code: def quantize_enumerate(x_real, min, max):
      """
      Randomly quantize in a way that preserves probability mass.
      We use a piecewise polynomial spline of order 3.
      """
      assert min < max
      lb = x_real.detach().floor()
  
      # This cubic spline interpolates over the nearest four integers, ensuring
      # piecewise quadratic gradients.
      s = x_real - lb
      ss = s * s
      t = 1 - s
      tt = t * t
      probs = torch.stack(
          [
              t * tt,
              4 + ss * (3 * s - 6),
              4 + tt * (3 * t - 6),
              s * ss,
          ],
          dim=-1,
      ) * (1 / 6)
      logits = safe_log(probs)
      q = torch.arange(-1.0, 3.0)
  
      x = lb.unsqueeze(-1) + q
      x = torch.max(x, 2 * min - 1 - x)
      x = torch.min(x, 2 * max + 1 - x)
      return x, logits
  
imports: import argparse
  import logging
  import math
  import re
  from collections import OrderedDict
  import torch
  import pyro
  import pyro.distributions
  import pyro.distributions.hmm
  import pyro.poutine
  from pyro.infer import MCMC, NUTS, config_enumerate, infer_discrete
  from pyro.infer.autoguide import init_to_value
  from pyro.ops.special import safe_log
  from pyro.ops.tensor_utils import convolve
  from pyro.util import warn_if_nan
label_desc: Use image node_id 11 for calling a global function with example usage: quantize_enumerate(x_real, min, max) and returns: x,  logits