text: # Copyright 2018 Google LLC
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     https://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import numpy as onp
  import scipy.stats as osp_stats
  
  from ... import lax
  from ...numpy.lax_numpy import _promote_args_like, _constant_like, _wraps
  from .. import special
  
  @_wraps(osp_stats.norm.logpdf)
  def logpdf(x, loc=0, scale=1):
    x, loc, scale = _promote_args_like(osp_stats.norm.logpdf, x, loc, scale)
    two = _constant_like(x, 2)
    scale_sqrd = lax.pow(scale, two)
    log_normalizer = lax.log(lax.mul(_constant_like(x, 2 * onp.pi), scale_sqrd))
    quadratic = lax.div(lax.pow(lax.sub(x, loc), two), scale_sqrd)
    return lax.div(lax.neg(lax.add(log_normalizer, quadratic)), two)
  
  
  @_wraps(osp_stats.norm.pdf)
  def pdf(x, loc=0, scale=1):
    return lax.exp(logpdf(x, loc, scale))
  
  
  @_wraps(osp_stats.norm.cdf)
  def cdf(x, loc=0, scale=1):
    x, loc, scale = _promote_args_like(osp_stats.norm.cdf, x, loc, scale)
    return special.ndtr(lax.div(lax.sub(x, loc), scale))
  
  
  @_wraps(osp_stats.norm.logcdf)
  def logcdf(x, loc=0, scale=1):
    x, loc, scale = _promote_args_like(osp_stats.norm.logcdf, x, loc, scale)
    return special.log_ndtr(lax.div(lax.sub(x, loc), scale))