The current implementation of std::sort in C++ uses Introsort and Insertion Sort together. When the total number of elements is less than a threshold (usually 16), then sort will only use insertion sort. In Introsort, when a certain depth is reached (the logarithmic value of the number of elements), the sort is converted to a heap sort.

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  /// This is a helper function...
  template<typename _RandomAccessIterator, typename _Compare>
    _GLIBCXX20_CONSTEXPR
    inline _RandomAccessIterator
    __unguarded_partition_pivot(_RandomAccessIterator __first,
                                _RandomAccessIterator __last, _Compare __comp)
    {
      _RandomAccessIterator __mid = __first + (__last - __first) / 2;
      std::__move_median_to_first(__first, __first + 1, __mid, __last - 1,
                                  __comp);
      return std::__unguarded_partition(__first + 1, __last, __first, __comp);
    }

  template<typename _RandomAccessIterator, typename _Compare>
    _GLIBCXX20_CONSTEXPR
    inline void
    __partial_sort(_RandomAccessIterator __first,
                   _RandomAccessIterator __middle,
                   _RandomAccessIterator __last,
                   _Compare __comp)
    {
      std::__heap_select(__first, __middle, __last, __comp);
      std::__sort_heap(__first, __middle, __comp);
    }

  /// This is a helper function for the sort routine.
  template<typename _RandomAccessIterator, typename _Size, typename _Compare>
    _GLIBCXX20_CONSTEXPR
    void
    __introsort_loop(_RandomAccessIterator __first,
                     _RandomAccessIterator __last,
                     _Size __depth_limit, _Compare __comp)
    {
      while (__last - __first > int(_S_threshold))
        {
          if (__depth_limit == 0)
            {
              std::__partial_sort(__first, __last, __last, __comp);
              return;
            }
          --__depth_limit;
          _RandomAccessIterator __cut =
            std::__unguarded_partition_pivot(__first, __last, __comp);
          std::__introsort_loop(__cut, __last, __depth_limit, __comp);
          __last = __cut;
        }
    }

  template<typename _RandomAccessIterator, typename _Compare>
    _GLIBCXX20_CONSTEXPR
    inline void
    __sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
           _Compare __comp)
    {
      if (__first != __last)
        {
          std::__introsort_loop(__first, __last,
                                std::__lg(__last - __first) * 2,
                                __comp);
          std::__final_insertion_sort(__first, __last, __comp);
        }
    }

  /**
   *  @brief Sort the elements of a sequence.
   *  @ingroup sorting_algorithms
   *  @param  __first   An iterator.
   *  @param  __last    Another iterator.
   *  @return  Nothing.
   *
   *  Sorts the elements in the range `[__first, __last)` in ascending order,
   *  such that for each iterator `i` in the range `[__first, __last - 1)`,
   *  `*(i+1) < *i` is false.
   *
   *  The relative ordering of equivalent elements is not preserved, use
   *  `stable_sort()` if this is needed.
  */
  template<typename _RandomAccessIterator>
    _GLIBCXX20_CONSTEXPR
    inline void
    sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
            _RandomAccessIterator>)
      __glibcxx_function_requires(_LessThanComparableConcept<
            typename iterator_traits<_RandomAccessIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);
      __glibcxx_requires_irreflexive(__first, __last);

      std::__sort(__first, __last, __gnu_cxx::__ops::__iter_less_iter());
    }

Looking at the functions here from the bottom up, the external call to std::sort is the first function below, and it uses std::__sort directly after some assertions, which is the penultimate function. In std::__sort, when the inside of the container is not empty, it is fixed to use introspection sort before insertion sort. In introspective sort (std::__introsort_loop), if the number of elements in the container is less than a threshold, nothing is done, which is equivalent to using only insertion sort when the number is small, and when the depth limit is reached, it will be switched to heap sort (i.e., the implementation of std::__partial_sort). Otherwise (std::__unguarded_partition_pivot) will pick the element that is in the middle of the container as the benchmark, move the ones that are smaller than the benchmark to the left, and the ones that are larger than the benchmark to the right, and recursively invoke it, i.e., the idea of fast sort.