code: def mpf_erf(x, prec, rnd=round_fast):
      sign, man, exp, bc = x
      if not man:
          if x == fzero:
              return fzero
          if x == finf:
              return fone
          if x == fninf:
              return fnone
          return fnan
      size = exp + bc
      lg = math.log
      # The approximation erf(x) = 1 is accurate to > x^2 * log(e,2) bits
      if size > 3 and 2 * (size - 1) + 0.528766 > lg(prec, 2):
          if sign:
              return mpf_perturb(fnone, 0, prec, rnd)
          else:
              return mpf_perturb(fone, 1, prec, rnd)
      # erf(x) ~ 2*x/sqrt(pi) close to 0
      if size < -prec:
          # 2*x
          x = mpf_shift(x, 1)
          c = mpf_sqrt(mpf_pi(prec + 20), prec + 20)
          # TODO: interval rounding
          return mpf_div(x, c, prec, rnd)
      wp = prec + abs(size) + 25
      # Taylor series for erf, fixed-point summation
      t = abs(to_fixed(x, wp))
      t2 = (t * t) >> wp
      s, term, k = t, 12345, 1
      while term:
          t = ((t * t2) >> wp) // k
          term = t // (2 * k + 1)
          if k & 1:
              s -= term
          else:
              s += term
          k += 1
      s = (s << (wp + 1)) // sqrt_fixed(pi_fixed(wp), wp)
      if sign:
          s = -s
      return from_man_exp(s, -wp, prec, rnd)
  
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 2 for calling a global function with example usage: mpf_erf(x, prec, rnd) and returns: from_man_exp, fnan, mpf_div, fzero, fone, fnone, mpf_perturb, mpf_perturb