api_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
import collections.abc
from contextlib import contextmanager
import copy
import enum
from functools import partial
import inspect
import importlib
import operator
import os
import platform
import re
import subprocess
import sys
import types
from typing import Callable, List, Optional
import unittest
import warnings
import weakref
import functools
import itertools as it
import operator as op
import gc

from absl import logging
from absl.testing import absltest, parameterized
import numpy as np

import concurrent.futures

import jax
import jax.numpy as jnp
from jax import float0, jit, grad, device_put, jacfwd, jacrev, hessian
from jax._src import core
from jax import lax
from jax import custom_batching
from jax._src import api, dtypes, dispatch, lib, api_util
from jax.errors import UnexpectedTracerError
from jax.interpreters import ad
from jax._src.interpreters import mlir
from jax.interpreters import xla
from jax.interpreters import pxla
from jax.interpreters import batching
from jax.interpreters import partial_eval as pe
from jax.sharding import PartitionSpec as P
from jax._src import array, sharding
from jax.experimental import pjit
from jax._src import config as jax_config
from jax._src import custom_derivatives
from jax import custom_derivatives as custom_derivatives_public
from jax._src import device_array
from jax._src import prng
from jax._src import xla_bridge
from jax._src.lib import xla_client
from jax._src import test_util as jtu
from jax import tree_util
from jax._src import linear_util as lu
import jax._src.util as jax_util
from jax._src.ad_checkpoint import saved_residuals
from jax.ad_checkpoint import checkpoint as new_checkpoint, checkpoint_name

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


python_version = (sys.version_info[0], sys.version_info[1])
numpy_version = jtu.numpy_version()

def _check_instance(self, x):
  if config.jax_array:
    self.assertIsInstance(x, array.ArrayImpl)
  else:
    self.assertIsInstance(x, device_array.DeviceArray)


class CPPJitTest(jtu.BufferDonationTestCase):
  """Shared tests between the Python and the C++ jax,jit implementations.

  Because the Python implementation supports more features, we need to have the
  Python tests that extend the C++ tests (and not the other way around).
  """

  @property
  def use_cpp_jit(self) -> bool:
    return True

  @property
  def jit(self):
    if jax.config.jax_jit_pjit_api_merge:
      return jax.jit
    return functools.partial(api._jit, self.use_cpp_jit)

  def test_jit_repr(self):
    def my_function():
      return
    jitted = jit(my_function)
    if jax.config.jax_jit_pjit_api_merge:
      fun_name = 'PjitFunction'
    else:
      fun_name = 'CompiledFunction'
    self.assertEqual(repr(jitted), f"<{fun_name} of {repr(my_function)}>")

  def test_jit_repr_errors(self):
    class Callable:
      def __call__(self): pass
      def __repr__(self):
        raise ValueError("invalid repr")

    # repr succeeds when underlying function repr fails.
    jitted = jit(Callable())
    if jax.config.jax_jit_pjit_api_merge:
      fun_name = 'PjitFunction'
    else:
      fun_name = 'CompiledFunction'
    self.assertEqual(repr(jitted), f"<{fun_name}>")

    # repr succeeds when object is malformed.
    del jitted.__wrapped__
    self.assertEqual(repr(jitted), f"<{fun_name}>")

  def test_jit_of_noncallable(self):
    self.assertRaisesRegex(TypeError, "Expected a callable value.*",
                           lambda: self.jit(3))

  def test_jit_of_generator(self):

    def gen(x):
      yield x

    self.assertRaisesRegex(TypeError,
                           "Expected a function, got a generator function.*",
                           lambda: self.jit(gen))

  @parameterized.parameters([
      # Integer support
      (1, 2, 3, 4, 5),
      # Numpy array support
      (
          np.asarray(1, np.int32),
          np.asarray(2, np.int32),
          np.asarray(3, np.int32),
          np.asarray(4, np.int32),
          np.asarray(5, np.int32),
      ),
  ])
  def test_jit_static_args(self, one, two, three, four, five):
    side = []

    def f(x, y, z, flag=False, flag2=False):
      del flag2  # unused
      assert flag
      side.append(None)
      return 100 * x + 10 * y + z

    f1 = self.jit(f, static_argnums=(3, 4))
    assert f1(one, two, three, True, False) == 123
    assert len(side) == 1
    assert f1(one, two, three, True, False) == 123
    assert len(side) == 1  # Obvious cache hit.
    assert f1(two, one, three, True, False) == 213
    assert len(side) == 1  # Should cache hit because same signature.
    assert f1(two, one, three, True, True) == 213
    assert len(side) == 2

    side[:] = []
    f2 = self.jit(f, static_argnums=(0, 2, 3, 4))
    assert f2(1, 2, 3, True, False) == 123
    assert len(side) == 1
    assert f2(1, 3, 3, True, False) == 133
    assert len(side) == 1
    assert f2(2, 2, 3, True, False) == 223
    assert len(side) == 2
    assert f2(2, 4, 3, True, False) == 243
    assert len(side) == 2
    assert f2(2, 4, 3, True, True) == 243
    assert len(side) == 3
    assert f2(2, 5, 3, True, True) == 253
    assert len(side) == 3

  def test_static_args_equality(self):
    class A():

      def __hash__(self):
        return 1

      def __eq__(self, other):
        return isinstance(other, A)

    side = []
    def f(x, static_arg):
      del static_arg
      side.append(None)
      return x * 100

    f1 = self.jit(f, static_argnums=(1,))

    self.assertEqual(f1(1, A()), 100)
    self.assertLen(side, 1)
    self.assertEqual(f1(1, A()), 100)
    self.assertLen(side, 1)
    if self.use_cpp_jit:
      f1_cpp = getattr(f1, "_cpp_jitted_f", f1)
      self.assertEqual(f1_cpp._cache_size(), 1)

  @parameterized.parameters([
      (1, 2, 3),
      (
          np.asarray(1, np.int32),
          np.asarray(2, np.int32),
          np.asarray(3, np.int32),
      ),
  ])
  def test_jit_kwargs(self, one, two, three):
    side = []
    # For the CPP jit, we need to clear the cache to prevent cache hits between
    # parameterized tests.
    if hasattr(self.jit, "cache_clear"):
      self.jit.cache_clear()

    def f(x, y, z):
      side.append(None)
      return 100 * x + 10 * y + z.astype(y.dtype)

    f = self.jit(f)
    assert f(one, two, three) == 123
    assert len(side) == 1
    assert f(one, two, three) == 123
    assert len(side) == 1

    assert f(one, two, z=three) == 123
    assert len(side) == 2  # actually recompiles from kwarg
    assert f(one, two, z=three) == 123
    assert len(side) == 2  # but should still cache

    f(one, two, z=np.zeros(3))  # doesn't crash
    if config.x64_enabled:
      # In the above call, three is of a new type (int64), thus it should
      # trigger a new compilation.
      assert len(side) == 3

  def test_jit_device(self):
    device = jax.devices()[-1]
    x = self.jit(lambda x: x, device=device)(3.)
    _check_instance(self, x)
    self.assertEqual(x.device(), device)

  @parameterized.named_parameters(
      ('jit', jax.jit),
      ('pjit', pjit.pjit),
  )
  @jtu.skip_on_devices("cpu")
  def test_jit_default_device(self, module):
    if jax.device_count() == 1:
      raise unittest.SkipTest("Test requires multiple devices")

    system_default_device = jnp.add(1, 1).device()
    test_device = jax.devices()[-1]
    self.assertNotEqual(system_default_device, test_device)

    f = module(lambda x: x + 1)
    self.assertEqual(f(1).device(), system_default_device)

    with jax.default_device(test_device):
      self.assertEqual(jnp.add(1, 1).device(), test_device)
      self.assertEqual(f(1).device(), test_device)

    self.assertEqual(jnp.add(1, 1).device(), system_default_device)
    self.assertEqual(f(1).device(), system_default_device)

    with jax.default_device(test_device):
      # Explicit `device` or `backend` argument to jit overrides default_device
      self.assertEqual(
          module(f, device=system_default_device)(1).device(),
          system_default_device)
      out = module(f, backend="cpu")(1)
      self.assertEqual(out.device().platform, "cpu")

      # Sticky input device overrides default_device
      sticky = jax.device_put(1, system_default_device)
      self.assertEqual(jnp.add(sticky, 1).device(), system_default_device)
      self.assertEqual(f(sticky).device(), system_default_device)

      # Test nested default_devices
      with jax.default_device(system_default_device):
        self.assertEqual(f(1).device(), system_default_device)
      self.assertEqual(f(1).device(), test_device)

    # Test a few more non-default_device calls for good luck
    self.assertEqual(jnp.add(1, 1).device(), system_default_device)
    self.assertEqual(f(sticky).device(), system_default_device)
    self.assertEqual(f(1).device(), system_default_device)

  # TODO(skye): make this work!
  def test_jit_default_platform(self):
    with self.assertRaisesWithLiteralMatch(
        ValueError, "jax.default_device must be passed a Device object "
        "(e.g. `jax.devices('cpu')[0]`), got: 'cpu'"):
      with jax.default_device("cpu"):
        jax.jit(lambda x: x + 1)(1)

  def test_complex_support(self):
    self.assertEqual(self.jit(lambda x: x + 1)(1 + 1j), 2 + 1j)


  @parameterized.parameters("static_argnums", "donate_argnums")
  def test_jit_argnums_overflow_error(self, argnum_type: str):
    def f(a, b, c):
      ...

    def g(a, /, b, *, c):
      ...

    def h(a, *args):
      ...

    def i():
      ...

    # Simplest cases
    self.jit(f, **{argnum_type: (0, 1)})
    self.jit(g, **{argnum_type: (0, 1)})
    self.jit(f, **{argnum_type: (0, 1, -3)})

    # Out of bounds without *args
    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(f, **{argnum_type: (0, 1, 3)})

    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(f, **{argnum_type: (0, 1, -4)})

    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(g, **{argnum_type: (0, 1, 3)})

    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(g, **{argnum_type: (0, 1, -3)})

    # Out of bounds with *args
    self.jit(h, **{argnum_type: (0, 999)})
    self.jit(h, **{argnum_type: (0, -999)})


    # No positional arguments
    self.jit(i, static_argnums=())
    self.jit(i)

  def test_jit_argnames_validation(self):
    def f(a, b, c):
      ...

    def g(a, b, **kwargs):
      ...

    def h(a, /, b, c, *args, **kwargs):
      ...

    # Simplest case
    self.jit(f, static_argnames=("b", "c"))

    # Undefined arg without **kwargs
    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(f, static_argnames=("b", "c", "not_defined"))

    # Undefined arg with **kwargs
    self.jit(g, static_argnames=("a", "b", "not_defined"))

    self.jit(h, static_argnames=("b", "c"))
    self.jit(h, static_argnames=("b", "c", "not_defined"))

    # Positional only
    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(h, static_argnames=("a", "c"))

    # Var positional
    # with self.assertRaises(ValueError):
    with self.assertWarns(SyntaxWarning):
      self.jit(h, static_argnames=("args", "c"))


  def test_jit_with_many_args_works(self):

    @self.jit
    def f(args_list):
      return sum(args_list)

    self.assertEqual(f(list(range(500))), sum(range(500)))

  # Jit and Donate arguments

  def test_jit_donate_argnums_warning_raised(self):
    x = jnp.array([1.0, 2.0], jnp.float32)
    y = jnp.array([1, 2], jnp.int32)
    f = self.jit(lambda x, y: x.sum() + jnp.float32(y.sum()), donate_argnums=(0, 1))
    with warnings.catch_warnings(record=True) as w:
      warnings.simplefilter("always")
      f(x, y)

      self.assertLen(w, 1)
      self.assertTrue(issubclass(w[-1].category, UserWarning))
      self.assertIn(
          "Some donated buffers were not usable:",
          str(w[-1].message))

  def test_jit_donate_argnums_invalidates_input(self):
    # We can't just use `lambda x: x` because JAX simplifies this away to an
    # empty XLA computation.
    move = self.jit(lambda x: x + x - x, donate_argnums=0)
    x = jnp.ones([])
    y = move(x)
    self.assertDeleted(x)
    self.assertEqual(y, 1.)

  def test_jit_donate_argnums_static_argnums(self):
    jit_fun = self.jit(
        lambda a, b, c, d: ((a + b + c), (a + b + d)),
        static_argnums=(0, 1),
        donate_argnums=(2, 3))

    c = jax.device_put(jnp.array([2., 2.]))
    d = jax.device_put(jnp.array([1., 1., 1., 1.]))
    e, f = jit_fun(1, 2, c, d)
    np.testing.assert_allclose(e, jnp.array([5., 5.]))
    np.testing.assert_allclose(f, jnp.array([4., 4., 4., 4.]))
    self.assertDeleted(c)
    self.assertDeleted(d)

  def test_jit_donate_argnums_weak_type(self):
    # input has weak-type, output does not have weak-type
    move = self.jit(lambda x: x.astype(int), donate_argnums=0)
    x = jnp.broadcast_to(2, (3,))
    move(x)
    self.assertDeleted(x)

  def test_jnp_array_copy(self):
    # https://github.com/google/jax/issues/3412

    @partial(self.jit, donate_argnums=(0,))
    def _test(array):
      return array.at[0].set(77)

    x = jnp.asarray([0, 1])
    x_copy = jnp.array(x, copy=True)
    with warnings.catch_warnings():
      warnings.simplefilter("ignore")
      _test(x)  # donation

    # Gives: RuntimeError: Invalid argument: CopyToHostAsync() called on invalid buffer.
    print(x_copy)  # doesn't crash

  def test_jit_global_cache(self):
    def f(x):
      assert python_should_be_executing
      return x

    python_should_be_executing = True
    self.jit(f)(2)
    python_should_be_executing = False
    self.jit(f)(3)

  def test_jit_cache_clear(self):
    @self.jit
    def f(x, y): return x + y

    client = jax.devices()[0].client
    gc.collect()
    num_live_initial = len(client.live_executables())
    f(1, 2).block_until_ready()
    gc.collect()
    num_live = len(client.live_executables())
    self.assertEqual(num_live_initial + 1, num_live)
    f.clear_cache()
    gc.collect()
    num_live = len(client.live_executables())
    self.assertEqual(num_live_initial, num_live)

  def test_jit_shallow_copy(self):
    def f(x):
      return copy.copy(x)
    self.jit(f)(1)

  def test_jit_deep_copy(self):
    def f(x):
      return copy.deepcopy(x)
    self.jit(f)(1)

  def test_disable_jit(self):
    effects = []

    @self.jit
    def f(x):
      effects.append(1)
      return x

    with api.disable_jit():
      f(2)
      f(2)
    assert len(effects) == 2

    f(2)
    f(2)
    assert len(effects) == 3

  def test_static_argnum_on_method(self):

    class A:

      @functools.partial(self.jit, static_argnums=(0,))
      def my_func_jit(self, x):
        return x+2

    A().my_func_jit(3)

  def test_static_argnum_on_static_method_is_not_supported(self):
    with self.assertRaisesRegex(TypeError, "Expected a callable value"):

      class A:

        @functools.partial(self.jit, static_argnums=(0,))
        @classmethod
        def my_classmethod_jit(cls, x):
          return x+2

  def test_staticmethod_is_not_supported(self):
    with self.assertRaisesRegex(TypeError,
                                "staticmethod arguments are not supported"):

      class A:

        @functools.partial(self.jit)
        @staticmethod
        def my_staticmethod_jit(x):
          return x + 2

  def test_concurrent_jit(self):
    @self.jit
    def f(x):
      return x + x - 3.

    xs = [self.rng().randn(i) for i in range(10)]
    with concurrent.futures.ThreadPoolExecutor() as executor:
      futures = [executor.submit(partial(f, x)) for x in xs]
      ys = [f.result() for f in futures]
    for x, y in zip(xs, ys):
      self.assertAllClose(x * 2 - 3., y)

  def test_trivial_computations(self):
    x = jnp.array([1, 2, 3])
    y = self.jit(lambda x: x)(x)
    self.assertEqual(x.unsafe_buffer_pointer(), y.unsafe_buffer_pointer())

    z1, z2 = self.jit(lambda x: (x, x))(x)
    self.assertEqual(z1.unsafe_buffer_pointer(), z2.unsafe_buffer_pointer())

    x1, x2 = jnp.array([1, 2]), jnp.array([2, 3])
    z1, z2, z3 = self.jit(lambda x, y: (y, 1, x))(x1, x2)
    self.assertEqual(z1.unsafe_buffer_pointer(), x2.unsafe_buffer_pointer())
    self.assertEqual(z3.unsafe_buffer_pointer(), x1.unsafe_buffer_pointer())
    self.assertEqual(z2, 1)

  def test_trivial_computations_with_tokens(self):
    @self.jit
    def noop(arr, token):
      return arr, token

    arr = jnp.ones(10)
    token = jax.lax.create_token()

    self.assertEqual(token, noop(arr, token)[1])

  def test_jit_bad_input(self):
    def f(x):
      return x

    with self.assertRaisesRegex(
        TypeError, r".* 'foo' of type <.*'str'> is not a valid JAX type"):
      self.jit(f)("foo")

    # Jax type objects aren't valid data arguments.
    if config.jax_jit_pjit_api_merge:
      err_str = "JAX scalar type .*int32.* cannot be interpreted as a JAX array."
    else:
      err_str = ".* '.*int32.*' of type <.*_ScalarMeta.*> is not a valid JAX type"

    with self.assertRaisesRegex(TypeError, err_str):
      self.jit(f)(jnp.int32)

  def test_jit_masked_array(self):
    x = np.ma.array([1, 2, 3], mask=[True, False, True])
    f = self.jit(lambda x: x)
    with self.assertRaisesRegex(ValueError, "numpy masked arrays are not supported"):
      f(x)

  def test_jit_on_all_devices(self):
    # Verifies we can run the same computation on every device present, even
    # if they are, for example, different models of GPU.
    data = self.rng().rand(1000).astype(np.float32)
    f = self.jit(jnp.negative)
    for device in jax.local_devices():
      x = device_put(data, device=device)
      np.testing.assert_array_equal(-data, f(x))

  def test_jit_nested_donate_ignored(self):
    jit_fun = self.jit(lambda x: self.jit(lambda y: y**2, donate_argnums=0)(x))
    a = jax.device_put(jnp.array(1))

    # NOTE(mattjj): stopped raising error here and instead just ignored
    # with self.assertRaisesRegex(ValueError, "nested.*not supported"):
    #   jit_fun(a)

    jit_fun(a)  # doesn't crash

  def test_jit_reference_dropping(self):
    x = jnp.ones(10)
    f = (lambda x: lambda: x)(x)  # reference to x in f's closure
    g = self.jit(f)
    x = weakref.ref(x)      # no more strong ref to x in this scope
    assert x() is not None  # x is still around
    f()                     # f runs
    g()                     # g runs
    g()                     # g runs a second time
    del f                   # delete the raw callable
    assert x() is not None  # x is still around
    g()                     # g still runs
    del g                   # no more references to x
    assert x() is None      # x is gone

  def test_jit_of_nonweakreferenceable_function(self):
    class CallableWithSlots:
      __slots__ = []
      def __call__(self, x):
        return x + 1

    c = CallableWithSlots()
    with self.assertRaisesRegex(TypeError, "cannot create weak reference.*"):
      weakref.ref(c)
    # Building a jit object does not crash.
    f = self.jit(c)
    with self.assertRaisesRegex(TypeError, "cannot create weak reference.*"):
      # Calling the jit object will fail, but not because of the C++ JIT. The
      # Python-level jit cache requires weak reference support.
      f(3)

  def test_jit_raises_on_first_invocation_on_non_hashable_static_argnum(self):
    if self.jit != api._python_jit:
      raise unittest.SkipTest("this test only applies to _python_jit")
    f = lambda x, y: x + 3
    jitted_f = self.jit(f, static_argnums=(1,))

    msg = ("Non-hashable static arguments are not supported, as this can lead "
           "to unexpected cache-misses. Static argument (index 1) of type "
           "<class 'numpy.ndarray'> for function <lambda> is non-hashable.")
    with self.assertRaisesRegex(ValueError, re.escape(msg)):
      jitted_f(1, np.asarray(1))

  def test_cpp_jit_raises_on_non_hashable_static_argnum(self):
    if not self.use_cpp_jit:
      raise unittest.SkipTest("this test only applies to _cpp_jit")

    f = lambda x, y: x + 3
    jitted_f = self.jit(f, static_argnums=[1])

    jitted_f(1, 1)

    msg = ("Non-hashable static arguments are not supported. An error occurred "
           ".*while trying to hash an object of type "
           "<class 'numpy\\.ndarray'>, 1. The error was:\nTypeError: "
           "unhashable type: 'numpy\\.ndarray'")

    with self.assertRaisesRegex(ValueError, msg):
      jitted_f(1, np.asarray(1))

    class HashableWithoutEq:

      def __hash__(self):
        return 1

      def __eq__(self, other):
        raise NotImplementedError(
            "A Python error is as is, without stack trace")

    with self.assertRaisesRegex(
        ValueError,
        re.escape("static arguments should be comparable using __eq__")):
      jitted_f(1, HashableWithoutEq())
      # __eq__ would only be called if we might have a cache hit. Call the
      # function a second time with exactly the same arguments to make sure that
      # we could.
      jitted_f(1, HashableWithoutEq())

  def test_cpp_jit_raises_other_exceptions_when_hashing_fails(self):
    class A:
      def __hash__(self):
        raise ValueError

    f = jax.jit(lambda x: x + 1, static_argnums=(0,))
    a = A()
    with self.assertRaisesRegex(ValueError, '^$'):  # no extra message
      f(a)

  def test_cpp_jitted_function_returns_PyBuffer(self):
    if not self.use_cpp_jit:
      raise unittest.SkipTest("this test only applies to _cpp_jit")

    jitted_f = self.jit(lambda a: a + 1)
    jitted_f(1)
    if config.jax_array:
      out = jitted_f(2)
      self.assertIsInstance(out.sharding, sharding.SingleDeviceSharding)
      self.assertIsInstance(out, array.ArrayImpl)
    else:
      self.assertIsInstance(jitted_f(2), device_array.Buffer)

  @parameterized.named_parameters(
      ('jit', jax.jit),
      ('pjit', pjit.pjit)
  )
  @jtu.skip_on_devices("cpu")
  def test_explicit_backend(self, module):
    f = lambda x: x + 1
    jitted_f = module(f, backend=jtu.device_under_test())
    jitted_f_cpu = module(f, backend="cpu")

    result = jitted_f(1.)
    result_cpu = jitted_f_cpu(1.)
    self.assertEqual(result.device().platform, jtu.device_under_test())
    self.assertEqual(result_cpu.device().platform, "cpu")

  @parameterized.named_parameters(
      ('jit', jax.jit),
      ('pjit', pjit.pjit)
  )
  @jtu.skip_on_devices("cpu")
  def test_device_to_device_copy_between_backends(self, module):
    # b/186624243
    f = lambda x: x + 1
    jitted_f = module(f, backend=jtu.device_under_test())
    jitted_f_cpu = module(f, backend="cpu")

    x = np.arange(30).reshape(1, 10, 3)
    result = jitted_f(x)
    result_cpu = jitted_f_cpu(result)
    result_2 = jitted_f(result_cpu)
    result_cpu_2 = jitted_f_cpu(result_2)
    self.assertAllClose(result_2, x + 3)
    self.assertAllClose(result_cpu_2, x + 4)

  @jtu.skip_on_devices("cpu")
  def test_mismatched_nested_backends(self):
    @partial(jax.jit, backend=jtu.device_under_test())
    def f(x):
      return jax.jit(lambda x: x + 1, backend="cpu")(x)

    if jax.config.jax_jit_pjit_api_merge:
      msg = 'Received incompatible devices for jitted computation'
    else:
      msg = ("Outer-jit backend specification .* must match explicit inner-jit "
             "backend specification cpu.")

    with self.assertRaisesRegex(ValueError, msg):
      f(1.)

  def test_omnistaging(self):
    # See https://github.com/google/jax/issues/5206

    # TODO(frostig): remove `wrap` once we always enable_custom_prng
    def wrap(arr):
      arr = np.array(arr, dtype=np.uint32)
      if config.jax_enable_custom_prng:
        return prng.random_wrap(arr, impl=jax.random.default_prng_impl())
      else:
        return arr

    key_list = [None]

    def init():
      key, subkey = jax.random.split(key_list[0])
      key_list[0] = key
      return jax.random.normal(subkey, ())

    key_list[0] = wrap([2384771982, 3928867769])
    init()
    self.jit(init)()
    self.assertIsInstance(key_list[0], core.Tracer)
    del key_list[0]

  def test_jit_wrapped_attributes(self):
    def f(x: int) -> int:
      """docstring of f."""
      return x + 1
    f.some_value = 4
    jf = self.jit(f)
    for attr in ["doc", "name", "module", "qualname", "annotations"]:
      self.assertEqual(
        {attr: getattr(f, f"__{attr}__")},
        {attr: getattr(jf, f"__{attr}__")})
    self.assertEqual(f.some_value, jf.some_value)

  def test_jit_python_builtin(self):
    x = jnp.array([1, 2])
    expected = x + 1
    jit_add = self.jit(operator.add, static_argnums=(1,))
    actual = jit_add(x, 1)
    self.assertArraysEqual(expected, actual)

  def test_infer_argnums_and_argnames(self):
    def f(x, y=1):
      pass

    sig = inspect.signature(f)

    argnums, argnames = api_util.infer_argnums_and_argnames(
        sig, argnums=None, argnames=None)
    assert argnums == ()
    assert argnames == ()

    argnums, argnames = api_util.infer_argnums_and_argnames(
        sig, argnums=0, argnames=None)
    assert argnums == (0,)
    assert argnames == ('x',)

    argnums, argnames = api_util.infer_argnums_and_argnames(
        sig, argnums=None, argnames='y')
    assert argnums == (1,)
    assert argnames == ('y',)

    argnums, argnames = api_util.infer_argnums_and_argnames(
        sig, argnums=0, argnames='y')  # no validation
    assert argnums == (0,)
    assert argnames == ('y',)

    def g(x, y, *args):
      pass

    sig = inspect.signature(g)

    argnums, argnames = api_util.infer_argnums_and_argnames(
        sig, argnums=(1, 2), argnames=None)
    assert argnums == (1, 2)
    assert argnames == ('y',)

    def h(x, y, **kwargs):
      pass

    sig = inspect.signature(h)

    argnums, argnames = api_util.infer_argnums_and_argnames(
        sig, argnums=None, argnames=('foo', 'bar'))
    assert argnums == ()
    assert argnames == ('foo', 'bar')

  def test_jit_with_static_argnames(self):

    def f(x):
      assert x == 'foo'
      return 1

    f_nums = self.jit(f, static_argnums=0)
    assert f_nums('foo') == 1
    assert f_nums(x='foo') == 1

    f_names = self.jit(f, static_argnames='x')
    assert f_names('foo') == 1
    assert f_names(x='foo') == 1

  def test_new_static_argnum_on_keyword_arguments(self):
    f = self.jit(lambda x: x, static_argnums=0)
    y = f(x=4)
    assert y == 4

  def test_new_static_argnum_with_default_arguments(self):
    f = self.jit(lambda x=4: x, static_argnums=0)
    y = f()
    assert y == 4

  def test_jit_with_mismatched_static_argnames(self):
    x_is_tracer, y_is_tracer = False, False
    def f(x, y):
      assert isinstance(x, core.Tracer) == x_is_tracer
      assert isinstance(y, core.Tracer) == y_is_tracer
      return 1

    # If both static_argnums and static_argnames are provided, they are allowed
    # to disagree and `jit` will respect the user's choices.
    f_nums = self.jit(f, static_argnums=1, static_argnames=())
    x_is_tracer, y_is_tracer = True, False
    assert f_nums(2, 'foo') == 1
    x_is_tracer, y_is_tracer = True, True
    assert f_nums(1, y=2) == 1

    f_names = self.jit(f, static_argnums=(), static_argnames='y')
    x_is_tracer, y_is_tracer = True, True
    assert f_names(2, 3) == 1
    x_is_tracer, y_is_tracer = True, False
    assert f_names(1, y='foo') == 1

    f_mixed = self.jit(f, static_argnums=(1,), static_argnames='x')
    x_is_tracer, y_is_tracer = True, False
    assert f_mixed(2, 'foo') == 1
    x_is_tracer, y_is_tracer = True, True
    assert f_mixed(1, y=3) == 1
    x_is_tracer, y_is_tracer = False, True
    assert f_mixed(x='foo', y=3) == 1

  # TODO(zhangqiaorjc): Test pruning constants after DCE pass prunes primitive
  # applications.
  @parameterized.parameters(2, 3, 4)
  def test_jit_with_pruned_args(self, num_args):
    def f(*args):
      used = np.array(2)
      return args[1] + used
    f_pruned = self.jit(f)
    args = range(num_args)
    with jtu.count_device_put() as count:
      np.testing.assert_allclose(f_pruned(*args), 3)
    self.assertEqual(count[0], 1)

  def testBuffersAreFreedPromptly(self):
    # Regression test for a bug where garbage collection was delayed too long
    # for NumPy buffers that are aliased zero-copy by the runtime.
    @self.jit
    def f(x):
      return x + 1

    refs = []
    x = np.ones((10000,), np.float32)
    for step in range(1000):
      x = f(x)
      refs.append(weakref.ref(x))
      x = np.asarray(x)

    # We expect most of the input buffers to have been garbage
    # collected in parallel with the execution. We can't call
    # block_until_ready() here because it would force a garbage collection.
    live_refs = len([ref for ref in refs if ref() is not None])
    self.assertLessEqual(live_refs, 100)

  def test_jit_lower_compile(self):
    def f(x):
      return jnp.sqrt(x ** 2) + 1.

    f_jit = self.jit(f)
    lowered = f_jit.lower(1.)
    compiled = lowered.compile()
    self.assertAllClose(compiled(1.), 2.)
    self.assertEqual(lowered.in_avals, compiled.in_avals)
    expected_dtype = np.float64 if config.x64_enabled else np.float32
    for obj in [lowered, compiled]:
      self.assertEqual(
          obj.in_avals,
          ((core.ShapedArray([], expected_dtype, weak_type=True),), {}))
      self.assertEqual(obj.in_tree, jax.tree_util.tree_flatten(((0,), {}))[1])

  def test_jit_lower_duck_typing(self):
    f_jit = self.jit(lambda x: 2 * x)
    f_low = f_jit.lower(jax.ShapeDtypeStruct((), 'float32'))  # doesn't crash
    f_exe = f_low.compile()
    self.assertAllClose(f_exe(jnp.float32(1.)), jnp.float32(2.))

  def test_jit_lower_compile_in_tree_mismatch(self):
    def f(x):
      return jnp.sqrt(x ** 2) + 1.

    f_jit = self.jit(f)
    f_low = f_jit.lower(1.)
    f_exe = f_low.compile()
    self.assertRaisesRegex(
        TypeError, "function compiled for .*, called with .*",
        lambda: f_exe([1.]))

  def test_jit_lower_compile_trivial(self):
    def f(x): return x
    out = self.jit(f).lower(1.).compile()(4.)
    self.assertAllClose(out, 4.)

  def test_jit_lower_compile_sharding_computation(self):
    if not config.jax_array:
      self.skipTest('with_sharding_constraint only works with the Array path '
                    'in jit.')
    s = sharding.SingleDeviceSharding(jax.devices()[0])
    def f(x): return pjit.with_sharding_constraint(x, s)
    out = self.jit(f).lower(1.).compile()(4.)
    self.assertAllClose(out, 4.)

  def test_jit_lower_compile_trivial_in_tree_mismatch(self):
    def f(x): return x
    f_exe = self.jit(f).lower(1.).compile()
    self.assertRaisesRegex(
        TypeError, "function compiled for .*, called with .*",
        lambda: f_exe([4.]))

  def test_jit_lower_compile_arg_type_mismatch(self):
    def f(x):
      return jnp.sqrt(x ** 2) + 1.

    x = jnp.array(1, dtype=int)
    x_f32 = x.astype(jnp.float32)
    x_i32 = x.astype(jnp.int32)
    f_exe = self.jit(f).lower(x_f32).compile()
    self.assertRaisesRegex(
        TypeError,
        "Computation was compiled for different input types and called with "
        "different types. One of the mismatches is:\n"
        "Compiled with:\n.*float32.*\n"
        "called with:\n.*int32.*",
        lambda: f_exe(x_i32))

  def test_jit_lower_compile_multi_arg(self):
    def f(*args):
      x, *_ = args
      return jnp.sqrt(x ** 2) + 1.
    f_exe = self.jit(f).lower(1., 1.).compile()
    self.assertAllClose(f_exe(1., 1.), 2.)

  def test_jit_lower_compile_trivial_multi_arg(self):
    def f(*args):
      x, *_ = args
      return x
    f_exe = self.jit(f).lower(1., 1.).compile()
    self.assertAllClose(f_exe(1., 1.), 1.)

  def test_jit_lower_donate_argnums_available(self):
    def f(*args):
      x, *_ = args
      return x + 4.
    f_low = self.jit(f, donate_argnums=(0,)).lower(1., 1.)
    f_com = f_low.compile()
    f_low.donate_argnums == f_com.donate_argnums == (0,)

  def test_jit_lower_compile_vmap(self):
    f = self.jit(lambda x: x + 4).lower(1.).compile()
    def err():
      return jax.vmap(lambda x: f(x) + 2)(jnp.ones(3))
    self.assertRaisesRegex(
        TypeError,
        "Cannot apply JAX transformations to a function lowered and compiled "
        "for a particular signature. Detected .*BatchTracer",
        err)

  def test_jit_lower_as_text(self):
    f = self.jit(lambda x: x + 4).lower(1.)
    self.assertIsInstance(f.as_text(), str)
    self.assertIsInstance(f.as_text(dialect='hlo'), str)
    self.assertIsInstance(f.as_text(dialect='mhlo'), str)
    self.assertIsInstance(f.as_text(dialect="stablehlo"), str)

  def test_jit_lower_compiler_ir(self):
    f = self.jit(lambda x: x + 4).lower(1.)
    self.assertIsNotNone(f.compiler_ir())
    self.assertIsNotNone(f.compiler_ir(dialect='hlo'))
    self.assertIsNotNone(f.compiler_ir(dialect='mhlo'))
    self.assertIsNotNone(f.compiler_ir(dialect="stablehlo"))

  def test_jit_lower_trivial_compiler_ir(self):
    f = self.jit(lambda x: x).lower(1.)
    self.assertIsNotNone(f.compiler_ir())
    self.assertIsNotNone(f.compiler_ir(dialect='hlo'))
    self.assertIsNotNone(f.compiler_ir(dialect='mhlo'))
    self.assertIsNotNone(f.compiler_ir(dialect="stablehlo"))

  def test_jit_lower_no_prunning(self):
    compiled = self.jit(lambda x, y: x + y).lower(1., 2.).compile()
    self.assertEqual(compiled._executable._kept_var_idx, {0, 1})
    self.assertLen(compiled._executable.in_avals, 2)

    compiled = self.jit(lambda x, y: x).lower(1., 2.).compile()
    self.assertEqual(compiled._executable._kept_var_idx, {0})
    self.assertLen(compiled._executable.in_avals, 1)

    compiled = self.jit(lambda x, y: x, keep_unused=True).lower(
        1., 2.).compile()
    self.assertEqual(compiled._executable._kept_var_idx, {0, 1})
    self.assertLen(compiled._executable.in_avals, 2)
    # Also works with jax.jit
    jitted_f = self.jit(lambda x, y: x, keep_unused=True)
    with jtu.count_device_put() as count:
      _ = jitted_f(1, 2)
    self.assertEqual(count[0], 1)

  @jtu.ignore_warning(category=DeprecationWarning)
  def test_jit_lower_compile_compiler_ir(self):
    # TODO(frostig): remove (deprecated)
    f = self.jit(lambda x: x + 4).lower(1.).compile()
    self.assertIsNotNone(f.compiler_ir())

  @jtu.ignore_warning(category=DeprecationWarning)
  def test_jit_lower_trivial_compile_compiler_ir(self):
    # TODO(frostig): remove (deprecated)
    f = self.jit(lambda x: x).lower(1.).compile()
    self.assertIsNotNone(f.compiler_ir())

  def test_jit_lower_compile_as_text(self):
    f = self.jit(lambda x: x).lower(1.).compile()
    g = self.jit(lambda x: x + 4).lower(1.).compile()
    self.assertIsInstance(f.as_text(), (str, type(None)))
    self.assertIsInstance(g.as_text(), (str, type(None)))

  @jtu.skip_on_xla_cpu_mlir
  def test_jit_lower_cost_analysis(self):
    # TODO(b/261771737): add support for uncompiled cost analysis in C API.
    if "PJRT C API" in xla_bridge.get_backend().platform_version:
      raise unittest.SkipTest("C API does not support uncompiled cost analysis")
    f = self.jit(lambda x: x).lower(1.)
    g = self.jit(lambda x: x + 4).lower(1.)
    f.cost_analysis()  # doesn't raise
    g.cost_analysis()  # doesn't raise

  @jtu.skip_on_xla_cpu_mlir
  def test_jit_lower_compile_cost_analysis(self):
    f = self.jit(lambda x: x).lower(1.).compile()
    g = self.jit(lambda x: x + 4).lower(1.).compile()
    f.cost_analysis()  # doesn't raise
    g.cost_analysis()  # doesn't raise

  @jtu.skip_on_xla_cpu_mlir
  def test_jit_lower_compile_memory_analysis(self):
    f = self.jit(lambda x: x).lower(1.).compile()
    g = self.jit(lambda x: x + 4).lower(1.).compile()
    f.memory_analysis()  # doesn't raise
    g.memory_analysis()  # doesn't raise

  def test_jit_lower_compile_executable(self):
    f = self.jit(lambda x: x).lower(1.).compile()
    g = self.jit(lambda x: x + 4).lower(1.).compile()
    self.assertIsNotNone(f.runtime_executable())
    self.assertIsNotNone(g.runtime_executable())

  def test_jit_enum_as_dict_keys_fails(self):
    class E(enum.Enum):
      A = 0
      B = 1

    @self.jit
    def f(d) -> float:
      return d[E.A]

    with self.assertRaisesRegex(TypeError, "'<' not supported.*"):
      f({E.A: 1.0, E.B: 2.0})

  def test_jit_static_argnums_requires_type_equality(self):
    # See: https://github.com/google/jax/pull/9311
    @partial(self.jit, static_argnums=(0,))
    def f(k):
      assert python_should_be_executing
      return k

    # Values of 'x' that compare as equal but have different types do not lead
    # to cache hits.
    for x in [1, True, 1.0]:
      python_should_be_executing = True
      self.assertEqual(x, f(x))
      python_should_be_executing = False
      self.assertEqual(x, f(x))

  def test_hitting_cpp_path(self):
    # pjit has a similar test in pjit_test.py
    if not self.use_cpp_jit or jax.config.jax_jit_pjit_api_merge:
      raise unittest.SkipTest("this test only applies to _cpp_jit")

    jit_impl = dispatch._xla_call_impl_lazy
    count = 0

    def jit_impl_and_count(*args, **kwargs):
      nonlocal count
      count += 1
      return jit_impl(*args, **kwargs)

    f = self.jit(lambda x: x + 1)

    try:
      dispatch._xla_call_impl_lazy = jit_impl_and_count
      f(0)
      self.assertEqual(count, 1)
      f(0)
      self.assertEqual(count, 1)
      f(1)
      self.assertEqual(count, 1)
      f(2)
      self.assertEqual(count, 1)
    finally:
      dispatch._xla_call_impl_lazy = jit_impl

  def test_caches_depend_on_axis_env(self):
    # https://github.com/google/jax/issues/9187
    f = lambda: lax.psum(1, "i")
    g = jax.jit(f)
    expected = jax.vmap(f, axis_name="i", axis_size=2, out_axes=None)()
    ans = jax.vmap(g, axis_name="i", axis_size=2, out_axes=None)()
    self.assertEqual(ans, expected)

    # This second call to g could erroneously get a cache hit.
    expected = jax.vmap(f, axis_name="i", axis_size=3, out_axes=None)()
    ans = jax.vmap(g, axis_name="i", axis_size=3, out_axes=None)()
    self.assertEqual(ans, expected)

  def test_caches_dont_depend_on_unnamed_axis_env(self):
    # https://github.com/google/jax/issues/9187
    f = jax.jit(lambda: jnp.sin(1))
    expected = f()
    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      ans = jax.vmap(f, axis_size=2, out_axes=None)()
    self.assertEqual(count[0], 0)  # no compiles
    self.assertArraysAllClose(ans, expected, check_dtypes=True)

  def test_cache_key_defaults(self):
    # https://github.com/google/jax/discussions/11875
    if not self.use_cpp_jit:
      raise unittest.SkipTest("this test only applies to _cpp_jit")
    f = self.jit(lambda x: (x ** 2).sum())
    self.assertEqual(f._cache_size(), 0)
    x = jnp.arange(5.0)
    for _ in range(3):
      _ = f(x)
    self.assertEqual(f._cache_size(), 1)


class PythonJitTest(CPPJitTest):

  @property
  def use_cpp_jit(self) -> bool:
    return False

class APITest(jtu.JaxTestCase):

  def test_grad_item(self):
    def f(x):
      if x.astype(bool).item():
        return x ** 2
      else:
        return x
    out = jax.grad(f)(2.0)
    self.assertEqual(out, 4)

  def test_jit_item(self):
    def f(x):
      return x.item()
    x = jnp.array(1.0)
    self.assertEqual(f(x), x)
    with self.assertRaisesRegex(core.ConcretizationTypeError, "Abstract tracer value"):
      jax.jit(f)(x)


  @parameterized.named_parameters(
      ('grad', jax.grad),
      ('jacfwd', jax.jacfwd),
      ('jacref', jax.jacrev),
  )
  def test_grad_wrap(self, transform):
    # Ensures that transforms wrap transformed functions with the correct signature.

    @partial(jit, static_argnames=['flag'])
    @transform
    def my_function(x, flag):
      return x if flag else jnp.zeros_like(x)

    self.assertEqual(my_function(1.0, False), 0.0)
    self.assertEqual(my_function(1.0, True), 1.0)

  def test_grad_bad_input(self):
    def f(x):
      return x

    self.assertRaisesRegex(
        TypeError, ".* 'foo' of type <.*'str'> is not a valid JAX type",
        lambda: grad(f)("foo"))

  def test_grad_argnums(self):
    def f(x, y, z, flag=False):
      assert flag
      return 1.0 * x + 2.0 * y + 3.0 * z

    assert grad(f)(1.0, 1.0, 1.0, flag=True) == 1.0
    assert grad(f, argnums=1)(1.0, 1.0, 1.0, flag=True) == 2.0
    assert grad(f, argnums=(2, 0))(1.0, 1.0, 1.0, flag=True) == (3.0, 1.0)

  def test_value_and_grad_argnums(self):
    def f(x, y, z, flag=False):
      assert flag
      return 1.0 * x + 2.0 * y + 3.0 * z

    y = f(1.0, 1.0, 1.0, flag=True)
    assert api.value_and_grad(f)(1.0, 1.0, 1.0, flag=True) == (y, 1.0)
    assert api.value_and_grad(f, argnums=1)(1.0, 1.0, 1.0, flag=True) == (y, 2.0)
    assert api.value_and_grad(f, argnums=(2, 0))(1.0, 1.0, 1.0, flag=True) == (y, (3.0, 1.0))

  def test_grad_of_jit(self):
    side = []

    @jit
    def f(x):
      side.append(None)
      return x * x

    assert grad(f)(1.0) == 2.0
    assert len(side) == 1
    assert grad(f)(2.0) == 4.0
    assert len(side) == 1

  def test_jit_of_grad(self):
    side = []

    @jit
    def f(x):
      side.append(None)
      return x * x

    g = jit(grad(f))
    assert g(1.0) == 2.0
    assert len(side) == 1
    assert g(2.0) == 4.0
    assert len(side) == 1

  @parameterized.named_parameters(
      {"testcase_name": f"_{transform.__name__}", "transform": transform}
      for transform in [grad, jacfwd, jacrev])
  def test_ad_weak_types(self, transform):
    out = transform(lambda x: x)(1.0)
    self.assertTrue(dtypes.is_weakly_typed(out))

  def test_bad_input(self):
    def f(x):
      return x

    self.assertRaisesRegex(
      TypeError, ".* 'foo' of type <.*'str'> is not a valid JAX type",
      lambda: grad(f)("foo"))

    self.assertRaisesRegex(
      TypeError, ".* 'foo' of type <.*'str'> is not a valid JAX type",
      lambda: jit(f)("foo"))

  def test_grad_tuple_output(self):
    jtu.check_raises(lambda: grad(lambda x: (x,x))(1.0), TypeError,
                     "Gradient only defined for scalar-output functions. ")

  def test_grad_unit_output(self):
    jtu.check_raises(lambda: grad(lambda x: ())(np.zeros(3)), TypeError,
                     "Gradient only defined for scalar-output functions. ")

  def test_grad_nonscalar_output(self):
    jtu.check_raises(lambda: grad(lambda x: x)(np.zeros(3)), TypeError,
                     "Gradient only defined for scalar-output functions. ")

  def test_unwrapped_numpy(self):
    def f(x):
      return np.exp(x)

    with self.assertRaisesRegex(Exception, "The numpy.ndarray conversion .*"):
      grad(f)(np.zeros(3))

  def test_binop_mismatch(self):
    def f(x, y):
      return x + y

    jtu.check_raises(
        lambda: f(jnp.zeros(3), jnp.zeros(4)),
        TypeError,
        "add got incompatible shapes for broadcasting: (3,), (4,).")

    jtu.check_raises(
        lambda: grad(f)(np.zeros(3), np.zeros(4)),
        TypeError,
        "add got incompatible shapes for broadcasting: (3,), (4,).")

  def test_dot_mismatch(self):
    def f(x, y):
      return jnp.dot(x, y)

    self.assertRaisesRegex(
      TypeError, "Incompatible shapes for dot: got \\(3L?,\\) and \\(4L?,\\).",
      lambda: grad(f)(np.zeros(3), np.zeros(4)))

  def test_abstract_error_message(self):
    for castfun in [float, complex, int]:
      def f(x):
        return castfun(x)

      self.assertRaisesRegex(
          TypeError,
          f"[Tt]ry using `x.astype\\({castfun.__name__}\\)`",
          lambda: jit(f)(1.0))

  def test_switch_value_jit(self):
    def f(x):
      y = x > 0
      if y:
        return x
      else:
        return -x

    assert grad(f)(1.0) == 1.0
    assert grad(f)(-1.0) == -1.0
    with self.assertRaisesRegex(core.ConcretizationTypeError,
                                "Abstract tracer value"):
      jit(f)(1)

  def test_list_index_err(self):
    L = [1, 2, 3]
    def f(n):
      return L[n]

    assert jit(f, static_argnums=(0,))(0) == L[0]
    self.assertRaisesRegex(
        TypeError,
        r"The __index__\(\) method was called on the JAX Tracer object.*",
        lambda: jit(f)(0))

  def test_range_err(self):
    def f(x, n):
      for i in range(n):
        x = x + i
      return x

    assert jit(f, static_argnums=(1,))(0, 5) == 10
    self.assertRaisesRegex(
        TypeError,
        r"The __index__\(\) method was called on the JAX Tracer object.*",
        lambda: jit(f)(0, 5))

  def test_cast_int(self):
    f = lambda x: int(x)
    self.assertRaisesRegex(
        TypeError,
        "('(?:JaxprTracer|DynamicJaxprTracer)' object cannot be interpreted as an integer"
        "|Abstract tracer value encountered where concrete value is expected.*)", lambda: jit(f)(0))

  def test_casts(self):
    for castfun in [hex, oct]:
      f = lambda x: castfun(x)
      self.assertRaisesRegex(
          TypeError,
          r"The __index__\(\) method was called on the JAX Tracer object.*", lambda: jit(f)(0))

  def test_unimplemented_interpreter_rules(self):
    foo_p = core.Primitive('foo')
    def foo(x):
      return foo_p.bind(x)

    jtu.check_raises(lambda: foo(1.0), NotImplementedError,
                     "Evaluation rule for 'foo' not implemented")

    jtu.check_raises(lambda: jit(foo)(1.0), NotImplementedError,
                     "Abstract evaluation for 'foo' not implemented")

    jtu.check_raises(lambda: grad(foo)(1.0), NotImplementedError,
                     "Differentiation rule for 'foo' not implemented")

    foo_p.def_abstract_eval(lambda x: x)

    jtu.check_raises_regexp(lambda: jit(foo)(1.0), NotImplementedError,
                     ".* rule for primitive 'foo' not found.*")

    foo_p.def_impl(lambda x: x)
    ad.defjvp(foo_p, lambda g, x: foo(g))

    jtu.check_raises(lambda: grad(foo)(1.0), NotImplementedError,
                     "Transpose rule (for reverse-mode differentiation) for 'foo' not implemented")

  def test_is_subclass(self):
    self.assertTrue(issubclass(device_array.DeviceArray, jax.Array))
    self.assertTrue(issubclass(device_array.Buffer, jax.Array))
    self.assertTrue(issubclass(pxla.ShardedDeviceArray, jax.Array))
    self.assertTrue(issubclass(pxla._ShardedDeviceArray, jax.Array))
    self.assertFalse(issubclass(np.ndarray, jax.Array))
    self.assertFalse(issubclass(device_array.DeviceArray, np.ndarray))
    self.assertFalse(issubclass(device_array.Buffer, np.ndarray))
    self.assertFalse(issubclass(pxla.ShardedDeviceArray, np.ndarray))
    self.assertFalse(issubclass(pxla._ShardedDeviceArray, np.ndarray))

  def test_is_instance(self):
    def f(x):
      self.assertIsInstance(x, jax.Array)
      self.assertNotIsInstance(x, np.ndarray)
      return x + 2
    jit(f)(3)
    jax.vmap(f)(np.arange(3))

  def test_device_put_and_get(self):
    x = np.arange(12.).reshape((3, 4)).astype("float32")
    dx = api.device_put(x)
    _check_instance(self, dx)
    self.assertIsInstance(dx, jax.Array)
    self.assertNotIsInstance(dx, np.ndarray)
    x2 = api.device_get(dx)
    self.assertNotIsInstance(x2, jax.Array)
    self.assertIsInstance(x2, np.ndarray)
    assert np.all(x == x2)

    y = [x, (2 * x, 3 * x)]
    dy = api.device_put(y)
    y2 = api.device_get(dy)
    self.assertIsInstance(y2, list)
    self.assertIsInstance(y2[0], np.ndarray)
    assert np.all(y2[0] == x)
    self.assertIsInstance(y2[1], tuple)
    self.assertIsInstance(y2[1][0], np.ndarray)
    assert np.all(y2[1][0] == 2 * x)
    self.assertIsInstance(y2[1][1], np.ndarray)
    assert np.all(y2[1][1] == 3 * x)

  @jax_config.jax_array(True)
  def test_device_put_sharding(self):
    mesh = jax.sharding.Mesh(jax.devices(), ('x',))
    s = sharding.NamedSharding(mesh, P('x'))
    x = jnp.arange(len(jax.devices()))

    y = jax.device_put(x, s)
    self.assertEqual(y.sharding, s)
    self.assertArraysAllClose(y, x)

    # this might hit a special fast path
    z = jax.device_put(y, s)
    self.assertEqual(z.sharding, s)
    self.assertArraysAllClose(z, x)
    self.assertIs(z, y)  # no copy

    w = jax.device_put(z)
    self.assertIs(w, z)

    u = jax.device_put(y, jax.devices()[0])
    self.assertArraysAllClose(u, y)
    self.assertEqual(u.device(), jax.devices()[0])

  @jax_config.jax_array(True)
  def test_device_put_sharding_tree(self):
    if jax.device_count() < 2:
      raise unittest.SkipTest("Test requires >= 2 devices")

    mesh = jax.sharding.Mesh(np.array(jax.devices()[:2]).reshape((2, 1)),
                             ("x", "y"))
    s1 = sharding.NamedSharding(mesh, P("x"))
    s2 = sharding.NamedSharding(mesh, P("y"))
    s3 = sharding.NamedSharding(mesh, P("x", "y"))

    x = jnp.arange(2)
    y = jnp.arange(2) + 10
    z = (jnp.arange(2) + 100).reshape((2, 1))

    out = jax.device_put((x, (y, z)), device=(s1, (s2, s3)))
    self.assertEqual(out[0].sharding, s1)
    self.assertEqual(out[1][0].sharding, s2)
    self.assertEqual(out[1][1].sharding, s3)

    self.assertArraysAllClose(out[0], x)
    self.assertArraysAllClose(out[1][0], y)
    self.assertArraysAllClose(out[1][1], z)

  @jax_config.jax_array(True)
  def test_device_put_sharding_tree_prefix(self):
    if jax.device_count() < 2:
      raise unittest.SkipTest("Test requires >= 2 devices")

    mesh = jax.sharding.Mesh(np.array(jax.devices()[:2]).reshape((2, 1)), ("x", "y"))
    s1 = sharding.NamedSharding(mesh, P("x"))
    s2 = sharding.NamedSharding(mesh, P("y"))

    x = jnp.arange(2)
    y = jnp.arange(2) + 10
    z = jnp.arange(2) + 100

    out = jax.device_put((x, (y, z)), device=(s1, s2))
    self.assertEqual(out[0].sharding, s1)
    self.assertEqual(out[1][0].sharding, s2)
    self.assertEqual(out[1][1].sharding, s2)

    self.assertArraysAllClose(out[0], x)
    self.assertArraysAllClose(out[1][0], y)
    self.assertArraysAllClose(out[1][1], z)

  @jax_config.jax_array(True)
  def test_device_put_sharding_mismatched_tree_same_leaf_count(self):
    if jax.device_count() < 2:
      raise unittest.SkipTest("Test requires >= 2 devices")

    mesh = jax.sharding.Mesh(np.array(jax.devices()[:2]).reshape((2, 1)), ("x", "y"))
    s1 = sharding.NamedSharding(mesh, P("x"))
    s2 = sharding.NamedSharding(mesh, P("y"))

    x = jnp.arange(2)
    y = jnp.arange(2) + 10
    z = jnp.arange(2) + 100

    with self.assertRaisesRegex(
        ValueError,
        "device_put device specification must be a tree prefix of the "
        r"corresponding value, got specification \(\(NamedSharding\(.*\), "
        r"NamedSharding\(.*\)\), NamedSharding\(.*\)\) for value tree "
        r"PyTreeDef\(\(\*, \(\*, \*\)\)\)."
    ):
      jax.device_put((x, (y, z)), device=((s1, s2), s2))

  @jax_config.jax_array(True)
  def test_device_put_sharding_mismatched_tree_different_leaf_count(self):
    if jax.device_count() < 2:
      raise unittest.SkipTest("Test requires >= 2 devices")

    mesh = jax.sharding.Mesh(np.array(jax.devices()[:2]).reshape((2, 1)), ("x", "y"))
    s1 = sharding.NamedSharding(mesh, P("x"))
    s2 = sharding.NamedSharding(mesh, P("y"))

    x = jnp.arange(2)
    y = jnp.arange(2) + 10
    z = jnp.arange(2) + 100

    with self.assertRaisesRegex(
        ValueError,
        "device_put device specification must be a tree prefix of the "
        r"corresponding value, got specification \(NamedSharding\(.*\), "
        r"NamedSharding\(.*\)\) for value tree PyTreeDef\(\(\*, \*, \*\)\)."
    ):
      jax.device_put((x, y, z), device=(s1, s2))


  def test_device_get_scalar(self):
    x = np.arange(12.).reshape((3, 4)).astype("float32")
    x = api.device_put(x)
    _check_instance(self, x)
    self.assertIsInstance(x.sharding, jax.sharding.SingleDeviceSharding)
    for s in x.addressable_shards:
      self.assertArraysEqual(s.data, x)
      self.assertEqual(s.replica_id, 0)
      self.assertEqual(s.index, (slice(None), slice(None)))
    y = [x, 2]
    y2 = api.device_get(y)
    self.assertIsInstance(y2, list)
    self.assertIsInstance(y2[0], np.ndarray)
    assert np.all(y2[0] == x)
    self.assertIsInstance(y2[1], int)
    self.assertEqual(y2[1], 2)

  @parameterized.parameters([(3,)], [(2, 0)])
  def test_device_put_across_devices(self, shape):
    if len(jax.local_devices()) < 2:
      raise unittest.SkipTest("this test requires multiple devices")
    d1, d2 = jax.local_devices()[:2]
    data = self.rng().randn(*shape).astype(np.float32)
    x = api.device_put(data, device=d1)
    if config.jax_array:
      self.assertEqual(x.device(), d1)
    else:
      self.assertEqual(x.device_buffer.device(), d1)

    y = api.device_put(x, device=d2)
    if config.jax_array:
      self.assertEqual(y.device(), d2)
    else:
      self.assertEqual(y.device_buffer.device(), d2)

    np.testing.assert_array_equal(data, np.array(y))
    # Make sure these don't crash
    api.device_put(x)
    api.device_put(y)

  @jtu.skip_on_devices("cpu")
  def test_device_put_across_platforms(self):
    default_device = jax.devices()[0]
    cpu_device = jax.devices("cpu")[0]

    np_arr = np.array([1,2,3])
    scalar = 1
    device_arr = jnp.array([1,2,3])
    if config.jax_array:
      assert device_arr.device() is default_device
    else:
      assert device_arr.device_buffer.device() is default_device

    for val in [np_arr, device_arr, scalar]:
      x = api.device_put(val, device=cpu_device)
      if config.jax_array:
        self.assertEqual(x.device(), cpu_device)
      else:
        self.assertEqual(x.device_buffer.device(), cpu_device)

  @jax.default_matmul_precision("float32")
  def test_jacobian(self):
    R = self.rng().randn
    A = R(4, 3)
    x = R(3)

    f = lambda x: jnp.dot(A, x)
    assert np.allclose(jacfwd(f)(x), A)
    assert np.allclose(jacrev(f)(x), A)

    f = lambda x: jnp.tanh(jnp.dot(A, x))
    assert np.allclose(jacfwd(f)(x), jacrev(f)(x))

  @jax.default_matmul_precision("float32")
  def test_hessian(self):
    R = self.rng().randn
    A = R(4, 4)
    x = R(4)

    f = lambda x: jnp.dot(x, jnp.dot(A, x))
    assert np.allclose(hessian(f)(x), A + A.T)

  @jax.default_matmul_precision("float32")
  def test_hessian_holomorphic(self):
    R = self.rng().randn
    A = R(4, 4)
    x = R(4).astype('complex64') * (1 + 2j)

    f = lambda x: jnp.dot(x, jnp.dot(A.astype(x.dtype), x))
    assert np.allclose(hessian(f, holomorphic=True)(x), A + A.T)

  @jax.default_matmul_precision("float32")
  def test_hessian_aux(self):
    R = self.rng().randn
    A = R(4, 4)
    x = R(4)

    f = lambda x: (jnp.dot(x, jnp.dot(A, x)), x)
    h, aux = hessian(f, has_aux=True)(x)
    assert np.allclose(h, A + A.T)
    assert np.allclose(aux, x)

  def test_std_basis(self):
    basis = api._std_basis(jnp.zeros(3))
    assert getattr(basis, "shape", None) == (3, 3)
    assert np.allclose(basis, np.eye(3))

    basis = api._std_basis(jnp.zeros((3, 3)))
    assert getattr(basis, "shape", None) == (9, 3, 3)
    assert np.allclose(basis, np.eye(9).reshape(9, 3, 3))

    basis = api._std_basis([0., (jnp.zeros(3), jnp.zeros((3, 4)))])
    assert isinstance(basis, list) and len(basis) == 2
    assert getattr(basis[0], "shape", None) == (16,)
    assert isinstance(basis[1], tuple) and len(basis[1]) == 2
    assert getattr(basis[1][0], "shape", None) == (16, 3)
    assert getattr(basis[1][1], "shape", None) == (16, 3, 4)

  @jtu.skip_on_devices("tpu")
  def test_jacobian_on_pytrees(self):
    for jacfun in [jacfwd, jacrev]:
      ans = jacfun(lambda x, y: (x, y))(0., 1.)
      expected = (1., 0.)
      self.assertAllClose(ans, expected, check_dtypes=False)

      ans = jacfun(lambda x, y: (x, y), 1)(0., 1.)
      expected = (0., 1.)
      self.assertAllClose(ans, expected, check_dtypes=False)

      ans = jacfun(lambda x, y: (x, y), (0, 1))(0., 1.)
      expected = ((1., 0.),
                  (0., 1.),)
      self.assertAllClose(ans, expected, check_dtypes=False)

      ans = jacfun(lambda x: x[:2])((1., 2., 3.))
      expected = ((1., 0., 0.),
                  (0., 1., 0.))
      self.assertAllClose(ans, expected, check_dtypes=False)

      R = self.rng().randn
      x = jnp.array(R(2))
      y = jnp.array(R(3))
      ans = jacfun(lambda x, y: {'x': x, 'xy': jnp.outer(x, y)})(x, y)
      expected = {'x': np.eye(2),
                  'xy': np.kron(np.eye(2), y[:, None]).reshape(2, 3, 2)}
      self.assertAllClose(ans, expected, check_dtypes=False)

  @jtu.skip_on_devices("tpu")
  def test_hessian_on_pytrees(self):
    ans = hessian(lambda x: jnp.array(x)**2)((1., 2.))
    expected = ((np.array([2., 0.]), np.array([0., 0.])),
                (np.array([0., 0.]), np.array([0., 2.])))
    self.assertAllClose(ans, expected, check_dtypes=False)

  @jtu.skip_on_devices("tpu")
  def test_issue1372(self):
    def quad(x):
      return jnp.dot(x, x)

    def f(x, u):
      return quad(x) + quad(u)

    x, u = jnp.ones(5), jnp.ones(2)

    rev = jacrev
    fwd = jacfwd

    # Diagonal entries
    self.assertEqual(rev(rev(f, 0), 0)(x, u).shape, (5, 5))
    self.assertEqual(rev(fwd(f, 0), 0)(x, u).shape, (5, 5))
    self.assertEqual(fwd(rev(f, 0), 0)(x, u).shape, (5, 5))
    self.assertEqual(fwd(fwd(f, 0), 0)(x, u).shape, (5, 5))
    self.assertEqual(rev(rev(f, 1), 1)(x, u).shape, (2, 2))
    self.assertEqual(rev(fwd(f, 1), 1)(x, u).shape, (2, 2))
    self.assertEqual(fwd(rev(f, 1), 1)(x, u).shape, (2, 2))
    self.assertEqual(fwd(fwd(f, 1), 1)(x, u).shape, (2, 2))

    # Off-diagonal entries by reverse-mode on the outside
    self.assertEqual(rev(rev(f, 1), 0)(x, u).shape, (2, 5))
    self.assertEqual(rev(fwd(f, 1), 0)(x, u).shape, (2, 5))
    self.assertEqual(rev(rev(f, 0), 1)(x, u).shape, (5, 2))
    self.assertEqual(rev(fwd(f, 0), 1)(x, u).shape, (5, 2))

    # Off-diagonal entries by forward-mode on the outside
    self.assertEqual(fwd(rev(f, 1), 0)(x, u).shape, (2, 5))
    self.assertEqual(fwd(fwd(f, 1), 0)(x, u).shape, (2, 5))
    self.assertEqual(fwd(rev(f, 0), 1)(x, u).shape, (5, 2))
    self.assertEqual(fwd(fwd(f, 0), 1)(x, u).shape, (5, 2))


  def test_large_device_constant(self):
    ans = jit(lambda x: 2 * x)(jnp.ones(int(2e6)))  # doesn't crash
    self.assertAllClose(ans, np.ones(int(2e6)) * 2., check_dtypes=False)

  def test_grad_and_aux_basic(self):
    g, aux = grad(lambda x: (x**3, [x**2]), has_aux=True)(3.)
    self.assertAllClose(g, grad(lambda x: x**3)(3.))
    self.assertAllClose(aux, [9.], check_dtypes=False)

  def test_grad_and_aux_error(self):
    with self.assertRaisesRegex(TypeError, "two-element tuple"):
      grad(lambda x: (1, 2, 3), has_aux=True)(1.)

    with self.assertRaisesRegex(TypeError, "two-element tuple"):
      grad(lambda x: x, has_aux=True)(1.)

    with self.assertRaisesRegex(TypeError, "two-element tuple"):
      grad(lambda x: (x,), has_aux=True)(1.)

  def test_grad_and_aux_nested(self):
    def f(x):
      g, aux = grad(lambda x: (x**3, [x**3]), has_aux=True)(x)
      return aux[0]

    f2 = lambda x: x**3

    self.assertEqual(grad(f)(4.), grad(f2)(4.))
    self.assertEqual(jit(grad(f))(4.), grad(f2)(4.))
    self.assertEqual(jit(grad(jit(f)))(4.), grad(f2)(4.))

    def f(x):
      g, aux = grad(lambda x: (x**3, [x**3]), has_aux=True)(x)
      return aux[0] * jnp.sin(x)

    f2 = lambda x: x**3 * jnp.sin(x)

    self.assertEqual(grad(f)(4.), grad(f2)(4.))
    self.assertEqual(jit(grad(f))(4.), grad(f2)(4.))
    self.assertEqual(jit(grad(jit(f)))(4.), grad(f2)(4.))

  def test_grad_and_aux_constant(self):
    g, aux = grad(lambda x: (x**3, [4.]), has_aux=True)(4.)
    self.assertEqual(g, grad(lambda x: x**3)(4.))
    self.assertEqual(aux, [4.])

    g, aux = grad(lambda x: (x**3, [x**2, 4.]), has_aux=True)(4.)
    self.assertEqual(g, grad(lambda x: x**3)(4.))
    self.assertEqual(aux, [4.**2, 4.])

  def test_grad_and_aux_no_tracers(self):
    # see https://github.com/google/jax/issues/1950
    def f(x):
      aux = dict(identity=x, p1=x+1)
      return x ** 2, aux

    _, aux = jax.grad(f, has_aux=True)(3.)
    self.assertIsInstance(aux, dict)
    for val in aux.values():
      self.assertNotIsInstance(val, core.Tracer)

  def test_jacfwd_and_aux_basic(self):
    jac, aux = jacfwd(lambda x: (x**3, [x**2]), has_aux=True)(3.)
    self.assertAllClose(jac, jacfwd(lambda x: x**3)(3.))
    self.assertAllClose(aux, [9.], check_dtypes=False)

  def test_jacrev_and_aux_basic(self):
    jac, aux = jacrev(lambda x: (x**3, [x**2]), has_aux=True)(3.)
    self.assertAllClose(jac, jacrev(lambda x: x**3)(3.))
    self.assertAllClose(aux, [9.], check_dtypes=False)

  def test_jacfwd_and_aux_nested(self):
    def f(x):
      jac, aux = jacfwd(lambda x: (x**3, [x**3]), has_aux=True)(x)
      return aux[0]

    f2 = lambda x: x**3

    self.assertEqual(jacfwd(f)(4.), jacfwd(f2)(4.))
    self.assertEqual(jit(jacfwd(f))(4.), jacfwd(f2)(4.))
    self.assertEqual(jit(jacfwd(jit(f)))(4.), jacfwd(f2)(4.))

    def f(x):
      jac, aux = jacfwd(lambda x: (x**3, [x**3]), has_aux=True)(x)
      return aux[0] * jnp.sin(x)

    f2 = lambda x: x**3 * jnp.sin(x)

    self.assertEqual(jacfwd(f)(4.), jacfwd(f2)(4.))
    self.assertEqual(jit(jacfwd(f))(4.), jacfwd(f2)(4.))
    self.assertEqual(jit(jacfwd(jit(f)))(4.), jacfwd(f2)(4.))

  def test_jacrev_and_aux_nested(self):
    def f(x):
      jac, aux = jacrev(lambda x: (x**3, [x**3]), has_aux=True)(x)
      return aux[0]

    f2 = lambda x: x**3

    self.assertEqual(jacrev(f)(4.), jacrev(f2)(4.))
    self.assertEqual(jit(jacrev(f))(4.), jacrev(f2)(4.))
    self.assertEqual(jit(jacrev(jit(f)))(4.), jacrev(f2)(4.))

    def f(x):
      jac, aux = jacrev(lambda x: (x**3, [x**3]), has_aux=True)(x)
      return aux[0] * jnp.sin(x)

    f2 = lambda x: x**3 * jnp.sin(x)

    self.assertEqual(jacrev(f)(4.), jacrev(f2)(4.))
    self.assertEqual(jit(jacrev(f))(4.), jacrev(f2)(4.))
    self.assertEqual(jit(jacrev(jit(f)))(4.), jacrev(f2)(4.))

  def test_jvp_and_aux_basic(self):
    fun = lambda x: (x**3, [x**2])
    primals, tangents, aux = api.jvp(fun, (3.,), (4.,), has_aux=True)
    expected_primals, expected_tangents = api.jvp(lambda x: x**3, (3.,), (4.,))
    self.assertAllClose(primals, expected_primals, check_dtypes=True)
    self.assertAllClose(tangents, expected_tangents, check_dtypes=True)
    self.assertEqual(aux, [3.**2])

  def test_jvp_mismatched_arguments(self):
    self.assertRaisesRegex(
      TypeError,
      ("primal and tangent arguments to jax.jvp must have the same tree "
       "structure"),
      lambda: api.jvp(lambda x, y: x * y, (np.float32(2),), ()))
    # If primals and tangents must both be tuples or both lists
    self.assertRaisesRegex(
      TypeError,
      ("primal and tangent arguments to jax.jvp must have the same tree "
       "structure"),
      lambda: api.jvp(lambda x, y: x * y, (np.float32(2),), [np.float32(2)]))
    self.assertRaisesRegex(
      TypeError,
      "primal and tangent arguments to jax.jvp do not match.",
      lambda: api.jvp(lambda x: -x, (np.float16(2),), (np.float32(4),)))
    # If primals and tangents are not of the same shape then raise error
    fun = lambda x: x+1
    with self.assertRaisesRegex(
      ValueError, "jvp called with different primal and tangent shapes"):
      api.jvp(fun, (jnp.array([1.,2.,3.]),), (jnp.array([1.,2.,3.,4.]),))
    with self.assertRaisesRegex(
      ValueError, "jvp called with different primal and tangent shapes"):
      api.jvp(fun, (jnp.float32(10.),), (jnp.array([1.,2.,3.], dtype=jnp.float32),))
    with self.assertRaisesRegex(
      ValueError, "jvp called with different primal and tangent shapes"):
      api.jvp(fun, (jnp.array([1.,2.,3.], dtype=jnp.float32),), (jnp.float32(20.),))
    with self.assertRaisesRegex(
      ValueError, "jvp called with different primal and tangent shapes"):
      api.jvp(fun, (jnp.array([1.,2.,3.]),), (20.,))

  def test_jvp_non_tuple_arguments(self):
    def f(x, y): return x + y
    self.assertRaisesRegex(
        TypeError,
        "primal and tangent arguments to jax.jvp must be tuples or lists; found float and tuple.",
        lambda: api.jvp(f, 0., (1.,)))
    self.assertRaisesRegex(
        TypeError,
        "primal and tangent arguments to jax.jvp must be tuples or lists; found tuple and ndarray.",
        lambda: api.jvp(f, (0.,), np.array([1., 2.])))

  def test_vjp_mismatched_arguments(self):
    _, pullback = api.vjp(lambda x, y: x * y, np.float32(3), np.float32(4))
    self.assertRaisesRegex(
      TypeError,
      "Tree structure of cotangent input.*does not match",
      lambda: pullback((np.float32(7), np.float32(100))))
    self.assertRaisesRegex(
      TypeError,
      "Type of cotangent input to vjp pullback.*is not the expected tangent type",
      lambda: pullback(np.float16(42)))

  def test_vjp_bad_cotangent_shape(self):
    x = np.ones((2, 5), dtype=np.float32)
    y = np.ones((5, 3), dtype=np.float32)
    def f_jax(x, y):
      return jnp.matmul(x, y)
    res, pullback = jax.vjp(f_jax, x, y)
    with self.assertRaisesRegex(
        ValueError,
        "Shape of cotangent input to vjp pullback function .* must be the same as the shape of corresponding primal input .*"):
      pullback(np.ones((2, 4), dtype=np.float32))

  def test_jvp_jit_cached(self):
    """Bug in caching in presence of JVP and JIT."""

    def func(x):
      def inner(y):
        return y * x

      # Must have two calls to the inner jit (the second one hits the cache)
      res1 = api.jit(inner)(4.)
      res2 = api.jit(inner)(5.)
      return res1 + res2

    self.assertAllClose((45., 9.), api.jvp(func, (5.,), (1.,)))

  def test_linear_transpose_abstract(self):
    x = types.SimpleNamespace(shape=(3,), dtype=np.dtype(np.float32))
    y = jnp.arange(3, dtype=np.float32)
    transpose_fun = api.linear_transpose(lambda x: 2 * x, x)
    z, = transpose_fun(y)
    self.assertArraysEqual(2 * y, z, check_dtypes=True)

  def test_linear_transpose_integer(self):
    f = lambda x: 2 * x
    transpose = api.linear_transpose(f, 1)
    actual, = transpose(3)
    expected = 6
    self.assertEqual(actual, expected)

  def test_linear_transpose_error(self):
    with self.assertRaisesRegex(
        TypeError, "linear_transpose only supports"):
      api.linear_transpose(lambda x: 2. * x, 1)
    transpose_fun = api.linear_transpose(lambda x: [x, x], 1.0)
    with self.assertRaisesRegex(TypeError, "cotangent tree does not match"):
      transpose_fun(1.0)

    transpose_fun = api.linear_transpose(lambda x: jnp.stack([x, x]), 1.0)
    with self.assertRaisesRegex(TypeError, "cotangent type does not match"):
      transpose_fun(1.0)

    transpose_fun = api.linear_transpose(lambda x: 1j * x, 1.0)
    with self.assertRaisesRegex(TypeError, "cotangent type does not match"):
      transpose_fun(1.0)

    transpose_fun = api.linear_transpose(lambda x: x, 1.0)
    with self.assertRaisesRegex(TypeError, "cotangent type does not match"):
      transpose_fun(1j)

  def test_linear_transpose_complex(self):
    f = lambda x: (1 + 2j) * x
    transpose = api.linear_transpose(f, 1j)
    actual, = transpose(3 + 4j)
    expected = -5 + 10j
    self.assertEqual(actual, expected)

  def test_linear_transpose_zeros(self):
    f = lambda x: x[0]
    transpose = api.linear_transpose(f, [1., 2.])
    actual, = transpose(3.)
    expected = [3., 0.]
    self.assertEqual(actual, expected)

  def test_complex_grad_raises_error(self):
    self.assertRaises(TypeError, lambda: grad(lambda x: jnp.sin(x))(1 + 2j))

  def test_holomorphic_grad(self):
    out = grad(lambda x: jnp.sin(x), holomorphic=True)(1 + 2j)
    expected = 2.0327230070196656 - 3.0518977991518j
    self.assertAllClose(out, expected, check_dtypes=False)

  def test_nonholomorphic_grad(self):
    zs = 0.5j * np.arange(5) + np.arange(5)

    def f(z):
      return jnp.sum(jnp.cos(jnp.abs(z)))

    ans = grad(f)(zs)
    expected = np.array([ 0.          + 0.j,
                          -0.80430663 + 0.40215331j,
                          -0.70368982 + 0.35184491j,
                           0.1886467  - 0.09432335j,
                           0.86873727 - 0.43436864j])
    self.assertAllClose(ans, expected, check_dtypes=False,
                        atol=jtu.default_gradient_tolerance,
                        rtol=jtu.default_gradient_tolerance)

  def test_complex_output_jacrev_raises_error(self):
    self.assertRaises(TypeError, lambda: jacrev(lambda x: jnp.sin(x))(1 + 2j))

  def test_nonholomorphic_jacrev(self):
    # code based on https://github.com/google/jax/issues/603
    zs = 0.5j * np.arange(5) + np.arange(5)

    def f(z):
      return jnp.cos(jnp.linalg.norm(2 * z))

    ans = jacrev(f)(zs)
    expected = grad(f)(zs)
    self.assertAllClose(ans, expected)

  @jax.numpy_dtype_promotion('standard')  # Test explicitly exercises implicit dtype promotion.
  def test_heterogeneous_jacfwd(self):
    # See https://github.com/google/jax/issues/7157
    # See https://github.com/google/jax/issues/7780
    x = np.array([2.0], dtype=np.float16)
    y = np.array([3.0], dtype=np.float32)
    a = (x, y)

    def f(tup):
      jtu._check_dtypes_match(tup, a)
      x, y = tup
      return x, y, x + y

    actual = jacfwd(f)(a)
    desired = ((np.array(1., dtype=np.float16), np.array(0., dtype=np.float16)),
               (np.array(0., dtype=np.float32), np.array(1., dtype=np.float32)),
               (np.array(1., dtype=np.float32), np.array(1., dtype=np.float32)))
    jtu._check_dtypes_match(actual, desired)
    jtu.check_eq(actual, desired)

  @jax.numpy_dtype_promotion('standard')  # Test explicitly exercises implicit dtype promotion.
  def test_heterogeneous_jacrev(self):
    # See https://github.com/google/jax/issues/7157
    # See https://github.com/google/jax/issues/7780
    x = np.array([2.0], dtype=np.float16)
    y = np.array([3.0], dtype=np.float32)
    a = (x, y)

    def f(tup):
      jtu._check_dtypes_match(tup, a)
      x, y = tup
      return x, y, x + y

    actual = jacrev(f)(a)
    desired = ((np.array(1., dtype=np.float16), np.array(0., dtype=np.float32)),
               (np.array(0., dtype=np.float16), np.array(1., dtype=np.float32)),
               (np.array(1., dtype=np.float16), np.array(1., dtype=np.float32)))
    jtu._check_dtypes_match(actual, desired)
    jtu.check_eq(actual, desired)

  def test_heterogeneous_grad(self):
    # See https://github.com/google/jax/issues/7157
    x = np.array(1.0+1j)
    y = np.array(2.0)
    a = (x, y)

    def f(tup):
      jtu._check_dtypes_match(tup, a)
      x, y = tup
      return jnp.square(jnp.abs(x)) + y

    actual = grad(f)(a)
    desired = (np.array(2 - 2j), np.array(1.))
    jtu._check_dtypes_match(actual, desired)
    jtu.check_eq(actual, desired)

  def test_complex_input_jacfwd_raises_error(self):
    self.assertRaises(TypeError, lambda: jacfwd(lambda x: jnp.sin(x))(1 + 2j))

  def test_legacy_devicearray_repr(self):
    dx = device_put(3.)
    str(dx.item())  # doesn't crash

  def test_devicearray_repr(self):
    x = device_put(jnp.zeros(3))
    _check_instance(self, x)
    repr(x)  # doesn't crash

    x = device_put(jnp.full(3, 1 + 1j))
    _check_instance(self, x)
    repr(x)  # doesn't crash

  def test_devicearray_delete(self):
    x = device_put(1.)
    x.delete()
    if config.jax_array:
      msg = "Array has been deleted."
    else:
      msg = "DeviceArray has been deleted."
    self.assertRaisesRegex(RuntimeError, msg, lambda: repr(x))

  def test_devicearray_block_until_ready(self):
    x = device_put(1.)
    y = x.block_until_ready()
    # Tests mostly that block_until_ready() does not produce an error.
    self.assertTrue(y is x)

  def test_block_until_ready_function(self):
    # Just tests that we don't error...
    pytree = (device_put(1.), np.ones(3))
    pytree = jax.block_until_ready(pytree)
    self.assertAllClose(pytree[0], jnp.array(1.), check_dtypes=False)
    self.assertAllClose(pytree[1], np.ones(3), check_dtypes=False)

  def test_devicearray_weakref_friendly(self):
    x = device_put(1.)
    y = weakref.ref(x)
    self.assertEqual(y(), 1.)
    del x
    self.assertIsNone(y())

  def test_namedtuple_transparency(self):
    # See https://github.com/google/jax/issues/446
    Point = collections.namedtuple("Point", ["x", "y"])

    def f(pt):
      return jnp.sqrt(pt.x ** 2 + pt.y ** 2)

    pt = Point(1., 2.)

    f(pt)  # doesn't crash
    g = api.grad(f)(pt)
    self.assertIsInstance(g, Point)

    f_jit = api.jit(f)
    self.assertAllClose(f(pt), f_jit(pt), check_dtypes=False)

  def test_namedtuple_subclass_transparency(self):
    # See https://github.com/google/jax/issues/806
    Point = collections.namedtuple("Point", ["x", "y"])

    class ZeroPoint(Point):
      def is_zero(self):
        return (self.x == 0) and (self.y == 0)

    pt = ZeroPoint(0., 0.)

    def f(pt):
      return 0. if pt.is_zero() else jnp.sqrt(pt.x ** 2 + pt.y ** 2)

    f(pt)  # doesn't crash
    _ = api.grad(f)(pt)
    self.assertIsInstance(pt, ZeroPoint)

  @parameterized.parameters(1, 2, 3)
  def test_shape_dtype_struct(self, i):
    s = api.ShapeDtypeStruct(shape=(i, 2, 3), dtype=jnp.float32)
    self.assertEqual(s.shape, (i, 2, 3))
    self.assertEqual(s.dtype, jnp.float32)
    self.assertEqual(s.ndim, 3)
    self.assertEqual(s.size, i * 2 * 3)
    self.assertLen(s, i)
    for f in (str, repr):
      self.assertEqual(
          f(s), f"ShapeDtypeStruct(shape=({i}, 2, 3), dtype=float32)")

  def test_shape_dtype_struct_scalar(self):
    s = api.ShapeDtypeStruct(shape=(), dtype=jnp.float32)
    self.assertEmpty(s.shape)
    self.assertEqual(s.size, 1)
    self.assertEqual(s.ndim, 0)
    with self.assertRaisesRegex(TypeError, "len[(][)] of unsized object"):
      _ = len(s)

  def test_shape_dtype_struct_hash(self):
    s1 = api.ShapeDtypeStruct(shape=(2, 3), dtype=jnp.float32)
    s2 = api.ShapeDtypeStruct(shape=(2, 3), dtype=jnp.float32)
    s3 = api.ShapeDtypeStruct(shape=(2, 4), dtype=jnp.float32)
    self.assertEqual(hash(s1), hash(s2))
    self.assertNotEqual(hash(s1), hash(s3))

  def test_shape_dtype_struct_invalid_shape(self):
    with self.assertRaisesRegex(TypeError, "'int' object is not iterable"):
      api.ShapeDtypeStruct(shape=4, dtype='float32')

  def test_shape_dtype_struct_dtype_none(self):
    with self.assertRaisesRegex(ValueError, "dtype must be specified"):
      api.ShapeDtypeStruct(shape=(), dtype=None)

  def test_eval_shape(self):
    def fun(x, y):
      return jnp.tanh(jnp.dot(x, y) + 3.)

    x = jnp.ones((2, 3))
    y = jnp.ones((3, 4))
    out_shape = api.eval_shape(fun, x, y)

    self.assertEqual(out_shape.shape, (2, 4))

  def test_eval_shape_constants(self):
    def fun():
      x = jnp.ones((2, 3))
      y = jnp.ones((3, 4))
      return jnp.tanh(jnp.dot(x, y) + 3.)

    out_shape = api.eval_shape(fun)

    self.assertEqual(out_shape.shape, (2, 4))

  def test_eval_shape_tuple_unpacking(self):
    def fun(x, y):
      a, b = x
      return a + b + y

    x = (jnp.ones(2), jnp.ones(2))
    y = 3.
    out_shape = api.eval_shape(fun, x, y)

    self.assertEqual(out_shape.shape, (2,))

  def test_eval_shape_tuple_itemgetting(self):
    def fun(x, y):
      return x[0] + x[1] + y

    x = (jnp.ones(2), jnp.ones(2))
    y = 3.
    out_shape = api.eval_shape(fun, x, y)

    self.assertEqual(out_shape.shape, (2,))

  def test_eval_shape_output_dict(self):
    def fun(x, y):
      return {'hi': x[0] + x[1] + y}

    x = (jnp.ones(2), jnp.ones(2))
    y = 3.
    out_shape = api.eval_shape(fun, x, y)
    out_shape = tree_util.tree_map(np.shape, out_shape)

    self.assertEqual(out_shape, {'hi': (2,)})

  def test_eval_shape_shape_error(self):
    def fun(x, y):
      return jnp.tanh(jnp.dot(x, y) + 3.)

    x = jnp.ones((3, 3))
    y = jnp.ones((4, 4))

    self.assertRaises(TypeError, lambda: api.eval_shape(fun, x, y))

  def test_eval_shape_duck_typing(self):
    def fun(A, b, x):
      return jnp.dot(A, x) + b

    class MyArgArray:
      def __init__(self, shape, dtype):
        self.shape = shape
        self.dtype = np.dtype(dtype)

    A = MyArgArray((3, 4), jnp.float32)
    b = MyArgArray((1, 5), jnp.float32)
    x = MyArgArray((4, 5), jnp.float32)
    out_shape = api.eval_shape(fun, A, b, x)

    self.assertEqual(out_shape.shape, (3, 5))

  def test_eval_shape_duck_typing2(self):
    # https://github.com/google/jax/issues/5683
    class EasyDict(dict):
      def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.__dict__ = self

    x = EasyDict(shape=(3,), dtype=np.dtype('float32'))
    out_shape = api.eval_shape(lambda x: x, x)  # doesn't crash
    self.assertEqual(out_shape.shape, (3,))

  def test_eval_shape_names(self):
    def fun(x, y):
      return lax.psum(x, 'i') + y

    class MyArgArray:
      def __init__(self, shape, dtype, named_shape):
        self.shape = shape
        self.dtype = jnp.dtype(dtype)
        self.named_shape = named_shape

    x = MyArgArray((3, 2), jnp.float32, {'i': 10})
    y = MyArgArray((3, 2), jnp.float32, {'j': 5})
    with core.extend_axis_env('i', 10, None):
      with core.extend_axis_env('j', 5, None):
        out_shape = api.eval_shape(fun, x, y)

    self.assertEqual(out_shape.named_shape, {'j': 5})

  def test_issue_871(self):
    T = jnp.array([[1., 2.], [3., 4.], [5., 6.]])
    x = jnp.array([1, 2, 3])
    msg = ("linearized function called on tangent values inconsistent with "
           "the original primal values")

    y, f_jvp = api.linearize(jnp.sum, x)
    with self.assertRaisesRegex(ValueError, msg):
      f_jvp(T)

    y, f_jvp = api.linearize(api.jit(jnp.sum), x)
    with self.assertRaisesRegex(ValueError, msg):
      f_jvp(T)

  def test_grad_of_int_errors(self):
    # Errors without allow_int=True
    dfn = grad(lambda x: x ** 2)
    self.assertRaisesRegex(
      TypeError,
      (r"grad requires real- or complex-valued inputs \(input dtype that is a "
       r"sub-dtype of np.inexact\), but got int.*."),
      lambda: dfn(3))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_jvp_of_int_identity(self):
    primals = (1,)
    tangents = (np.zeros(shape=(), dtype=float0),)

    _, out = api.jvp(lambda x: x, primals, tangents)
    self.assertEqual(out, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_jvp_of_int_add(self):
    primals = (2,)
    tangents = (np.zeros(shape=(), dtype=float0),)

    _, out_tangent = api.jvp(lambda x: x+1, primals, tangents)
    self.assertEqual(out_tangent, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_jit_jvp_of_int(self):
    primals = (2,)
    tangents = (np.zeros(shape=(), dtype=float0),)

    _, out_tangent = api.jvp(jax.jit(lambda x: x+1), primals, tangents)
    self.assertEqual(out_tangent, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_vjp_of_int_index(self):
    primal, fn_vjp = api.vjp(lambda x, i: x[i], np.ones(2)*2, 1)
    tangent_x, tangent_i = fn_vjp(1.)
    self.assertEqual(primal, 2.)
    self.assertAllClose(tangent_x, jnp.array([0., 1.]))
    self.assertEqual(tangent_i, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_vjp_of_int_shapes(self):
    out, fn_vjp = api.vjp(lambda x: lax.reshape(x, (2, 2)), np.ones((4, 1),
                                                                    dtype=int))
    tangent, = fn_vjp(out)
    self.assertArraysEqual(tangent, np.zeros(shape=(4, 1), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_jit_vjp_of_int(self):
    primal, fn_vjp = api.vjp(lambda x, y: x+y, 2, 1)
    tangent_x, tangent_i = jax.jit(fn_vjp)(1)
    self.assertEqual(primal, 3)
    self.assertEqual(tangent_x, np.zeros(shape=(), dtype=float0))
    self.assertEqual(tangent_i, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_vjp_of_int_fulllike(self):
    # Regression test for tangent and cotangent mismatch in convert_element_type
    # transpose rule wrt a ConstVar
    f = lax.full_like
    out, vjp = api.vjp(f, jnp.zeros((2, 2)), 1)
    self.assertAllClose(out, jnp.ones((2, 2)))
    tangent_x, tangent_y = vjp(out)
    self.assertAllClose(tangent_x, jnp.zeros((2, 2)))
    self.assertEqual(tangent_y, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_grad_of_int(self):
    # Need real-valued output, but testing integer input.
    out = api.grad(lambda x: x+0., allow_int=True)(1)
    self.assertEqual(out, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_grad_of_bool(self):
    def cond(pred):
      return lax.cond(pred, lambda _: 1., lambda _: 2., 1.)
    value, grd = api.value_and_grad(cond, allow_int=True)(True)
    self.assertEqual(value, 1.)
    self.assertEqual(grd, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_grad_of_int_index(self):
    grad_x, grad_i = api.grad(lambda x, i: x[i], argnums=(0, 1),
                              allow_int=True)(np.ones(2), 1)
    self.assertAllClose(grad_x, jnp.array([0., 1.]))
    self.assertEqual(grad_i, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_jit_grad_of_int(self):
    grad_f = api.grad(lambda x, i: x[i], argnums=(0, 1), allow_int=True)
    grad_x, grad_i = jax.jit(grad_f)(np.ones(2), 1)
    self.assertAllClose(grad_x, jnp.array([0., 1.]))
    self.assertEqual(grad_i, np.zeros(shape=(), dtype=float0))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_float0_reshape(self):
    # dtype-agnostic operations are supported
    float0_array = jax.grad(lambda x: jnp.sum(x+0.),
                            allow_int=True)(np.ones((2, 4), dtype=int))

    self.assertArraysEqual(float0_array.reshape((4, 2)),
                           np.zeros((4, 2), dtype=float0))
    self.assertArraysEqual(float0_array.transpose(),
                           np.zeros((4, 2), dtype=float0))

  def test_float0_error(self):
    # float0 is incompatible with other dtypes
    float0_array = jax.grad(lambda x: x+0., allow_int=True)(1)
    error_text = "float0s do not support any operations by design"

    with self.assertRaisesRegex(TypeError, error_text):
      # dispatch via DeviceArray
      _ = float0_array + jnp.zeros(())

    with self.assertRaisesRegex(TypeError, error_text):
      # dispatch via lax
      _ = lax.add(float0_array, jnp.zeros(()))

  def test_grad_complex_result_errors(self):
    dfn = grad(lambda x: x ** 2 + 1j)
    self.assertRaisesRegex(
      TypeError,
      (r"grad requires real-valued outputs \(output dtype that is a "
       r"sub-dtype of np.floating\), but got complex.*"),
      lambda: dfn(3.))

  def test_holomorphic_grad_of_float_errors(self):
    dfn = grad(lambda x: x ** 2, holomorphic=True)
    self.assertRaisesRegex(
      TypeError,
      (r"grad with holomorphic=True requires inputs with complex dtype, "
       r"but got float.*"),
      lambda: dfn(3.))

  def test_holomorphic_jacrev_of_float_errors(self):
    dfn = jacrev(lambda x: x ** 2, holomorphic=True)
    self.assertRaisesRegex(
      TypeError,
      (r"jacrev with holomorphic=True requires inputs with complex dtype, "
       r"but got float.*"),
      lambda: dfn(3.))

  def test_holomorphic_jacfwd_of_float_errors(self):
    dfn = jacfwd(lambda x: x ** 2, holomorphic=True)
    self.assertRaisesRegex(
      TypeError,
      (r"jacfwd with holomorphic=True requires inputs with complex dtype, "
       r"but got float.*"),
      lambda: dfn(3.))

  def test_jacfwd_of_complex_errors(self):
    dfn = jacfwd(lambda x: x ** 2)
    self.assertRaisesRegex(
      TypeError,
      (r"jacfwd requires real-valued inputs \(input dtype that is a "
       r"sub-dtype of np.floating\), but got complex.*"),
      lambda: dfn(3. + 1j))

  def test_xla_computation(self):
    # these tests basically check the examples in the xla_computation docstring

    def e(x):
      return jnp.sin(jnp.cos(x))
    c = api.xla_computation(e)(2.)
    self.assertIn('cosine', c.as_hlo_text())
    self.assertIn('sine', c.as_hlo_text())

    def f(x):
      return x - lax.psum(x, 'i')
    axis_env = [('i', 4)]
    c = api.xla_computation(f, axis_env=axis_env)(2)
    self.assertIn('all-reduce', c.as_hlo_text())
    self.assertIn('replica_groups={{0,1,2,3}}', c.as_hlo_text())

    def g(x):
      rowsum = lax.psum(x, 'i')
      colsum = lax.psum(x, 'j')
      allsum = lax.psum(x, ('i', 'j'))
      return rowsum, colsum, allsum
    axis_env = [('i', 4), ('j', 2)]
    c = api.xla_computation(g, axis_env=axis_env)(5.)
    self.assertIn('all-reduce', c.as_hlo_text())
    self.assertIn('replica_groups={{0,2,4,6},{1,3,5,7}}', c.as_hlo_text())
    self.assertIn('replica_groups={{0,1},{2,3},{4,5},{6,7}}', c.as_hlo_text())
    self.assertIn('replica_groups={{0,1,2,3,4,5,6,7}}', c.as_hlo_text())

    def h(x):
      rowsum = lax.psum(x, 'i', axis_index_groups=[[0, 1], [2, 3]])
      colsum = lax.psum(x, 'j')
      return rowsum, colsum
    axis_env = [('i', 4), ('j', 2)]
    c = api.xla_computation(h, axis_env=axis_env)(5.)
    self.assertIn('all-reduce', c.as_hlo_text())
    self.assertIn('replica_groups={{0,2},{4,6},{1,3},{5,7}}', c.as_hlo_text())
    self.assertIn('replica_groups={{0,1},{2,3},{4,5},{6,7}}', c.as_hlo_text())

  def test_xla_computation_args(self):
    def foo(x, y, z):
      return x + y + z

    c = api.xla_computation(foo)(1., 2., 3.)
    self.assertEqual(len(c.program_shape().parameter_shapes()), 3)

    c = api.xla_computation(foo, tuple_args=True)(1., 2., 3.)
    param_shapes = c.program_shape().parameter_shapes()
    self.assertEqual(len(param_shapes), 1)
    self.assertEqual(param_shapes[0].xla_element_type(),
                     xla_client.PrimitiveType.TUPLE)

  def test_xla_computation_duck_typing(self):
    def foo(x, y, z):
      return x + y + z

    x = jax.ShapeDtypeStruct((), np.float32)
    y = jax.ShapeDtypeStruct((), np.float32)
    z = jax.ShapeDtypeStruct((), np.float32)

    c = api.xla_computation(foo)(x, y, z)
    self.assertEqual(len(c.program_shape().parameter_shapes()), 3)

    c = api.xla_computation(foo, tuple_args=True)(1., 2., 3.)
    param_shapes = c.program_shape().parameter_shapes()
    self.assertEqual(len(param_shapes), 1)
    self.assertEqual(param_shapes[0].xla_element_type(),
                     xla_client.PrimitiveType.TUPLE)

  def test_compiler_ir(self):
    # TODO(phawkins): merge these tests with the `xla_computation` tests.
    def e(x):
      return jnp.sin(jnp.cos(x))
    hlo = api.jit(e).lower(2.).compiler_ir(dialect="hlo").as_hlo_text()
    self.assertIn(' cosine', hlo)
    self.assertIn(' sine', hlo)
    mhlo = str(api.jit(e).lower(2.).compiler_ir(dialect="mhlo"))
    self.assertIn('mhlo.cosine', mhlo)
    self.assertIn('mhlo.sine', mhlo)
    stablehlo = str(api.jit(e).lower(2.).compiler_ir(dialect="stablehlo"))
    self.assertIn("stablehlo.cosine", stablehlo)
    self.assertIn("stablehlo.sine", stablehlo)

  def test_staging_out_multi_replica(self):
    def f(x):
      return api.pmap(jnp.mean)(x)
    xla_comp = api.xla_computation(f)
    xla_comp(jnp.arange(8)).as_hlo_text()  # doesn't crash

  def test_xla_computation_instantiate_constant_outputs(self):
    def f():
      return jnp.zeros((3, 4))

    xla_comp = api.xla_computation(f)()
    out_shape, = xla_comp.program_shape().result_shape().tuple_shapes()
    self.assertEqual(out_shape.dimensions(), (3, 4))

  def test_xla_computation_static_argnums(self):
    def f(x, y):
      return x + y

    xla_comp = api.xla_computation(f, static_argnums=(1,))(2, 3)
    hlo_text = xla_comp.as_hlo_text()
    self.assertIn("constant(3)", hlo_text)
    # The static arguments should be removed from the function being compiled,
    # thus the function should have only a single argument.
    self.assertIn("parameter(0)", hlo_text)
    self.assertNotIn("parameter(1)", hlo_text)

  def test_xla_computation_return_shape(self):
    _, shape_tree = api.xla_computation(lambda x: (x + 1, jnp.zeros(2, jnp.float32)),
                                        return_shape=True)(np.int32(1))
    expected = (api.ShapeDtypeStruct(shape=(), dtype=jnp.int32),
                api.ShapeDtypeStruct(shape=(2,), dtype=jnp.float32))
    self.assertEqual(shape_tree, expected)

  def test_xla_computation_partitioned(self):
    def f(x, y):
      return jnp.dot(x, y) + 1

    x = jax.ShapeDtypeStruct((8, 8), np.float32)
    y = jax.ShapeDtypeStruct((8, 16), np.float32)
    xla_comp = api.xla_computation(f, in_parts=(P(2, 2), None),
                                   out_parts=P(4, 1))(x, y)
    hlo_text = xla_comp.as_hlo_text()
    self.assertIn('sharding={devices=[2,2]0,1,2,3}', hlo_text)
    self.assertIn('sharding={replicated}', hlo_text)
    self.assertIn('sharding={{devices=[4,1]0,1,2,3}}', hlo_text)

  def test_xla_computation_replicated_and_partitioned(self):
    def f(x, y):
      return jnp.dot(x, y), lax.psum(x, 'i')

    x = jax.ShapeDtypeStruct((8, 8), np.float32)
    y = jax.ShapeDtypeStruct((8, 16), np.float32)
    axis_env = [('i', 4)]
    xla_comp = api.xla_computation(f, axis_env=axis_env,
                                   in_parts=(P(2, 2), None),
                                   out_parts=(P(4, 1), None))(x, y)
    hlo_text = xla_comp.as_hlo_text()
    self.assertIn('all-reduce', hlo_text)
    self.assertIn('replica_groups={{0,1,2,3}}', hlo_text)
    self.assertIn('sharding={devices=[2,2]0,1,2,3}', hlo_text)
    self.assertIn('sharding={replicated}', hlo_text)
    self.assertIn('sharding={{devices=[4,1]0,1,2,3}, {replicated}}', hlo_text)

  def test_xla_computation_psum_constant(self):
    f = lambda: jax.lax.psum(1, "i")
    api.xla_computation(f, axis_env=[("i", 2)])()  # doesn't crash

  @jtu.ignore_warning(message="Some donated buffers were not usable")
  def test_xla_computation_donate_argnums(self):
    api.xla_computation(lambda x: None, donate_argnums=(0,))(3)  # doesn't crash

  def test_xla_computation_lower_fun_axis_env(self):
    axis_name = 'i'
    def fn(x):
      y = lax.all_gather(
              x, axis_name=axis_name)
      return y * lax.axis_index(axis_name).astype(jnp.float32)

    input_x = jnp.ones((5,6,4), dtype=jnp.float32)
    axis_env = [(axis_name, jax.local_device_count())]
    _ = api.xla_computation(fn, axis_env=axis_env, backend='cpu')(input_x)

  def test_xla_computation_axis_env(self):
    def fn(x):
      z = x * jax.lax.axis_index('i').astype(jnp.float32)
      def inner_fn(carry, a):
        return carry + a, ()
      return jax.lax.scan(inner_fn, jnp.zeros_like(z[0]), z)

    x = jnp.ones((5, 6, 4), dtype=jnp.float32)
    _ = jax.xla_computation(fn, axis_env=(('i', 8),), backend='cpu')(x)

  def test_concurrent_device_get_and_put(self):
    def f(x):
      for _ in range(100):
        y = jax.device_put(x)
        x = jax.device_get(y)
      return x

    xs = [self.rng().randn(i) for i in range(10)]
    with concurrent.futures.ThreadPoolExecutor() as executor:
      futures = [executor.submit(partial(f, x)) for x in xs]
      ys = [f.result() for f in futures]
    for x, y in zip(xs, ys):
      self.assertAllClose(x, y)

  def test_dtype_from_builtin_types(self):
    for dtype in [bool, int, float, complex]:
      with warnings.catch_warnings(record=True) as caught_warnings:
        x = jnp.array(0, dtype=dtype)
      self.assertEmpty(caught_warnings)
      assert x.dtype == dtypes.canonicalize_dtype(dtype)

  def test_dtype_warning(self):
    # cf. issue #1230
    if config.x64_enabled:
      raise unittest.SkipTest("test only applies when x64 is disabled")

    def check_warning(warn, nowarn):
      with warnings.catch_warnings(record=True) as w:
        warnings.simplefilter("always")

        nowarn()  # get rid of extra startup warning

        prev_len = len(w)
        nowarn()
        assert len(w) == prev_len

        warn()
        assert len(w) > 0
        msg = str(w[-1].message)
        expected_prefix = "Explicitly requested dtype "
        self.assertEqual(expected_prefix, msg[:len(expected_prefix)])

        prev_len = len(w)
        nowarn()
        assert len(w) == prev_len

    check_warning(lambda: jnp.array([1, 2, 3], dtype="float64"),
                  lambda: jnp.array([1, 2, 3], dtype="float32"))
    check_warning(lambda: jnp.array([1, 2, 3], dtype="float64"),
                  lambda: jnp.array([1, 2, 3], dtype=float))
    check_warning(lambda: jnp.ones(3, dtype=np.float64),
                  lambda: jnp.ones(3))
    check_warning(lambda: jnp.ones(3, dtype=np.float64),
                  lambda: jnp.ones(3, dtype=float))
    check_warning(lambda: jnp.ones_like(3, dtype=np.int64),
                  lambda: jnp.ones_like(3, dtype=np.int32))
    check_warning(lambda: jnp.zeros(3, dtype="int64"),
                  lambda: jnp.zeros(3, dtype="int32"))
    check_warning(lambda: jnp.zeros_like(3, dtype="float64"),
                  lambda: jnp.zeros_like(3, dtype="float32"))
    check_warning(lambda: jnp.full((2, 3), 1, dtype="int64"),
                  lambda: jnp.full((2, 3), 1))
    check_warning(lambda: jnp.ones(3).astype("float64"),
                  lambda: jnp.ones(3).astype("float32"))
    check_warning(lambda: jnp.eye(3, dtype=np.float64),
                  lambda: jnp.eye(3))
    check_warning(lambda: jnp.arange(3, dtype=np.float64),
                  lambda: jnp.arange(3, dtype=np.float32))
    check_warning(lambda: jnp.linspace(0, 3, dtype=np.float64),
                  lambda: jnp.linspace(0, 3, dtype=np.float32))
    check_warning(lambda: jnp.tri(2, dtype="float64"),
                  lambda: jnp.tri(2, dtype="float32"))
    check_warning(lambda: jnp.arange(1).astype("float64"),
                  lambda: jnp.arange(1).astype(float))
    check_warning(lambda: jnp.arange(1.0).astype("int64"),
                  lambda: jnp.arange(1.0).astype(int))

  def test_error_for_invalid_dtype(self):
    with self.assertRaisesRegex(TypeError, ".*not a valid JAX array type.*"):
      lax.add(jnp.array(7), np.array("hello"))

  def test_vmap_preserves_docstr(self):
    def superfun(a):
      """Does things with stuff."""
      pass

    self.assertRegex(api.vmap(superfun).__doc__, "\n".join([
        "Vectorized version of superfun.*",
        "",
        "Original documentation:",
        "",
        superfun.__doc__,
    ]))

  def test_vmap_in_axes_list(self):
    # https://github.com/google/jax/issues/2367
    dictionary = {'a': 5., 'b': jnp.ones(2)}
    x = jnp.zeros(3)
    y = jnp.arange(3.)


    def f(dct, x, y):
      return dct['a'] + dct['b'] + x + y

    out1 = api.vmap(f, (None, 0, 0))(dictionary, x, y)
    out2 = api.vmap(f, [None, 0, 0])(dictionary, x, y)
    self.assertAllClose(out1, out2)

  def test_vmap_in_axes_tree_prefix_error(self):
    # https://github.com/google/jax/issues/795
    value_tree = jnp.ones(3)
    self.assertRaisesRegex(
        ValueError,
        "vmap in_axes specification must be a tree prefix of the corresponding "
        r"value, got specification \(0, 0\) for value tree "
        + re.escape(f"{tree_util.tree_structure((value_tree,))}."),
        lambda: api.vmap(lambda x: x, in_axes=(0, 0))(value_tree)
    )

  def test_vmap_in_axes_leaf_types(self):
    with self.assertRaisesRegex(
        TypeError, r"vmap in_axes must be an int, None, or .*"):
      api.vmap(lambda x: x, in_axes=(jnp.array([1., 2.]),))(jnp.array([1., 2.]))

  def test_vmap_out_axes_leaf_types(self):
    with self.assertRaisesRegex(
        TypeError, r"vmap out_axes must be an int, None, or .*"):
      api.vmap(lambda x: x, out_axes=(jnp.array([1., 2.]),))(jnp.array([1., 2.]))

  def test_vmap_unbatched_object_passthrough_issue_183(self):
    # https://github.com/google/jax/issues/183
    fun = lambda f, x: f(x)
    vfun = api.vmap(fun, (None, 0))
    ans = vfun(lambda x: x + 1, jnp.arange(3))
    self.assertAllClose(ans, np.arange(1, 4), check_dtypes=False)

  def test_vmap_mismatched_keyword(self):
    # https://github.com/google/jax/issues/10193
    @jax.vmap
    def f(x, y):
      return x + y

    with self.assertRaisesRegex(
        ValueError,
        "vmap got inconsistent sizes for array axes to be mapped:\n"
        r"  \* one axis had size 1: axis 0 of argument x of type int32\[1\];"
        "\n"
        r"  \* one axis had size 2: axis 0 of argument y of type int32\[2\]"):
      f(jnp.array([1], 'int32'), y=jnp.array([1, 2], 'int32'))

  def test_vmap_mismatched_axis_sizes_error_message_issue_705(self):
    # https://github.com/google/jax/issues/705
    def h(a, b):
      return jnp.sum(a) + jnp.sum(b)

    X = self.rng().randn(10, 4).astype('float32')
    U = self.rng().randn(10, 2).astype('float32')

    with self.assertRaisesRegex(
        ValueError,
        "vmap got inconsistent sizes for array axes to be mapped:\n"
        r"  \* one axis had size 10: axis 0 of argument a of type float32\[10,4\];""\n"
        r"  \* one axis had size 2: axis 1 of argument b of type float32\[10,2\]"):
      api.vmap(h, in_axes=(0, 1))(X, U)

    with self.assertRaisesRegex(
        ValueError,
        "vmap got inconsistent sizes for array axes to be mapped:\n"
        r"  \* most axes \(2 of them\) had size 10, e.g. axis 0 of argument x "
        r"of type float32\[10,4\];" "\n"
        r"  \* one axis had size 2: axis 1 of argument y of type float32\[10,2\]"):
      api.vmap(lambda x, y, z: None, in_axes=(0, 1, 0))(X, U, X)

    with self.assertRaisesRegex(
        ValueError,
        "vmap got inconsistent sizes for array axes to be mapped:\n"
        r"  \* most axes \(2 of them\) had size 2, e.g. axis 1 of argument b\[0\] "
        r"of type float32\[10,2\];" "\n"
        r"  \* one axis had size 10: axis 0 of argument a of type float32\[10,4\]"):
      api.vmap(h, in_axes=(0, 1))(X, [U, U])

    error = (r"vmap was requested to map its argument along axis 0, which "
             r"implies that its rank should be at least 1, but is only 0 "
             r"\(its shape is \(\)\)")
    with self.assertRaisesRegex(ValueError, error):
      # The mapped inputs cannot be scalars
      api.vmap(lambda x: x)(1.)

    with self.assertRaisesRegex(
        ValueError, "vmap must have at least one non-None value in in_axes"):
      # If the output is mapped, there must be a non-None in_axes
      api.vmap(lambda x: x, in_axes=None)(jnp.array([1., 2.]))

    error = (r"vmap was requested to map its argument along axis 1, which "
             r"implies that its rank should be at least 2, but is only 1 "
             r"\(its shape is \(2,\)\)")
    with self.assertRaisesRegex(ValueError, error):
      api.vmap(lambda x: x, in_axes=1)(jnp.array([1., 2.]))

    # Error is: TypeError: only integer scalar arrays can be converted to a scalar index
    with self.assertRaisesRegex(
        ValueError,
        "vmap out_axes specification must be a tree prefix of the "
        "corresponding value.*"):
      api.vmap(lambda x: x, in_axes=0, out_axes=(2, 3))(jnp.array([1., 2.]))

    with self.assertRaisesRegex(
        ValueError,
        r"vmap has mapped output \(axis_name='foo'\) but out_axes is None"):
      # If the output is mapped (user-named axis), then there must be some
      # out_axes specified.
      api.vmap(lambda x: x, out_axes=None, axis_name="foo")(jnp.array([1., 2.]))

    with self.assertRaisesRegex(
        ValueError,
        "vmap has mapped output but out_axes is None"):
      # If the output is mapped (unnamed axis), then there must be some out_axes
      # specified.
      api.vmap(lambda x: x, out_axes=None)(jnp.array([1., 2.]))

  def test_vmap_structured_in_axes(self):

    A, B, C, D = 2, 3, 4, 5
    K = 6  # batch size
    x = np.ones((K, A, B))  # batch axis in different locations
    y = np.ones((B, K, C))
    z = np.ones((C, D, K))

    def foo(tree_arg):
      x, (y, z) = tree_arg
      return jnp.dot(x, jnp.dot(y, z))

    tree = (x, (y, z))
    vfoo = api.vmap(foo, in_axes=((0, (1, 2)),))
    self.assertEqual(vfoo(tree).shape, (6, 2, 5))

    Point = collections.namedtuple("Point", ["x", "y"])
    tree = (x, Point(y, z))
    vfoo = api.vmap(foo, in_axes=((0, Point(1, 2)),))
    self.assertEqual(vfoo(tree).shape, (6, 2, 5))

    def foo(tree_arg):
      x, dct = tree_arg
      y, z = dct['a'], dct['b']
      return jnp.dot(x, jnp.dot(y, z))

    tree = (x, {'a': y, 'b': z})
    vfoo = api.vmap(foo, in_axes=((0, {'a': 1, 'b': 2}),))
    self.assertEqual(vfoo(tree).shape, (6, 2, 5))

    tree = (x, collections.OrderedDict([('a', y), ('b', z)]))
    vfoo = api.vmap(
        foo, in_axes=((0, collections.OrderedDict([('a', 1), ('b', 2)])),))
    self.assertEqual(vfoo(tree).shape, (6, 2, 5))

  def test_vmap_in_axes_bool_error(self):
    # https://github.com/google/jax/issues/6372
    with self.assertRaisesRegex(TypeError, "must be an int"):
      api.vmap(lambda x: x, in_axes=False)(jnp.zeros(3))

  def test_pmap_in_axes_bool_error(self):
    # https://github.com/google/jax/issues/6372
    with self.assertRaisesRegex(TypeError, "must be an int"):
      api.pmap(lambda x: x, in_axes=False)(jnp.zeros(1))

  def test_vmap_empty_arguments(self):
    with self.assertRaisesRegex(
        ValueError,
        "vmap wrapped function must be passed at least one argument "
        r"containing an array, got empty \*args=\(\{\},\) and \*\*kwargs=\{\}"):
      api.vmap(lambda x: x)({})

  def test_pmap_empty_arguments(self):
    with self.assertRaisesRegex(
        ValueError,
        "pmap wrapped function must be passed at least one argument "
        r"containing an array, got empty \*args=\(\{\},\) and \*\*kwargs=\{\}"):
      api.pmap(lambda x: x)({})

  def test_pmap_global_cache(self):
    def f(x, y):
      return x, y

    x = np.ones((1, 1, 1))

    # All defaults
    with jtu.assert_num_jit_and_pmap_compilations(1):
      for _ in range(2):
        api.pmap(f)(x, x)

    # With axis name
    with jtu.assert_num_jit_and_pmap_compilations(1):
      for _ in range(2):
        api.pmap(f, 'i')(x, x)

    # With in_axes and out_axes
    for x_in, y_in, x_out, y_out in it.product(*((0, 1, 2) for _ in range(4))):
      with jtu.assert_num_jit_and_pmap_compilations(1):
        for _ in range(2):
          api.pmap(f, 'i', in_axes=(x_in, y_in), out_axes=(x_out, y_out))(x, x)

    # Forward-mode AD on the outside
    with jtu.assert_num_jit_and_pmap_compilations(1):
      for _ in range(2):
        api.jvp(api.pmap(f), (x, x), (x, x))

    # Reverse-mode AD on the outside. One compilation for forward, one for backward.
    with jtu.assert_num_jit_and_pmap_compilations(2):
      for _ in range(2):
        api.vjp(api.pmap(f), x, x)[1]((x, x))

  def test_device_array_repr(self):
    rep = jnp.ones(()) + 1.
    if config.jax_array:
      msg = 'Array'
    else:
      msg = 'DeviceArray'
    self.assertStartsWith(repr(rep), msg)

  def test_device_array_hash(self):
    rep = jnp.ones((1,)) + 1.
    _check_instance(self, rep)
    self.assertNotIsInstance(rep, collections.abc.Hashable)
    with self.assertRaisesRegex(TypeError, 'unhashable type'):
      hash(rep)

  def test_grad_without_enough_args_error_message(self):
    # https://github.com/google/jax/issues/1696
    def f(x, y): return x + y
    df = api.grad(f, argnums=0)
    self.assertRaisesRegex(
        TypeError,
        "differentiating with respect to argnums=0 requires at least 1 "
        "positional arguments to be passed by the caller, but got only 0 "
        "positional arguments.",
        lambda: partial(df, x=0.)(y=1.))

  def test_jit_compilation_time_logging(self):
    @api.jit
    def f(x):
      return x * 2

    # make sure some initial warnings & cached operations already happen.
    f(jnp.ones(2))

    prev_level = logging.get_verbosity()
    try:
      logging.set_verbosity('DEBUG')
      with self.assertLogs(level=logging.DEBUG) as l:
        f(2.)
    finally:
      logging.set_verbosity(prev_level)
    self.assertGreaterEqual(len(l.output), 3)  # 3 lines
    self.assertTrue(any('Finished tracing' in line for line in l.output))
    self.assertTrue(any('Compiling f' in line for line in l.output))
    self.assertTrue(any('Finished XLA compilation' in line for line in l.output))

  def test_grad_of_jit_compilation_caching(self):
    if not hasattr(self, "assertLogs"):
      raise unittest.SkipTest("test requires assertLogs (python 3)")

    # make sure some initial warnings & cached operations already happen.
    api.grad(api.jit(lambda x: x))(1.0)

    @api.jit
    def f(x):
      return jnp.sin(x)

    prev_level = logging.get_verbosity()
    try:
      logging.set_verbosity('DEBUG')
      with self.assertLogs(level=logging.DEBUG) as l:
        ans1 = api.grad(f)(2.)
        ans2 = api.grad(f)(3.)
    finally:
      logging.set_verbosity(prev_level)
    self.assertGreaterEqual(len(l.output), 2 * 3)  # one for fwd, one for bwd, 3 lines each
    self.assertAllClose(ans1, np.cos(2.), check_dtypes=False)
    self.assertAllClose(ans2, np.cos(3.), check_dtypes=False)

  def test_grad_of_jit_compilation_caching2(self):
    # Like the above test, but instead of logging use our compile counters.

    # make sure some initial convert element type operations are pre-cached.
    api.grad(api.jit(lambda x: x))(1.0)

    @api.jit
    def f(x):
      return jnp.sin(x)

    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      _  = jax.grad(f)(3.)
    self.assertEqual(count[0], 2)  # one for fwd, one for bwd

    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      _  = jax.grad(f)(3.)
      _  = jax.grad(f)(4.)
    self.assertEqual(count[0], 0)  # cache hits on both fwd and bwd

  def test_grad_does_not_unflatten_tree_with_none(self):
    # https://github.com/google/jax/issues/7546
    class CustomNode(list):
      pass

    def unflatten(unused_aux_data, children):
      self.assertIsNotNone(children[0])
      return CustomNode(children)

    tree_util.register_pytree_node(CustomNode, lambda x: (x, None), unflatten)
    grad(lambda x: x[0])(CustomNode([0.]))

  def test_trivial_computations(self):
    x = jnp.array([1, 2, 3])
    y = api.jit(lambda x: x)(x)
    self.assertEqual(x.unsafe_buffer_pointer(), y.unsafe_buffer_pointer())

    z1, z2 = api.jit(lambda x: (x, x))(x)
    self.assertEqual(z1.unsafe_buffer_pointer(), z2.unsafe_buffer_pointer())

    x1, x2 = jnp.array([1, 2]), jnp.array([2, 3])
    z1, z2, z3 = api.jit(lambda x, y: (y, 1, x))(x1, x2)
    self.assertEqual(z1.unsafe_buffer_pointer(), x2.unsafe_buffer_pointer())
    self.assertEqual(z3.unsafe_buffer_pointer(), x1.unsafe_buffer_pointer())
    self.assertEqual(z2, 1)

  def test_nested_jit_hoisting(self):
    @api.jit
    def f(x, y):
      z = 2 * x
      return y + z, 3

    @api.jit
    def g(x):
      return f(2, x)

    mlir_jaxpr_subcomp = mlir.jaxpr_subcomp

    jaxprs = []
    def mlir_jaxpr_subcomp_and_collect(c, jaxpr, *args, **kwargs):
      jaxprs.append(jaxpr)
      return mlir_jaxpr_subcomp(c, jaxpr, *args, **kwargs)

    try:
      mlir.jaxpr_subcomp = mlir_jaxpr_subcomp_and_collect
      ans = g(3)
    finally:
      mlir.jaxpr_subcomp = mlir_jaxpr_subcomp

    self.assertEqual(ans, (7, 3))
    self.assertLen(jaxprs, 2)
    outer_jaxpr, inner_jaxpr = jaxprs

    self.assertLen(outer_jaxpr.eqns, 1)
    if jax.config.jax_jit_pjit_api_merge:
      prim_name = 'pjit'
      jaxpr_param = 'jaxpr'
    else:
      prim_name = 'xla_call'
      jaxpr_param = 'call_jaxpr'
    self.assertEqual(outer_jaxpr.eqns[0].primitive.name, f'{prim_name}')
    subjaxpr_1 = outer_jaxpr.eqns[0].params[f"{jaxpr_param}"]
    self.assertEqual(str(subjaxpr_1), str(inner_jaxpr))
    self.assertLen(inner_jaxpr.eqns, 2)
    self.assertEqual(inner_jaxpr.eqns[-2].primitive.name, 'mul')
    self.assertEqual(inner_jaxpr.eqns[-1].primitive.name, 'add')

  def test_primitive_compilation_cache(self):
    with jtu.count_primitive_compiles() as count:
      lax.add(1, 2)
      lax.add(2, 3)
    self.assertEqual(count[0], 1)

  def test_arange_jit(self):
    # see https://github.com/google/jax/issues/553
    def fun(x):
      r = jnp.arange(x.shape[0])[x]
      return r

    jit(fun)(jnp.array([0, 1, 2], dtype=jnp.int32))  # doesn't crash

  def helper_save_tracer(self, x):
    self._saved_tracer = x
    return x

  def test_escaped_tracers_different_top_level_traces(self):
    api.jit(self.helper_save_tracer)(0.)
    with self.assertRaisesRegex(
        UnexpectedTracerError, "Encountered an unexpected tracer"):
      api.jit(lambda x: self._saved_tracer)(0.)

  def test_escaped_tracers_cant_lift_sublevels(self):
    api.jit(self.helper_save_tracer)(0.)
    with self.assertRaisesRegex(
        UnexpectedTracerError,
        re.compile(
          "Encountered an unexpected tracer",
          re.DOTALL)):
      api.jit(lambda x: x)(self._saved_tracer)

  def test_escaped_tracers_tracer_from_higher_level(self):
    api.grad(self.helper_save_tracer)(0.)
    with self.assertRaisesRegex(
        UnexpectedTracerError,
        re.compile(
          "Encountered an unexpected tracer.*Tracer from a higher level",
          re.DOTALL)):
      api.grad(lambda x: x)(self._saved_tracer)

  def test_escaped_tracers_incompatible_sublevel(self):
    def func1(x):
      api.jit(self.helper_save_tracer)(0.)
      # Use the tracer
      return x + self._saved_tracer
    with self.assertRaisesRegex(
        UnexpectedTracerError,
        re.compile("Encountered an unexpected tracer",
                   re.DOTALL)):
      api.jit(func1)(2.)

  def test_escaped_tracers_cant_lift(self):
    def func1(x):
      api.grad(self.helper_save_tracer)(0.)
      return x + self._saved_tracer
    with self.assertRaisesRegex(
        UnexpectedTracerError,
        re.compile("Encountered an unexpected tracer.*Can't lift",
                   re.DOTALL)):
      api.grad(func1)(2.)

  def test_escaped_tracers_not_among_input_tracers(self):
    def func1(x):
      api.grad(self.helper_save_tracer)(x)
      # Use the tracer
      return x + self._saved_tracer

    if jax.config.jax_jit_pjit_api_merge:
      msg = "Encountered an unexpected tracer"
    else:
      msg = "Encountered an unexpected tracer.*Tracer not in input tracers"

    with self.assertRaisesRegex(
        UnexpectedTracerError, re.compile(msg, re.DOTALL)):
      api.jit(func1)(2.0)

  def test_escaped_tracer_omnistaging(self):
    count = 1

    @jit
    def f():
      nonlocal count
      count = jnp.add(count, 1)
    f()  # leaked a tracer! but currently undetected

    def f(x, c):
      jnp.add(count, 1)
      return None, None

    @jit
    def g():
      lax.scan(f, None, None, length=2)

    with self.assertRaisesRegex(UnexpectedTracerError,
                                "was created on line"):
      g()

  def test_escaped_tracer_omnistaging_top_trace(self):
    count = 1

    def f(_, __):
      nonlocal count
      count = jnp.add(count, 1)
      return None, None

    lax.scan(f, None, None, length=2)  # leaked a tracer! (of level 1!)

    with self.assertRaisesRegex(UnexpectedTracerError,
                                "was created on line"):
      # The following call will try and raise the ones array to the count tracer
      # level, which is no longer live.
      jax.jit(jnp.add)(jnp.ones(()), count)

  def test_escaped_tracer_transform_name(self):
    with self.assertRaisesRegex(UnexpectedTracerError,
                                "for jit"):
      jax.jit(self.helper_save_tracer)(1)
      _ = self._saved_tracer+1

    with self.assertRaisesRegex(UnexpectedTracerError,
                                "for pmap"):
      jax.pmap(self.helper_save_tracer)(jnp.ones((1, 2)))
      _ = self._saved_tracer+1

    with self.assertRaisesRegex(UnexpectedTracerError,
                                "for eval_shape"):
      jax.eval_shape(self.helper_save_tracer, 1)
      _ = self._saved_tracer+1

  def test_escaped_tracer_shape_dtype(self):
    with self.assertRaisesRegex(core.UnexpectedTracerError, r"int32\[4,3\]"):
      jax.jit(self.helper_save_tracer)(jnp.ones((4, 3), dtype=jnp.int32))
      _ = self._saved_tracer+1

  def test_pmap_static_kwarg_error_message(self):
    # https://github.com/google/jax/issues/3007
    def f(a, b):
      return a + b

    g = jax.pmap(f, static_broadcasted_argnums=(1,))

    msg = (r"pmapped function has static_broadcasted_argnums=\(1,\) but was "
           r"called with only 1 positional argument. All static broadcasted "
           r"arguments must be passed positionally.")
    with self.assertRaisesRegex(ValueError, msg):
      g(jnp.ones((1, 1)), b=1)

  def test_vmap_unmapped_last(self):
    @partial(jax.vmap, out_axes=-1)
    def f(x):
      return np.zeros((2,))
    f(np.zeros((5,)))

  # TODO(jakevdp): re-enable this if possible.
  @unittest.skipIf(True, "broken by convert_element_type change.")
  def test_xla_constant_dedup(self):
    y = np.array([7, 14], dtype=np.float32)
    def f(x):
      return x + y + y

    x = np.array([1, 2], dtype=np.float32)
    hlo_lines = jax.xla_computation(f)(x).as_hlo_text().split('\n')
    hlo_lines = {s.strip() for s in hlo_lines}
    self.assertIn('constant.1 = f32[2]{0} constant({7, 14})', hlo_lines)
    self.assertNotIn('constant.2 = f32[2]{0} constant({7, 14})', hlo_lines)

  def test_eval_context(self):
    @jit
    def f():
      with core.eval_context():
        assert jnp.add(1, 1) == 2

    f()  # doesn't crash

  def test_concrete_error_because_arg_unary(self):
    @jax.jit
    def f(x):
      if x > 0:
        return x
      else:
        return 0

    msg = r"on the value of the argument 'x'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(1)

  def test_concrete_error_because_arg_binary(self):
    @jax.jit
    def f(x, y):
      if x > y:
        return x
      else:
        return y

    msg = r"on the values of the arguments 'x' and 'y'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(1, 2)

  def test_concrete_error_because_arg_ternary(self):
    @jax.jit
    def f(x, y, z):
      if x > z:
        return x
      else:
        return y

    msg = r"on the values of the arguments 'x' and 'z'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(1, 2, 3)

    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(1, 2, z=3)

    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(1, y=2, z=3)

  def test_concrete_error_because_arg_varargs(self):
    @jax.jit
    def f(*args):
      x, y, z = args
      if x > z:
        return x
      else:
        return y

    msg = r"on the values of the argument 'args'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(1, 2, 3)

  def test_concrete_error_because_arg_kwargs(self):
    @jax.jit
    def f(**kwargs):
      x, y, z = kwargs['x'], kwargs['y'], kwargs['z']
      if x > z:
        return x
      else:
        return y

    msg = r"on the values of the argument 'kwargs'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f(x=1, y=2, z=3)

  def test_concrete_error_because_arg_pytree(self):
    @jax.jit
    def f(xy, z):
      x, y = xy
      if x > 0:
        return x
      else:
        return y

    msg = r"on the value of the argument 'xy'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f((1, 2), z=3)

  def test_concrete_error_because_const(self):
    @jax.jit
    def f():
      assert jnp.add(1, 1) > 0

    msg = "on these lines"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f()

  def test_concrete_error_because_const_2(self):
    @jax.jit
    def f():
      result = sum(jnp.add(1, 1) for _ in range(6))
      assert result > 0

    msg = "Additional originating lines are not shown."
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      f()

  def test_concrete_error_with_nested_call(self):
    @jax.jit
    def f(x, y):
      if y:
        return x

    @jax.jit
    def g(x):
      return f(x, True)

    msg = r"on the value of the argument 'y'"
    with self.assertRaisesRegex(core.ConcretizationTypeError, msg):
      g(1)

  def test_xla_computation_zeros_doesnt_device_put(self):
    with jtu.count_device_put() as count:
      api.xla_computation(lambda: jnp.zeros(3))()
    self.assertEqual(count[0], 0)

  def test_join_concrete_arrays_with_omnistaging(self):
    # https://github.com/google/jax/issues/4622
    x = jnp.array([1., 2., 3.])
    y = jnp.array([1., 2., 4.])

    @jit
    def f():
      core.lattice_join(core.ConcreteArray(x.dtype, x),
                        core.ConcreteArray(y.dtype, y))

    f()  # doesn't crash

  def test_linearize_aval_error(self):
    # https://github.com/google/jax/issues/4622
    f = lambda x: x

    # these should not error
    _, f_jvp = api.linearize(f, 1.)
    f_jvp(1.)
    _, f_jvp = api.linearize(f, np.ones(2, np.int32))
    f_jvp(np.zeros(2, float0))

    # these should error
    _, f_jvp = api.linearize(f, 1.)
    with self.assertRaisesRegex(ValueError, "tangent values inconsistent"):
      f_jvp(1)
    _, f_jvp = api.linearize(f, np.ones(2, np.int32))
    with self.assertRaisesRegex(ValueError, "tangent values inconsistent"):
      f_jvp(np.ones(2, np.int32))

  def test_grad_of_token_consuming_primitive(self):
    # https://github.com/google/jax/issues/5463
    tokentest_p = core.Primitive("tokentest")
    tokentest_p.def_impl(partial(xla.apply_primitive, tokentest_p))
    tokentest_p.def_abstract_eval(lambda x, y: x)
    mlir.register_lowering(tokentest_p, lambda ctx, x, y: [x])
    ad.defjvp(tokentest_p, (lambda g, x, token: x), None)

    token = jax.lax.create_token(123)
    arr = jnp.ones((3, 2))
    res, vjp_fun = jax.vjp(lambda x: tokentest_p.bind(x, token), arr)
    # Should not crash.
    vjp_fun(arr)

  def test_jit_returning_token(self):
    x = jax.jit(jax.lax.create_token)(1.0)
    self.assertIsInstance(x, core.Token)

  def test_jit_capturing_token(self):
    tok = core.token
    _, y = jax.jit(lambda x: (x + 2, tok))(7)
    self.assertIsInstance(y, core.Token)

  def test_leak_checker_catches_a_jit_leak(self):
    with jax.checking_leaks():
      lst = []

      @jit
      def f(x):
        lst.append(x)
        return x

      with self.assertRaisesRegex(Exception, r"Leaked"):
        f(3)

  def test_leak_checker_catches_a_pmap_leak(self):
    with jax.checking_leaks():
      lst = []

      @api.pmap
      def f(x):
        lst.append(x)
        return x

      with self.assertRaisesRegex(Exception, r"Leaked"):
        f(np.ones(1))

  def test_leak_checker_catches_a_grad_leak(self):
    with jax.checking_leaks():
      lst = []

      def f(x):
        lst.append(x)
        return x

      with self.assertRaisesRegex(Exception, r"Leaked trace"):
        api.grad(f)(3.)

  def test_leak_checker_avoids_false_positives(self):
    with jax.checking_leaks():
      api.vmap(lambda x: x)(np.arange(3.))  # doesn't crash

      @jit
      def f(x):
        return x
      f(3)  # doesn't crash
      api.vmap(f)(np.arange(3))  # doesn't crash
      api.grad(f)(3.)  # doesn't crash

      @api.pmap
      def f(x):
        return x
      f(np.ones(1))  # doesn't crash
      api.vmap(f)(np.ones((1, 1)))  # doesn't crash

  def test_leak_checker_catches_a_scan_leak(self):
    with jax.checking_leaks():
      lst = []

      to_scan = lambda c, x: (lst.append(c) or jnp.sin(c), None)

      with self.assertRaisesRegex(Exception, r"Leaked trace"):
        lax.scan(to_scan, 1., np.arange(3.))

  def test_leak_checker_avoids_false_positives_scan(self):
    with jax.checking_leaks():
      to_scan = lambda c, x: (jnp.sin(c), None)
      lax.scan(to_scan, 1., np.arange(3.))  # doesn't crash

  def test_leak_checker_avoids_false_positives_scan_jvp(self):
    with jax.checking_leaks():
      to_scan = lambda c, x: (c, None)

      def f(x):
        lax.scan(to_scan, x, None, length=1)
      api.jvp(f, (3.,), (1.,))  # doesn't crash

  def test_leak_checker_avoids_false_positives_scan_vmap(self):
    with jax.checking_leaks():
      to_scan = lambda c, _: (1., None)

      @api.vmap
      def f(x):
        lax.scan(to_scan, x, None, length=1)
      f(np.arange(5.))  # doesn't crash

  def test_leak_checker_avoids_false_positives_scan_vmap_2(self):
    with jax.checking_leaks():
      to_scan = lambda c, _: (c, None)

      @api.vmap
      def f(x):
        lax.scan(to_scan, x, None, length=1)
      f(np.arange(5.))  # doesn't crash

  def test_leak_checker_catches_a_sublevel_leak(self):
    with jax.checking_leaks():
      @jit
      def f(x):
        lst = []
        @jit
        def g(x):
          lst.append(x)
          return x

        x = g(x)
        return x

      if jax.config.jax_jit_pjit_api_merge:
        msg = r'Leaked trace MainTrace\(2,DynamicJaxprTrace\)'
      else:
        msg = r'Leaked sublevel'

      with self.assertRaisesRegex(Exception, f"{msg}"):
        f(3)

  def test_leak_checker_avoids_false_positive_custom_jvp(self):
    # see https://github.com/google/jax/issues/5636
    with jax.checking_leaks():
      @api.custom_jvp
      def t(y):
        return y

      def t_jvp(p, t):
        pass

      t.defjvp(t_jvp)

      @jit
      def s(y):
        return t(y)
      s(3)  # doesn't crash

  def test_leak_checker_internal_error(self):
    def apply_fn(inp):
      fn = jax.checkpoint(lambda x: jax.nn.relu(1.0 * x))
      return jax.vjp(fn, inp)

    with jax.check_tracer_leaks():
      jax.jit(apply_fn)(1.0)  # don't crash

  def test_leak_checker_reference_chain(self):
    class A:
      def __init__(self, dct):
        self.dct = dct

    a = A({})
    x = jnp.arange(3)

    def sketch(x):
      def foo():
        return x
      a.dct['hi'] = [foo]
      return x

    # TODO(mattjj): full test msg below fails (harmlessly) on CI, investigate
    msg = (
        r"This BatchTracer with object id [0-9]+ was created on line:\n"
        r"  .*\n"
        r"<BatchTracer [0-9]+> is referred to by"
    )

    # msg = (
    #     r"This BatchTracer with object id [0-9]+ was created on line:\n"
    #     r"  .*\n"
    #     r"<BatchTracer [0-9]+> is referred to by <function [0-9]+> \(foo\) "
    #     r"closed-over variable x\n"
    #     r"<function [0-9]+> is referred to by <list [0-9]+>\[0\]\n"
    #     r"<list [0-9]+> is referred to by <dict [0-9]+>\['hi'\]\n"
    #     r"<dict [0-9]+> is referred to by <A [0-9]+>\.dct\n"
    # )

    with jax.check_tracer_leaks():
      with self.assertRaisesRegex(Exception, msg):
        jax.vmap(sketch)(x)

  def test_default_backend(self):
    first_local_device = jax.local_devices()[0]
    self.assertEqual(first_local_device.platform, jax.default_backend())

  @jtu.skip_on_devices("cpu")
  def test_default_device(self):
    system_default_device = jnp.zeros(2).device()
    test_device = jax.devices("cpu")[-1]

    # Sanity check creating array using system default device
    self.assertEqual(jnp.ones(1).device(), system_default_device)

    # Create array with default_device set
    with jax.default_device(test_device):
      # Hits cached primitive path
      self.assertEqual(jnp.ones(1).device(), test_device)
      # Uncached
      self.assertEqual(jnp.zeros((1, 2)).device(), test_device)

    # Test that we can reset to system default device
    self.assertEqual(jnp.ones(1).device(), system_default_device)

  def test_dunder_jax_array(self):
    # https://github.com/google/jax/pull/4725

    class AlexArray:
      def __init__(self, jax_val):
        self.jax_val = jax_val
      def __jax_array__(self):
        return self.jax_val
      dtype = property(lambda self: self.jax_val.dtype)
      shape = property(lambda self: self.jax_val.shape)

    x = AlexArray(jnp.array([1., 2., 3.]))
    y = jnp.sin(x)
    self.assertAllClose(y, jnp.sin(jnp.array([1., 2., 3.])))
    y = api.grad(api.jit(lambda x: jnp.sin(x).sum()))(x)
    self.assertAllClose(y, jnp.cos(jnp.array([1., 2., 3.])))

    x = AlexArray(jnp.array([[1., 2., 3.]]))
    y = api.pmap(jnp.sin)(x)
    self.assertAllClose(y, jnp.sin(jnp.array([[1., 2., 3.]])))

    x = jnp.array(1)
    a = AlexArray(x)
    for f in [jnp.isscalar, jnp.size, jnp.shape, jnp.dtype]:
      self.assertEqual(f(x), f(a))

    x = AlexArray(jnp.array(1))
    a1 = jnp.array(x)
    self.assertAllClose(1, a1)

    a2 = jnp.array(((x, x), [x, x]))
    self.assertAllClose(np.array(((1, 1), (1, 1))), a2)

  def test_constant_handler_mro(self):
    # https://github.com/google/jax/issues/6129

    class Foo(enum.IntEnum):
      bar = 1

    @api.pmap
    def f(_):
      return Foo.bar

    ans = f(jnp.arange(1))  # doesn't crash
    expected = jnp.arange(1) + 1
    self.assertAllClose(ans, expected, check_dtypes=False)

  @parameterized.named_parameters([
      {"testcase_name": f"{dtype.__name__}", "dtype": dtype}
      for dtype in jtu.dtypes.all])
  def test_constant_handlers(self, dtype):
    # https://github.com/google/jax/issues/9380
    @jax.jit
    def f():
      return jnp.exp(dtype(0))
    f()  # doesn't error

  def test_large_python_ints(self):
    with self.assertRaises(OverflowError):
      jnp.multiply(2 ** 100, 3.)

    out = lax.convert_element_type(2 ** 100, jnp.float32)  # doesn't crash
    self.assertArraysEqual(out, np.float32(2 ** 100))

  def test_dot_precision_context_manager(self):
    x = jnp.zeros((2, 2))

    with jax.default_matmul_precision(None):
      jnp.dot(x, x)  # doesn't crash
      jaxpr = jax.make_jaxpr(jnp.dot)(x, x)
    # self.assertIn('precision=None', str(jaxpr))
    self.assertIs(jaxpr.jaxpr.eqns[0].params['precision'], None)

    with jax.default_matmul_precision("bfloat16"):
      x @ x  # doesn't crash
      jaxpr = jax.make_jaxpr(op.matmul)(x, x)
    self.assertIn('Precision.DEFAULT', str(jaxpr))

    with jax.default_matmul_precision("tensorfloat32"):
      jnp.dot(x, x)  # doesn't crash
      jaxpr = jax.make_jaxpr(jnp.dot)(x, x)
    self.assertIn('Precision.HIGH', str(jaxpr))

    with jax.default_matmul_precision("float32"):
      jnp.dot(x, x)  # doesn't crash
      jaxpr = jax.make_jaxpr(jnp.dot)(x, x)
    self.assertIn('Precision.HIGHEST', str(jaxpr))

    dot = partial(jnp.dot, precision=lax.Precision.HIGHEST)
    with jax.default_matmul_precision("tensorfloat32"):
      dot(x, x)  # doesn't crash
      jaxpr = jax.make_jaxpr(dot)(x, x)
    self.assertIn('Precision.HIGHEST', str(jaxpr))

  def test_dot_precision_flag(self):
    x = jnp.zeros((2, 2))

    prev_val = config._read("jax_default_matmul_precision")
    try:
      config.FLAGS.jax_default_matmul_precision = "tensorfloat32"
      jnp.dot(x, x)  # doesn't crash
      jaxpr = jax.make_jaxpr(jnp.dot)(x, x)
    finally:
      config.FLAGS.jax_default_matmul_precision = prev_val
    self.assertIn('Precision.HIGH', str(jaxpr))
    self.assertEqual(prev_val, config._read("jax_default_matmul_precision"))

    prev_val = config._read("jax_default_matmul_precision")
    try:
      config.update('jax_default_matmul_precision','tensorfloat32')
      jnp.dot(x, x)  # doesn't crash
      jaxpr = jax.make_jaxpr(jnp.dot)(x, x)
    finally:
      config.update('jax_default_matmul_precision', prev_val)
    self.assertIn('Precision.HIGH', str(jaxpr))
    self.assertEqual(prev_val, config._read("jax_default_matmul_precision"))

  def test_dot_precision_forces_retrace(self):
    num_traces = 0

    def g(x):
      nonlocal num_traces
      num_traces += 1
      return jnp.dot(x, x)
    def f_cond(x):
      return lax.cond(True, g, g, x)

    @jax.jit
    def f_jit(x):
      nonlocal num_traces
      num_traces += 1
      return jnp.dot(x, x)

    for f in [f_jit, f_cond]:
      # Use _read() to read the flag value rather than threadlocal value.
      precision = config._read('jax_default_matmul_precision')
      try:
        num_traces = 0
        x = jnp.zeros((2, 2))
        f(x)
        self.assertEqual(num_traces, 1)
        f(x)
        self.assertEqual(num_traces, 1)
        with jax.default_matmul_precision("tensorfloat32"):
          f(x)
          self.assertEqual(num_traces, 2)
          FLAGS.jax_default_matmul_precision = "float32"
          f(x)
          self.assertGreaterEqual(num_traces, 2)
        nt = num_traces
        f(x)
        self.assertEqual(num_traces, nt + 1)
        f(x)
        self.assertEqual(num_traces, nt + 1)
      finally:
        FLAGS.jax_default_matmul_precision = precision

  def test_backward_pass_ref_dropping(self):
    refs = []

    @api.custom_vjp
    def f(x):
      return x
    def f_fwd(x):
      return x, None
    def f_rev(_, g):
      assert len(refs) != 2 or refs[0]() is None
      zero = np.zeros(())
      refs.append(weakref.ref(zero))
      return (zero,)
    f.defvjp(f_fwd, f_rev)

    api.grad(lambda x: f(f(f(x))))(1.)

  def test_jit_inline(self):
    @partial(api.jit, inline=False)
    def f(x):
      return x * 2

    jaxpr = api.make_jaxpr(f)(3)
    if jax.config.jax_jit_pjit_api_merge:
      self.assertIn('pjit', str(jaxpr))
    else:
      self.assertIn('xla_call', str(jaxpr))

    @partial(api.jit, inline=True)
    def f(x):
      return x * 2

    jaxpr = api.make_jaxpr(f)(3)
    if jax.config.jax_jit_pjit_api_merge:
      self.assertNotIn('pjit', str(jaxpr))
    else:
      self.assertNotIn('xla_call', str(jaxpr))

  # Repro for https://github.com/google/jax/issues/7229.
  def test_compute_with_large_transfer(self):
    def f(x, delta):
      return x + jnp.asarray(delta, x.dtype)

    # A large and potentially unaligned array to trigger non-zero-copy and
    # async device array copy.
    xs = self.rng().uniform(0., 1., size=(10, 131, 111, 3)).astype(np.float32)
    for x in xs:
      delta = self.rng().uniform(-0.5, 0.5, size=())
      jitted_f = api.jit(f)
      np.testing.assert_allclose(jitted_f(x, delta), f(x, delta))

  def test_vjp_fun_jit(self):
    # test that the function returned by vjp can be returned
    # from and passed to jitted functions
    f = lambda x: 2. * x

    @partial(jit, static_argnums=0)
    def linearize_vjp(f, x):
      _, vjp_fun = api.vjp(f, x)
      return vjp_fun

    linearized = linearize_vjp(f, 1.)
    actual = jit(lambda f, x: f(x))(linearized, 3.)
    expected = (6.,)
    self.assertEqual(actual, expected)

  def test_linearize_fun_jit(self):
    # test that the function returned by linearize can be returned
    # from and passed to jitted functions
    f = lambda x: 2. * x

    @partial(jit, static_argnums=0)
    def linearize(f, x):
      _, jvp_fun = api.linearize(f, x)
      return jvp_fun

    linearized = linearize(f, 1.)
    actual = jit(lambda f, x: f(x))(linearized, 3.)
    expected = 6.
    self.assertEqual(actual, expected)

  def test_linear_transpose_fun_jit(self):
    # test that the function returned by linear_transpose can be returned
    # from and passed to jitted functions
    f = lambda x: 2. * x

    @partial(jit, static_argnums=0)
    def transpose(f, x):
      return api.linear_transpose(f, x)

    transposed = transpose(f, 1.)
    actual = jit(lambda f, x: f(x))(transposed, 3.)
    expected = (6.,)
    self.assertEqual(actual, expected)

  def test_leaked_tracer_issue_7613(self):
    # from https://github.com/google/jax/issues/7613
    import numpy.random as npr

    def sigmoid(x):
      return 1. / (1. + jnp.exp(-x))

    x = jnp.ones((1, 50))
    A = jnp.array(npr.randn(50, 50), dtype=x.dtype)

    @jax.jit
    def loss(A, x):
      h = jax.nn.sigmoid(A * x)
      return jnp.sum((h - x)**2)

    with jax.checking_leaks():
      _ = jax.grad(loss)(A, x)  # doesn't crash

  def test_vmap_caching(self):
    # https://github.com/google/jax/issues/7621

    f = lambda x: jnp.square(x).mean()
    jf = jax.jit(f)
    x = jax.random.uniform(jax.random.PRNGKey(0), shape=(8, 4))

    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      for _ in range(5):
        jax.hessian(jf)(x).block_until_ready()

      n = count[0]
      # The exact number of compilations may vary depending on the number of
      # jit decorators in the function above, but it should not grow after an
      # initial warmup phase.
      for _ in range(5):
        jax.hessian(jf)(x).block_until_ready()

    self.assertEqual(count[0], n)

  def test_jnp_array_doesnt_device_put(self):
    with jtu.count_device_put() as count:
      api.make_jaxpr(lambda: jnp.array(3))()
    self.assertEqual(count[0], 0)

  def test_rank_promotion_forces_retrace(self):
    num_traces = 0

    def g(x):
      nonlocal num_traces
      num_traces += 1
      return x + x
    def f_cond(x):
      return lax.cond(True, g, g, x)

    @jax.jit
    def f_jit(x):
      nonlocal num_traces
      num_traces += 1
      return x + x

    for f in [f_jit, f_cond]:
      # Use _read() to read the flag value rather than threadlocal value.
      allow_promotion = config._read('jax_numpy_rank_promotion')
      try:
        FLAGS.jax_numpy_rank_promotion = "allow"
        num_traces = 0
        @jax.jit
        def f(x):
          nonlocal num_traces
          num_traces += 1
          return x + x
        x = jnp.zeros((2, 2))
        f(x)
        self.assertEqual(num_traces, 1)
        f(x)
        self.assertEqual(num_traces, 1)
        with jax.numpy_rank_promotion("warn"):
          f(x)
          self.assertEqual(num_traces, 2)
          FLAGS.jax_numpy_rank_promotion = "raise"
          f(x)
          self.assertGreaterEqual(num_traces, 2)
        nt = num_traces
        f(x)
        self.assertEqual(num_traces, nt + 1)
        f(x)
        self.assertEqual(num_traces, nt + 1)
      finally:
        FLAGS.jax_numpy_rank_promotion = allow_promotion

  def test_grad_negative_argnums(self):
    def f(x, y):
      return x.sum() * y.sum()

    x = jax.random.normal(jax.random.PRNGKey(0), (16, 16))
    y = jax.random.normal(jax.random.PRNGKey(1), (16, 16))
    g = jax.grad(f, argnums=-1)
    g(x, y)  # doesn't crash

  def test_jit_negative_static_argnums(self):
    g = jax.jit(lambda x, y: x * y, static_argnums=-1)
    g(1, 2)  # doesn't crash

  def test_fastpath_cache_confusion(self):
    # https://github.com/google/jax/issues/12542
    @jax.jit
    def a(x):
      return ()

    @jax.jit
    def b(x):
      return a(x)


    @jax.jit
    def g(x):
      return x, x

    @jax.jit
    def h(x):
      return g(x)

    jaxpr = jax.make_jaxpr(h)(7)
    core.eval_jaxpr(jaxpr.jaxpr, jaxpr.consts, 7)

    b(8)  # don't crash

  def test_fastpath_cache_confusion2(self):
    @jax.jit
    def a():  # note nullary function, still staged out though
      return ()

    @jax.jit
    def b(x):
      return a()


    @jax.jit
    def g(x):
      return x, x

    @jax.jit
    def h(x):
      return g(x)

    jaxpr = jax.make_jaxpr(h)(7)
    core.eval_jaxpr(jaxpr.jaxpr, jaxpr.consts, 7)

    b(8)  # don't crash

  def test_vjp_multiple_arguments_error_message(self):
    # https://github.com/google/jax/issues/13099
    def foo(x):
      return (x, x)
    _, f_vjp = jax.vjp(foo, 1.0)
    with self.assertRaisesRegex(TypeError, "applied to foo"):
      f_vjp(1.0, 1.0)

  def test_shapedtypestruct_sharding_error(self):
    with self.assertRaisesRegex(
        ValueError,
        "sharding should be an instance of `jax.sharding.Sharding`."):
      jax.ShapeDtypeStruct((8, 2), np.float32,
                           sharding=jax.sharding.PartitionSpec('x'))


class RematTest(jtu.JaxTestCase):

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_basic(self, remat):
    @remat
    def g(x):
      return lax.sin(lax.sin(x)), 3.

    def f(x):
      x, _ = g(x)
      return x

    ans = f(2.)
    expected = np.sin(np.sin(2.))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans, f_lin = api.linearize(f, 2.)
    expected = np.sin(np.sin(2.))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = f_lin(3.)
    expected = np.cos(np.sin(2.)) * np.cos(2.) * 3.
    self.assertAllClose(ans, expected, check_dtypes=False)

    sin_calls = []
    cos_calls = []
    sin_impl = lax.sin_p.impl
    cos_impl = lax.cos_p.impl
    try:
      lax.sin_p.def_impl(lambda x: sin_calls.append(1) or sin_impl(x))
      lax.cos_p.def_impl(lambda x: cos_calls.append(1) or cos_impl(x))
      f_lin(3.)
    finally:
      lax.sin_p.def_impl(sin_impl)
      lax.cos_p.def_impl(cos_impl)
    self.assertEqual(len(sin_calls), 1)
    self.assertEqual(len(cos_calls), 2)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_freevars(self, remat):
    def f1(x):
      y = 2 * jnp.sin(x)
      z = jnp.cos(x) * jnp.sin(y)
      return z

    def f2(x):
      y = 2 * jnp.sin(x)
      z = remat(lambda x: jnp.cos(x) * jnp.sin(y))(x)
      return z

    ans, f_lin = api.linearize(f2, 2.)
    expected, f_lin_expected = api.linearize(f1, 2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = f_lin(3.)
    expected = f_lin_expected(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_remat_concrete_error(self):
    @api.remat  # no static_argnums or concrete
    def g(x):
      if x > 0:
        return lax.sin(x)
      else:
        return lax.cos(x)

    with self.assertRaisesRegex(core.ConcretizationTypeError, "static_argnums"):
      g(3.)

    @partial(api.remat, static_argnums=(0,))  # using static_argnums but...
    def g(x):
      if x > 0:  # jnp operations still get staged!
        return lax.sin(x)
      else:
        return lax.cos(x)

    with self.assertRaisesRegex(core.ConcretizationTypeError, "static_argnums"):
      g(jnp.array(3.))

    # But don't raise an error mentioning static_argnums here:
    @api.remat
    def g(x):
      jax.jit(lambda: 0 if jnp.add(1, 1) else 0)()
      return lax.sin(x)

    try:
      g(jnp.array(3.))
    except core.ConcretizationTypeError as e:
      msg = str(e)
    self.assertNotIn('static_argnums', msg)

  def test_remat_grad_python_control_flow_static_argnums(self):
    @partial(api.remat, static_argnums=(0,))
    def g(x):
      with jax.ensure_compile_time_eval():
        x_pos = x > 0
      if x_pos:
        return lax.sin(x), 3.
      else:
        return lax.cos(x), 4.

    def f(x):
      x, _ = g(x)
      return x

    ans = f(2.)
    expected = np.sin(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(f)(2.)
    expected = np.cos(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_remat_grad_python_control_flow_unhashable_static_argnums(self):
    @partial(api.remat, static_argnums=(0,))
    def g(x):
      x = x.val
      with jax.ensure_compile_time_eval():
        x_pos = x > 0
      if x_pos:
        return lax.sin(x), 3.
      else:
        return lax.cos(x), 4.

    def f(x):
      x, _ = g(x)
      return x

    class A:
      def __init__(self, val):
        self.val = val
      def __hash__(self):
        raise TypeError

    ans = f(A(2.))
    expected = np.sin(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: f(A(x)))(2.)
    expected = np.cos(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_remat_retracing(self):
    # This is *not* a very important behavior; remat doesn't need to provide
    # caching guarantees with the same importance as jit. But even so, in the
    # interest of not redoing tracing work (and thus make jax.remat more
    # feasible to use in eager mode), this test checks that we don't re-trace
    # the remat-decorated function.
    count = 0

    @api.remat
    def g(x):
      nonlocal count
      count += 1
      return lax.sin(x), 3.

    def f(x):
      x, _ = g(x)
      return x

    for _ in range(10):
      y = f(2.)
      y.block_until_ready()
    self.assertEqual(count, 1)

  def test_remat_static_agnums_retracing(self):
    # This is *not* a super important behavior; remat doesn't need to provide
    # caching guarantees with the same importance as jit. But even so, in the
    # interest of not redoing tracing work (and thus make jax.remat more
    # feasible to use in eager mode), this test checks that we don't re-trace
    # the remat-decorated function *even with static_argnums*. See also the
    # above test, which doesn't check for static_argnums.
    count = 0

    @partial(api.remat, static_argnums=(0,))
    def g(x):
      nonlocal count
      count += 1
      with jax.ensure_compile_time_eval():
        x_pos = x > 0
      if x_pos:
        return lax.sin(x), 3.
      else:
        return lax.cos(x), 4.

    def f(x):
      x, _ = g(x)
      return x

    for _ in range(10):
      y = f(2.)
      y.block_until_ready()
    self.assertEqual(count, 1)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_jit(self, remat):
    @remat
    def g(x):
      return lax.sin(lax.sin(x))

    def f_(x):
      return g(x)
    f = api.jit(f_)

    ans = f(2.)
    expected = np.sin(np.sin(2.))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(f)(2.)
    expected = np.cos(np.sin(2.)) * np.cos(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jit(api.grad(f_))(2.)
    expected = np.cos(np.sin(2.)) * np.cos(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_vmap(self, remat):
    @remat
    def g(x):
      return lax.sin(lax.sin(x))

    x = np.arange(3.)

    ans = api.vmap(g)(x)
    expected = np.sin(np.sin(x))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jacfwd(g)(x)
    expected = np.diag(np.cos(np.sin(x)) * np.cos(x))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jacrev(g)(x)
    expected = np.diag(np.cos(np.sin(x)) * np.cos(x))
    self.assertAllClose(ans, expected, check_dtypes=False)

    # Make sure that introducing constants in vmap works.
    constant_introducing_p = core.Primitive('introduce_constant')
    constant_introducing_p.def_abstract_eval(core.raise_to_shaped)
    def _constant_introducing_batcher(xs, ds):
      (x,), (d,) = xs, ds
      return (x + np.arange(x.size, dtype=x.dtype).reshape(x.shape)), d
    batching.primitive_batchers[constant_introducing_p] = _constant_introducing_batcher

    api.vmap(remat(constant_introducing_p.bind))(jnp.ones(20))

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_vmap_not_leading_dim(self, remat):
    @remat
    def g(x):
      return lax.sin(lax.sin(x))

    x = np.arange(3 * 5.).reshape(3, 5)

    ans = api.vmap(g, 1, 0)(x)
    expected = np.sin(np.sin(x)).T
    self.assertAllClose(ans, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_higher_order_autodiff(self, remat):
    def f(x):
      return lax.cos(lax.sin(x))
    g = remat(f)

    ans = api.grad(api.grad(g))(3.)
    expected = api.grad(api.grad(f))(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_scan(self, remat):
    to_scan = lambda c, x: (jnp.sin(c), None)

    def f_noremat(x):
      y, _ = lax.scan(to_scan, x, np.arange(3.))
      return y

    def f_yesremat(x):
      y, _ = lax.scan(remat(to_scan), x, np.arange(3.))
      return y

    ans = f_yesremat(4.)
    expected = f_noremat(4.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(f_yesremat)(4.)
    expected = api.grad(f_noremat)(4.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    jaxpr = api.make_jaxpr(api.linearize(f_yesremat, 4.)[1])(1.)
    scan_eqn, = jaxpr.jaxpr.eqns
    self.assertIn(' cos ', str(scan_eqn.params['jaxpr']))

    jaxpr = api.make_jaxpr(api.vjp(f_yesremat, 4.)[1])(1.)
    scan_eqn, = jaxpr.jaxpr.eqns
    self.assertIn(' cos ', str(scan_eqn.params['jaxpr']))

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_no_redundant_flops(self, remat):
    # see https://github.com/google/jax/pull/1749#issuecomment-558267584

    @api.jit
    def g(x):
      return f(2., x)

    @remat
    def f(x, y):
      return jnp.sin(x) * y

    # We swap out sin_p's impl rule to count how many times it's invoked
    called = []
    sin_impl = lax.sin_p.impl
    try:
      lax.sin_p.def_impl(lambda x: called.append(1) or sin_impl(x))
      api.grad(g)(3.)
    finally:
      lax.sin_p.def_impl(sin_impl)
    num_calls = len(called)
    self.assertLessEqual(num_calls, 1)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_binomial_checkpointing(self, remat):
    def binom_checkpoint(funs):
      if len(funs) == 1:
        return funs[0]
      else:
        f1 = binom_checkpoint(funs[:len(funs)//2])
        f2 = binom_checkpoint(funs[len(funs)//2:])
        return remat(lambda x: f1(f2(x)))

    f1 = binom_checkpoint([jnp.sin, jnp.sin, jnp.sin, jnp.sin])
    f2 = lambda x: jnp.sin(jnp.sin(jnp.sin(jnp.sin(x))))
    x = 4.
    self.assertAllClose(f1(x), f2(x), check_dtypes=False)
    self.assertAllClose(api.grad(f1)(x), api.grad(f2)(x), check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_symbolic_zeros(self, remat):
    # code from https://github.com/google/jax/issues/1907

    key = jax.random.PRNGKey(0)
    key, split = jax.random.split(key)
    n = 5

    def func(D0):
      def shift(R, dR, **unused_kwargs):
        return R + dR

      def apply_fn(R):
        return D0 * R

      Rinit = jax.random.uniform(split, (n,3), minval=0.0, maxval=5.0,
                                 dtype=jnp.float32)

      def move(R,i):
        F = apply_fn(R)
        return shift(R, 0.001 * F), jnp.array([0.])

      move = remat(move)
      R, temp = lax.scan(move, Rinit, jnp.arange(2))
      return R[0, 0]

    api.grad(func)(5.0)  # doesn't crash

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_jit2(self, remat):
    @api.jit
    def f(x):
      y = 2 * x

      @remat
      def g():
        return y

      return g()

    self.assertAllClose(f(3), 6, check_dtypes=False)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_nontrivial_env(self, remat):
    # simplified from https://github.com/google/jax/issues/2030

    @remat
    def foo(state, dt=0.5, c=1):
      u, u_t = state
      u_tt = c**2 * u
      u_t = u_t + u_tt * dt
      return (u, u_t)

    @partial(api.jit, static_argnums=(1,))
    def _multi_step(state, count, dt, c):
      f = lambda s, _: (foo(s, dt, c), _)
      return lax.scan(f, state, None, count)

    def multi_step(state, count, dt=1/jnp.sqrt(2), c=1):
      return _multi_step(state, count, dt, c)

    def loss(u0, target, steps, dt=1/jnp.sqrt(2), c=1):
      init = (u0, jnp.zeros_like(u0))
      (uf, _), _ = multi_step(init, steps, dt, c)
      return ((uf - target) ** 2).mean()

    target = jnp.zeros((128, 128))
    u0 = jnp.ones_like(target)
    loss(u0, target, 10)  # doesn't crash

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_jit3(self, remat):
    # https://github.com/google/jax/issues/2180
    def f(w, x):
      a = jnp.dot(x, w)
      b = jnp.einsum("btd,bTd->btT", a, a)
      c = jnp.einsum("btT,btd->btd", b, a)
      return jnp.sum(c)

    w = jnp.ones([1, 1])
    x = jnp.ones([1, 1, 1])
    f = remat(f)
    api.grad(f)(w, x)  # doesn't crash

    @api.jit
    def mul(a, b):
      return a * b

    def f(w, x):
      a = mul(w, x)
      b = mul(a, a)
      return b

    w = 1.
    x = 1.
    f = remat(f)
    api.grad(f)(w, x)  # doesn't crash

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_scan2(self, remat):
    # https://github.com/google/jax/issues/1963

    def scan_bug(x0):
      f = lambda x, _: (x + 1, None)
      def scanned_f(x, _):
        return lax.scan(f, x, xs=None, length=1)[0], None
      x, _ = remat(scanned_f)(x0, None)
      return x

    jax.grad(scan_bug)(1.0)  # doesn't crash

  def test_remat_jit_static_argnum_omnistaging(self):
    # https://github.com/google/jax/issues/2833
    # NOTE(mattjj): after #3370, this test doesn't actually call remat...
    def named_call(f):
      def named_f(*args):
        f_ = lu.wrap_init(lambda: (f(*args),))
        out, = core.call_p.bind(f_)
        return out
      return named_f

    def f(a_bool, y):
      if a_bool:
        return y + 1
      else:
        return y

    api.jit(named_call(f), static_argnums=0)(True, 1)  # no crash

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_remat_eval_counter(self, remat):
    # https://github.com/google/jax/issues/2737
    add_one_p = core.Primitive('add_one')
    add_one = add_one_p.bind

    num_evals = 0

    @contextmanager
    def assertEvals(n):
      start = num_evals
      yield
      assert num_evals - start == n

    def add_one_impl(x):
      nonlocal num_evals
      num_evals += 1
      return x + 1
    add_one_p.def_impl(add_one_impl)

    def add_one_jvp(pin, tin):
      pout = add_one(pin[0])
      return pout, pout * tin[0]
    ad.primitive_jvps[add_one_p] = add_one_jvp

    add_one_p.def_abstract_eval(lambda x: x)

    v = np.zeros((1,))

    f = remat(add_one)
    g = remat(lambda x: add_one(f(x)))

    # 2 calls needed to evaluate g
    with assertEvals(2):
      _, vjp = jax.vjp(g, v)
    # 2 calls made while transposing g, 1 call made while transposing f
    with assertEvals(3):
      vjp(v)

    @jax_util.curry
    def call(f, *args):
      return core.call(
          lu.wrap_init(lambda *args: [f(*args)]),
          *args, name='foo')[0]

    f = call(add_one)
    g = remat(lambda x: add_one(f(x)))

    # 2 calls needed to evaluate g
    with assertEvals(2):
      _, vjp = jax.vjp(g, v)
    # 2 calls made while transposing g, no reevaluation for transposition of f
    with assertEvals(2):
      vjp(v)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_escaped_tracer_remat(self, remat):
    # b/169779185
    def f():
      seq = [jnp.zeros([])]
      def g():
        seq[0] += 1  # this is line 7 btw
        return seq[0]

      remat(g)()
      remat(lambda: g())()  # lambda defeats caching

    with self.assertRaisesRegex(UnexpectedTracerError, "global state"):
      api.jit(f)()

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_no_cse_widget_on_primals(self, remat):
    @remat
    def g(x):
      return lax.sin(lax.sin(x)), 3.

    def f(x):
      x, _ = g(x)
      return x

    c = api.xla_computation(f)(2.)
    self.assertNotIn('while', c.as_hlo_text())
    self.assertNotIn('conditional', c.as_hlo_text())
    self.assertNotIn('opt-barrier', c.as_hlo_text())

    c = api.xla_computation(grad(f))(2.)
    text = c.as_hlo_text()
    self.assertTrue('while' in text or 'conditional' in text
                    or 'opt-barrier' in text)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_no_cse_widget_with_prevent_cse_false(self, remat):
    @partial(remat, prevent_cse=False)
    def g(x):
      return lax.sin(lax.sin(x)), 3.

    def f(x):
      x, _ = g(x)
      return x

    c = api.xla_computation(f)(2.)
    self.assertNotIn('while', c.as_hlo_text())
    self.assertNotIn('conditional', c.as_hlo_text())

    c = api.xla_computation(grad(f))(2.)
    self.assertNotIn('while', c.as_hlo_text())
    self.assertNotIn('conditional', c.as_hlo_text())

  @parameterized.named_parameters(
      {"testcase_name": f"_{policy_name}_{remat_name}", "remat": remat,
       "policy": policy, "in_jaxpr2": in_jaxpr2, "not_in_jaxpr2": not_in_jaxpr2}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ]
      for policy_name, policy, in_jaxpr2, not_in_jaxpr2 in [
          ('save_anything', lambda *_, **__: True, [], [' sin ', ' cos ']),
          ('save_nothing',  lambda *_, **__: False, [' sin ', ' cos '], []),
          ('save_sin',  lambda p, *_, **__: str(p) == 'sin', [' cos '], [' sin ']),
      ])
  def test_remat_custom_policy(self, remat, policy, in_jaxpr2, not_in_jaxpr2):
    for square in [lambda x: x * x, api.jit(lambda x: x * x)]:
      f = remat(lambda x: jnp.sin(square(jnp.sin(x))), policy=policy)
      y, f_lin = api.linearize(f, 1.)
      ydot = f_lin(2.)
      jaxpr_text = str(f_lin.func.args[0])
      for substr in in_jaxpr2:
        self.assertIn(substr, jaxpr_text)
      for substr in not_in_jaxpr2:
        self.assertNotIn(substr, jaxpr_text)
      y_expected, ydot_expected = api.jvp(lambda x: jnp.sin(square(jnp.sin(x))),
                                          [1.], [2.])
      self.assertAllClose(y, y_expected)
      self.assertAllClose(ydot, ydot_expected)
      jtu.check_grads(f, (3.,), order=2, modes=['fwd', 'rev'])

  @parameterized.named_parameters(
      {"testcase_name": f"_{remat_name}", "remat": remat}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ])
  def test_remat_custom_policy_save_cos(self, remat):
    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    f = remat(lambda x: jnp.sin(jnp.sin(x)),  # different function
              policy=save_cos)
    _, f_lin = api.linearize(f, 1.)
    jaxpr_text = str(f_lin.func.args[0])
    self.assertNotIn(' sin ', jaxpr_text)
    self.assertNotIn(' cos ', jaxpr_text)
    jtu.check_grads(f, (3.,), order=2, modes=['fwd', 'rev'])

  @parameterized.named_parameters(
      {"testcase_name": f"_{remat_name}", "remat": remat}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ])
  def test_remat_checkpoint_dots(self, remat):
    @partial(remat, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(x):
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      return x

    _, f_lin = api.linearize(f, jnp.ones((2, 2)))
    jaxpr_text = str(f_lin.func.args[0])
    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' dot_'), 6)
    jtu.check_grads(f, (jnp.ones((2, 2)),), order=2, modes=['fwd', 'rev'])

  @parameterized.named_parameters(
      {"testcase_name": f"_{remat_name}", "remat": remat}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ])
  def test_remat_checkpoint_dots_with_no_batch_dims(self, remat):
    @partial(remat, policy=jax.checkpoint_policies.checkpoint_dots_with_no_batch_dims)
    def f(x):
      x = jnp.einsum('ij,jk->ik', x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      x = jnp.einsum('ij,jk->ik', x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      x = jnp.einsum('ij,jk->ik', x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      return x

    _, f_lin = api.linearize(f, jnp.ones((2, 2)))
    jaxpr_text = str(f_lin.func.args[0])
    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' dot_general'), 6)
    jtu.check_grads(f, (jnp.ones((2, 2)),), order=2, modes=['fwd', 'rev'])

  @parameterized.named_parameters(
      {"testcase_name": f"_{remat_name}", "remat": remat}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ])
  def test_remat_checkpoint_dots_with_no_batch_dims2(self, remat):
    @partial(remat, policy=jax.checkpoint_policies.checkpoint_dots_with_no_batch_dims)
    def f(x):
      x = jnp.einsum('nij,njk->nik', x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      x = jnp.einsum('nij,njk->nik', x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      x = jnp.einsum('nij,njk->nik', x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x)
      return x

    _, f_lin = api.linearize(f, jnp.ones((3, 2, 2)))
    jaxpr_text = str(f_lin.func.args[0])
    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' dot_general'), 9)
    jtu.check_grads(f, (jnp.ones((3, 2, 2)),), order=2, modes=['fwd', 'rev'])

  @parameterized.named_parameters(
      {"testcase_name": f"_{remat_name}", "remat": remat}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ])
  def test_remat_checkpoint_dots_jit(self, remat):
    @api.jit
    @partial(remat, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(x):
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x * 1e-3)
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x * 1e-3)
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = jnp.sin(x * 1e-3)
      return x

    _, f_lin = api.linearize(f, jnp.ones((2, 2)))
    jaxpr_text = str(f_lin.func.args[0])
    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' dot_'), 6)
    jtu.check_grads(f, (jnp.ones((2, 2)),), order=2, modes=['fwd', 'rev'])

  def test_remat_checkpoint_dots_inside_scan(self):
    x = jnp.ones((5,))

    def f(W):
      @partial(api.remat, policy=jax.checkpoint_policies.checkpoint_dots)
      def f(x):
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        return x

      def body(x, _): return f(x), None
      return lax.scan(body, x, None, length=2)[0]

    _, f_vjp = api.vjp(f, jnp.ones((5, 5)))
    jaxpr_text = str(f_vjp.args[0].func.args[1])

    # Two sine calls in the backward pass because while we don't save sines
    # within the (rematted) body function, we can save the scan carry, which
    # effectively saves one sine. Three cosines for the Jacobian coefficients.
    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' cos '), 3)
    # Six calls to dot_general in the backward pass because we save the primal
    # matmuls and only compure the backward pass ones (two for each primal one).
    self.assertEqual(jaxpr_text.count(' dot_'), 6)

    jtu.check_grads(api.jit(f), (jnp.ones((5, 5)),), order=2,
                    modes=['fwd', 'rev'])

  def test_remat_custom_jvp_policy(self):
    @api.custom_jvp
    def sin(x):
      return jnp.sin(x)
    def sin_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return sin(x), jnp.cos(x) * g
    sin.defjvp(sin_jvp)

    @partial(api.remat, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(x):
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = sin(x * 1e-3)
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = sin(x * 1e-3)
      x = jnp.dot(x, x, precision=lax.Precision.HIGHEST)
      x = sin(x * 1e-3)
      return x

    jtu.check_grads(f, (3.,), order=2, modes=['fwd', 'rev'])

    def g(x):
      return lax.scan(lambda x, _: (f(x), None), x, None, length=2)[0]
    jtu.check_grads(g, (3.,), order=2, modes=['fwd', 'rev'])

  def test_remat_custom_vjp_policy(self):
    @api.custom_vjp
    def sin(x):
      return jnp.sin(x)
    def sin_fwd(x):
      return sin(x), x
    def sin_bwd(x, y_bar):
      return (jnp.cos(x) * y_bar,)
    sin.defvjp(sin_fwd, sin_bwd)

    @partial(api.remat, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(x):
      @partial(api.named_call, name="dot")
      def dot2(y, z):
        return jnp.dot(x, jnp.dot(y, z, precision=lax.Precision.HIGHEST),
                       precision=lax.Precision.HIGHEST)

      x = dot2(x, x)
      x = sin(x * 1e-3)
      x = dot2(x, x)
      x = sin(x * 1e-3)
      x = dot2(x, x)
      x = sin(x * 1e-3)
      return x

    jtu.check_grads(f, (3.,), order=2, modes=['rev'])

    def g(x):
      return lax.scan(lambda x, _: (f(x), None), x, None, length=2)[0]
    jtu.check_grads(g, (3.,), order=2, modes=['rev'])

  @parameterized.named_parameters(
      {"testcase_name": f"_{remat_name}", "remat": remat}
      for remat_name, remat in [
          ('old_remat', api.remat),
          ('new_remat', new_checkpoint),
      ])
  def test_remat_dropvar_policy(self, remat):
    def f(x):
      return x, x

    @partial(remat, policy=jax.checkpoint_policies.checkpoint_dots)
    def g(x):
      x = api.grad(lambda x: f(x)[0])(x)
      return x

    api.grad(g)(3.)

  def test_remat_custom_jvp_linear_policy(self):
    @api.custom_jvp
    def sum(x):
      return jnp.sum(x, axis=0)
    @sum.defjvp
    def sum_jvp(primals, tangents):
      (x,), (xdot,) = primals, tangents
      return sum(x), sum(xdot)

    @partial(api.remat, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(x):
      return sum(x)
    jtu.check_grads(f, (jnp.ones(3),), order=2, modes=['fwd', 'rev'])

    def g(x):
      return lax.scan(lambda _, x: (None, f(x)), None, x)[1]
    jtu.check_grads(g, (jnp.ones((2, 3)),), order=2, modes=['fwd', 'rev'])

  def test_constants_not_hoisted(self):
    # The old implementation of remat worked by data dependence, and so
    # (potentially large) constants would not be rematerialized and could be
    # wastefully instantiated. This test checks that the newer remat
    # implementation avoids that. See https://github.com/google/jax/pull/8191.

    # no residuals from constants created inside jnp.einsum
    @partial(new_checkpoint, policy=lambda *_, **__: False)
    def f(x):
      return jnp.einsum('ii->i', x)
    res_avals = saved_residuals(f, jnp.ones((2, 2)))
    self.assertLen(res_avals, 0)

    # no residuals from jnp.zeros
    @partial(new_checkpoint, policy=lambda *_, **__: False)
    def f(x):
      return jnp.zeros_like(x) * x
    res_avals = saved_residuals(f, jnp.ones((2, 2)))
    self.assertLen(res_avals, 0)

    # no residuals from jnp.zeros, but input must be saved
    @partial(new_checkpoint, policy=lambda *_, **__: False)
    def f(x):
      return jnp.zeros_like(x) * jnp.sin(x)
    res_avals = saved_residuals(f, jnp.ones((2, 2)))
    self.assertLen(res_avals, 1)

  def test_name_denylist(self):
    def f(x):
      y = checkpoint_name(jnp.multiply(2., 2.), 'y')
      z = checkpoint_name(jnp.multiply(2., 2.), 'z')
      w = checkpoint_name(jnp.multiply(2., 2.), 'w')
      u = jnp.multiply(2., 2.)
      return (((x * y) * z) * w) * u

    policy = jax.checkpoint_policies.save_any_names_but_these('y', 'z', 'w')
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 0)  # can't save anything

    policy = jax.checkpoint_policies.save_any_names_but_these('z', 'w')
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 1)  # can save only y

    policy = jax.checkpoint_policies.save_any_names_but_these('w')
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 2)  # can save y and z

    policy = jax.checkpoint_policies.save_any_names_but_these()
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 3)  # can save y, z, and w

  def test_name_allowlist(self):
    def f(x):
      y = checkpoint_name(jnp.multiply(2., 2.), 'y')
      z = checkpoint_name(jnp.multiply(2., 2.), 'z')
      w = checkpoint_name(jnp.multiply(2., 2.), 'w')
      u = jnp.multiply(2., 2.)
      return (((x * y) * z) * w) * u

    policy = jax.checkpoint_policies.save_only_these_names('y', 'z', 'w')
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 3)  # can save y, z, and w

    policy = jax.checkpoint_policies.save_only_these_names('z', 'w')
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 2)  # can save z and w

    policy = jax.checkpoint_policies.save_only_these_names('w')
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 1)  # can save w

    policy = jax.checkpoint_policies.save_only_these_names()
    res = saved_residuals(new_checkpoint(f, policy=policy), 1.)
    self.assertLen(res, 0)  # can't save anything!

  def test_saved_residuals_utility(self):
    def f(x, y):
      x1, x2 = x
      z = checkpoint_name(jnp.sin(3.), 'z')
      return z * ((x1 * x2) * y) * np.array([3.])

    res = saved_residuals(f, (2., 3.), y=4.)
    self.assertLen(res, 6)
    self.assertEqual(res[0][0].shape, (1,))
    self.assertEqual(res[0][1], "from a constant")
    self.assertEqual(res[1][0].shape, ())
    self.assertEqual(res[1][1], "from the argument 'x'")
    self.assertEqual(res[2][0].shape, ())
    self.assertEqual(res[2][1], "from the argument 'x'")
    self.assertEqual(res[3][0].shape, ())
    self.assertEqual(res[3][1], "from the argument 'y'")
    self.assertEqual(res[4][0].shape, ())
    self.assertStartsWith(res[4][1], "named 'z'")
    self.assertEqual(res[5][0].shape, ())

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_policy', partial(api.remat, policy=lambda *_, **__: False)),
          ('_new', partial(new_checkpoint, policy=lambda *_, **__: False)),
      ])
  def test_checkpoint_dropvars(self, remat):
    @remat
    def f(x):
      _, x = api.jit(lambda: (x, x))()
      return x

    _ = api.grad(f)(3.)  # doesn't crash

  def test_dce_keeps_eqns_with_used_outputs_but_no_used_inputs(self):
    @new_checkpoint
    def f(x):
      c = jax.jit(lambda: 3.)()
      return c * x

    _ = jax.grad(f)(3.)  # doesn't crash

  def test_linearize_caching(self):
    # https://github.com/google/jax/issues/9661
    identity = jax.checkpoint(jax.jit(lambda x: 2 * x))
    _, f_lin = jax.linearize(identity, 1.)
    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      for _ in range(20):
        f_lin(1.).block_until_ready()
    self.assertEqual(count[0], 1)  # cached after first execution

  def test_vjp_caching(self):
    # https://github.com/google/jax/issues/9661
    identity = jax.checkpoint(jax.jit(lambda x: 2 * x))
    _, f_vjp = jax.vjp(identity, 1.)
    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      for _ in range(20):
        f_vjp(1.)[0].block_until_ready()
    self.assertEqual(count[0], 1)  # fwd execute_trivial, backward_pass on bwd

  def test_vjp_caching_static_argnums(self):
    identity = jax.remat(lambda x, y: jax.jit(lambda x: 2 * x if y else x)(x),
                         static_argnums=(1,))
    _, f_vjp = jax.vjp(identity, 1., True)
    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      for _ in range(20):
        f_vjp(1.)[0].block_until_ready()
    self.assertEqual(count[0], 1)  # fwd execute_trivial, backward_pass on bwd

  def test_fwd_caching(self):
    # see above test also
    identity = jax.checkpoint(jax.jit(lambda x: 2 * x))
    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      for _ in range(20):
        y, _ = jax.vjp(identity, 1.)
        y.block_until_ready()
    self.assertEqual(count[0], 1)

  def test_fwd_caching_static_argnums(self):
    # see above test also
    identity = jax.checkpoint(jax.jit(lambda x: 2 * x), static_argnums=(0,))
    with jtu.count_jit_and_pmap_compiles() as count:  # noqa: F841
      for _ in range(20):
        y = identity(1.)
        y.block_until_ready()
    self.assertEqual(count[0], 1)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_of_scan(self, remat):
    to_scan = lambda c, _: (jnp.sin(c), jnp.sin(c))
    f = lambda x: lax.scan(to_scan, x, None, length=3)
    jtu.check_grads(remat(f), (3.,), order=2, modes=['rev'])

    jaxpr = api.make_jaxpr(api.linearize(remat(f), 4.)[1])(1.)
    self.assertIn(' sin ', str(jaxpr))
    self.assertIn(' cos ', str(jaxpr))

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_const_in_jvp_scan(self, remat):
    @api.custom_jvp
    def f(x):
      return x * jnp.arange(3.)
    @f.defjvp
    def f_jvp(primals, tangents):
      (x,), (xdot,) = primals, tangents
      return f(x), xdot * jnp.arange(3.)

    @remat
    def g(x):
      def body(c, _):
        return f(c), None
      y, _ = jax.lax.scan(body, x, None, length=1)
      return y.sum()

    jax.grad(g)(jnp.arange(3.))  # doesn't crash

  def test_remat_checkpoint_dots_outside_scan(self):
    # see also above test test_remat_checkpoint_dots_inside_scan
    x = jnp.ones((5,))

    @partial(new_checkpoint, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(W):
      def f(x):
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        return x

      def body(x, _): return f(x), None
      return lax.scan(body, x, None, length=2)[0]

    _, f_vjp = api.vjp(f, jnp.ones((5, 5)))
    jaxpr = f_vjp.args[0].func.args[1]
    jaxpr_text = str(jaxpr)

    self.assertEqual(jaxpr_text.count(' sin '), 3)
    self.assertEqual(jaxpr_text.count(' cos '), 3)
    # Six calls to dot_general in the backward pass because we save the primal
    # matmuls and only compure the backward pass ones (two for each primal one).
    self.assertEqual(jaxpr_text.count(' dot_'), 6)

    jtu.check_grads(api.jit(f), (jnp.ones((5, 5)),), order=2,
                    modes=['fwd', 'rev'])

  def test_remat_of_scan_policy(self):
    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    to_scan = lambda c, _: (jnp.sin(c), jnp.sin(c))
    f = new_checkpoint(lambda x: lax.scan(to_scan, x, None, length=3),
                       policy=save_cos)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])

    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

  def test_remat_of_scan_funky_custom_jvp(self):
    def scan_apply(f, x):
      y, _ = lax.scan(lambda x, _: (f(x), None), x, None, length=1)
      return y

    @api.custom_jvp
    def sin(x):
      return jnp.sin(x)
    def sin_jvp(primals, tangents):
      x, = primals
      xdot, = tangents
      y, c = jax.jit(lambda: (jnp.sin(x), jnp.cos(x)))()
      ydot = c * xdot
      return y, ydot
    sin.defjvp(sin_jvp)

    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    f = new_checkpoint(partial(scan_apply, sin), policy=save_cos)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    save_sin = lambda prim, *_, **__: str(prim) == 'sin'
    f = new_checkpoint(partial(scan_apply, sin), policy=save_sin)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(partial(scan_apply, sin),
                       policy=jax.checkpoint_policies.everything_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    f = new_checkpoint(partial(scan_apply, sin),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 1)  # +1 b/c dce fixed point
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(lambda x: scan_apply(sin, scan_apply(sin, x)),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 2)  # +1 b/c dce fixed point
    self.assertEqual(jaxpr_text.count(' cos '), 2)

  def test_remat_of_scan_funky_custom_jvp2(self):
    # Like the above test but instead of using jit inside custom_jvp, use scan.

    def scan_apply(f, x):
      y, _ = lax.scan(lambda x, _: (f(x), None), x, None, length=1)
      return y

    @api.custom_jvp
    def sin(x):
      return jnp.sin(x)
    def sin_jvp(primals, tangents):
      x, = primals
      xdot, = tangents
      y, c = scan_apply(lambda xs: (jnp.sin(xs[0]), jnp.cos(xs[1])), (x, x))
      ydot = c * xdot
      return y, ydot
    sin.defjvp(sin_jvp)

    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    f = new_checkpoint(partial(scan_apply, sin), policy=save_cos)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 1)  # +1 b/c dce fixed point
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    save_sin = lambda prim, *_, **__: str(prim) == 'sin'
    f = new_checkpoint(partial(scan_apply, sin), policy=save_sin)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(partial(scan_apply, sin),
                       policy=jax.checkpoint_policies.everything_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    f = new_checkpoint(partial(scan_apply, sin),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 1)  # +1 b/c dce fixed point
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(lambda x: scan_apply(sin, scan_apply(sin, x)),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 2)  # +1 b/c dce fixed point
    self.assertEqual(jaxpr_text.count(' cos '), 2)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_of_cond(self, remat):
    true_fn  = lambda c: (jnp.sin(c), jnp.sin(c))
    false_fn = lambda c: (jnp.sin(c), jnp.sin(c))
    f = lambda x: lax.cond(x > 0., true_fn, false_fn, x)
    jtu.check_grads(remat(f), (3.,), order=2, modes=['rev'])

    jaxpr = api.make_jaxpr(api.linearize(remat(f), 4.)[1])(1.)
    self.assertNotIn(' sin ', str(jaxpr))
    self.assertIn(' cos ', str(jaxpr))

    true_fn  = lambda c: jnp.sin(jnp.sin(c))
    false_fn = lambda c: c
    f = lambda x: lax.cond(x > 0., true_fn, false_fn, x)
    jtu.check_grads(remat(f), (3.,), order=2, modes=['rev'])

    jaxpr = api.make_jaxpr(api.linearize(remat(f), 4.)[1])(1.)
    self.assertIn(' sin ', str(jaxpr))
    self.assertIn(' cos ', str(jaxpr))

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_const_in_jvp_cond(self, remat):
    @api.custom_jvp
    def f(x):
      return x * jnp.arange(3.)
    @f.defjvp
    def f_jvp(primals, tangents):
      (x,), (xdot,) = primals, tangents
      return f(x), xdot * jnp.arange(3.)

    @remat
    def g(x):
      y = jax.lax.cond(x.sum() > 0, f, lambda x: x, x)
      return y.sum()

    jax.grad(g)(jnp.arange(3.))  # doesn't crash

  def test_remat_checkpoint_dots_inside_cond(self):
    x = jnp.ones((5,))

    def f(W):
      @partial(api.remat, policy=jax.checkpoint_policies.checkpoint_dots)
      def f(x):
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        return x

      return lax.cond(x.sum() > 0, f, lambda x: x, x)

    _, f_vjp = api.vjp(f, jnp.ones((5, 5)))
    jaxpr_text = str(f_vjp.args[0].func.args[1])

    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' cos '), 3)
    # Five calls to dot_general in the backward pass because we have two for
    # each forward-pass dot, except for the first which only has one (as we are
    # differentiating with respect to only W and not x).
    self.assertEqual(jaxpr_text.count(' dot_'), 5)

    jtu.check_grads(api.jit(f), (jnp.ones((5, 5)),), order=2,
                    modes=['fwd', 'rev'])

  def test_remat_checkpoint_dots_outside_cond(self):
    # see also above test test_remat_checkpoint_dots_inside_cond
    # The behavior between the two tests is essentially identical, whereas for
    # scan different things are saved based on this difference in remat
    # placement (because of the carry).
    x = jnp.ones((5,))

    @partial(new_checkpoint, policy=jax.checkpoint_policies.checkpoint_dots)
    def f(W):
      def f(x):
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        x = jnp.sin(jnp.dot(x, W, precision=lax.Precision.HIGHEST))
        return x

      return lax.cond(x.sum() > 0, f, lambda x: x, x)

    _, f_vjp = api.vjp(f, jnp.ones((5, 5)))
    jaxpr = f_vjp.args[0].func.args[1]
    jaxpr_text = str(jaxpr)

    self.assertEqual(jaxpr_text.count(' sin '), 2)
    self.assertEqual(jaxpr_text.count(' cos '), 3)
    self.assertEqual(jaxpr_text.count(' dot_'), 5)

    jtu.check_grads(api.jit(f), (jnp.ones((5, 5)),), order=2,
                    modes=['fwd', 'rev'])

  def test_remat_of_cond_policy(self):
    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    f = new_checkpoint(lambda x: lax.cond(x > 0, jnp.sin, lambda x: x, x),
                       policy=save_cos)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])

    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

  def test_remat_of_cond_funky_custom_jvp(self):
    def cond_apply(f, x):
      return lax.cond(x.sum() > -jnp.inf, f, lambda x: x, x)

    @api.custom_jvp
    def sin(x):
      return jnp.sin(x)
    def sin_jvp(primals, tangents):
      x, = primals
      xdot, = tangents
      y, c = jax.jit(lambda: (jnp.sin(x), jnp.cos(x)))()
      ydot = c * xdot
      return y, ydot
    sin.defjvp(sin_jvp)

    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    f = new_checkpoint(partial(cond_apply, sin), policy=save_cos)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    save_sin = lambda prim, *_, **__: str(prim) == 'sin'
    f = new_checkpoint(partial(cond_apply, sin), policy=save_sin)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(partial(cond_apply, sin),
                       policy=jax.checkpoint_policies.everything_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    f = new_checkpoint(partial(cond_apply, sin),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(lambda x: cond_apply(sin, cond_apply(sin, x)),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 1)
    self.assertEqual(jaxpr_text.count(' cos '), 2)

  def test_remat_of_cond_funky_custom_jvp2(self):
    # Like the above test but instead of using jit inside custom_jvp, use cond.

    def cond_apply(f, x):
      return lax.cond(True, f, lambda x: x, x)

    @api.custom_jvp
    def sin(x):
      return jnp.sin(x)
    def sin_jvp(primals, tangents):
      x, = primals
      xdot, = tangents
      y, c = cond_apply(lambda xs: (jnp.sin(xs[0]), jnp.cos(xs[1])), (x, x))
      ydot = c * xdot
      return y, ydot
    sin.defjvp(sin_jvp)

    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    f = new_checkpoint(partial(cond_apply, sin), policy=save_cos)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    save_sin = lambda prim, *_, **__: str(prim) == 'sin'
    f = new_checkpoint(partial(cond_apply, sin), policy=save_sin)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(partial(cond_apply, sin),
                       policy=jax.checkpoint_policies.everything_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 0)

    f = new_checkpoint(partial(cond_apply, sin),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 0)
    self.assertEqual(jaxpr_text.count(' cos '), 1)

    f = new_checkpoint(lambda x: cond_apply(sin, cond_apply(sin, x)),
                       policy=jax.checkpoint_policies.nothing_saveable)
    jtu.check_grads(f, (3.,), order=2, modes=['rev'])
    jaxpr = api.make_jaxpr(api.linearize(f, 4.)[1])(1.)
    jaxpr_text = str(jaxpr)
    self.assertEqual(jaxpr_text.count(' sin '), 1)
    self.assertEqual(jaxpr_text.count(' cos '), 2)

  @parameterized.named_parameters(
      {"testcase_name": f"{suffix}", "remat": remat}
      for suffix, remat in [
          ('', api.remat),
          ('_new', new_checkpoint),
      ])
  def test_remat_of_while_loop(self, remat):
    def cond_fn(carry):
      i, _ = carry
      return i < 3
    def body_fn(carry):
      i, x = carry
      return i + 1, jnp.sin(x)
    def f(x):
      _, y = lax.while_loop(cond_fn, body_fn, (0, x))
      return y

    _, f_lin = jax.linearize(remat(f), 3.)
    y_dot = f_lin(1.0)
    expected = jax.grad(lambda x: jnp.sin(jnp.sin(jnp.sin(x))))(3.)
    self.assertArraysAllClose(y_dot, expected, check_dtypes=False)

    jaxpr = api.make_jaxpr(jax.linearize(remat(f), 4.)[1])(1.)
    self.assertIn(' sin ', str(jaxpr))
    self.assertIn(' cos ', str(jaxpr))

  def test_remat_of_while_loop_policy(self):
    def cond_fn(carry):
      i, _ = carry
      return i < 3
    def body_fn(carry):
      i, x = carry
      return i + 1, jnp.sin(x)
    def f(x):
      _, y = lax.while_loop(cond_fn, body_fn, (0, x))
      return y

    # even with a policy, we can't save residuals (w/o dynamic shapes)!
    save_cos = lambda prim, *_, **__: str(prim) == 'cos'
    g = new_checkpoint(f, policy=save_cos)
    jaxpr = api.make_jaxpr(jax.linearize(g, 4.)[1])(1.)
    self.assertIn(' sin ', str(jaxpr))
    self.assertIn(' cos ', str(jaxpr))


class JaxprTest(jtu.JaxTestCase):

  def test_scalar_literals(self):
    jaxpr = api.make_jaxpr(lambda x: x + 2)(42)
    self.assertLen(jaxpr.jaxpr.constvars, 0)

  def test_abstract_inputs(self):
    jaxpr = api.make_jaxpr(lambda x: x + 2.)(
        types.SimpleNamespace(shape=(), dtype=np.dtype(np.float32)))
    self.assertEqual(jaxpr.in_avals[0].shape, ())
    self.assertEqual(jaxpr.in_avals[0].dtype, np.float32)

  def test_const(self):
    def fun(x):
      return (x, 1., np.zeros(1, dtype=jnp.float32))

    expected = "{ lambda a:f32[1]; b:f32[]. let  in (b, 1.0, a) }"
    jaxpr = api.make_jaxpr(fun)(jnp.float32(0.))
    self.assertMultiLineStrippedEqual(expected, str(jaxpr))

  def test_cond(self):
    def f(x):
      return lax.cond(x >= 0.,
                      x + 1.,
                      lambda xt: xt + x,
                      x + 2.,
                      lambda xf: xf - x)
    expected = """{ lambda ; a:f32[]. let
    b:bool[] = ge a 0.0
    c:f32[] = add a 1.0
    d:f32[] = add a 2.0
    e:i32[] = convert_element_type[new_dtype=int32 weak_type=False] b
    f:f32[] = cond[
      branches=(
        { lambda ; g_:f32[] h:f32[] i:f32[] j:f32[]. let
            k:f32[] = sub j h
          in (k,) }
        { lambda ; l:f32[] m_:f32[] n:f32[] o:f32[]. let
            p:f32[] = add n l
          in (p,) }
      )
      linear=(False, False, False, False)
    ] e a a c d
  in (f,) }"""
    jaxpr = api.make_jaxpr(f)(jnp.float32(3.))
    self.assertMultiLineStrippedEqual(expected, str(jaxpr))

  def test_make_jaxpr_static_argnums(self):
    def f(x, y):
      return x + y

    jaxpr = api.make_jaxpr(f, static_argnums=(1,))(2, 3)
    self.assertIn('3', str(jaxpr))

  def test_make_jaxpr_return_shape(self):
    _, shape_tree = api.make_jaxpr(lambda x: (x + 1, jnp.zeros(2, jnp.float32)),
                                   return_shape=True)(jnp.int32(1))
    expected = (api.ShapeDtypeStruct(shape=(), dtype=jnp.int32),
                api.ShapeDtypeStruct(shape=(2,), dtype=jnp.float32))
    self.assertEqual(shape_tree, expected)

  def test_make_jaxpr_axis_env(self):
    def f(x):
      return x - lax.psum(x, 'i')
    jaxpr = api.make_jaxpr(f, axis_env=[('i', 4)])(2)
    self.assertIn('psum', str(jaxpr))

  def test_make_jaxpr_named(self):
    def f(x):
      return x - lax.psum(x, 'i')

    x = api.ShapeDtypeStruct(
        shape=(2, 3), dtype=jnp.dtype(jnp.float32), named_shape={'i': 10})
    jaxpr = api.make_jaxpr(f, axis_env=[('i', 10)])(x)
    named_shapes = [v.aval.named_shape for v in jaxpr.jaxpr.eqns[1].invars]
    self.assertEqual(named_shapes, [{'i': 10}, {}])

  @parameterized.parameters(True, False)
  def test_vjp_reduce_axes_jaxpr(self, gy_batched):
    def f(w, x):
      return jnp.sin(jnp.dot(x, w))

    w = api.ShapeDtypeStruct(
        shape=(3, 4), dtype=jnp.float32, named_shape={})
    x = api.ShapeDtypeStruct(
        shape=(3,), dtype=jnp.float32, named_shape={'batch': 2})
    gy = api.ShapeDtypeStruct(
        shape=(4,), dtype=jnp.float32,
        named_shape={'batch': 2} if gy_batched else {})

    # per-example
    jaxpr, shapes = api.make_jaxpr(
        lambda w, x, gy: api.vjp(f, w, x)[1](gy), axis_env=[('batch', 2)],
        return_shape=True)(w, x, gy)
    expected = (api.ShapeDtypeStruct(
        shape=(3, 4), dtype=jnp.float32, named_shape={'batch': 2}), x)
    self.assertEqual(shapes, expected)
    self.assertNotIn('psum', str(jaxpr))

    # reduced
    jaxpr, shapes = api.make_jaxpr(
        lambda w, x, gy: api.vjp(f, w, x, reduce_axes=('batch',))[1](gy),
        axis_env=[('batch', 2)],
        return_shape=True)(w, x, gy)
    expected = (w, x)
    self.assertEqual(shapes, expected)
    self.assertIn('psum', str(jaxpr))

  def test_weak_type_jit_invariance(self):
    y = jnp.broadcast_to(3., (3,))
    self.assertTrue(y.aval.weak_type)

    def f():
      return lax.convert_element_type(y, 'float32')

    self.assertEqual(f().aval.weak_type, api.jit(f)().aval.weak_type)

  def test_elide_trivial_convert_element_types(self):
    # since we apply convert_element_type to a numpy.ndarray, the primitive is
    # still bound and thus would appear in the jaxpr if we didn't clean it up
    if config.x64_enabled:
      x = np.arange(3, dtype='float64')
    else:
      x = np.arange(3, dtype='float32')

    cet = partial(lax.convert_element_type, new_dtype=x.dtype)
    jaxpr = api.make_jaxpr(lambda: cet(cet(cet(x))))()
    self.assertLen(jaxpr.eqns, 0)

  def test_elide_trivial_broadcasts(self):
    # since we apply broadcast to a numpy.ndarray, the primitive is still bound
    # and thus would appear in the jaxpr if we didn't clean it up
    jaxpr = api.make_jaxpr(lambda: lax.broadcast(np.float32(3), ()))()
    self.assertLen(jaxpr.jaxpr.eqns, 0)

  def test_convert_element_type_literal_constant_folding(self):
    # this convert_elemnt_type is nontrivial, but because it's on a scalar we
    # constant-fold it
    cet = partial(lax.convert_element_type, new_dtype='float16')
    jaxpr = api.make_jaxpr(lambda: cet(3.))()
    self.assertLen(jaxpr.eqns, 0)


class DCETest(jtu.JaxTestCase):

  def assert_dce_result(self, jaxpr: core.Jaxpr, used_outputs: List[bool],
                        expected_used_inputs: List[bool],
                        expected_num_eqns: Optional[int] = None,
                        check_diff: bool = True):
    jaxpr_dce, used_inputs = pe.dce_jaxpr(jaxpr, used_outputs)
    core.check_jaxpr(jaxpr_dce)
    self.assertEqual(used_inputs, expected_used_inputs)
    if expected_num_eqns is not None:
      all_jaxprs = it.chain([jaxpr_dce], core.subjaxprs(jaxpr_dce))
      num_eqns = sum(len(subjaxpr.eqns) for subjaxpr in all_jaxprs)
      self.assertEqual(num_eqns, expected_num_eqns, msg=str(jaxpr_dce))

    rand_ = jtu.rand_small(np.random.RandomState(0))
    rand  = lambda v: rand_(v.aval.shape, v.aval.dtype)
    consts = [rand(v) for v in jaxpr.constvars]
    inputs = [rand(v) for v in jaxpr.invars   ]
    inputs_dce = [x for x, used in zip(inputs, used_inputs) if used]
    full_outs = core.eval_jaxpr(jaxpr    , consts, *inputs)
    expected_outs_dce = [y for y, used in zip(full_outs, used_outputs) if used]
    outs = core.eval_jaxpr(jaxpr_dce, consts, *inputs_dce)
    self.assertAllClose(outs, expected_outs_dce)

    if check_diff and expected_num_eqns != 0:
      f = lambda *args: core.eval_jaxpr(jaxpr_dce, consts, *args)
      jtu.check_grads(f, inputs_dce, order=2, modes=['rev'])

  def test_dce_jaxpr_scan_nontrivial_fixedpoint_carry(self):
    # The idea is that each element of the output carry tuple depends on the
    # corresponding carried input as well as the one to the left. The extensive
    # inputs and outputs aren't used here; just the carry depending on itself.
    def f(lst):
      def body(c, _):
        return [c[0]] + [c1 + c2 for c1, c2 in zip(c[:-1], c[1:])], None
      out, _ = jax.lax.scan(body, lst, None, length=len(lst))
      return out
    jaxpr = api.make_jaxpr(f)([1., 2., 3., 4.]).jaxpr
    self.assertLen(jaxpr.eqns, 1)
    self.assertLen(jaxpr.eqns[0].params['jaxpr'].jaxpr.eqns, 3)

    # If we use all but the last element, all but the first input is used, and
    # only one eqn is pruned.
    self.assert_dce_result(
        jaxpr,  used_outputs=[True, True, True, False],
        expected_used_inputs=[True, True, True, False],
        expected_num_eqns=1 + 2)  # one outer scan eqn, two adds in the body

    # Same as above if we just pull on the third element.
    self.assert_dce_result(
        jaxpr,  used_outputs=[False, False, True, False],
        expected_used_inputs=[True, True, True, False],
        expected_num_eqns=1 + 2)  # one outer scan eqn, two adds in the body

    # If we use all but the last two elements, the last two inputs are not used,
    # and two eqns can be pruned.
    self.assert_dce_result(
        jaxpr,  used_outputs=[True, True, False, False],
        expected_used_inputs=[True, True, False, False],
        expected_num_eqns=1 + 1)  # one outer scan eqn, one add in body

    # If we only use the last element, no eqns can be pruned.
    self.assert_dce_result(
        jaxpr,  used_outputs=[False, False, False, True],
        expected_used_inputs=[True, True, True, True],
        expected_num_eqns=1 + 3)  # one outer scan eqn, three adds in body

  def test_dce_jaxpr_scan_nontrivial_fixedpoint_carry_2(self):
    # This is much like the above test, except with a more interesting
    # dependence structure among the carry elements. Also add a const and
    # extensive input.
    hidden_sequence = [1, 2, 3, 5, 8]
    def f(lst):
      def body(c, _):
        _ = jnp.sin(np.array([3., 1., 4.]))
        sub_c = [c[i] for i in hidden_sequence]
        sub_c = [sub_c[0]] + [c1 * c2 for c1, c2 in zip(sub_c[:-1], sub_c[1:])]
        new_c = list(c)
        for i, elt in zip(hidden_sequence, sub_c):
          new_c[i] = elt
        return new_c, None
      out, _ = jax.lax.scan(body, lst, np.arange(len(lst), dtype='float32'))
      return out
    jaxpr = api.make_jaxpr(f)([1., 2., 3., 4., 5., 6., 7., 8., 9., 10.]).jaxpr
    self.assertLen(jaxpr.eqns, 1)
    self.assertLen(jaxpr.eqns[0].params['jaxpr'].jaxpr.eqns, 5)

    # If we use the value at index 8 only, all the hidden sequence must be kept
    # and no eqns can be pruned.
    used_outputs = [False] * 10
    used_outputs[8] = True
    expected_used_inputs = [False] * 10
    for i in hidden_sequence:
      expected_used_inputs[i] = True
    self.assert_dce_result(
        jaxpr,   used_outputs=used_outputs,
        expected_used_inputs=expected_used_inputs,
        expected_num_eqns=1 + 4)

    # If we use the value at any indices not in the hidden sequence, none of the
    # hidden sequence must be kept and we can prune all body eqns.
    used_outputs = [False] * 10
    expected_used_inputs = [False] * 10
    used_outputs[9] = expected_used_inputs[9] = True
    self.assert_dce_result(
        jaxpr,   used_outputs=used_outputs,
        expected_used_inputs=expected_used_inputs,
        expected_num_eqns=1)  # 1 b/c scan doesn't have fwding rule
    used_outputs[7] = expected_used_inputs[7] = True
    used_outputs[6] = expected_used_inputs[6] = True
    self.assert_dce_result(
        jaxpr,   used_outputs=used_outputs,
        expected_used_inputs=expected_used_inputs,
        expected_num_eqns=1)

    # If we use the value at index 3 only, some of the hidden sequence must be
    # kept but the rest pruned.
    used_outputs = [False] * 10
    used_outputs[3] = True
    expected_used_inputs = [False] * 10
    expected_used_inputs[1] = expected_used_inputs[2] = \
        expected_used_inputs[3] = True
    self.assert_dce_result(
        jaxpr,   used_outputs=used_outputs,
        expected_used_inputs=expected_used_inputs,
        expected_num_eqns=1 + 2)

  def test_dce_jaxpr_scan_nontrivial_fixedpoint_extensive_output(self):
    # Here we test how using the extensive output affects the carry.
    def f(lst):
      def body(c, _):
        return [c[-1], *c[:-1]], c[-1]
      _, ys = jax.lax.scan(body, lst, None, length=len(lst))
      return ys
    jaxpr = api.make_jaxpr(f)([1., 2., 3., 4.]).jaxpr
    self.assertLen(jaxpr.eqns, 1)

    # If we only use the extensive output, all carry elements are needed, and we
    # need to keep the scan itself.
    self.assert_dce_result(
        jaxpr,   used_outputs=[True],
        expected_used_inputs=[True, True, True, True],
        expected_num_eqns=1)

    # If we don't use the extensive output, no carry elements are needed, and we
    # don't need to keep the scan.
    self.assert_dce_result(
        jaxpr,   used_outputs=[False],
        expected_used_inputs=[False, False, False, False],
        expected_num_eqns=0)

  def test_dce_jaxpr_scan_extensive_input(self):
    # Here we test an extensive input affecting the carry.
    def cumprod(xs):
      def body(c, x):
        return c * x, c
      c, ys = jax.lax.scan(body, jnp.float32(1.), xs)
      return c, ys
    jaxpr = api.make_jaxpr(cumprod)(jnp.arange(1., 5., dtype='float32')).jaxpr

    # If we only use the carry output or extensive output, we need the input.
    self.assert_dce_result(
        jaxpr,   used_outputs=[True, False],
        expected_used_inputs=[True],
        expected_num_eqns=2)
    self.assert_dce_result(
        jaxpr,   used_outputs=[False, True],
        expected_used_inputs=[True],
        expected_num_eqns=2)

    # If we don't use either output, the scan is eliminated.
    self.assert_dce_result(
        jaxpr,   used_outputs=[False, False],
        expected_used_inputs=[False],
        expected_num_eqns=0)

  def test_dce_jaxpr_scan_overpruning(self):
    # This is a regression test for a specific issue.
    @api.remat
    def scanned_f(c, x):
      out = jnp.tanh(c * x)
      return out, out

    def f(xs):
      return lax.scan(scanned_f, jnp.array(1., 'float32'), xs)

    xs = jnp.arange(10., dtype='float32')
    jaxpr = api.make_jaxpr(lambda xs: api.linearize(f, xs)[1])(xs).jaxpr

    jaxpr, used_inputs = pe.dce_jaxpr(jaxpr, [True] * len(jaxpr.outvars))
    self.assertLen(jaxpr.eqns, 1)
    self.assertLen(jaxpr.eqns[-1].params['jaxpr'].jaxpr.eqns, 2)

  def test_dce_jaxpr_scan_const_in_jvp(self):
    # The main point of this test is to check for a crash.
    @api.custom_jvp
    def f(x):
      return x * np.arange(3.)
    @f.defjvp
    def f_jvp(primals, tangents):
      (x,), (xdot,) = primals, tangents
      return f(x), xdot * np.arange(3.)

    def g(x):
      def body(c, _):
        return f(c), None
      y, _ = jax.lax.scan(body, x, None, length=1)
      return y

    jaxpr = api.make_jaxpr(lambda x, xdot: api.jvp(g, (x,), (xdot,))
                           )(np.arange(3.), np.arange(3.)).jaxpr

    self.assert_dce_result(
        jaxpr,   used_outputs=[True, True],
        expected_used_inputs=[True, True])

    self.assert_dce_result(
        jaxpr,   used_outputs=[True, False],
        expected_used_inputs=[True, False])

  def test_dce_jaxpr_scan_results(self):
    # This doesn't test whether DCE is doing nontrivial work; instead it tests
    # whether the result after applying DCE computes different values. If
    # dce_jaxpr were an identity function, it'd pass this test!
    def f(cs, xs):
      def body(c, x):
        return (c[0], c[0] + c[1], jnp.arange(3.)), x
      cs, xs = jax.lax.scan(body, cs, xs)
      return cs[::2], xs[::2]

    cs = 1., 2., jnp.arange(3.)
    xs = jnp.arange(3.), jnp.arange(3.) + 5
    jaxpr_ = jax.make_jaxpr(f)(cs, xs)
    jaxpr, consts = jaxpr_.jaxpr, jaxpr_.consts
    jaxpr_pruned, used_inputs = pe.dce_jaxpr(jaxpr, [True] * len(jaxpr.outvars))

    args = (*cs, *xs)
    result1 = core.eval_jaxpr(jaxpr       , consts, *cs, *xs)
    pruned_args = [x for x, used in zip(args, used_inputs) if used]
    result2 = core.eval_jaxpr(jaxpr_pruned, consts, *pruned_args)
    self.assertAllClose(result1, result2)

  def test_dce_jaxpr_cond_trivial(self):
    x = jnp.array(1., dtype='float32')

    # start with 7 eqns, use both outputs so nothing can be pruned
    def f(x1, x2):
      return lax.cond(x1 > 0,
                      lambda x1, x2: (jnp.sin(x1), jnp.sin(x2)),
                      lambda x1, x2: (jnp.sin(x1), jnp.sin(x2)),
                      x1, x2)
    jaxpr = jax.make_jaxpr(f)(x, x).jaxpr
    self.assert_dce_result(jaxpr, [True, True], [True, True], 7)

    # use neither output so everything can be pruned
    self.assert_dce_result(jaxpr, [False, False], [False, False], 0)

  def test_dce_jaxpr_cond_nontrivial(self):
    x = jnp.array(1., dtype='float32')

    # start with 7 eqns, dont use an output so an eqn can be trimmed on each
    # side and x2 _can_ be pruned
    def f(x1, x2):
      return lax.cond(x1 > 0,
                      lambda x1, x2: (jnp.sin(x1), jnp.sin(x2)),
                      lambda x1, x2: (jnp.sin(x1), jnp.sin(x1)),
                      x1, x2)
    jaxpr = jax.make_jaxpr(f)(x, x).jaxpr
    self.assert_dce_result(jaxpr, [True, False], [True, False], 5)

    # start with 7 eqns, dont use an output so an eqn can be trimmed on each
    # side, but x2 _can't_ be pruned b/c of a swap
    def f(x1, x2):
      return lax.cond(x1 > 0,
                      lambda x1, x2: (jnp.sin(x1), jnp.sin(x2)),
                      lambda x1, x2: (jnp.sin(x2), jnp.sin(x1)),
                      x1, x2)
    jaxpr = jax.make_jaxpr(f)(x, x).jaxpr
    self.assert_dce_result(jaxpr, [True, False], [True, True], 5)

    # start with 7 eqns, only use x1 on one side and x2 on the other, so we
    # can't prune any inputs or eqns
    def f(x1, x2):
      return lax.cond(x1 > 0,
                      lambda x1, x2: (jnp.sin(x1), jnp.sin(x1)),
                      lambda x1, x2: (jnp.sin(x2), jnp.sin(x2)),
                      x1, x2)
    jaxpr = jax.make_jaxpr(f)(x, x).jaxpr
    self.assert_dce_result(jaxpr, [True, True], [True, True], 7)
    # use only one output, so we can prune eqns but not inputs
    self.assert_dce_result(jaxpr, [True, False], [True, True], 5)


class CustomJVPTest(jtu.JaxTestCase):

  def test_basic(self):
    @api.custom_jvp
    def f(x):
      return jnp.sin(x)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * jnp.cos(x) * g
    f.defjvp(f_jvp)

    x = 3.
    self.assertAllClose(f(x), jnp.sin(x))
    self.assertAllClose(api.jvp(f, (x,), (1.,)),
                        (jnp.sin(x), 2 * jnp.cos(x)))
    self.assertAllClose(api.grad(f)(x), 2 * jnp.cos(x))

  def test_invariance(self):
    @api.custom_jvp
    def f(x):
      return jnp.cos(2 * x) / 2.
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return (f(x), 3 * g)
    f.defjvp(f_jvp)
    def f2(x):
      y, _ = api.jvp(f, (x,), (x,))
      return y
    def f3(x):
      y, _ = api.jvp(f2, (x,), (x,))
      return y
    x = 1.
    self.assertAllClose(api.jvp(f, (x,), (x,)),
                        api.jvp(f2, (x,), (x,)),
                        check_dtypes=False)
    self.assertAllClose(api.jvp(f, (x,), (x,)),
                        api.jvp(f3, (x,), (x,)),
                        check_dtypes=False)

  def test_python_control_flow(self):
    @api.custom_jvp
    def f(x):
      if x > 0:
        return jnp.sin(x)
      else:
        return jnp.cos(x)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      if x > 0:
        return f(x), 2 * g
      else:
        return f(x), 3 * g
    f.defjvp(f_jvp)
    x = 2.
    self.assertAllClose(f(x), jnp.sin(x))
    self.assertAllClose(f(-x), jnp.cos(-x))
    self.assertAllClose(api.jvp(f, (x,), (1.,)),
                        (jnp.sin(x), 2.),
                        check_dtypes=False)
    self.assertAllClose(api.jvp(f, (-x,), (1.,)),
                        (jnp.cos(-x), 3.),
                        check_dtypes=False)
    self.assertAllClose(api.grad(f)(x), 2., check_dtypes=False)
    self.assertAllClose(api.grad(f)(-x), 3., check_dtypes=False)

  def test_vmap(self):
    @api.custom_jvp
    def f(x):
      assert jnp.ndim(x) == 0
      return jnp.sin(x)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      assert jnp.ndim(x) == jnp.ndim(g) == 0
      return f(x), 2 * jnp.cos(x) * g
    f.defjvp(f_jvp)

    x = jnp.arange(3.)
    xx = jnp.arange(6.).reshape(2, 3)

    # vmap of f
    self.assertAllClose(api.vmap(f)(x), jnp.sin(x))
    self.assertAllClose(api.vmap(api.vmap(f))(xx), jnp.sin(xx))

    # vmap of jvp of f
    self.assertAllClose(api.vmap(lambda x: api.jvp(f, (x,), (x,)))(x),
                        (jnp.sin(x), 2 * jnp.cos(x) * x))
    self.assertAllClose(api.vmap(api.vmap(lambda x: api.jvp(f, (x,), (x,))))(xx),
                        (jnp.sin(xx), 2 * jnp.cos(xx) * xx))

    # jvp of vmap of f
    self.assertAllClose(api.jvp(api.vmap(f), (x,), (x,)),
                        (jnp.sin(x), 2 * jnp.cos(x) * x))
    self.assertAllClose(api.jvp(api.vmap(api.vmap(f)), (xx,), (xx,)),
                        (jnp.sin(xx), 2 * jnp.cos(xx) * xx))

    # vmap of jvp of vmap of f
    self.assertAllClose(api.vmap(lambda x: api.jvp(api.vmap(f), (x,), (x,)))(xx),
                        (jnp.sin(xx), 2 * jnp.cos(xx) * xx))

  def test_jit(self):
    @api.custom_jvp
    def f(x):
      return jnp.sin(x)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * jnp.cos(x) * g
    f.defjvp(f_jvp)

    x = 3.

    # jit
    self.assertAllClose(api.jit(f)(x), jnp.sin(x))
    self.assertAllClose(api.jit(api.jit(f))(x), jnp.sin(x))

    # jit of jvp
    self.assertAllClose(api.jit(lambda x: api.jvp(f, (x,), (x,)))(x),
                        (jnp.sin(x), 2 * jnp.cos(x) * x),
                        check_dtypes=False)

    # jvp of jit
    self.assertAllClose(api.jvp(api.jit(f), (x,), (x,)),
                        (jnp.sin(x), 2 * jnp.cos(x) * x),
                        check_dtypes=False)

  def test_pytrees(self):
    @api.custom_jvp
    def f(x):
      return {'b': jnp.sin(x['a'])}
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), {'b': 2 * jnp.cos(x['a']) * g['a']}
    f.defjvp(f_jvp)
    x = {'a': 3.}
    self.assertAllClose(f(x)['b'], jnp.sin(x['a']))
    self.assertAllClose(api.jvp(f, (x,), (x,)),
                        ({'b': jnp.sin(x['a'])},
                         {'b': 2 * jnp.cos(x['a']) * x['a']}),
                        check_dtypes=False)

  def test_kwargs(self):
    # from https://github.com/google/jax/issues/1938
    @api.custom_jvp
    def my_fun(x, y, c=1.):
      return c * (x + y)
    def my_jvp(primals, tangents):
      x, y, c = primals
      t_x, t_y, t_c = tangents
      return my_fun(x, y, c), t_c
    my_fun.defjvp(my_jvp)
    f = lambda x, y: jnp.square(my_fun(x, y, c=2.)).sum()
    f(10., 5.)  # doesn't crash
    api.jvp(f, (10., 5.), (1., 1.))  # doesn't crash

  def test_initial_style(self):
    @api.custom_jvp
    def f(x):
      return 3 * x
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * g
    f.defjvp(f_jvp)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.grad(foo)(3.)
    expected = 2.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.jit(foo))(3.)
    expected = 2.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jit(api.grad(foo))(3.)
    expected = 2.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.grad(foo))(3.)
    expected = 0.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.grad(api.jit(foo)))(3.)
    expected = 0.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.jit(api.grad(foo)))(3.)
    expected = 0.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jit(api.grad(api.grad(foo)))(3.)
    expected = 0.
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_initial_style_vmap(self):
    @api.custom_jvp
    def f(x):
      assert jnp.ndim(x) == 0
      return 3 * x
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * g
    f.defjvp(f_jvp)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.vmap(foo)(jnp.ones(3))
    expected = 3. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.vmap(api.jit(foo))(jnp.ones(3))
    expected = 3. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jit(api.vmap(foo))(jnp.ones(3))
    expected = 3. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.vmap(foo)(x).sum())(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.vmap(api.jit(foo))(x).sum())(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.jit(api.vmap(foo))(x).sum())(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.jit(lambda x: api.vmap(foo)(x).sum()))(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jit(api.grad(lambda x: api.vmap(foo)(x).sum()))(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_initial_style_vmap_with_collective(self):

    @api.custom_jvp
    def f(x):
      return lax.psum(x, 'foo')

    @f.defjvp
    def f_jvp(xs, ts):
      x, = xs
      t, = ts
      return lax.psum(x, 'foo'), t

    def g(x):
      jaxpr = api.make_jaxpr(f)(x)
      return core.eval_jaxpr(jaxpr.jaxpr, [], x)[0]

    v = api.vmap(lambda _, x: g(x), axis_name='foo', in_axes=(0, None),
        out_axes=None)(jnp.arange(4.), 2.)
    self.assertAllClose(v, 8.)

  def test_closed_over_tracers_error_message(self):
    def f(x):
      @api.custom_jvp
      def g(y):
        return x + y
      def g_jvp(primals, tangents):
        return g(x), 2 * primals[0]
      g.defjvp(g_jvp)
      return g(1.)

    self.assertRaises(ad.CustomJVPException, lambda: api.jvp(f, (3.,), (1.,)))
    self.assertRaises(ad.CustomJVPException, lambda: api.grad(f)(3.))

  def test_nondiff_arg(self):
    @partial(api.custom_jvp, nondiff_argnums=(0,))
    def app(f, x):
      return f(x)
    def app_jvp(f, primals, tangents):
      (x,), (t,) = primals, tangents
      return app(f, x), 3 * t
    app.defjvp(app_jvp)

    ans = app(lambda x: 2 * x, 1)
    expected = 2
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jvp(lambda x: app(lambda y: 2 * y, x), (1.,), (1.,))
    expected = (2., 3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_nondiff_arg_jit_tracer(self):
    # This test would pass with "final-style" JIT tracing, but that was
    # misleading: it doesn't work with "initial-style" staging, i.e. control
    # flow primitives like jax.lax.scan or even pjit. The behavior isn't very
    # useful either: instead of using nondiff_argnums here, a user can just pass
    # such inputs as ordinary arguments, and ignore the corresponding tangents.
    # Then nondiff_argnums can be reserved for (1) non jaxtype data (like a
    # string- or callable-valued argument which parameterizes the function or
    # rule) or (2) static data (e.g. integers which parameterize shapes).
    raise unittest.SkipTest("behavior no longer supported")

    @partial(api.custom_jvp, nondiff_argnums=(0,))
    def f(x, y):
      return x * y
    def f_jvp(x, primals, tangents):
      (y,), (t_y,) = primals, tangents
      return f(x, y), 5 * t_y
    f.defjvp(f_jvp)

    @jit
    def g(x, y):
      return f(x, y)

    ans = api.jvp(lambda y: g(2., y), (3.,), (1.,))
    expected = (6., 5.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_nondiff_arg_vmap_tracer(self):
    @partial(api.custom_jvp, nondiff_argnums=(0,))
    def f(x, y):
      return x * y
    def f_jvp(x, primals, tangents):
      (y,), (t_y,) = primals, tangents
      return f(x, y), 5 * t_y
    f.defjvp(f_jvp)

    g = jax.vmap(f)

    ans = api.jvp(lambda y: g(jnp.array([2.]), y),
                  (jnp.array([3.]),), (jnp.array([1.]),))
    expected = (jnp.array([6.]), jnp.array([5.]))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_nondiff_arg_hiding_jvp_tracer(self):
    def f(x):
      @partial(api.custom_jvp, nondiff_argnums=(0,))
      def g(h, x):
        return h(x)
      @g.defjvp
      def g_jvp(h, primals, tangents):
        x, = primals
        t, = tangents
        return g(h, x), 2. * t
      h = lambda y: x + y  # capture x
      return g(h, x)

    with self.assertRaisesRegex(ad.CustomJVPException, "Detected differentiation"):
      api.jvp(f, (2.,), (1.,))

  def test_vmap_axes(self):
    raise unittest.SkipTest("TODO")  # TODO(mattjj): write test

  def test_pmap(self):
    raise unittest.SkipTest("TODO")  # TODO(mattjj): write test

  def test_missing_jvp_rule_error_message(self):
    @api.custom_jvp
    def foo(x):
      return x ** 2

    self.assertRaisesRegex(
        AttributeError,
        r"No JVP defined for custom_jvp function foo using defjvp.",
        lambda: foo(2))
    self.assertRaisesRegex(
        AttributeError,
        r"No JVP defined for custom_jvp function foo using defjvp.",
        lambda: api.jvp(foo, (2.,), (1.,)))
    self.assertRaisesRegex(
        AttributeError,
        r"No JVP defined for custom_jvp function foo using defjvp.",
        lambda: api.grad(foo)(2.))

  def test_jvp_rule_inconsistent_pytree_structures_error_message(self):
    @api.custom_jvp
    def f(x):
      return (x**2,)

    @f.defjvp
    def foo_jvp(primals, tangents):
      x, = primals
      t, = tangents
      return f(x), [2 * x * t, x]

    f(2.)  # doesn't crash
    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom JVP rule foo_jvp for function f "
            "must produce primal and tangent outputs "
            "with equal container (pytree) structures, but got "
            "{} and {} respectively.".format(
                tree_util.tree_structure((1,)),
                tree_util.tree_structure([1, 2]))
        ),
        lambda: api.jvp(f, (2.,), (1.,)))

  def test_primal_tangent_aval_disagreement_error_message(self):
    @api.custom_jvp
    def f(x):
      return x ** 2

    @f.defjvp
    def foo_jvp(primals, tangents):
      x, = primals
      t, = tangents
      return f(x), jnp.reshape(t, (1,))

    f(2.)  # doesn't crash
    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom JVP rule must produce primal and tangent outputs "
            "with equal shapes and dtypes, but got float32[] and float32[1] "
            "respectively."),
        lambda: api.jvp(f, (jnp.float32(2.),), (jnp.float32(1.),)))

  def test_jvp_rule_doesnt_return_pair_error_message(self):
    # https://github.com/google/jax/issues/2516

    @api.custom_jvp
    def f(x):
      return x ** 2

    @f.defjvp
    def foo_jvp(primals, tangents):
      x, = primals
      t, = tangents
      return t

    f(2.)  # doesn't crash
    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom JVP rule foo_jvp for function f "
            "must produce a pair (list or tuple of length two) "
            "representing primal and tangent outputs, but got 1.0"),
        lambda: api.jvp(f, (2.,), (1.,)))

  def test_jvp_rule_primal_out_type_doesnt_match_primal_error_message(self):
    # https://github.com/lucidrains/flash-attention-jax/issues/7

    def scan_apply(f, x):
      y, _ = jax.lax.scan(lambda x, _: (f(x), None), x, None, length=1)
      return y

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

    @f.defjvp
    def f_jvp(primals, tangents):
      (x,), (xdot,) = primals, tangents
      return (x, x), (xdot, xdot)

    x = jnp.float32(1.)
    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom JVP rule f_jvp for function f must produce a pair "
            "(list or tuple of length two) where the first element represents "
            "the primal output (equal in value to the output of the "
            "custom_jvp-decorated function f, and in particular of the "
            "same container/pytree structure), but instead the JVP rule "
            "output's first element had container/pytree structure:\n"
            "    (float32[], float32[])\n"
            "while the custom_jvp-decorated function f had output "
            "container/pytree structure:\n"
            "    float32[]."
        ),
        lambda: jax.jvp(lambda x: scan_apply(f, x), (x,), (x,)))

    @f.defjvp
    def f_jvp2(primals, tangents):
      (x,), (xdot,) = primals, tangents
      return jnp.zeros((3, *x.shape), x.dtype), xdot

    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom JVP rule f_jvp2 for function f must produce a pair "
            "(list or tuple of length two) where the first element represents "
            "the primal output (equal in value to the output of the "
            "custom_jvp-decorated function f, and in particular "
            "with leaves of the same shape/dtype), but instead the JVP rule "
            "output's first element had shapes/dtypes of:\n"
            "    float32[3]\n"
            "while the custom_jvp-decorated function f had output shapes/dtypes"
            " of:\n"
            "    float32[]"
        ),
        lambda: jax.jvp(lambda x: scan_apply(f, x), (x,), (x,)))

  def test_multiple_rule_invocations(self):
    @jax.custom_jvp
    def expit(x):
      return 1 / (1 + lax.exp(-x))

    @expit.defjvp
    def _expit_jvp(primals, tangents):
      (x,), (t,) = primals, tangents
      ans = expit(x)
      t_out = t * ans * (1 - ans)
      return ans, t_out

    def scanned_fun(c, _):
      return [expit(c[0])] + [c[i-1] + c[i] for i in range(1, len(c))], None

    def foo(x):
      zero = jnp.zeros_like(x)
      c, _ = lax.scan(scanned_fun, [x, zero, zero, zero, zero], None, length=10)
      return c[-1]

    # just make sure these don't crash
    foo(3.)
    grad(foo)(3.)
    grad(lambda x: jax.vmap(foo)(x).sum())(jnp.arange(3.))

  def test_hard_stuff(self):
    arr = jnp.ones((5, 2, 2))
    api.jit(jax.vmap(jnp.linalg.det))(arr)  # doesn't crash

  def test_hard_stuff2(self):
    @jax.custom_jvp
    def f(x):
      return lax.tie_in(x, np.zeros(x.shape, x.dtype))

    @f.defjvp
    def f_jvp(primals, tangents):
      x, = primals
      t, = tangents
      return f(x), t

    # don't crash
    jax.jit(jax.vmap(f))(jnp.arange(3.))
    jax.jit(jax.vmap(jax.grad(f)))(jnp.arange(3.))
    jax.jit(jax.grad(lambda x: jax.vmap(f)(x).sum()))(jnp.arange(3.))
    jax.grad(lambda x: jax.vmap(f)(x).sum())(jnp.arange(3.))
    jax.jvp(jax.vmap(f), (jnp.arange(3.),), (jnp.ones(3),))

  def test_hard_stuff3(self):
    @jax.custom_jvp
    def relu(x):
      return jnp.maximum(x, 0)

    @relu.defjvp
    def _relu_jvp(primals, tangents):
      x, = primals
      t, = tangents
      return relu(x), lax.select(x > 0, t, lax.full_like(t, 0))

    def scanned_fun(c, _):
      return [relu(c[0])] + [c[i-1] + c[i] for i in range(1, len(c))], None

    def f(x):
      zero = jnp.zeros_like(x)
      c, _ = lax.scan(scanned_fun, [x, zero, zero, zero, zero], None, length=10)
      return c[-1]

    # don't crash
    jax.jit(jax.vmap(f))(jnp.arange(3.))
    jax.jit(jax.vmap(jax.grad(f)))(jnp.arange(3.))
    jax.jit(jax.grad(lambda x: jax.vmap(f)(x).sum()))(jnp.arange(3.))
    jax.grad(lambda x: jax.vmap(f)(x).sum())(jnp.arange(3.))
    jax.jvp(jax.jit(jax.vmap(f)), (jnp.arange(3.),), (jnp.ones(3),))

  def test_eval_shape(self):
    @jax.custom_jvp
    def expit(x):
      return 1 / (1 + lax.exp(-x))

    @expit.defjvp
    def _expit_jvp(primals, tangents):
      (x,), (t,) = primals, tangents
      ans = expit(x)
      t_out = t * ans * (1 - ans)
      return ans, t_out

    # don't crash
    api.eval_shape(expit, jnp.ones((2, 3)))
    api.eval_shape(api.grad(lambda x: expit(x).sum()), jnp.ones((2, 3)))

  def test_jaxpr_zeros(self):
    # from https://github.com/google/jax/issues/2657
    @api.custom_jvp
    def f(A, b):
      return A @ b

    def f_jvp(primals, tangents):
      A, b = primals
      dA, db = tangents
      z = f(A, b)
      dz = A @ db + dA @ b
      return z, dz

    f.defjvp(f_jvp)

    def experiment(theta):
      def step(q, _):
        z = f(jnp.eye(3), jnp.ones(3) * theta)
        q += z[0]
        return q, q

      q = 0.
      q, _ = lax.scan(step, q, None, 4)
      return q

    grad(experiment)(1.)  # doesn't crash

  def test_linear_in_scan(self):
    @api.custom_jvp
    def f(x):
      return -x

    @f.defjvp
    def f_jvp(primals, tangents):
      x, = primals
      x_dot, = tangents
      return f(x), f(x_dot)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.grad(foo)(3.)
    expected = -1.
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_custom_jvps_first_rule_is_none(self):
    # https://github.com/google/jax/issues/3389
    @api.custom_jvp
    def f(x, y):
      return x ** 2 * y

    f.defjvps(None, lambda x_dot, primal_out, x, y: 2 * x * y * x_dot)
    ans = grad(f, 1)(2., 3.)  # doesn't crash
    expected = 12.
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_concurrent_initial_style(self):
    # https://github.com/google/jax/issues/3843
    def unroll(param, sequence):
      def scan_f(prev_state, inputs):
        return prev_state, jax.nn.sigmoid(param * inputs)
      return jnp.sum(jax.lax.scan(scan_f, None, sequence)[1])

    def run():
      return jax.grad(unroll)(jnp.array(1.0), jnp.array([1.0]))

    expected = run()

    # we just don't want this to crash
    n_workers = 2
    with concurrent.futures.ThreadPoolExecutor(max_workers=n_workers) as e:
      futures = []
      for _ in range(n_workers):
        futures.append(e.submit(run))
      results = [f.result() for f in futures]
    for ans in results:
      self.assertAllClose(ans, expected)

  def test_nondiff_argnums_vmap_tracer(self):
    # https://github.com/google/jax/issues/3964
    @partial(jax.custom_jvp, nondiff_argnums=(0, 2))
    def sample(shape, param, seed):
      return jax.random.uniform(key=seed, shape=shape, minval=param)

    @sample.defjvp
    def sample_jvp(shape, seed, primals, tangents):
      param, = primals
      dparam, = tangents
      dparam = jnp.broadcast_to(dparam, shape)
      samples = sample(shape, param, seed)
      return samples, samples * dparam  # dummy jvp for proof of concept

    # check these don't crash
    jax.vmap(lambda seed: sample((2,3), 1., seed))(
        jax.random.split(jax.random.PRNGKey(1), 10))
    jax.jvp(lambda x: sample((2, 3), x, jax.random.PRNGKey(1)),
            (1.,), (1.,))

  def test_fun_with_nested_calls_2(self):
    def call(f, *args):
      f = api.custom_jvp(f)
      f.defjvp(lambda primals, tangents: (f(*primals), sum(tangents)))
      return f(*args)

    def fun_with_nested_calls_2(x):
      def bar(y):
        def baz(w):
          q = call(lambda x: y, x)
          q = q + call(lambda: y)
          q = q + call(lambda y: w + y, y)
          q = call(lambda w: call(jnp.sin, x) * y, 1.0) + q
          return q
        return api.jit(baz)(x)
      return call(bar, x)

    # test these don't crash
    self.assertAllClose(api.jit(fun_with_nested_calls_2)(3.),
                        fun_with_nested_calls_2(3.))
    api.vmap(fun_with_nested_calls_2)(jnp.arange(3.))

  def test_closure_with_vmap(self):
    # https://github.com/google/jax/issues/3822
    alpha = np.float32(2.)

    def sample(seed):
      @api.custom_jvp
      def f(alpha):
        return jax.random.gamma(seed, alpha, shape=[])

      @f.defjvp
      def f_jvp(primal, tangent):
        alpha = primal
        dalpha = tangent
        sample = f(alpha)
        partial_alpha = lax.random_gamma_grad(alpha, sample)
        return sample, partial_alpha * dalpha
      return f(alpha)

    api.vmap(sample)(jax.random.split(jax.random.PRNGKey(1), 3))  # don't crash

  def test_closure_with_vmap2(self):
    # https://github.com/google/jax/issues/8783
    def h(z):
      def f(x):
        @jax.custom_jvp
        def g(y):
          return x * y

        # NOTE: rule closes over vmap tracer
        @g.defjvp
        def g_jvp(primals, tangents):
          (y,), (ydot,) = primals, tangents
          return x * y, x * ydot

        return g(z)  # NOTE: no vmapped arg

      return jax.vmap(f)(jnp.arange(3., dtype='float32'))

    primals, tangents = jax.jvp(h, (jnp.float32(1.),), (jnp.float32(2.),))
    self.assertAllClose(primals ,     jnp.arange(3., dtype='float32'))
    self.assertAllClose(tangents, 2 * jnp.arange(3., dtype='float32'))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_float0(self):
    @api.custom_jvp
    def f(x, y):
      return x, y
    def f_jvp(primals, _):
      # we need a defined (non-float0) tangent to trigger the rule
      return primals, (2., 1)
    f.defjvp(f_jvp)

    primals = (2., 3)
    tangents = (np.ones(()), np.zeros((), float0),)
    expected_tangents = (2., np.zeros((), float0))
    self.assertArraysEqual(api.jvp(f, primals, tangents),
                           (primals, expected_tangents))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_float0_initial_style(self):
    @api.custom_jvp
    def f(x, y):
      return x, y
    def f_jvp(primals, _):
      x, y = primals
      return (x, y), (2., 1)
    f.defjvp(f_jvp)

    def foo(x, y):
      out, _ = lax.scan(lambda c, _: (f(*c), None), (x, y), None, length=1)
      return out

    primals = (2., 3)
    tangents = (np.ones(()), np.zeros((), float0),)
    expected_tangents = (2., np.zeros((), float0))
    self.assertArraysEqual(api.jvp(foo, primals, tangents),
                           (primals, expected_tangents))

  def test_remat(self):
    @api.custom_jvp
    def f(x):
      return jnp.sin(x)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * jnp.cos(x) * g
    f.defjvp(f_jvp)

    @api.remat
    def g(x):
      return f(f(x))

    ans = g(2.)
    expected = np.sin(np.sin(2.))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(g)(2.)
    expected = 4. * api.grad(lambda x: jnp.sin(jnp.sin(x)))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_remat_higher_order(self):
    @api.custom_jvp
    def f(x):
      return jnp.sin(x)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * jnp.cos(x) * g
    f.defjvp(f_jvp)

    def g(x):
      return f(f(x))

    ans = api.grad(api.grad(new_checkpoint(g)))(2.)
    expected = api.grad(api.grad(g))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(new_checkpoint(api.grad(g)))(2.)
    expected = api.grad(api.grad(g))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.grad(api.grad(new_checkpoint(g))))(2.)
    expected = api.grad(api.grad(api.grad(g)))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_initial_style_vmap_2(self):
    # This is like test_initial_style_vmap except the primal function closes
    # over an array constant.
    y = jnp.arange(1., 4.)

    @api.custom_jvp
    def f(x):
      assert jnp.ndim(x) == 0
      return 3 * x * jnp.sum(y)
    def f_jvp(primals, tangents):
      x, = primals
      g, = tangents
      return f(x), 2 * g
    f.defjvp(f_jvp)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.grad(lambda x: api.vmap(foo)(x).sum())(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.vmap(api.jit(foo))(x).sum())(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.jit(api.vmap(foo))(x).sum())(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.jit(lambda x: api.vmap(foo)(x).sum()))(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.jit(api.grad(lambda x: api.vmap(foo)(x).sum()))(jnp.ones(3))
    expected = 2. * jnp.ones(3)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_custom_jvp_vmap_broadcasting_interaction(self):
    # https://github.com/google/jax/issues/6452
    def f2(y, z):
      v1 = z
      v2 = jnp.sum(y) + z
      return jnp.logaddexp(v1, v2)

    def f1(y, z):
      v = api.vmap(lambda _y: f2(_y, z))(y)
      return jnp.sum(v)

    y = jnp.ones((3, 2))
    f = lambda z: f1(y, z)
    z = 0.1
    val, g = api.value_and_grad(f)(z)
    self.assertEqual(val.shape, ())
    self.assertEqual(g.shape, ())

  def test_custom_jvp_vmap_broadcasting_interaction_2(self):
    # https://github.com/google/jax/issues/5849
    @api.custom_jvp
    def transform(box, R):
      if jnp.isscalar(box) or box.size == 1:
        return R * box
      elif box.ndim == 2:
        return jnp.einsum('ij,j->i', box, R)
      raise ValueError()

    @transform.defjvp
    def transform_jvp(primals, tangents):
      box, R = primals
      dbox, dR = tangents
      return (transform(box, R), dR + transform(dbox, R))

    def periodic_general(box):
      def displacement_fn(Ra, Rb, **kwargs):
        _box = kwargs.get('box', box)
        return transform(_box, Ra - Rb)

      return displacement_fn

    N = 250

    scalar_box = 1.0
    displacement = periodic_general(scalar_box)

    key = jax.random.PRNGKey(0)
    R = jax.random.uniform(key, (N, 2))

    def energy_fn(box):
      d = partial(displacement, box=box)
      d = api.vmap(api.vmap(d, (None, 0)), (0, None))
      return jnp.sum(d(R, R) ** 2)

    self.assertEqual(grad(energy_fn)(scalar_box).shape, ())

  def test_custom_jvp_implicit_broadcasting(self):
    # https://github.com/google/jax/issues/6357
    if config.x64_enabled:
      raise unittest.SkipTest("test only applies when x64 is disabled")

    @jax.custom_jvp
    def projection_unit_simplex(x: jax.Array) -> jax.Array:
      """Projection onto the unit simplex."""
      s = 1.0
      n_features = x.shape[0]
      u = jnp.sort(x)[::-1]
      cssv = jnp.cumsum(u) - s
      ind = jnp.arange(n_features, dtype=x.dtype) + 1
      cond = u - cssv / ind > 0
      idx = jnp.count_nonzero(cond)
      threshold = cssv[idx - 1] / idx.astype(x.dtype)
      return jax.nn.relu(x - threshold)


    @projection_unit_simplex.defjvp
    def projection_unit_simplex_jvp(primals, tangents):
      x, = primals
      x_dot, = tangents
      primal_out = projection_unit_simplex(x)
      supp = (primal_out > 0).astype(x_dot.dtype)
      card = jnp.count_nonzero(supp).astype(x_dot.dtype)
      tangent_out = supp * x_dot - (jnp.dot(supp, x_dot) / card) * supp
      return primal_out, tangent_out

    rng = self.rng()
    x = rng.rand(5).astype(np.float32)

    J_rev = jax.jacrev(projection_unit_simplex)(x)
    J_fwd = jax.jacfwd(projection_unit_simplex)(x)

    p = projection_unit_simplex(x)
    support = (p > 0).astype(jnp.float32)
    cardinality = jnp.count_nonzero(support).astype(support.dtype)
    J_true = jnp.diag(support) - jnp.outer(support, support) / cardinality
    self.assertAllClose(J_true, J_fwd)
    self.assertAllClose(J_true, J_rev)

    proj = jax.vmap(projection_unit_simplex)

    def fun(X):
      return jnp.sum(proj(X) ** 2)

    rng = self.rng()
    X = rng.rand(4, 5).astype(np.float32)
    U = rng.rand(4, 5)
    U /= np.sqrt(np.sum(U ** 2))
    U = U.astype(np.float32)

    eps = 1e-3
    dir_deriv_num = (fun(X + eps * U) - fun(X - eps * U)) / (2 * eps)
    dir_deriv = jnp.vdot(jax.grad(fun)(X), U)
    self.assertAllClose(dir_deriv, dir_deriv_num, atol=1e-3)

  def test_vmap_inside_defjvp(self):
    # https://github.com/google/jax/issues/3201
    seed = 47
    key = jax.random.PRNGKey(seed)
    mat = jax.random.normal(key, (2, 3))

    @jax.custom_jvp
    def f(mat, aux):
      num_rows, num_cols = mat.shape
      return jnp.ones((num_rows, 1)) / num_cols

    @f.defjvp
    def f_jvp(primals, tangents):
      mat, aux = primals
      vec, _ = tangents
      output = f(*primals)
      num_rows, num_cols = mat.shape
      size = num_rows * num_cols
      # -----
      bd_mat = mat.reshape(1, 1, num_rows, num_cols)
      bd_mat = jnp.tile(bd_mat, reps=(num_rows, num_cols))
      bd_mat = bd_mat.reshape(size, num_rows, num_cols)
      # -----
      rowsum = jnp.sum(mat, axis=1, keepdims=True)
      colsum = jnp.sum(mat, axis=0, keepdims=True)
      bd_rowsum = jnp.tile(rowsum, reps=(1, num_rows))
      bd_colsum = jnp.tile(colsum, reps=(num_cols, 1))
      # -----
      bd_vec = vec.reshape(size, 1)
      # -----
      def operate(mx, val):
        buf = 0
        for i in range(2):
          buf = buf + jnp.matmul(mx, bd_colsum) / jnp.power(aux, i)
        buf = jnp.matmul(bd_rowsum, buf)
        return buf * val[None, :]
      # -----
      # Vertorizing will raise shape error
      bd_buf = jax.vmap(operate, in_axes=(0, 0), out_axes=0)(bd_mat, bd_vec)
      # -----
      bd_buf = bd_buf / aux
      jvp = jnp.sum(bd_buf, axis=0)
      jvp = jnp.mean(jvp, axis=1, keepdims=True)
      # -----
      # JVP ends successfully, but still raise an error
      return (output, jvp)

    jax.grad(lambda mat, aux: jnp.sum(f(mat, aux)))(mat, 0.5)  # doesn't crash

  def test_custom_jvp_unbroadcasting(self):
    # https://github.com/google/jax/issues/3056
    a = jnp.array([1., 1.])

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

    @f.defjvp
    def f_jvp(primals, tangents):
      x, = primals
      dx, = tangents
      return a * x, a * dx

    shape = grad(lambda x: jnp.sum(f(x)))(jnp.array(1.)).shape
    self.assertEqual(shape, ())

  def test_maybe_perturbed_internal_helper_function(self):
    # This is a unit test for an internal API. We include it so as not to
    # regress https://github.com/google/jax/issues/9567. For an explanation of
    # this helper function, see https://github.com/google/jax/issues/6415.
    def f(x):
      def g(y, _):
        z = y * x
        self.assertTrue(custom_derivatives._maybe_perturbed(z))
        return y, None
      g(1, None)
      return lax.scan(g, 1, xs=None, length=1)[0]

    jax.jvp(f, (1.0,), (1.0,))  # assertions inside f

  def test_maybe_perturbed_int_regression(self):
    # see https://github.com/google/jax/discussions/9951

    @jax.jit
    def f():
      x = jnp.array(1)
      _, aux_args = custom_derivatives.closure_convert(lambda: x)
      self.assertEmpty(aux_args)
    f()

  def test_sinc_constant_function_batching(self):
    # https://github.com/google/jax/pull/10756
    batch_data = jnp.arange(15.).reshape(5, 3)

    @jax.vmap
    def f(x):
      return jax.lax.map(jnp.sinc, x)
    g = lambda param: f(param * batch_data).sum()

    @jax.vmap
    def f_ref(x):
      return jnp.stack([jnp.sinc(x_) for x_ in x])
    g_ref = lambda param: f_ref(param * batch_data).sum()

    grad     = jax.grad(g    )(0.1)  # doesn't crash
    grad_ref = jax.grad(g_ref)(0.1)
    self.assertAllClose(grad, grad_ref, check_dtypes=False)

  @parameterized.named_parameters(
      ('jit_vmap', True, True),
      ('jit', True, False),
      ('vmap', False, True),
      ('', False, False),
  )
  def test_symbolic_zero_custom_jvp(self, maybe_jit, maybe_vmap):
    def f(static_scalar, static_array, dyn_scalar, dyn_array):
      out1 = static_scalar + dyn_scalar
      out2 = static_array + dyn_array
      return out1, out2

    def _pack(x):
      return lax.broadcast(x, (1,))

    def _unpack(x):
      (x,) = x
      return x

    def _vmap(fun):
      def _fun(*args):
        args = tree_util.tree_map(_pack, args)
        out = jax.vmap(fun)(*args)
        out = tree_util.tree_map(_unpack, out)
        return out
      return _fun

    f = api.custom_jvp(f)

    @partial(f.defjvp, symbolic_zeros=True)
    def f_jvp(primals, tangents):
      static_scalar, *_ = primals
      t_static, t_static_arr, t_dyn_scalar, t_dyn_array = tangents
      self.assertIs(type(t_static)    , custom_derivatives_public.SymbolicZero)
      self.assertIs(type(t_static_arr), custom_derivatives_public.SymbolicZero)
      self.assertEqual(t_static.shape, ())
      self.assertEqual(t_static_arr.shape, (2,))
      return f(*primals), (static_scalar + 90, t_dyn_array + 91)

    def g(dyn_scalar, dyn_array):
      if maybe_vmap:
        f_ = _vmap(f)
      else:
        f_ = f
      return f_(1., jnp.array([2., 3.]), dyn_scalar, dyn_array)

    def run(primal_ins, tangent_ins):
      return jax.jvp(g, primal_ins, tangent_ins)

    if maybe_jit:
      run = jax.jit(run)

    primal_ins = (4., jnp.array([5., 6.]))
    tangent_ins = (7., jnp.array([8., 9.]))
    primal_outs, tangent_outs = run(primal_ins, tangent_ins)
    primal_out1, primal_out2 = primal_outs
    tangent_out1, tangent_out2 = tangent_outs
    scalar_dtype = jax.Array if maybe_jit or maybe_vmap else float
    self.assertIsInstance(primal_out1, scalar_dtype)
    self.assertAllClose(primal_out1, 5.)
    self.assertIsInstance(tangent_out1, scalar_dtype)
    self.assertAllClose(tangent_out1, 91.)
    self.assertIsInstance(primal_out2, jax.Array)
    self.assertArraysAllClose(primal_out2, jnp.array([7., 9.]))
    self.assertIsInstance(tangent_out2, jax.Array)
    self.assertArraysAllClose(tangent_out2, jnp.array([99., 100.]))

  def test_symbolic_zero_custom_jvp_vmap_output(self):
    @api.custom_jvp
    def f(x, y):
      return x * y

    @partial(f.defjvp, symbolic_zeros=True)
    def f_jvp(primals, tangents):
      x, y = primals
      x_dot, y_dot = tangents
      self.assertIs(type(y_dot), custom_derivatives_public.SymbolicZero)
      return f(x, y), y_dot

    jax.grad(lambda x, y: jax.vmap(f)(x, y).sum())(jnp.ones(3), jnp.ones(3))


class CustomVJPTest(jtu.JaxTestCase):

  def test_basic(self):
    @api.custom_vjp
    def f(x):
      return jnp.sin(x)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    x = 3.
    self.assertAllClose(f(x), jnp.sin(x))
    self.assertAllClose(api.grad(f)(x), 2 * jnp.cos(x))
    self.assertAllClose(api.value_and_grad(f)(x),
                        (jnp.sin(x), 2 * jnp.cos(x)))

  def test_invariance(self):
    @api.custom_vjp
    def f(x):
      return jnp.cos(2 * x) / 2.
    def f_fwd(x):
      return (f(x), x)
    def f_rev(x, g):
      return (g * 3,)
    f.defvjp(f_fwd, f_rev)
    def f2(x):
      y, _ = api.value_and_grad(f)(x)
      return y
    def f3(x):
      y, _ = api.value_and_grad(f2)(x)
      return y
    x = 1.
    self.assertAllClose(f(x), f2(x), check_dtypes=False)
    self.assertAllClose(f(x), f3(x), check_dtypes=False)
    self.assertAllClose(api.grad(f)(x), api.grad(f2)(x),
                        check_dtypes=False)
    self.assertAllClose(api.grad(f)(x), api.grad(f3)(x),
                        check_dtypes=False)

  def test_python_control_flow(self):
    @api.custom_vjp
    def f(x):
      if x > 0:
        return jnp.sin(x)
      else:
        return jnp.cos(x)
    def f_fwd(x):
      if x > 0:
        return f(x), x
      else:
        return f(x), x
    def f_rev(x, g):
      if x > 0:
        return (2 * g,)
      else:
        return (3 * g,)
    f.defvjp(f_fwd, f_rev)
    x = 2.
    self.assertAllClose(f(x), jnp.sin(x))
    self.assertAllClose(f(-x), jnp.cos(-x))
    self.assertAllClose(api.value_and_grad(f)(x), (jnp.sin(x), 2.),
                        check_dtypes=False)
    self.assertAllClose(api.value_and_grad(f)(-x), (jnp.cos(-x), 3.),
                        check_dtypes=False)

  def test_vmap(self):
    @api.custom_vjp
    def f(x):
      assert jnp.ndim(x) == 0
      return jnp.sin(x)
    def f_fwd(x):
      assert jnp.ndim(x) == 0
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    x = jnp.arange(3.)
    xx = jnp.arange(6.).reshape(2, 3)

    # vmap of f
    self.assertAllClose(api.vmap(f)(x), jnp.sin(x))
    self.assertAllClose(api.vmap(api.vmap(f))(xx), jnp.sin(xx))

    # vmap of grad of f
    self.assertAllClose(api.vmap(api.grad(f))(x), 2 * jnp.cos(x))
    self.assertAllClose(api.vmap(api.value_and_grad(f))(x),
                        (jnp.sin(x), 2 * jnp.cos(x)))
    self.assertAllClose(api.vmap(api.vmap(api.grad(f)))(xx), 2 * jnp.cos(xx))
    self.assertAllClose(api.vmap(api.vmap(api.value_and_grad(f)))(xx),
                        (jnp.sin(xx), 2 * jnp.cos(xx)))

    # grad of vmap of f
    self.assertAllClose(api.grad(lambda x: api.vmap(f)(x).sum())(x),
                        2 * jnp.cos(x))
    self.assertAllClose(api.grad(lambda x: api.vmap(api.vmap(f))(x).sum())(xx),
                        2 * jnp.cos(xx))

    # vmap of grad of vmap of f
    self.assertAllClose(api.vmap(api.grad(lambda x: api.vmap(f)(x).sum()))(xx),
                        2 * jnp.cos(xx))

  def test_jit(self):
    @api.custom_vjp
    def f(x):
      return jnp.sin(x)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    x = 3.

    # jit
    self.assertAllClose(api.jit(f)(x), jnp.sin(x))
    self.assertAllClose(api.jit(api.jit(f))(x), jnp.sin(x))

    # jit of grad
    self.assertAllClose(api.jit(api.grad(f))(x), 2 * jnp.cos(x),
                        check_dtypes=False)

    # grad of jit
    self.assertAllClose(api.grad(api.jit(f))(x), 2 * jnp.cos(x),
                        check_dtypes=False)

  def test_pytrees(self):
    @api.custom_vjp
    def f(x):
      return {'b': jnp.sin(x['a'])}
    def f_fwd(x):
      return f(x), {'r': jnp.cos(x['a'])}
    def f_bwd(res, g):
      cos_x = res['r']
      return ({'a': 2 * cos_x * g['b']},)
    f.defvjp(f_fwd, f_bwd)
    x = {'a': 3.}
    self.assertAllClose(f(x)['b'], jnp.sin(x['a']))
    self.assertAllClose(api.grad(lambda x: f(x)['b'])(x),
                        {'a': 2 * jnp.cos(x['a'])})

  def test_jvp_error(self):
    @api.custom_vjp
    def f(x):
      return jnp.sin(x)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    self.assertRaisesRegex(
        TypeError,
        r"can't apply forward-mode autodiff \(jvp\) to a custom_vjp function.",
        lambda: api.jvp(f, (3.,), (1.,)))
    self.assertRaisesRegex(
        TypeError,
        r"can't apply forward-mode autodiff \(jvp\) to a custom_vjp function.",
        lambda: api.jvp(api.vmap(f), (jnp.arange(3.),), (jnp.ones(3),)))
    self.assertRaisesRegex(
        TypeError,
        r"can't apply forward-mode autodiff \(jvp\) to a custom_vjp function.",
        lambda: api.jvp(jit(f), (3.,), (1.,)))

  def test_kwargs(self):
    # from https://github.com/google/jax/issues/1938
    @api.custom_vjp
    def my_fun(x, y, c=1.):
      return c * (x + y)
    my_fun.defvjp(lambda x, y, c=1.: (my_fun(c, y, c), None),
                  lambda _, g: (g, g, g))
    f = lambda x, y: jnp.square(my_fun(x, y, c=2.)).sum()
    f(10., 5.)  # doesn't crash
    api.grad(f)(10., 5.)  # doesn't crash

  def test_initial_style(self):
    @api.custom_vjp
    def f(x):
      return jnp.sin(x)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.grad(foo)(3.)
    expected = 2. * jnp.cos(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.grad(foo))(3.)
    expected = -2. * jnp.sin(3.)
    self.assertAllClose(ans, expected)

  def test_initial_style_vmap(self):
    @api.custom_vjp
    def f(x):
      assert jnp.ndim(x) == 0
      return 3 * x
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.vmap(foo)(jnp.arange(3.))
    expected = 3. * jnp.arange(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.vmap(foo)(x).sum())(jnp.arange(3.))
    expected = 2. * jnp.cos(jnp.arange(3.))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_nondiff_arg(self):
    @partial(api.custom_vjp, nondiff_argnums=(0,))
    def app(f, x):
      return f(x)
    def app_fwd(f, x):
      return app(f, x), jnp.cos(x)
    def app_rev(f, cos_x, g):
      return (cos_x * g,)
    app.defvjp(app_fwd, app_rev)

    ans = app(lambda x: 2 * x, 1)
    expected = 2
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.value_and_grad(lambda x: app(lambda y: 2 * y, x))(1.)
    expected = (2., jnp.cos(1.))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_closed_over_jit_tracer(self):
    # See the comment in CustomJVPTest.test_nondiff_arg_jit_tracer.
    raise unittest.SkipTest("behavior no longer supported")

    # This test is similar to test_nondiff_arg_tracer except it uses lexical
    # closure rather than the nondiff_argnums mechanism. We decided to disallow
    # tracers in nondiff_argnums to greatly simplify bookkeeping while still
    # supporting the cases for which it is necessary.
    def outer(x):
      @api.custom_vjp
      def f(y):
        return x * y
      def f_fwd(y):
        return f(y), jnp.cos(y)
      def f_rev(cos_y, g):
        return (cos_y * g,)
      f.defvjp(f_fwd, f_rev)
      return f

    @jit
    def g(x, y):
      return outer(x)(y)

    ans = g(2, 3.)
    expected = 6.
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(g, 1)(2., 3.)
    expected = jnp.cos(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_closed_over_vmap_tracer(self):
    def outer(x):
      @api.custom_vjp
      def f(y):
        return x * y
      def f_fwd(y):
        return f(y), jnp.cos(y)
      def f_rev(cos_y, g):
        return (cos_y * g,)
      f.defvjp(f_fwd, f_rev)
      return f

    @api.vmap
    def g(x):
      return outer(x)(3.)

    ans = g(np.arange(3.))
    expected = np.arange(3.) * 3
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_closed_over_tracer3(self):
    def outer(x):
      @api.custom_vjp
      def f(y):
        return x * y
      def f_fwd(y):
        return f(y), (x, jnp.cos(y))
      def f_rev(res, g):
        x, cos_y = res
        return (cos_y * g * x,)
      f.defvjp(f_fwd, f_rev)
      return api.grad(f)

    @api.vmap
    def g(x):
      return outer(x)(3.)

    ans = g(np.arange(3.))
    expected = np.cos(3.) * np.arange(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_nondiff_arg_tracer_error(self):
    # This is similar to the old (now skipped) test_nondiff_arg_tracer, except
    # we're testing for the error message that that usage pattern now raises.

    @partial(api.custom_vjp, nondiff_argnums=(0,))
    def f(x, y):
      return x * y
    def f_fwd(x, y):
      return f(x, y), jnp.cos(y)
    def f_rev(x, cos_y, g):
      return (cos_y * g,)
    f.defvjp(f_fwd, f_rev)

    @jit
    def g(x, y):
      return f(x, y)

    with self.assertRaisesRegex(UnexpectedTracerError, "custom_vjp"):
      _ = g(2, 3.)
    with self.assertRaisesRegex(UnexpectedTracerError, "custom_vjp"):
      _ = api.grad(g, 1)(2., 3.)

  def test_vmap_axes(self):
    raise unittest.SkipTest("TODO")  # TODO(mattjj): write test

  def test_pmap(self):
    raise unittest.SkipTest("TODO")  # TODO(mattjj): write test

  def test_missing_vjp_rule_error(self):
    @api.custom_vjp
    def foo(x):
      return x ** 2

    self.assertRaisesRegex(
        AttributeError,
        r"No VJP defined for custom_vjp function foo using defvjp.",
        lambda: foo(2))
    self.assertRaisesRegex(
        AttributeError,
        r"No VJP defined for custom_vjp function foo using defvjp.",
        lambda: api.grad(foo)(2.))

  def test_vjp_rule_inconsistent_pytree_structures_error(self):
    @api.custom_vjp
    def f(x):
      return x

    def foo_fwd(x):
      return x, None

    def foo_bwd(_, g):
      return (g, g)

    f.defvjp(foo_fwd, foo_bwd)

    f(2)  # doesn't crash
    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom VJP rule must produce an output with the same container "
            "(pytree) structure as the args tuple of the primal function, "
            "and in particular must produce a tuple of length equal to the "
            "number of arguments to the primal function, but got VJP output "
            "structure {} for primal input structure {}.".format(
                tree_util.tree_structure((1, 1)),
                tree_util.tree_structure((1,)))
        ),
        lambda: api.grad(f)(2.))

  def test_vjp_bwd_returns_non_tuple_error(self):
    @api.custom_vjp
    def f(x):
      return x

    def foo_fwd(x):
      return x, None

    def foo_bwd(_, g):
      return 2. * g  # Should be a tuple

    f.defvjp(foo_fwd, foo_bwd)
    with self.assertRaisesRegex(TypeError, "Custom VJP rule .* must produce a tuple"):
      api.grad(f)(3.)

  def test_fwd_rule_primal_out_type_doesnt_match_primal_error_message(self):
    # https://github.com/lucidrains/flash-attention-jax/issues/7

    def scan_apply(f, x):
      y, _ = jax.lax.scan(lambda x, _: (f(x), None), x, None, length=1)
      return y

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

    def f_fwd(x):
      return (x, x), None

    def f_bwd(_, y_bar):
      return (y_bar,)

    f.defvjp(f_fwd, f_bwd)

    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom VJP fwd rule f_fwd for function f must produce a pair "
            "(list or tuple of length two) where the first element represents "
            "the primal output (equal to the output of the "
            "custom_vjp-decorated function f) and the second element "
            "represents residuals (i.e. values stored from the forward "
            "pass for use on the backward pass), but instead the fwd rule "
            "output's first element had container/pytree structure:\n"
            "    (float32[], float32[])\n"
            "while the custom_vjp-decorated function f had output "
            "container/pytree structure:\n"
            "    float32[]."
        ),
        lambda: jax.grad(lambda x: scan_apply(f, x))(jnp.float32(1.)))

    def f_fwd2(x):
      return jnp.zeros((3, *x.shape), x.dtype), None

    def f_bwd2(_, y_bar):
      return (y_bar,)

    f.defvjp(f_fwd2, f_bwd2)

    self.assertRaisesRegex(
        TypeError,
        re.escape(
            "Custom VJP fwd rule f_fwd2 for function f must produce a pair "
            "(list or tuple of length two) where the first element represents "
            "the primal output (equal to the output of the "
            "custom_vjp-decorated function f) and the second element "
            "represents residuals (i.e. values stored from the forward "
            "pass for use on the backward pass), but instead the fwd rule "
            "output's first element had shapes/dtypes of:\n"
            "    float32[3]\n"
            "while the custom_vjp-decorated function f had output "
            "shapes/dtypes of:\n"
            "    float32[]"
        ),
        lambda: jax.grad(lambda x: scan_apply(f, x))(jnp.float32(1.)))

  def test_issue2511(self):
    arr = jnp.ones((5, 2, 2))
    foo = lambda x: api.vmap(jnp.linalg.det, (0,))(x)
    api.jit(foo)(arr)  # doesn't crash

  def test_lowering_out_of_traces(self):
    # https://github.com/google/jax/issues/2578

    class F(collections.namedtuple("F", ["a"])):
      def __call__(self, x):
        return jax.nn.relu(self.a) * x

    @jax.jit
    def g(f, x):
      return f(x)

    jax.grad(g, argnums=(1,))(F(2.0), 0.)  # doesn't crash

  def test_clip_gradient(self):
    # https://github.com/google/jax/issues/2784
    @api.custom_vjp
    def _clip_gradient(lo, hi, x):
      return x  # identity function when not differentiating

    def clip_gradient_fwd(lo, hi, x):
      return x, (lo, hi,)

    def clip_gradient_bwd(res, g):
      lo, hi = res
      return (None, None, jnp.clip(g, lo, hi),)

    _clip_gradient.defvjp(clip_gradient_fwd, clip_gradient_bwd)

    def clip_gradient(x):
      lo = -0.1
      hi = x + 0.1
      return _clip_gradient(lo, hi, x)

    g = jax.grad(clip_gradient)(0.1)  # doesn't crash
    self.assertAllClose(g, jnp.array(0.2))

  def test_nestable_vjp(self):
    # Verify that https://github.com/google/jax/issues/3667 is resolved.
    def f(x):
      return x ** 2

    @api.custom_vjp
    def g(x):
      return f(x)

    def g_fwd(x):
      y, f_vjp = api.vjp(f, x)
      return y, f_vjp

    def g_bwd(f_vjp, y_bar):
      return f_vjp(y_bar)

    g.defvjp(g_fwd, g_bwd)

    # Check that VJP can be nested in simple situations.  For this to pass,
    # vjp has to return a PyTree.
    _, g_vjp = api.vjp(g, 1.0)
    y, = g_vjp(1.0)
    self.assertAllClose(y, jnp.array(2.0))

    # Check that VJP can be nested in complex situations.  For this to pass,
    # vjp can't treat the closed-over tracer x as a static argument.
    @jit
    def z(x):
      _, g_vjp = api.vjp(g, x)
      return g_vjp
    y, = z(1.0)(3.0)
    self.assertAllClose(y, jnp.array(6.0))

  def test_initial_style_vmap_2(self):
    # https://github.com/google/jax/issues/4173
    x = jnp.ones((10, 3))

    # Create the custom function
    @api.custom_vjp
    def custom_fun(x):
      return x.sum()

    def forward(x):
      return x.sum(), (jnp.ones_like(x),)

    def backward(res, g):
      return g * res[0],

    custom_fun.defvjp(forward, backward)

    def train_fun(x):

      def summed_fun(x):
        return api.vmap(custom_fun)(x).sum()

      return api.grad(summed_fun)(x)

    def scan_body(carry, inputs):
      x = carry
      return carry, train_fun(x)

    scan_range = jnp.arange(4)
    lax.scan(scan_body, x, scan_range)  # don't crash

  def test_initial_style_vmap_3(self):
    # This is like test_initial_style_vmap except the primal function closes
    # over an array constant.
    y = jnp.arange(1., 4.)

    @api.custom_vjp
    def f(x):
      assert jnp.ndim(x) == 0
      return 3 * x * jnp.sum(y)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    def foo(x):
      out, _  = lax.scan(lambda c, _: (f(c), None), x, None, length=1)
      return out

    ans = api.vmap(foo)(jnp.arange(3.))
    expected = 3. * jnp.arange(3.) * 6
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(lambda x: api.vmap(foo)(x).sum())(jnp.arange(3.))
    expected = 2. * jnp.cos(jnp.arange(3.))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_initial_style_vmap_with_collective(self):

    @api.custom_vjp
    def f(x):
      return lax.psum(x, 'foo')

    def f_fwd(x):
      return lax.psum(x, 'foo'), None

    def f_bwd(res, dx):
      return dx
    f.defvjp(f_fwd, f_bwd)

    def g(x):
      jaxpr = api.make_jaxpr(f)(x)
      return core.eval_jaxpr(jaxpr.jaxpr, [], x)[0]

    out = api.vmap(lambda _, x: g(x), axis_name='foo', in_axes=(0, None),
        out_axes=None)(jnp.arange(4.), 2.)
    self.assertAllClose(out, 8.)

  def test_bwd_closes_over_tracer(self):
    def f(y):
      @jax.custom_vjp
      def f(x):
        return 2. * jnp.sin(x)

      def fwd(x):
        return f(x), ()

      def bwd(_, g):
        return (2. * jnp.cos(y) * g,)  # capture!

      f.defvjp(fwd, bwd)

      return jax.grad(f)(1.)

    ans = jax.jit(f)(2.)
    self.assertAllClose(ans, 2. * jnp.cos(2.))

    ans = jax.vmap(f)(jnp.arange(3.))
    self.assertAllClose(ans, 2. * jnp.cos(jnp.arange(3.)))

    ans = jax.jit(jax.vmap(f))(jnp.arange(3.))
    self.assertAllClose(ans, 2. * jnp.cos(jnp.arange(3.)))

    ans = jax.vmap(jax.jit(f))(jnp.arange(3.))
    self.assertAllClose(ans, 2. * jnp.cos(jnp.arange(3.)))

    ans = jax.grad(f)(4.)
    self.assertAllClose(ans, -2. * jnp.sin(4.))

  def test_fwd_closes_over_tracer(self):
    def f(y):
      @jax.custom_vjp
      def f(x):
        return 2. * jnp.sin(x)

      def fwd(x):
        return f(x), y

      def bwd(y, g):
        return (2. * jnp.cos(y) * g,)  # capture!

      f.defvjp(fwd, bwd)

      return jax.grad(f)(1.)

    ans = jax.jit(f)(2.)
    self.assertAllClose(ans, 2. * jnp.cos(2.))

    ans = jax.vmap(f)(jnp.arange(3.))
    self.assertAllClose(ans, 2. * jnp.cos(jnp.arange(3.)))

    ans = jax.jit(jax.vmap(f))(jnp.arange(3.))
    self.assertAllClose(ans, 2. * jnp.cos(jnp.arange(3.)))

    ans = jax.vmap(jax.jit(f))(jnp.arange(3.))
    self.assertAllClose(ans, 2. * jnp.cos(jnp.arange(3.)))

    ans = jax.grad(f)(4.)
    self.assertAllClose(ans, -2. * jnp.sin(4.))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_float0(self):
    @api.custom_vjp
    def f(x, _):
      return x
    def f_fwd(x, _):
      # we need a defined (non-float0) tangent to trigger the rule
      return x, (2., 1)
    def f_rev(*_):
      return (2., 1)
    f.defvjp(f_fwd, f_rev)

    x = 2.
    y = 3
    self.assertEqual(api.grad(f, allow_int=True, argnums=(0, 1))(x, y),
                     (2., np.zeros(shape=(), dtype=float0)))

  @unittest.skipIf(numpy_version == (1, 21, 0),
                   "https://github.com/numpy/numpy/issues/19305")
  def test_float0_initial_style(self):
    @api.custom_vjp
    def f(x):
      return x
    def f_fwd(x):
      return x, (2., x)
    def f_rev(*_):
      return ((2., 1),)
    f.defvjp(f_fwd, f_rev)

    def foo(x, y):
      out, _ = lax.scan(lambda c, _: (f(c), None), (x, y), None, length=1)
      return out[0]

    x = 2.
    y = 3
    self.assertEqual(api.grad(foo, allow_int=True, argnums=(0, 1))(x, y),
                     (2., np.zeros(shape=(), dtype=float0)))

  def test_remat(self):
    @api.custom_vjp
    def f(x):
      return jnp.sin(x)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    @api.remat
    def g(x):
      return f(f(x))

    ans = g(2.)
    expected = np.sin(np.sin(2.))
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(g)(2.)
    expected = 4. * api.grad(lambda x: jnp.sin(jnp.sin(x)))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_remat_higher_order(self):
    @api.custom_vjp
    def f(x):
      return jnp.sin(x)
    def f_fwd(x):
      return f(x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (2 * cos_x * g,)
    f.defvjp(f_fwd, f_rev)

    def g(x):
      return f(f(x))

    ans = api.grad(api.grad(api.remat(g)))(2.)
    expected = api.grad(api.grad(g))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.remat(api.grad(g)))(2.)
    expected = api.grad(api.grad(g))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

    ans = api.grad(api.grad(api.grad(api.remat(g))))(2.)
    expected = api.grad(api.grad(api.grad(g)))(2.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_bwd_nones(self):
    @api.custom_vjp
    def f(x, y):
      return x * jnp.sin(y)
    def f_fwd(x, y):
      return f(x, y), jnp.cos(y)
    def f_rev(cos, g):
      return (None, 2 * cos * g)
    f.defvjp(f_fwd, f_rev)

    ans = api.grad(lambda x: f(x, x))(3.)
    expected = 2 * jnp.cos(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_bwd_nones_vmap(self):
    @api.custom_vjp
    def f(x, y):
      return x * jnp.sin(y)
    def f_fwd(x, y):
      return f(x, y), jnp.cos(y)
    def f_rev(cos, g):
      return (None, 2 * cos * g)
    f.defvjp(f_fwd, f_rev)

    ans = api.grad(lambda x: api.vmap(f)(x, x).sum())(jnp.arange(3.))
    expected = 2 * jnp.cos(jnp.arange(3.))
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_bwd_nones_pytree(self):
    @api.custom_vjp
    def f(xs, y):
      x1, x2 = xs
      return x1 * x2 * jnp.sin(y)
    def f_fwd(xs, y):
      return f(xs, y), jnp.cos(y)
    def f_rev(cos, g):
      return (None, 2 * cos * g)
    f.defvjp(f_fwd, f_rev)

    ans = api.grad(lambda x: f((x, x), x))(3.)
    expected = 2 * jnp.cos(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_custom_vjp_closure_4521(self):
    # https://github.com/google/jax/issues/4521
    @api.custom_vjp
    def g(x, y):
      return None
    def g_fwd(x, y):
      return None, y
    def g_bwd(residuals, z_bar):
      assert False

    g.defvjp(g_fwd, g_bwd)

    def f(xs, y):
      v_g = api.vmap(g, in_axes=(0, None), out_axes=None)
      v_g(xs, y)

    def scan_body(xs, _):
      y = jnp.zeros(1)
      _, vjp_f = api.vjp(f, xs, y)
      vjp_f(None)
      return xs, None

    lax.scan(scan_body, jnp.ones(5), None, 100)  # doesn't crash

  def test_float0_bwd_none(self):
    @api.custom_vjp
    def f(i, x):
      return jnp.sin(x)
    def f_fwd(i, x):
      return f(i, x), jnp.cos(x)
    def f_rev(cos_x, g):
      return (None, 2 * cos_x * g)
    f.defvjp(f_fwd, f_rev)

    ans = api.grad(f, 1)(jnp.array([1, 2]), 3.)  # doesn't crash
    expected = 2 * jnp.cos(3.)
    self.assertAllClose(ans, expected, check_dtypes=False)

  def test_custom_gradient(self):
    @api.custom_gradient
    def f(x):
      return x ** 2, lambda g: (g * x,)

    self.assertAllClose(f(3.), 9., check_dtypes=False)
    self.assertAllClose(api.grad(f)(3.), 3., check_dtypes=False)
    self.assertAllClose(api.grad(api.grad(f))(3.), 1., check_dtypes=False)

  def test_custom_gradient_2(self):
    @api.custom_gradient
    def f(x, y):
      return x * y, lambda g: (y, x)

    self.assertAllClose(f(3., 4.), 12., check_dtypes=False)
    self.assertAllClose(api.grad(f, argnums=(0, 1))(3., 4.), (4., 3.),
                        check_dtypes=False)

  def test_custom_gradient_3(self):
    @api.custom_gradient
    def f(x):
      vjp = lambda g: (jnp.cos(x) * jnp.arange(3., 6.),)
      return jnp.sum(jnp.sin(x)), vjp

    self.assertAllClose(f(jnp.arange(3)), jnp.sum(jnp.sin(jnp.arange(3.))),
                        check_dtypes=False)
    self.assertAllClose(
        api.grad(f)(jnp.arange(3.)),
        api.grad(lambda x: jnp.sum(jnp.sin(x)))(jnp.arange(3.)) * jnp.arange(3., 6.),
        check_dtypes=False)

  def test_custom_gradient_can_return_singleton_value_in_vjp(self):
    @api.custom_gradient
    def f(x):
      return x ** 2, lambda g: g * x

    self.assertAllClose(f(3.), 9., check_dtypes=False)
    self.assertAllClose(api.grad(f)(3.), 3., check_dtypes=False)
    self.assertAllClose(api.grad(api.grad(f))(3.), 1., check_dtypes=False)

  def test_closure_convert(self):
    def cos_after(fn, x):
      converted_fn, aux_args = jax.closure_convert(fn, x)
      self.assertLessEqual(len(aux_args), 1)
      return _cos_after(converted_fn, x, *aux_args)

    @partial(api.custom_vjp, nondiff_argnums=(0,))
    def _cos_after(fn, x, *args):
      return jnp.cos(fn(x, *args))

    def fwd(fn, x, *args):
      y = _cos_after(fn, x, *args)
      return y, (x, args)

    def rev(fn, res, g):
      x, args = res
      x_bar = 17. * x
      args_bars = [42. * a for a in args]
      return (x_bar, *args_bars)

    _cos_after.defvjp(fwd, rev)

    def dist(c, x):
      return jnp.sum((x - c) ** 2.)

    def solve(c, x):
      def closure(x):
        return dist(c, x)
      return cos_after(closure, x)

    c, x = 2. * jnp.ones(2), jnp.ones(2)
    expected = jnp.cos(dist(c, x))
    self.assertAllClose(solve(c, x), expected, check_dtypes=False)
    g_c, g_x = api.grad(solve, argnums=(0, 1))(c, x)
    self.assertAllClose(g_c, 42. * c, check_dtypes=False)
    self.assertAllClose(g_x, 17. * x, check_dtypes=False)

  def test_closure_convert_mixed_consts(self):
    # Like test_closure_convert, but close over values that
    # participate in AD as well as values that do not.
    # See https://github.com/google/jax/issues/6415

    def cos_after(fn, x):
      converted_fn, aux_args = jax.closure_convert(fn, x)
      self.assertLessEqual(len(aux_args), 1)
      return _cos_after(converted_fn, x, *aux_args)

    @partial(api.custom_vjp, nondiff_argnums=(0,))
    def _cos_after(fn, x, *args):
      return jnp.cos(fn(x, *args))

    def fwd(fn, x, *args):
      y = _cos_after(fn, x, *args)
      return y, (x, args)

    def rev(fn, res, g):
      x, args = res
      x_bar = 17. * x
      args_bars = [42. * a for a in args]
      return (x_bar, *args_bars)

    _cos_after.defvjp(fwd, rev)

    def dist(c, s, x):
      return jnp.sum(s * (x - c) ** 2.)

    def solve(c, s, x):
      def closure(x):
        return dist(c, s, x)
      return cos_after(closure, x)

    c, s, x = 2. * jnp.ones(2), 3. * jnp.ones(2), jnp.ones(2)
    expected = jnp.cos(dist(c, s, x))
    self.assertAllClose(solve(c, s, x), expected, check_dtypes=False)
    g_c, g_x = api.grad(solve, argnums=(0, 2))(c, s, x)
    self.assertAllClose(g_c, 42. * c, check_dtypes=False)
    self.assertAllClose(g_x, 17. * x, check_dtypes=False)

  def test_float0_cotangents_automatically_handled(self):
    @jax.custom_vjp
    def f(x, y):
      return x

    def f_fwd(x, y):
      return x, None

    def f_bwd(_, zbar):
      return (0., 1)

    f.defvjp(f_fwd, f_bwd)

    jax.jit(lambda x: jax.vjp(f, 0., x)[1](1.))(1)  # doesn't crash

  def test_custom_vjp_scan_batching_edge_case(self):
    # https://github.com/google/jax/issues/5832
    @jax.custom_vjp
    def mul(x, coeff): return x * coeff
    def mul_fwd(x, coeff): return mul(x, coeff), (x, coeff)
    def mul_bwd(res, g):
      x, coeff = res
      g_x = g * coeff
      g_coeff = (x * g).sum()
      return g_x, g_coeff
    mul.defvjp(mul_fwd, mul_bwd)

    def scan_over_mul(x, coeff):
      def f_(x, t):
        return mul(x, coeff), None
      y, _ = jax.lax.scan(f_, x, jnp.arange(3))
      return y

    key = jax.random.PRNGKey(0)
    key1, key2 = jax.random.split(key, 2)
    x_batch = jax.random.normal(key1, (3, 2))
    covector_batch = jax.random.normal(key2, (3, 2))
    coeff = jnp.array(1., dtype=x_batch.dtype)

    batched_scan_over_mul = jax.vmap(scan_over_mul, in_axes=(0, None), out_axes=0)
    res, vjp_fun = jax.vjp(batched_scan_over_mul, x_batch, coeff)
    vjp_fun(covector_batch)  # doesn't crash

    jtu.check_grads(batched_scan_over_mul, (x_batch, coeff), order=2,
                    modes=['rev'])

  def test_closure_with_vmap2(self):
    # https://github.com/google/jax/issues/8783
    def h(z):
      def f(x):
        @jax.custom_vjp
        def g(y):
          return x * y

        def g_fwd(y):
          return x * y, (x, x * y, y)
        def g_rev(res, w_bar):
          x, *_ = res
          return (x * w_bar,)
        g.defvjp(g_fwd, g_rev)

        return g(z)

      return jax.vmap(f)(jnp.arange(3., dtype='float32')).sum()

    jtu.check_grads(h, (jnp.float32(3.14),), order=1, modes=['rev'])

  def test_pytrees_not_required_to_contain_nones(self):
    class A(list):
      pass

    def unflatten(_, children):
      assert children[0] is not None
      return A(children)

    tree_util.register_pytree_node(A, lambda x: (x, None), unflatten)

    @jax.custom_vjp
    def f(x):
      return x[0]
    def f_fwd(x):
      return x[0], None
    def f_bwd(_, g):
      return A([g]),
    f.defvjp(f_fwd, f_bwd)

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

  def test_vmap_vjp_called_twice(self):
    # https://github.com/google/jax/pull/14728
    @jax.custom_vjp
    def f(x):
      return x
    f.defvjp(lambda x: (x, None), lambda _, y_bar: (y_bar,))

    _, f_vjp = jax.vjp(jax.vmap(f), jnp.array([3.]))
    f_vjp(jnp.array([3.]))
    f_vjp(jnp.array([3.]))  # doesn't crash


def transpose_unary(f, x_example):
  def transposed(y):
    x, = api.linear_transpose(f, x_example)(y)
    return x
  return transposed


# This class wraps api.custom_transpose in order to pass in a
# particular tree of output type on each call. Otherwise it forwards
# all attribute access.
class _custom_transpose:
  def __init__(self, out_types, fun):
    self.out_types = out_types
    self.fun = api.custom_transpose(fun)

  def __getattr__(self, name):
    return getattr(self.fun, name)

  def __call__(self, *args):
    return self.fun(self.out_types, *args)


# This function is meant to be used as a decorator that delegates to
# custom_transpose but makes it easy to specify output argument types
# by example. If used directly a decorator (i.e. not invoked with
# example arguments), assumes a scalar-valued function.
#
# TODO(frostig): remove this (and its uses) once custom_transpose offers
# an option of inferring output types.
def custom_transpose(example_out):
  if isinstance(example_out, Callable):
    out_type = core.get_aval(0.).at_least_vspace()
    return _custom_transpose(out_type, example_out)
  return partial(
      _custom_transpose,
      tree_util.tree_map(
          lambda x: core.get_aval(x).at_least_vspace(), example_out))


class CustomTransposeTest(jtu.JaxTestCase):

  def test_linear_call(self):
    def f(x, y):
      def fn(r, x): return x / r
      def tp(r, t): return t / r
      return x + api.linear_call(fn, tp, y, x)

    def f_ref(x, y):
      return x + x / y

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), f_ref(x, y))

    f1     = lambda x: f(x, y)
    f1_ref = lambda x: f_ref(x, y)
    self.assertAllClose(transpose_unary(f1,     x)(x),
                        transpose_unary(f1_ref, x)(x))

  def test_linear_call_incorrect_transpose(self):
    def f(x, y):
      def fn(r, x): return x / r
      def tp(r, t): return t / (2. * r)  # nb: not the true transpose
      return x + api.linear_call(fn, tp, y, x)

    def f_ref(x, y):
      return x + x / y

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), f_ref(x, y))

    f1     = lambda x: f(x, y)
    f1_ref = lambda x: f_ref(x, 2. * y)  # nb: double the reference divisor
    self.assertAllClose(transpose_unary(f1,     x)(x),
                        transpose_unary(f1_ref, x)(x))

  def test_linear_call_transpose_transpose_transpose(self):
    def fn(r, x): return x / r
    def tp(r, t): return t / (2. * r)  # nb: untrue transpose
    def f_(x, y):
      return x + api.linear_call(fn, tp, y, x)

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    f = lambda x: f_(x, y)
    ft   = transpose_unary(f,   x)
    ftt  = transpose_unary(ft,  x)
    fttt = transpose_unary(ftt, x)
    self.assertAllClose(ft(x), x + tp(y, x))
    self.assertAllClose(f(x),  ftt(x))
    self.assertAllClose(ft(x), fttt(x))

  def test_linear_call_scalar_to_vector(self):
    def f(c, x):
      def fn(_, x):
        return [x, x]

      def tp(_, t):
        t1, t2 = t
        return t1 + t2

      return api.linear_call(fn, tp, (), c * x)

    def f_ref(c, x):
      return [c * x, c * x]

    c, x = 2., 3.
    t = [4., 5.]
    self.assertAllClose(f(c, x), f_ref(c, x))
    self.assertAllClose(transpose_unary(partial(f,     c), x)(t),
                        transpose_unary(partial(f_ref, c), x)(t))

  def test_linear_call_nested(self):
    # identity function with an untrue transpose of 0
    def id_(x):
      def f(_, x): return x
      def t(_, t): return 0.
      return api.linear_call(f, t, (), x)

    # identity function with an untrue transpose of 7, and where both
    # forward and transpose have custom transpositions that should
    # never end up invoked.
    def f(x):
      def f_(_, x): return id_(x)
      def t_(_, t): return id_(7.)
      return api.linear_call(f_, t_, (), x)

    x = 5.
    id_t  = transpose_unary(id_,  x)
    id_tt = transpose_unary(id_t, x)
    ft   = transpose_unary(f,    x)
    ftt  = transpose_unary(ft,   x)
    fttt = transpose_unary(ftt,  x)

    self.assertAllClose(id_(x),   x)
    self.assertAllClose(id_t(x),  0.)
    self.assertAllClose(id_tt(x), x)

    self.assertAllClose(f(x),    x)
    self.assertAllClose(ft(x),   7.)
    self.assertAllClose(ftt(x),  x)
    self.assertAllClose(fttt(x), 7.)

  def test_linear_call_jit(self):
    def f(x, y):
      def fn(r, x): return x / r
      def tp(r, t): return t / r
      return x + api.linear_call(fn, tp, y, x)

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), jax.jit(f)(x, y))

    f1 = lambda x: f(x, y)
    self.assertAllClose(transpose_unary(f1, x)(x),
                        jax.jit(transpose_unary(f1, x))(x))

  def test_basic(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return t / r

      return x + fn(y, x)

    def f_ref(x, y):
      return x + x / y

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), f_ref(x, y))

    f1     = lambda x: f(x, y)
    f1_ref = lambda x: f_ref(x, y)
    self.assertAllClose(transpose_unary(f1,     x)(x),
                        transpose_unary(f1_ref, x)(x))

  def test_incorrect_transpose(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return t / (2. * r)  # nb: not the true transpose

      return x + fn(y, x)

    def f_ref(x, y):
      return x + x / y

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), f_ref(x, y))

    f1     = lambda x: f(x, y)
    f1_ref = lambda x: f_ref(x, 2. * y)  # nb: double the reference divisor
    self.assertAllClose(transpose_unary(f1,     x)(x),
                        transpose_unary(f1_ref, x)(x))

  def test_transpose_transpose_transpose(self):
    @custom_transpose(jnp.ones(2))
    def fn(r, x): return x / r
    @custom_transpose(jnp.ones(2))
    def tp(r, t): return t / (2. * r)  # nb: untrue transpose

    fn.def_transpose(tp)
    tp.def_transpose(fn)

    def f_(x, y):
      return x + fn(y, x)

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    f = lambda x: f_(x, y)
    ft   = transpose_unary(f,   x)
    ftt  = transpose_unary(ft,  x)
    fttt = transpose_unary(ftt, x)
    self.assertAllClose(ft(x), x + tp(y, x))
    self.assertAllClose(f(x),  ftt(x))
    self.assertAllClose(ft(x), fttt(x))

  def test_scalar_to_vector(self):
    def f(c, x):
      @custom_transpose([0., 0.])
      def fn(_, x):
        return [x, x]

      @fn.def_transpose
      def tp(_, t):
        t1, t2 = t
        return t1 + t2

      return fn((), c * x)

    def f_ref(c, x):
      return [c * x, c * x]

    c, x = 2., 3.
    t = [4., 5.]
    self.assertAllClose(f(c, x), f_ref(c, x))
    self.assertAllClose(transpose_unary(partial(f,     c), x)(t),
                        transpose_unary(partial(f_ref, c), x)(t))

  def test_nested(self):
    # identity function with an untrue transpose of 0
    def id_(x):
      f = custom_transpose(lambda _, x: x)
      t = custom_transpose(lambda _, t: 0.)
      f.def_transpose(t)
      t.def_transpose(f)
      return f((), x)

    # identity function with an untrue transpose of 7, and where both
    # forward and transpose have custom transpositions that should
    # never end up invoked.
    def f(x):
      f_ = custom_transpose(lambda _, x: id_(x))
      t_ = custom_transpose(lambda _, t: id_(7.))
      f_.def_transpose(t_)
      t_.def_transpose(f_)
      return f_((), x)

    x = 5.
    id_t  = transpose_unary(id_,  x)
    id_tt = transpose_unary(id_t, x)
    ft   = transpose_unary(f,    x)
    ftt  = transpose_unary(ft,   x)
    fttt = transpose_unary(ftt,  x)

    self.assertAllClose(id_(x),   x)
    self.assertAllClose(id_t(x),  0.)
    self.assertAllClose(id_tt(x), x)

    self.assertAllClose(f(x),    x)
    self.assertAllClose(ft(x),   7.)
    self.assertAllClose(ftt(x),  x)
    self.assertAllClose(fttt(x), 7.)

  def test_one_degree(self):
    T = lambda f: transpose_unary(f, 0.)

    @custom_transpose
    def f(_, z): return 2. * z
    @f.def_transpose
    def ft(_, z): return 3. * z

    f = partial(f, ())
    self.assertAllClose(2., f(1.))
    self.assertAllClose(3., T(f)(1.))
    self.assertAllClose(3., T(T(f))(1.))
    self.assertAllClose(3., T(T(T(f)))(1.))
    self.assertAllClose(3., T(T(T(T(f))))(1.))  # ...

  def test_two_degrees(self):
    T = lambda f: transpose_unary(f, 0.)

    @custom_transpose
    def f(_, z): return 2. * z

    @f.def_transpose
    @custom_transpose
    def ft(_, z): return 3. * z

    @ft.def_transpose
    def ftt(_, z): return 7. * z

    f = partial(f, ())
    self.assertAllClose(2., f(1.))
    self.assertAllClose(3., T(f)(1.))
    self.assertAllClose(7., T(T(f))(1.))
    self.assertAllClose(7., T(T(T(f)))(1.))
    self.assertAllClose(7., T(T(T(T(f))))(1.))  # ...

  def test_symmetric(self):
    T = lambda f: transpose_unary(f, 0.)

    @custom_transpose
    def f(_, z): return 2. * z
    @custom_transpose
    def g(_, z): return 3. * z

    f.def_transpose(g)
    g.def_transpose(f)

    f = partial(f, ())
    self.assertAllClose(2., f(1.))
    self.assertAllClose(3., T(f)(1.))
    self.assertAllClose(2., T(T(f))(1.))
    self.assertAllClose(3., T(T(T(f)))(1.))
    self.assertAllClose(2., T(T(T(T(f))))(1.))  # ...

  def test_recursive(self):
    T = lambda f: transpose_unary(f, 0.)

    @custom_transpose
    def f(c, z): return c * z

    @f.def_transpose
    def ft(c, z): return f(c + 1., z)

    g = partial(f, 1.)
    self.assertAllClose(1., g(1.))
    self.assertAllClose(2., T(g)(1.))
    self.assertAllClose(3., T(T(g))(1.))
    self.assertAllClose(4., T(T(T(g)))(1.))
    self.assertAllClose(5., T(T(T(T(g))))(1.))  # ...

  def test_jvp_lin(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return t / r
      return x + fn(y, x)

    def f_ref(x, y): return x + x / y

    x, y, tx = 6., 3., 1.
    g = lambda x: f(x, y)
    g_ref = lambda x: f_ref(x, y)
    self.assertAllClose(api.jvp(g, [x], [tx]), api.jvp(g_ref, [x], [tx]))

  def test_jvp_res(self):
    raise unittest.SkipTest('unimplemented')  # TODO(frostig)

    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return t / r
      return x + fn(y, x)

    def f_ref(x, y): return x + x / y

    x, y, ty = 6., 3., 1.
    g = lambda y: f(x, y)
    g_ref = lambda y: f_ref(x, y)
    self.assertAllClose(api.jvp(g, [y], [ty]), api.jvp(g_ref, [y], [ty]))

  def test_jvp_both(self):
    raise unittest.SkipTest('unimplemented')  # TODO(frostig)

    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return t / r
      return x + fn(y, x)

    def f_ref(x, y): return x + x / y

    x, y, tx, ty = 6., 3., 1., 1.
    self.assertAllClose(api.jvp(f,     [x, y], [tx, ty]),
                        api.jvp(f_ref, [x, y], [tx, ty]))

  def test_make_jaxpr(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return 2 * t / r

      return x + fn(y, x)

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    f_ = lambda x: f(x, y)
    f_t = transpose_unary(f_, x)

    jaxpr = api.make_jaxpr(f_)(x)
    self.assertIn('custom_transpose_call', str(jaxpr))

    jaxpr_t = api.make_jaxpr(f_t)(x)
    self.assertNotIn('custom_transpose_call', str(jaxpr_t))

  def test_jit(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return 2 * t / r

      return x + fn(y, x)

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), jax.jit(f)(x, y))

    f_ = lambda x: f(x, y)
    f_t = transpose_unary(f_, x)
    g_ = jax.jit(f_)
    g_t = transpose_unary(g_, x)
    self.assertAllClose(f_(x), jax.jit(f_)(x))
    self.assertAllClose(f_t(x), jax.jit(f_t)(x))
    self.assertAllClose(f_(x), g_(x))
    self.assertAllClose(f_t(x), g_t(x))

  def test_jit_recursive(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return 2 * fn(r, t)

      return x + fn(y, x)

    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.
    self.assertAllClose(f(x, y), jax.jit(f)(x, y))

    f_ = lambda x: f(x, y)
    f_t = transpose_unary(f_, x)
    g_ = jax.jit(f_)
    g_t = transpose_unary(g_, x)
    self.assertAllClose(f_(x), jax.jit(f_)(x))
    self.assertAllClose(f_t(x), jax.jit(f_t)(x))
    self.assertAllClose(f_(x), g_(x))
    self.assertAllClose(f_t(x), g_t(x))

  def test_cond(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return 2 * t / r

      return x + fn(y, x)

    def cond_wrap(f):
      return lambda i, x: lax.cond(i > 0, f, lambda x: x, x,
                                   linear=(True,))

    i = 7.
    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.

    f_ = lambda x: f(x, y)
    f_t = transpose_unary(f_, x)
    g_ = partial(cond_wrap(f_), i)
    g_t = transpose_unary(g_, x)

    self.assertAllClose(f_(x), g_(x))
    self.assertAllClose(f_t(x), g_t(x))

  def test_cond_recursive(self):
    def f(x, y):
      @custom_transpose(jnp.ones(2))
      def fn(r, x): return x / r
      @fn.def_transpose
      def tp(r, t): return 2 * fn(r, t)

      return x + fn(y, x)

    def cond_wrap(f):
      return lambda i, x: lax.cond(i > 0, f, lambda x: x, x,
                                   linear=(True,))

    i = 7.
    x = jnp.ones(2) * 6.
    y = jnp.ones(2) * 3.

    f_ = lambda x: f(x, y)
    f_t = transpose_unary(f_, x)
    g_ = partial(cond_wrap(f_), i)
    g_t = transpose_unary(g_, x)

    self.assertAllClose(f_(x), g_(x))
    self.assertAllClose(f_t(x), g_t(x))


class CustomVmapTest(jtu.JaxTestCase):

  def test_basic(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      xs_batched, = in_batched
      self.assertEqual(xs_batched, True)
      self.assertEqual(axis_size, xs.shape[0])
      return jnp.cos(xs), xs_batched

    x, xs = jnp.array(1.), jnp.arange(3)
    y = f(x)
    self.assertAllClose(y, jnp.sin(x))
    ys = api.vmap(f)(xs)
    self.assertAllClose(ys, jnp.cos(xs))

  @jax.numpy_dtype_promotion('standard')
  def test_closure(self):
    z = jnp.array([2., 1., 3.])

    @api.custom_vmap
    def f(x): return z + jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, *args):
      self.assertEqual(len(in_batched), 1)
      self.assertEqual(len(args), 1)
      xs, = args
      xs_batched, = in_batched
      self.assertEqual(xs_batched, True)
      self.assertEqual(axis_size, xs.shape[0])
      return z + jnp.cos(xs), xs_batched

    x, xs = jnp.array(1.), jnp.arange(3)
    y = f(x)
    self.assertAllClose(y, z + jnp.sin(x))
    ys = api.vmap(f)(xs)
    self.assertAllClose(ys, z + jnp.cos(xs))

  def test_rule_multi_output(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x), jnp.cos(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      return (jnp.cos(xs), jnp.sin(xs)), tuple(in_batched * 2)

    x, xs = jnp.array(1.), jnp.arange(3)
    y1, y2 = f(x)
    self.assertAllClose(y1, jnp.sin(x))
    self.assertAllClose(y2, jnp.cos(x))
    ys1, ys2 = api.vmap(f)(xs)
    self.assertAllClose(ys1, jnp.cos(xs))
    self.assertAllClose(ys2, jnp.sin(xs))

  def test_nary(self):
    @api.custom_vmap
    def f(x, y): return jnp.sin(x) + y ** 2.

    @f.def_vmap
    def rule(axis_size, in_batched, xs, ys):
      self.assertEqual(in_batched, [True, True])
      self.assertEqual(axis_size, 3)
      self.assertEqual(axis_size, xs.shape[0])
      self.assertEqual(axis_size, ys.shape[0])
      return jnp.cos(xs) + ys ** 2., True

    xs, ys = jnp.arange(3.0), jnp.arange(3.0)
    zs = api.vmap(f)(xs, ys)
    self.assertAllClose(zs, jnp.cos(xs) + ys ** 2.)

  def test_nary_mixed_batching(self):
    @api.custom_vmap
    def vector_dot(u, v):
      self.assertEqual(u.ndim, 1)
      self.assertEqual(v.ndim, 1)
      return u @ v

    size = 4
    vlen = 3
    in_batched_log = []

    @vector_dot.def_vmap
    def vector_dot_vmap_rule(axis_size, in_batched, u, v):
      in_batched_log.append(in_batched)
      self.assertEqual(axis_size, size)
      u_batched, v_batched = in_batched
      if u_batched:
        self.assertEqual(u.ndim, 2)
        self.assertEqual(u.shape[0], size)
      else:
        self.assertEqual(u.ndim, 1)
        self.assertEqual(u.shape[0], vlen)
      if v_batched:
        self.assertEqual(v.ndim, 2)
        self.assertEqual(v.shape[0], size)
      else:
        self.assertEqual(v.ndim, 1)
        self.assertEqual(v.shape[0], vlen)
      if u_batched and v_batched:
        out = jnp.sum(u * v, axis=1)
      else:
        out = u @ v if u_batched else v @ u
      return out, u_batched or v_batched

    f = vector_dot
    v = lambda *shape: jnp.ones(shape)

    y = api.vmap(f, in_axes=(0, None))(v(4, 3), v(3))
    self.assertAllClose(y, v(4, 3) @ v(3))
    y = api.vmap(f, in_axes=(1, None))(v(3, 4), v(3))
    self.assertAllClose(y, v(3, 4).T @ v(3))
    y = api.vmap(f, in_axes=(None, 0))(v(3), v(4, 3))
    self.assertAllClose(y, v(3) @ v(4, 3).T)
    y = api.vmap(f, in_axes=(0, 0))(v(4, 3), v(4, 3))
    self.assertAllClose(y, jnp.sum(v(4, 3) * v(4, 3), axis=1))
    self.assertEqual(in_batched_log[0], [True, False])
    self.assertEqual(in_batched_log[1], [True, False])
    self.assertEqual(in_batched_log[2], [False, True])
    self.assertEqual(in_batched_log[3], [True, True])

  def test_rule_input_signature(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    rule_args = []

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      rule_args.append((axis_size, in_batched))
      return jnp.cos(xs), in_batched[0]

    xs = jnp.arange(3)
    _ = api.vmap(f)(xs)
    (axis_size, in_batched), = rule_args
    self.assertIs(type(axis_size), int)
    self.assertIs(type(in_batched), list)
    self.assertEqual(len(in_batched), 1)

  def test_rule_output_vs_batching_output_mismatch(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def test_rule_abc(axis_size, in_batched, xs):
      return [jnp.sin(xs), jnp.cos(xs)], in_batched

    xs = jnp.arange(3)
    self.assertRaisesRegex(
        ValueError,
        'structure of output value and output batching specification '
        r'returned by custom vmap rule \(test_rule_abc\) do not match.*',
        lambda: api.vmap(f)(xs))

  def test_rule_vs_call_output_mismatch(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def test_rule_abc2(axis_size, in_batched, xs):
      return [jnp.sin(xs)], in_batched

    xs = jnp.arange(3)
    self.assertRaisesRegex(
        ValueError,
        r'structure of output returned by custom vmap rule \(test_rule_abc2\) '
        r'does not match that of original custom-vmapped function.*',
        lambda: api.vmap(f)(xs))

  def test_jvp_basic(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(axis_size, 3)
      self.assertEqual(in_batched, [True])
      return jnp.cos(xs), in_batched[0]

    f_jvp = lambda x, tx: api.jvp(f, [x], [tx])

    x, tx = jnp.array(1.), jnp.array(2.)
    xs, txs = jnp.arange(3.), jnp.arange(3.) * 2.

    y, ty = f_jvp(x, tx)
    self.assertAllClose(y, jnp.sin(x))
    self.assertAllClose(ty, jnp.cos(x) * tx)

    ys, tys = api.vmap(f_jvp)(xs, txs)
    self.assertAllClose(ys, jnp.cos(xs))
    self.assertAllClose(tys, -jnp.sin(xs) * txs)

    ys, tys = api.jvp(api.vmap(f), [xs], [txs])
    self.assertAllClose(ys, jnp.cos(xs))
    self.assertAllClose(tys, -jnp.sin(xs) * txs)

  @jax.numpy_dtype_promotion('standard')
  def test_jvp_closure(self):
    z = jnp.array([2., 1., 3.])
    def bcast(x): return z + x - z

    @api.custom_vmap
    def f(x): return z + jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(axis_size, 3)
      self.assertEqual(in_batched, [True])
      return z + jnp.cos(xs), in_batched[0]

    f_jvp = lambda x, tx: api.jvp(f, [x], [tx])

    x, tx = jnp.array(1.), jnp.array(2.)
    xs, txs = jnp.arange(3.), jnp.arange(3.) * 2.

    y, ty = f_jvp(x, tx)
    self.assertAllClose(y, z + jnp.sin(x))
    self.assertAllClose(ty, bcast(jnp.cos(x)) * tx)

    ys, tys = api.vmap(f_jvp)(xs, txs)
    self.assertAllClose(ys, z + jnp.cos(xs))
    self.assertAllClose(tys, bcast(-jnp.sin(xs)) * txs)

    ys, tys = api.jvp(api.vmap(f), [xs], [txs])
    self.assertAllClose(ys, z + jnp.cos(xs))
    self.assertAllClose(tys, bcast(-jnp.sin(xs)) * txs)

  def test_jvp_nary(self):
    @api.custom_vmap
    def f(x, y): return jnp.sin(x) + y

    @f.def_vmap
    def rule(axis_size, in_batched, xs, ys):
      self.assertEqual(axis_size, 3)
      self.assertEqual(in_batched, [True, True])
      return jnp.cos(xs) + ys, True

    f_jvp = lambda x, y, tx, ty: api.jvp(f, [x, y], [tx, ty])

    x, y, tx, ty = jnp.arange(4.)
    xs, ys, txs, tys = 4. + jnp.arange(3. * 4).reshape((4, 3))

    zs, tzs = api.vmap(f_jvp)(xs, ys, txs, tys)
    self.assertAllClose(zs, jnp.cos(xs) + ys)
    self.assertAllClose(tzs, -jnp.sin(xs) * txs + tys)

    zs, tzs = api.jvp(api.vmap(f), [xs, ys], [txs, tys])
    self.assertAllClose(zs, jnp.cos(xs) + ys)
    self.assertAllClose(tzs, -jnp.sin(xs) * txs + tys)

  def test_jvp_extra_batched_tangents(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(axis_size, 3)
      self.assertEqual(in_batched, [False])
      return jnp.cos(xs), in_batched[0]

    f_jvp = lambda x, tx: api.jvp(f, [x], [tx])

    txs = 2. + jnp.arange(3.)
    x = jnp.array(1, dtype=txs.dtype)
    y, tys = api.vmap(f_jvp, in_axes=(None, 0), out_axes=(None, 0))(x, txs)
    self.assertAllClose(y, jnp.cos(x))
    self.assertAllClose(tys, -jnp.sin(x) * txs)

  def test_jacfwd(self):
    # jacfwd is another way to exercise extra-batched tangents

    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(axis_size, 3)
      self.assertEqual(in_batched, [False])
      return jnp.cos(xs), in_batched[0]

    x = jnp.arange(3.) + .72
    j = api.jacfwd(f)(x)
    self.assertAllClose(j, -jnp.diag(jnp.sin(x)))

  def test_jvp_extra_batched_primals(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(axis_size, 3)
      self.assertEqual(in_batched, [False])
      return jnp.cos(xs), in_batched[0]

    f_jvp = lambda x, tx: api.jvp(f, [x], [tx])

    xs = jnp.arange(3.)
    tx = jnp.array(4, dtype=xs.dtype)
    ys, tys = api.vmap(f_jvp, in_axes=(0, None))(xs, tx)
    self.assertAllClose(ys, jnp.cos(xs))
    self.assertAllClose(tys, -jnp.sin(xs) * tx)

  def test_jvp_extra_batched_primals_with_linear_vmap_rule(self):
    # When a function is linear, its Jacobian is constant. JAX's JVP
    # of linear functions takes advantage of this: when mapping over a
    # batch of primals relative to a fixed (i.e. symbolically
    # replicated) tangent, output tangents remain replicated as well
    # (i.e. JAX will not broadcast them). This is true in general, and
    # this test checks that vmapped JVPs continue to behave this way
    # when custom_vmap is involved and the custom vmap rule is linear.

    @api.custom_vmap
    def f_linear(x): return 7. * x

    @f_linear.def_vmap
    def linear_rule(axis_size, in_batched, xs):
      return 11. * xs, in_batched[0]

    @api.custom_vmap
    def f_nonlinear(x): return jnp.sin(x)

    @f_nonlinear.def_vmap
    def nonlinear_rule(axis_size, in_batched, xs):
      return jnp.cos(xs), in_batched[0]

    f_lin_jvp = lambda x, tx: api.jvp(f_linear, [x], [tx])
    f_non_jvp = lambda x, tx: api.jvp(f_nonlinear, [x], [tx])
    xs = jnp.arange(3.)
    tx = jnp.array(4., dtype=xs.dtype)

    # doesn't err
    _ = api.vmap(f_lin_jvp, in_axes=(0, None), out_axes=(0, None))(xs, tx)

    # does err
    self.assertRaisesRegex(
        ValueError, 'vmap has mapped output but out_axes is None',
        lambda: api.vmap(
            f_non_jvp, in_axes=(0, None), out_axes=(0, None))(xs, tx))

  def test_jvp_dataflow_violation(self):
    # The jvp-of-custom-vmap machinery should not assume the standard
    # dataflow constraint on the JVP of the custom vmap rule (primal
    # outputs independent of tangent inputs). Both jvp and vmap are
    # "forward" transformations under which, at present, we don't
    # enforce the JVP dependence diagram. Because output primals can
    # depend on input tangents, extra-batched input tangents can
    # create batched output primals, as this test checks.

    @api.custom_jvp
    def cos_with_invalid_dataflow_jvp(x): return jnp.cos(x)

    @cos_with_invalid_dataflow_jvp.defjvp
    def invalid_dataflow_jvp(x, tx):
      [x], [tx] = x, tx
      return jnp.cos(x * tx), tx

    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      return cos_with_invalid_dataflow_jvp(xs), in_batched[0]

    f_jvp = lambda x, tx: api.jvp(f, [x], [tx])
    txs = 2. + jnp.arange(3.)
    x = jnp.array(1, dtype=txs.dtype)

    # doesn't err
    ys, tys = api.vmap(f_jvp, in_axes=(None, 0))(x, txs)
    self.assertAllClose(ys, jnp.cos(x * txs))
    self.assertAllClose(tys, txs)

    # does err
    self.assertRaisesRegex(
        ValueError, 'vmap has mapped output but out_axes is None',
        lambda: api.vmap(
            f_jvp, in_axes=(None, 0), out_axes=(None, 0))(x, txs))

  def test_tree(self):
    tree_sin = partial(tree_util.tree_map, jnp.sin)
    tree_cos = partial(tree_util.tree_map, jnp.cos)

    x, xs = jnp.array(1.), jnp.arange(3)
    x  = (x,  [x  + 1, x  + 2], [x  + 3], x  + 4)
    xs = (xs, [xs + 1, xs + 2], [xs + 3], xs + 4)
    in_batched_ref = tree_util.tree_map(lambda _: True, x)

    @api.custom_vmap
    def f(xs): return tree_sin(xs)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(in_batched, [in_batched_ref])
      sz, = {z.shape[0] for z in tree_util.tree_leaves(xs)}
      self.assertEqual(axis_size, sz)
      return tree_cos(xs), in_batched[0]

    y = f(x)
    self.assertAllClose(y, tree_sin(x))
    ys = api.vmap(f)(xs)
    self.assertAllClose(ys, tree_cos(xs))

  def test_tree_with_nones(self):
    tree_sin = partial(tree_util.tree_map, jnp.sin)
    tree_cos = partial(tree_util.tree_map, jnp.cos)

    x, xs = jnp.array(1.), jnp.arange(3)
    x  = (x,  [x  + 1, None], [x  + 3], None)
    xs = (xs, [xs + 1, None], [xs + 3], None)
    in_batched_ref = tree_util.tree_map(lambda _: True, x)

    @api.custom_vmap
    def f(xs): return tree_sin(xs)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(in_batched, [in_batched_ref])
      sz, = {z.shape[0] for z in tree_util.tree_leaves(xs)}
      self.assertEqual(axis_size, sz)
      return tree_cos(xs), in_batched[0]

    y = f(x)
    self.assertAllClose(y, tree_sin(x))
    ys = api.vmap(f)(xs)
    self.assertAllClose(ys, tree_cos(xs))

  def test_jit(self):
    @api.custom_vmap
    def f(x): return jnp.sin(x)

    @f.def_vmap
    def rule(axis_size, in_batched, xs):
      self.assertEqual(in_batched, [True])
      self.assertEqual(axis_size, xs.shape[0])
      return jnp.cos(xs), in_batched[0]

    x, xs = jnp.array(1.), jnp.arange(3)
    self.assertAllClose(f(x), jit(f)(x))
    self.assertAllClose(jit(api.vmap(f))(xs), api.vmap(f)(xs))
    self.assertAllClose(api.vmap(jit(f))(xs), api.vmap(f)(xs))

  def test_sequential_vmap_basic(self):
    @custom_batching.sequential_vmap
    def f(x):
      return x + 1.

    def vmap_ref(xs):
      return lax.map(f, xs)

    xs = jnp.arange(3.)
    jaxpr = api.make_jaxpr(api.vmap(f))(xs)
    jaxpr_ref = api.make_jaxpr(vmap_ref)(xs)

    self.assertEqual(str(jaxpr), str(jaxpr_ref))

  def test_sequential_vmap_nary_same_batching(self):
    @custom_batching.sequential_vmap
    def f(x, y):
      return x + y

    def vmap_ref(xs, ys):
      return lax.map(lambda args: f(*args), (xs, ys))

    xs, ys = jnp.arange(3.), 4. + jnp.arange(3.)
    jaxpr = api.make_jaxpr(api.vmap(f))(xs, ys)
    jaxpr_ref = api.make_jaxpr(vmap_ref)(xs, ys)

    self.assertEqual(str(jaxpr), str(jaxpr_ref))

  def test_sequential_vmap_nary_mixed_batching(self):
    @custom_batching.sequential_vmap
    def f(x, y):
      return x + y

    def vmap_ref(xs, y):
      return lax.map(lambda x: f(x, y), xs)

    xs, y = jnp.arange(3.), 4.
    jaxpr = api.make_jaxpr(api.vmap(f, in_axes=(0, None)))(xs, y)
    jaxpr_ref = api.make_jaxpr(vmap_ref)(xs, y)

    self.assertEqual(str(jaxpr), str(jaxpr_ref))


class CustomApiTest(jtu.JaxTestCase):
  """Test interactions among the custom_{vmap,jvp,vjp,transpose,*} APIs"""

  def test_method_forwarding(self):
    @api.custom_vmap
    @api.custom_jvp
    @api.custom_transpose
    def f(x): return 2. * x

    # none of these err:
    @f.def_vmap
    def f_batch(sz, b, xs): return 2. * xs
    @f.defjvp
    def f_jvp(x, tx): return 2. * x, 2. * tx
    @f.def_transpose
    def f_transpose(x): return 2. * x

  def test_def_method_forwarding_all_permutations(self):
    for wraps in it.permutations([
        api.custom_jvp, api.custom_transpose, api.custom_vmap]):
      f = lambda x: x + 1.
      for wrap in wraps:
        f = wrap(f)
      for methods in it.permutations(['defjvp', 'def_vmap', 'def_transpose']):
        for method in methods:
          self.assertIsInstance(getattr(f, method), Callable)

    for decorators in it.permutations([
        api.custom_vjp, api.custom_transpose, api.custom_vmap]):
      f = lambda x: x + 1.
      for decorator in decorators:
        f = decorator(f)
      for methods in it.permutations(['defvjp', 'def_vmap', 'def_transpose']):
        for method in methods:
          self.assertIsInstance(getattr(f, method), Callable)


class BufferDonationTest(jtu.BufferDonationTestCase):

  def test_pmap_donate_argnums_invalidates_input(self):
    move = api.pmap(lambda x: x + x - x, donate_argnums=0)
    n = jax.local_device_count()
    x = api.pmap(lambda x: x)(jnp.ones([n]))
    y = move(x)
    self.assertDeleted(x)
    np.testing.assert_allclose(y, [1.] * n)

  def test_pmap_nested_donate_ignored(self):
    pmap_fun = jit(lambda x: api.pmap(lambda y: y ** 2, donate_argnums=0)(x))
    a = api.pmap(lambda x: x)(jnp.array([1]))

    # NOTE(mattjj): stopped raising error here and instead just ignored
    # with self.assertRaisesRegex(ValueError, "nested.*not supported"):
    #   pmap_fun(a)

    pmap_fun(a)  # doesn't crash


class NamedCallTest(jtu.JaxTestCase):

  def test_default_name(self):

    @api.named_call
    def my_test_function(x):
      return x**2

    @jax.jit
    def f(x):
      return my_test_function(x)

    c = jax.xla_computation(f)(2)
    print_opts = xla_client._xla.HloPrintOptions.short_parsable()
    print_opts.print_metadata = True
    hlo_text = c.as_hlo_module().to_string(print_opts)
    self.assertIn("my_test_function", hlo_text)

  def test_non_jaxtype_arg(self):
    # For the test to fail without the invalid JaxType filter we need to pass
    # in a valid JaxType that forces the invalid Jaxtype to be raised to an
    # abstract value.
    def f(not_a_jaxtype, a_jaxtype):
      # then Jax needs to try and evaluate the abstractified non-JaxType
      if not_a_jaxtype:
        return a_jaxtype
      return 0

    f = api.named_call(f, name="test")
    out = jax.jit(f, static_argnums=(0,))("not a Jaxtype", 1)
    self.assertEqual(out, 1)

  @parameterized.parameters(jax.jit, jax.grad, jax.vmap, jax.remat)
  def test_jax_transforms(self, transform):
    f = jnp.sum
    x = jnp.array([1.])

    unnamed_out = transform(f)(x)
    named_out = transform(api.named_call(f, name="test"))(x)

    self.assertEqual(unnamed_out, named_out)

  def test_static_argnums(self):
    f = api.named_call(lambda x, y: y if x else None, name="test")
    f = jax.jit(f, static_argnums=(0,))
    out = f(True, 5)
    self.assertEqual(out, 5)

  def test_partial_eval(self):
    f = api.named_call(lambda x, y: y if x else None, name="test")
    f = jax.jit(functools.partial(f, True))
    out = f(5)
    self.assertEqual(out, 5)

  @jtu.sample_product(
    [dict(func=func, jit=jit)
      for func in ['identity', 'asarray', 'device_put']
      for jit in jtu.JIT_IMPLEMENTATION
      if not (jit._name == "noop" and func == 'identity')
    ],
  )
  def test_integer_overflow(self, jit, func):
    funcdict = {
      'identity': lambda x: x,
      'asarray': jnp.asarray,
      'device_put': api.device_put,
    }

    f = jit(funcdict[func])

    int_dtype = dtypes.canonicalize_dtype(jnp.int64)
    int_max = np.iinfo(int_dtype).max
    int_min = np.iinfo(int_dtype).min

    self.assertEqual(f(int_max).dtype, int_dtype)
    self.assertEqual(f(int_min).dtype, int_dtype)
    self.assertRaises(OverflowError, f, int_max + 1)
    self.assertRaises(OverflowError, f, int_min - 1)


class BackendsTest(jtu.JaxTestCase):

  @unittest.skipIf(not sys.executable, "test requires sys.executable")
  @unittest.skipIf(platform.system() == "Darwin",
                   "Warning doesn't apply on Mac")
  @jtu.skip_on_devices("gpu", "tpu")
  def test_cpu_warning_suppression(self):
    warning_expected = (
      "import jax; "
      "jax.numpy.arange(10)")
    warning_not_expected = (
      "import jax; "
      "jax.config.update('jax_platform_name', 'cpu'); "
      "jax.numpy.arange(10)")

    result = subprocess.run([sys.executable, '-c', warning_expected],
                            check=True, capture_output=True)
    assert "No GPU/TPU found" in result.stderr.decode()

    result = subprocess.run([sys.executable, '-c', warning_not_expected],
                            check=True, capture_output=True)
    assert "No GPU/TPU found" not in result.stderr.decode()


class CleanupTest(jtu.JaxTestCase):
  def test_call_wrapped_second_phase_cleanup(self):
    try:
      jax.vmap(lambda x: x, out_axes=None)(jnp.arange(3))
    except:
      assert core.trace_state_clean()  # this is the hard one
    assert core.trace_state_clean()


class EnvironmentInfoTest(jtu.JaxTestCase):
  @parameterized.parameters([True, False])
  def test_print_environment_info(self, return_string):
    with jtu.capture_stdout() as stdout:
      result = jax.print_environment_info(return_string=return_string)
    if return_string:
      self.assertEmpty(stdout())
    else:
      self.assertIsNone(result)
      result = stdout()
    assert f"jax:    {jax.__version__}" in result
    assert f"jaxlib: {lib.version_str}" in result
    assert f"numpy:  {np.__version__}" in result

class AutodidaxTest(jtu.JaxTestCase):
  def test_autodidax_smoketest(self):
    autodidax_file = os.path.join(
      os.path.dirname(os.path.dirname(__file__)),
      'docs',
      'autodidax.py')
    if not os.path.exists(autodidax_file):
      self.skipTest("Cannot locate autodidax.py")
    spec = importlib.util.spec_from_file_location('autodidax', autodidax_file)
    autodidax_module = importlib.util.module_from_spec(spec)
    spec.loader.exec_module(autodidax_module)

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