Is usleep() in C implemented as busy wait?

The function usleep has been removed from SUSv4. You should probably use nanosleep instead or timers (setitimer, etc).

As R.. notes in the comments, should the sleep be implemented as a busy wait:

• The thread would continue to use the CPU
• Other (lower-priority) threads wouldn't get a chance to run

Thus:

• Some might use signals (I think SUSv3 mentioned SIGALARM?)
• Some might use fancy timers

(usleep is not part of the C standard, but of an ancient POSIX standard. But see below.)

No, the POSIX specification of usleep clearly states

The usleep() function will cause the calling thread to be suspended from execution ...

so this clearly requires that it suspends execution and lets the resources to other processes or threads.

As already be mentioned by others, the POSIX function nanosleep is now replacing usleep and you should use that. C (since C11) has a function thrd_sleep that is modeled after nanosleep.

Just be aware that both usleep() and nanosleep() can be interrupted by a signal. nanosleep() lets you pass in an extra timespec pointer where the remaining time will be stored if that happens. So if you really need to guarantee your delay times, you'll probably want to write a simple wrapper around nanosleep().

Beware that this is not tested, but something along these lines:

int myNanoSleep(time_t sec, long nanosec)
{
   /* Setup timespec */
   struct timespec req;
   req.tv_sec = sec;
   req.tv_nsec = nanosec;

   /* Loop until we've slept long enough */
   do 
   {
      /* Store remainder back on top of the original required time */
      if( 0 != nanosleep( &req, &req ) )
      {
          /* If any error other than a signal interrupt occurs, return an error */
          if(errno != EINTR)
             return -1; 
      }
      else
      {
          /* nanosleep succeeded, so exit the loop */
          break;
      }
   } while( req.tv_sec > 0 || req.tv_nsec > 0 )
   return 0; /* Return success */
}

And if you ever need to wake the thread for something other than a periodic timeout, take a look at condition variables and pthread_cond_timedwait().