lax_control_flow_test.py

# Copyright 2018 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.


import collections
from functools import partial
import itertools
import operator
import re
import unittest

from absl.testing import absltest
from absl.testing import parameterized

import numpy as np

import jax
from jax import core
from jax import dtypes
from jax.errors import UnexpectedTracerError
from jax import lax
from jax import random
from jax._src import test_util as jtu
from jax import tree_util
from jax._src.util import unzip2
from jax.experimental import maps
from jax.ad_checkpoint import checkpoint as new_checkpoint, checkpoint_policies
import jax.numpy as jnp  # scan tests use numpy
import jax.scipy as jsp
from jax._src.lax import control_flow as lax_control_flow
from jax._src.lax.control_flow import for_loop

from jax.config import config
config.parse_flags_with_absl()


# Some tests are useful for testing both lax.cond and lax.switch. This function
# provides a lax.cond-compatible interface to a two-branch lax.switch. Several
# tests in this file are parameterized such that they either call into lax.cond
# or into this function.
def cond_via_switch(pred, true_fun, false_fun, op, *args):
  if len(args) > 0:
    assert len(args) == 1
    true_op, _true_fun, false_op, _false_fun = true_fun, false_fun, op, args[0]
    op = (false_op, true_op)
    false_fun = lambda op: _false_fun(op[0])
    true_fun = lambda op: _true_fun(op[1])
  index = lax.convert_element_type(pred, np.int32)
  return lax.switch(index, [false_fun, true_fun], op)

def cond_with_new_checkpoint(pred, true_fun, false_fun, op, *args):
  if args:
    true_op, _true_fun, false_op, _false_fun = true_fun, false_fun, op, args[0]
    op = (false_op, true_op)
    false_fun = lambda op: _false_fun(op[0])
    true_fun = lambda op: _true_fun(op[1])
  index = lax.convert_element_type(pred, np.int32)
  fn = lambda index, op: lax.switch(index, [false_fun, true_fun], op)
  return new_checkpoint(fn)(index, op)

COND_IMPLS = [
    (lax.cond, 'cond'),
    (cond_via_switch, 'switch'),
    (cond_with_new_checkpoint, 'new_checkpoint'),
]


# We wanted to try all scan tests with the scan partial evaluation rule that
# happens under ad_checkpoint.checkpoint, so we make a scan wrapper which
# wraps a ad_checkpoint.checkpoint around the computation.
def scan_with_new_checkpoint(f, *args, **kwargs):
  return new_checkpoint(partial(lax.scan, f, **kwargs),
                        policy=checkpoint_policies.nothing_saveable)(*args)
def scan_with_new_checkpoint2(f, *args, **kwargs):
  return new_checkpoint(partial(lax.scan, f, **kwargs),
                        policy=checkpoint_policies.everything_saveable)(*args)

def scan_with_for(f, *args, **kwargs):
  return for_loop.scan(f, *args, **kwargs)

def scan_with_remat_for(f, *args, **kwargs):
  return jax.remat(lambda *args: for_loop.scan(f, *args, **kwargs))(*args)

SCAN_IMPLS = [
    (lax.scan, 'unroll1'),
    (partial(lax.scan, unroll=2), 'unroll2'),
    (scan_with_new_checkpoint , 'new_checkpoint'),
    (scan_with_new_checkpoint2, 'new_checkpoint2'),
]

SCAN_IMPLS_WITH_FOR = [
    (lax.scan, 'unroll1'),
    (partial(lax.scan, unroll=2), 'unroll2'),
    (scan_with_new_checkpoint , 'new_checkpoint'),
    (scan_with_new_checkpoint2, 'new_checkpoint2'),
    (scan_with_for, 'for_loop'),
    (scan_with_remat_for, 'for_loop_remat'),
]

def while_loop_new_checkpoint(cond_fun, body_fun, init_val):
  return new_checkpoint(partial(lax.while_loop, cond_fun, body_fun))(init_val)

WHILE_LOOP_IMPLS = [
    (lax.while_loop, 'while_loop'),
    (while_loop_new_checkpoint, 'new_checkpoint'),
]


def while_loop_reference(cond, body, carry):
  while cond(carry):
    carry = body(carry)
  return carry


def scan_reference(f, init, xs):
  carry = init
  ys = []
  for x in xs:
    (carry, y) = f(carry, x)
    ys.append(lax.reshape(y, (1,) + np.shape(y)))
  ys = lax.concatenate(ys, 0)
  return carry, ys


ignore_jit_of_pmap_warning = partial(
  jtu.ignore_warning, message=".*jit-of-pmap.*")


class LaxControlFlowTest(jtu.JaxTestCase):

  def setUp(self):
    super().setUp()
    lax_control_flow._initial_style_open_jaxpr.cache_clear()
    lax_control_flow._initial_style_jaxpr.cache_clear()
    lax_control_flow._initial_style_jaxprs_with_common_consts.cache_clear()

  def testCallableErrors(self):
    not_callable = 42
    with self.assertRaisesRegex(TypeError, "lax.fori_loop.*callable.*"):
      lax.fori_loop(0, 1, not_callable, 0)
    with self.assertRaisesRegex(TypeError, "lax.while_loop.*callable.*"):
      lax.while_loop(not_callable, not_callable, 0)
    with self.assertRaisesRegex(TypeError, "lax.switch:.*callable.*"):
      lax.switch(0, [not_callable])
    with self.assertRaisesRegex(TypeError, "lax.cond.*callable.*"):
      lax.cond(0, not_callable, not_callable)
    with self.assertRaisesRegex(TypeError, "lax.scan.*callable.*"):
      lax.scan(not_callable, 0, 1)
    with self.assertRaisesRegex(TypeError, "lax.associative_scan.*callable.*"):
      lax.associative_scan(not_callable, 0)

  def testWhileWithTuple(self):
    limit = 10

    def loop_cond(state):
      pos, _ = state
      return lax.lt(pos, limit)

    def loop_body(state):
      pos, count = state
      return (lax.add(pos, 1), lax.add(count, 1))

    def loop(init):
      result = lax.while_loop(loop_cond, loop_body, (init, 0))
      _, count = result
      return count

    cloop = jax.jit(loop)

    self.assertEqual(loop(2), limit - 2)
    self.assertEqual(cloop(2), limit - 2)
    self.assertEqual(cloop(2), limit - 2)
    self.assertEqual(cloop(3), limit - 3)

  def testWhileWithManyArgs(self):
    nargs = 256

    def loop_cond(state):
      return lax.lt(state[0], 2)

    def loop_body(state):
      return tuple(lax.add(s, 1) for s in state)

    _ = lax.while_loop(loop_cond, loop_body, (0,) * nargs)

  def testNestedWhile(self):

    def outer_loop(num):  # pylint: disable=missing-docstring
      def cond_fun(state):
        num, i, _ = state
        return lax.lt(i, num)

      def body_fun(state):
        num, i, count = state
        return (num, lax.add(i, 1), inner_loop(i, count))

      init_val = (num, 0, 0)
      _, i, count = lax.while_loop(cond_fun, body_fun, init_val)
      return (i, count)

    def inner_loop(i, count):  # pylint: disable=missing-docstring
      def cond_fun(state):
        i, j, _ = state
        return lax.le(j, i)

      def body_fun(state):
        i, j, count = state
        return (i, lax.add(j, 1), lax.add(count, 1))

      init_val = (i, 0, count)
      _, _, count = lax.while_loop(cond_fun, body_fun, init_val)
      return count

    cloop = jax.jit(outer_loop)

    self.assertEqual(outer_loop(3), (3, 6))
    self.assertEqual(cloop(3), (3, 6))
    self.assertEqual(cloop(3), (3, 6))
    self.assertEqual(cloop(2), (2, 3))
    self.assertEqual(cloop(4), (4, 10))

  def testWhileWithClosure(self):

    def loop(init, local_limit, inc):

      def loop_cond(state):
        pos, _ = state
        return lax.lt(pos, local_limit)

      def loop_body(state):
        effect[0] = True
        pos, count = state
        return (lax.add(pos, 1), lax.add(count, inc))

      result = lax.while_loop(loop_cond, loop_body, (init, 0))
      _, count = result
      return count

    cloop = jax.jit(loop)

    limit = 10
    effect = [False]
    self.assertEqual(loop(2, limit, 1), limit - 2)
    assert effect[0]
    effect[0] = False
    self.assertEqual(cloop(2, limit, 1), limit - 2)
    assert effect[0]
    effect[0] = False
    self.assertEqual(cloop(2, limit, 1), limit - 2)
    self.assertEqual(cloop(3, limit, 1), limit - 3)
    assert not effect[0]

  def testWhileWithClosureJit(self):

    def loop(init, local_limit, inc):

      def loop_cond(state):
        pos, _ = state
        return lax.lt(pos, local_limit)

      def loop_body(state):
        effect[0] = True
        pos, count = state
        f = lambda pos, inc: (lax.add(pos, 1), lax.add(count, inc))
        return jax.jit(f)(pos, inc)

      result = lax.while_loop(loop_cond, loop_body, (init, 0))
      _, count = result
      return count

    cloop = jax.jit(loop)

    limit = 10
    effect = [False]
    self.assertEqual(loop(2, limit, 1), limit - 2)
    assert effect[0]
    effect[0] = False
    self.assertEqual(cloop(2, limit, 1), limit - 2)
    assert effect[0]
    effect[0] = False
    self.assertEqual(cloop(2, limit, 1), limit - 2)
    self.assertEqual(cloop(3, limit, 1), limit - 3)
    assert not effect[0]

  def testWhileTypeErrors(self):
    """Test typing error messages for while."""
    tuple_treedef = tree_util.tree_structure((1., 1.))
    leaf_treedef = tree_util.tree_structure(0.)
    with self.assertRaisesRegex(TypeError,
        re.escape(f"cond_fun must return a boolean scalar, but got pytree {tuple_treedef}.")):
      lax.while_loop(lambda c: (1., 1.), lambda c: c, 0.)
    with  self.assertRaisesRegex(TypeError,
        re.escape("cond_fun must return a boolean scalar, but got output type(s) [ShapedArray(float32[])].")):
      lax.while_loop(lambda c: np.float32(1.), lambda c: c, np.float32(0.))
    with self.assertRaisesRegex(TypeError,
        re.escape("body_fun output and input must have same type structure, "
                  f"got {tuple_treedef} and {leaf_treedef}.")):
      lax.while_loop(lambda c: True, lambda c: (1., 1.), 0.)
    with self.assertRaisesWithLiteralMatch(TypeError,
        ("body_fun output and input must have identical types, got\n"
         "('ShapedArray(bool[])', "
         "'DIFFERENT ShapedArray(bool[]) vs. "
         "ShapedArray(float32[])').")):
      lax.while_loop(lambda c: True, lambda c: (True, True),
                     (np.bool_(True), np.float32(0.)))

  def testNestedWhileWithDynamicUpdateSlice(self):
    num = 5

    def update_entry(arr, val, i, j):
      val = lax.reshape(val, [1, 1])
      return lax.dynamic_update_slice(arr, val, (i, j))

    def outer_loop(arr):  # pylint: disable=missing-docstring

      def cond_fun(state):
        i, num, _, _ = state
        return lax.lt(i, num)

      def body_fun(state):
        i, num, arr, out = state
        return (lax.add(i, 1), num, arr, inner_loop(i, arr, out))

      out = np.zeros(arr.shape, dtype=arr.dtype)
      init_val = (0, num, arr, out)
      _, _, _, out = lax.while_loop(cond_fun, body_fun, init_val)
      return out

    def inner_loop(i, arr, out):  # pylint: disable=missing-docstring

      def cond_fun(state):
        i, j, _, _ = state
        return lax.le(j, i)

      def body_fun(state):
        i, j, arr, out = state
        arr_i = lax.dynamic_index_in_dim(arr, i, 0, False)
        arr_i_j = lax.dynamic_index_in_dim(arr_i, j, 0, False)
        out = update_entry(out, arr_i_j, i, j)
        return (i, lax.add(j, 1), arr, out)

      init_val = (i, 0, arr, out)
      _, _, _, out = lax.while_loop(cond_fun, body_fun, init_val)
      return out

    cloop = jax.jit(outer_loop)
    arr = self.rng().randn(5, 5)
    self.assertAllClose(outer_loop(arr), np.tril(arr), check_dtypes=False)
    self.assertAllClose(cloop(arr), np.tril(arr), check_dtypes=False)
    self.assertAllClose(cloop(arr), np.tril(arr), check_dtypes=False)

  def testLoopWithConjunctionCondition(self):
    def sum_first_n(arr, num):  # pylint: disable=missing-docstring
      def cond_fun(state):
        arr, num, i, _ = state
        return lax.bitwise_and(lax.lt(i, num), lax.lt(i, arr.shape[0]))

      def body_fun(state):
        arr, num, i, total = state
        arr_i = lax.dynamic_index_in_dim(arr, i, 0, False)
        return (arr, num, i + 1, total + arr_i)

      init_val = (arr, num, 0, 0.)
      _, _, _, total = lax.while_loop(cond_fun, body_fun, init_val)
      return total

    cfun = jax.jit(sum_first_n)
    x = self.rng().randn(10).astype(jnp.float_)

    for num in [0, 5, 10, 15]:
      self.assertAllClose(sum_first_n(x, num), np.sum(x[:num]),
                          check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)

  def testWhileLoopBatched(self):
    def fun(x):
      return lax.while_loop(lambda x: x < 3, lambda x: x + 2, x)

    ans = jax.vmap(fun)(np.array([0, 1, 2, 3]))
    expected = np.array([4, 3, 4, 3])
    self.assertAllClose(ans, expected, check_dtypes=False)

    fun = jax.jit(fun)
    ans = jax.vmap(fun)(np.array([0, 1, 2, 3]))
    expected = np.array([4, 3, 4, 3])
    self.assertAllClose(ans, expected, check_dtypes=False)

  def testWhileLoopAxisIndexBatched(self):
    def fun(x):
      return lax.while_loop(lambda x: x < lax.axis_index('i'), lambda x: x + 2, x)

    ans = jax.vmap(fun, axis_name='i')(np.array([0, 0, 0, 0], dtype='int32'))
    expected = np.array([0, 2, 2, 4])
    self.assertAllClose(ans, expected, check_dtypes=False)

    fun = jax.jit(fun)
    ans = jax.vmap(fun, axis_name='i')(np.array([0, 0, 0, 0], dtype='int32'))
    expected = np.array([0, 2, 2, 4])
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = jax.vmap(lambda _, x: fun(x), axis_name='i', in_axes=(0, None))(
        np.array([0, 0, 0, 0]), 0)
    expected = np.array([0, 2, 2, 4], dtype='int32')
    self.assertAllClose(ans, expected, check_dtypes=False)

  def testWhileLoopBatchedWithConstBody(self):
    def f(x):
      def body_fn(_): return jnp.asarray(0., dtype=jnp.float32)
      def cond_fn(_): return jnp.logical_not(False) == False
      return jax.lax.while_loop(cond_fn, body_fn, x)
    x = jnp.arange(5, dtype=jnp.float32)
    self.assertAllClose(jax.vmap(f)(x), x)

  def testWhileLoopCondConstsBatched(self):
    def fun(x, y):
      return lax.while_loop(lambda x: x < y, lambda x: x + 2, x)

    ans = jax.vmap(fun, in_axes=(None, 0))(0, np.array([2, 3]))
    expected = np.array([2, 4])
    self.assertAllClose(ans, expected, check_dtypes=False)

  def testWhileLoopBodyConstsBatched(self):
    def fun(x, y):
      return lax.while_loop(lambda x: x < 3, lambda x: x + y, x)

    ans = jax.vmap(fun, in_axes=(None, 0))(0, jnp.array([2, 3]))
    expected = np.array([4, 3])
    self.assertAllClose(ans, expected, check_dtypes=False)

  def testWhileLoopTupleBatched(self):
    def cond_fun(loop_carry):
      x, y = loop_carry
      return x + y < 5

    def body_fun(loop_carry):
      x, y = loop_carry
      x = x + 1
      return x, y

    def fun(x, y):
      return lax.while_loop(cond_fun, body_fun, (x, y))

    ans = jax.vmap(fun)(np.array([0, 0]), np.array([1, 2]))
    expected = (np.array([4, 3]), np.array([1, 2]))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_issue_3204(self):
    # Error during XLA code generation for vmap of nested loops
    def test(a, b):
      val = 0
      i = 0
      j = 0

      condfun_1 = lambda inp: inp[1] < a + 1
      condfun_2 = lambda inp: inp[2] < b + 1

      def bodyfun_1(inp):
        val, i, j = inp
        j = 0

        def bodyfun_2(inp):
          val, i, j = inp
          val += i + j
          j += 1
          return (val, i, j)

        result = lax.while_loop(condfun_2, bodyfun_2, (val, i, j))
        val = result[0]
        i += 1
        return (val, i, j)

      result = lax.while_loop(condfun_1, bodyfun_1, (val, i, j))
      return result[0]

    arr = np.arange(5)
    vmap_test = jax.vmap(test, (0, 0))
    vmap_test(arr, arr)

  def testForiLoopErrors(self):
    """Test typing error messages for while."""
    with self.assertRaisesRegex(
      TypeError, "arguments to fori_loop must have equal types"):
      lax.fori_loop(np.int16(0), jnp.int32(10), (lambda i, c: c), jnp.float32(7))

  def testForiLoopBatched(self):
    def body_fun(i, loop_carry):
      x, y = loop_carry
      x = x + 1
      y = y + 2
      return x, y

    def fun(x):
      return lax.fori_loop(0, 10, body_fun, (x, 0))

    ans = jax.vmap(fun)(np.array([0, 1]))
    expected = (np.array([10, 11]), np.array([20, 20]))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def testForiLoopBatchedIssue1190(self):
    cond_fun = lambda carry: carry[0] < 4
    body_fun = lambda carry: (carry[0] + 1, carry[1] + 1)
    f = lambda x: lax.while_loop(cond_fun, body_fun, (0, x))
    jaxpr = jax.make_jaxpr(jax.vmap(f))(jnp.arange(3))
    eqn = jaxpr.jaxpr.eqns[0]
    self.assertIs(eqn.primitive, lax.while_p)
    self.assertEqual(eqn.params['cond_jaxpr'].in_avals[0].shape, ())

  def testForiLoopBasic(self):
    def body_fun(i, tot):
      return lax.add(tot, i)

    def count(num):
      return lax.fori_loop(0, num, body_fun, 0)

    self.assertEqual(count(2), 1)
    self.assertEqual(count(3), 3)
    self.assertEqual(count(4), 6)

    for args_maker in [lambda: [2], lambda: [3], lambda: [4]]:
      self._CompileAndCheck(count, args_maker)

  def testForiLoopClosure(self):
    def count(num):
      def body_fun(i, tot):
        return lax.add(num, lax.add(tot, i))
      return lax.fori_loop(0, num, body_fun, 0)

    cfun = jax.jit(count)

    self.assertEqual(count(2), 1 + 2**2)
    self.assertEqual(count(2), cfun(2))
    self.assertEqual(count(3), 3 + 3**2)
    self.assertEqual(count(3), cfun(3))
    self.assertEqual(count(4), 6 + 4**2)
    self.assertEqual(count(4), cfun(4))

  def testForiLoopTupleState(self):
    def sum_first_n(arr, num):
      def body_fun(i, state):
        arr, total = state
        arr_i = lax.dynamic_index_in_dim(arr, i, 0, False)
        return (arr, lax.add(total, arr_i))

      init_val = (arr, arr.dtype.type(0))
      _, total = lax.fori_loop(0, lax.min(arr.shape[0], num), body_fun,
                               init_val)
      return total

    cfun = jax.jit(sum_first_n)
    x = self.rng().randn(10).astype(jnp.float_)

    for num in [0, 5, 10, 15]:
      self.assertAllClose(sum_first_n(x, num), np.sum(x[:num]),
                          check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)

  def testForiLoopDictState(self):
    def sum_first_n(arr, num):
      def body_fun(i, state):
        arr, total = state['arr'], state['total']
        arr_i = lax.dynamic_index_in_dim(arr, i, 0, False)
        return {'arr': arr, 'total': lax.add(total, arr_i)}

      init_val = {'arr': arr, 'total': arr.dtype.type(0)}
      out_val = lax.fori_loop(0, lax.min(arr.shape[0], num), body_fun, init_val)
      return out_val['total']

    cfun = jax.jit(sum_first_n)
    x = self.rng().randn(10).astype(jnp.float_)

    for num in [0, 5, 10, 15]:
      self.assertAllClose(sum_first_n(x, num), np.sum(x[:num]),
                          check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)

  def testForiLoopEmptyTupleInState(self):
    def sum_first_n(arr, num):
      def body_fun(i, state):
        arr, total, _ = state
        arr_i = lax.dynamic_index_in_dim(arr, i, 0, False)
        return (arr, lax.add(total, arr_i), ())

      init_val = (arr, arr.dtype.type(0), ())
      _, tot, _ = lax.fori_loop(0, lax.min(arr.shape[0], num), body_fun, init_val)
      return tot

    cfun = jax.jit(sum_first_n)
    x = self.rng().randn(10).astype(jnp.float_)

    for num in [0, 5, 10, 15]:
      self.assertAllClose(sum_first_n(x, num), np.sum(x[:num]),
                          check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)
      self.assertAllClose(cfun(x, num), np.sum(x[:num]), check_dtypes=False)

  def testForiLoopIssue8152(self):
    y = lax.fori_loop(lower=0, upper=0, body_fun=lambda x, i: x + i, init_val=1.)
    self.assertAllClose(y, 1., check_dtypes=False)

    # trivial fori_loop should work - even when jit is disabled
    with jax.disable_jit():
      y = lax.fori_loop(lower=0, upper=0, body_fun=lambda x, i: x + i, init_val=1.)
    self.assertAllClose(y, 1., check_dtypes=False)

    # scan with length 0 should work with jit, but raise an error without
    def should_raise_wo_jit():
      carry, out = lax.scan(lambda c, x: (c + x, x), 0., np.array([]))
      return carry
    self.assertAllClose(should_raise_wo_jit(), 0., check_dtypes=False)
    with jax.disable_jit():
      self.assertRaises(ValueError, should_raise_wo_jit)

  def testCond(self):
    def fun(x):
      if x < 3:
        return (x, x)
      else:
        y = lax.mul(2, x)
        return y, lax.mul(2, y)

    @jax.jit
    def cfun(x):
      def false_fun(x):
        y = lax.mul(2, x)
        return y, lax.mul(2, y)
      return lax.cond(lax.lt(x, 3), lambda x: (x, x), false_fun, x)

    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(0), (0, 0))
    self.assertEqual(fun(1), cfun(1))
    self.assertEqual(fun(1), (1, 1))
    self.assertEqual(fun(2), cfun(2))
    self.assertEqual(fun(2), (2, 2))
    self.assertEqual(fun(3), cfun(3))
    self.assertEqual(fun(3), (6, 12))
    self.assertEqual(fun(4), cfun(4))
    self.assertEqual(fun(4), (8, 16))

  def testCondPredIsNone(self):
    # see https://github.com/google/jax/issues/11574
    def f(pred, x):
      return lax.cond(pred, lambda x: x + 1, lambda x: x + 2, x)

    self.assertRaisesRegex(TypeError, "cond predicate is None",
                           lambda: f(None, 1.))
    self.assertRaisesRegex(TypeError, "cond predicate is None",
                           lambda: jax.jit(f)(None, 1.))

  def testCondTwoOperands(self):
    # see https://github.com/google/jax/issues/8469
    add, mul = lax.add, lax.mul

    def fun(x):
      return add(x, x) if x == 0 else mul(x, x)

    def cfun(x):
      return lax.cond(x == 0, add, mul, x, x)

    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))
    cfun = jax.jit(cfun)
    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))

  def testCondThreeOperands(self):
    add = lambda x, y, z: x + y + z
    mul = lambda x, y, z: x * y * z

    def fun(x):
      return add(x, x, x) if x == 0 else mul(x, x, x)

    def cfun(x):
      return lax.cond(x == 0, add, mul, x, x, x)

    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))
    cfun = jax.jit(cfun)
    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))

  def testSwitch(self):
    def branch(x):
      y = lax.mul(2, x)
      return y, lax.mul(2, y)

    branches = [lambda x: (x, x),
                branch,
                lambda x: (x, -x)]

    def fun(x):
      if x <= 0:
        return branches[0](x)
      elif x == 1:
        return branches[1](x)
      else:
        return branches[2](x)

    def cfun(x):
      return lax.switch(x, branches, x)

    self.assertEqual(fun(-1), cfun(-1))
    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))
    self.assertEqual(fun(2), cfun(2))
    self.assertEqual(fun(3), cfun(3))

    cfun = jax.jit(cfun)

    self.assertEqual(fun(-1), cfun(-1))
    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))
    self.assertEqual(fun(2), cfun(2))
    self.assertEqual(fun(3), cfun(3))

  def testSwitchMultiOperands(self):
    branches = [lax.add, lax.mul]

    def fun(x):
      i = 0 if x <= 0 else 1
      return branches[i](x, x)

    def cfun(x):
      return lax.switch(x, branches, x, x)

    self.assertEqual(fun(-1), cfun(-1))
    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))
    self.assertEqual(fun(2), cfun(2))
    cfun = jax.jit(cfun)
    self.assertEqual(fun(-1), cfun(-1))
    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(fun(1), cfun(1))
    self.assertEqual(fun(2), cfun(2))

  def testSwitchResidualsMerge(self):
    def get_conds(fun):
      jaxpr = jax.make_jaxpr(jax.grad(fun))(0., 0)
      return [eqn for eqn in jaxpr.jaxpr.eqns if eqn.primitive.name == 'cond']

    def branch_invars_len(cond_eqn):
      lens = [len(jaxpr.jaxpr.invars) for jaxpr in cond_eqn.params['branches']]
      assert len(set(lens)) == 1
      return lens[0]

    def branch_outvars_len(cond_eqn):
      lens = [len(jaxpr.jaxpr.outvars) for jaxpr in cond_eqn.params['branches']]
      assert len(set(lens)) == 1
      return lens[0]

    branches1 = [
        lambda x: jnp.sin(x),
        lambda x: jnp.cos(x)]   # branch residuals overlap, should be reused
    branches2 = branches1 + [
        lambda x: jnp.sinh(x)]  # another overlapping residual, expect reuse
    branches3 = branches2 + [
        lambda x: jnp.sin(x) + jnp.cos(x)]  # requires one more residual slot
    def fun1(x, i):
      return lax.switch(i + 1, branches1, x)
    def fun2(x, i):
      return lax.switch(i + 1, branches2, x)
    def fun3(x, i):
      return lax.switch(i + 1, branches3, x)

    fwd1, bwd1 = get_conds(fun1)
    fwd2, bwd2 = get_conds(fun2)
    fwd3, bwd3 = get_conds(fun3)

    fwd1_num_out = branch_outvars_len(fwd1)
    fwd2_num_out = branch_outvars_len(fwd2)
    fwd3_num_out = branch_outvars_len(fwd3)
    assert fwd1_num_out == fwd2_num_out
    assert fwd3_num_out == fwd2_num_out + 1

    bwd1_num_in = branch_invars_len(bwd1)
    bwd2_num_in = branch_invars_len(bwd2)
    bwd3_num_in = branch_invars_len(bwd3)
    assert bwd1_num_in == bwd2_num_in
    assert bwd3_num_in == bwd2_num_in + 1

  def testOneBranchSwitch(self):
    branch = lambda x: -x
    f = lambda i, x: lax.switch(i, [branch], x)
    x = 7.
    self.assertEqual(f(-1, x), branch(x))
    self.assertEqual(f(0, x), branch(x))
    self.assertEqual(f(1, x), branch(x))
    cf = jax.jit(f)
    self.assertEqual(cf(-1, x), branch(x))
    self.assertEqual(cf(0, x), branch(x))
    self.assertEqual(cf(1, x), branch(x))
    cf = jax.jit(f, static_argnums=0)
    self.assertEqual(cf(-1, x), branch(x))
    self.assertEqual(cf(0, x), branch(x))
    self.assertEqual(cf(1, x), branch(x))

  def testIssue1379(self):
    def fun(pred):
      return lax.cond(pred, lambda x: (True, x), lambda x: (False, x), pred)

    @jax.jit
    def cfun(pred):
      return fun(pred)

    self.assertEqual(fun(0), cfun(0), (False,0))
    self.assertEqual(fun(0.), cfun(0.), (False,0.))
    self.assertEqual(fun(1), cfun(1), (True,1))
    self.assertEqual(fun(1.), cfun(1.), (True,1.))

    # test that proper errors are raised for wrong types
    for pred in ["abc", [], [1,2]]:
      for f in [fun, cfun]:
        self.assertRaises(TypeError, f, pred)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testNestedCond(self, cond):
    def fun(x):
      if x < 2:
        return lax.mul(2, x)
      else:
        if x < 5:
          return lax.mul(3, x)
        else:
          return lax.mul(4, x)

    @jax.jit
    def cfun(x):
      return cond(
          lax.lt(x, 2),
          lambda x: lax.mul(2, x),
          lambda x: cond(lax.lt(x, 5),
                         x, lambda x: lax.mul(3, x),
                         4, lambda y: lax.mul(y, x)),
          x)

    self.assertEqual(cfun(1), 2)
    self.assertEqual(cfun(3), 9)
    self.assertEqual(cfun(6), 24)
    self.assertEqual(cfun(1), fun(1))
    self.assertEqual(cfun(3), fun(3))
    self.assertEqual(cfun(6), fun(6))

  def testCondTypeErrors(self):
    """Test typing error messages for  cond."""
    with self.assertRaisesRegex(TypeError,
        re.escape("Pred type must be either boolean or number, got <function")):
      lax.cond(lambda x: True, lambda top: 2., lambda fop: 3., 1.)
    with self.assertRaisesRegex(TypeError,
        re.escape("Pred must be a scalar, got foo of type <class 'str'>")):
      lax.cond("foo", lambda top: 2., lambda fop: 3., 1.)
    with self.assertRaisesRegex(TypeError,
        re.escape("Pred must be a scalar, got (1.0, 1.0) of type <class 'tuple'>")):
      lax.cond((1., 1.), lambda top: 2., lambda fop: 3., 1.)
    with self.assertRaisesRegex(TypeError,
        re.escape("true_fun and false_fun output must have same type structure, "
                  f"got {tree_util.tree_structure(2.)} and {tree_util.tree_structure((3., 3.))}.")):
      lax.cond(True, lambda top: 2., lambda fop: (3., 3.), 1.)
    with self.assertRaisesRegex(
        TypeError,
        "true_fun and false_fun output must have identical types, got\n"
        r"DIFFERENT ShapedArray\(float32\[1\]\) vs. "
        r"ShapedArray\(float32\[\].*\)."):
      lax.cond(True,
               lambda top: jnp.array([1.], jnp.float32),
               lambda fop: jnp.float32(1.),
               1.)

  def testSwitchErrors(self):
    """Test typing error messages for switch."""
    with self.assertRaisesRegex(TypeError,
        re.escape("Index type must be an integer, got <function")):
      lax.switch(lambda x: True, [lambda _: 2., lambda _: 3.], 1.)
    with self.assertRaisesRegex(TypeError,
        re.escape("Index type must be an integer, got foo.")):
      lax.switch("foo", [lambda _: 2., lambda _: 3.], 1.)
    with self.assertRaisesRegex(TypeError,
        re.escape("Branch index must be scalar, got (1.0, 1.0) of shape (2,).")):
      lax.switch((1., 1.), [lambda _: 2., lambda _: 3.], 1.)
    with self.assertRaisesRegex(ValueError,
        re.escape("Empty branch sequence")):
      lax.switch(0, [], 1.)
    with self.assertRaisesRegex(TypeError,
        re.escape("branch 0 and 1 outputs must have same type structure, "
                  f"got {tree_util.tree_structure(2.)} and {tree_util.tree_structure((3., 3.))}.")):
      lax.switch(1, [lambda _: 2., lambda _: (3., 3.)], 1.)
    with self.assertRaisesRegex(
        TypeError,
        "branch 0 and 1 outputs must have identical types, got\n"
        r"DIFFERENT ShapedArray\(float32\[1\]\) "
        r"vs. ShapedArray\(float32\[\].*\)."):
      lax.switch(1, [lambda _: jnp.array([1.], jnp.float32),
                     lambda _: jnp.float32(1.)],
                 1.)

  def testCondOneBranchConstant(self):
    def fun(x):
      if x < 3:
        return 5.
      else:
        return x

    @jax.jit
    def cfun(x):
      return lax.cond(lax.lt(x, 3), lambda x: 5, lambda x: x, x)

    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(cfun(0), 5)
    self.assertEqual(fun(4), cfun(4))
    self.assertEqual(cfun(4), 4)

  def testCondOneBranchConstantTuple(self):
    def fun(x):
      if x < 3:
        return (1., 2., 3.)
      else:
        return (x, 2., 4.)

    @jax.jit
    def cfun(x):
      return lax.cond(lax.lt(x, 3),
                      lambda x: (1, 2., 3.),
                      lambda x: (x, 2., 4.),
                      x)

    self.assertEqual(fun(0), cfun(0))
    self.assertEqual(cfun(0), (1, 2., 3.))
    self.assertEqual(fun(4), cfun(4))
    self.assertEqual(cfun(4), (4, 2., 4.))

  def testCondBatched(self):
    def fun(x, y, z):
      pred = lax.lt(x, 3)
      true_fun = lambda y: y
      false_fun = lambda z: lax.neg(z)
      return lax.cond(pred, y, true_fun, z, false_fun)

    # these cases stay as cond
    x = jnp.array(2)
    y = jnp.array([1, 2])
    z = jnp.array([3, 4])
    ans = jax.vmap(fun, (None, 0, 0))(x, y, z)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (None, 0, 0)))(x, y, z)
    expected = np.array([1, 2])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" not in str(jaxpr)

    x = jnp.array(4)
    ans = jax.vmap(fun, (None, 0, 0))(x, y, z)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (None, 0, 0)))(x, y, z)
    expected = np.array([-3, -4])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" not in str(jaxpr)

    fun = jax.jit(fun)
    ans = jax.vmap(fun, (None, 0, 0))(x, y, z)
    expected = np.array([-3, -4])
    self.assertAllClose(ans, expected, check_dtypes=False)

    z = jnp.array(5)
    ans = jax.vmap(fun, (None, 0, None))(x, y, z)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (None, 0, None)))(x, y, z)
    expected = np.array([-5, -5])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" not in str(jaxpr)


    # these cases become select
    x = jnp.array([2, 4])
    ans = jax.vmap(fun, (0, 0, None))(x, y, z)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (0, 0, None)))(x, y, z)
    expected = np.array([1, -5])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" in str(jaxpr)

    z = jnp.array([3, 4])
    ans = jax.vmap(fun)(x, y, z)
    jaxpr = jax.make_jaxpr(jax.vmap(fun))(x, y, z)
    expected = np.array([1, -4])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" in str(jaxpr)

  def testSwitchBatched(self):
    def fun(index, x, y, z):
      branches = [lambda xyz: xyz[0],
                  lambda xyz: lax.neg(xyz[1]),
                  lambda xyz: lax.sign(xyz[2])]
      return lax.switch(index, branches, (x, y, z))

    # these cases stay as cond
    x = jnp.array(0)
    y = jnp.array([1, 2])
    z = jnp.array([3, 4])
    w = jnp.array(9)
    ans = jax.vmap(fun, (None, 0, 0, None))(x, y, z, w)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (None, 0, 0, None)))(x, y, z, w)
    expected = np.array([1, 2])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" not in str(jaxpr)

    x = jnp.array(1)
    ans = jax.vmap(fun, (None, 0, 0, None))(x, y, z, w)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (None, 0, 0, None)))(x, y, z, w)
    expected = np.array([-3, -4])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" not in str(jaxpr)

    fun = jax.jit(fun)
    ans = jax.vmap(fun, (None, 0, 0, None))(x, y, z, w)
    expected = np.array([-3, -4])
    self.assertAllClose(ans, expected, check_dtypes=False)

    z = jnp.array(5)
    ans = jax.vmap(fun, (None, 0, None, None))(x, y, z, w)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (None, 0, None, None)))(x, y, z, w)
    expected = np.array([-5, -5])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" not in str(jaxpr)


    # these cases become select
    x = jnp.array([0, 1])
    ans = jax.vmap(fun, (0, 0, None, None))(x, y, z, w)
    jaxpr = jax.make_jaxpr(jax.vmap(fun, (0, 0, None, None)))(x, y, z, w)
    expected = np.array([1, -5])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" in str(jaxpr)

    z = jnp.array([3, 4])
    w = jnp.array([9, 9])
    ans = jax.vmap(fun)(x, y, z, w)
    jaxpr = jax.make_jaxpr(jax.vmap(fun))(x, y, z, w)
    expected = np.array([1, -4])
    self.assertAllClose(ans, expected, check_dtypes=False)
    assert "select" in str(jaxpr)

  def testCondJVP(self):
    def fun_ref(x):
      if x < 3:
        return (x, x)
      else:
        y = 2 * x
        return y, 2 * y

    def fun(x):
      def false_fun(x):
        y = 2 * x
        return y, 2 * y
      return lax.cond(x < 3, lambda x: (x, x), false_fun, x)

    x = 3.14
    ans = jax.jvp(fun, (x,), (x,))
    expected = jax.jvp(fun_ref, (x,), (x,))
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x,), order=2, modes=["fwd"])

    x = 2.72
    ans = jax.jvp(fun, (x,), (x,))
    expected = jax.jvp(fun_ref, (x,), (x,))
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x,), order=2, modes=["fwd"])

  def testSwitchJVP(self):
    def branch(x):
      y = 2 * x
      return y, 2 * y

    branches = [lambda x: (x, x),
                branch,
                lambda x: (x, -x)]

    def fun_ref(x):
      idx = x // 1
      if idx <= 0:
        return branches[0](x)
      elif idx == 1:
        return branches[1](x)
      else:
        return branches[2](x)

    def fun(x):
      idx = lax.convert_element_type(x // 1, np.int32)
      return lax.switch(idx, branches, x)

    for x in [-0.7, 0.7, 1.7, 2.7, 3.7]:
      ans = jax.jvp(fun, (x,), (x,))
      expected = jax.jvp(fun_ref, (x,), (x,))
      self.assertAllClose(ans, expected, check_dtypes=False)
      jtu.check_grads(fun, (x,), order=2, modes=["fwd"])

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondJVP2(self, cond):
    def fun_ref(x):
      if x < 3:
        return 2.
      else:
        return 2. * x

    def fun(x):
      return cond(x < 3, None, lambda _: 2., x, lambda x: 2. * x)

    x = 3.14
    ans = jax.jvp(fun, (x,), (x,))
    expected = jax.jvp(fun_ref, (x,), (x,))
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x,), order=2, modes=["fwd"])

    x = 2.72
    ans = jax.jvp(fun, (x,), (x,))
    expected = jax.jvp(fun_ref, (x,), (x,))
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x,), order=2, modes=["fwd"])

  def testCondGrad(self):
    def f_ref(x):
      return 3. * x if x < 2 else jnp.sin(x)

    @jax.jit
    def f(x):
      return lax.cond(x < 2, lambda x: 3. * x, lambda x: jnp.sin(x), x)

    x = 2.14
    ans = jax.grad(f)(x)
    expected = jax.grad(f_ref)(x)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(f, (x,), order=2, modes=["fwd", "rev"])

    x = 1.72
    ans = jax.grad(f)(x)
    expected = jax.grad(f_ref)(x)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(f, (x,), order=2, modes=["fwd", "rev"])

  def testCondGradVmapNan(self):
    eps = 1e-3

    def safe1(x):
      return lax.cond(x < eps, lambda _: eps, lambda _: jnp.sqrt(x), ())

    out = jax.grad(lambda x: jax.vmap(safe1)(x).sum())(np.zeros(10))
    self.assertFalse(np.isnan(out).any())

  def testSwitchGrad(self):
    branches = [lambda x: 3. * x,
                lambda x: jnp.sin(x),
                lambda x: -x]

    def f_ref(x):
      idx = x // 1
      if idx <= 0:
        return branches[0](x)
      elif idx == 1:
        return branches[1](x)
      else:
        return branches[2](x)

    @jax.jit
    def f(x):
      idx = lax.convert_element_type(x // 1, np.int32)
      return lax.switch(idx, branches, x)

    for x in [-0.7, 0.7, 1.7, 2.7, 3.7]:
      ans = jax.grad(f)(x)
      expected = jax.grad(f_ref)(x)
      self.assertAllClose(ans, expected, check_dtypes=False)
      jtu.check_grads(f, (x,), order=2, modes=["fwd", "rev"])

  def testSwitchGradWithWeakTypeMismatch(self):  # issue #4696, PR #4896
    dtype = dtypes.canonicalize_dtype(np.float64)
    dtype = jnp.float32 if dtype == jnp.float32 else jnp.float64

    branches = [
        lambda x: x,             # This preserves the weak type of x.
        lambda x: x + dtype(1),  # This strips the weak type of x.
    ]

    def f_ref(x):
      i = x.astype(jnp.int32)
      return branches[i](x)

    def f(x):
      return lax.switch(x.astype(jnp.int32), branches, x)

    for x in [0., 1.]:
      ans = jax.grad(f)(x)
      expected = jax.grad(f_ref)(x)
      self.assertAllClose(ans, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondGrad2(self, cond):
    def f_ref(x):
      z = jnp.array([1., 2.], x.dtype) * x if x[0] < 2 else jnp.sin(x)
      return z.sum()

    def _f(x):
      return cond(
          x[0] < 2,
          lambda x: jnp.array([1., 2.], x.dtype) * x,
          lambda x: jnp.sin(x),
          x)

    f = lambda x: jax.jit(_f)(x).sum()

    x = 2.14 * jnp.ones(2)
    ans = jax.grad(f)(x)
    expected = jax.grad(f_ref)(x)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(f, (x,), order=2, modes=["fwd", "rev"])

    x = 1.72 * jnp.ones(2)
    ans = jax.grad(f)(x)
    expected = jax.grad(f_ref)(x)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(f, (x,), order=2, modes=["fwd", "rev"],
                    rtol={jnp.float32: 1e-2, jnp.float64: 2e-3})

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondGrad3(self, cond):
    def fun_ref(x):
      if x < 3:
        return 2.
      else:
        return 2. * x

    def fun(x):
      return cond(x < 3, None, lambda _: 2., x, lambda x: 2. * x)

    x = 3.14
    ans = jax.grad(fun)(x)
    expected = jax.grad(fun_ref)(x)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x,), order=2, modes=["fwd", "rev"])

    x = 2.72
    ans = jax.grad(fun)(x)
    expected = jax.grad(fun_ref)(x)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x,), order=2, modes=["fwd", "rev"])

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondGrad4(self, cond):
    if cond is cond_with_new_checkpoint and 'tpu' in jtu.device_under_test():
      raise unittest.SkipTest("tpu bug")  # TODO(parkers): tpu bug ehibited here
    def fun_ref(x, y):
      if x < 3:
        return 2. * jnp.sin(y)
      else:
        return 2. * jnp.cos(x)

    @jax.jit
    def fun(x, y):
      return cond(
          x < 3,
          None, lambda _: 2. * jnp.sin(y),
          x,  lambda x: 2. * x)

    y = 5.8
    x = 3.14
    ans = jax.grad(fun, 1)(x, y)
    expected = jax.grad(fun_ref, 1)(x, y)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x, y), order=2, modes=["fwd", "rev"])

    x = 2.72
    ans = jax.grad(fun, 1)(x, y)
    expected = jax.grad(fun_ref, 1)(x, y)
    self.assertAllClose(ans, expected, check_dtypes=False)
    jtu.check_grads(fun, (x, y), order=2, modes=["fwd", "rev"])

  def testCondLinearize(self):
    def f(x):
      return lax.cond(x < 2, lambda x: 3. * x, lambda x: jnp.sin(x), x)
    y, f_lin = jax.linearize(f, 1.)
    self.assertAllClose(y, 3., check_dtypes=False)
    self.assertAllClose(f_lin(2.), 6., check_dtypes=False)
    y, f_lin = jax.linearize(f, 4.)
    self.assertAllClose(y, jnp.sin(4.), check_dtypes=False)
    self.assertAllClose(f_lin(2.), jnp.cos(4.) * 2., check_dtypes=False)

  def testSwitchLinearize(self):
    branches = [lambda x: 3. * x,
                lambda x: jnp.sin(x),
                lambda x: -x]
    def f(x):
      idx = lax.convert_element_type(x // 1, np.int32)
      return lax.switch(idx, branches, x)

    # branch 0
    y, f_lin = jax.linearize(f, -1.)
    self.assertAllClose(y, -3., check_dtypes=False)
    self.assertAllClose(f_lin(2.), 6., check_dtypes=False)
    y, f_lin = jax.linearize(f, 0.)
    self.assertAllClose(y, 0., check_dtypes=False)
    self.assertAllClose(f_lin(2.), 6., check_dtypes=False)

    # branch 1
    y, f_lin = jax.linearize(f, 1.)
    self.assertAllClose(y, jnp.sin(1.), check_dtypes=False)
    self.assertAllClose(f_lin(2.), jnp.cos(1.) * 2., check_dtypes=False)

    # branch 2
    y, f_lin = jax.linearize(f, 2.)
    self.assertAllClose(y, -2., check_dtypes=False)
    self.assertAllClose(f_lin(2.), -2., check_dtypes=False)
    y, f_lin = jax.linearize(f, 3.)
    self.assertAllClose(y, -3., check_dtypes=False)
    self.assertAllClose(f_lin(2.), -2., check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondLinearize2(self, cond):
    def f_ref(x):
      z = jnp.array([1., 2.], x.dtype) * x if x[0] < 2 else jnp.cos(jnp.sin(x))
      return z.sum()

    def f(x):
      return cond(
          x[0] < 2,
          lambda x: jnp.array([1., 2.], x.dtype) * x,
          lambda x: jnp.cos(jnp.sin(x)),
          x).sum()

    x = 2.14 * jnp.ones(2)
    y, f_lin = jax.linearize(f, x)
    y_ref, f_lin_ref = jax.linearize(f_ref, x)
    self.assertAllClose(y, y_ref, check_dtypes=False)
    self.assertAllClose(f_lin(x), f_lin_ref(x), check_dtypes=False)

    x = -2.14 * jnp.ones(2)
    y, f_lin = jax.linearize(f, x)
    y_ref, f_lin_ref = jax.linearize(f_ref, x)
    self.assertAllClose(y, y_ref, check_dtypes=False)
    self.assertAllClose(f_lin(x), f_lin_ref(x), check_dtypes=False)

    f = jax.jit(f)
    x = 2.14 * jnp.ones(2)
    y, f_lin = jax.linearize(f, x)
    y_ref, f_lin_ref = jax.linearize(f_ref, x)
    self.assertAllClose(y, y_ref, check_dtypes=False)
    self.assertAllClose(f_lin(x), f_lin_ref(x), check_dtypes=False)

  def testCondJit(self):
    def f(x):
      return lax.cond(x < 2, lambda x: 3. * x, lambda x: jnp.sin(x), x)
    y = jax.jit(f)(1.)
    expected = f(1.)
    self.assertAllClose(y, expected, check_dtypes=False)
    y = jax.jit(f)(4.)
    expected = f(4.)
    self.assertAllClose(y, expected, check_dtypes=False)

  def testSwitchJit(self):
    branches = [lambda x: 3. * x,
                lambda x: jnp.sin(x),
                lambda x: -x]
    def f(x):
      idx = lax.convert_element_type(x // 1, np.int32)
      return lax.switch(idx, branches, x)
    for x in [-1., 0., 1., 2., 3.]:
      y = jax.jit(f)(x)
      expected = f(x)
      self.assertAllClose(y, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondJitDisabled(self, cond):
    def f_ref(x):
      return 3. * x if x < 2 else jnp.sin(x)
    def f(x):
      return cond(x < 2, lambda x: 3. * x, lambda x: jnp.sin(x), x)

    with jax.disable_jit():
      y = f(1.)
      expected = f_ref(1.)
      self.assertAllClose(y, expected, check_dtypes=False)

    with jax.disable_jit():
      y = jax.jit(f)(1.)
      expected = f(1.)
      self.assertAllClose(y, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondWithConsts(self, cond):
    def f(x):
      return cond(x < 2,
                  lambda x: np.array([1., 2.]) * x,
                  lambda x: np.array([3., 4.]) * jnp.sin(x),
                  x)

    def f_ref(x):
      if x < 2:
        return np.array([1., 2.]) * x
      else:
        return np.array([3., 4.]) * np.sin(x)

    y = f(1.)
    expected = f_ref(1.)
    self.assertAllClose(y, expected, check_dtypes=False)
    y = f(4.)
    expected = f_ref(4.)
    self.assertAllClose(y, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondJitWithConsts(self, cond):
    def f(x):
      return cond(x < 2,
                  lambda x: np.array([1., 2.]) * x,
                  lambda x: np.array([3., 4.]) * jnp.sin(x),
                  x)

    y = jax.jit(f)(1.)
    expected = f(1.)
    self.assertAllClose(y, expected, check_dtypes=False)
    y = jax.jit(f)(4.)
    expected = f(4.)
    self.assertAllClose(y, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_{name}", "cond": cond}
      for cond, name in COND_IMPLS)
  def testCondVmapGrad(self, cond):
    # https://github.com/google/jax/issues/2264
    def f_1(x): return x ** 2
    def f_2(x): return x ** 3

    def f(x): return cond(x > 0, f_1, f_2, x)
    def g(x): return jnp.where(x > 0, f_1(x), f_2(x))

    x = jnp.linspace(-1, 1, 20)
    ans = jax.vmap(jax.grad(f))(x)
    expected = jax.vmap(jax.grad(g))(x)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def testIssue1263(self):
    def f(rng, x):
      cond = random.bernoulli(rng)
      return lax.cond(cond, x, lambda x: x, jnp.abs(x) - 1., lambda x: x)

    def body_fn(i, state):
      rng, x = state
      key, subkey = random.split(rng)
      return key, f(subkey, x)

    def g(rng, x):
      return lax.fori_loop(0, 10, body_fn, (rng, x))

    jax.vmap(g)(random.split(random.PRNGKey(0), 3), jnp.ones((3, 4)))

  def testIssue514(self):
    # just check this doesn't crash
    lax.cond(True,
            (0, 0), lambda x: (x[0], 0),
            (1, 1), lambda x: x)

  def testIssue649(self):
    from jax import lax

    def body(x):
      a, b = x
      return (7, b + 1)

    def cond(x):
      a, b = x
      return b < 10

    out = lax.while_loop(cond, body, (33, 4))
    self.assertEqual(out, (7, 10))

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_scan=}_{jit_f=}_impl={scan_name}",
       "jit_scan": jit_scan, "jit_f": jit_f, "scan": scan_impl,
       "impl_name": scan_name}
      for jit_scan in [False, True]
      for jit_f in [False, True]
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def testScanImpl(self, jit_scan, jit_f, scan, impl_name):
    rng = self.rng()

    d = rng.randn(2)
    def f(c, a):
      assert a.shape == (3,)
      assert c.shape == (4,)
      b = jnp.cos(jnp.sum(jnp.sin(a)) + jnp.sum(jnp.cos(c)) + jnp.sum(jnp.tan(d)))
      c = jnp.sin(c * b)
      assert b.shape == ()
      return c, b

    if jit_f:
      f = jax.jit(f)
    if jit_scan:
      scan = jax.jit(scan, static_argnums=(0,))

    as_ = rng.randn(5, 3)
    c = rng.randn(4)

    ans =                scan(f, c, as_)
    expected = scan_reference(f, c, as_)
    rtol = {np.float64: 1.4e-15}
    atol = {np.float64: 8e-15}
    if impl_name == "for":
      rtol[np.float32] = 8e-5
      atol[np.float32] = 3e-5
    self.assertAllClose(
        ans,
        expected,
        check_dtypes=False,
        rtol=rtol,
        atol=atol)

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_scan=}_{jit_f=}_impl={scan_name}",
       "jit_scan": jit_scan, "jit_f": jit_f, "scan": scan_impl}
      for jit_scan in [False, True]
      for jit_f in [False, True]
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def testScanJVP(self, jit_scan, jit_f, scan):
    rng = self.rng()

    d = rng.randn(2)
    def f(c, a):
      assert a.shape == (3,)
      assert c.shape == (4,)
      b = jnp.cos(jnp.sum(jnp.sin(a)) + jnp.sum(jnp.cos(c)) + jnp.sum(jnp.tan(d)))
      c = jnp.sin(c * b)
      assert b.shape == ()
      return c, b

    if jit_f:
      f = jax.jit(f)
    if jit_scan:
      scan = jax.jit(scan, static_argnums=(0,))

    as_ = rng.randn(5, 3)
    c = rng.randn(4)

    ans = jax.jvp(     lambda c, as_:           scan(f, c, as_), (c, as_), (c, as_))
    expected = jax.jvp(lambda c, as_: scan_reference(f, c, as_), (c, as_), (c, as_))
    tol = {np.float64: 1e-12, np.float32: 1e-4}
    self.assertAllClose(ans, expected, check_dtypes=False, rtol=tol, atol=tol)

    jtu.check_grads(partial(scan, f), (c, as_), order=2, modes=["fwd"])

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_scan=}_{jit_f=}_impl={scan_name}",
       "jit_scan": jit_scan, "jit_f": jit_f, "scan": scan_impl}
      for jit_scan in [False, True]
      for jit_f in [False, True]
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def testScanLinearize(self, jit_scan, jit_f, scan):
    rng = self.rng()

    d = rng.randn(2)
    def f(c, a):
      assert a.shape == (3,)
      assert c.shape == (4,)
      b = jnp.cos(jnp.sum(jnp.sin(a)) + jnp.sum(jnp.cos(c)) + jnp.sum(jnp.tan(d)))
      c = jnp.sin(c * b)
      assert b.shape == ()
      return c, b

    if jit_f:
      f = jax.jit(f)
    if jit_scan:
      scan = jax.jit(scan, static_argnums=(0,))

    as_ = rng.randn(5, 3)
    c = rng.randn(4)

    if scan is scan_with_new_checkpoint2:
      rtol = {np.float64: 1e-12, np.float32: 1e-4}
    elif scan is scan_with_for:
      rtol = {np.float64: 1e-12, np.float32: 1e-4}
    else:
      rtol = {np.float64: 1e-14, np.float32: 1e-4}

    ans = jax.linearize(lambda c, as_:                scan(f, c, as_), c, as_)[1](c, as_)
    expected = jax.linearize(lambda c, as_: scan_reference(f, c, as_), c, as_)[1](c, as_)
    self.assertAllClose(ans, expected, check_dtypes=False, rtol=rtol)

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_scan=}_{jit_f=}_impl={scan_name}",
       "jit_scan": jit_scan, "jit_f": jit_f, "scan": scan_impl}
      for jit_scan in [False, True]
      for jit_f in [False, True]
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  @jtu.skip_on_flag("jax_skip_slow_tests", True)
  def testScanGrad(self, jit_scan, jit_f, scan):
    rng = self.rng()

    d = rng.randn(2)
    def f(c, a):
      assert a.shape == (3,)
      assert c.shape == (4,)
      b = jnp.sum(jnp.sin(a)) + jnp.sum(jnp.sin(c)) + jnp.sum(jnp.sin(d))
      c = jnp.sin(c * b)
      assert b.shape == ()
      return c, b

    if jit_f:
      f = jax.jit(f)
    if jit_scan:
      scan = jax.jit(scan, static_argnums=(0,))

    as_ = rng.randn(5, 3)
    c = rng.randn(4)

    ans = jax.grad(lambda c, as_:      list(          scan(f, c, as_))[0].sum())(c, as_)
    expected = jax.grad(lambda c, as_: list(scan_reference(f, c, as_))[0].sum())(c, as_)
    if scan is scan_with_new_checkpoint:
      rtol = {np.float32: 5e-5, np.float64: 1e-13}
      atol = 1e-5
    elif scan is scan_with_for:
      rtol = {np.float32: 2e-5, np.float64: 1e-13}
      atol = {np.float32: 6e-2, np.float64: 1e-13}
    else:
      rtol = {np.float32: 2e-5, np.float64: 1e-13}
      atol = 1e-5
    self.assertAllClose(ans, expected, check_dtypes=False, rtol=rtol, atol=atol)

    rtol = 5e-3 if scan is not scan_with_new_checkpoint2 else 5e-2
    atol = 5e-2 if "tpu" in jtu.device_under_test() else 1e-3
    jtu.check_grads(partial(scan, f), (c, as_), order=2, modes=["rev"],
                    atol=atol, rtol=rtol)

  @jtu.skip_on_devices("tpu")  # TPU lacks precision for this test.
  @jtu.skip_on_flag("jax_skip_slow_tests", True)
  def testScanRnn(self):
    r = self.rng()

    n_in = 4
    n_hid = 2
    n_out = 1
    length = 3

    W_trans = r.randn(n_hid, n_hid + n_in).astype(jnp.float_)
    W_out = r.randn(n_out, n_hid + n_in).astype(jnp.float_)
    params = W_trans, W_out

    inputs = r.randn(length, n_in).astype(jnp.float_)
    targets = r.randn(length, n_out).astype(jnp.float_)

    def step(params, state, input):
      W_trans, W_out = params
      stacked = jnp.concatenate([state, input])
      output = jnp.tanh(jnp.dot(W_out, stacked))
      next_state = jnp.tanh(jnp.dot(W_trans, stacked))
      return next_state, output

    def rnn(params, inputs):
      init_state = jnp.zeros(n_hid)
      _, outputs = lax.scan(partial(step, params), init_state, inputs)
      return outputs

    @jax.jit
    def loss(params, inputs, targets):
      predictions = rnn(params, inputs)
      return jnp.sum((predictions - targets)**2)

    # evaluation doesn't crash
    loss(params, inputs, targets)

    # jvp evaluation doesn't crash
    jax.jvp(lambda params: loss(params, inputs, targets), (params,), (params,))

    # jvp numerical check passes
    jtu.check_grads(loss, (params, inputs, targets), order=2, modes=["fwd"],
                    rtol={np.float32: 2e-2, np.float64: 1e-6})

    # linearize works
    _, expected = jax.jvp(loss, (params, inputs, targets),
                          (params, inputs, targets))
    _, linfun = jax.linearize(loss, params, inputs, targets)
    ans = linfun(params, inputs, targets)
    self.assertAllClose(ans, expected, check_dtypes=False)

    # gradient evaluation doesn't crash
    jax.grad(loss)(params, inputs, targets)

    # gradient check passes
    jtu.check_grads(loss, (params, inputs, targets), order=2, rtol=2e-2)

    # we can vmap to batch things
    batch_size = 7
    batched_inputs = r.randn(batch_size, length, n_in).astype(jnp.float_)
    batched_targets = r.randn(batch_size, length, n_out).astype(jnp.float_)
    batched_loss = jax.vmap(lambda x, y: loss(params, x, y))
    losses = batched_loss(batched_inputs, batched_targets)
    expected = np.stack(list(map(lambda x, y: loss(params, x, y),
                                  batched_inputs, batched_targets)))
    self.assertAllClose(losses, expected, check_dtypes=False, rtol=1e-2)

  @parameterized.named_parameters(
      {"testcase_name": f"_impl={scan_name}", "scan": scan_impl}
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def testIssue711(self, scan):
    # Tests reverse-mode differentiation through a scan for which the scanned
    # function also involves reverse-mode differentiation.
    # See https://github.com/google/jax/issues/711
    def harmonic_bond(conf, params):
      return jnp.sum(conf * params)

    def minimize_structure(test_params):
      energy_fn = partial(harmonic_bond, params=test_params)

      def apply_carry(carry, _):
        i, x = carry
        new_x = x - 0.1 * jax.grad(energy_fn)(x)
        new_carry = (i+1, new_x)
        return new_carry, _

      x0 = jnp.array([1., 2., 3.])
      carry_final, _ = scan(apply_carry, (0, x0), jnp.zeros((75, 0)))
      _, x_final = carry_final
      return x_final

    initial_params = 0.5
    minimize_structure(initial_params)  # doesn't crash

    def loss(test_params):
      x_final = minimize_structure(test_params)
      return jnp.sum(jnp.sin(1.0 - x_final))

    jax.grad(loss)(0.25)  # doesn't crash

  def testIssue744(self):
    Point = collections.namedtuple('Point', ['x', 'y'])
    p0 = Point(x=jnp.array(1), y=jnp.array(2))

    def plus_one(p, iter_idx):
      return Point(p.x+1, p.y+1), iter_idx

    self.assertRaisesRegex(
        ValueError,
        'scan got value with no leading axis to scan over.*',
        lambda: lax.scan(plus_one, p0, list(range(5))))

  def testScanTypeErrors(self):
    """Test typing error messages for scan."""
    a = jnp.arange(5)
    # Body output not a tuple
    with self.assertRaisesRegex(TypeError,
        re.escape("scan body output must be a pair, got ShapedArray(float32[]).")):
      lax.scan(lambda c, x: np.float32(0.), 0, a)
    with  self.assertRaisesRegex(TypeError,
        re.escape("scan carry output and input must have same type structure, "
                  f"got {tree_util.tree_structure((0, 0, 0,))} "
                  f"and {tree_util.tree_structure((1, (2, 3)))}")):
      lax.scan(lambda c, x: ((0, 0, 0), x), (1, (2, 3)), a)
    with self.assertRaisesRegex(TypeError,
        re.escape("scan carry output and input must have same type structure, "
                  f"got {tree_util.tree_structure(a)} and {tree_util.tree_structure(None)}.")):
      lax.scan(lambda c, x: (0, x), None, a)
    with self.assertRaisesWithLiteralMatch(
        TypeError,
        "scan carry output and input must have identical types, got\n"
        "DIFFERENT ShapedArray(int32[]) vs. ShapedArray(float32[])."):
      lax.scan(lambda c, x: (np.int32(0), x), np.float32(1.0), a)
    with self.assertRaisesRegex(TypeError,
        re.escape("scan carry output and input must have same type structure, "
                  f"got {tree_util.tree_structure(a)} and {tree_util.tree_structure((1, 2))}.")):
      lax.scan(lambda c, x: (0, x), (1, 2), a)

  @parameterized.named_parameters(
      {"testcase_name": f"_{scan_name}",
       "scan": scan_impl}
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def testScanHigherOrderDifferentiation(self, scan):
    d = 0.75
    def f(c, a):
      b = jnp.sin(c * jnp.sum(jnp.cos(d * a)))
      c = 0.9 * jnp.cos(d * jnp.sum(jnp.sin(c * a)))
      return c, b

    as_ = jnp.arange(6.).reshape((3, 2))
    c = jnp.array(1, dtype=as_.dtype)

    jtu.check_grads(lambda c, as_: scan(f, c, as_), (c, as_),
                    modes=["rev"], order=2, rtol={np.float32: 6e-3})

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_scan=}_{jit_f=}_{in_axes=}_impl={scan_name}",
       "jit_scan": jit_scan, "jit_f": jit_f, "in_axes": in_axes,
       "scan": scan_impl}
      for jit_scan in [False, True]
      for jit_f in [False, True]
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR
      for in_axes in itertools.product([None, 0, 1], [None, 0, 1, 2])
      if in_axes != (None, None))
  def testScanVmap(self, jit_scan, jit_f, in_axes, scan):
    rng = self.rng()

    d = rng.randn(2)
    def f(c, a):
      assert a.shape == (3,)
      assert c.shape == (4,)
      b = jnp.cos(jnp.sum(jnp.sin(a)) + jnp.sum(jnp.cos(c)) + jnp.sum(jnp.tan(d)))
      c = jnp.sin(c * b)
      assert b.shape == ()
      return c, b

    if jit_f:
      f = jax.jit(f)
    if jit_scan:
      scan = jax.jit(scan, static_argnums=(0,))

    as_shape = [5, 3]
    c_shape = [4]

    c_bdim, as_bdim = in_axes
    if c_bdim is not None:
      c_shape.insert(c_bdim, 7)
    if as_bdim is not None:
      as_shape.insert(as_bdim, 7)

    as_ = rng.randn(*as_shape)
    c = rng.randn(*c_shape)

    ans = jax.vmap(lambda c, as_:                scan(f, c, as_), in_axes)(c, as_)
    expected = jax.vmap(lambda c, as_: scan_reference(f, c, as_), in_axes)(c, as_)
    self.assertAllClose(ans, expected, check_dtypes=False,
                        rtol=1e-5, atol=1e-5)

  def testScanVmapTuples(self):
    def f(c, a):
      a1, a2 = a
      c1, c2 = c
      b = jnp.sum(jnp.cos(a1)) * jnp.sum(jnp.tan(c2 * a2))
      c = c1 * jnp.sin(jnp.sum(a1 * a2)), c2 * jnp.cos(jnp.sum(a1))
      return c, b

    in_axes = (0, (1, 2))

    r = self.rng()
    as_ = (r.randn(3, 7), r.randn(3, 4, 7))
    c = (r.randn(7, 2), r.randn(7))

    expected_c_out, expected_bs = [], []
    for i in range(7):
      c_out, bs = lax.scan(f, (c[0][i], c[1][i]), (as_[0][:,i], as_[1][:,:,i]))
      expected_c_out.append(c_out)
      expected_bs.append(bs)
    expected_c_out_0, expected_c_out_1 = unzip2(expected_c_out)
    expected_c_out = (jnp.stack(expected_c_out_0), jnp.stack(expected_c_out_1))
    expected_bs = jnp.stack(expected_bs)
    expected = expected_c_out, expected_bs

    ans = jax.vmap(lambda c, as_:            lax.scan(f, c, as_), in_axes)(c, as_)
    self.assertAllClose(ans, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"_impl={scan_name}", "scan": scan_impl}
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def testScanVmapFixpoint(self, scan):
    def f(carry_init):
      def scan_body(c, x):
        # The carry is a 4-tuple, the last element starts batched,
        # and the carry is shifted left at each iteration.
        return ((c[1], c[2], c[3], 0.), None)
      return scan(scan_body, (0., 1., 2., carry_init), jnp.zeros(2))
    carry_init = jnp.array([3., 4., 5.])
    carry_out, _ = jax.vmap(f)(carry_init)
    self.assertAllClose(carry_out[3], jnp.array([0., 0., 0.]), check_dtypes=False)
    self.assertAllClose(carry_out[2], jnp.array([0., 0., 0.]), check_dtypes = False)
    # After two shifts, we get the carry_init
    self.assertAllClose(carry_out[1], carry_init, check_dtypes=False)
    self.assertAllClose(carry_out[0], jnp.array([2., 2., 2.]), check_dtypes = False)

  def testIssue757(self):
    # code from https://github.com/google/jax/issues/757
    def fn(a):
      return jnp.cos(a)

    def loop(val):
      iterations = 10

      def apply_carry(x, i):
        return jax.grad(fn, argnums=(0,))(x)[0], i

      final_val, _ = lax.scan(apply_carry, val, jnp.arange(iterations))
      return final_val

    arg = 0.5
    jax.jit(jax.jacfwd(loop, argnums=(0,)))(arg)  # doesn't crash

  def testIssue804(self):
    num_devices = jax.device_count()
    f = partial(lax.scan, lambda c, x: (c + lax.psum(x, "i") , c), 0.)
    jax.pmap(f, axis_name="i")(jnp.ones((num_devices, 4)))  # doesn't crash

  def testMap(self):
    f = lambda x: x ** 2
    xs = jnp.arange(10)
    expected = xs ** 2
    actual = lax.map(f, xs)
    self.assertAllClose(actual, expected)

  def testMapEmpty(self):
    # https://github.com/google/jax/issues/2412
    ans = lax.map(lambda x: x * x, jnp.array([]))
    expected = jnp.array([])
    self.assertAllClose(ans, expected)

  def testCaching(self):
    def cond(x):
      assert python_should_be_executing
      return x < 5

    def body(x):
      assert python_should_be_executing
      return x + 2

    python_should_be_executing = True
    lax.while_loop(cond, body, 0)

    python_should_be_executing = False
    lax.while_loop(cond, body, 0)

  # This second caching test shows a different kind of caching that we haven't
  # implemented (but could!), namely that Python functions that are distinct
  # objects but are equivalent functions trigger cache hits. This kind of
  # caching could be salient when using lambda functions with control flow:
  #
  #   lax.while_loop(lambda x: x < 5, lambda x: x + 2, 0)
  #   lax.while_loop(lambda x: x < 5, lambda x: x + 2, 0)
  #
  # To get a cache hit on the second line we'd need to form a jaxpr and
  # compare them for equality (including the literals on identity). We could
  # implement that by adding a __hash__/__eq__ to core.Jaxpr and
  # core.ClosedJaxpr (see #1221).
  @unittest.skip("not implemented")
  def testCaching2(self):
    def cond(x):
      assert python_should_be_executing
      return x < 5

    def body(x):
      assert python_should_be_executing
      return x + 2

    python_should_be_executing = True
    lax.while_loop(cond, body, 0)

    def cond(x):
      assert python_should_be_executing
      return x < 5

    def body(x):
      assert python_should_be_executing
      return x + 2

    python_should_be_executing = False
    lax.while_loop(cond, body, 0)

  def test_caches_depend_on_axis_env(self):
    # https://github.com/google/jax/issues/9187
    scanned_f = lambda _, __: (lax.psum(1, 'i'), None)
    f = lambda: lax.scan(scanned_f, 0, None, length=1)[0]
    ans = jax.vmap(f, axis_name='i', axis_size=2, out_axes=None)()
    self.assertEqual(ans, 2)
    ans = jax.vmap(f, axis_name='i', axis_size=3, out_axes=None)()
    self.assertEqual(ans, 3)

  def testWhileCondConstant(self):
    out = lax.while_loop(lambda _: False, lambda _: (), ())  # doesn't crash
    self.assertEqual(out, ())

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_loop=}_{jit_body=}_{jit_cond=}",
       "jit_loop": jit_loop, "jit_body": jit_body, "jit_cond": jit_cond}
      for jit_loop in [False, True]
      for jit_body in [False, True]
      for jit_cond in [False, True])
  def testWhileJVP(self, jit_loop=True, jit_body=False, jit_cond=True):
    cond = lambda x: x[0, 2] <= 8
    body = lambda x: x * x

    if jit_cond:
      cond = jax.jit(cond)
    if jit_body:
      body = jax.jit(body)

    loop = partial(lax.while_loop, cond, body)
    if jit_loop:
      loop = jax.jit(loop)

    loop_ref = partial(while_loop_reference, cond, body)

    x = jnp.arange(9.).reshape((3, 3))
    ans = jax.jvp(loop, (x,), (x,))
    expected = jax.jvp(loop_ref, (x,), (x,))
    self.assertAllClose(ans, expected, check_dtypes=False)

    jtu.check_grads(loop, (x,), order=2, modes=["fwd"])

  @parameterized.named_parameters(
      {"testcase_name": f"_{jit_loop=}_{jit_body=}_{jit_cond=}_impl={while_name}",
       "jit_loop": jit_loop, "jit_body": jit_body, "jit_cond": jit_cond,
       "while_loop": while_impl}
      for jit_loop in [False, True]
      for jit_body in [False, True]
      for jit_cond in [False, True]
      for while_impl, while_name in WHILE_LOOP_IMPLS)
  def testWhileLinearize(self, while_loop, jit_loop=True, jit_body=False,
                         jit_cond=True):
    cond = lambda x: x[0, 2] <= 8
    body = lambda x: x * x

    if jit_cond:
      cond = jax.jit(cond)
    if jit_body:
      body = jax.jit(body)

    loop = partial(while_loop, cond, body)
    if jit_loop:
      loop = jax.jit(loop)

    loop_ref = partial(while_loop_reference, cond, body)

    x = jnp.arange(9.).reshape((3, 3))
    y, f_lin = jax.linearize(loop, x)
    ydot = f_lin(x)
    y_expected, ydot_expected = jax.jvp(loop_ref, (x,), (x,))
    self.assertAllClose(y, y_expected, check_dtypes=False)
    self.assertAllClose(ydot, ydot_expected, check_dtypes=False)

  def testWhileJVPViaForiLoop(self):
    f = lambda x: lax.fori_loop(0, 3, lambda i, x: x * 2, x)
    self.assertAllClose(f(2.), 16., check_dtypes=False)
    self.assertAllClose(jax.jvp(f, (2.,), (1.,)), (16., 8.), check_dtypes=False)
    jtu.check_grads(f, (2.,), order=2, modes=["fwd"])

    f = lambda x: lax.fori_loop(0, 3, lambda i, x: x * (i + 1), x)
    self.assertAllClose(f(2.), 12., check_dtypes=False)
    self.assertAllClose(jax.jvp(f, (2.,), (1.,)), (12., 6.), check_dtypes=False)
    jtu.check_grads(f, (2.,), order=2, modes=["fwd"])

  def testWhileJVPWithGrowingNonzeroTangents(self):
    rng = self.rng()

    def cond(state):
      i, x, y, z = state
      return i < 2

    def body(state):
      i, x, y, z = state
      y = x * x
      z = y * y
      return i + 1, x, y, z

    y, z = rng.randn(2), rng.randn(2)
    def loop(loop_impl, x):
      return loop_impl(cond, body, (0, x, y, z))[1]

    loop_lax = partial(loop, lax.while_loop)
    loop_ref = partial(loop, while_loop_reference)

    x = rng.randn(2)
    ans = jax.jvp(loop_lax, (x,), (x,))
    expected = jax.jvp(loop_ref, (x,), (x,))
    self.assertAllClose(ans, expected, check_dtypes=False)

    jtu.check_grads(loop_lax, (x,), order=2, modes=["fwd"])

  def testStaticForiGrad(self):
    func = lambda x: lax.fori_loop(x, x + 2., lambda i, c: c, x)
    jax.grad(func)(1.)  # doesn't crash
    jax.linearize(func, 1.)  # doesn't crash

  @parameterized.named_parameters(
      dict(testcase_name=f"_{loop=}", loop=loop)
      for loop in ["while", "fori_inside_cond", "fori_inside_scan"])
  def testWhileGradError(self, loop: str = "fori_inside_scan"):
    # Raise error for vjp for loops
    if loop == "while":
      func = lambda x: lax.while_loop(lambda i: i < 5., lambda i: i + 1., x)
    elif loop == "fori_inside_jit":
      func = jax.jit(lambda x: lax.fori_loop(x, x + 2., lambda i, c: c, x))
    elif loop == "fori_inside_cond":
      func = lambda x: lax.cond(
          True,
          x, lambda x: lax.fori_loop(x, x + 2., lambda i, c: c, x),
          1., lambda x: x)
    elif loop == "fori_inside_scan":
      func = lambda x: lax.scan(
          lambda c, x: (lax.fori_loop(x, x + 2., lambda i, c1: c1 * c, x), None),
          x, np.ones(2))[0]
    else:
      assert False

    with self.assertRaisesRegex(ValueError, "Reverse-mode differentiation does not work for lax.while_loop"):
      jax.grad(func)(1.)

    jax.linearize(func, 1.)  # Linearization works

  def testIssue1316(self):
    def f(carry, _):
      c, key = carry
      key, _ = random.split(key)
      return (c, key), ()

    key = random.PRNGKey(0)
    jax.grad(lambda c: lax.scan(f, (c, key), np.ones(3))[0][0])(0.)  # doesn't crash

  def testIssue1361(self):
    @jax.jit
    def jit_run_scan(x):
      def fun(carry, _):
        x, _ = carry
        return (2 * x, 0.), None
      (x, _), _ = lax.scan(fun, (x, 0.), jnp.arange(3))
      return x

    jax.grad(lambda x: jit_run_scan(x))(0.)  # doesn't crash

  def testIssue810(self):
    def loss(A):
      def step(x, i):
        return jnp.matmul(A, x), None
      init_x = jnp.zeros(A.shape[-1:])
      last_x, _ = lax.scan(step, init_x, jnp.arange(10))
      return jnp.sum(last_x)

    A = jnp.zeros((3, 3))
    # The second DUS was unnecessarily replicating A across time.
    # We check XLA because _scan_impl is "underneath" the jaxpr language.
    s = str(jax.xla_computation(jax.grad(loss))(A).as_hlo_text())
    assert s.count("dynamic-update-slice(") < 2

  def testScanLengthArg(self):
    def arange(n):
      return lax.scan(lambda c, _: (c + 1, c), 0, None, length=n)[1]

    ans = arange(10)
    expected = np.arange(10)
    self.assertAllClose(ans, expected, check_dtypes=False)

  @ignore_jit_of_pmap_warning()
  def test_while_loop_of_pmap(self):
    # code from jsnoek@

    def body(i, x):
      result = jax.pmap(lambda z: lax.psum(jnp.sin(z), 'i'), axis_name='i')(x)
      return result + x
    f_loop = lambda x: lax.fori_loop(0, 3, body, x)  # noqa: F821
    ans = f_loop(jnp.ones(jax.device_count()))
    del body, f_loop

    def body2(i, x):
      result = jnp.broadcast_to(jnp.sin(x).sum(), x.shape)
      return result + x
    g_loop = lambda x: lax.fori_loop(0, 3, body2, x)
    expected = g_loop(jnp.ones(jax.device_count()))

    self.assertAllClose(ans, expected, check_dtypes=False)

  @ignore_jit_of_pmap_warning()
  def test_while_loop_of_pmap_error_message(self):

    def body(i, x):
      result = jax.pmap(lambda z: lax.psum(jnp.sin(z), 'i'), axis_name='i')(x)
      return result + x
    f_loop = lambda x: lax.fori_loop(0, 3, body, x)

    too_big = 2 * jax.device_count()

    self.assertRaisesRegex(
        ValueError,
        re.escape(
            "compiling computation `scan` that requires {} "
            "replicas, but only {} XLA devices are available."
            .format(too_big, jax.device_count())),
        lambda: f_loop(jnp.ones(too_big)))

  @parameterized.named_parameters(
      {"testcase_name": f"_{scan_name}",
       "scan": scan_impl}
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def test_scan_reverse(self, scan):
    def cumsum(x, reverse):
      return scan(lambda c, x: (c + x, c + x), 0, x, reverse=reverse)[1]

    x = np.array([3, 1, 4, 1, 5, 9])
    self.assertAllClose(np.cumsum(x), cumsum(x, False), check_dtypes=False)
    self.assertAllClose(np.cumsum(x[::-1])[::-1], cumsum(x, True), check_dtypes=False)

    with jax.disable_jit():
      self.assertAllClose(np.cumsum(x), cumsum(x, False), check_dtypes=False)
    with jax.disable_jit():
      self.assertAllClose(np.cumsum(x[::-1])[::-1], cumsum(x, True), check_dtypes=False)

  def test_scan_unroll(self):
    d = jnp.ones(2)
    def f(c, a):
      assert a.shape == (3,)
      assert c.shape == (4,)
      b = jnp.cos(jnp.sum(jnp.sin(a)) + jnp.sum(jnp.cos(c)) + jnp.sum(jnp.tan(d)))
      c = jnp.sin(c * b)
      assert b.shape == ()
      return c, b

    xs = jnp.ones((5, 3))
    c = jnp.ones(4)

    scan = lambda c, xs: lax.scan(f, c, xs)
    scan_unrolled = lambda c, xs: lax.scan(f, c, xs, unroll=2)

    # jaxprs should be the same size
    self.assertEqual(
        len(str(jax.make_jaxpr(scan)(c, xs))),
        len(str(jax.make_jaxpr(scan_unrolled)(c, xs))))

    # but HLO should grow due to unrolling
    self.assertLess(
        len(str(jax.xla_computation(scan)(c, xs).as_hlo_text())),
        len(str(jax.xla_computation(scan_unrolled)(c, xs).as_hlo_text())))

  def test_disable_jit_cond_with_vmap(self):
    # https://github.com/google/jax/issues/3093
    def fn(t):
      return lax.cond(t > 0, 0, lambda x: 0, 0, lambda x: 1)
    fn = jax.vmap(fn)

    with jax.disable_jit():
      _ = fn(jnp.array([1]))  # doesn't crash

  def test_disable_jit_while_loop_with_vmap(self):
    # https://github.com/google/jax/issues/2823
    def trivial_while(y):
      return lax.while_loop(lambda x: x < 10.0, lambda x: x + 1.0, y)
    with jax.disable_jit():
      jax.vmap(trivial_while)(jnp.array([3.0,4.0]))  # doesn't crash

  def test_vmaps_of_while_loop(self):
    # https://github.com/google/jax/issues/3164
    def f(x, n): return lax.fori_loop(0, n, lambda _, x: x + 1, x)
    x, n = jnp.arange(3), jnp.arange(4)
    jax.vmap(jax.vmap(f, (None, 0)), (0, None))(x, n)  # doesn't crash


  @parameterized.named_parameters(
      {"testcase_name": f"_{shape}_{axis=}",
       "shape": shape, "axis": axis}
      for shape in [
        [0], [1], [2], [3], [5], [10], [1000],
        [2, 3], [7, 5], [5, 6, 7]
      ]
      for axis in range(-len(shape), len(shape) - 1))
  def testAssociativeScanUnstructured(self, shape, axis):
    data = np.arange(np.prod(shape)).reshape(shape) + 7
    expected = np.cumsum(data, axis=axis)
    result = lax.associative_scan(operator.add, data, axis=axis)
    self.assertAllClose(result, expected, check_dtypes=False)

  def testAssociativeScanUnstructured1000Reverse(self):
    data = np.arange(1000) + 32
    expected = np.cumsum(data[::-1])[::-1]
    result = lax.associative_scan(operator.add, data, reverse=True)
    self.assertAllClose(result, expected, check_dtypes=False)

  def testAssociativeScanStructured3(self):
    pair = collections.namedtuple('pair', ('first', 'second'))
    data = pair(first=np.array([0., 1., 2.]),
                second=np.array([0., 10., 20.]))

    def fn(a, b):
      return pair(first=a.first + b.first,
                  second=a.second + b.second)

    result = lax.associative_scan(fn, elems=data)
    self.assertAllClose(result.first, np.array([0., 1., 3.]),
                        check_dtypes=False)
    self.assertAllClose(result.second, np.array([0., 10., 30.]),
                        check_dtypes=False)

  def testAssociativeScanOfBools(self):
    x = jnp.array([False, True, True, True, False, True])
    y = lax.associative_scan(lax.bitwise_xor, x)
    self.assertArraysEqual(np.array([False, True, False, True, True, False]), y)

  @parameterized.named_parameters({"testcase_name": f"_{shape}", "shape": shape}
                                  for shape in [2, 43, 100])
  def testAssociativeScanSolvingRegressionTest(self, shape):
    # This test checks that the batching rule doesn't raise for a batch
    # sensitive function (solve).
    ms = np.repeat(np.eye(2).reshape(1, 2, 2), shape, axis=0)
    vs = np.ones((shape, 2))

    @jax.vmap
    def fn(a, b):
      m1, v1 = a
      m2, v2 = b
      return m1 + m2, jsp.linalg.solve(m1, v2) + jsp.linalg.solve(m2, v1)

    _ = lax.associative_scan(fn, elems=(ms, vs))

  def test_scan_typecheck_param(self):
    d = jnp.ones(2)
    def f(c, a):
      b = jnp.cos(jnp.sum(a) + jnp.sum(c) + jnp.sum(d))
      c = jnp.sin(c * b)
      return c, b

    xs = jnp.ones((5, 3))
    c = jnp.ones(4)
    scan_fun = lambda c, xs: lax.scan(f, c, xs)

    def new_jaxpr():
      jaxpr = jax.make_jaxpr(scan_fun)(c, xs).jaxpr
      scan = next(eqn for eqn in jaxpr.eqns if eqn.primitive.name == 'scan')
      return jaxpr, scan

    jaxpr, eqn = new_jaxpr()
    eqn.params['reverse'] = 4
    self.assertRaisesRegex(
        core.JaxprTypeError,
        re.escape('invalid scan param reverse of type int, bool required: 4'),
        lambda: core.check_jaxpr(jaxpr))

    jaxpr, eqn = new_jaxpr()
    eqn.params['num_consts'] = -3
    self.assertRaisesRegex(
        core.JaxprTypeError,
        re.escape('invalid scan param num_consts of type int, '
                  'non-negative int required: -3'),
        lambda: core.check_jaxpr(jaxpr))

  def test_cond_typecheck_param(self):
    def new_jaxpr():
      jaxpr = jax.make_jaxpr(
          lambda x: lax.switch(0, [jnp.sin, jnp.cos], x))(1.).jaxpr
      cond = next(eqn for eqn in jaxpr.eqns if eqn.primitive.name == 'cond')
      return jaxpr, cond

    jaxpr, eqn = new_jaxpr()
    eqn.params['branches'] = (4, 2)
    self.assertRaisesRegex(
        core.JaxprTypeError,
        re.escape('invalid cond param branches of type tuple, '
                  'tuple of ClosedJaxpr required: (4, 2)'),
        lambda: core.check_jaxpr(jaxpr))

    jaxpr, eqn = new_jaxpr()
    eqn.params['linear'] = (4, 2)
    self.assertRaisesRegex(
        core.JaxprTypeError,
        re.escape('invalid cond param linear of type tuple, '
                  'tuple of bool required: (4, 2)'),
        lambda: core.check_jaxpr(jaxpr))

    jaxpr, eqn = new_jaxpr()
    eqn.params['linear'] = 'multi\nline'
    self.assertRaisesRegex(
        core.JaxprTypeError,
        r'invalid cond param linear of type str, '
        r'tuple of bool required:\nmulti\nline',
        lambda: core.check_jaxpr(jaxpr))

  def test_cond_transformation_rule_with_consts(self):
    # https://github.com/google/jax/pull/9731

    @jax.custom_jvp
    def f(x):
      return x

    @f.defjvp
    def f_jvp(primals, tangents):
      (x,), (xdot,) = primals, tangents
      const = np.arange(3, dtype=x.dtype)
      return x * const, xdot * const

    g = lambda x: jax.lax.cond(True, f, lambda x: x, x)
    x = np.arange(3, dtype='float32')
    jax.jvp(g, (x,), (x,))  # doesn't crash

  @parameterized.named_parameters(
      {"testcase_name": f"_dtype={dtype.__name__}", "dtype": dtype}
      for dtype in jtu.dtypes.all_integer)
  def test_scan_init_weak_type(self, dtype):
    def func(carry, x):
      return carry + x, x
    init_weak = 0  # Python scalars are weakly-typed.
    x = jnp.ones(5, dtype=dtype)
    carry, result = lax.scan(func, init_weak, x)
    self.assertEqual(carry, x.sum(dtype=carry.dtype))
    self.assertArraysEqual(result, x)

  @parameterized.named_parameters(
      {"testcase_name": f"_dtype={dtype.__name__}", "dtype": dtype}
      for dtype in jtu.dtypes.all_integer)
  def test_while_loop_init_weak_type(self, dtype):
    # This tests whether lax.while_loop can properly handle weakly-typed
    # initial values.
    def cond_fun(val):
      return val < 2
    def body_fun(val):
      return val + increment
    increment = jnp.array(1, dtype=dtype)
    init_weak = 0  # Python scalars are weakly-typed.
    result = lax.while_loop(cond_fun, body_fun, init_weak)
    self.assertArraysEqual(result, jnp.full_like(increment, 2))

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', None),
          ('new_remat', new_checkpoint),
      ])
  def test_scan_vjp_forwards_extensive_residuals(self, remat):
    # https://github.com/google/jax/issues/4510
    def cumprod(x):
      s = jnp.ones((2, 32), jnp.float32)
      return lax.scan(lambda s, x: (x*s, s), s, x)
    if remat is not None:
      cumprod = remat(cumprod)

    rng = self.rng()
    x = jnp.asarray(rng.randn(32, 2, 32).astype('float32'))
    _, vjp_fun = jax.vjp(cumprod, x)

    # Need to spelunk into vjp_fun. This is fragile, and if it causes problems
    # just skip this test and make an issue for mattjj.
    *_, ext_res = vjp_fun.args[0].args[0]
    self.assertIs(ext_res, x)

    if remat is not None:
      # TODO(mattjj): make the numpy.ndarray test pass w/ remat
      raise unittest.SkipTest("new-remat-of-scan doesn't convert numpy.ndarray")

    x = rng.randn(32, 2, 32).astype('float32')  # numpy.ndarray, not DeviceArray
    _, vjp_fun = jax.vjp(cumprod, x)
    *_, ext_res = vjp_fun.args[0].args[0]
    self.assertIsInstance(ext_res, jax.Array)

  def test_scan_vmap_collectives(self):
    def scan_f(state, x):
      s = lax.psum(state, 'i') * x
      return state, s

    def scan(state, xs):
      return lax.scan(scan_f, state, xs)

    scan_v = jax.vmap(scan, in_axes=0, out_axes=0, axis_name='i')
    self.assertAllClose(
      scan_v(jnp.ones([1]), jnp.arange(5.).reshape((1, 5))),
      (jnp.array([1.]), jnp.array([[0., 1., 2., 3., 4.]])), check_dtypes=False)

  def test_xla_cpu_gpu_loop_cond_bug(self):
    # https://github.com/google/jax/issues/5900
    def deriv(f):
      return lambda x, *args: jax.linearize(lambda x: f(x, *args), x)[1](1.0)

    def _while_loop(cond_fun, body_fun, init_val, max_iter):
      def _iter(val):
        next_val = body_fun(val)
        next_cond = True
        return next_val, next_cond

      def _fun(tup, _):
        val, cond = tup
        return jax.lax.cond(cond, _iter, lambda x: (x, False), val), _

      init = (init_val, cond_fun(init_val))
      return jax.lax.scan(_fun, init, None, length=max_iter)[0][0]

    def my_pow(x, y):
      def body_fun(val):
        return val * x
      def cond_fun(val):
        return True
      return _while_loop(cond_fun, body_fun, 1.0, y)

    self.assertAllClose(deriv(my_pow)(3.0, 1), 1.0, check_dtypes=False)

  def test_unexpected_tracer_error(self):
    with self.assertRaisesRegex(UnexpectedTracerError, "for while_loop"):
      lst = []
      def side_effecting_body(val):
        lst.append(val)
        return val+1
      lax.while_loop(lambda x: x < 2, side_effecting_body, 1)
      lst[0] += 1

    with self.assertRaisesRegex(UnexpectedTracerError, "for scan"):
      lst = []
      def side_effecting_scan(carry, val):
        lst.append(val)
        return carry, val+1
      lax.scan(side_effecting_scan, None, jnp.ones((2, 2)))
      lst[0] += 1

  def test_while_loop_fixed_point_with_nested_named_axes(self):
    def f(x):
      z = x + lax.axis_index('a').astype(x.dtype)
      y = x + lax.axis_index('b').astype(x.dtype)
      def cond(carry):
        i, x = carry
        return x < 5
      def body(carry):
        i, x = carry
        return i + 1, x + lax.psum(y, 'b')
      return lax.while_loop(cond, body, (0, z))[1]
    maps.xmap(f, axis_sizes=dict(a=2, b=10), out_axes=(['a']), in_axes={})(1.)

  def test_while_loop_fixed_point_with_batched_pred_and_consts(self):
    def f(i, x):
      def cond(carry):
        i, x = carry
        return i < 5
      def body(carry):
        i, z = carry
        # Close over const with batch dim = 1
        return i + 1, z + x
      return lax.while_loop(cond, body, (i, jnp.ones(3)))[1]
    jax.vmap(f, in_axes=(0, 1))(jnp.arange(4), jnp.ones((3, 4)))

  def test_cond_ad_batched_unit(self):
    # see issue #9985
    def cond_id(x):
      return lax.cond(x < 0., lambda x: x, lambda x: x, x)
    jax.vmap(jax.jacrev(lambda x: cond_id(cond_id(x))))(jnp.ones(1))

  @parameterized.named_parameters(
      {"testcase_name": "impl={}".format(scan_name), "scan": scan_impl}
      for scan_impl, scan_name in SCAN_IMPLS_WITH_FOR)
  def test_scan_hoisting_consts(self, scan):
    A = jnp.arange(4.).reshape(2, 2)
    B = jnp.arange(4.).reshape(2, 2) + 1.

    def f(x):
      def body(c, _):
        c1, c2, c3 = c
        return (jnp.dot(A, c1), jnp.dot(B, c2), jnp.dot(jnp.sin(B), c3)), None
      init_carry = (x * jnp.ones(2), x * jnp.ones(2), x * jnp.ones(2))
      (c1, c2, c3), _ = scan(body, init_carry, None, length=3)
      return jnp.sum(c1) + jnp.sum(c2) + jnp.sum(c3)

    jax.grad(f)(1.)  # doesn't crash

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