code: def forward(ctx, z):
      c = torch.tensor(
          [
              0.00048204,
              -0.00142906,
              0.0013200243174,
              0.0009461589032,
              -0.0045563339802,
              0.00556964649138,
              0.00125993961762116,
              -0.01621575378835404,
              0.02629651521057465,
              -0.001829764677455021,
              2 * (1 - math.pi / 3),
              (4 - math.pi) / 3,
              1,
              1,
          ],
          dtype=z.dtype,
          device=z.device,
      )
  
      r = torch.tensor(
          [
              1.2753666447299659525,
              5.019049726784267463450,
              6.1602098531096305441,
              7.409740605964741794425,
              2.9788656263939928886,
          ],
          dtype=z.dtype,
          device=z.device,
      )
  
      q = torch.tensor(
          [
              2.260528520767326969592,
              9.3960340162350541504,
              12.048951927855129036034,
              17.081440747466004316,
              9.608965327192787870698,
              3.3690752069827527677,
          ],
          dtype=z.dtype,
          device=z.device,
      )
  
      log_phi_z = torch.zeros_like(z)
  
      # Three cases to handle: An entry of z is near zero, an entry of z is small, or an entry of z neither of these.
      z_near_zero = z.pow(2).lt(0.04)
      z_is_small = z.lt(-1)
      z_is_ordinary = ~(z_near_zero | z_is_small)
  
      # Case 1: Entries of z that are near zero
      if z_near_zero.sum() > 0:
          log_phi_first = -z.masked_select(z_near_zero).div_(
              math.sqrt(2 * math.pi)
          )
          f = 0
          for c_i in c.tolist():
              f = log_phi_first.mul(c_i + f)
  
          log_phi_z.masked_scatter_(
              z_near_zero, f.mul_(-2).sub_(math.log(2))
          )
  
      # Case 2: Entries of z that are very small
      if z_is_small.sum() > 0:
          z_where_z_is_small = z.masked_select(z_is_small)
          numerator = torch.tensor(
              0.5641895835477550741, dtype=z.dtype, device=z.device
          )
          numerator = numerator.expand_as(z_where_z_is_small)
          denominator = torch.tensor(
              1.0, dtype=z.dtype, device=z.device
          )
          denominator = denominator.expand_as(z_where_z_is_small)
  
          for r_i in r:
              numerator = (
                  -z_where_z_is_small.mul(numerator.div(math.sqrt(2)))
                  + r_i
              )
  
          for q_i in q:
              denominator = (
                  -z_where_z_is_small.mul(denominator.div(math.sqrt(2)))
                  + q_i
              )
  
          e = numerator.div(denominator)
          log_phi_z.masked_scatter_(
              z_is_small,
              torch.log(e / 2) - z_where_z_is_small.pow(2).div_(2),
          )
  
          ctx.denominator = denominator
          ctx.numerator = numerator
  
      log_phi_z.masked_scatter_(
          z_is_ordinary,
          torch.log(
              Normal(0.0, 1.0).cdf(z.masked_select(z_is_ordinary))
          ),
      )
  
      ctx.save_for_backward(z, log_phi_z)
      return log_phi_z
  
imports: import math
  import torch
  from torch.autograd import Function
  from torch.distributions import Normal
label_desc: Use image node_id 1 for calling the LogNormalCDF obj's underlying member method code with example usage: obj.forward(ctx, z) and returns: log_phi_z