(Almost) all of this will be in libc as well, but this stuff should be a part
of libk (the libc makefile's FREE_OBJS variable). Anything not on this list
that the kernel will need that isn't otherwise a part of the libc is probably 
best put in kernel dev, rather than in libc dev (e.g. info on the elf format 
or endianness). This also isn't a complete list. This is based off what the 
Linux klibc has that overlaps with what a POSIX-compliant libc has. We may need 
to add more from the POSIX libc, and I may have not put in dependencies here or
there (types that are needed, or macros, or functions, or whatever).

X - complete; ~ - prototype exists; ? - not sure if done
Unless otherwise specified, *() denotes a function, *[] an array variable,
* \* a pointer, [A-Z_0-9]+ a macro, [a-z_0-9] a variable or type, and anything
prefixed with struct is a struct.
(hello() is a function, hello[] is an array, hello * is a pointer, HELLO is a
 macro, HELLO() is a function macro, hello is a variable or type, and 
 struct hello is a struct.)

arpa/inet.h
  inet_addr()
  inet_ntoa()
  inet_ntop()
  inet_pton()
assert.h (complete)
ctype.h (complete as far as libk is concerned - don't need locale variants)
dirent.h
  DIR type
  struct dirent
  alphasort()
  closedir()
  fdopendir()
  opendir()
  readdir()
  dirrd()
  scandir()
errno.h (complete)
fcntl.h
  struct flock
  open()
  openat()
  creat()
  fcntl()
  Neccesary macros for the above
fnmatch.h
  X FNM_NOMATCH
  X FNM_PATHNAME
  X FNM_PERIOD
  X FNM_NOESCAPE
  ~ fnmatch()
grp.h
  X struct group
  ~ getgrid()
  ~ getgrnam()
inttypes.h
  imaxabs()
  strtoimax()
limits.h (complete)
net/if.h
netinet/in.h
netinet/tcp.h
poll.h
pwd.h
  struct passwd
  getpwuid()
  getpwman()
sched.h
  struct sched_param
  sched_setscheduler()
  sched_yield()
setjmp.h
  sigjmp_buf[]
  setjmp()
  longjmp()
  sigsetjmp()
  siglongjmp()
signal.h
  sig_atomic_t
  SIGRTMIN
  SIGRTMAX
  sigemptyset()
  sigfillset()
  sigaddset()
  sigdelset()
  sigismember()
  signal()
  sigaction()
  sigprocmask()
  sigpending()
  sigsuspend()
  raise()
  kill()
stdarg.h
  AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
  AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
  AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
  AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
stdbool.h (complete)
stddef.h (complete)
stdint.h (complete)
stdio.h
  X FILE type
  X EOF
  X BUFSIZ
  X _IO*BF
  X stdin, stdout, stderr
  ~ fopen()
  ~ fdopen()
  ~ fclose()
  ~ fseek()
  ~ rewind()
  ~ fputs()
  fputs_unlocked()
  X puts()
  ~ fputc()
  ~ putc()
  X putchar()
  fputc_unlocked()
  putchar_unlocked()
  putc_unlocked()
  ~ fgetc()
  fgetc_unlocked()
  ~ fgets()
  fgets_unlocked()
  ~ getc()
  ~ getchar()
  getc_unlocked()
  getchar_unlocked()
  ~ ungetc()
  X printf()
  ~ vprintf()
  ~ fprintf()
  ~ vfprintf()
  ~ sprintf()
  ~ vsprintf()
  ~ snprintf()
  ~ vsnprintf()
  ~ sscanf()
  ~ vsscanf()
  ? perror()
  rename()
  renameat()
  remove()
  ~ fread()
  ~ fwrite()
  ftell()
  ~ ferror()
  ~ feof()
  fileno()
  ~ clearrerr()
stdlib.h
  X EXIT_FAILURE
  X EXIT_SUCCESS
  ? abort()
  X abs()
  ~ system()
  ~ atexit()
  ~ atoi()
  ~ atol()
  ~ atoll
  ~ exit()
  ~_Exit()
  X labs()
  X llabs()
  ~ strtol()
  ~ strtoll()
  ~ strtoul()
  ~ strtoull()
  ~ getenv()
  putenv()
  setenv()
  unsetenv()
  X bsearch()
  ~ qsort()
  X srand()
  X rand()
  srand48()
  jrand48()
  mrand48()
  nrand48()
  lrand48()
  random()
  srandom()
  unlockpt()
  ptsname()
  posix_openpt()
  grantpt()
  realpath()
string.h
  memccpy()
  memchr()
  X memcmp()
  X memcpy()
  X memmove()
  X memset()
  X strcat()
  ~ strchr()
  X strcmp()
  ~ strcpy()
  X strcspn()
  strdup()
  ~ strerror()
  strsignal()
  X strlen()
  ~ strncat()
  ~ strncmp()
  ~ strncpy()
  strpbrk()
  ~ strstr()
  X strtok()
  strtok_r()
sys/mman.h
  mmap()
  munmap()
  shm_open()
  shm_unlink()
  msync()
  mprotect()
  mlockall()
  munlockall()
  mlock()
  munlock()
sys/resource.h
  getpriority()
  setpriority()
  getrusage()
sys/select.h
  FD_CLR()
  FD_ISSET()
  FD_SET()
  FD_ZERO()
  FD_SETSIZE
  select()
  pselect()
sys/socket.h
  X sa_family_t
  X struct sockaddr
  X socklen_t
  struct msghdr
  struct cmsghdr
  CMSG_DATA()
  CMSG_NXTHDR()
  CMSG_FIRSTHDR()
  accept()
  bind()
  connect()
  getpeername()
  getsockname()
  getsockopt()
  listen()
  recv()
  recvfrom()
  recvmsg()
  send()
  sendmsg()
  sendto()
  setsockopt()
  shutdown()
  socket()
  socketpair()
sys/stat.h
  S_IFMT macro family
  S_I[RWX](USR|GRP|OTH) and related macros
  S_IS. macro family
  stat()
  fstat()
  fstatat()
  lstat()
  umask()
  mknod()
  mknodat()
  mkfifo()
  utimensat()
  fchmodat()
sys/statvfs.h
  struct statvfs
  fstatvfs()
  statvfs()
sys/time.h
  gettimeofday()
  gettitimer()
  settitimer()
  utimes()
sys/uio.h
  struct iovec
  readv()
  writev()
sys/un.h
  ???
sys/utsname.h
  X struct utsname
  ~ uname()
sys/wait.h
  WEXITSTATUS()
  WTERMSIG()
  WIFEXITED()
  WIFSTOPPED()
  WIFSIGNALED()
  WSTOPSIG()
  X wait()
  waitpid()
syslog.h
  ~ closelog()
  ~ openlog()
  ~ syslog()
termios.h
  TCSANOW
  TCSADRAIN
  TCSAFLUSH
  tcgetattr()
  tcsetattr()
  tcflow()
  tcflush()
  tcdrain()
  tcgetsid()
  tcsendbreak()
  cfgetospeed()
  cfgetispeed()
  cfsetospeed()
  cfsetispeed()
time.h
  X time()
  ~ nanosleep()
unistd.h
  X F_OK
  X R_OK
  X W_OK
  X X_OK
  STDERR_FILENO
  STDIN_FILENO
  STDOUT_FILENO
  access()
  chdir()
  chown()
  close()
  dup()
  dup2()
  _exit()
  execl()
  execle()
  execlp()
  execv()
  execve()
  execvp()
  faccessat()
  fchdir()
  fchown()
  fchownat()
  fdatasync()
  fork()
  fsync()
  ftruncate()
  getegid()
  geteuid()
  getgid()
  getgroups()
  gethostname()
  getopt()
  getuid()
  isatty()
  lchown()
  link()
  linkat()
  lseek()
  nice()
  pipe()
  pread()
  pwrite()
  read()
  readlink()
  readlinkat()
  rmdir()
  setegid()
  seteuid()
  setgid()
  setuid()
  sleep()
  symlink()
  symlinkat()
  sync()
  unlink()
  unlinkat()
  write()
utime.h
  struct utimbuf
  utime()