How can OpenMP know how many loop instances are nested?

How can OpenMP know how many loop instances are nested?

Is it explicitly counted by compiler?

The OpenMP runtime keeps track of this information in thread-local variables.

Probably one of the most popular OpenMP implementations out there, libgomp, is open-source; That means one can read not just its documentation but also its source code entirely free.

The implementation of omp_get_level() is here:

int
omp_get_level (void)
{
  return gomp_thread ()->ts.level;
}

The implementation of gomp_thread() is here. It retrieves a pointer to a thread-local structure.

#if defined __nvptx__
extern struct gomp_thread *nvptx_thrs __attribute__((shared));
static inline struct gomp_thread *gomp_thread (void)
{
  int tid;
  asm ("mov.u32 %0, %%tid.y;" : "=r" (tid));
  return nvptx_thrs + tid;
}
#elif defined HAVE_TLS || defined USE_EMUTLS
extern __thread struct gomp_thread gomp_tls_data;
static inline struct gomp_thread *gomp_thread (void)
{
  return &gomp_tls_data;
}
#else
extern pthread_key_t gomp_tls_key;
static inline struct gomp_thread *gomp_thread (void)
{
  return pthread_getspecific (gomp_tls_key);
}
#endif

The data structure ts is a struct gomp_team_state that, amongst others, contains:

  [...]
  /* Nesting level.  */
  unsigned level;

  /* Active nesting level.  Only active parallel regions are counted.  */
  unsigned active_level;
  [...]

And whenever #pragma omp parallel is used, the compiler extracts the body of the parallel section into a subfunction and generates a complicated set of function calls that eventually lead to gomp_team_start(), which contains:

#ifdef LIBGOMP_USE_PTHREADS
void
gomp_team_start (void (*fn) (void *), void *data, unsigned nthreads,
                 unsigned flags, struct gomp_team *team)
{

  [...]

  ++thr->ts.level;
  if (nthreads > 1)
    ++thr->ts.active_level;