# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
#
# 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
#
#     http://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.
# ==============================================================================
"""Experimental library that exposes XLA operations directly in TensorFlow.

It is sometimes useful to be able to build HLO programs directly from
TensorFlow. This file provides Tensorflow operators that mirror the semantics of
HLO operators as closely as possible.

Note: Most of the operators defined in this module are used by the jax2tf
converter (see go/jax2tf for details) and are used in SavedModel produced
by jax2tf. Hence, we need to maintain backwards compatibility for these
operators. Please reach out to the JAX team if you want to make changes.
"""

from tensorflow.compiler.tf2xla.ops import gen_xla_ops
from xla import xla_data_pb2
from tensorflow.core.framework import attr_value_pb2
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import bitwise_ops
from tensorflow.python.ops import gen_math_ops
from tensorflow.python.ops import gen_random_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import random_ops
from tensorflow.python.ops import random_ops_util
from tensorflow.python.ops import special_math_ops
from tensorflow.python.ops.numpy_ops import np_utils

# TODO(phawkins): provide wrappers for all XLA operators. Currently the missing
# ops include:
# infeed/outfeed (available via tf.contrib.tpu)
# collectives, e.g., cross-replica-sum (available via tf.contrib.tpu)
# conditional
# gather/scatter
# collapse

# This file reuses builtin names (following XLA's names, so we can call things
# like xla.max), so we capture the builtin versions here.
# pylint: disable=redefined-builtin
_max = max
_min = min
_slice = slice  # pylint: disable=invalid-name

constant = constant_op.constant

# Unary operators.

# For most arithmetic operators there is a TensorFlow operator
# that exactly corresponds to each XLA operator. Rather than defining
# XLA-specific variants, we reuse the corresponding TensorFlow operator.
# TODO(phawkins): It would be even better to have TensorFlow operators that 1:1
# wrap every HLO operator, because that would allow us to be confident that the
# semantics match.


def _unary_op(fn):
  """Wrapper that restricts `fn` to have the correct signature."""

  def unary_op_wrapper(x, name=None):
    return fn(x, name=name)

  return unary_op_wrapper


abs = _unary_op(math_ops.abs)
# TODO(phawkins): implement clz.
conj = _unary_op(math_ops.conj)
cos = _unary_op(math_ops.cos)
ceil = _unary_op(math_ops.ceil)
digamma = _unary_op(math_ops.digamma)
erf = _unary_op(math_ops.erf)
erfc = _unary_op(math_ops.erfc)
erfinv = _unary_op(math_ops.erfinv)
ndtri = _unary_op(math_ops.ndtri)
exp = _unary_op(math_ops.exp)
expm1 = _unary_op(math_ops.expm1)
floor = _unary_op(math_ops.floor)
imag = _unary_op(math_ops.imag)
is_finite = _unary_op(math_ops.is_finite)
lgamma = _unary_op(math_ops.lgamma)
log = _unary_op(math_ops.log)
log1p = _unary_op(math_ops.log1p)
logical_not = _unary_op(math_ops.logical_not)
neg = _unary_op(math_ops.neg)
real = _unary_op(math_ops.real)
# TODO(phawkins): unlike xla::Round, this rounds to even instead of zero for
# numbers halfway between two integers.
round = _unary_op(math_ops.round)
sin = _unary_op(math_ops.sin)
sign = _unary_op(math_ops.sign)
tan = _unary_op(math_ops.tan)
tanh = _unary_op(math_ops.tanh)

# Bessel
bessel_i0e = _unary_op(special_math_ops.bessel_i0e)
bessel_i1e = _unary_op(special_math_ops.bessel_i1e)

# Binary operators

# The main difference between TensorFlow and XLA binary ops is the broadcasting
# semantics. TensorFlow uses Numpy-style broadcasting semantics, whereas XLA
# requires an explicit specification of which dimensions to broadcast if the
# arguments have different ranks.


def _broadcasting_binary_op(fn):
  """Wraps a binary Tensorflow operator and performs XLA-style broadcasting."""

  def broadcasting_binary_op_wrapper(x, y, broadcast_dims=None, name=None):
    """Inner wrapper function."""
    broadcast_dims = broadcast_dims or []
    broadcast_dims = ops.convert_to_tensor(broadcast_dims, dtypes.int64)
    # Rather than relying on having static shape information in the TensorFlow
    # graph, we use an XlaBroadcastHelper op that can compute the correct shapes
    # at JIT compilation time.
    x, y = gen_xla_ops.xla_broadcast_helper(x, y, broadcast_dims)
    return fn(x, y, name=name)

  return broadcasting_binary_op_wrapper


# Map from TF signed types to TF unsigned types.
_SIGNED_TO_UNSIGNED_TABLE = {
    dtypes.int8: dtypes.uint8,
    dtypes.int16: dtypes.uint16,
    dtypes.int32: dtypes.uint32,
    dtypes.int64: dtypes.uint64,
}

# Map from TF unsigned types to TF signed types.
_UNSIGNED_TO_SIGNED_TABLE = {
    dtypes.uint8: dtypes.int8,
    dtypes.uint16: dtypes.int16,
    dtypes.uint32: dtypes.int32,
    dtypes.uint64: dtypes.int64,
}


def _shift_right_logical_helper(x, y, name=None):
  """Performs an integer right logical shift irrespective of input type."""
  assert y.dtype == x.dtype
  dtype = x.dtype
  signed = dtype in _SIGNED_TO_UNSIGNED_TABLE
  if signed:
    unsigned_dtype = _SIGNED_TO_UNSIGNED_TABLE[dtype]
    x = math_ops.cast(x, unsigned_dtype)
    y = math_ops.cast(y, unsigned_dtype)
  output = bitwise_ops.right_shift(x, y, name=name)
  if signed:
    output = math_ops.cast(output, dtype)
  return output


def _shift_right_arithmetic_helper(x, y, name=None):
  """Performs an integer right arithmetic shift irrespective of input type."""
  assert y.dtype == x.dtype
  dtype = x.dtype
  unsigned = dtype in _UNSIGNED_TO_SIGNED_TABLE
  if unsigned:
    signed_dtype = _UNSIGNED_TO_SIGNED_TABLE[dtype]
    x = math_ops.cast(x, signed_dtype)
    y = math_ops.cast(y, signed_dtype)
  output = bitwise_ops.right_shift(x, y, name=name)
  if unsigned:
    output = math_ops.cast(output, dtype)
  return output


add = _broadcasting_binary_op(math_ops.add)
sub = _broadcasting_binary_op(math_ops.sub)
mul = _broadcasting_binary_op(math_ops.mul)
div = _broadcasting_binary_op(math_ops.div)
rem = _broadcasting_binary_op(gen_math_ops.mod)
max = _broadcasting_binary_op(math_ops.maximum)
min = _broadcasting_binary_op(math_ops.minimum)
atan2 = _broadcasting_binary_op(math_ops.atan2)
complex = _broadcasting_binary_op(math_ops.complex)
logical_and = _broadcasting_binary_op(math_ops.logical_and)
logical_or = _broadcasting_binary_op(math_ops.logical_or)
logical_xor = _broadcasting_binary_op(math_ops.logical_xor)
eq = _broadcasting_binary_op(math_ops.equal)
ne = _broadcasting_binary_op(math_ops.not_equal)
ge = _broadcasting_binary_op(math_ops.greater_equal)
gt = _broadcasting_binary_op(math_ops.greater)
le = _broadcasting_binary_op(math_ops.less_equal)
lt = _broadcasting_binary_op(math_ops.less)
pow = _broadcasting_binary_op(math_ops.pow)
shift_left = _broadcasting_binary_op(bitwise_ops.left_shift)
shift_right_logical = _broadcasting_binary_op(_shift_right_logical_helper)
shift_right_arithmetic = _broadcasting_binary_op(_shift_right_arithmetic_helper)

igamma = _broadcasting_binary_op(math_ops.igamma)
igamma_grad_a = _broadcasting_binary_op(gen_math_ops.igamma_grad_a)
random_gamma_grad = _broadcasting_binary_op(gen_random_ops.random_gamma_grad)
igammac = _broadcasting_binary_op(math_ops.igammac)
polygamma = _broadcasting_binary_op(math_ops.polygamma)
zeta = _broadcasting_binary_op(math_ops.zeta)


def _binary_op(fn):
  """Wrapper that restricts `fn` to have the correct signature."""

  def binary_op_wrapper(x, y, name=None):
    return fn(x, y, name=name)

  return binary_op_wrapper


transpose = _binary_op(array_ops.transpose)
rev = _binary_op(array_ops.reverse)

bitcast_convert_type = array_ops.bitcast


def broadcast(x, dims, name=None):
  x = ops.convert_to_tensor(x)
  shape = array_ops.concat(
      [constant_op.constant(dims), array_ops.shape(x)], axis=0
  )
  return array_ops.broadcast_to(x, shape, name=name)


def clamp(a, x, b, name=None):
  return min(max(a, x, name=name), b, name=name)


concatenate = array_ops.concat


def conv(
    lhs,
    rhs,
    window_strides,
    padding,
    lhs_dilation,
    rhs_dilation,
    dimension_numbers,
    feature_group_count=1,
    precision_config=None,
    preferred_element_type=None,
    name=None,
    use_v2=False,
    batch_group_count=1,
):
  """Wraps the XLA ConvGeneralDilated operator.

  ConvGeneralDilated is the most general form of XLA convolution and is
  documented at
  https://www.tensorflow.org/performance/xla/operation_semantics#conv_convolution

  Args:
    lhs: the input tensor
    rhs: the kernel tensor
    window_strides: the inter-window strides
    padding: the padding to apply at the start and end of each input dimensions
    lhs_dilation: dilation to apply between input elements
    rhs_dilation: dilation to apply between kernel elements
    dimension_numbers: a `ConvolutionDimensionNumbers` proto.
    feature_group_count: number of feature groups for grouped convolution.
    precision_config: a `xla.PrecisionConfig` proto.
    preferred_element_type: the result `dtype`.
    name: an optional name for the operator.
    use_v2: an optional request to use the XlaConvV2 op even if not necessary.
    batch_group_count: number of batch groups or grouped filters.

  Returns:
    A tensor representing the output of the convolution.
  """
  precision_config_proto = ""
  if precision_config:
    precision_config_proto = precision_config.SerializeToString()
  needs_v2 = (
      preferred_element_type
      or (lhs.dtype != rhs.dtype)
      or batch_group_count > 1
  )
  if preferred_element_type is None:
    preferred_element_type = np_utils.result_type(lhs.dtype, rhs.dtype)
  if needs_v2 or use_v2:
    return gen_xla_ops.xla_conv_v2(
        lhs,
        rhs,
        window_strides=window_strides,
        padding=padding,
        lhs_dilation=lhs_dilation,
        rhs_dilation=rhs_dilation,
        feature_group_count=feature_group_count,
        batch_group_count=batch_group_count,
        dimension_numbers=dimension_numbers.SerializeToString(),
        precision_config=precision_config_proto,
        preferred_element_type=preferred_element_type,
        name=name,
    )
  return gen_xla_ops.xla_conv(
      lhs,
      rhs,
      window_strides=window_strides,
      padding=padding,
      lhs_dilation=lhs_dilation,
      rhs_dilation=rhs_dilation,
      feature_group_count=feature_group_count,
      dimension_numbers=dimension_numbers.SerializeToString(),
      precision_config=precision_config_proto,
      name=name,
  )


convert_element_type = math_ops.cast


def dot(lhs, rhs, name=None):
  return math_ops.tensordot(lhs, rhs, axes=1, name=name)


DotDimensionNumbers = xla_data_pb2.DotDimensionNumbers
PrecisionConfig = xla_data_pb2.PrecisionConfig


def dot_general(
    lhs,
    rhs,
    dimension_numbers,
    precision_config=None,
    preferred_element_type=None,
    name=None,
    use_v2=False,
):
  precision_config_proto = ""
  if precision_config:
    precision_config_proto = precision_config.SerializeToString()
  needs_v2 = preferred_element_type or (lhs.dtype != rhs.dtype)
  if preferred_element_type is None:
    preferred_element_type = np_utils.result_type(lhs.dtype, rhs.dtype)
  if needs_v2 or use_v2:
    return gen_xla_ops.xla_dot_v2(
        lhs,
        rhs,
        dimension_numbers=dimension_numbers.SerializeToString(),
        precision_config=precision_config_proto,
        preferred_element_type=preferred_element_type,
        name=name,
    )
  return gen_xla_ops.xla_dot(
      lhs,
      rhs,
      dimension_numbers=dimension_numbers.SerializeToString(),
      precision_config=precision_config_proto,
      name=name,
  )


def self_adjoint_eig(a, lower, max_iter, epsilon):
  return gen_xla_ops.xla_self_adjoint_eig(a, lower, max_iter, epsilon)


def svd(a, max_iter, epsilon, precision_config=None):
  precision_config_proto = ""
  if precision_config:
    precision_config_proto = precision_config.SerializeToString()
  return gen_xla_ops.xla_svd(a, max_iter, epsilon, precision_config_proto)


dynamic_slice = gen_xla_ops.xla_dynamic_slice
dynamic_update_slice = gen_xla_ops.xla_dynamic_update_slice
einsum = gen_xla_ops.xla_einsum

# TODO(phawkins): generalize tf.pad to support interior padding, and then remove
# the XLA-specific pad operator.
pad = gen_xla_ops.xla_pad


def random_normal(mu, sigma, dims, name=None):
  mu = ops.convert_to_tensor(mu)
  return random_ops.random_normal(
      dims, mean=mu, stddev=sigma, dtype=mu.dtype, name=name
  )


def random_uniform(minval, maxval, dims, name=None):
  minval = ops.convert_to_tensor(minval)
  return random_ops.random_uniform(
      dims, minval, maxval, dtype=minval.dtype, name=name
  )


def rng_bit_generator(algorithm, initial_state, shape, dtype):
  """Stateless PRNG bit generator.

  Wraps the XLA RngBitGenerator operator, documented at
    https://www.tensorflow.org/performance/xla/operation_semantics#rngbitgenerator.

  Args:
    algorithm: The PRNG algorithm to use, one of tf.random.Algorithm.{PHILOX,
      THREEFRY, AUTO_SELECT}.
    initial_state: Initial state for the PRNG algorithm. For THREEFRY, it should
      be a u64[2] and for PHILOX a u64[3].
    shape: The output shape of the generated data.
    dtype: The type of the tensor.

  Returns:
    a tuple with a new state and generated data of the given shape.
  """
  alg_int = random_ops_util.convert_alg_to_int(algorithm)
  return gen_xla_ops.xla_rng_bit_generator(
      alg_int, initial_state, shape, dtype=dtype
  )


recv = gen_xla_ops.xla_recv
reduce = gen_xla_ops.xla_reduce
variadic_reduce = gen_xla_ops.xla_variadic_reduce_v2

ops.no_gradient("XlaVariadicReduce")


def reduce_window(
    operand,
    init,
    reducer,
    window_dimensions,
    window_strides=None,
    base_dilations=None,
    window_dilations=None,
    padding=None,
    name=None,
):
  """Wraps the XLA ReduceWindow operator.

  ReduceWindow is documented at
  https://www.tensorflow.org/performance/xla/operation_semantics#reducewindow .

  Args:
    operand: the input tensor
    init: a scalar tensor representing the initial value for the reduction
    reducer: a reduction function that combines a pair of scalars.
    window_dimensions: shape of the window, as a list of integers
    window_strides: inter-window strides, as a list of integers. Optional; if
      omitted, defaults to strides of 1.
    padding: padding to apply to 'operand'. List of (low, high) pairs of
      integers that specify the padding to apply before and after each
      dimension. Optional; if omitted, defaults to no padding.
    name: the operator name, or None.

  Returns:
    A tensor that represents the output of the reduce_window operator.
  """
  window_strides = window_strides or [1] * len(window_dimensions)
  base_dilations = base_dilations or [1] * len(window_dimensions)
  window_dilations = window_dilations or [1] * len(window_dimensions)
  padding = padding or [(0, 0)] * len(window_dimensions)
  return gen_xla_ops.xla_reduce_window(
      input=operand,
      init_value=init,
      window_dimensions=window_dimensions,
      window_strides=window_strides,
      base_dilations=base_dilations,
      window_dilations=window_dilations,
      padding=padding,
      computation=reducer,
      name=name,
  )


replica_id = gen_xla_ops.xla_replica_id

# Set a static bound for the given input value as a hint to Xla compiler,
# returns the same value.
# Usage:
# def f(t, p):
#   p = xla.set_bound(p, 3) # Tells xla the constraint that p <= 3.
#   return t[:p]            # xla knows the bound of the slice is 3.
set_bound = gen_xla_ops.xla_set_bound

# Make a static dimension into a xla bounded dynamic dimension. The current
# static dimension size will become the bound and the second operand becomes the
# dynamic size of the dimension.
#
# This should mostly be used for testing.
#
# def f():
#   array = tf.convert_to_tensor([[1, 2, 3, 4, 5]])
#   # Tells xla the valid size of the array is 3.
#   dim = 0
#   p = xla_set_dynamic_dimension_size(array, dim, 3)
#   assert(reduce_sum(p) == 6) # xla knows only the first 3 elements are valid.
set_dynamic_dimension_size = gen_xla_ops.xla_set_dynamic_dimension_size

# Inverse of xla_set_dynamic_dimension_size. Make an xla bounded dynamic
# dimension into a static dimension. The bound of the size of dimension
# `dim_index` becomes the static dimension size.
remove_dynamic_dimension_size = gen_xla_ops.xla_remove_dynamic_dimension_size


def reshape(x, new_sizes, dimensions=None, name=None):
  if dimensions is not None:
    x = array_ops.transpose(x, dimensions)
  x = array_ops.reshape(x, new_sizes, name=name)
  return x


def select(condition, x, y, name=None):
  return array_ops.where(condition, x, y, name)


select_and_scatter = gen_xla_ops.xla_select_and_scatter
send = gen_xla_ops.xla_send


def slice(x, start_dims, limit_dims, strides):
  spec = [
      _slice(start, limit, stride)
      for (start, limit, stride) in zip(start_dims, limit_dims, strides)
  ]
  return x[tuple(spec)]


sharding = gen_xla_ops.xla_sharding


@ops.RegisterGradient("XlaSharding")
def _sharding_grad(op, grad):
  """Gradient for XlaSharding op."""
  sharding_attr = op.get_attr("sharding")
  grad_sharding = gen_xla_ops.xla_sharding(
      grad,
      sharding=sharding_attr,
      unspecified_dims=op.get_attr("unspecified_dims"),
  )
  # pylint: disable=protected-access
  grad_sharding.op._set_attr(
      "_XlaSharding", attr_value_pb2.AttrValue(s=sharding_attr)
  )
  return [grad_sharding]


spmd_full_to_shard_shape = gen_xla_ops.xla_spmd_full_to_shard_shape
spmd_shard_to_full_shape = gen_xla_ops.xla_spmd_shard_to_full_shape


@ops.RegisterGradient("XlaSpmdFullToShardShape")
def _spmd_full_to_shard_shape_grad(op, grad):
  s2f = gen_xla_ops.xla_spmd_shard_to_full_shape(
      grad,
      manual_sharding=op.get_attr("manual_sharding"),
      full_shape=op.inputs[0].shape.as_list(),
      dim=op.get_attr("dim"),
      unspecified_dims=op.get_attr("unspecified_dims"),
  )
  return [s2f]


@ops.RegisterGradient("XlaSpmdShardToFullShape")
def _spmd_shard_to_full_shape_grad(op, grad):
  f2s = gen_xla_ops.xla_spmd_full_to_shard_shape(
      grad,
      manual_sharding=op.get_attr("manual_sharding"),
      dim=op.get_attr("dim"),
      unspecified_dims=op.get_attr("unspecified_dims"),
  )
  return [f2s]


sort = gen_xla_ops.xla_sort
key_value_sort = gen_xla_ops.xla_key_value_sort
variadic_sort = gen_xla_ops.xla_variadic_sort
while_loop = gen_xla_ops.xla_while
dequantize = gen_xla_ops.xla_dequantize
custom_call = gen_xla_ops.xla_custom_call


def custom_call_v2(
    call_target_name,
    operands,
    result_specs,
    backend_config=None,
    has_side_effect=None,
    name=None,
):
  """Emits an HLO `CustomCall` operation with multiple outputs.

  See `CustomCall` specification at
    https://tensorflow.org/xla/operation_semantics#customcall,
  and `mhlo.custom_call` specification at
    https://tensorflow.org/mlir/hlo_ops#mhlocustom_call_mlirmhlocustomcallop.

  Args:
    call_target_name: Name of the user function. The function signature must
      conform to version 3 of the API, see
      `API_VERSION_STATUS_RETURNING_UNIFIED`. All operands and results assumed
      to be in the default layout.
    operands: A sequence of tensors with possibly different types.
    result_specs: A sequence of tensor specs for all results.
    backend_config: A string that encodes a metadata for the backend. Empty
      string by default.
    has_side_effect: Indicates whether the custom call has side effects. `False`
      by default.
    name: Optional name of the operation.

  Returns:
    A tuple of output tensors.
  """
  return gen_xla_ops.xla_custom_call_v2(
      operands=operands,
      call_target_name=call_target_name,
      backend_config="" if backend_config is None else backend_config,
      has_side_effect=False if has_side_effect is None else has_side_effect,
      result_dtypes=tuple(spec.dtype for spec in result_specs),
      result_shapes=tuple(spec.shape for spec in result_specs),
      name=name,
  )


# pylint: disable=g-doc-args
# pylint: disable=g-doc-return-or-yield
def call_module(
    args,
    *,
    version=4,
    module,
    Tout,
    Sout,
    platforms=(),
    function_list=(),
    has_token_input_output=False,
    disabled_checks=(),
    use_shardy_partitioner=False,
):
  """See documentation for the XlaCallModule op.

  https://github.com/search?q=repo%3Atensorflow%2Ftensorflow+path%3Axla_ops.cc+xlacallmodule&type=code
  """
  res = gen_xla_ops.xla_call_module(
      args,
      version=version,
      module=module,
      dim_args_spec=(),
      Tout=Tout,
      Sout=Sout,
      platforms=platforms,
      function_list=function_list,
      has_token_input_output=has_token_input_output,
      disabled_checks=disabled_checks,
      use_shardy_partitioner=use_shardy_partitioner,
  )
  # Since XLACallModule op is stateful, zero return function will return the TF
  # op under tf.function. It creates trouble for downstream codes.
  # Here we force it return empty tuple to work around it.
  # TODO(johnqiangzhang): Figure out a better way to handle control dependency.
  if isinstance(res, ops.Operation):
    res = ()
  return res


def call_module_maximum_supported_version():
  """Maximum version of XlaCallModule op supported.

  See versioning details documentation for the XlaCallModule op at:
  https://github.com/search?q=repo%3Atensorflow%2Ftensorflow+path%3Axla_call_module+%22int+kVersionMaximumSupported%22&type=code
  """
  return 10

# pylint: enable=g-doc-args
# pylint: enable=g-doc-return-or-yield


def call_module_disable_check_platform():
  # For use with xla_call_module.disabled_checks.
  return "platform"


def gather(
    operand,
    start_indices,
    dimension_numbers,
    slice_sizes,
    indices_are_sorted=False,
    name=None,
):
  return gen_xla_ops.xla_gather(
      operand,
      start_indices,
      slice_sizes=slice_sizes,
      dimension_numbers=dimension_numbers.SerializeToString(),
      indices_are_sorted=indices_are_sorted,
      name=name,
  )


def scatter(
    operand,
    scatter_indices,
    updates,
    update_computation,
    dimension_numbers,
    indices_are_sorted=False,
    name=None,
):
  return gen_xla_ops.xla_scatter(
      operand,
      scatter_indices,
      updates,
      update_computation=update_computation,
      dimension_numbers=dimension_numbers.SerializeToString(),
      indices_are_sorted=indices_are_sorted,
      name=name,
  )


def optimization_barrier(*args):
  return gen_xla_ops.xla_optimization_barrier(args)


def reduce_precision(operand, exponent_bits, mantissa_bits):
  return gen_xla_ops.xla_reduce_precision(operand, exponent_bits, mantissa_bits)
