text: # Copyright 2019 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
  
  from jax.abstract_arrays import ShapedArray
  from jax.core import Primitive
  from jax.interpreters import xla
  from ..interpreters import ad
  from ..interpreters import batching
  
  
  def fft(x, fft_type, fft_lengths=None):
    if fft_lengths is None:
      fft_lengths = x.shape
    elif len(fft_lengths) == 0:
      # XLA FFT doesn't support 0-rank.
      return x
    else:
      fft_lengths = tuple(fft_lengths)
    return fft_p.bind(x, fft_type=fft_type, fft_lengths=fft_lengths)
  
  def fft_impl(x, fft_type, fft_lengths):
    return xla.apply_primitive(fft_p, x, fft_type=fft_type, fft_lengths=fft_lengths)
  
  def fft_abstract_eval(x, fft_type, fft_lengths):
    return ShapedArray(x.shape, x.dtype)
  
  def fft_translation_rule(c, x, fft_type, fft_lengths):
    return c.Fft(x, fft_type, fft_lengths)
  
  def fft_transpose_rule(t, fft_type, fft_lengths):
    return fft(t, fft_type, fft_lengths),
  
  def fft_batching_rule(batched_args, batch_dims, fft_type, fft_lengths):
    x, = batched_args
    bd, = batch_dims
    x = batching.moveaxis(x, bd, 0)
    return fft(x, fft_type, fft_lengths), 0
  
  fft_p = Primitive('fft')
  fft_p.def_impl(fft_impl)
  fft_p.def_abstract_eval(fft_abstract_eval)
  xla.translations[fft_p] = fft_translation_rule
  ad.deflinear(fft_p, fft_transpose_rule)
  batching.primitive_batchers[fft_p] = fft_batching_rule
  