code: def fastlog(x: Optional[MPF_TUP]) -> tUnion[int, Any]:
      """Fast approximation of log2(x) for an mpf value tuple x.
  
      Explanation
      ===========
  
      Calculated as exponent + width of mantissa. This is an
      approximation for two reasons: 1) it gives the ceil(log2(abs(x)))
      value and 2) it is too high by 1 in the case that x is an exact
      power of 2. Although this is easy to remedy by testing to see if
      the odd mpf mantissa is 1 (indicating that one was dealing with
      an exact power of 2) that would decrease the speed and is not
      necessary as this is only being used as an approximation for the
      number of bits in x. The correct return value could be written as
      "x[2] + (x[3] if x[1] != 1 else 0)".
          Since mpf tuples always have an odd mantissa, no check is done
      to see if the mantissa is a multiple of 2 (in which case the
      result would be too large by 1).
  
      Examples
      ========
  
      >>> from sympy import log
      >>> from sympy.core.evalf import fastlog, bitcount
      >>> s, m, e = 0, 5, 1
      >>> bc = bitcount(m)
      >>> n = [1, -1][s]*m*2**e
      >>> n, (log(n)/log(2)).evalf(2), fastlog((s, m, e, bc))
      (10, 3.3, 4)
      """
  
      if not x or x == fzero:
          return MINUS_INF
      return x[2] + x[3]
  
imports: from __future__ import annotations
  from typing import Tuple, Optional, Union, Callable, List, Dict, Type, TYPE_CHECKING, Any, overload
  import math
  import mpmath.libmp
  from mpmath import make_mpc, make_mpf, mp, mpc, mpf, nsum, quadts, quadosc, workprec
  from mpmath import inf
  from mpmath.libmp import from_int, from_man_exp, from_rational, fhalf, fnan, finf, fninf, fnone, fone, fzero, mpf_abs, mpf_add, mpf_atan, mpf_atan2, mpf_cmp, mpf_cos, mpf_e, mpf_exp, mpf_log, mpf_lt, mpf_mul, mpf_neg, mpf_pi, mpf_pow, mpf_pow_int, mpf_shift, mpf_sin, mpf_sqrt, normalize, round_nearest, to_int, to_str
  from mpmath.libmp import bitcount
  from mpmath.libmp.backend import MPZ
  from mpmath.libmp.libmpc import _infs_nan
  from mpmath.libmp.libmpf import dps_to_prec, prec_to_dps
  from .sympify import sympify
  from .singleton import S
  from sympy.external.gmpy import SYMPY_INTS
  from sympy.utilities.iterables import is_sequence
  from sympy.utilities.lambdify import lambdify
  from sympy.utilities.misc import as_int
label_desc: Use image node_id 2 for calling a global function with example usage: fastlog(x) and returns: unknown, MINUS_INF