Let's look at how this works internally (I'm using kernel 4.1.20). The way file descriptors are allocated in Linux is with __alloc_fd. When you do a open syscall, do_sys_open is called. This routine gets a free file descriptor from get_unused_fd_flags:
long do_sys_open(int dfd, const char __user *filename, int flags, umode_t mode)
{
...
fd = get_unused_fd_flags(flags);
if (fd >= 0) {
struct file *f = do_filp_open(dfd, tmp, &op);
get_unused_d_flags calls __alloc_fd setting minimum and maximum fd:
int get_unused_fd_flags(unsigned flags)
{
return __alloc_fd(current->files, 0, rlimit(RLIMIT_NOFILE), flags);
}
__alloc_fd gets the file descriptor table for the process, and gets the fd as next_fd, which is actually set from the previous time it ran:
int __alloc_fd(struct files_struct *files,
unsigned start, unsigned end, unsigned flags)
{
...
fd = files->next_fd;
...
if (start <= files->next_fd)
files->next_fd = fd + 1;
So you can see how file descriptors indeed grow monotonically... up to certain point. When the fd reaches the maximum, __alloc_fd will try to find the smallest unused file descriptor:
if (fd < fdt->max_fds)
fd = find_next_zero_bit(fdt->open_fds, fdt->max_fds, fd);
At this point the file descriptors will not be growing monotonically anymore, but instead will jump trying to find free file descriptors. After this, if the table gets full, it will be expanded:
error = expand_files(files, fd);
At which point they will grow again monotonically.
Hope this helps