# Copyright 2020 The JAX Authors.
#
# 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 functools import partial
import itertools
import math
from typing import Optional, cast
import unittest

from absl.testing import absltest

import numpy as np

import jax
import jax.numpy as jnp
from jax import dtypes
from jax import lax

from jax._src import test_util as jtu
from jax._src.internal_test_util import lax_test_util
from jax._src.lax import windowed_reductions as lax_windowed_reductions
from jax._src.lib import xla_client
from jax._src.util import safe_map, safe_zip

from jax import config
config.parse_flags_with_absl()
FLAGS = config.FLAGS

map, unsafe_map = safe_map, map
zip, unsafe_zip = safe_zip, zip


class LaxVmapTest(jtu.JaxTestCase):

  def _CheckBatching(self, op, bdim_size, bdims, shapes, dtypes, rng,
                     rtol=None, atol=None, multiple_results=False):
    batched_shapes = map(partial(lax_test_util.add_bdim, bdim_size), bdims, shapes)
    args = [rng(shape, dtype) for shape, dtype in zip(batched_shapes, dtypes)]
    args_slice = lax_test_util.args_slicer(args, bdims)
    ans = jax.vmap(op, bdims)(*args)
    if bdim_size == 0:
      args = [rng(shape, dtype) for shape, dtype in zip(shapes, dtypes)]
      out = op(*args)
      if not multiple_results:
        expected = np.zeros((0,) + out.shape, out.dtype)
      else:
        expected = [np.zeros((0,) + o.shape, o.dtype) for o in out]
    else:
      outs = [op(*args_slice(i)) for i in range(bdim_size)]
      if not multiple_results:
        expected = np.stack(outs)
      else:
        expected = [np.stack(xs) for xs in zip(*outs)]
    self.assertAllClose(ans, expected, rtol=rtol, atol=atol)

  @jtu.sample_product(
    [dict(lhs_shape=lhs_shape, rhs_shape=rhs_shape,
          batch_group_count=batch_group_count,
          feature_group_count=feature_group_count)
     for batch_group_count, feature_group_count in [(1, 1), (2, 1), (1, 2)]
     for b, i, j in itertools.product([1, 2], repeat=3)
     for lhs_shape in [(b * batch_group_count, i * feature_group_count, 6, 7)]
     for rhs_shape in [(j * batch_group_count * feature_group_count, i, 1, 2)]],
    [dict(lhs_bdim=lhs_bdim, rhs_bdim=rhs_bdim)
        for lhs_bdim in itertools.chain([cast(Optional[int], None)], range(5))
        for rhs_bdim in itertools.chain([cast(Optional[int], None)], range(5))
        if (lhs_bdim, rhs_bdim) != (None, None)
    ],
    [dict(dimension_numbers=dim_nums, perms=perms)
     for dim_nums, perms in [
       (("NCHW", "OIHW", "NCHW"), ([0, 1, 2, 3], [0, 1, 2, 3])),
       (("NHWC", "HWIO", "NHWC"), ([0, 2, 3, 1], [2, 3, 1, 0])),
       (("NHWC", "OIHW", "NCHW"), ([0, 2, 3, 1], [0, 1, 2, 3])),
       (("HWCN", "HWIO", "HWCN"), ([2, 3, 1, 0], [2, 3, 1, 0])),
    ]],
    strides=[(1, 1), (1, 2), (2, 1)],
    padding=[((0, 0), (0, 0)), ((1, 0), (0, 1)), ((0, -1), (0, 0))],
    lhs_dil=[(1, 1), (2, 1)],
    rhs_dil=[(1, 1), (2, 2)],
    bdim_size=list(range(5)),
    dtype=[np.float32],
  )
  def testConvGeneralDilatedBatching(
      self, lhs_shape, rhs_shape, dtype, strides, padding, lhs_dil, rhs_dil,
      dimension_numbers, perms, feature_group_count, batch_group_count,
      lhs_bdim, rhs_bdim, bdim_size):
    rng = jtu.rand_default(self.rng())
    tol = 1e-1 if dtypes.finfo(dtype).bits <= 32 else 1e-3

    # permute shapes to match dim_spec, scale by feature_group_count
    lhs_perm, rhs_perm = perms
    lhs_shape = list(np.take(lhs_shape, lhs_perm))
    rhs_shape = list(np.take(rhs_shape, rhs_perm))

    conv = partial(lax.conv_general_dilated, window_strides=strides,
                   padding=padding, lhs_dilation=lhs_dil, rhs_dilation=rhs_dil,
                   dimension_numbers=dimension_numbers,
                   feature_group_count=feature_group_count,
                   batch_group_count=batch_group_count,
                   precision=lax.Precision.HIGHEST)
    self._CheckBatching(conv, bdim_size, (lhs_bdim, rhs_bdim),
                        (lhs_shape, rhs_shape), (dtype, dtype), rng, rtol=tol,
                        atol=tol)

  @jtu.sample_product(
    [dict(from_dtype=f, to_dtype=t)
      for f, t in itertools.product([np.float32, np.int32, "float32", "int32"],
                                    repeat=2)
    ],
    [dict(shape=shape, bdims=bdims)
     for shape in [(2, 3)] for bdims in lax_test_util.all_bdims(shape)]
  )
  def testConvertElementType(self, shape, from_dtype, to_dtype, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.convert_element_type(x, to_dtype)
    self._CheckBatching(op, 10, bdims, (shape,), (from_dtype,), rng)

  @jtu.sample_product(
    [dict(shape=shape, bdims=bdims)
     for shape in [(2, 4)] for bdims in lax_test_util.all_bdims(shape)],
    dtype=lax_test_util.float_dtypes,
    nexp=[1, 3, 5],
    nmant=[0, 2, 4],
  )
  def testReducePrecision(self, shape, dtype, nmant, nexp, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.reduce_precision(x, exponent_bits=nexp, mantissa_bits=nmant)
    self._CheckBatching(op, 10, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(from_dtype=f, to_dtype=t)
      for f, t in itertools.product([np.float32, np.int32, "float32", "int32"],
                                    repeat=2)
    ],
    [dict(shape=shape, bdims=bdims)
     for shape in [(2, 3)] for bdims in lax_test_util.all_bdims(shape)]
  )
  def testBitcastElementType(self, shape, from_dtype, to_dtype, bdims,):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.bitcast_convert_type(x, to_dtype)
    self._CheckBatching(op, 10, bdims, (shape,), (from_dtype,), rng)

  @jtu.sample_product(
    [dict(min_shape=min_shape, operand_shape=operand_shape, max_shape=max_shape,
          bdims=bdims)
      for min_shape, operand_shape, max_shape in [
          [(), (2, 3), ()],
          [(2, 3), (2, 3), ()],
          [(), (2, 3), (2, 3)],
          [(2, 3), (2, 3), (2, 3)],
      ]
      for bdims in lax_test_util.all_bdims(min_shape, operand_shape, max_shape)
    ],
    dtype=lax_test_util.default_dtypes,
  )
  def testClamp(self, min_shape, operand_shape, max_shape, dtype, bdims):
    rng = jtu.rand_default(self.rng())
    shapes = [min_shape, operand_shape, max_shape]
    self._CheckBatching(lax.clamp, 10, bdims, shapes, [dtype] * 3, rng)

  @jtu.sample_product(
    [dict(lhs_shape=lhs_shape, rhs_shape=rhs_shape, bdims=bdims)
      for lhs_shape in [(3,), (4, 3)] for rhs_shape in [(3,), (3, 6)]
      for bdims in lax_test_util.all_bdims(lhs_shape, rhs_shape)],
    dtype=lax_test_util.default_dtypes,
  )
  def testDot(self, lhs_shape, rhs_shape, dtype, bdims):
    rng = jtu.rand_default(self.rng())
    op = partial(lax.dot, precision=lax.Precision.HIGHEST)
    self._CheckBatching(op, 5, bdims, (lhs_shape, rhs_shape), (dtype, dtype),
                        rng, rtol={np.float16: 5e-2, np.float64: 5e-14})

  @jtu.sample_product(
    [dict(bdims=bdims, lhs_shape=lhs_shape, rhs_shape=rhs_shape,
          lhs_contracting=lhs_contracting, rhs_contracting=rhs_contracting)
      for lhs_shape, rhs_shape, lhs_contracting, rhs_contracting in [
          [(5,), (5,), [0], [0]],
          [(5, 7), (5,), [0], [0]],
          [(7, 5), (5,), [1], [0]],
          [(3, 5), (2, 5), [1], [1]],
          [(5, 3), (5, 2), [0], [0]],
          [(5, 3, 2), (5, 2, 4), [0], [0]],
          [(5, 3, 2), (5, 2, 4), [0,2], [0,1]],
          [(5, 3, 2), (3, 5, 2, 4), [0,2], [1,2]],
          [(1, 2, 2, 3), (1, 2, 3, 1), [1], [1]],
          [(3, 2), (2, 4), [1], [0]],
      ]
      for bdims in lax_test_util.all_bdims(lhs_shape, rhs_shape)],
    dtype=lax_test_util.default_dtypes,
  )
  def testDotGeneralContractOnly(self, lhs_shape, rhs_shape, dtype,
                                 lhs_contracting, rhs_contracting, bdims):
    rng = jtu.rand_small(self.rng())
    dimension_numbers = ((lhs_contracting, rhs_contracting), ([], []))
    dot = partial(lax.dot_general, dimension_numbers=dimension_numbers)
    self._CheckBatching(dot, 5, bdims, (lhs_shape, rhs_shape), (dtype, dtype),
                        rng)

  @jtu.sample_product(
    [dict(lhs_shape=lhs_shape, rhs_shape=rhs_shape,
          dimension_numbers=dimension_numbers, bdims=bdims)
      for lhs_shape, rhs_shape, dimension_numbers in [
          ((3, 3, 2), (3, 2, 4), (([2], [1]), ([0], [0]))),
          ((3, 3, 2), (2, 3, 4), (([2], [0]), ([0], [1]))),
          ((3, 4, 2, 4), (3, 4, 3, 2), (([2], [3]), ([0, 1], [0, 1]))),
      ]
      for bdims in lax_test_util.all_bdims(lhs_shape, rhs_shape)],
    dtype=lax_test_util.default_dtypes)
  def testDotGeneralContractAndBatch(self, lhs_shape, rhs_shape, dtype,
                                     dimension_numbers, bdims):
    rng = jtu.rand_small(self.rng())
    dot = partial(lax.dot_general, dimension_numbers=dimension_numbers)
    self._CheckBatching(dot, 5, bdims, (lhs_shape, rhs_shape), (dtype, dtype),
                        rng)

    # Checks that batching didn't introduce any transposes or broadcasts.
    jaxpr = jax.make_jaxpr(dot)(np.zeros(lhs_shape, dtype),
                                np.zeros(rhs_shape, dtype))
    for eqn in jtu.iter_eqns(jaxpr.jaxpr):
      self.assertFalse(eqn.primitive in ["transpose", "broadcast"])

  @jtu.sample_product(
    [dict(shape=shape, bdims=bdims)
     for shape in [(), (2, 3)] for bdims in lax_test_util.all_bdims(shape)],
    dtype=lax_test_util.default_dtypes,
    broadcast_sizes=[(), (2,), (1, 2)],
  )
  def testBroadcast(self, shape, dtype, broadcast_sizes, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.broadcast(x, broadcast_sizes)
    self._CheckBatching(op, 5, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(inshape=inshape, outshape=outshape,
          broadcast_dimensions=broadcast_dimensions, bdims=bdims)
      for inshape, outshape, broadcast_dimensions in [
          ([2], [2, 2], [0]),
          ([2], [2, 2], [1]),
          ([2], [2, 3], [0]),
          ([], [2, 3], []),
      ]
      for bdims in lax_test_util.all_bdims(inshape)],
    dtype=lax_test_util.default_dtypes,
  )
  @unittest.skip("this test has failures in some cases")  # TODO(mattjj)
  def testBroadcastInDim(self, inshape, dtype, outshape, dimensions, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.broadcast_in_dim(x, outshape, dimensions)
    self._CheckBatching(op, 5, bdims, (inshape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(arg_shape=arg_shape, dimensions=dimensions, bdims=bdims)
      for arg_shape, dimensions in [
          [(1,), (0,)],
          [(1,), (-1,)],
          [(2, 1, 4), (1,)],
          [(2, 1, 4), (-2,)],
          [(2, 1, 3, 1), (1,)],
          [(2, 1, 3, 1), (1, 3)],
          [(2, 1, 3, 1), (3,)],
          [(2, 1, 3, 1), (1, -1)],
      ]
      for bdims in lax_test_util.all_bdims(arg_shape)],
  )
  def testSqueeze(self, arg_shape, dimensions, bdims):
    dtype = np.float32
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.squeeze(x, dimensions)
    self._CheckBatching(op, 10, bdims, (arg_shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(arg_shape=arg_shape, out_shape=out_shape, dimensions=dimensions,
          bdims=bdims)
      for arg_shape, dimensions, out_shape in [
          [(3, 4), None, (12,)],
          [(2, 1, 4), None, (8,)],
          [(2, 2, 4), None, (2, 8)],
          [(2, 2, 4), (0, 1, 2), (2, 8)],
          [(2, 2, 4), (1, 0, 2), (8, 2)],
          [(2, 2, 4), (2, 1, 0), (4, 2, 2)]
      ]
      for bdims in lax_test_util.all_bdims(arg_shape)],
    dtype=lax_test_util.default_dtypes,
  )
  def testReshape(self, arg_shape, out_shape, dtype, dimensions, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.reshape(x, out_shape, dimensions=dimensions)
    self._CheckBatching(op, 10, bdims, (arg_shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(shape=shape, bdims=bdims)
     for shape in [(2, 3)] for bdims in lax_test_util.all_bdims(shape, ())],
    dtype=lax_test_util.default_dtypes,
    pads=[[(1, 2, 1), (0, 1, 0)]],
  )
  def testPad(self, shape, dtype, pads, bdims):
    rng = jtu.rand_small(self.rng())
    fun = lambda operand, padding: lax.pad(operand, padding, pads)
    self._CheckBatching(fun, 5, bdims, (shape, ()), (dtype, dtype), rng)

  @jtu.sample_product(
    [dict(arg_shape=arg_shape, pred_shape=pred_shape, bdims=bdims)
      for arg_shape in [(), (3,), (2, 3)]
      for pred_shape in ([(), arg_shape] if arg_shape else [()])
      for bdims in lax_test_util.all_bdims(pred_shape, arg_shape, arg_shape)],
    arg_dtype=lax_test_util.default_dtypes,
  )
  def testSelect(self, pred_shape, arg_shape, arg_dtype, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda c, x, y: lax.select(c < 0, x, y)
    self._CheckBatching(op, 5, bdims, (pred_shape, arg_shape, arg_shape,),
                        (arg_dtype, arg_dtype, arg_dtype), rng)

  @jtu.sample_product(
    [dict(shape=shape, starts=start_indices, limits=limit_indices,
          strides=strides, bdims=bdims)
      for shape, start_indices, limit_indices, strides in [
        [(3,), (1,), (2,), None],
        [(7,), (4,), (7,), None],
        [(5,), (1,), (5,), (2,)],
        [(8,), (1,), (6,), (2,)],
        [(5, 3), (1, 1), (3, 2), None],
        [(5, 3), (1, 1), (3, 1), None],
        [(7, 5, 3), (4, 0, 1), (7, 1, 3), None],
        [(5, 3), (1, 1), (2, 1), (1, 1)],
        [(5, 3), (1, 1), (5, 3), (2, 1)],
      ]
      for bdims in lax_test_util.all_bdims(shape)
    ],
    dtype=lax_test_util.default_dtypes,
  )
  def testSlice(self, shape, dtype, starts, limits, strides, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.slice(x, starts, limits, strides)
    self._CheckBatching(op, 5, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(shape=shape, perm=perm, bdims=bdims)
      for shape, perm in [
        [(3, 4), (1, 0)],
        [(3, 4), (0, 1)],
        [(3, 4, 5), (2, 1, 0)],
        [(3, 4, 5), (1, 0, 2)],
      ]
      for bdims in lax_test_util.all_bdims(shape)
     ],
    dtype=lax_test_util.default_dtypes,
  )
  def testTranspose(self, shape, dtype, perm, bdims):
    rng = jtu.rand_default(self.rng())
    op = lambda x: lax.transpose(x, perm)
    self._CheckBatching(op, 5, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(init_val=init_val, op=op, dtype=dtype)
      for init_val, op, dtypes in [
          (0, lax.add, lax_test_util.default_dtypes),
          (1, lax.mul, lax_test_util.default_dtypes),
          # non-monoidal for everything except unsigned integers
          (0, lax.max, lax_test_util.all_dtypes),
          (-np.inf, lax.max, lax_test_util.float_dtypes),
          (dtypes.iinfo(np.int32).min, lax.max, [np.int32]),
          (dtypes.iinfo(np.int64).min, lax.max, [np.int64]),
          (np.inf, lax.min, lax_test_util.float_dtypes),
          (dtypes.iinfo(np.int32).max, lax.min, [np.int32]),
          (dtypes.iinfo(np.int64).max, lax.min, [np.int64]),
          (dtypes.iinfo(np.uint32).max, lax.min, [np.uint32]),
          (dtypes.iinfo(np.uint64).max, lax.min, [np.uint64]),
      ]
      for dtype in dtypes],
    [dict(shape=shape, dims=dims, bdims=bdims)
      for shape, dims in [
          [(3, 4, 5), (0,)], [(3, 4, 5), (1, 2)],
          [(3, 4, 5), (0, 2)], [(3, 4, 5), (0, 1, 2)]
      ]
      for bdims in lax_test_util.all_bdims(shape)],
  )
  def testReduce(self, op, init_val, shape, dtype, dims, bdims):
    rng = jtu.rand_small(self.rng())
    init_val = np.asarray(init_val, dtype=dtype)
    fun = lambda operand: lax.reduce(operand, init_val, op, dims)
    self._CheckBatching(fun, 5, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(shape=shape, dims=dims, bdims=bdims)
      for shape, dims in [
          [(3, 4, 5), (0,)], [(3, 4, 5), (1, 2)],
          [(3, 4, 5), (0, 2)], [(3, 4, 5), (0, 1, 2)]
      ]
      for bdims in lax_test_util.all_bdims(shape, shape)],
    dtype=lax_test_util.default_dtypes,
  )
  def testVariadicReduce(self, shape, dtype, dims, bdims):
    def op(a, b):
      x1, y1 = a
      x2, y2 = b
      return x1 + x2, y1 * y2
    rng = jtu.rand_small(self.rng())
    init_val = tuple(np.asarray([0, 1], dtype=dtype))
    fun = lambda x, y: lax.reduce((x, y), init_val, op, dims)
    self._CheckBatching(fun, 5, bdims, (shape, shape), (dtype, dtype), rng,
                        multiple_results=True)

  @jtu.sample_product(
    [dict(shape=shape, bdims=bdims, dim=dim)
      for shape in [(3, 4, 5)]
      for bdims in lax_test_util.all_bdims(shape)
      for dim in range(len(shape))],
    op=[lax.argmin, lax.argmax],
    dtype=lax_test_util.default_dtypes,
  )
  def testArgminmax(self, op, shape, dtype, dim, bdims):
    rng = jtu.rand_default(self.rng())
    fun = lambda operand: op(operand, dim, np.int32)
    self._CheckBatching(fun, 5, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(init_val=init_val, op=op, dtype=dtype)
     for init_val, op, dtypes in [
        (0, lax.add, [np.float32]),
        (-np.inf, lax.max, [np.float32]),
        (np.inf, lax.min, [np.float32]),
     ]
     for dtype in dtypes],
    [dict(shape=shape, dims=dims, strides=strides, padding=padding,
          base_dilation=base_dilation, window_dilation=window_dilation)
      for shape, dims, strides, padding, base_dilation, window_dilation in (
        itertools.chain(
          itertools.product(
            [(4, 6)],
            [(2, 1), (1, 2)],
            [(1, 1), (2, 1), (1, 2)],
            ["VALID", "SAME", [(0, 3), (1, 2)]],
            [(1, 1), (2, 3)],
            [(1, 1), (1, 2)]),
          itertools.product(
            [(3, 2, 4, 6)], [(1, 1, 2, 1), (2, 1, 2, 1)],
            [(1, 2, 2, 1), (1, 1, 1, 1)],
            ["VALID", "SAME", [(0, 1), (1, 0), (2, 3), (0, 2)]],
            [(1, 1, 1, 1), (2, 1, 3, 2)],
            [(1, 1, 1, 1), (1, 2, 2, 1)])))
    ],
  )
  def testReduceWindow(self, op, init_val, dtype, shape, dims, strides, padding,
                       base_dilation, window_dilation):
    rng = jtu.rand_small(self.rng())
    init_val = np.asarray(init_val, dtype=dtype)

    def fun(operand):
      return lax.reduce_window(operand, init_val, op, dims, strides, padding,
                               base_dilation, window_dilation)

    for bdims in lax_test_util.all_bdims(shape):
      self._CheckBatching(fun, 3, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(op=op, dtype=dtype)
      for op, types in [
          (lax.cumsum, [np.float32, np.float64]),
          (lax.cumprod, [np.float32, np.float64]),
      ]
      for dtype in types],
    [dict(shape=shape, bdims=bdims, axis=axis)
      for shape in [[10], [3, 4, 5]]
      for axis in range(len(shape))
      for bdims in lax_test_util.all_bdims(shape)],
    reverse=[False, True],
  )
  def testCumulativeReduce(self, op, shape, dtype, axis, bdims, reverse):
    rng_factory = (jtu.rand_default if dtypes.issubdtype(dtype, np.integer)
                   else jtu.rand_small)
    rng = rng_factory(self.rng())
    self._CheckBatching(partial(op, axis=axis, reverse=reverse), 7, bdims,
                        (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(shape=shape, dims=dims, strides=strides, bdims=bdims)
     for shape, dims, strides in itertools.chain(
        itertools.product(
            [(4, 6)],
            [(2, 1), (1, 2)],
            [(1, 1), (2, 1), (1, 2)]),
        itertools.product(
            [(3, 2, 4, 6)], [(1, 1, 2, 1), (2, 1, 2, 1)],
            [(1, 2, 2, 1), (1, 1, 1, 1)]))
     for bdims in lax_test_util.all_bdims(shape, shape)
    ],
    dtype=lax_test_util.float_dtypes,
    padding=["VALID", "SAME"]
  )
  @jtu.ignore_warning(message="Using reduced precision for gradient.*")
  def testSelectAndGatherAdd(self, dtype, padding, shape, dims, strides, bdims):
    rng = jtu.rand_small(self.rng())
    def fun(operand, tangents):
      pads = lax.padtype_to_pads(operand.shape, dims, strides, padding)
      ones = (1,) * len(operand.shape)
      return lax_windowed_reductions._select_and_gather_add(
          operand, tangents, lax.ge_p, dims, strides, pads, ones, ones)

    self._CheckBatching(fun, 3, bdims, (shape, shape), (dtype, dtype), rng)

  @jtu.sample_product(
    dtype=lax_test_util.float_dtypes,
    padding=["VALID", "SAME"],
    shape=[(3, 2, 4, 6)],
    dims=[(1, 1, 2, 1)],
    strides=[(1, 2, 2, 1), (1, 1, 1, 1)],
  )
  def testSelectAndScatterAdd(self, dtype, padding, shape, dims, strides):
    rng = jtu.rand_small(self.rng())

    pads = lax.padtype_to_pads(shape, dims, strides, padding)

    def fun(operand, cotangents):
      return lax_windowed_reductions._select_and_scatter_add(
          operand, cotangents, lax.ge_p, dims, strides, pads)
    ones = (1,) * len(shape)
    cotangent_shape = jax.eval_shape(
      lambda x: lax_windowed_reductions._select_and_gather_add(
          x, x, lax.ge_p, dims, strides, pads, ones, ones),
      np.ones(shape, dtype)).shape

    for bdims in lax_test_util.all_bdims(cotangent_shape, shape):
      self._CheckBatching(fun, 3, bdims, (cotangent_shape, shape),
                          (dtype, dtype), rng)

  @jtu.sample_product(
    [dict(shape=shape, fft_ndims=fft_ndims, bdims=bdims)
    for shape in [(5,), (3, 4, 5), (2, 3, 4, 5)]
    for bdims in lax_test_util.all_bdims(shape)
    for fft_ndims in range(0, min(3, len(shape)) + 1)],
  )
  def testFft(self, fft_ndims, shape, bdims):
    rng = jtu.rand_default(self.rng())
    ndims = len(shape)
    axes = range(ndims - fft_ndims, ndims)
    fft_lengths = tuple(shape[axis] for axis in axes)
    op = lambda x: lax.fft(x, xla_client.FftType.FFT, fft_lengths)
    self._CheckBatching(op, 5, bdims, [shape], [np.complex64], rng,
                        rtol=1e-5)

  @jtu.sample_product(
    [dict(shape=shape, idxs=idxs, dnums=dnums, slice_sizes=slice_sizes,
          bdims=bdims)
      for shape, idxs, dnums, slice_sizes in [
          ((5,), np.array([[0], [2]]), lax.GatherDimensionNumbers(
            offset_dims=(), collapsed_slice_dims=(0,), start_index_map=(0,)),
            (1,)),
          ((10,), np.array([[0], [0], [0]]), lax.GatherDimensionNumbers(
            offset_dims=(1,), collapsed_slice_dims=(), start_index_map=(0,)),
            (2,)),
          ((10, 5,), np.array([[0], [2], [1]]), lax.GatherDimensionNumbers(
            offset_dims=(1,), collapsed_slice_dims=(0,), start_index_map=(0,)),
            (1, 3)),
          ((10, 5), np.array([[0, 2], [1, 0]]), lax.GatherDimensionNumbers(
            offset_dims=(1,), collapsed_slice_dims=(0,), start_index_map=(0, 1)),
            (1, 3)),
      ]
      for bdims in lax_test_util.all_bdims(shape, idxs.shape)],
    dtype=lax_test_util.all_dtypes
  )
  def testGather(self, shape, dtype, idxs, dnums, slice_sizes, bdims):
    fun = partial(lax.gather, dimension_numbers=dnums, slice_sizes=slice_sizes)
    self._CheckBatching(fun, 0, bdims, [shape, idxs.shape], [dtype, idxs.dtype],
                        jtu.rand_default(self.rng()))
    self._CheckBatching(fun, 5, bdims, [shape, idxs.shape], [dtype, idxs.dtype],
                        jtu.rand_default(self.rng()))

  @jtu.sample_product(
    [dict(arg_shape=arg_shape, idxs=idxs, update_shape=update_shape,
          dnums=dnums, bdims=bdims)
      for arg_shape, idxs, update_shape, dnums in [
          ((5,), np.array([[0], [2]]), (2,), lax.ScatterDimensionNumbers(
            update_window_dims=(), inserted_window_dims=(0,),
            scatter_dims_to_operand_dims=(0,))),
          ((10,), np.array([[0], [0], [0]]), (3, 2), lax.ScatterDimensionNumbers(
            update_window_dims=(1,), inserted_window_dims=(),
            scatter_dims_to_operand_dims=(0,))),
          ((10, 5,), np.array([[0], [2], [1]]), (3, 3), lax.ScatterDimensionNumbers(
            update_window_dims=(1,), inserted_window_dims=(0,),
            scatter_dims_to_operand_dims=(0,))),
      ]
      for bdims in lax_test_util.all_bdims(arg_shape, idxs.shape, update_shape)],
    dtype=lax_test_util.float_dtypes
  )
  def testScatterAdd(self, arg_shape, dtype, idxs, update_shape, dnums, bdims):
    fun = partial(lax.scatter_add, dimension_numbers=dnums)
    self._CheckBatching(fun, 5, bdims, [arg_shape, idxs.shape, update_shape],
                        [dtype, idxs.dtype, dtype], jtu.rand_default(self.rng()),
                        rtol={np.float16: 5e-3, dtypes.bfloat16: 7e-2})

  @jtu.sample_product(
    [dict(arg_shape=arg_shape, idxs=idxs, update_shape=update_shape,
          dnums=dnums, bdims=bdims)
      for arg_shape, idxs, update_shape, dnums in [
          ((5,), np.array([[0], [2]]), (2,), lax.ScatterDimensionNumbers(
            update_window_dims=(), inserted_window_dims=(0,),
            scatter_dims_to_operand_dims=(0,))),
          ((10,), np.array([[0], [0], [0]]), (3, 2), lax.ScatterDimensionNumbers(
            update_window_dims=(1,), inserted_window_dims=(),
            scatter_dims_to_operand_dims=(0,))),
          ((10, 5,), np.array([[0], [2], [1]]), (3, 3), lax.ScatterDimensionNumbers(
            update_window_dims=(1,), inserted_window_dims=(0,),
            scatter_dims_to_operand_dims=(0,))),
      ]
      for bdims in lax_test_util.all_bdims(arg_shape, idxs.shape)],
    dtype=lax_test_util.float_dtypes,
  )
  def testScatterApply(self, arg_shape, dtype, idxs, update_shape, dnums, bdims):
    fun = partial(lax.scatter_apply, func=jnp.sin, update_shape=update_shape, dimension_numbers=dnums)
    self._CheckBatching(fun, 5, bdims, [arg_shape, idxs.shape],
                        [dtype, idxs.dtype], jtu.rand_default(self.rng()),
                        rtol={np.float16: 5e-3, dtypes.bfloat16: 7e-2})

  def testShapeUsesBuiltinInt(self):
    x = lax.iota(np.int32, 3) + 1
    self.assertIsInstance(x.shape[0], int)  # not np.int64

  def testBroadcastShapesReturnsPythonInts(self):
    shape1, shape2 = (1, 2, 3), (2, 3)
    out_shape = lax.broadcast_shapes(shape1, shape2)
    self.assertTrue(all(type(s) is int for s in out_shape))

  def testBroadcastShapesFaultyInputs(self):
    err_shape1, err_shape2 = (-1,), "hello"
    # negative inputs should fail while informing about illegal negative indices...
    with self.assertRaisesRegex(TypeError, "Only non-negative indices are allowed.*"):
      lax.broadcast_shapes(err_shape1)
    # ... while non-integers should error earlier, in the canonicalize_shape machinery.
    with self.assertRaisesRegex(TypeError, "Shapes must be 1D sequences.*"):
      lax.broadcast_shapes(err_shape2)  # pytype: disable=wrong-arg-types

  @jtu.sample_product(
    [dict(shape=shape, bdims=bdims)
      for shape in [(4,), (3, 5, 3)]
      for bdims in lax_test_util.all_bdims(shape)],
    k=[1, 3],
    dtype=lax_test_util.default_dtypes,
  )
  # The top_k indices for integer arrays with identical entries won't match between
  # vmap'd version and manual reference, so only test unique integer arrays for int_dtypes.
  # Note also that we chose 3 * 5 * 3 * 5 such that it fits in the range of
  # values a bfloat16 can represent exactly to avoid ties.
  def testTopK(self, shape, dtype, k, bdims):
    rng = jtu.rand_int(self.rng(), high=math.prod(shape))
    # _CheckBatching doesn't work with tuple outputs, so test outputs separately.
    op1 = lambda x: lax.top_k(x, k=k)[0]
    self._CheckBatching(op1, 5, bdims, (shape,), (dtype,), rng)
    op2 = lambda x: lax.top_k(x, k=k)[1]
    self._CheckBatching(op2, 5, bdims, (shape,), (dtype,), rng)

  @jtu.sample_product(
    [dict(shape=shape, bdims=bdims, dimension=dimension, arity=arity)
      for shape in [(2, 3)]
      for dimension in [0, 1]
      for arity in range(3)
      for bdims in lax_test_util.all_bdims(*((shape,) * arity))
     ],
    is_stable=[False, True]
  )
  def testSort(self, shape, dimension, arity, bdims, is_stable):
    rng = jtu.rand_default(self.rng())
    if arity == 1:
      fun = partial(lax.sort, dimension=dimension)
      self._CheckBatching(fun, 5, bdims, (shape,) * arity, (np.float32,) * arity,
                          rng)
    else:
      for i in range(arity):
        fun = lambda *args, i=i: lax.sort(args,
                                          dimension=dimension,
                                          is_stable=is_stable)[i]
        self._CheckBatching(fun, 5, bdims, (shape,) * arity,
                            (np.float32,) * arity, rng)

  # TODO Concatenate
  # TODO Reverse
  # TODO DynamicSlice
  # TODO DynamicUpdateSlice
  # TODO Collapse
  # TODO Scatter

  # TODO(b/183233858): variadic reduce-window is not implemented on XLA:GPU
  @jtu.skip_on_devices("gpu")
  def test_variadic_reduce_window(self):
    # https://github.com/google/jax/discussions/9818 and
    # https://github.com/google/jax/issues/9837
    def normpool(x):
      norms = jnp.linalg.norm(x, axis=-1)
      idxs = jnp.arange(x.shape[0])

      def g(a, b):
        an, ai = a
        bn, bi = b
        which = an >= bn
        return (jnp.where(which, an, bn), jnp.where(which, ai, bi))

      inf = jnp.array(np.inf, dtype=norms.dtype)
      one = jnp.array(1, dtype=idxs.dtype)
      _, idxs = lax.reduce_window((norms, idxs), (-inf, -one), g,
                        window_dimensions=(2,), window_strides=(2,),
                        padding=((0, 0),))
      return x[idxs]

    inpt = jnp.array([
      [1.0, 0.0, 1.0],
      [2.0, 2.0, 0.0],
      [3.0, 0.0, 1.0],
      [0.0, 1.0, 1.0],
    ])
    output = jax.vmap(normpool)(inpt[None, ...])  # doesn't crash
    expected = jnp.array([[[2.0, 2.0, 0.0], [3.0, 0.0, 1.0]]])
    self.assertAllClose(output, expected, check_dtypes=False)


if __name__ == '__main__':
  absltest.main(testLoader=jtu.JaxTestLoader())
