code: def mpc_ellipk(z, prec, rnd=round_fast):
      re, im = z
      if im == fzero:
          if re == finf:
              return mpc_zero
          if mpf_le(re, fone):
              return mpf_ellipk(re, prec, rnd), fzero
      wp = prec + 15
      a = mpc_sqrt(mpc_sub(mpc_one, z, wp), wp)
      v = mpc_agm1(a, wp)
      r = mpc_mpf_div(mpf_pi(wp), v, prec, rnd)
      return mpc_shift(r, -1)
  
imports: import operator
  import math
  from .backend import MPZ_ZERO, MPZ_ONE, BACKEND, xrange, exec_
  from .libintmath import gcd
  from .libmpf import ComplexResult, round_fast, round_nearest, negative_rnd, bitcount, to_fixed, from_man_exp, from_int, to_int, from_rational, fzero, fone, fnone, ftwo, finf, fninf, fnan, mpf_sign, mpf_add, mpf_abs, mpf_pos, mpf_cmp, mpf_lt, mpf_le, mpf_gt, mpf_min_max, mpf_perturb, mpf_neg, mpf_shift, mpf_sub, mpf_mul, mpf_div, sqrt_fixed, mpf_sqrt, mpf_rdiv_int, mpf_pow_int, to_rational
  from .libelefun import mpf_pi, mpf_exp, mpf_log, pi_fixed, mpf_cos_sin, mpf_cos, mpf_sin, mpf_sqrt, agm_fixed
  from .libmpc import mpc_one, mpc_sub, mpc_mul_mpf, mpc_mul, mpc_neg, complex_int_pow, mpc_div, mpc_add_mpf, mpc_sub_mpf, mpc_log, mpc_add, mpc_pos, mpc_shift, mpc_is_infnan, mpc_zero, mpc_sqrt, mpc_abs, mpc_mpf_div, mpc_square, mpc_exp
  from .libintmath import ifac
  from .gammazeta import mpf_gamma_int, mpf_euler, euler_fixed
label_desc: Use image node_id 28 for calling a global function with example usage: mpc_ellipk(z, prec, rnd) and returns: mpc_shift, mpc_zero, mpf_ellipk,  fzero