rocm_jax/jax/_src/prng.py

# 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.
from __future__ import annotations

from collections.abc import Callable, Iterator, Sequence
from functools import partial, reduce
import math
import operator as op
from typing import Any, NamedTuple

import numpy as np

import jax
from jax import lax
from jax import numpy as jnp
from jax import tree_util

from jax._src import api_util
from jax._src import api
from jax._src import config as config
from jax._src import core
from jax._src import dispatch
from jax._src import dtypes
from jax._src import pretty_printer as pp
from jax._src import source_info_util
from jax._src import tree_util as tree_util_internal
from jax._src import typing
from jax._src.api import jit, vmap
from jax._src.dtypes import float0
from jax._src.interpreters import ad
from jax._src.interpreters import batching
from jax._src.interpreters import mlir
from jax._src.interpreters import pxla
from jax._src.interpreters import xla
from jax._src.lax import lax as lax_internal
from jax._src.lib import gpu_prng
from jax._src.lib import xla_client as xc
from jax._src.lib.mlir import ir
from jax._src.lib.mlir.dialects import hlo
from jax._src.numpy.array_methods import (
    _array_operators, _set_array_base_attributes, _IndexUpdateHelper)
from jax._src.sharding_impls import (
    NamedSharding, PmapSharding, physical_sharding, logical_sharding)
from jax._src.typing import Array
from jax._src.util import safe_map, safe_zip

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

Device = xc.Device
Shard = Any  # TODO(jakevdp): fix circular imports and import Shard
Shape = tuple[int, ...]

UINT_DTYPES = {
    8: jnp.uint8, 16: jnp.uint16, 32: jnp.uint32, 64: jnp.uint64}

# -- PRNG implementation interface

class PRNGImpl(NamedTuple):
  """Specifies PRNG key shape and operations.

  A PRNG implementation is determined by a key type ``K`` and a
  collection of functions that operate on such keys. The key type
  ``K`` is an array type with element type uint32 and shape specified
  by ``key_shape``. The type signature of each operations is::

    seed :: int[] -> K
    fold_in :: K -> int[] -> K
    split[shape] :: K -> K[*shape]
    random_bits[shape, bit_width] :: K -> uint<bit_width>[*shape]

  A PRNG implementation is adapted to an array-like object of keys
  ``K`` by the ``PRNGKeyArray`` class, which should be created via the
  ``random_seed`` function.
  """
  key_shape: Shape
  seed: Callable
  split: Callable
  random_bits: Callable
  fold_in: Callable
  name: str = '<unnamed>'
  tag: str = '?'

  def __hash__(self) -> int:
    return hash(self.tag)

  def __str__(self) -> str:
    return self.tag

  def pprint(self):
    ty = self.__class__.__name__
    return (pp.text(f"{ty} [{self.tag}] {{{self.name}}}:") +
            pp.nest(2, pp.group(pp.brk() + pp.join(pp.brk(), [
              pp.text(f"{k} = {v}") for k, v in self._asdict().items()
            ]))))


prngs = {}

def register_prng(impl: PRNGImpl):
  if impl.name in prngs:
    raise ValueError(f'PRNG with name {impl.name} already registered: {impl}')
  prngs[impl.name] = impl


# -- PRNG key arrays

def _check_prng_key_data(impl, key_data: typing.Array):
  ndim = len(impl.key_shape)
  if not all(hasattr(key_data, attr) for attr in ['ndim', 'shape', 'dtype']):
    raise TypeError("JAX encountered invalid PRNG key data: expected key_data "
                    f"to have ndim, shape, and dtype attributes. Got {key_data}")
  if key_data.ndim < 1:
    raise TypeError("JAX encountered invalid PRNG key data: expected "
                    f"key_data.ndim >= 1; got ndim={key_data.ndim}")
  if key_data.shape[-ndim:] != impl.key_shape:
    raise TypeError("JAX encountered invalid PRNG key data: expected key_data.shape to "
                    f"end with {impl.key_shape}; got shape={key_data.shape} for {impl=}")
  if key_data.dtype not in [np.uint32, float0]:
    raise TypeError("JAX encountered invalid PRNG key data: expected key_data.dtype = uint32; "
                    f"got dtype={key_data.dtype}")


class PRNGKeyArray(jax.Array):
  """An array of PRNG keys backed by an RNG implementation.

  This class lifts the definition of a PRNG, provided in the form of a
  ``PRNGImpl``, into an array-like pytree class. Instances of this
  class behave like an array whose base elements are keys, hiding the
  fact that keys are typically arrays (of ``uint32`` dtype) themselves.

  PRNGKeyArrays are also restricted relative to JAX arrays in that
  they do not expose arithmetic operations. They instead expose
  wrapper methods around the PRNG implementation functions (``split``,
  ``random_bits``, ``fold_in``).
  """
  # TODO(jakevdp): potentially add tolist(), tobytes(),
  #    device_buffer, device_buffers, __cuda_interface__()

  _impl: PRNGImpl
  _base_array: typing.Array
  _consumed: bool | np.ndarray  # Used in jax.experimental.key_reuse.
  _source_info: None | source_info_util.SourceInfo = None

  def __init__(self, impl, key_data: Any):
    assert not isinstance(key_data, core.Tracer)
    _check_prng_key_data(impl, key_data)
    self._impl = impl
    self._base_array = key_data
    self._consumed = False  # TODO(jakevdp): default to True here?

  def block_until_ready(self):
    _ = self._base_array.block_until_ready()
    return self

  def copy_to_host_async(self):
    _ = self._base_array.copy_to_host_async()

  @property
  def aval(self):
    return keys_shaped_array(self._impl, self.shape)

  @property
  def shape(self):
    return base_arr_shape_to_keys_shape(self._impl, self._base_array.shape)

  @property
  def size(self):
    return math.prod(self.shape)

  @property
  def ndim(self):
    return len(self.shape)

  @property
  def dtype(self):
    return KeyTy(self._impl)

  @property
  def itemsize(self):
    return self.dtype.itemsize

  _device = property(op.attrgetter('_base_array._device'))
  _committed = property(op.attrgetter('_base_array._committed'))
  device = property(op.attrgetter('_base_array.device'))
  devices = property(op.attrgetter('_base_array.devices'))  # type: ignore[assignment]
  is_fully_addressable = property(op.attrgetter('_base_array.is_fully_addressable'))  # type: ignore[assignment]
  is_fully_replicated = property(op.attrgetter('_base_array.is_fully_replicated'))  # type: ignore[assignment]
  delete = property(op.attrgetter('_base_array.delete'))  # type: ignore[assignment]
  is_deleted = property(op.attrgetter('_base_array.is_deleted'))  # type: ignore[assignment]
  on_device_size_in_bytes = property(op.attrgetter('_base_array.on_device_size_in_bytes'))  # type: ignore[assignment]
  unsafe_buffer_pointer = property(op.attrgetter('_base_array.unsafe_buffer_pointer'))  # type: ignore[assignment]

  def addressable_data(self, index: int) -> PRNGKeyArray:
    return PRNGKeyArray(self._impl, self._base_array.addressable_data(index))

  @property
  def addressable_shards(self) -> list[Shard]:
    return [
        type(s)(
            device=s._device,
            sharding=s._sharding,
            global_shape=s._global_shape,
            data=PRNGKeyArray(self._impl, s._data),
        )
        for s in self._base_array.addressable_shards
    ]

  @property
  def global_shards(self) -> list[Shard]:
    return [
        type(s)(
            device=s._device,
            sharding=s._sharding,
            global_shape=s._global_shape,
            data=PRNGKeyArray(self._impl, s._data),
        )
        for s in self._base_array.global_shards
    ]

  @property
  def sharding(self):
    return logical_sharding(self.aval, self._base_array.sharding)

  @property
  def committed(self):
    return self._base_array.committed

  def _is_scalar(self):
    base_ndim = len(self._impl.key_shape)
    return self._base_array.ndim == base_ndim

  def __len__(self):
    if self._is_scalar():
      raise TypeError('len() of unsized object')
    return len(self._base_array)

  def __iter__(self) -> Iterator[PRNGKeyArray]:
    if self._is_scalar():
      raise TypeError('iteration over a 0-d key array')
    # TODO(frostig): we may want to avoid iteration by slicing because
    # a very common use of iteration is `k1, k2 = split(key)`, and
    # slicing/indexing may be trickier to track for linearity checking
    # purposes. Maybe we can:
    # * introduce an unpack primitive+traceable (also allow direct use)
    # * unpack upfront into shape[0] many keyarray slices
    # * return iter over these unpacked slices
    # Whatever we do, we'll want to do it by overriding
    # ShapedArray._iter when the element type is KeyTy...
    return (PRNGKeyArray(self._impl, k) for k in iter(self._base_array))

  def __repr__(self):
    return (f'Array({self.shape}, dtype={self.dtype.name}) overlaying:\n'
            f'{self._base_array}')

  def pprint(self):
    pp_keys = pp.text('shape = ') + pp.text(str(self.shape))
    pp_impl = pp.text('impl = ') + self._impl.pprint()
    return str(pp.group(
      pp.text('PRNGKeyArray:') +
      pp.nest(2, pp.brk() + pp_keys + pp.brk() + pp_impl)))

  def copy(self):
    out = self.__class__(self._impl, self._base_array.copy())
    out._consumed = self._consumed  # TODO(jakevdp): is this correct?
    return out

  __hash__ = None  # type: ignore[assignment]
  __array_priority__ = 100

  def __array__(self, dtype: np.dtype | None = None, copy: bool | None = None) -> np.ndarray:
    raise TypeError("JAX array with PRNGKey dtype cannot be converted to a NumPy array."
                    " Use jax.random.key_data(arr) if you wish to extract the underlying"
                    " integer array.")

  # Overwritten immediately below
  @property
  def at(self)                  -> _IndexUpdateHelper: assert False  # type: ignore[override]
  @property
  def T(self)                   -> PRNGKeyArray: assert False
  def __getitem__(self, _)      -> PRNGKeyArray: assert False
  def flatten(self, *_, **__)   -> PRNGKeyArray: assert False
  def ravel(self, *_, **__)     -> PRNGKeyArray: assert False
  def reshape(self, *_, **__)   -> PRNGKeyArray: assert False
  def squeeze(self, *_, **__)   -> PRNGKeyArray: assert False
  def swapaxes(self, *_, **__)  -> PRNGKeyArray: assert False
  def take(self, *_, **__)      -> PRNGKeyArray: assert False
  def transpose(self, *_, **__) -> PRNGKeyArray: assert False

_set_array_base_attributes(PRNGKeyArray, include=[
    *(f"__{op}__" for op in _array_operators),
    'at', 'flatten', 'ravel', 'reshape',
    'squeeze', 'swapaxes', 'take', 'transpose', 'T'])

api_util._shaped_abstractify_handlers[PRNGKeyArray] = op.attrgetter('aval')

def prngkeyarray_flatten(x):
  return (x._base_array,), x._impl

def prngkeyarray_unflatten(impl, children):
  base_array, = children
  return PRNGKeyArray(impl, base_array)

tree_util_internal.dispatch_registry.register_node(
    PRNGKeyArray, prngkeyarray_flatten, prngkeyarray_unflatten)


# TODO(frostig): remove, rerouting callers directly to random_seed
def seed_with_impl(impl: PRNGImpl, seed: int | typing.ArrayLike) -> PRNGKeyArray:
  return random_seed(seed, impl=impl)


def keys_shaped_array(impl, shape):
  return core.ShapedArray(shape, KeyTy(impl))

def base_arr_shape_to_keys_shape(impl, base_arr_shape):
  base_ndim = len(impl.key_shape)
  return base_arr_shape[:-base_ndim]


class KeyTyRules:
  allow_conversion: bool = False

  @staticmethod
  def full(shape, fill_value, dtype):
    physical_shape = (*shape, *dtype._impl.key_shape)
    if hasattr(fill_value, 'dtype') and jnp.issubdtype(fill_value.dtype, dtypes.prng_key):
      key_data = jnp.broadcast_to(random_unwrap(fill_value), physical_shape)
    else:
      key_data = lax.full(physical_shape, fill_value, dtype=np.dtype('uint32'))
    # TODO(frostig,mattjj,vanderplas,lenamartens): consider this consumed from
    # the outset.
    return random_wrap(key_data, impl=dtype._impl)

  @staticmethod
  def physical_element_aval(dtype) -> core.ShapedArray:
    return core.ShapedArray(dtype._impl.key_shape, jnp.dtype('uint32'))

  @staticmethod
  def physical_const(val) -> Array:
    return val._base_array

  @staticmethod
  def result_handler(sticky_device, aval):
    def handler(_, buf):
      buf.aval = core.ShapedArray(buf.shape, buf.dtype)
      return PRNGKeyArray(aval.dtype._impl, buf)
    return handler

  @staticmethod
  def local_sharded_result_handler(aval, sharding, indices):
    phys_aval = core.physical_aval(aval)
    key_shape = aval.dtype._impl.key_shape
    phys_handler_maker = pxla.local_result_handlers[core.ShapedArray]

    # set up a grounded sharding (with a grounded sharding spec)
    if isinstance(sharding, (PmapSharding, NamedSharding)):
      phys_sharding = physical_sharding(aval, sharding)
    else:
      assert False, f'impossible sharding {sharding} in local sharded result handler'

    # set up grounded indices
    trailing_inds = [slice(None)] * len(key_shape)
    phys_indices = [(*inds, *trailing_inds) for inds in indices]

    # make a physical handler
    phys_handler = phys_handler_maker(phys_aval, phys_sharding, phys_indices)

    # set up a handler that calls the physical one and wraps back up
    def handler(bufs):
      return PRNGKeyArray(aval.dtype._impl, phys_handler(bufs))

    return handler

  @staticmethod
  def global_sharded_result_handler(aval, out_sharding, committed):
    phys_aval = core.physical_aval(aval)
    phys_handler_maker = pxla.global_result_handlers[core.ShapedArray]

    phys_sharding = physical_sharding(aval, out_sharding)
    phys_handler = phys_handler_maker(phys_aval, phys_sharding, committed)
    def handler(bufs):
      return PRNGKeyArray(aval.dtype._impl, phys_handler(bufs))
    return handler

  @staticmethod
  def make_sharded_array(aval, sharding, arrays, committed):
    phys_aval = core.physical_aval(aval)
    phys_handler_maker = pxla.global_result_handlers[core.ShapedArray]
    phys_arrays = [random_unwrap(arr) for arr in arrays]

    phys_sharding = physical_sharding(aval, sharding)
    phys_handler = phys_handler_maker(phys_aval, phys_sharding, committed)
    phys_result = phys_handler(phys_arrays)
    return PRNGKeyArray(aval.dtype._impl, phys_result)

  @staticmethod
  def device_get(val):
    buffer = api.device_get(random_unwrap(val))
    return random_wrap(buffer, impl=val.dtype._impl)

  @staticmethod
  def device_put_sharded(vals, aval, sharding, devices):
    physical_aval = core.physical_aval(aval)
    physical_buffers = tree_util.tree_map(random_unwrap, vals)
    phys_sharding = physical_sharding(aval, sharding)
    physical_result = pxla.batched_device_put(physical_aval, phys_sharding,
                                              physical_buffers, list(devices))
    return random_wrap(physical_result, impl=aval.dtype._impl)

  @staticmethod
  def device_put_replicated(val, aval, sharding, devices):
    physical_aval = core.physical_aval(aval)
    assert len(xla.aval_to_xla_shapes(physical_aval)) == 1
    physical_buf = random_unwrap(val)
    phys_sharding = physical_sharding(aval, sharding)
    physical_result = pxla.batched_device_put(
        physical_aval, phys_sharding, [physical_buf] * len(devices), devices)
    return random_wrap(physical_result, impl=aval.dtype._impl)

  @staticmethod
  def tangent_dtype(_):
    return dtypes.float0

  # TODO(mattjj,frostig): even though the key dtype shouldn't appear in
  # tangents, our ad.replace_float0s in custom_jvp/vjp means passing in zeros
  # like the primal to user rules
  @staticmethod
  def zero(_):
    return np.zeros((), dtypes.float0)


class KeyTy(dtypes.ExtendedDType):
  _impl: PRNGImpl  # TODO(mattjj,frostig): protocol really
  _rules = KeyTyRules
  type = dtypes.prng_key

  def __init__(self, impl):
    self._impl = impl

  @property
  def name(self) -> str:
    return f'key<{self._impl.tag}>'

  @property
  def itemsize(self) -> int:
    return math.prod(self._impl.key_shape) * np.dtype('uint32').itemsize

  def __repr__(self) -> str:
    return self.name

  def __eq__(self, other):
    return type(other) is KeyTy and self._impl == other._impl

  def __hash__(self) -> int:
    return hash((self.__class__, self._impl))


core.pytype_aval_mappings[PRNGKeyArray] = lambda x: x.aval
xla.pytype_aval_mappings[PRNGKeyArray] = lambda x: x.aval

xla.canonicalize_dtype_handlers[PRNGKeyArray] = lambda x: x


def key_array_shard_arg_handler(xs: Sequence[PRNGKeyArray], shardings, layouts):
  arrs = [x._base_array for x in xs]
  phys_shardings = [physical_sharding(x.aval, sharding)
                    for x, sharding in zip(xs, shardings)]
  # TODO(yashkatariya): `layouts` should be converted to physical layouts.
  return pxla.shard_args(phys_shardings, layouts, arrs)


pxla.shard_arg_handlers[PRNGKeyArray] = key_array_shard_arg_handler


def key_array_constant_handler(x):
  arr = x._base_array
  return mlir.get_constant_handler(type(arr))(arr)
mlir.register_constant_handler(PRNGKeyArray, key_array_constant_handler)


# -- primitives

def iterated_vmap_unary(n, f):
  for _ in range(n):
    f = api.vmap(f)
  return f

# TODO(frostig): Revise the following two functions? These basically
# undo the singleton dimensions added by `batching.defbroadcasting`.
# It works, but introduces some possibly-redundant squeezes. Can we
# borrow from other broadcasting primitives instead?

def squeeze_vmap(f, left):
  def squeeze_vmap_f(x, y):
    if left:
      x = jnp.squeeze(x, axis=0)
      axes = (None, 0)
    else:
      y = jnp.squeeze(y, axis=0)
      axes = (0, None)
    return api.vmap(f, in_axes=axes, out_axes=0)(x, y)
  return squeeze_vmap_f

def iterated_vmap_binary_bcast(shape1, shape2, f):
  ndim1, ndim2 = len(shape1), len(shape2)
  if ndim1 == ndim2 == 0:
    return f
  if 0 in [ndim1, ndim2]:
    if ndim1 == 0:
      return lambda x, y: iterated_vmap_unary(ndim2, lambda y: f(x, y))(y)
    else:
      return lambda x, y: iterated_vmap_unary(ndim1, lambda x: f(x, y))(x)
  assert len(shape1) == len(shape2)
  for sz1, sz2 in reversed(zip(shape1, shape2)):
    if sz1 == sz2:
      f = api.vmap(f, out_axes=0)
    else:
      assert sz1 == 1 or sz2 == 1, (sz1, sz2)
      f = squeeze_vmap(f, sz1 == 1)
  return f


def random_seed(seeds: int | typing.ArrayLike, impl: PRNGImpl) -> PRNGKeyArray:
  # Avoid overflow error in X32 mode by first converting ints to int64.
  # This breaks JIT invariance for large ints, but supports the common
  # use-case of instantiating with Python hashes in X32 mode.
  if isinstance(seeds, int):
    seeds_arr = jnp.asarray(np.int64(seeds))
  else:
    seeds_arr = jnp.asarray(seeds)
  if config.random_seed_offset.value:
    seeds_arr += config.random_seed_offset.value
  return random_seed_p.bind(seeds_arr, impl=impl)

random_seed_p = core.Primitive('random_seed')
ad.defjvp_zero(random_seed_p)
batching.defvectorized(random_seed_p)

@random_seed_p.def_abstract_eval
def random_seed_abstract_eval(seeds_aval, *, impl):
  return keys_shaped_array(impl, seeds_aval.shape)

@random_seed_p.def_impl
def random_seed_impl(seeds, *, impl):
  base_arr = random_seed_impl_base(seeds, impl=impl)
  return PRNGKeyArray(impl, base_arr)

def random_seed_impl_base(seeds, *, impl):
  seed = iterated_vmap_unary(np.ndim(seeds), impl.seed)
  return seed(seeds)

def random_seed_lowering(ctx, seeds, *, impl):
  aval, = ctx.avals_in
  seed = iterated_vmap_unary(aval.ndim, impl.seed)
  seed_lowering = mlir.lower_fun(seed, multiple_results=False)
  return mlir.delegate_lowering(
      ctx, seed_lowering, seeds,
      avals_out=map(core.physical_aval, ctx.avals_out))

mlir.register_lowering(random_seed_p, random_seed_lowering)


def random_split(keys, shape: Shape):
  return random_split_p.bind(keys, shape=shape)

random_split_p = core.Primitive('random_split')
ad.defjvp_zero(random_split_p)
batching.defvectorized(random_split_p)

@random_split_p.def_abstract_eval
def random_split_abstract_eval(keys_aval, *, shape):
  return keys_shaped_array(keys_aval.dtype._impl, (*keys_aval.shape, *shape))

@random_split_p.def_impl
def random_split_impl(keys, *, shape):
  base_arr = random_split_impl_base(
      keys._impl, keys._base_array, keys.ndim, shape=shape)
  return PRNGKeyArray(keys._impl, base_arr)

def random_split_impl_base(impl, base_arr, keys_ndim, *, shape):
  split = iterated_vmap_unary(keys_ndim, lambda k: impl.split(k, shape))
  return split(base_arr)

def random_split_lowering(ctx, keys, *, shape):
  aval, = ctx.avals_in
  impl = aval.dtype._impl
  split = iterated_vmap_unary(aval.ndim, lambda k: impl.split(k, shape))
  split_lowering = mlir.lower_fun(split, multiple_results=False)
  return mlir.delegate_lowering(
      ctx, split_lowering, keys,
      avals_in=[core.physical_aval(aval)],
      avals_out=map(core.physical_aval, ctx.avals_out))

mlir.register_lowering(random_split_p, random_split_lowering)


def random_fold_in(keys, msgs):
  return random_fold_in_p.bind(keys, jnp.asarray(msgs))

random_fold_in_p = core.Primitive('random_fold_in')
ad.defjvp_zero(random_fold_in_p)
batching.defbroadcasting(random_fold_in_p)

@random_fold_in_p.def_abstract_eval
def random_fold_in_abstract_eval(keys_aval, msgs_aval):
  shape = lax_internal.broadcasting_shape_rule(
      'random_fold_in', keys_aval, msgs_aval)
  return core.ShapedArray(shape, keys_aval.dtype)

@random_fold_in_p.def_impl
def random_fold_in_impl(keys, msgs):
  base_arr = random_fold_in_impl_base(
      keys._impl, keys._base_array, msgs, keys.shape)
  return PRNGKeyArray(keys._impl, base_arr)

def random_fold_in_impl_base(impl, base_arr, msgs, keys_shape):
  fold_in = iterated_vmap_binary_bcast(
      keys_shape, np.shape(msgs), impl.fold_in)
  return fold_in(base_arr, msgs)

def random_fold_in_lowering(ctx, keys, msgs):
  keys_aval, msgs_aval = ctx.avals_in
  impl = keys_aval.dtype._impl
  fold_in = iterated_vmap_binary_bcast(
      keys_aval.shape, msgs_aval.shape, impl.fold_in)
  fold_in_lowering = mlir.lower_fun(fold_in, multiple_results=False)
  return mlir.delegate_lowering(
      ctx, fold_in_lowering, keys, msgs,
      avals_in=[core.physical_aval(keys_aval), msgs_aval],
      avals_out=map(core.physical_aval, ctx.avals_out))

mlir.register_lowering(random_fold_in_p, random_fold_in_lowering)


def random_bits(keys, bit_width, shape):
  return random_bits_p.bind(keys, bit_width=bit_width, shape=shape)

random_bits_p = core.Primitive('random_bits')
ad.defjvp_zero(random_bits_p)
batching.defvectorized(random_bits_p)

@random_bits_p.def_abstract_eval
def random_bits_abstract_eval(keys_aval, *, bit_width, shape):
  out_shape = (*keys_aval.shape, *shape)
  out_dtype = dtypes.dtype(f'uint{bit_width}')
  return core.ShapedArray(out_shape, out_dtype)

@random_bits_p.def_impl
def random_bits_impl(keys, *, bit_width, shape):
  return random_bits_impl_base(keys._impl, keys._base_array, keys.ndim,
                               bit_width=bit_width, shape=shape)

def random_bits_impl_base(impl, base_arr, keys_ndim, *, bit_width, shape):
  bits = iterated_vmap_unary(
      keys_ndim, lambda k: impl.random_bits(k, bit_width, shape))
  return bits(base_arr)

def random_bits_lowering(ctx, keys, *, bit_width, shape):
  aval, = ctx.avals_in
  impl = aval.dtype._impl
  bits = iterated_vmap_unary(
      aval.ndim, lambda k: impl.random_bits(k, bit_width, shape))
  bits_lowering = mlir.lower_fun(bits, multiple_results=False)
  ctx_new = ctx.replace(avals_in=[core.physical_aval(aval)])
  out = bits_lowering(ctx_new, keys)
  ctx.set_tokens_out(ctx_new.tokens_out)
  return out

mlir.register_lowering(random_bits_p, random_bits_lowering)


# The following wrap/unwrap primitives are at least a stopgap for
# backwards compatibility, namely when `config.jax_enable_custom_prng`
# is False. We need to convert key arrays to and from underlying
# uint32 base array, and we may need to do so under a jit. For
# example, we want to support:
#
#   keys = jax.jit(random.split)(key)
#
# where `key` and `keys` are both acceptably old-style uint32 arrays
# so long as enable_custom_prng is False. The way we handle this is
# that `random.split` adapts the input/output by converting to/from
# key arrays across its call to `random_split`. So we rely on these
# wrap/unwrap casting primitives to allow that conversion under jit.
#
# We may want to keep both around for testing and debugging escape
# hatches. We can rename them `unsafe` for emphasis, and/or issue a
# warning on entry to the traceable.
#
# TODO(frostig): Consider removal once we always enable_custom_prng.

def random_wrap(base_arr, *, impl):
  _check_prng_key_data(impl, base_arr)
  return random_wrap_p.bind(base_arr, impl=impl)

random_wrap_p = core.Primitive('random_wrap')
ad.defjvp_zero(random_wrap_p)

@random_wrap_p.def_abstract_eval
def random_wrap_abstract_eval(base_arr_aval, *, impl):
  shape = base_arr_shape_to_keys_shape(impl, base_arr_aval.shape)
  return keys_shaped_array(impl, shape)

@random_wrap_p.def_impl
def random_wrap_impl(base_arr, *, impl):
  return PRNGKeyArray(impl, base_arr)

def random_wrap_lowering(ctx, base_arr, *, impl):
  return [base_arr]

def random_wrap_batch_rule(batched_args, batch_dims, *, impl):
  x, = batched_args
  d, = batch_dims
  x = batching.bdim_at_front(x, d, 1)
  return random_wrap(x, impl=impl), 0

mlir.register_lowering(random_wrap_p, random_wrap_lowering)
batching.primitive_batchers[random_wrap_p] = random_wrap_batch_rule


def random_unwrap(keys):
  if not jnp.issubdtype(keys.dtype, dtypes.prng_key):
    raise TypeError(f'random_unwrap takes key array operand, got {keys.dtype=}')
  return random_unwrap_p.bind(keys)

random_unwrap_p = core.Primitive('random_unwrap')
ad.defjvp_zero(random_unwrap_p)
batching.defvectorized(random_unwrap_p)

@random_unwrap_p.def_abstract_eval
def random_unwrap_abstract_eval(keys_aval):
  return core.physical_aval(keys_aval)

@random_unwrap_p.def_impl
def random_unwrap_impl(keys):
  return keys._base_array

def random_unwrap_lowering(ctx, keys):
  return [keys]

mlir.register_lowering(random_unwrap_p, random_unwrap_lowering)


# -- threefry2x32 PRNG implementation


def _is_threefry_prng_key(key: typing.Array) -> bool:
  try:
    return key.shape == (2,) and key.dtype == np.uint32
  except AttributeError:
    return False


def threefry_seed(seed: typing.Array) -> typing.Array:
  """Create a single raw threefry PRNG key from an integer seed.

  Args:
    seed: a 64- or 32-bit integer used as the value of the key.

  Returns:
    The PRNG key contents, modeled as an array of shape (2,) and dtype
    uint32. The key is constructed from a 64-bit seed by effectively
    bit-casting to a pair of uint32 values (or from a 32-bit seed by
    first padding out with zeros).
  """
  return _threefry_seed(seed)

@partial(jit, inline=True)
def _threefry_seed(seed: typing.Array) -> typing.Array:
  if seed.shape:
    raise TypeError(f"PRNG key seed must be a scalar; got {seed!r}.")
  if not np.issubdtype(seed.dtype, np.integer):
    raise TypeError(f"PRNG key seed must be an integer; got {seed!r}")
  convert = lambda k: lax.expand_dims(lax.convert_element_type(k, np.uint32), [0])
  k1 = convert(
      lax.shift_right_logical(seed, lax_internal._const(seed, 32)))
  with config.numpy_dtype_promotion('standard'):
    # TODO(jakevdp): in X64 mode, this can generate 64-bit computations for 32-bit
    # inputs. We should avoid this.
    k2 = convert(jnp.bitwise_and(seed, np.uint32(0xFFFFFFFF)))
  return lax.concatenate([k1, k2], 0)


def _make_rotate_left(dtype):
  if not jnp.issubdtype(dtype, np.integer):
    raise TypeError("_rotate_left only accepts integer dtypes.")
  nbits = np.array(jnp.iinfo(dtype).bits, dtype)

  def _rotate_left(x, d):
    if lax.dtype(d) != dtype:
      d = lax.convert_element_type(d, dtype)
    if lax.dtype(x) != dtype:
      x = lax.convert_element_type(x, dtype)
    return lax.shift_left(x, d) | lax.shift_right_logical(x, nbits - d)
  return _rotate_left


### hash function and split

def _threefry2x32_abstract_eval(*args):
  if any(a.dtype != jnp.uint32 for a in args):
    raise TypeError("Arguments to threefry2x32 must have uint32 type, got {}"
                    .format(args))
  if all(isinstance(arg, core.ShapedArray) for arg in args):
    shape = lax_internal.broadcasting_shape_rule(*args)
    aval = core.ShapedArray(shape, jnp.dtype(jnp.uint32))
  else:
    raise TypeError(f"Arguments to threefry2x32 must all be arrays, got {args}")
  return (aval,) * 2


rotate_left = _make_rotate_left(np.uint32)


def apply_round(v, rot):
  v = v[:]
  v[0] = v[0] + v[1]
  v[1] = rotate_left(v[1], rot)
  v[1] = v[0] ^ v[1]
  return v


def rotate_list(xs):
  return xs[1:] + xs[:1]


def rolled_loop_step(i, state):
  x, ks, rotations = state
  for r in rotations[0]:
    x = apply_round(x, r)
  new_x = [x[0] + ks[0], x[1] + ks[1] + jnp.asarray(i + 1, dtype=np.uint32)]
  return new_x, rotate_list(ks), rotate_list(rotations)


def _threefry2x32_lowering(key1, key2, x1, x2, use_rolled_loops=True):
  """Apply the Threefry 2x32 hash.

  Args:
    keypair: a pair of 32bit unsigned integers used for the key.
    count: an array of dtype uint32 used for the counts.

  Returns:
    An array of dtype uint32 with the same shape as `count`.
  """
  x = [x1, x2]

  rotations = [np.array([13, 15, 26, 6], dtype=np.uint32),
               np.array([17, 29, 16, 24], dtype=np.uint32)]
  ks = [key1, key2, key1 ^ key2 ^ np.uint32(0x1BD11BDA)]

  x[0] = x[0] + ks[0]
  x[1] = x[1] + ks[1]

  if use_rolled_loops:
    x, _, _ = lax.fori_loop(0, 5, rolled_loop_step, (x, rotate_list(ks), rotations))

  else:
    for r in rotations[0]:
      x = apply_round(x, r)
    x[0] = x[0] + ks[1]
    x[1] = x[1] + ks[2] + np.uint32(1)

    for r in rotations[1]:
      x = apply_round(x, r)
    x[0] = x[0] + ks[2]
    x[1] = x[1] + ks[0] + np.uint32(2)

    for r in rotations[0]:
      x = apply_round(x, r)
    x[0] = x[0] + ks[0]
    x[1] = x[1] + ks[1] + np.uint32(3)

    for r in rotations[1]:
      x = apply_round(x, r)
    x[0] = x[0] + ks[1]
    x[1] = x[1] + ks[2] + np.uint32(4)

    for r in rotations[0]:
      x = apply_round(x, r)
    x[0] = x[0] + ks[2]
    x[1] = x[1] + ks[0] + np.uint32(5)

  return tuple(x)


_threefry2x32_lowering_rule = mlir.lower_fun(
    partial(_threefry2x32_lowering, use_rolled_loops=False),
    multiple_results=True)

_threefry2x32_cpu_lowering_rule = mlir.lower_fun(
    partial(_threefry2x32_lowering, use_rolled_loops=True),
    multiple_results=True)


def _threefry2x32_gpu_lowering_rule(lowering_func, ctx, k1, k2, x1, x2):
  if not config.threefry_gpu_kernel_lowering.value:  # back to default lowering
    return _threefry2x32_lowering_rule(ctx, k1, k2, x1, x2)

  aval_out, aval_out_2 = ctx.avals_out
  assert aval_out == aval_out_2
  k1_aval, k2_aval, x1_aval, x2_aval = ctx.avals_in
  rank = len(aval_out.shape)
  if 0 in aval_out.shape:
    zeros = mlir.full_like_aval(ctx, 0, aval_out)
    return [zeros, zeros]
  def _broadcast(x, aval):
    return mlir.broadcast_in_dim(ctx, x, aval_out,
                                 broadcast_dimensions=range(rank - len(aval.shape), rank))

  out_len = reduce(op.mul, aval_out.shape, 1)
  if not core.is_constant_dim(out_len):
    length = mlir.eval_dynamic_shape_as_tensor(ctx, [out_len])
    length = mlir.hlo.convert(
        ir.RankedTensorType.get((1,), ir.IntegerType.get_signless(64)),
        length)
    output_shape = mlir.eval_dynamic_shape_as_tensor(ctx, aval_out.shape)
  else:
    length = int(out_len)  # will be passed statically
    output_shape = None

  return lowering_func(
      (_broadcast(k1, k1_aval), _broadcast(k2, k2_aval)),
      (_broadcast(x1, x1_aval), _broadcast(x2, x2_aval)), length,
      output_shape,
      False,  # forward_compatibility_mode
  )


threefry2x32_p = core.Primitive("threefry2x32")
threefry2x32_p.multiple_results = True
threefry2x32_p.def_impl(partial(dispatch.apply_primitive, threefry2x32_p))
threefry2x32_p.def_abstract_eval(_threefry2x32_abstract_eval)
batching.defbroadcasting(threefry2x32_p)
mlir.register_lowering(
    threefry2x32_p, _threefry2x32_lowering_rule)
mlir.register_lowering(
    threefry2x32_p, _threefry2x32_cpu_lowering_rule, platform='cpu')
mlir.register_lowering(
    threefry2x32_p,
    partial(_threefry2x32_gpu_lowering_rule, gpu_prng.cuda_threefry2x32),
    platform='cuda')
mlir.register_lowering(
    threefry2x32_p,
    partial(_threefry2x32_gpu_lowering_rule, gpu_prng.rocm_threefry2x32),
    platform='rocm')


def iota_2x32_shape(shape):
  """Reshaped ``uint64`` iota, as two parallel ``uint32`` arrays.

  Setting aside representation, this function essentially computes the
  equivalent of::

    jax.lax.iota(dtype=np.uint64, size=math.prod(shape)).reshape(shape)

  However:

  * It returns two parallel ``uint32`` arrays instead of one
    ``uint64`` array. This renders it invariant under either setting of
    the system-wide ``jax_enable_x64`` configuration flag.

  * It lowers in a way such that the compiler's automatic SPMD
    partitioner recognizes its partitionability.

  For example::

    >>> import numpy as np
    >>> from jax import lax
    >>> from jax._src import prng

    >>> prng.iota_2x32_shape((3, 4))
    [Array([[0, 0, 0, 0],
            [0, 0, 0, 0],
            [0, 0, 0, 0]], dtype=uint32),
     Array([[ 0,  1,  2,  3],
            [ 4,  5,  6,  7],
            [ 8,  9, 10, 11]], dtype=uint32)]

    >>> def reshaped_iota(shape):
    ...   return lax.iota(size=math.prod(shape), dtype=np.uint32).reshape(shape)
    ...
    >>> reshaped_iota((3, 4))
    Array([[ 0,  1,  2,  3],
           [ 4,  5,  6,  7],
           [ 8,  9, 10, 11]], dtype=uint32)

  Args:
    shape: the output shape

  Returns:
    A pair of ``uint32`` arrays ``(counts_hi, counts_lo)``, both of
    shape ``shape``, representing the higher-order and lower-order 32
    bits of the 64 bit unsigned iota.
  """
  if len(shape) == 0:
    return (jnp.zeros((), np.dtype('uint32')),) * 2
  return iota_2x32_shape_p.bind(shape=shape)

iota_2x32_shape_p = core.Primitive('iota_2x32_shape')
iota_2x32_shape_p.multiple_results = True
iota_2x32_shape_p.def_impl(partial(dispatch.apply_primitive, iota_2x32_shape_p))

@iota_2x32_shape_p.def_abstract_eval
def iota_2x32_shape_abstract_eval(*, shape):
  return (core.ShapedArray(shape, np.dtype('uint32')),) * 2

def bcast_iotas_to_reshaped_iota(
    add: Callable[[ir.Value, ir.Value], ir.Value],
    mul: Callable[[core.DimSize, ir.Value], ir.Value],
    shape: core.Shape,
    iotas: Sequence[ir.Value]) -> ir.Value:
  strides: core.Shape = (*(np.cumprod(shape[1:][::-1])[::-1]), 1)
  return reduce(add, [mul(s, i) for i, s in zip(iotas, strides)])

def iota_2x32_shape_lowering(ctx, *, shape):
  aval_out, _ = ctx.avals_out
  aval_u64 = core.ShapedArray(shape, np.dtype('uint64'))

  def _add(x: ir.Value, y: ir.Value) -> ir.Value:
    return mlir.hlo.add(x, y)

  def _mul(x: core.DimSize, y: ir.Value) -> ir.Value:
    if core.is_constant_dim(x):
      x_const = mlir.ir_constant(np.array(x, np.dtype('uint64')))
    else:
      x_shape, = mlir.eval_dynamic_shape(ctx, (x,))
      x_const = hlo.convert(
          ir.RankedTensorType.get(
              [],
              mlir.dtype_to_ir_type(np.dtype('uint64'))), x_shape)
    x_bcast = mlir.broadcast_in_dim(ctx, x_const, aval_u64,
                                    broadcast_dimensions=[])
    return mlir.hlo.multiply(x_bcast, y)

  assert len(shape) > 0

  iotas = [mlir.iota(ctx, aval_u64, dimension=dimension)
           for dimension in range(len(shape))]
  counts = bcast_iotas_to_reshaped_iota(_add, _mul, shape, iotas)
  shift = mlir.ir_constant(np.array(32, np.dtype('uint64')))
  shift = mlir.broadcast_in_dim(ctx, shift, aval_u64,
                                broadcast_dimensions=[])
  counts_shifted = mlir.hlo.shift_right_logical(counts, shift)
  counts_lo = mlir.hlo.convert(mlir.aval_to_ir_type(aval_out), counts)
  counts_hi = mlir.hlo.convert(mlir.aval_to_ir_type(aval_out), counts_shifted)
  return counts_hi, counts_lo
mlir.register_lowering(iota_2x32_shape_p, iota_2x32_shape_lowering)


@partial(jit, inline=True)
def threefry_2x32(keypair, count):
  """Apply the Threefry 2x32 hash.

  Args:
    keypair: a pair of 32bit unsigned integers used for the key.
    count: an array of dtype uint32 used for the counts.

  Returns:
    An array of dtype uint32 with the same shape as `count`.
  """
  key1, key2 = keypair
  if not lax.dtype(key1) == lax.dtype(key2) == lax.dtype(count) == np.uint32:
    msg = "threefry_2x32 requires uint32 arguments, got {}"
    raise TypeError(msg.format([lax.dtype(x) for x in [key1, key2, count]]))

  odd_size = count.size % 2
  if not isinstance(odd_size, int):
    msg = ("jax.random functions have limited support for shape polymorphism "
           "when using threefry. "
           f"In particular, the array size ({count.size}) must be even.")
    raise core.InconclusiveDimensionOperation(msg)

  if odd_size:
    x = list(jnp.split(jnp.concatenate([count.ravel(), np.uint32([0])]), 2))
  else:
    x = list(jnp.split(count.ravel(), 2))

  x = threefry2x32_p.bind(key1, key2, x[0], x[1])
  out = jnp.concatenate(x)
  assert out.dtype == np.uint32
  return lax.reshape(out[:-1] if odd_size else out, count.shape)


def threefry_split(key: typing.Array, shape: Shape) -> typing.Array:
  shape = tuple(unsafe_map(core.concrete_dim_or_error, shape))
  return _threefry_split(key, shape)

@partial(jit, static_argnums=(1,))
def _threefry_split(key, shape) -> typing.Array:
  if config.threefry_partitionable.value:
    return _threefry_split_foldlike(key, shape)
  else:
    return _threefry_split_original(key, shape)

@partial(jit, static_argnums=(1,), inline=True)
def _threefry_split_original(key, shape) -> typing.Array:
  num = math.prod(shape)
  counts = lax.iota(np.uint32, num * 2)
  return lax.reshape(threefry_2x32(key, counts), (*shape, 2))

@partial(jit, static_argnums=(1,), inline=True)
def _threefry_split_foldlike(key, shape) -> typing.Array:
  k1, k2 = key
  counts1, counts2 = iota_2x32_shape(shape)
  bits1, bits2 = threefry2x32_p.bind(k1, k2, counts1, counts2)
  return jnp.stack([bits1, bits2], axis=bits1.ndim)


def threefry_fold_in(key: typing.Array, data: typing.Array) -> typing.Array:
  assert not data.shape
  return _threefry_fold_in(key, jnp.uint32(data))

@jit
def _threefry_fold_in(key, data):
  return threefry_2x32(key, threefry_seed(data))


def threefry_random_bits(key: typing.Array, bit_width, shape):
  """Sample uniform random bits of given width and shape using PRNG key."""
  if not _is_threefry_prng_key(key):
    raise TypeError("threefry_random_bits got invalid prng key.")
  if bit_width not in (8, 16, 32, 64):
    raise TypeError("requires 8-, 16-, 32- or 64-bit field width.")

  if config.threefry_partitionable.value:
    return _threefry_random_bits_partitionable(key, bit_width, shape)
  else:
    return _threefry_random_bits_original(key, bit_width, shape)

def _threefry_random_bits_partitionable(key: typing.Array, bit_width, shape):
  if all(core.is_constant_dim(d) for d in shape) and math.prod(shape) > 2 ** 64:
    raise NotImplementedError('random bits array of size exceeding 2 ** 64')

  k1, k2 = key
  counts1, counts2 = iota_2x32_shape(shape)
  bits1, bits2 = threefry2x32_p.bind(k1, k2, counts1, counts2)

  dtype = UINT_DTYPES[bit_width]
  if bit_width == 64:
    bits_hi = lax.convert_element_type(bits1, dtype)
    bits_lo = lax.convert_element_type(bits2, dtype)
    return lax.shift_left(bits_hi, dtype(32)) | bits_lo
  elif bit_width == 32:
    return bits1 ^ bits2
  else:
    return lax.convert_element_type(bits1 ^ bits2, dtype)

@partial(jit, static_argnums=(1, 2), inline=True)
def _threefry_random_bits_original(key: typing.Array, bit_width, shape):
  size = math.prod(shape)
  # Compute ceil(bit_width * size / 32) in a way that is friendly to shape
  # polymorphism
  max_count, r = divmod(bit_width * size, 32)
  if r > 0:
    max_count += 1

  if core.is_constant_dim(max_count):
    nblocks, rem = divmod(max_count, jnp.iinfo(np.uint32).max)
  else:
    nblocks, rem = 0, max_count

  if not nblocks:
    bits = threefry_2x32(key, lax.iota(np.uint32, rem))
  else:
    keys = threefry_split(key, (nblocks + 1,))
    subkeys, last_key = keys[:-1], keys[-1]
    blocks = vmap(threefry_2x32, in_axes=(0, None))(subkeys, lax.iota(np.uint32, jnp.iinfo(np.uint32).max))
    last = threefry_2x32(last_key, lax.iota(np.uint32, rem))
    bits = lax.concatenate([blocks.ravel(), last], 0)

  dtype = UINT_DTYPES[bit_width]
  if bit_width == 64:
    bits = [lax.convert_element_type(x, dtype) for x in jnp.split(bits, 2)]
    bits = lax.shift_left(bits[0], dtype(32)) | bits[1]
  elif bit_width in [8, 16]:
    # this is essentially bits.view(dtype)[:size]
    bits = lax.bitwise_and(
      np.uint32(np.iinfo(dtype).max),
      lax.shift_right_logical(
        lax.broadcast(bits, (1,)),
        lax.mul(
          np.uint32(bit_width),
          lax.broadcasted_iota(np.uint32, (32 // bit_width, 1), 0)
        )
      )
    )
    bits = lax.reshape(bits, ((max_count * 32 // bit_width),), (1, 0))
    bits = lax.convert_element_type(bits, dtype)[:size]
  return lax.reshape(bits, shape)


threefry_prng_impl = PRNGImpl(
    key_shape=(2,),
    seed=threefry_seed,
    split=threefry_split,
    random_bits=threefry_random_bits,
    fold_in=threefry_fold_in,
    name='threefry2x32',
    tag='fry')

register_prng(threefry_prng_impl)


# -- RngBitGenerator PRNG implementation

# This code is experimental!
# https://www.tensorflow.org/xla/operation_semantics#rngbitgenerator
# Notice that the RngBitGenerator operations are not guaranteed to be
# stable/deterministic across backends or compiler versions. Correspondingly, we
# reserve the right to change any of these implementations at any time!

def _rbg_seed(seed: typing.Array) -> typing.Array:
  assert not seed.shape
  halfkey = threefry_seed(seed)
  return jnp.concatenate([halfkey, halfkey])

def _rbg_split(key: typing.Array, shape: Shape) -> typing.Array:
  if config.threefry_partitionable.value:
    _threefry_split = _threefry_split_foldlike
  else:
    _threefry_split = _threefry_split_original
  halfkeys = key.reshape(2, 2)
  return vmap(
      _threefry_split, (0, None), len(shape))(halfkeys, shape).reshape(
          *shape, 4)

def _rbg_fold_in(key: typing.Array, data: typing.Array) -> typing.Array:
  assert not data.shape
  return vmap(_threefry_fold_in, (0, None), 0)(key.reshape(2, 2), data).reshape(4)

def _rbg_random_bits(key: typing.Array, bit_width: int, shape: Sequence[int]
                     ) -> typing.Array:
  if not key.shape == (4,) and key.dtype == jnp.dtype('uint32'):
    raise TypeError("_rbg_random_bits got invalid prng key.")
  if bit_width not in (8, 16, 32, 64):
    raise TypeError("requires 8-, 16-, 32- or 64-bit field width.")
  _, bits = lax.rng_bit_generator(key, shape, dtype=UINT_DTYPES[bit_width])
  return bits

rbg_prng_impl = PRNGImpl(
    key_shape=(4,),
    seed=_rbg_seed,
    split=_rbg_split,
    random_bits=_rbg_random_bits,
    fold_in=_rbg_fold_in,
    name='rbg',
    tag='rbg')

register_prng(rbg_prng_impl)


def _unsafe_rbg_split(key: typing.Array, shape: Shape) -> typing.Array:
  # treat 10 iterations of random bits as a 'hash function'
  num = math.prod(shape)
  _, keys = lax.rng_bit_generator(key, (10 * num, 4), dtype='uint32')
  return lax.slice_in_dim(
      keys, start_index=None, limit_index=None, stride=10).reshape(*shape, 4)

def _unsafe_rbg_fold_in(key: typing.Array, data: typing.Array) -> typing.Array:
  assert not data.shape
  _, random_bits = lax.rng_bit_generator(_rbg_seed(data), (10, 4), dtype='uint32')
  return key ^ random_bits[-1]

unsafe_rbg_prng_impl = PRNGImpl(
    key_shape=(4,),
    seed=_rbg_seed,
    split=_unsafe_rbg_split,
    random_bits=_rbg_random_bits,
    fold_in=_unsafe_rbg_fold_in,
    name='unsafe_rbg',
    tag='urbg')

register_prng(unsafe_rbg_prng_impl)