double initialization.

The stdio_sync_filebuf is an internal buffer for istream/ostream and it is meant to handle cstdio FILE* operations to get/put input/output data, with implementation here https://github.com/gcc-mirror/gcc/blob/master/libstdc%2B%2B-v3/include/ext/stdio_sync_filebuf.h#L56 . It inherits from std::basic_streambuf.

So cout is constructed in-place with stdio_sync_filebuf<char> as parameter. It is the first constructor mentioned here https://en.cppreference.com/w/cpp/io/basic_ostream/basic_ostream .

Now, because the stuff is constructed in-place, you might wonder how is the memory allocated? From https://github.com/gcc-mirror/gcc/blob/master/libstdc%2B%2B-v3/src/c%2B%2B98/globals_io.cc#L50 :

  // Standard stream objects.
  // NB: Iff <iostream> is included, these definitions become wonky.
  typedef char fake_istream[sizeof(istream)]
  __attribute__ ((aligned(__alignof__(istream))));
  typedef char fake_ostream[sizeof(ostream)]
  __attribute__ ((aligned(__alignof__(ostream))));
  fake_istream cin;
  fake_ostream cout;
  fake_ostream cerr;
  fake_ostream clog;

The objects are just empty char buffers of proper size and proper alignment.

And yes, you can construct ostream yourself, with __gnu_cxx::stdio_sync_filebuf on GCC:

#include <fstream>
#include <ext/stdio_sync_filebuf.h>
int main() {
    __gnu_cxx::stdio_sync_filebuf<char> mybuf_cout_sync(stdout);
    std::ostream os(&mybuf_cout_sync);
    os << "Hello world!\n";
    return 0;
}

Or, to be portable, you would write your own class that inherits from std::streambuf and construct ostream from it yourself. There are many examples online, like for example here https://stackoverflow.com/a/51250032/9072753 .