code: def _do_fp_log_private(
      prot, x: "TFEPrivateTensor", base: "float", precision: int = 1
  ):
      k = prot.fixedpoint_config.precision_fractional
      m = k + prot.fixedpoint_config.precision_integral
      n = prot.int_factory.nbits
      logn = (
          int(log2(n) + 1) * 2
      )  # enough bit length to represent the exponent \in [0, 128)
      assert x.is_scaled, "Er.. tricky here."
      assert (
          2 * k > m
      ), "We assume 2^{-j} can be represent with 2k-bit precisions for all j in [0, m)"
      assert base >= 2.0, "log(x, base) shoule with base >= 2."
      adjust = 1.0 / np.log2(base)
      with tf.name_scope("fp_log"):
          # bit-decomposition. Make sure the higher bits are all 0 via shifting.
          x_bits = (prot.a2b(x, m) << (n - m)) >> (n - m)
          y_bits = prefix_ORs(x_bits, m)
          z_bits = y_bits ^ (y_bits >> 1)
          rev_z_bits = prot.bit_reverse(z_bits)
  
          exponent = prot.b2a(
              rev_z_bits >> (n - 2 * k - 1), 2 * k
          )  # NOTE: shift 1-less.
          exponent.is_scaled = True
  
          log_exponent = (
              prot.b2a(prot.xor_indices(z_bits), logn) * 2**k
          )  # j + k with k-bit precision
          log_exponent.is_scaled = True
          log_exponent = log_exponent - k
          if base != 2.0:
              log_exponent = log_exponent * adjust
  
          frac = x * exponent  # frac is in the interval [1., 2.]
          # The approximation coefficients are for log2(x), we need to
          # adjust them via multiplying 1./log2(base)
          """ """
          log_frac = (
              (-0.4326728 * adjust) * frac + (2.276597 * adjust)
          ) * frac + (-1.843924 * adjust)
          return log_frac + log_exponent
  
imports: from math import ceil
  from math import log2
  import numpy
  import tensorflow
  from ..protocol import TFEPrivateTensor
  from ..protocol import TFEPublicTensor
label_desc: Use image node_id 11 for calling a global function with example usage: _do_fp_log_private(prot, x, base, precision) and returns: unknown