# Copyright 2021 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.
"""See primitives_test docstring for how the Jax2TfLimitations are used."""

from collections.abc import Sequence
import itertools
from typing import Any, Callable, Optional, Union

import jax
from jax import lax
from jax import numpy as jnp
from jax import config
from jax._src import test_util as jtu
from jax._src import dtypes
from jax.experimental.jax2tf.tests import primitive_harness
import numpy as np

DType = Any


class Jax2TfLimitation(primitive_harness.Limitation):
  """Specific primitive limitations for jax2tf.

  See the primitive_test module docstring for details.
  """

  # Bitmask values for encoding limitations specific to native lowering
  FOR_NATIVE = 1
  FOR_NON_NATIVE = 2

  def __init__(
      self,
      description: str,
      *,
      devices: Union[str, Sequence[str]] = ("cpu", "gpu", "tpu"),
      dtypes: Sequence[DType] = (),
      enabled: bool = True,
      # jax2tf specific
      modes=("eager", "graph", "compiled"),
      native_serialization=FOR_NON_NATIVE,
      skip_tf_run=False,
      expect_tf_error: bool = True,
      skip_comparison=False,
      custom_assert: Optional[Callable] = None,
      tol=None):
    """See the primitive_harness.Limitation common arguments.

    Args :
      modes: one of "eager", "graph", "compiled"
      for_native_serialization: A bitmask with some of {FOR_NATIVE, FOR_NON_NATIVE}
        to specify how the limitation applies to native and non-native lowering.
      skip_tf_run: if set will skip the TF execution. Use this sparingly,
        prefer `expect_tf_error`. Use only when the test cannot recover from
        the TF error.
      expect_tf_error: if set, then expect a TF error in the given mode when
        executing the result of jax2tf conversion. If not set, then the
        limitation must have a custom_assert or non-default tol.
      skip_comparison: skips the numeric comparison.
      tol: a tolerance to use for both atol and rtol. We will use the maximum
        tolerance over all the applicable limitations, irrespective of their
        order.
      custom_assert: if given, then execute as
        `custom_assert(tst, result_jax, result_tf, args=args, tol=tol, err_msg)`
        , where `tst` is the current TestCase instance, and args are the input
        arguments that the harness created. The `tol` is the maximum tolerance
        based on the applicable limitations. `err_msg` is passed to NumPy
        assert methods.
        `result_tf` is already converted to NumPy arrays.
    """
    super().__init__(
        description, devices=devices, dtypes=dtypes, enabled=enabled)
    if isinstance(modes, str):
      modes = (modes,)
    assert all(m in ["eager", "graph", "compiled"] for m in modes), "Invalid modes: {modes}"
    self.modes = modes
    self.native_serialization = native_serialization
    self.expect_tf_error = expect_tf_error
    self.skip_tf_run = skip_tf_run
    self.custom_assert = custom_assert
    self.tol = tol
    self.skip_comparison = skip_comparison

  def get_max_tolerance_limitation(
      self, limitations: Sequence["Jax2TfLimitation"]
  ) -> Optional["Jax2TfLimitation"]:
    """Pick the tolerance limitation that establishes the maximum tolerance."""
    # TODO: it would be best if the limitations with tolerance are mutually exclusive
    # and we don't have to compute the maximum
    # TODO: we made this an instance method only so that we don't have to import
    # this module from tf_test.util.
    max_tol_lim = None
    for l in limitations:
      if l.tol is not None:
        if max_tol_lim is None or l.tol > max_tol_lim.tol:
          max_tol_lim = l
    return max_tol_lim

  def filter(  # type: ignore[override]
      self,
      dtype: Optional[DType] = None,
      device: Optional[str] = None,
      mode: Optional[str] = None) -> bool:
    """Checks if this limitation is enabled for dtype and device and mode."""
    native_serialization_mask = (
        Jax2TfLimitation.FOR_NATIVE
        if config.jax2tf_default_native_serialization
        else Jax2TfLimitation.FOR_NON_NATIVE)
    return ((mode is None or mode in self.modes) and
            (self.native_serialization & native_serialization_mask) and
            super().filter(device=device, dtype=dtype))

  @classmethod
  def limitations_for_harness(
      cls, harness: primitive_harness.Harness) -> Sequence["Jax2TfLimitation"]:
    group_method = getattr(cls, harness.group_name, None)
    if harness.group_name in cls.harness_groups_no_limitations:
      assert group_method is None, (
          f"Harness group '{harness.group_name}' is both in "
          f"'harness_groups_no_limitations' and has a custom "
          f"Jax2TfLimitation.classmethod defined (see module docstring)")
      return []
    else:
      assert group_method is not None, (
          f"Harness group '{harness.group_name}' must be either part of "
          f"'harness_groups_no_limitations' or must have a custom "
          f"Jax2TfLimitation.classmethod defined (see module docstring)")
      limitations = group_method(harness)
      assert isinstance(limitations, (list, tuple))
      return limitations

  # We keep here the explicit set of groups for which we don't have limitations
  harness_groups_no_limitations = {
      "abs", "add", "add_any", "and", "atan2", "bitcast_convert_type",
      "broadcast", "broadcast_in_dim", "ceil", "clamp", "concatenate",
      "cos", "cosh", "complex", "conj", "convert_element_type", "cummax",
      "cummin", "device_put", "dynamic_slice", "dynamic_update_slice", "exp",
      "eq", "floor", "gather", "ge", "gt", "imag", "iota", "iota_2x32_shape",
      "is_finite", "le", "logistic", "lt", "log", "mul", "ne", "neg", "not",
      "or", "pad", "population_count", "random_categorical", "random_uniform",
      "random_randint", "reduce", "reduce_and", "reduce_precision",
      "reduce_prod", "reduce_or",
      "reduce_sum", "reduce_window_mul", "reduce_window_min",
      "reduce_window_max", "real", "reshape", "rev", "rsqrt", "select_n",
      "select_and_scatter_add", "shift_left", "shift_right_logical",
      "shift_right_arithmetic", "sign", "sin", "sinh", "slice", "sqrt",
      "squeeze", "stop_gradient", "sub", "tie_in", "transpose", "xor",
      "zeros_like"
  }

  @classmethod
  def helper_get_trig_custom_limitation(cls, np_inverse):

    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      operand, = args
      tst.assertAllClose(
          operand, np_inverse(result_tf), atol=tol, rtol=tol, err_msg=err_msg)

    return custom_numeric(
        description="May return different but still correct results",
        dtypes=[np.complex64, np.complex128],
        custom_assert=custom_assert)

  @classmethod
  def random_seed(cls, handess: primitive_harness.Harness):
    return [custom_random_keys_output()]

  @classmethod
  def random_split(cls, handess: primitive_harness.Harness):
    return [custom_random_keys_output()]

  @classmethod
  def random_fold_in(cls, handess: primitive_harness.Harness):
    return [custom_random_keys_output()]

  @classmethod
  def acos(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(
            dtypes=[np.complex64],
            devices=("cpu", "gpu"),
            tol=1e-4,
            modes=("eager", "graph", "compiled")),
        custom_numeric(
            dtypes=[np.complex128],
            devices=("cpu", "gpu"),
            tol=1e-13,
            modes=("eager", "graph", "compiled")),
    ]

  @classmethod
  def acosh(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.complex64], devices=("cpu", "gpu", "tpu"),
                       tol=1e-3),
        custom_numeric(dtypes=[np.complex128], devices=("cpu", "gpu"), tol=1e-12),
        cls.helper_get_trig_custom_limitation(np.cosh)
    ]

  @classmethod
  def approx_top_k(cls, harness: primitive_harness.Harness):
    supported_dtypes = jtu.supported_dtypes()
    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      del tol, err_msg
      # Tests only that the indices correspond to the returned values
      jax_values, jax_indices = result_jax
      tf_values, tf_indices = result_tf
      operand, = args
      def operand_values(indices):
        if operand.ndim == 1:
          return operand[indices]
        elif operand.ndim == 2:
          return operand[np.arange(operand.shape[0]).reshape((-1, 1)), indices]
        else:
          assert False
      tst.assertAllClose(operand_values(jax_indices), jax_values)
      tst.assertAllClose(operand_values(tf_indices), tf_values)

    return [
        missing_tf_kernel(
            dtypes=[t for t in [jnp.bfloat16, np.float16, np.float32, np.float64]
                    if t in supported_dtypes],
            devices=("cpu", "gpu"),
            modes=("graph", "eager")),
        Jax2TfLimitation(
            "compilation not supported for float64.",
            dtypes=[np.float64],
            devices=("cpu", "gpu"),
            modes=("compiled",)),
        custom_numeric(
            dtypes=[t for t in [jnp.bfloat16, np.float16, np.float32, np.float64]
                    if t in supported_dtypes],
            devices=("cpu", "gpu"),
            modes=("eager", "graph"),
            custom_assert=custom_assert)]

  @classmethod
  def argmax(cls, harness: primitive_harness.Harness):
    return [
        Jax2TfLimitation(
            "different results when the input contains NaN and enable_xla=False",
            dtypes=jtu.dtypes.all_inexact,
            devices=("cpu", "gpu", "tpu"),
            modes=("eager", "graph", "compiled"),
            expect_tf_error=False,
            skip_comparison=True,
            enabled=("nan_" in harness.name and not harness.params["enable_xla"])),
    ]

  @classmethod
  def argmin(cls, harness: primitive_harness.Harness):
    return cls.argmax(harness)

  @classmethod
  def asin(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.complex64], devices=("cpu", "gpu"), tol=1e-4,
                       modes=("eager", "graph", "compiled")),
        custom_numeric(dtypes=[np.complex64], devices=("tpu", "gpu"), tol=2e-4,
                       modes=("eager", "graph", "compiled")),
        custom_numeric(dtypes=[np.complex128], devices=("cpu", "gpu"), tol=1e-12,
                       modes=("eager", "graph", "compiled")),
        cls.helper_get_trig_custom_limitation(np.sin)
    ]

  @classmethod
  def asinh(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.complex64], devices=("cpu", "gpu", "tpu"),
                       tol=1e-3),
        custom_numeric(dtypes=[np.complex128], devices=("cpu", "gpu"), tol=1e-12),
        cls.helper_get_trig_custom_limitation(np.sinh)
    ]

  @classmethod
  def atan(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.complex64], devices=("cpu", "gpu"), tol=1e-5),
        custom_numeric(dtypes=[np.complex64], devices=("tpu"), tol=1e-3),
        custom_numeric(dtypes=[np.complex128], devices=("cpu", "gpu"), tol=1e-12),
        cls.helper_get_trig_custom_limitation(np.tan)
    ]

  @classmethod
  def atanh(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.float64], tol=1e-14),
        custom_numeric(dtypes=[np.complex64], tol=1e-3),
        custom_numeric(dtypes=[np.complex128], devices=("cpu", "gpu"), tol=1e-12),
        cls.helper_get_trig_custom_limitation(np.tanh)
    ]

  @classmethod
  def bessel_i0e(cls, harness: primitive_harness.Harness):
    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph"))
    ]

  @classmethod
  def bessel_i1e(cls, harness: primitive_harness.Harness):
    return cls.bessel_i0e(harness)

  @classmethod
  def cbrt(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.float32], devices=("tpu"), tol=1e-5),
    ]

  @classmethod
  def cholesky(cls, harness: primitive_harness.Harness):

    def custom_assert(tst, result_jax, result_tf, *, tol, err_msg, **_):
      # cholesky_p returns garbage in the strictly upper triangular part of the
      # result, so we can safely ignore that part.
      tst.assertAllClose(
          jnp.tril(result_jax), result_tf, atol=tol, err_msg=err_msg)

    return [
        # TODO: very high tolerance
        custom_numeric(
            dtypes=[np.float32, np.complex64],
            tol=1e-2,
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled")),
        custom_numeric(
            dtypes=[np.float64, np.complex128],
            tol=1e-6,
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled")),
        custom_numeric(
            dtypes=[dtypes.bfloat16, np.float16],
            tol=5e-2,
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled")),
        custom_numeric(
            custom_assert=custom_assert,
            description=(
                "May return different values in the strictly upper triangular "
                "part of the result. This does not matter for correctness, "
                "because this part of the matrix is not considered in the result."
            ),
            modes=("eager", "graph", "compiled"))
    ]

  @classmethod
  def conv_general_dilated(cls, harness: primitive_harness.Harness):
    prefer_elem = harness.params["preferred_element_type"]
    return [
        Jax2TfLimitation(
          "Non-deterministic NaN for conv_general_dilated with preferred_element_type",
          dtypes=[
            jnp.int32, np.int16, np.int64
          ],
          devices=["cpu", "gpu", "tpu"],
          modes=("eager", "graph", "compiled"),
          enabled=(prefer_elem is not None
                   and prefer_elem in [jnp.bfloat16, np.float16, np.float32, np.float64]),
          skip_comparison=True),
        # Even in compiled mode, for GPU we see a bit of discrepancy but
        # very minor.
        custom_numeric(dtypes=[np.float32], devices="gpu",
                       modes=("eager", "graph", "compiled"),
                       tol=1e-5),
        custom_numeric(dtypes=[np.float32], devices="cpu",
                       modes=("eager", "graph", "compiled"),
                       tol=1e-4,
                       native_serialization=Jax2TfLimitation.FOR_NATIVE | Jax2TfLimitation.FOR_NON_NATIVE),
        custom_numeric(description="higher numeric inaccuracy when `enable_xla=False`",
                       modes=("eager", "graph", "compiled"),
                       enabled=(not harness.params["enable_xla"]),
                       tol=5e-3)
    ]

  @classmethod
  def cumlogsumexp(cls, harness):
    return [
        # JAX uses a different lowering for CPU and GPU.
        custom_numeric(
            dtypes=(np.float16, jnp.bfloat16),
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled"),
            tol=5e-1)
    ]


  @classmethod
  def cumprod(cls, harness):
    return [
        # JAX uses a different lowering for CPU and GPU.
        custom_numeric(
            dtypes=(np.float16, jnp.bfloat16),
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled"),
            tol=5e-1)
    ]

  @classmethod
  def cumsum(cls, harness):
    return [
        # JAX uses a different lowering for CPU and GPU.
        custom_numeric(
            dtypes=(np.float16, jnp.bfloat16),
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled"),
            tol=5e-1)
    ]

  @classmethod
  def custom_linear_solve(cls, harness: primitive_harness.Harness):
    return [
        Jax2TfLimitation(
            "TODO: large numerical discrepancy",
            dtypes=[np.float32],
            devices="tpu",
            expect_tf_error=False,
            skip_comparison=True),
        custom_numeric(dtypes=[np.float32], devices="tpu", tol=0.01),
        custom_numeric(tol=1e-3),
    ]

  @classmethod
  def digamma(cls, harness: primitive_harness.Harness):
    dtype = harness.dtype

    # In the bfloat16 case, TF and lax both return NaN in undefined cases.
    # digamma is not defined at 0 and -1
    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      # lax.digamma returns NaN and tf.math.digamma returns inf
      arg, = args
      special_cases = (arg == 0.) | (arg == -1.)
      nr_special_cases = np.count_nonzero(special_cases)
      tst.assertAllClose(
          np.full((nr_special_cases,), dtype(np.nan)),
          result_jax[special_cases],
          err_msg=err_msg)
      tst.assertAllClose(
          np.full((nr_special_cases,), dtype(np.inf)),
          result_tf[special_cases],
          err_msg=err_msg)
      # non-special cases are equal
      tst.assertAllClose(
          result_jax[~special_cases],
          result_tf[~special_cases],
          atol=tol,
          rtol=tol,
          err_msg=err_msg)

    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph")),
        custom_numeric(dtypes=[np.float64], tol=1e-13),
        custom_numeric(dtypes=[np.float32], devices=["cpu", "gpu"], tol=1e-3),
        custom_numeric(
            dtypes=[dtypes.bfloat16],
            custom_assert=custom_assert,
            description=(
                "May return different results at singularity points 0 and -1."
                "JAX returns nan and TF returns inf"))
    ]

  @classmethod
  def div(cls, harness: primitive_harness.Harness):
    return [
        Jax2TfLimitation(
            "TF integer division fails if divisor contains 0; JAX returns NaN",
            dtypes=[
                np.uint8, np.int8, np.uint16, np.uint32, np.uint64, np.int8,
                np.int16, np.int32, np.int64
            ],
            # Only the harnesses with "singularity" will have divide by 0
            enabled=("singularity" in harness.name))
    ]

  @classmethod
  def dot_general(cls, harness: primitive_harness.Harness):
    prefer_elem = harness.params["preferred_element_type"]
    return [
        missing_tf_kernel(dtypes=[np.bool_],),
        # TODO(b/189287598)
        Jax2TfLimitation(
            "Non-deterministic NaN for dot_general with preferred_element_type on GPU (b/189287598)",
            dtypes=[
                jnp.bfloat16, np.float16, np.float32, np.complex64
            ],
            devices="gpu",
            modes=("eager", "graph", "compiled"),
            enabled=(prefer_elem is not None),
            skip_comparison=True),
        # TODO(b/241740367) - note this only occurs when X64 is enabled.
        Jax2TfLimitation(
            "Large tolerances when upcasting with preferred_element_type on CPU (b/241740367)",
            devices=["cpu", "gpu", "tpu"],
            enabled=prefer_elem and np.dtype(harness.dtype) < np.dtype(prefer_elem),
            skip_comparison=True),
        # TODO(necula): look into this, but this is only for non-native serialization
        Jax2TfLimitation(
            "Errors when lhs_dtype != rhs_dtype for non-native serialization with 64-bit types",
            devices=["cpu", "gpu", "tpu"],
            enabled=(harness.dtype != harness.params["rhs_dtype"] and
                     (harness.dtype in [np.int64, np.uint64, np.float64] or
                      harness.params["rhs_dtype"] in [np.int64, np.uint64, np.float64])),
            skip_comparison=True),
      # TODO(necula): look into this, but this is only for non-native serialization and enable_xla=False
      Jax2TfLimitation(
        "Errors for non-native serialization with enable_xla=False for certain input dtype combinations",
        devices=["cpu", "gpu", "tpu"],
        enabled=(not harness.params["enable_xla"] and
                 (harness.dtype in [np.int16, np.uint32, np.uint16] or
                  harness.params["rhs_dtype"] in [np.int16, np.uint32, np.uint16] or
                  # Some combinations end up being widened to a larger type that is not
                  # supported
                  (harness.dtype, harness.params["rhs_dtype"]) in [
                    (np.float16, jnp.bfloat16),
                    (np.int32, np.float16),
                    (np.int8, np.float16),
                    (np.int8, np.uint8),
                  ])),
        skip_comparison=True,
        skip_tf_run=True),
        # TODO(necula): look into this, but this is only for non-native serialization
        Jax2TfLimitation(
            "Crash when lhs_dtype != rhs_dtype for non-native serialization on TPU for complex numbers",
            devices=["tpu"],
            enabled=(harness.dtype != harness.params["rhs_dtype"] and
                     (harness.dtype in [np.complex64, np.complex128] or
                      harness.params["rhs_dtype"] in [np.complex64, np.complex128])),
            skip_comparison=True,
            skip_tf_run=True),
        # JAX performs float16 matmuls in float32 on CPU, so the JAX result
        # may be more precise.
        custom_numeric(dtypes=[np.float16], devices=["cpu"], tol=1e-2,
                       modes=("eager", "graph", "compiled")),
    ]

  @classmethod
  def eig(cls, harness: primitive_harness.Harness):
    compute_left_eigenvectors = harness.params["compute_left_eigenvectors"]
    compute_right_eigenvectors = harness.params["compute_right_eigenvectors"]
    dtype = harness.dtype

    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      operand, = args
      inner_dimension = operand.shape[-1]

      # Test ported from tests.linlag_test.testEig
      # Norm, adjusted for dimension and type.
      def norm(x):
        norm = np.linalg.norm(x, axis=(-2, -1))
        return norm / ((inner_dimension + 1) * jnp.finfo(dtype).eps)

      def check_right_eigenvectors(a, w, vr):
        tst.assertTrue(
            np.all(norm(np.matmul(a, vr) - w[..., None, :] * vr) < 100))

      def check_left_eigenvectors(a, w, vl):
        rank = len(a.shape)
        aH = jnp.conj(a.transpose(list(range(rank - 2)) + [rank - 1, rank - 2]))
        wC = jnp.conj(w)
        check_right_eigenvectors(aH, wC, vl)

      def check_eigenvalue_is_in_array(eigenvalue, eigenvalues_array):
        tol = None
        # TODO(bchetioui): numerical discrepancies
        if dtype in [np.float32, np.complex64]:
          tol = 1e-4
        elif dtype in [np.float64, np.complex128]:
          tol = 1e-13
        closest_diff = min(abs(eigenvalues_array - eigenvalue))
        tst.assertAllClose(
            closest_diff,
            np.array(0., closest_diff.dtype),
            atol=tol,
            err_msg=err_msg)

      all_w_jax, all_w_tf = result_jax[0], result_tf[0]
      for idx in itertools.product(*map(range, operand.shape[:-2])):
        w_jax, w_tf = all_w_jax[idx], all_w_tf[idx]
        for i in range(inner_dimension):
          check_eigenvalue_is_in_array(w_jax[i], w_tf)
          check_eigenvalue_is_in_array(w_tf[i], w_jax)

      if compute_left_eigenvectors:
        check_left_eigenvectors(operand, all_w_tf, result_tf[1])
      if compute_right_eigenvectors:
        check_right_eigenvectors(operand, all_w_tf,
                                 result_tf[1 + compute_left_eigenvectors])

    return [
        # Eig does not work in JAX on gpu or tpu
        Jax2TfLimitation(
            "function not compilable", modes="compiled", devices="cpu"),
        Jax2TfLimitation(
            "TF Conversion of eig is not implemented when both compute_left_eigenvectors and compute_right_eigenvectors are set to True",
            enabled=(compute_left_eigenvectors and compute_right_eigenvectors)),
        custom_numeric(
            custom_assert=custom_assert,
            description=("May return the eigenvalues and eigenvectors in a "
                         "potentially different order. The eigenvectors may "
                         "also be different, but equally valid."))
    ]

  @classmethod
  def eigh(cls, harness: primitive_harness.Harness):
    dtype = harness.dtype

    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      operand, = args
      inner_dimension = operand.shape[-1]

      def check_right_eigenvectors(a, w, vr):
        tol = 1e-16
        # TODO(bchetioui): tolerance needs to be very high in compiled mode,
        # specifically for eigenvectors.
        if dtype == np.float64:
          tol = 2e-5
        elif dtype == np.float32:
          tol = 1e-2
        elif dtype in [dtypes.bfloat16, np.complex64]:
          tol = 1e-3
        elif dtype == np.complex128:
          tol = 2e-5
        tst.assertAllClose(
            np.matmul(a, vr) - w[..., None, :] * vr,
            np.zeros(a.shape, dtype=vr.dtype),
            atol=tol,
            # For bfloat16 the np.matmul returns float32 result.
            check_dtypes=False,
            err_msg=err_msg)

      def check_eigenvalue_is_in_array(eigenvalue, eigenvalues_array):
        tol = None
        if dtype in [dtypes.bfloat16, np.float32, np.complex64]:
          tol = 1e-3
        elif dtype in [np.float64, np.complex128]:
          tol = 1e-5
        closest_diff = min(abs(eigenvalues_array - eigenvalue))
        tst.assertAllClose(
            closest_diff,
            np.array(0., closest_diff.dtype),
            atol=tol,
            err_msg=err_msg)

      _, all_w_jax = result_jax
      all_vr_tf, all_w_tf = result_tf

      for idx in itertools.product(*map(range, operand.shape[:-2])):
        w_jax, w_tf = all_w_jax[idx], all_w_tf[idx]
        for i in range(inner_dimension):
          check_eigenvalue_is_in_array(w_jax[i], w_tf)
          check_eigenvalue_is_in_array(w_tf[i], w_jax)

      check_right_eigenvectors(operand, all_w_tf, all_vr_tf)

    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices="tpu",
            enabled=(harness.params["shape"] != (0, 0)),  # This actually works!
        ),
        Jax2TfLimitation(
            "TODO: numeric discrepancies",
            dtypes=[np.float16],
            devices="tpu",
            expect_tf_error=False,
            skip_comparison=True),
        custom_numeric(
            custom_assert=custom_assert,
            description=("May return the eigenvalues and eigenvectors in a "
                         "potentially different order. The eigenvectors may "
                         "also be different, but equally valid."),
            modes=("eager", "graph", "compiled"))
    ]

  @classmethod
  def erf(cls, harness: primitive_harness.Harness):
    return []

  @classmethod
  def erfc(cls, harness: primitive_harness.Harness):
    return []

  @classmethod
  def erf_inv(cls, harness: primitive_harness.Harness):
    # erf_inv is not defined for arg <= -1 or arg >= 1
    def custom_assert(tst, result_jax, result_tf, *, args, tol,
                      err_msg):  # noqa: F811
      arg, = args
      # for arg < -1 or arg > 1
      # lax.erf_inv returns NaN; tf.math.erf_inv return +/- inf
      special_cases = (arg < -1.) | (arg > 1.)
      # non-special cases are equal
      tst.assertAllClose(
          result_jax[~special_cases],
          result_tf[~special_cases],
          atol=tol,
          rtol=tol,
          err_msg=err_msg)

    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16, np.float16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph")),
        custom_numeric(dtypes=[np.float32, np.float64], tol=1e-4),
        custom_numeric(
            dtypes=[np.float32, np.float64],
            custom_assert=custom_assert,
            description=(
                "May return different results at undefined points (< -1 or > 1):"
                " JAX returns `NaN` and TF returns `+inf` or `-inf`.")),
    ]

  @classmethod
  def expm1(cls, harness: primitive_harness.Harness):
    return [custom_numeric(dtypes=[np.float64], tol=1e-5)]

  @classmethod
  def fft(cls, harness):
    return [
        Jax2TfLimitation(
            "TF function not compilableble",
            devices=("cpu", "gpu"),
            dtypes=[np.float64],
            modes="compiled"),
        Jax2TfLimitation(
            "TF function not compilableble for IFFT and IRFFT",
            devices=("cpu", "gpu"),
            dtypes=[np.complex128],
            modes="compiled",
            enabled=(str(harness.params["fft_type"]) in ["FftType.IFFT",
                                                         "FftType.IRFFT"])),
        # TODO: very high tolerance
        custom_numeric(tol=1e-3, modes=("eager", "graph", "compiled")),
    ]

  @classmethod
  def _pow_test_util(cls, harness: primitive_harness.Harness):

    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      # NaNs are mismatched, but assertAllClose will also behave weirdly for
      # complex numbers containing np.inf as one of their components. See
      # https://github.com/numpy/numpy/issues/15959 for more details.
      mask = (
          np.isnan(result_jax) + np.isnan(result_tf) + np.isinf(result_jax) +
          np.isinf(result_tf))
      tst.assertAllClose(
          result_jax[~mask], result_tf[~mask], rtol=tol, err_msg=err_msg)

    return [
        custom_numeric(
            dtypes=[np.float32, np.complex64], devices=("cpu", "gpu"),
            tol=1e-3),
        custom_numeric(
            dtypes=[np.float64, np.complex128],
            devices=("cpu", "gpu"),
            tol=5e-5),
        custom_numeric(
            dtypes=[np.complex64, np.complex128],
            custom_assert=custom_assert,
        )
    ]

  @classmethod
  def igamma(cls, harness: primitive_harness.Harness):
    dtype = harness.dtype

    # igamma is not defined when the first argument is <=0
    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      arg1, arg2 = args
      # lax.igamma returns NaN when arg1 == arg2 == 0; tf.math.igamma returns 0
      special_cases = (arg1 == 0.) & (arg2 == 0.)
      nr_special_cases = np.count_nonzero(special_cases)
      tst.assertAllClose(
          np.full((nr_special_cases,), np.nan, dtype=dtype),
          result_jax[special_cases])
      tst.assertAllClose(
          np.full((nr_special_cases,), 0., dtype=dtype),
          result_tf[special_cases])
      if harness.dtype == np.float32:
        tol = 1e-5
      # non-special cases are equal
      tst.assertAllClose(
          result_jax[~special_cases],
          result_tf[~special_cases],
          atol=tol,
          rtol=tol,
          err_msg=err_msg)

    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16, np.float16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph")),
        custom_numeric(
            custom_assert=custom_assert,
            description=(
                "May return different results at undefined points "
                "(both arguments 0). JAX returns `NaN` and TF returns 0 or "
                "JAX returns 1 and TF returns `NaN`"))
    ]

  @classmethod
  def igammac(cls, harness: primitive_harness.Harness):
    dtype = harness.dtype

    # igammac is not defined when the first argument is <=0
    def custom_assert(tst, result_jax, result_tf, *, args, tol,
                      err_msg):  # noqa: F811
      arg1, arg2 = args
      # lax.igammac returns 1. when arg1 <= 0; tf.math.igammac returns NaN
      special_cases = (arg1 <= 0.) | (arg2 <= 0)
      nr_special_cases = np.count_nonzero(special_cases)
      tst.assertAllClose(
          np.full((nr_special_cases,), 1., dtype=dtype),
          result_jax[special_cases],
          err_msg=err_msg)
      tst.assertAllClose(
          np.full((nr_special_cases,), np.nan, dtype=dtype),
          result_tf[special_cases],
          err_msg=err_msg)
      # non-special cases are equal
      tst.assertAllClose(
          result_jax[~special_cases],
          result_tf[~special_cases],
          atol=tol,
          rtol=tol,
          err_msg=err_msg)

    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16, np.float16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph")),
        custom_numeric(dtypes=[np.float64], tol=1e-9),
        custom_numeric(devices="gpu", tol=1e-3),
        custom_numeric(
            custom_assert=custom_assert,
            devices=("cpu", "gpu"),
            description=(
                "May return different results at undefined points "
                "(both arguments less or equal 0). JAX returns `NaN` and TF returns 0 or "
                "JAX returns 1 and TF returns `NaN`")),
    ]

  @classmethod
  def integer_pow(cls, harness: primitive_harness.Harness):
    y = harness.params["y"]
    return [
        # TODO: on TPU, for f16, we get different results with eager mode
        # than with compiled mode.
        Jax2TfLimitation(
            "Different overflow behavior. ",
            dtypes=[np.float16, jnp.bfloat16],
            devices="tpu",
            expect_tf_error=False,
            modes=("eager", "graph"),
            skip_comparison=True),
        Jax2TfLimitation(
            "Different overflow behavior for large exponents. ",
            dtypes=[
                np.int8, np.int16, np.int32, np.int64, np.float16, jnp.bfloat16,
                np.float32, np.complex64, np.complex128
            ],
            enabled=(abs(y) > 10),
            expect_tf_error=False,
            modes=("eager", "graph"),
            skip_comparison=True),
        custom_numeric(dtypes=[dtypes.bfloat16], tol=2e-2)
    ] + list(cls._pow_test_util(harness))

  @classmethod
  def pow(cls, harness: primitive_harness.Harness):
    return cls._pow_test_util(harness)

  @classmethod
  def lgamma(cls, harness: primitive_harness.Harness):
    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph")),
        custom_numeric(dtypes=[np.float64], tol=1e-11),
        custom_numeric(dtypes=[np.float32], tol=1e-3)
    ]

  @classmethod
  def log1p(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.complex128], tol=3e-14),
        custom_numeric(dtypes=[np.float64], tol=1e-10),
        custom_numeric(dtypes=[np.float32], tol=1e-3)
    ]

  @classmethod
  def lu(cls, harness: primitive_harness.Harness):
    dtype = harness.dtype

    def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
      operand, = args
      lu, pivots, perm = result_tf
      batch_dims = operand.shape[:-2]
      m, n = operand.shape[-2], operand.shape[-1]

      def _make_permutation_matrix(perm):
        result = []
        for idx in itertools.product(*map(range, operand.shape[:-1])):
          result += [0 if c != perm[idx] else 1 for c in range(m)]
        result = np.reshape(np.array(result, dtype=dtype), [*batch_dims, m, m])
        return result

      k = min(m, n)
      l = jnp.tril(lu, -1)[..., :, :k] + jnp.eye(m, k, dtype=dtype)
      u = jnp.triu(lu)[..., :k, :]
      p_mat = _make_permutation_matrix(perm)

      tst.assertArraysEqual(
          lax.linalg.lu_pivots_to_permutation(pivots, m), perm)
      tst.assertAllClose(
          jnp.matmul(p_mat, operand),
          jnp.matmul(l, u),
          atol=tol,
          rtol=tol,
          err_msg=err_msg)

    return [
        custom_numeric(
            dtypes=[np.float32, np.complex64], devices="tpu", tol=0.1),
        custom_numeric(
            dtypes=[np.float32, np.complex64], devices=("cpu", "gpu"),
            tol=1e-5),
        custom_numeric(
            dtypes=[np.float64, np.complex128],
            modes=("eager", "graph"),
            tol=1e-13),
        custom_numeric(
            dtypes=[np.float64, np.complex128], modes=("compiled"), tol=1e-14),
        custom_numeric(
            custom_assert=custom_assert,
            description=("May return different, but also correct, results when "
                         "the decomposition is not unique"),
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled")),
    ]

  @classmethod
  def max(cls, harness: primitive_harness.Harness):
    # TODO(bchetioui): discrepancies between TF & JAX when comparing with NaN;
    # JAX always returns NaN, while TF returns the value NaN is compared with.
    def custom_assert(tst, result_jax, result_tf, err_msg, **_):
      mask = np.isnan(result_jax)
      tst.assertAllClose(result_jax[~mask], result_tf[~mask], err_msg=err_msg)

    return [
        custom_numeric(
            custom_assert=custom_assert,
            description=(
                "May return different values when one of the values is NaN. "
                "JAX always returns NaN, while TF returns the value NaN is compared with."
            ),
            modes=("eager", "graph", "compiled"),
            native_serialization=Jax2TfLimitation.FOR_NON_NATIVE),
        # TODO(b/269996580)
        custom_numeric(
            custom_assert=custom_assert,
            devices="cpu",
            description=(
                "TF and JAX use different values of the compiler flag "
                "xla_cpu_enable_fast_min_max compiler flag and therefore have "
                "different behavior of NaN propagation through min/max."
            ),
            modes=("eager", "graph", "compiled"),
            native_serialization=Jax2TfLimitation.FOR_NATIVE)
    ]

  @classmethod
  def min(cls, harness: primitive_harness.Harness):
    # TODO(bchetioui): discrepancies between TF & JAX when comparing with NaN;
    # JAX always returns NaN, while TF returns the value NaN is compared with.
    def custom_assert(tst, result_jax, result_tf, *, err_msg, **_):
      mask = np.isnan(result_jax)
      tst.assertAllClose(result_jax[~mask], result_tf[~mask], err_msg=err_msg)

    return [
        custom_numeric(
            custom_assert=custom_assert,
            description=(
                "May return different values when one of the values is NaN. "
                "JAX always returns NaN, while TF returns the value NaN is compared with."
            ),
            modes=("eager", "graph", "compiled"),
            native_serialization=Jax2TfLimitation.FOR_NON_NATIVE),
        # TODO(b/269996580)
        custom_numeric(
            custom_assert=custom_assert,
            devices="cpu",
            description=(
                "TF and JAX use different values of the compiler flag "
                "xla_cpu_enable_fast_min_max compiler flag and therefore have "
                "different behavior of NaN propagation through min/max."
            ),
            modes=("eager", "graph", "compiled"),
            native_serialization=Jax2TfLimitation.FOR_NATIVE)
    ]

  @classmethod
  def nextafter(cls, harness: primitive_harness.Harness):
    return [missing_tf_kernel(dtypes=[np.float16, dtypes.bfloat16])]

  @classmethod
  def qr(cls, harness: primitive_harness.Harness):
    # See https://github.com/google/jax/pull/3775#issuecomment-659407824;
    #     # jit_compile=True breaks for complex types.
    # TODO: see https://github.com/google/jax/pull/3775#issuecomment-659407824.
    # - for now, the performance of the HLO QR implementation called when
    #   compiling with TF is expected to have worse performance than the
    #   custom calls made in JAX.
    return [
        custom_numeric(
            dtypes=[np.float64, np.complex128],
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled"),
            tol=1e-13),
        custom_numeric(
            dtypes=[np.float32, np.complex64],
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled"),
            tol=1e-4),
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices="tpu",
        )
    ]

  @classmethod
  def random_gamma(cls, harness: primitive_harness.Harness):
    return [custom_numeric(devices="tpu", tol=1e-3)]

  @classmethod
  def reduce_max(cls, harness: primitive_harness.Harness):
    # Unlike reduce_window_max, we use a native TF op: tf.reduce_max, which
    # does not work for complex
    return [missing_tf_kernel(dtypes=[np.complex64, np.complex128])]

  @classmethod
  def reduce_min(cls, harness: primitive_harness.Harness):
    return cls.reduce_max(harness)

  @classmethod
  def reduce_window_add(cls, harness: primitive_harness.Harness):
    return [
        Jax2TfLimitation(
            "Small deviations on GPU for large inputs and enable_xla=False",
            dtypes=[np.float32],
            devices="gpu",
            modes=("eager", "graph", "compiled"),
            expect_tf_error=False,
            skip_comparison=False,
            enabled=not harness.params["enable_xla"],
            tol=3e-5),
        Jax2TfLimitation(
            "Large deviations on TPU for enable_xla=False",
            dtypes=[np.float16, np.float32],
            devices="tpu",
            modes=("eager", "graph", "compiled"),
            expect_tf_error=False,
            skip_comparison=True,
            enabled=not harness.params["enable_xla"]),
      custom_numeric(devices="cpu", dtypes=[np.float32],
                     modes=("eager", "graph", "compiled",), tol=1e-5),
      custom_numeric(devices=("cpu", "gpu"), dtypes=[np.float16],
                     modes=("eager", "graph", "compiled",), tol=5e-3),
    ]

  @classmethod
  def regularized_incomplete_beta(cls, harness: primitive_harness.Harness):
    return [
        custom_numeric(dtypes=[np.float64], tol=1e-14),
        missing_tf_kernel(dtypes=[np.float16, dtypes.bfloat16])
    ]

  @classmethod
  def rem(cls, harness: primitive_harness.Harness):
    return [
        Jax2TfLimitation(
            "TF integer division fails if divisor contains 0; JAX returns NaN",
            dtypes=[
                np.uint8, np.int8, np.uint16, np.uint32, np.uint64, np.int8,
                np.int16, np.int32, np.int64
            ],
            skip_comparison=True,
            # Only the harnesses with "singularity" will have divide by 0
            enabled=("singularity" in harness.name)),
        Jax2TfLimitation(
            "TF division of inf by inf returns inf while in JAX returns nan",
            dtypes=[
                np.float32,
            ],
            devices="gpu",
            skip_comparison=True,
            enabled=("singularity_inf_by_inf" in harness.name)),
    ]

  @classmethod
  def rng_bit_generator(cls, harness: primitive_harness.Harness):
    return []

  @classmethod
  def round(cls, harness: primitive_harness.Harness):
    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices=("cpu", "gpu"),
            modes=("eager", "graph"))
    ]

  @classmethod
  def scatter(cls, harness):
    return [
        Jax2TfLimitation(
            "out-of-bounds scatters are not supported in graph and eager mode",
            dtypes=jtu.dtypes.all_inexact,
            devices=("cpu", "gpu", "tpu"),
            modes=("eager", "graph"),
            expect_tf_error=True,
            skip_comparison=True,
            enabled=("modes_out_of_bounds" in harness.name and not harness.params["enable_xla"])),
      custom_numeric(modes=("eager", "graph", "compiled"),
                     dtypes=[np.float16], tol=5e-3,
                     enabled=(not harness.params["enable_xla"])),
    ]

  @classmethod
  def scatter_add(cls, harness):
    return cls.scatter(harness)

  @classmethod
  def scatter_mul(cls, harness):
    return cls.scatter(harness)

  @classmethod
  def scatter_max(cls, harness):
    return cls.scatter(harness)

  @classmethod
  def scatter_min(cls, harness):
    return cls.scatter(harness)

  @classmethod
  def select_and_gather_add(cls, harness):
    return [
        # This JAX primitives is not not exposed directly in the JAX API
        # but arises from JVP of `lax.reduce_window` for reducers
        # `lax.max` or `lax.min`. It also arises from second-order
        # VJP of the same. Implemented using XlaReduceWindow.
        Jax2TfLimitation((
            "jax2tf unimplemented for 64-bit inputs because the current implementation "
            "relies on packing two values into a single value. This can be "
            "fixed by using a variadic XlaReduceWindow, when available"),
                         dtypes=[np.float64],
                         devices=("cpu", "gpu"))
    ]

  @classmethod
  def sort(cls, harness: primitive_harness.Harness):
    return [
        Jax2TfLimitation(
            # I think that this is because TF is running on CPU even for GPU tests?
            "TODO: TF non-stable multiple-array sort",
            devices="gpu",
            enabled=(harness.params["num_arrays"] > 1 and
                     not harness.params["is_stable"]),
            expect_tf_error=False,
            skip_comparison=True),
    ]

  @classmethod
  def svd(cls, harness: primitive_harness.Harness):
    # TODO: slow test
    compute_uv = harness.params["compute_uv"]

    # Both `r_jax` and `r_tf` are 3-Tuples containing the SVD results:
    # `S` (singular values), `U` (left singular vectors), and `Vh` (the
    # adjoint of the right singular vectors). Note that the TF results are
    # obtained through `_svd` in jax/experimental/jax2tf/jax2tf.py.
    def custom_assert(tst, r_jax, r_tf, *, args, tol, err_msg):

      def reconstruct_operand(result):
        # Reconstructing operand as documented in numpy.linalg.svd (see
        # https://numpy.org/doc/stable/reference/generated/numpy.linalg.svd.html)
        s, u, v = result
        U = u[..., :s.shape[-1]]
        V = v[..., :s.shape[-1], :]
        S = s[..., None, :]
        return jnp.matmul(U * S, V, precision=lax.Precision.HIGHEST)

      # Compares the shapes.
      def compare_shapes(r_jax, r_tf):
        shapes_jax = [result.shape for result in r_jax]
        shapes_tf = [result.shape for result in r_tf]
        tst.assertEqual(shapes_jax, shapes_tf)

      # Compares reconstructed operand.
      # Computes backward error https://www.netlib.org/lapack/lug/node97.html
      # and uses the maximum backward error if there are batch dimensions.
      # The backward error is bounded by some constant multiplying the machine
      # precision.
      # TODO: Compares the operand instead of the reconstructed operand.
      def compare_reconstructed_operand(r_jax, r_tf, tol):
        operand_jax = reconstruct_operand(r_jax)
        operand_tf = reconstruct_operand(r_tf)
        error_norm = jnp.linalg.norm(operand_jax - operand_tf,
                                              axis=(-2, -1))
        backward_error = (error_norm /
                          jnp.linalg.norm(operand_jax, axis=(-2, -1)))
        max_backward_error = jnp.amax(backward_error)
        tst.assertLess(max_backward_error, tol)

      # Computes the absolute gap between singular value `\sigma_i` and the
      # nearest other singular value and for all singular values. The absolute
      # gap is used to approximate the upper bound of angular difference
      # between the computed and the true singular vectors. If the matrix is
      # rectangular `m != n`, the gap for the smallest nonzero singular value
      # should also consider the gap between it and zero. Note that this code
      # relies on the singular values being in descending order.
      def compute_absolute_gap(s, m, n):
        forward_appendant = np.inf if m == n else 0
        forward_diff = jnp.diff(s, axis=-1, append=forward_appendant)
        backward_diff = jnp.diff(
            s[..., ::-1], axis=-1, append=np.inf)[..., ::-1]
        absolute_gap = jnp.minimum(jnp.abs(forward_diff),
                                   jnp.abs(backward_diff))
        return absolute_gap

      # See `CompareSingularVectors` in
      # tensorflow/python/kernel_tests/linalg/svd_op_test.py
      def compare_singular_vectors(x, y, *, error_bound):
        # Singular vectors are only unique up to sign (complex phase factor for
        # complex matrices), so we normalize the sign first.
        sum_of_ratios = jnp.sum(jnp.divide(y, x), -2, keepdims=True)
        phases = jnp.divide(sum_of_ratios, jnp.abs(sum_of_ratios))
        x *= phases

        # Note that in general `sqrt(sum(squares))` is not a stable way to
        # compute l2 vector norms, but it should be OK for normalization
        # factors of vectors with norm ~= 1 as here.
        def dot_column_wise(a, b):
          output = jnp.sum(jnp.einsum('...ij,...ij->...ij', a.conj(), b,
                                      precision=lax.Precision.HIGHEST),
                           axis=-2)
          return jnp.real(output)

        cos_angular_diff = (
            dot_column_wise(x, y) /
            jnp.sqrt(dot_column_wise(x, x) * dot_column_wise(y, y)))

        # Values of `\cos(angular_diff)` outside the interval [0, 1] are clipped
        # to the interval edges. For example, `\cos(angular_diff)` could contain
        # values like 1.0000001 on float32, which are clipped to 1.0. It is
        # possible that anything other than `cos_angular_diff` can be outside
        # the interval [0, 1] due to roundoff.
        cos_angular_diff = jnp.clip(cos_angular_diff, a_min=0.0, a_max=1.0)

        angular_diff = jnp.arccos(cos_angular_diff)

        # TODO: removes the slack factor on the angular difference.
        # It is possible that the singular vectors are not accurate to much more
        # than O(\sqrt(eps)), which is likely a property of the SVD algorithms
        # in question; revisit with better understanding of the SVD algorithms.
        if x.dtype in [np.float32, np.complex64]:
          slack_factor = 2E4
        elif x.dtype in [np.float64, np.complex128]:
          slack_factor = 2E9

        np.testing.assert_array_less(angular_diff,
                                     slack_factor * error_bound)

      if compute_uv:
        # Compares the shapes.
        compare_shapes(r_jax, r_tf)

        # Compares the singular values. Each computed singular value `\sigma_i`
        # differs from the true `\sigma_i`* by at most
        # `|\sigma_i - \sigma_i*| <= \epsilon \sigma_1`, where `\sigma_1` is the
        # largest singular value and `\epsilon` denotes the machine precision.
        s_jax, s_tf = r_jax[0], r_tf[0]
        tst.assertAllClose(s_jax, s_tf, atol=tol, rtol=tol, err_msg=err_msg)

        # Compares the reconstructed operand.
        compare_reconstructed_operand(r_jax, r_tf, tol)

        # Compares the singular vectors.
        # We only compare the first `rank` singular vectors since the remainder
        # forms an arbitrary orthonormal basis for the (row- or column-) null
        # space, whose exact value depends on implementation details.
        # TODO: A better estimation on the rank?
        rank = r_jax[0].shape[-1]

        # Computes the upper bound for angular difference of singular vectors.
        # The upper bound has the shape of `[..., k]`, where `...` denotes the
        # batch dimensions and `k` is the number of nonzero singular values.
        m = r_jax[1].shape[-2]
        n = r_jax[2].shape[-2]
        absolute_gap = compute_absolute_gap(r_jax[0], m, n)
        epsilon = jnp.finfo(r_jax[0].dtype).eps
        sigma_largest = (r_jax[0][..., 0])[..., None]
        upperbound_singular_vectors = epsilon * sigma_largest / absolute_gap
        upperbound_singular_vectors = upperbound_singular_vectors[..., :rank]

        # Left singular vectors.
        u_jax = r_jax[1][..., :rank]
        u_tf = r_tf[1][..., :rank]
        compare_singular_vectors(u_jax, u_tf,
                                 error_bound=upperbound_singular_vectors)

        # Right singular vectors.
        v_jax = jnp.swapaxes(r_jax[2][..., :rank, :], -2, -1).conj()
        v_tf = jnp.swapaxes(r_tf[2][..., :rank, :], -2, -1).conj()
        compare_singular_vectors(v_jax, v_tf,
                                 error_bound=upperbound_singular_vectors)
      else:
        tst.assertAllClose(r_jax, r_tf, atol=tol, rtol=tol, err_msg=err_msg)

    return [
        # Works in JAX for complex due to custom calls on cpu and gpu
        Jax2TfLimitation(
            "function not compilable. Implemented using `tf.linalg.svd` and `tf.linalg.adjoint`",
            dtypes=[np.complex64, np.complex128],
            devices=("cpu", "gpu"),
            modes=("compiled",)),
        Jax2TfLimitation(
            "Large numerical discrepancy",
            dtypes=[np.float16],
            devices=("tpu"),
            modes=("eager", "graph", "compiled"),
            skip_comparison=True),
        missing_tf_kernel(dtypes=[dtypes.bfloat16], devices="tpu"),
        missing_tf_kernel(dtypes=[np.complex64, np.complex128],
                          modes=("compiled", "graph"),
                          devices="tpu"),
        custom_numeric(
            tol=1e-4,
            dtypes=[np.float32, np.complex64],
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled")),
        # TODO: this is very low tolerance for f64
        custom_numeric(
            tol=1e-4,
            dtypes=[np.float64, np.complex128],
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled")),
        custom_numeric(
            tol=1e-4,
            description="custom numeric comparison when compute_uv on CPU/GPU",
            custom_assert=custom_assert,
            devices=("cpu", "gpu"),
            modes=("eager", "graph", "compiled"),
            enabled=(compute_uv == True)),
        custom_numeric(
            tol=1e-5,
            description="custom numeric comparison when !compute_uv on TPU",
            dtypes=[np.float32, np.complex64],
            custom_assert=custom_assert,
            devices=("tpu"),
            modes=("eager", "graph", "compiled"),
            enabled=not compute_uv),
        custom_numeric(
            tol=1e-2,
            description="custom numeric comparison when compute_uv on TPU",
            dtypes=[np.float32, np.float64, np.complex64, np.complex128],
            custom_assert=custom_assert,
            devices=("tpu"),
            modes=("eager", "graph", "compiled"),
            enabled=(compute_uv == True)),
    ]

  @classmethod
  def tan(cls, harness):
    return [
        custom_numeric(dtypes=[np.complex64], devices="tpu", tol=1e-4),
        custom_numeric(dtypes=[np.complex64], devices=("cpu", "gpu"), tol=1e-3),
        custom_numeric(dtypes=[np.complex128], devices=("cpu", "gpu"), tol=1e-12)
    ]

  @classmethod
  def tanh(cls, harness):
    return [
        custom_numeric(dtypes=[np.complex128], tol=1e-7),
        custom_numeric(dtypes=[np.complex64], tol=1e-4)
    ]

  @classmethod
  def top_k(cls, harness):

    def custom_assert(tst, result_jax, result_tf, *, err_msg, **_):
      assert len(result_jax) == len(result_tf)
      # TODO: TF and JAX sort [inf, nan] differently.
      first_arr_jax, first_arr_tf = result_jax[0], result_tf[0]
      if np.all(first_arr_jax == first_arr_tf):
        for arr_jax, arr_tf in zip(result_jax, result_tf):
          tst.assertArraysEqual(arr_jax, arr_tf, err_msg=err_msg)
      else:
        mask_jax = np.isnan(first_arr_jax) | np.isinf(first_arr_jax)
        mask_tf = np.isnan(first_arr_tf) | np.isinf(first_arr_tf)
        tst.assertArraysEqual(
            first_arr_jax[~mask_jax], first_arr_tf[~mask_tf], err_msg=err_msg)

    return [
        custom_numeric(
            dtypes=[np.float16, dtypes.bfloat16, np.float32, np.float64],
            custom_assert=custom_assert,
            description=(
                "Produces different results when the array contains `inf` and `NaN`"
                " (they are sorted differently in TF vs. XLA)."))
    ]

  @classmethod
  def triangular_solve(cls, harness: primitive_harness.Harness):
    return [
        missing_tf_kernel(
            dtypes=[dtypes.bfloat16],
            devices=("gpu", "cpu"),
            modes=("eager", "graph")),
        missing_tf_kernel(
            dtypes=[np.float16],
            devices=("gpu", "cpu"),
            modes=("eager", "graph")),
        custom_numeric(dtypes=[np.float32], tol=5e-3,
                       modes=("eager", "graph", "compiled"))
    ]

  @classmethod
  def tridiagonal_solve(cls, harness: primitive_harness.Harness):
    return []

def custom_numeric(
    *,
    description="custom numeric comparison",
    dtypes=(),  # All
    modes=(
        "eager",
        "graph",
    ),  # By default we should not need tolerance for
    # "compiled"
    devices=("cpu", "gpu", "tpu"),
    custom_assert=None,
    enabled=True,
    native_serialization=Jax2TfLimitation.FOR_NON_NATIVE,
    tol=None) -> Jax2TfLimitation:

  return Jax2TfLimitation(
      description,
      expect_tf_error=False,
      dtypes=dtypes,
      devices=devices,
      modes=modes,
      custom_assert=custom_assert,
      enabled=enabled,
      native_serialization=native_serialization,
      tol=tol)

def custom_random_keys_output():
  def custom_assert(tst, result_jax, result_tf, *, args, tol, err_msg):
    # Here we handle both new-style and old-style keys; see JEP 9263
    def unwrap_keys(keys):
      if jax.dtypes.issubdtype(keys.dtype, jax.dtypes.prng_key):
        return jax._src.prng.random_unwrap(keys)
      else:
        return keys

    tst.assertAllClose(unwrap_keys(result_jax), result_tf,
                       atol=tol, rtol=tol, err_msg=err_msg)

  return custom_numeric(
      description="Returns JAX key arrays, so compare underlying base array",
      modes=("eager", "graph", "compiled"),
      custom_assert=custom_assert)


def missing_tf_kernel(*,
    description="op not defined for dtype",
    dtypes,
    modes=("eager", "graph", "compiled"),
    devices=("cpu", "gpu", "tpu"),
    native_serialization = Jax2TfLimitation.FOR_NON_NATIVE,
    enabled=True) -> Jax2TfLimitation:

  return Jax2TfLimitation(
      description, dtypes=dtypes, devices=devices, modes=modes, enabled=enabled,
      native_serialization=native_serialization)
