# Copyright 2022 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.
"""Module for the loop primitives."""
from __future__ import annotations
from collections.abc import Sequence
from functools import partial
import inspect
import itertools
import operator
from typing import Any, Callable, TypeVar
import jax
import weakref
from jax._src import config
from jax._src import core
from jax._src import linear_util as lu
from jax._src.core import ConcreteArray, ShapedArray, raise_to_shaped
from jax.tree_util import (tree_flatten, tree_unflatten, treedef_is_leaf,
tree_map, tree_flatten_with_path, keystr)
from jax._src.api_util import shaped_abstractify
from jax._src.tree_util import equality_errors
from jax._src import ad_checkpoint
from jax._src import ad_util
from jax._src import api
from jax._src import dispatch
from jax._src import dtypes
from jax._src import effects
from jax._src import source_info_util
from jax._src import util
from jax._src.interpreters import ad
from jax._src.interpreters import batching
from jax._src.interpreters import mlir
from jax._src.interpreters import partial_eval as pe
from jax._src.interpreters import xla
from jax._src.lax import lax
from jax._src.lax import slicing
from jax._src.lax import windowed_reductions
from jax._src.lib.mlir import ir
from jax._src.lib.mlir.dialects import hlo
from jax._src import state
from jax._src.state import discharge as state_discharge
from jax._src.numpy.ufuncs import logaddexp
from jax._src.traceback_util import api_boundary
from jax._src.typing import Array
from jax._src.util import (partition_list, safe_map, safe_zip, split_list,
unzip2, weakref_lru_cache, merge_lists)
import numpy as np
from jax._src.lax.control_flow.common import (
_abstractify, _avals_short, _check_tree_and_avals, _initial_style_jaxpr,
_initial_style_jaxpr_attrs, _make_closed_jaxpr_attrs, _prune_zeros,
_typecheck_param)
_map = safe_map
zip = safe_zip
T = TypeVar('T')
BooleanNumeric = Any # A bool, or a Boolean array.
### Helper functions
def _promote_weak_typed_inputs(in_vals, in_avals, out_avals):
"""Promote weakly-typed in_vals to be compatible with out_avals.
Args:
in_vals : flattened list of input values.
in_avals : corresponding list of avals.
out_avals : list of target output avals.
Returns:
in_vals_new : flattened list of modified in_vals with no weak types.
changed : bool; true if in_vals required modification.
"""
if len(in_vals) != len(in_avals) or len(in_avals) != len(out_avals):
# Calling function is responsible for catching this.
return in_vals, False
weak_mismatches = [i for i, (a1, a2) in enumerate(zip(in_avals, out_avals))
if getattr(a1, 'weak_type', False) and not core.typematch(a1, a2)]
if not weak_mismatches:
return in_vals, False
for i in weak_mismatches:
new_dtype = dtypes.result_type(in_vals[i], out_avals[i])
in_vals[i] = lax.convert_element_type(in_vals[i], new_dtype)
return in_vals, True
### scan
Carry = TypeVar('Carry')
X = TypeVar('X')
Y = TypeVar('Y')
[docs]
@api_boundary
def scan(f: Callable[[Carry, X], tuple[Carry, Y]],
init: Carry,
xs: X,
length: int | None = None,
reverse: bool = False,
unroll: int | bool = 1,
_split_transpose: bool = False) -> tuple[Carry, Y]:
"""Scan a function over leading array axes while carrying along state.
The `Haskell-like type signature`_ in brief is
.. code-block:: haskell
scan :: (c -> a -> (c, b)) -> c -> [a] -> (c, [b])
where for any array type specifier ``t``, ``[t]`` represents the type with an additional
leading axis, and if ``t`` is a pytree (container) type with array leaves then ``[t]``
represents the type with the same pytree structure and corresponding leaves
each with an additional leading axis.
When the type of ``xs`` (denoted `a` above) is an array type or None, and the type
of ``ys`` (denoted `b` above) is an array type, the semantics of :func:`~scan` are
given roughly by this Python implementation::
def scan(f, init, xs, length=None):
if xs is None:
xs = [None] * length
carry = init
ys = []
for x in xs:
carry, y = f(carry, x)
ys.append(y)
return carry, np.stack(ys)
Unlike that Python version, both ``xs`` and ``ys`` may be arbitrary pytree
values, and so multiple arrays can be scanned over at once and produce multiple
output arrays. ``None`` is actually a special case of this, as it represents an
empty pytree.
Also unlike that Python version, :func:`~scan` is a JAX primitive and is
lowered to a single WhileOp. That makes it useful for reducing
compilation times for JIT-compiled functions, since native Python
loop constructs in an :func:`~jax.jit` function are unrolled, leading to large
XLA computations.
Finally, the loop-carried value ``carry`` must hold a fixed shape and dtype
across all iterations (and not just be consistent up to NumPy rank/shape
broadcasting and dtype promotion rules, for example). In other words, the type
``c`` in the type signature above represents an array with a fixed shape and
dtype (or a nested tuple/list/dict container data structure with a fixed
structure and arrays with fixed shape and dtype at the leaves).
.. note::
:py:func:`scan` compiles ``f``, so while it can be combined with
:py:func:`jit`, it's usually unnecessary.
Args:
f: a Python function to be scanned of type ``c -> a -> (c, b)``, meaning
that ``f`` accepts two arguments where the first is a value of the loop
carry and the second is a slice of ``xs`` along its leading axis, and that
``f`` returns a pair where the first element represents a new value for
the loop carry and the second represents a slice of the output.
init: an initial loop carry value of type ``c``, which can be a scalar,
array, or any pytree (nested Python tuple/list/dict) thereof, representing
the initial loop carry value. This value must have the same structure as
the first element of the pair returned by ``f``.
xs: the value of type ``[a]`` over which to scan along the leading axis,
where ``[a]`` can be an array or any pytree (nested Python
tuple/list/dict) thereof with consistent leading axis sizes.
length: optional integer specifying the number of loop iterations, which
must agree with the sizes of leading axes of the arrays in ``xs`` (but can
be used to perform scans where no input ``xs`` are needed).
reverse: optional boolean specifying whether to run the scan iteration
forward (the default) or in reverse, equivalent to reversing the leading
axes of the arrays in both ``xs`` and in ``ys``.
unroll: optional positive int or bool specifying, in the underlying
operation of the scan primitive, how many scan iterations to unroll within
a single iteration of a loop. If an integer is provided, it determines how
many unrolled loop iterations to run within a single rolled iteration of
the loop. If a boolean is provided, it will determine if the loop is
competely unrolled (i.e. `unroll=True`) or left completely unrolled (i.e.
`unroll=False`).
_split_transpose: experimental optional bool specifying whether to further
split the transpose into a scan (computing activation gradients), and a
map (computing gradients corresponding to the array arguments). Enabling
this may increase memory requirements, and so is an experimental feature
that may evolve or even be rolled back.
Returns:
A pair of type ``(c, [b])`` where the first element represents the final
loop carry value and the second element represents the stacked outputs of
the second output of ``f`` when scanned over the leading axis of the inputs.
.. _Haskell-like type signature: https://wiki.haskell.org/Type_signature
"""
if not callable(f):
raise TypeError("lax.scan: f argument should be a callable.")
xs_flat, xs_tree = tree_flatten(xs)
try:
lengths = [x.shape[0] for x in xs_flat]
except AttributeError as err:
msg = "scan got value with no leading axis to scan over: {}."
raise ValueError(
msg.format(', '.join(str(x) for x in xs_flat
if not hasattr(x, 'shape')))) from err
if length is not None:
length = int(length)
if not all(length == l for l in lengths):
msg = ("scan got `length` argument of {} which disagrees with "
"leading axis sizes {}.")
raise ValueError(msg.format(length, [x.shape[0] for x in xs_flat]))
else:
unique_lengths = set(lengths)
if len(unique_lengths) > 1:
msg = "scan got values with different leading axis sizes: {}."
raise ValueError(msg.format(', '.join(str(x.shape[0]) for x in xs_flat)))
elif len(unique_lengths) == 0:
msg = "scan got no values to scan over and `length` not provided."
raise ValueError(msg)
else:
length, = unique_lengths
if config.disable_jit.value:
if length == 0:
raise ValueError("zero-length scan is not supported in disable_jit() mode because the output type is unknown.")
carry = init
ys = []
maybe_reversed = reversed if reverse else lambda x: x
for i in maybe_reversed(range(length)):
xs_slice = [_index_array(i, core.get_aval(x), x) for x in xs_flat]
carry, y = f(carry, tree_unflatten(xs_tree, xs_slice))
ys.append(y)
stack = lambda *ys: jax.numpy.stack(ys)
stacked_y = tree_map(stack, *maybe_reversed(ys))
return carry, stacked_y
xs_avals = [core.raise_to_shaped(core.get_aval(x)) for x in xs_flat]
x_avals = [core.mapped_aval(length, 0, aval) for aval in xs_avals]
def _create_jaxpr(init):
init_flat, init_tree = tree_flatten(init)
in_flat, in_tree = tree_flatten((init, xs))
carry_avals = tuple(_map(_abstractify, init_flat))
jaxpr, consts, out_tree, attrs_tracked = _initial_style_jaxpr_attrs(
f, in_tree, (*carry_avals, *x_avals), "scan")
out_tree_children = out_tree.children()
if len(out_tree_children) != 2:
msg = "scan body output must be a pair, got {}."
raise TypeError(msg.format(tree_unflatten(out_tree, jaxpr.out_avals)))
carry_avals_out = jaxpr.out_avals[:out_tree_children[0].num_leaves]
return (init_flat, carry_avals, carry_avals_out, init_tree, in_flat, jaxpr,
consts, out_tree, out_tree_children, attrs_tracked)
# The carry input and output avals must match exactly. However, we want to account for
# the case when init contains weakly-typed values (e.g. Python scalars), with avals that
# may not match the output despite being compatible by virtue of their weak type.
# To do this, we compute the jaxpr in two passes: first with the raw inputs, and if
# necessary, a second time with modified init values.
init_flat, carry_avals, carry_avals_out, init_tree, *rest = _create_jaxpr(init)
new_init_flat, changed = _promote_weak_typed_inputs(init_flat, carry_avals, carry_avals_out)
if changed:
init = tree_unflatten(init_tree, new_init_flat)
init_flat, carry_avals, carry_avals_out, init_tree, *rest = _create_jaxpr(init)
in_flat, jaxpr, consts, out_tree, out_tree_children, attrs_tracked = rest
num_carry = len(init_flat)
_check_scan_carry_type(f, init, out_tree_children[0], carry_avals_out)
disallowed_effects = effects.control_flow_allowed_effects.filter_not_in(jaxpr.effects)
if disallowed_effects:
raise NotImplementedError(
f'Effects not supported in `scan`: {disallowed_effects}')
if isinstance(unroll, bool):
unroll = max(length, 1) if unroll else 1
if attrs_tracked:
in_state = _get_states(attrs_tracked)
in_carry, in_ext = split_list(in_flat, [num_carry])
in_flat = [*in_state, *in_carry, *in_ext]
num_carry += len(attrs_tracked)
out = scan_p.bind(*consts, *in_flat,
reverse=reverse, length=length, jaxpr=jaxpr,
num_consts=len(consts), num_carry=num_carry,
linear=(False,) * (len(consts) + len(in_flat)),
unroll=unroll,
_split_transpose=_split_transpose)
if attrs_tracked:
out_state, out = split_list(out, [len(attrs_tracked)])
_set_states(attrs_tracked, out_state)
return tree_unflatten(out_tree, out)
def _set_states(attrs_tracked, vals):
from jax.experimental.attrs import jax_setattr # type: ignore
for ((obj, attr), val) in zip(attrs_tracked, vals):
jax_setattr(obj, attr, val)
def _get_states(attrs_tracked):
from jax.experimental.attrs import jax_getattr # type: ignore
return [jax_getattr(obj, attr) for (obj, attr) in attrs_tracked]
def _check_scan_carry_type(body_fun, in_carry, out_carry_tree, out_avals):
try:
sig = inspect.signature(body_fun)
except (ValueError, TypeError):
sig = None
carry_name = sig and list(sig.parameters)[0]
if carry_name:
component = lambda p: (f'the input carry component {carry_name}{keystr(p)}'
if p else f'the input carry {carry_name}')
else:
component = lambda p: (f'the input carry at path {keystr(p)}'
if p else 'the input carry')
leaves_and_paths, in_carry_tree = tree_flatten_with_path(in_carry)
paths, in_carry_flat = unzip2(leaves_and_paths)
in_avals = _map(_abstractify, in_carry_flat)
if in_carry_tree != out_carry_tree:
try:
out_carry = tree_unflatten(out_carry_tree, out_avals)
except:
out_carry = None
if out_carry is None:
differences = [f'the input tree structure is:\n{in_carry_tree}\n',
f'the output tree structure is:\n{out_carry_tree}\n']
else:
differences = '\n'.join(
f' * {component(path)} is a {thing1} but the corresponding component '
f'of the carry output is a {thing2}, so {explanation}\n'
for path, thing1, thing2, explanation
in equality_errors(in_carry, out_carry))
raise TypeError(
"Scanned function carry input and carry output must have the same "
"pytree structure, but they differ:\n"
f"{differences}\n"
"Revise the scanned function so that its output is a pair where the "
"first element has the same pytree structure as the first argument."
)
if not all(_map(core.typematch, in_avals, out_avals)):
differences = '\n'.join(
f' * {component(path)} has type {in_aval.str_short()}'
' but the corresponding output carry component has type '
f'{out_aval.str_short()}{_aval_mismatch_extra(in_aval, out_aval)}\n'
for path, in_aval, out_aval in zip(paths, in_avals, out_avals)
if not core.typematch(in_aval, out_aval))
raise TypeError(
"Scanned function carry input and carry output must have equal types "
"(e.g. shapes and dtypes of arrays), "
"but they differ:\n"
f"{differences}\n"
"Revise the scanned function so that all output types (e.g. shapes "
"and dtypes) match the corresponding input types."
)
def _aval_mismatch_extra(a1: core.AbstractValue, a2: core.AbstractValue) -> str:
assert not core.typematch(a1, a2)
if isinstance(a1, core.ShapedArray) and isinstance(a2, core.ShapedArray):
dtype_mismatch = a1.dtype != a2.dtype
shape_mismatch = a1.shape != a2.shape
return (', so ' * (dtype_mismatch or shape_mismatch) +
'the dtypes do not match' * dtype_mismatch +
' and also ' * (dtype_mismatch and shape_mismatch) +
'the shapes do not match' * shape_mismatch)
return ''
def _scan_impl_unrolled(*args, reverse, length, num_consts, num_carry, linear,
f_impl, x_avals, y_avals):
consts, init, xs = split_list(args, [num_consts, num_carry])
carry = init
ys = []
for i in range(length):
i_ = length - i - 1 if reverse else i
x = _map(partial(_index_array, i_), x_avals, xs)
out = f_impl(*consts, *carry, *x)
carry, y = split_list(out, [num_carry])
ys.append(y)
ys = list(reversed(ys)) if reverse else ys
ys = list(zip(*ys))
ys = _map(_stack, y_avals, ys)
return (*carry, *ys)
def _scan_impl_loop(*args, reverse, length, num_consts, num_carry, linear,
f_impl, x_avals, y_avals):
consts, init, xs = split_list(args, [num_consts, num_carry])
def cond_fun(vals):
i, *_ = vals
return i < length
def body_fun(vals):
[i], carry, ys = split_list(vals, [1, num_carry])
i_ = length - i - 1 if reverse else i
# TODO(jakevdp)[key-reuse]: this key reuse logic is not quite right,
# because the scan body may consume any keys within it.
xs_unconsumed = _map(jax.random.clone, xs)
x = _map(partial(_dynamic_index_array, i_), x_avals, xs_unconsumed)
out_flat = f_impl(*consts, *carry, *x)
carry_out, y_updates = split_list(out_flat, [num_carry])
ys_out = _map(partial(_update_array, i_), y_avals, ys, y_updates)
return [i + 1] + carry_out + ys_out
# TODO(jakevdp)[key-reuse]: mark xs consumed here if f_impl consumes them.
ys_init = _map(partial(_empty_array, length), y_avals)
if length == 0:
return init + ys_init
else:
init_val = [lax._const(length, 0)] + init + ys_init
_, *outs = while_loop(cond_fun, body_fun, init_val)
return outs
def _scan_impl_block_unrolled(*args, reverse, length, num_consts, num_carry,
linear, block_length, f_impl, x_avals, y_avals):
consts, init, xs = split_list(args, [num_consts, num_carry])
num_blocks, rem = divmod(length, block_length)
assert rem == 0
partition = partial(_partition_leading, num_blocks, block_length)
xs_block = _map(partition, x_avals, xs)
prepend_aval = partial(_prepend_dim_to_aval, block_length)
x_block_avals = _map(prepend_aval, x_avals)
y_block_avals = _map(prepend_aval, y_avals)
f_impl_block = partial(
_scan_impl_unrolled, reverse=reverse, length=block_length,
num_consts=num_consts, num_carry=num_carry, linear=linear,
f_impl=f_impl, x_avals=x_avals, y_avals=y_avals)
outs = _scan_impl_loop(
*consts, *init, *xs_block, reverse=reverse, length=num_blocks,
num_consts=num_consts, num_carry=num_carry, linear=linear,
f_impl=f_impl_block, x_avals=x_block_avals, y_avals=y_block_avals)
carry, ys_blocks = split_list(outs, [num_carry])
combine = partial(_combine_leading, num_blocks, block_length)
ys = _map(combine, y_avals, ys_blocks)
return (*carry, *ys)
def _scan_impl(*args, reverse, length, num_consts, num_carry, jaxpr, linear,
unroll, _split_transpose):
del _split_transpose
_, _, x_avals = split_list(jaxpr.in_avals, [num_consts, num_carry])
_, y_avals = split_list(jaxpr.out_avals, [num_carry])
f_impl = core.jaxpr_as_fun(jaxpr)
if unroll == 1:
return _scan_impl_loop(
*args, reverse=reverse, length=length, num_consts=num_consts,
num_carry=num_carry, linear=linear, f_impl=f_impl, x_avals=x_avals,
y_avals=y_avals)
consts, init, xs = split_list(args, [num_consts, num_carry])
num_blocks, rem = divmod(length, unroll)
length_div = num_blocks * unroll
if rem > 0:
if reverse:
split = partial(_split_leading_dim, rem)
xs_rem, xs = unzip2(_map(split, x_avals, xs))
else:
split = partial(_split_leading_dim, length_div)
xs, xs_rem = unzip2(_map(split, x_avals, xs))
outs = _scan_impl_block_unrolled(
*consts, *init, *xs, reverse=reverse, length=length_div,
num_consts=num_consts, num_carry=num_carry, linear=linear,
block_length=unroll, f_impl=f_impl, x_avals=x_avals, y_avals=y_avals)
carry, ys = split_list(outs, [num_carry])
if rem > 0:
outs = _scan_impl_unrolled(
*consts, *carry, *xs_rem, reverse=reverse, length=rem,
num_consts=num_consts, num_carry=num_carry, linear=linear,
f_impl=f_impl, x_avals=x_avals, y_avals=y_avals)
carry, ys_rem = split_list(outs, [num_carry])
if reverse:
ys = _map(_concatenate, y_avals, ys_rem, ys)
else:
ys = _map(_concatenate, y_avals, ys, ys_rem)
return (*carry, *ys)
def _stack(aval, vals):
vals = [lax.expand_dims(x, (0,)) for x in vals]
return lax.concatenate(vals, 0)
def _concatenate(aval, x1, x2):
return lax.concatenate([x1, x2], 0)
def _split_leading_dim(i, aval, x):
assert x.ndim >= 1
return (slicing.slice_in_dim(x, 0, i),
slicing.slice_in_dim(x, i, x.shape[0]))
def _dynamic_index_array(i, aval, x):
return slicing.dynamic_index_in_dim(x, i, keepdims=False)
def _index_array(i, aval, x):
return slicing.index_in_dim(x, i, keepdims=False)
def _empty_array(sz, aval):
return lax.broadcast(lax.empty(aval.dtype), (sz, *aval.shape))
def _update_array(i, aval, xs, x):
return slicing.dynamic_update_index_in_dim(xs, x, i, 0)
def _partition_leading(sz0, sz1, aval, x):
assert x.ndim >= 1
assert x.shape[0] == sz0 * sz1
return lax.reshape(x, (sz0, sz1, *x.shape[1:]))
def _combine_leading(sz0, sz1, aval, x):
assert x.ndim >= 2
assert x.shape[0] == sz0
assert x.shape[1] == sz1
return lax.collapse(x, 0, 2)
def _prepend_dim_to_aval(sz, aval):
return core.unmapped_aval(sz, core.no_axis_name, 0, aval)
def _scan_abstract_eval(*args, reverse, length, num_consts, num_carry, jaxpr,
linear, unroll, _split_transpose):
carry_avals, y_avals = split_list(jaxpr.out_avals, [num_carry])
ys_avals = _map(partial(_prepend_dim_to_aval, length), y_avals)
return carry_avals + ys_avals, jaxpr.effects
def _scan_jvp(primals, tangents, reverse, length, jaxpr, num_consts, num_carry,
linear, unroll, _split_transpose):
num_xs = len(jaxpr.in_avals) - num_carry - num_consts
num_ys = len(jaxpr.out_avals) - num_carry
nonzeros = [type(t) is not ad_util.Zero for t in tangents]
const_nz, init_nz, xs_nz = split_list(nonzeros, [num_consts, num_carry])
# Fixpoint computation of which carry are not ad.zero: either
# non-zero from init, or the carry out is non-zero. Each iteration promotes
# at least one carry to non-zero. We need at most len(carry) iterations,
# but we need one last iteration to prepare the jaxpr based on the final
# carry_nz.
carry_nz = init_nz
for _ in range(1 + len(carry_nz)):
nonzeros = const_nz + carry_nz + xs_nz
jaxpr_jvp, nonzeros_out = ad.jvp_jaxpr(
jaxpr, nonzeros, instantiate=carry_nz + [False] * num_ys)
carry_nz_out, _ = nonzeros_out[:num_carry], nonzeros_out[num_carry:]
if carry_nz_out == carry_nz:
break
else:
carry_nz = _map(operator.or_, carry_nz, carry_nz_out)
else:
assert False, "Fixpoint not reached"
tangents = [ad.instantiate_zeros(t) if nz else t
for t, nz in zip(tangents, nonzeros)]
consts, init, xs = split_list(primals, [num_consts, num_carry])
all_tangents = split_list(tangents, [num_consts, num_carry])
consts_dot, init_dot, xs_dot = _map(_prune_zeros, all_tangents)
jaxpr_jvp_rearranged = ad.rearrange_binders(
jaxpr_jvp,
[num_consts, num_carry, num_xs], [len(consts_dot), len(init_dot), len(xs_dot)],
[num_carry, num_ys], [len(init_dot), sum(nonzeros_out) - len(init_dot)])
consts_linear, init_linear, xs_linear = split_list(linear, [num_consts, num_carry])
jaxpr_jvp_linear = tuple(consts_linear + [True] * len(consts_dot)
+ init_linear + [True] * len(init_dot)
+ xs_linear + [True] * len(xs_dot))
out_flat = scan_p.bind(
*(consts + consts_dot + init + init_dot + xs + xs_dot),
reverse=reverse, length=length, jaxpr=jaxpr_jvp_rearranged,
num_consts=num_consts + len(consts_dot),
num_carry=num_carry + len(init_dot),
linear=jaxpr_jvp_linear, unroll=unroll,
_split_transpose=_split_transpose)
carry, carry_dot, ys, ys_dot = split_list(out_flat, [num_carry, len(init_dot), num_ys])
primals_out = carry + ys
tangents_out_iter = iter(carry_dot + ys_dot)
tangents_out = [next(tangents_out_iter) if nz else ad_util.Zero.from_value(p)
for p, nz in zip(primals_out, nonzeros_out)]
return primals_out, tangents_out
def _scan_partial_eval(trace, *tracers, reverse, length, num_consts, num_carry,
jaxpr, linear, unroll, _split_transpose):
num_ys = len(jaxpr.out_avals) - num_carry
unknowns = [not t.pval.is_known() for t in tracers]
const_uk, init_uk, xs_uk = split_list(unknowns, [num_consts, num_carry])
# Fixpoint computation of which carry elements are unknown. Each iteration
# promotes at least one carry to unknown. We need at most len(carry)
# iterations, but we need one last iteration to prepare the jaxpr based on the
# final carry_uk.
carry_uk = init_uk
for _ in range(1 + len(carry_uk)):
unknowns = const_uk + carry_uk + xs_uk
jaxpr_known, jaxpr_unknown, out_uk, res_avals = pe.partial_eval_jaxpr_nounits(
jaxpr, unknowns, instantiate=carry_uk + [False] * num_ys)
carry_uk_out, ys_uk = split_list(out_uk, [num_carry])
if carry_uk_out == carry_uk:
break
else:
carry_uk = _map(operator.or_, carry_uk, carry_uk_out)
else:
assert False, "Fixpoint not reached"
num_res = len(res_avals)
del res_avals, carry_uk_out
# Instantiate those inputs which must be treated as unknown from the fixpoint.
tracers = [trace.instantiate_const(t) if uk else t
for t, uk in zip(tracers, unknowns)]
# The residual inputs and outputs of the jaxprs produced haven't yet been
# adapted to the scan calling convention; in particular, jaxpr_known has its
# residual outputs all at the end, meaning they're extensive outputs (which is
# fully general but may be wasteful for residuals which are loop-invariant)
# while jaxpr_unknown has its corresponding residual inputs at the front (just
# as a convention with partial_eval_jaxpr_nounits), making them constant
# inputs. To make them consistent, we move the residual inputs on
# jaxpr_unknown to the end, even though we may move some back in the sequel.
jaxpr_unknown = pe.move_binders_to_back(
jaxpr_unknown, [True] * num_res + [False] * sum(unknowns))
# At this point, all residuals are treated as extensive outputs of jaxpr_known
# (and extensive inputs to jaxpr_unknown). But residuals that are loop-
# invariant can be hoisted out of the scan, rather than letting them get
# broadcast (as in e.g. scanning multiplication by a constant matrix; we don't
# want to broadcast the matrix!). So, outside the loop we perform a partial
# evaluation with known 'const' inputs (but all other inputs unknown).
const_pvals = [pe.PartialVal.known(t.pval.get_known())
for t in tracers[:num_consts] if t.pval.is_known()]
other_pvals = [pe.PartialVal.unknown(aval)
for aval in jaxpr_known.in_avals[len(const_pvals):]]
with source_info_util.reset_name_stack():
jaxpr_known_, invar_pvals_out, jaxpr_known_consts = pe.trace_to_jaxpr_nounits(
lu.wrap_init(core.jaxpr_as_fun(jaxpr_known)), const_pvals + other_pvals,
instantiate=[True] * (len(out_uk) - sum(out_uk)) + [False] * num_res)
jaxpr_known = pe.ClosedJaxpr(pe.convert_constvars_jaxpr(jaxpr_known_), ())
# The above trace_to_jaxpr_nounits call computed loop-invariant residuals
# (known values in invar_pvals_out) and also computed loop-invariant values
# needed by the new jaxpr_known (in jaxpr_known_consts, which replace the
# previous consts). We need to collect the computed inteisive residuals, and
# move corresponding intensive residual binders in jaxpr_unknown to the front.
res_pvals = invar_pvals_out[len(invar_pvals_out) - num_res:]
intensive_res = [pval.get_known() for pval in res_pvals if pval.is_known()]
jaxpr_unknown = pe.move_binders_to_front(
jaxpr_unknown,
[False] * sum(unknowns) + [pval.is_known() for pval in res_pvals])
del const_pvals, other_pvals, invar_pvals_out, jaxpr_known_, res_pvals
# We use `jaxpr_known_consts` when we call scan_p.bind with jaxpr_known, and
# we use `intensive_res` when we build the jaxpr eqn with jaxpr_unknown.
# As another optimization, for any extensive inputs that are just forwarded to
# extensive outputs, to avoid a copy (which would be looping over
# dynamic-update-slice) we'd rather forward the input tracer/value. That means
# pruning some outputs from jaxpr_known here, and updating `out_flat` below.
fwds_known = pe._jaxpr_forwarding(jaxpr_known.jaxpr)
# Prune fwds_known to include only extensive input to extensive output.
fwds_known = [in_idx if out_idx >= num_carry - sum(carry_uk) and
in_idx is not None and
in_idx >= len(jaxpr_known_consts) + num_carry - sum(carry_uk)
else None for out_idx, in_idx in enumerate(fwds_known)]
# Drop any extensive output we can instead get by forwarding an input.
# TODO(mattjj): use pe.dce_jaxpr here, though need a fixpoint
jaxpr_known_, () = jaxpr_known.jaxpr, jaxpr_known.consts
jaxpr_known_ = jaxpr_known_.replace(
outvars=[x for x, i in zip(jaxpr_known_.outvars, fwds_known) if i is None])
jaxpr_known = core.ClosedJaxpr(jaxpr_known_, ())
del jaxpr_known_
# We use `fwds_known` below when forming the output of scanning jaxpr_known.
# Run the known part of the scan (if it has any outputs or effects).
known_inputs = (list(jaxpr_known_consts) +
[t.pval.get_known() for t in tracers[num_consts:]
if t.pval.is_known()])
if not jaxpr_known.out_avals and not jaxpr_known.effects:
out_known = []
else:
linear_known = [False] * len(known_inputs) # conservative!
out_known = scan_p.bind(
*known_inputs, reverse=reverse, length=length, jaxpr=jaxpr_known,
num_consts=len(jaxpr_known_consts), num_carry=num_carry - sum(carry_uk),
linear=tuple(linear_known), unroll=unroll,
_split_transpose=_split_transpose)
del linear_known
# Complete the known output by filling in forwarded values using fwds_known.
out_known_iter = iter(out_known)
out_known = [next(out_known_iter) if f is None
else _maybe_put(known_inputs[f]) for f in fwds_known]
assert next(out_known_iter, None) is None
del known_inputs, out_known_iter
# Split known outputs from residuals.
out_known, extensive_res = split_list(out_known, [len(out_uk) - sum(out_uk)])
assert len(intensive_res) + len(extensive_res) == num_res
# Create input tracers for jaxpr_unknown bind.
unknown_inputs = [t for t in tracers if not t.pval.is_known()]
intensive_res = _map(trace.new_instantiated_const, intensive_res)
extensive_res = _map(trace.new_instantiated_const, extensive_res)
# Create output tracers for jaxpr_unknown bind, adapting extensive shapes.
carry_avals, y_avals = split_list(jaxpr_unknown.out_avals, [sum(carry_uk)])
ys_avals = [core.unmapped_aval(length, core.no_axis_name, 0, y_aval)
for y_aval in y_avals]
out_tracers = [pe.JaxprTracer(trace, pe.PartialVal.unknown(a), None)
for a in itertools.chain(carry_avals, ys_avals)]
del carry_avals, y_avals
# Create equation.
linear_unknown = tuple([False] * len(intensive_res) +
[l for l, uk in zip(linear, unknowns) if uk] +
[False] * len(extensive_res))
name_stack = source_info_util.current_name_stack()[len(trace.name_stack):]
source = source_info_util.current().replace(name_stack=name_stack)
assert len(out_tracers) == len(jaxpr_unknown.out_avals)
eqn = pe.new_eqn_recipe([*intensive_res, *unknown_inputs, *extensive_res],
out_tracers, scan_p,
dict(reverse=reverse, length=length, unroll=unroll,
jaxpr=jaxpr_unknown, linear=linear_unknown,
num_consts=len(intensive_res) + sum(const_uk),
num_carry=sum(carry_uk),
_split_transpose=_split_transpose),
jaxpr_unknown.effects, source)
for t in out_tracers: t.recipe = eqn
# Merge known and unknown outputs into final result.
return util.merge_lists(out_uk, out_known, out_tracers)
def _maybe_put(x):
if isinstance(x, np.ndarray):
return dispatch._put_x(
x,
jax.sharding.SingleDeviceSharding(jax.local_devices(backend='cpu')[0]),
shaped_abstractify(x),
False,
)
else:
return x
def _scan_transpose(cts, *args, reverse, length, num_consts,
num_carry, jaxpr, linear, unroll, _split_transpose):
# we've only implemented transposing scans with specific lin/nonlin patterns
consts_lin, init_lin, xs_lin = split_list(linear, [num_consts, num_carry])
num_ires = len(consts_lin) - sum(consts_lin)
num_eres = len(xs_lin) - sum(xs_lin)
if consts_lin != [False] * num_ires + [True] * (len(consts_lin) - num_ires):
raise NotImplementedError
if xs_lin != [True] * (len(xs_lin) - num_eres) + [False] * num_eres:
raise NotImplementedError
if not all(init_lin):
pass # TODO(mattjj): error check https://github.com/google/jax/issues/1963
consts, _, xs = split_list(args, [num_consts, num_carry])
ires, _ = split_list(consts, [num_ires])
_, eres = split_list(xs, [sum(xs_lin)])
assert not any(ad.is_undefined_primal(r) for r in ires)
assert not any(ad.is_undefined_primal(r) for r in eres)
carry_avals, y_avals = split_list(jaxpr.out_avals, [num_carry])
ct_carry, ct_ys = split_list(cts, [num_carry])
ct_carry = _map(ad.instantiate_zeros, ct_carry)
ct_ys_is_zeros = tuple(type(ct_y) is ad.Zero for ct_y in ct_ys)
ct_ys = [x for x in ct_ys if type(x) is not ad.Zero]
ct_consts = _map(ad_util.zeros_like_aval, jaxpr.in_avals[num_ires:num_consts])
# jaxpr :: [ires, T d] -> [T c] -> [T a, eres] -> ([T c], [T b])
# jaxpr_trans :: [ires] -> [CT d, CT c] -> [CT b, eres] -> ([CT d, CT c], [CT a])
jaxpr_trans, attrs_tracked = _transpose_scan_jaxpr(
jaxpr, num_ires, num_consts - num_ires, num_eres, ct_ys_is_zeros)
linear_trans = ([False] * num_ires + [False] * len(attrs_tracked) +
[True] * (len(ct_consts) + len(ct_carry) + len(ct_ys)) +
[False] * num_eres)
in_state = _get_states(attrs_tracked)
transpose_inputs = *ires, *in_state, *ct_consts, *ct_carry, *ct_ys, *eres
transpose_num_out_carry = num_consts-num_ires+num_carry+len(attrs_tracked)
if not _split_transpose:
outs = scan_p.bind(
*transpose_inputs,
reverse=not reverse, length=length, jaxpr=jaxpr_trans,
num_consts=num_ires,
num_carry=transpose_num_out_carry,
linear=tuple(linear_trans), unroll=unroll,
_split_transpose=False)
else:
inst_mask = [False] * transpose_num_out_carry + [True] * (
len(jaxpr_trans.out_avals) - transpose_num_out_carry)
unknowns_mask = [False] * (len(transpose_inputs) - len(eres)) + [
True
] * len(eres)
# The residuals may contain original parameters (e.g. forwarded extensive
# array arguments) and residuals from the primal. Hence we iterate and
# update all values of the mask that we've set to True (i.e. 'unknown') to
# see if we should actually push them to the known computation in order to
# perform the scan (known) - map (unknown) split. The test effectively is
# done by comparing the output masks.
#
# TODO(dvytin): improve performance by doing backwards abstract eval.
#
# For example, a mask arising from a relu() is an extensive residual, yet
# only really used in the backpropagation scan, not in the unknown map. But
# an intermediate activation of a matmul will be used only in the map part.
# If we were to erroneously push the relu mask to the unknown part, then,
# in the output, the partial evaluator will also pull the loop-carried state
# to the unknown, and that is something we can test by comparing the output
# mask of pe against our intended inst mask.
for index in range(len(jaxpr_trans.in_avals)):
if unknowns_mask[index]:
mask_for_dependence = [False]*len(jaxpr_trans.in_avals)
mask_for_dependence[index] = True # try moving this to unknown
_, _, outs_for_dependence, _ = pe.partial_eval_jaxpr_nounits(
jaxpr_trans, mask_for_dependence, inst_mask)
if inst_mask != outs_for_dependence:
unknowns_mask[index] = False
jaxpr_known_body, jaxpr_unknown_body, outs_mask, res_avals = (
pe.partial_eval_jaxpr_nounits(jaxpr_trans, unknowns_mask, inst_mask)
)
num_knowns = len(outs_mask) - sum(outs_mask)
linear_list = list(linear_trans)
known_linear = [
l for mask, l in zip(unknowns_mask, linear_list) if not mask
]
unknown_linear = [l for mask, l in zip(unknowns_mask, linear_list) if mask]
unknown_linear = [False] * len(res_avals) + unknown_linear
known_args = [
arg for mask, arg in zip(unknowns_mask, transpose_inputs) if not mask
]
unknown_args = [
arg for mask, arg in zip(unknowns_mask, transpose_inputs) if mask
]
# 1. Apply the known scan.
knowns_and_residual = scan_p.bind(
*known_args,
reverse=not reverse,
length=length,
num_consts=num_ires,
num_carry=transpose_num_out_carry,
jaxpr=jaxpr_known_body,
linear=tuple(known_linear),
unroll=unroll,
_split_transpose=False, # Just generate the loop now.
)
known_results, residuals = split_list(knowns_and_residual, [num_knowns])
# 2. Apply the unknown map to residuals and unknown arguments.
unknown_results = scan_p.bind(
*residuals, *unknown_args,
reverse=reverse, # Keep reverse as is for better scheduling.
length=length,
num_consts=0,
num_carry=0,
jaxpr=jaxpr_unknown_body,
linear=tuple(unknown_linear),
unroll=unroll,
_split_transpose=False, # Just generate the loop now.
)
known_results_iter = iter(known_results)
unknown_results_iter = iter(unknown_results)
outs = [
next(known_results_iter) if not mask else next(unknown_results_iter)
for mask in outs_mask
]
out_state, outs = split_list(outs, [len(attrs_tracked)])
_set_states(attrs_tracked, out_state)
ct_consts, ct_init, ct_xs = split_list(outs, [num_consts - num_ires, num_carry])
return [None] * num_ires + ct_consts + ct_init + ct_xs + [None] * num_eres
# transpose_scan_jaxpr :: ([res1, c, a, res2] -> b)
# -> ([res1, CT c, CT b, res2] -> [CT c, CT a])
@weakref_lru_cache
def _transpose_scan_jaxpr(jaxpr, num_res1, num_c, num_res2,
ct_ys_is_zeros):
num_a = len(jaxpr.in_avals) - num_res1 - num_c - num_res2
# TODO: allow input cotangent avals to be batched relative to jaxpr.in_avals
# if an axis isn't reduced
res1_avals, c_avals, a_avals, res2_avals = split_list(
jaxpr.in_avals, [num_res1, num_c, num_a])
num_ys = len(ct_ys_is_zeros)
num_b = len(jaxpr.out_avals) - num_ys
# TODO: Also propagate ad.Zero through b_carry_avals until fixed point.
b_carry_avals, b_ys_avals = split_list(list(jaxpr.out_avals), [num_b])
b_ys_avals_stripped = [
aval for aval, is_zero in zip(b_ys_avals, ct_ys_is_zeros) if not is_zero
]
@lu.wrap_init
def transposed(*res1_cbar_bbar_res2):
res1, c_bar, b_bar, ys_bar_stripped, res2 = split_list(
res1_cbar_bbar_res2,
[num_res1, num_c, num_b, len(b_ys_avals_stripped)])
ys_bar_stripped_iter = iter(ys_bar_stripped)
ys_bar = [
ad.Zero(aval) if is_zero else next(ys_bar_stripped_iter)
for aval, is_zero in zip(b_ys_avals, ct_ys_is_zeros)
]
# TODO(mattjj): c_avals should be _tangent_ types here...
primals = (res1 + [ad.UndefinedPrimal(aval) for aval in c_avals] +
[ad.UndefinedPrimal(aval) for aval in a_avals] + res2)
cbar_abar = ad.backward_pass(
jaxpr.jaxpr, False, jaxpr.consts, primals, b_bar + ys_bar)
_, new_c_bar, a_bar, _ = split_list(cbar_abar, [num_res1, num_c, num_a])
a_bar = _map(ad.instantiate_zeros, a_bar)
c_bar = _map(ad.instantiate_zeros, _map(ad.add_tangents, c_bar, new_c_bar))
return c_bar + a_bar
return _make_closed_jaxpr_attrs(
transposed, tuple(res1_avals + c_avals + b_carry_avals +
b_ys_avals_stripped + res2_avals))
def _scan_batching_rule(spmd_axis_name, axis_size, axis_name, main_type, args,
dims, reverse, length,
jaxpr, num_consts, num_carry, linear, unroll,
_split_transpose):
num_ys = len(jaxpr.out_avals) - num_carry
orig_batched = [d is not batching.not_mapped for d in dims]
const_batched, init_batched, xs_batched = split_list(orig_batched, [num_consts, num_carry])
# Fixpoint computation of which carry are batched: either
# batched from init, or the carry out is batched. Each iteration promotes
# at least one carry to batched. We need at most len(carry) iterations,
# but we need one last iteration to prepare the jaxpr based on the final
# carry_batched.
carry_batched = init_batched
for _ in range(1 + len(carry_batched)):
batched = const_batched + carry_batched + xs_batched
jaxpr_batched, batched_out = batching.batch_jaxpr(
jaxpr, axis_size, batched,
instantiate=carry_batched + [False] * num_ys,
axis_name=axis_name,
spmd_axis_name=spmd_axis_name,
main_type=main_type)
carry_batched_out, ys_batched = batched_out[:num_carry], batched_out[num_carry:]
if carry_batched_out == carry_batched:
break
else:
carry_batched = _map(operator.or_, carry_batched, carry_batched_out)
else:
assert False, "Fixpoint not reached"
consts, init, xs = split_list(args, [num_consts, num_carry])
consts_bdims, init_bdims, xs_bdims = split_list(dims, [num_consts, num_carry])
new_consts = [batching.moveaxis(x, d, 0) if d is not batching.not_mapped and d != 0
else x for x, d in zip(consts, consts_bdims)]
new_init = [batching.broadcast(x, axis_size, 0) if now_batched and not was_batched
else batching.moveaxis(x, d, 0) if now_batched else x
for x, d, was_batched, now_batched in
zip(init, init_bdims, init_batched, carry_batched)]
new_xs = [batching.moveaxis(x, d, 1) if d is not batching.not_mapped and d != 1
else x for x, d in zip(xs, xs_bdims)]
new_args = new_consts + new_init + new_xs
outs = scan_p.bind(
*new_args, reverse=reverse, length=length, jaxpr=jaxpr_batched,
num_consts=num_consts, num_carry=num_carry, linear=linear, unroll=unroll,
_split_transpose=_split_transpose)
carry_bdims = [0 if b else batching.not_mapped for b in carry_batched]
ys_bdims = [1 if b else batching.not_mapped for b in ys_batched]
return outs, carry_bdims + ys_bdims
@weakref_lru_cache
def _cached_scan_pad_jaxpr(jaxpr):
return core.ClosedJaxpr(*pe.pad_jaxpr(jaxpr.jaxpr, jaxpr.consts))
def _scan_padding_rule(in_avals, out_avals, *args, jaxpr, **params):
return scan_p.bind(*args, jaxpr=_cached_scan_pad_jaxpr(jaxpr), **params)
def _scan_dce_rule(used_outputs: list[bool], eqn: core.JaxprEqn
) -> tuple[list[bool], core.JaxprEqn]:
jaxpr = eqn.params['jaxpr']
num_consts, num_carry = eqn.params['num_consts'], eqn.params['num_carry']
num_xs = len(jaxpr.in_avals) - num_consts - num_carry
used_carry_out, used_extensive_out = split_list(used_outputs, [num_carry])
for i in range(1 + num_carry):
used_outputs = used_carry_out + used_extensive_out
jaxpr_dce, used_inputs = pe.dce_jaxpr(
jaxpr.jaxpr, used_outputs,
instantiate=[False] * num_consts + used_carry_out + [False] * num_xs)
used_consts, used_carry_in, used_extensive_in = \
split_list(used_inputs, [num_consts, num_carry])
if list(used_carry_in) == list(used_carry_out):
break
else:
used_carry_out = _map(operator.or_, used_carry_out, used_carry_in)
else:
assert False, "Fixpoint not reached"
if config.enable_checks.value: core.check_jaxpr(jaxpr.jaxpr)
new_linear = [l for l, u in zip(eqn.params['linear'], used_inputs) if u]
new_params = dict(eqn.params, num_consts=sum(used_consts),
num_carry=sum(used_carry_in), linear=tuple(new_linear),
jaxpr=core.ClosedJaxpr(jaxpr_dce, jaxpr.consts))
# TODO(mattjj,sharadmv): don't assume effects are never DCE'd?
new_invars = [v for v, used in zip(eqn.invars, used_inputs) if used]
new_outvars = [v for v, used in zip(eqn.outvars, used_outputs) if used]
_, new_effects = eqn.primitive.abstract_eval(*[v.aval for v in new_invars],
**new_params)
new_eqn = pe.new_jaxpr_eqn(
new_invars,
new_outvars,
eqn.primitive, new_params, new_effects, eqn.source_info)
assert len(new_eqn.invars ) == len(new_params['jaxpr'].in_avals )
assert len(new_eqn.outvars) == len(new_params['jaxpr'].out_avals)
return used_inputs, new_eqn
# TODO(mattjj): de-duplicate code with _scan_partial_eval
def _scan_partial_eval_custom(saveable, unks_in, inst_in, eqn):
jaxpr = eqn.params['jaxpr']
num_consts, num_carry = eqn.params['num_consts'], eqn.params['num_carry']
num_ys = len(jaxpr.out_avals) - num_carry
# Fixpoint (trivial on 'inst_in', since we might as well make all inputs
# available as DCE can subsequently prune any unused ones)
const_uk, carry_uk, xs_uk = split_list(unks_in, [num_consts, num_carry])
for _ in range(1 + len(carry_uk)):
unks_in = const_uk + carry_uk + xs_uk
jaxpr_known_, jaxpr_staged_, unks_out, inst_out, num_res = \
pe.partial_eval_jaxpr_custom(
jaxpr.jaxpr, in_unknowns=unks_in, in_inst=True,
ensure_out_unknowns=carry_uk + [False] * num_ys,
ensure_out_inst=True, saveable=saveable)
carry_uk_out, ys_uk = split_list(unks_out, [num_carry])
if carry_uk_out == carry_uk:
break
else:
carry_uk = _map(operator.or_, carry_uk, carry_uk_out)
else:
assert False, "Fixpoint not reached"
jaxpr_known = core.ClosedJaxpr(jaxpr_known_ , jaxpr.consts)
jaxpr_staged = core.ClosedJaxpr(jaxpr_staged_, jaxpr.consts)
# Move all residual binders to the back of jaxpr_staged so they're extensive.
# TODO(mattjj): make jaxpr_staged only take instantiated inputs
res_avals = jaxpr_staged.in_avals[:num_res]
jaxpr_staged = pe.move_binders_to_back(
jaxpr_staged, [True] * num_res + [False] * len(jaxpr.in_avals))
# Instantiate all inputs (b/c jaxpr_staged takes all inputs, corresponding to
# passing in_inst argument to partial_eval_jaxpr_custom above).
new_inst = [x for x, inst in zip(eqn.invars, inst_in)
if type(x) is core.Var and not inst]
inst_in = [True] * len(inst_in)
# As an optimization, hoist loop-invariant residuals out of the loop rather
# than using extensive outputs for them. See _scan_partial_eval for comments.
num_const_known = len(const_uk) - sum(const_uk)
num_carry_known = len(carry_uk) - sum(carry_uk)
num_xs_known = len( xs_uk) - sum( xs_uk)
jaxpr_known_hoist, jaxpr_known_loop, loop_dep, consts_known_lp_avals = \
pe.partial_eval_jaxpr_nounits(
jaxpr_known,
[False] * num_const_known + [True] * (num_carry_known + num_xs_known),
[True] * (len(unks_out) - sum(unks_out)) + [False] * num_res)
# jaxpr_known_hoist produces intensive residuals followed by the constants for
# jaxpr_known_loop. We adjust jaxpr_staged to accept intensive res as consts.
_, loop_dep_res = split_list(loop_dep, [len(loop_dep) - num_res])
jaxpr_staged = pe.move_binders_to_front(
jaxpr_staged, [False] * sum(inst_in) + _map(operator.not_, loop_dep_res))
num_intensive_res = len(loop_dep_res) - sum(loop_dep_res)
del loop_dep, num_carry_known, num_xs_known, const_uk
# Create residual variables.
intensive_avals, ext_avals_mapped = partition_list(loop_dep_res, res_avals)
ext_avals = [core.unmapped_aval(eqn.params['length'], core.no_axis_name, 0, a)
for a in ext_avals_mapped]
newvar = core.gensym()
intensive_res = _map(newvar, intensive_avals)
extensive_res = _map(newvar, ext_avals)
# Create known eqn, which is a call_p combining evaluation of
# jaxpr_known_hoist and a scan of jaxpr_known_loop.
ins_known, _ = partition_list(unks_in, eqn.invars)
out_binders_known, _ = partition_list(unks_out, eqn.outvars)
# jaxpr_known_loop takes as input constants output as res by jaxpr_known_hoist
# (corresponding to consts_known_lp_avals) followed by known carry and xs.
linear_known_ = [l for l, uk in zip(eqn.params['linear'], unks_in) if not uk]
_, linear_known_ = split_list(linear_known_, [num_const_known])
linear_known = [False] * len(consts_known_lp_avals) + linear_known_
params_known = dict(eqn.params, jaxpr=jaxpr_known_loop,
num_consts=len(consts_known_lp_avals),
num_carry=len(carry_uk)-sum(carry_uk),
linear=tuple(linear_known))
@lu.wrap_init
def known(*ins_known):
consts_known_hoist, ins_known_lp = split_list(ins_known, [num_const_known])
out_hoist = core.jaxpr_as_fun(jaxpr_known_hoist)(*consts_known_hoist)
intensive_res, consts_known_lp = split_list(out_hoist, [num_intensive_res])
out_loop = scan_p.bind(*consts_known_lp, *ins_known_lp, **params_known)
return [*intensive_res, *out_loop]
call_jaxpr_, _, call_jaxpr_consts, () = pe.trace_to_jaxpr_dynamic(
known, [v.aval for v in ins_known])
call_jaxpr = core.ClosedJaxpr(call_jaxpr_, call_jaxpr_consts)
eqn_known = pe.new_jaxpr_eqn(
ins_known, [*intensive_res, *out_binders_known, *extensive_res],
core.closed_call_p, dict(call_jaxpr=call_jaxpr), call_jaxpr.effects,
eqn.source_info)
# Create the staged eqn.
_, out_binders_staged = partition_list(inst_out, eqn.outvars)
linear_staged = ([False] * len(intensive_res) + list(eqn.params['linear']) +
[False] * len(extensive_res))
params_staged = dict(eqn.params, jaxpr=jaxpr_staged,
num_consts=len(intensive_res) + eqn.params['num_consts'],
linear=tuple(linear_staged))
eqn_staged = pe.new_jaxpr_eqn([*intensive_res, *eqn.invars, *extensive_res],
out_binders_staged, eqn.primitive,
params_staged, jaxpr_staged.effects,
eqn.source_info)
new_vars = [*new_inst, *intensive_res, *extensive_res]
return eqn_known, eqn_staged, unks_out, inst_out, new_vars
def _scan_typecheck(bind_time, *in_atoms, reverse, length, num_consts,
num_carry, jaxpr, linear, unroll, _split_transpose):
del _split_transpose
if not bind_time:
_, *in_atoms = in_atoms
avals = [x.aval for x in in_atoms]
tc = partial(_typecheck_param, 'scan')
tc(reverse, 'reverse', 'bool', type(reverse) is bool)
tc(num_consts, 'num_consts', 'non-negative int',
type(num_consts) is int and num_consts >= 0)
tc(num_carry, 'num_carry', 'non-negative int',
type(num_carry) is int and num_carry >= 0)
tc(jaxpr, 'jaxpr', 'ClosedJaxpr', type(jaxpr) is core.ClosedJaxpr)
tc(linear, 'linear', 'tuple of bool',
type(linear) is tuple and all(type(x) is bool for x in linear))
tc(unroll, 'unroll', 'positive int', type(unroll) is int and unroll > 0)
tc(length, 'length', 'non-negative int', length >= 0)
if len(linear) != len(avals):
raise core.JaxprTypeError(
f'scan param linear has length {len(linear)} for {len(avals)} operands')
const_avals, init_avals, x_avals = split_list(avals, [num_consts, num_carry])
const_avals_jaxpr, init_avals_jaxpr, x_avals_jaxpr = split_list(
jaxpr.in_avals, [num_consts, num_carry])
carry_avals_jaxpr, y_avals_mapped = split_list(jaxpr.out_avals, [num_carry])
x_avals_mapped = _map(partial(core.mapped_aval, length, 0), x_avals)
y_avals = [core.unmapped_aval(length, core.no_axis_name, 0, a)
for a in y_avals_mapped]
if not all(_map(core.typematch, init_avals_jaxpr, carry_avals_jaxpr)):
raise core.JaxprTypeError(
f'scan input carry input and output types mismatch: '
f'\n{_avals_short(init_avals_jaxpr)}\nvs\n{_avals_short(carry_avals_jaxpr)}')
if not all(_map(core.typecompat, const_avals_jaxpr, const_avals)):
raise core.JaxprTypeError(
f'scan jaxpr takes input const types\n{_avals_short(const_avals_jaxpr)},\n'
f'called with consts of type\n{_avals_short(const_avals)}')
if not all(_map(core.typecompat, init_avals_jaxpr, init_avals)):
raise core.JaxprTypeError(
f'scan jaxpr takes input carry types\n{_avals_short(init_avals_jaxpr)},\n'
f'called with initial carry of type\n{_avals_short(init_avals)}')
if not all(_map(core.typecompat, x_avals_jaxpr, x_avals_mapped)):
raise core.JaxprTypeError(
f'scan jaxpr takes input sequence types\n{_avals_short(x_avals_jaxpr)},\n'
f'called with sequence whose items have type\n{_avals_short(x_avals_mapped)}')
return [*init_avals, *y_avals], jaxpr.effects
def _scan_pp_rule(eqn, context, settings):
printed_params = dict(eqn.params)
del printed_params['linear']
if eqn.params['num_consts'] + eqn.params['num_carry'] == len(eqn.invars):
del printed_params['length']
if printed_params['unroll'] == 1:
del printed_params['unroll']
if printed_params['num_carry'] == 0:
del printed_params['num_carry']
if printed_params['num_consts'] == 0:
del printed_params['num_consts']
if not printed_params['reverse']:
del printed_params['reverse']
if not printed_params['_split_transpose']:
del printed_params['_split_transpose']
return core._pp_eqn(eqn.replace(params=printed_params), context, settings)
def _scan_state_discharge_rule(in_avals, out_avals, *args, jaxpr, num_consts,
num_carry, linear, unroll, reverse, length,
_split_transpose):
jaxpr, consts = jaxpr.jaxpr, jaxpr.consts
if consts: raise NotImplementedError
consts, carry, xs = split_list(args, [num_consts, num_carry])
consts_linear, carry_linear, xs_linear = split_list(
linear, [num_consts, num_carry])
consts_avals, carry_avals, xs_avals = split_list(in_avals,
[num_consts, num_carry])
is_ref = [isinstance(a, state.AbstractRef) for a in consts_avals]
remaining_const_avals, in_ref_avals = partition_list(is_ref, consts_avals)
remaining_consts, in_refs = partition_list(is_ref, consts)
remaining_consts_linear, in_refs_linear = partition_list(is_ref, consts_linear)
num_refs = sum(is_ref)
num_extensive_in = len(in_avals) - num_carry - num_consts
num_extensive_out = len(out_avals) - num_carry
num_remaining_consts = num_consts - num_refs
discharged_jaxpr, discharged_consts = state_discharge.discharge_state(jaxpr, ())
if discharged_consts:
raise NotImplementedError("Discharged jaxpr has consts. If you see this, "
"please open an issue at "
"https://github.com/google/jax/issues")
# The discharged jaxpr will have output refs stashed at the end
def wrapped(*refs_and_args):
consts, refs, carry, xs = split_list(refs_and_args, [num_remaining_consts,
num_refs,
num_carry])
consts_with_refs = merge_lists(is_ref, consts, refs)
outs_and_refs = core.eval_jaxpr(discharged_jaxpr, (), *consts_with_refs,
*carry, *xs)
carry, ys, out_refs = split_list(outs_and_refs, [num_carry,
num_extensive_out])
assert len(out_refs) == num_refs
return [*out_refs, *carry, *ys]
new_in_avals = [*remaining_const_avals, *[a.inner_aval for a in in_ref_avals],
*carry_avals,
*[core.mapped_aval(length, 0, a) for a in xs_avals]]
new_jaxpr, _, (), () = pe.trace_to_jaxpr_dynamic(lu.wrap_init(wrapped), new_in_avals)
new_linear = (*remaining_consts_linear, *in_refs_linear,
*carry_linear, *xs_linear)
all_out = scan_p.bind(*remaining_consts, *in_refs, *carry, *xs,
jaxpr=core.ClosedJaxpr(new_jaxpr, ()),
length=length,
num_consts=num_remaining_consts,
num_carry=num_refs + num_carry,
unroll=unroll,
reverse=reverse,
linear=new_linear, _split_transpose=_split_transpose)
refs_out, carry_out, ys_out = split_list(all_out, [num_refs, num_carry])
new_invals = [*merge_lists(is_ref, [None] * num_remaining_consts, refs_out),
*[None] * num_carry, *[None] * num_extensive_in]
assert len(new_invals) == len(in_avals)
return new_invals, [*carry_out, *ys_out]
def scan_bind(*args, **params):
if config.enable_checks.value:
avals = _map(core.get_aval, args)
in_atoms = [core.Var('', a) for a in avals] # dummies
_scan_typecheck(True, *in_atoms, **params)
core.check_jaxpr(params['jaxpr'].jaxpr)
return core.AxisPrimitive.bind(scan_p, *args, **params)
scan_p = core.AxisPrimitive("scan")
scan_p.multiple_results = True
scan_p.def_custom_bind(scan_bind)
scan_p.def_impl(partial(dispatch.apply_primitive, scan_p))
scan_p.def_effectful_abstract_eval(_scan_abstract_eval)
ad.primitive_jvps[scan_p] = _scan_jvp
ad.reducing_transposes[scan_p] = _scan_transpose
pe.custom_partial_eval_rules[scan_p] = _scan_partial_eval
xla.register_initial_style_primitive(scan_p)
mlir.register_lowering(scan_p,
mlir.lower_fun(_scan_impl, multiple_results=True))
batching.axis_primitive_batchers[scan_p] = partial(_scan_batching_rule, None)
batching.spmd_axis_primitive_batchers[scan_p] = _scan_batching_rule
core.custom_typechecks[scan_p] = partial(_scan_typecheck, False)
pe.partial_eval_jaxpr_custom_rules[scan_p] = _scan_partial_eval_custom
pe.padding_rules[scan_p] = _scan_padding_rule
pe.dce_rules[scan_p] = _scan_dce_rule
state_discharge.register_discharge_rule(scan_p)(_scan_state_discharge_rule)
# TODO(mattjj,frostig): un-comment this pp rule
# core.pp_eqn_rules[scan_p] = _scan_pp_rule
### while_loop
[docs]
@api_boundary
def while_loop(cond_fun: Callable[[T], BooleanNumeric],
body_fun: Callable[[T], T],
init_val: T) -> T:
"""Call ``body_fun`` repeatedly in a loop while ``cond_fun`` is True.
The `Haskell-like type signature`_ in brief is
.. code-block:: haskell
while_loop :: (a -> Bool) -> (a -> a) -> a -> a
The semantics of ``while_loop`` are given by this Python implementation::
def while_loop(cond_fun, body_fun, init_val):
val = init_val
while cond_fun(val):
val = body_fun(val)
return val
Unlike that Python version, ``while_loop`` is a JAX primitive and is lowered
to a single WhileOp. That makes it useful for reducing compilation times
for jit-compiled functions, since native Python loop constructs in an ``@jit``
function are unrolled, leading to large XLA computations.
Also unlike the Python analogue, the loop-carried value ``val`` must hold a
fixed shape and dtype across all iterations (and not just be consistent up to
NumPy rank/shape broadcasting and dtype promotion rules, for example). In
other words, the type ``a`` in the type signature above represents an array
with a fixed shape and dtype (or a nested tuple/list/dict container data
structure with a fixed structure and arrays with fixed shape and dtype at the
leaves).
Another difference from using Python-native loop constructs is that
``while_loop`` is not reverse-mode differentiable because XLA computations
require static bounds on memory requirements.
.. note::
:py:func:`while_loop` compiles ``cond_fun`` and ``body_fun``, so while it
can be combined with :py:func:`jit`, it's usually unnecessary.
Args:
cond_fun: function of type ``a -> Bool``.
body_fun: function of type ``a -> a``.
init_val: value of type ``a``, a type that can be a scalar, array, or any
pytree (nested Python tuple/list/dict) thereof, representing the initial
loop carry value.
Returns:
The output from the final iteration of body_fun, of type ``a``.
.. _Haskell-like type signature: https://wiki.haskell.org/Type_signature
"""
if not (callable(body_fun) and callable(cond_fun)):
raise TypeError("lax.while_loop: body_fun and cond_fun arguments should be callable.")
if config.disable_jit.value:
try:
val = init_val
while cond_fun(val):
val = body_fun(val)
return val
except core.ConcretizationTypeError:
# Can't run this while_loop in Python (e.g. because there's a vmap
# transformation on it), so we fall back to the primitive version.
pass
def _create_jaxpr(init_val):
init_vals, in_tree = tree_flatten((init_val,))
init_avals = tuple(_map(_abstractify, init_vals))
cond_jaxpr, cond_consts, cond_tree = _initial_style_jaxpr(
cond_fun, in_tree, init_avals, "while_cond")
body_jaxpr, body_consts, body_tree = _initial_style_jaxpr(
body_fun, in_tree, init_avals, "while_loop")
if not treedef_is_leaf(cond_tree) or len(cond_jaxpr.out_avals) != 1:
msg = "cond_fun must return a boolean scalar, but got pytree {}."
raise TypeError(msg.format(cond_tree))
pred_aval = cond_jaxpr.out_avals[0]
if (not isinstance(pred_aval, ShapedArray)
or pred_aval.strip_weak_type().strip_named_shape() != ShapedArray((), np.bool_)):
msg = "cond_fun must return a boolean scalar, but got output type(s) {}."
raise TypeError(msg.format(cond_jaxpr.out_avals))
return init_vals, init_avals, body_jaxpr, in_tree, cond_jaxpr, cond_consts, body_consts, body_tree
# The body input and output avals must match exactly. However, we want to account for
# the case when init contains weakly-typed values (e.g. Python scalars), with avals that
# may not match the output despite being compatible by virtue of their weak type.
# To do this, we compute the jaxpr in two passes: first with the raw inputs, and if
# necessary, a second time with modified init values.
init_vals, init_avals, body_jaxpr, in_tree, *rest = _create_jaxpr(init_val)
new_init_vals, changed = _promote_weak_typed_inputs(init_vals, init_avals, body_jaxpr.out_avals)
if changed:
new_init_val, = tree_unflatten(in_tree, new_init_vals)
init_vals, init_avals, body_jaxpr, in_tree, *rest = _create_jaxpr(new_init_val)
cond_jaxpr, cond_consts, body_consts, body_tree = rest
in_tree_children = in_tree.children()
assert len(in_tree_children) == 1
_check_tree_and_avals("body_fun output and input",
body_tree, body_jaxpr.out_avals,
in_tree_children[0], init_avals)
joined_effects = core.join_effects(cond_jaxpr.effects, body_jaxpr.effects)
disallowed_effects = effects.control_flow_allowed_effects.filter_not_in(joined_effects)
if disallowed_effects:
raise NotImplementedError(
f'Effects not supported in `while`: {disallowed_effects}')
outs = while_p.bind(*cond_consts, *body_consts, *init_vals,
cond_nconsts=len(cond_consts), cond_jaxpr=cond_jaxpr,
body_nconsts=len(body_consts), body_jaxpr=body_jaxpr)
return tree_unflatten(body_tree, outs)
def _join_while_effects(body_jaxpr, cond_jaxpr, body_nconsts, cond_nconsts
) -> effects.Effects:
joined_effects = set()
for eff in cond_jaxpr.effects:
if isinstance(eff, effects.JaxprInputEffect):
index = eff.input_index
if index >= cond_nconsts:
index += body_nconsts
eff = eff.replace(input_index=index)
joined_effects.add(eff)
for eff in body_jaxpr.effects:
if isinstance(eff, effects.JaxprInputEffect):
index = eff.input_index + cond_nconsts
eff = eff.replace(input_index=index)
joined_effects.add(eff)
return joined_effects
def _while_loop_abstract_eval(*avals, cond_jaxpr, body_jaxpr, body_nconsts,
cond_nconsts):
del avals
joined_effects = _join_while_effects(body_jaxpr, cond_jaxpr, body_nconsts,
cond_nconsts)
disallowed_effects = effects.control_flow_allowed_effects.filter_not_in(joined_effects)
if disallowed_effects:
raise NotImplementedError(
f'Effects not supported in `while`: {disallowed_effects}')
return _map(raise_to_shaped, body_jaxpr.out_avals), joined_effects
def _while_loop_batching_rule(spmd_axis_name, axis_size, axis_name, main_type,
args, dims, cond_nconsts, cond_jaxpr,
body_nconsts, body_jaxpr):
from jax._src.callback import _IOEffect, _OrderedIOEffect
if any(_OrderedIOEffect in fn.effects for fn in [body_jaxpr, cond_jaxpr]):
raise Exception("Ordered IO effects not supported in vmap.")
orig_batched = [d is not batching.not_mapped for d in dims]
cconst_bat, bconst_bat, init_bat = split_list(orig_batched, [cond_nconsts, body_nconsts])
cconsts, bconsts, init = split_list(args, [cond_nconsts, body_nconsts])
cconst_dims, bconst_dims, init_dims = split_list(dims, [cond_nconsts, body_nconsts])
carry_bat = init_bat
# Fixpoint computation of which carry are batched: either
# batched from init, or the carry out is batched. Each iteration promotes
# at least one carry to batched. We need at most len(carry) iterations to
# reach a fixpoint.
for _ in range(1 + len(carry_bat)):
_, carry_bat_out = batching.batch_jaxpr(
body_jaxpr, axis_size, bconst_bat + carry_bat, instantiate=carry_bat,
axis_name=axis_name, spmd_axis_name=spmd_axis_name, main_type=main_type)
if carry_bat == carry_bat_out:
break
carry_bat = safe_map(operator.or_, carry_bat, carry_bat_out)
else:
assert False, "Fixpoint not reached"
# Knowing how the carry is batched now, we can determine if the predicate is
# batched.
_, (pred_bat,) = batching.batch_jaxpr(
cond_jaxpr, axis_size, cconst_bat + carry_bat, instantiate=False,
axis_name=axis_name, spmd_axis_name=spmd_axis_name, main_type=main_type)
if pred_bat:
# If the predicate is batched, we have to batch *all* of the carry
# regardless of if the body needs it.
if any(_IOEffect in fn.effects for fn in [body_jaxpr, cond_jaxpr]):
raise Exception("Unordered IO effects not supported in while_loop "
"with batched predicate")
carry_bat = [True] * len(carry_bat)
carry_dims = [0] * len(carry_bat)
body_jaxpr_batched, _ = batching.batch_jaxpr_axes(
body_jaxpr, axis_size, bconst_dims + carry_dims,
carry_dims, axis_name=axis_name, spmd_axis_name=spmd_axis_name,
main_type=main_type)
cond_jaxpr_batched, _ = batching.batch_jaxpr_axes(
cond_jaxpr, axis_size, cconst_dims + carry_dims, [0],
axis_name=axis_name, spmd_axis_name=spmd_axis_name,
main_type=main_type)
else:
# If the predicate is not batched, we can look at the `cond_jaxpr`'s out
# shape to determine the rank of the predicate. From this rank we pick the
# dims of the carry to be batched to ensure that the predicate shape is a
# prefix of the carry in and out shapes. We can then batch the `body_jaxpr`
# according to these new batch dims.
cond_rank = len(cond_jaxpr.out_avals[0].shape)
carry_dims = [cond_rank if b else None for b in carry_bat]
body_jaxpr_batched, _ = batching.batch_jaxpr_axes(
body_jaxpr, axis_size, bconst_dims + carry_dims, carry_dims,
axis_name=axis_name, spmd_axis_name=spmd_axis_name, main_type=main_type)
# Now we need to rebatch the `cond_jaxpr` according to the new dims of the
# carry.
cond_jaxpr_batched, _ = batching.batch_jaxpr_axes(
cond_jaxpr, axis_size, cconst_dims + carry_dims, (None,),
axis_name=axis_name, spmd_axis_name=spmd_axis_name, main_type=main_type)
# To prepare the `init` to the `while_p`, we broadcast values if they are
# unbatched and need to have an out axis. If their current batch axis does not
# match the one it needs to be for the translation rule to work, we move it
# into place.
new_init = []
for x, old_axis, new_axis in zip(init, init_dims, carry_dims):
if old_axis is batching.not_mapped and new_axis is not batching.not_mapped:
new_init.append(batching.broadcast(x, axis_size, new_axis))
elif old_axis is batching.not_mapped and new_axis is batching.not_mapped:
new_init.append(x)
else:
assert new_axis is not batching.not_mapped
new_init.append(batching.moveaxis(x, old_axis, new_axis))
outs = while_p.bind(*(cconsts + bconsts + new_init),
cond_nconsts=cond_nconsts, cond_jaxpr=cond_jaxpr_batched,
body_nconsts=body_nconsts, body_jaxpr=body_jaxpr_batched)
return outs, carry_dims
def _while_loop_jvp(primals, tangents, cond_nconsts, cond_jaxpr, body_nconsts,
body_jaxpr):
nonzeros = [type(t) is not ad_util.Zero for t in tangents]
cconst_nz, bconst_nz, init_nz = split_list(nonzeros, [cond_nconsts, body_nconsts])
carry_nz = init_nz
for _ in range(1 + len(carry_nz)):
body_nonzeros = bconst_nz + carry_nz
body_jvp, nonzeros_out = ad.jvp_jaxpr(
body_jaxpr, body_nonzeros, instantiate=carry_nz)
if nonzeros_out == carry_nz:
break
carry_nz = _map(operator.or_, carry_nz, nonzeros_out)
else:
assert False, "Fixpoint not reached"
nonzeros = cconst_nz + body_nonzeros
tangents = [ad.instantiate_zeros(t) if nz else t
for t, nz in zip(tangents, nonzeros)]
cconst, bconst, init = split_list(primals, [cond_nconsts, body_nconsts])
_, bconst_dot, init_dot = split_list(tangents, [cond_nconsts, body_nconsts])
bconst_dot = _prune_zeros(bconst_dot)
init_dot = _prune_zeros(init_dot)
num_carry = len(primals) - cond_nconsts - body_nconsts
body_jvp_rearranged = ad.rearrange_binders(
body_jvp,
[body_nconsts, num_carry], [len(bconst_dot), len(init_dot)],
[num_carry], [len(init_dot)])
newvar = core.gensym()
invars_aug = (
cond_jaxpr.jaxpr.invars + [newvar(core.get_aval(x)) for x in init_dot])
cond_jaxpr_augmented = core.Jaxpr(cond_jaxpr.jaxpr.constvars,
invars_aug,
cond_jaxpr.jaxpr.outvars,
cond_jaxpr.jaxpr.eqns,
cond_jaxpr.jaxpr.effects)
cond_jaxpr_augmented = core.ClosedJaxpr(cond_jaxpr_augmented, cond_jaxpr.consts)
out = while_p.bind(
*(cconst + bconst + bconst_dot + init + init_dot),
cond_nconsts=cond_nconsts,
cond_jaxpr=cond_jaxpr_augmented,
body_nconsts=len(bconst) + len(bconst_dot),
body_jaxpr=body_jvp_rearranged)
out_carry, out_carry_dot = split_list(out, [num_carry])
out_tangents_iter = iter(out_carry_dot)
out_tangents = [next(out_tangents_iter) if nz else ad_util.Zero.from_value(p)
for p, nz in zip(out_carry, nonzeros_out)]
return out_carry, out_tangents
def _while_partial_eval(trace: pe.JaxprTrace, *tracers: pe.Tracer, cond_nconsts: int,
cond_jaxpr: pe.ClosedJaxpr, body_nconsts: int,
body_jaxpr: pe.ClosedJaxpr) -> Sequence[pe.Tracer]:
# As long as some carry (and hence output) are known and the output of
# `cond_jaxpr` is known, we use a portion of the loop body to compute the
# known outputs of the `while_loop`. For the unknown outputs we generate a
# jaxpr to run the whole while, including recomputing the known parts,
# basically like building in checkpointing/rematieralization. This means that
# we don't actually save any computation by partial evaluation if there are
# unknown outputs.
#
# What this achieves is twofold: jax.linearize works, and we can give a proper
# error for reverse differentiation of `while`.
unknowns = [not t.pval.is_known() for t in tracers]
params = dict(cond_nconsts=cond_nconsts, cond_jaxpr=cond_jaxpr,
body_nconsts=body_nconsts, body_jaxpr=body_jaxpr)
cond_consts_uk, body_consts_uk, carry_init_uk = \
split_list(unknowns, [cond_nconsts, body_nconsts])
# Fixpoint computation of unknown carry. Each iteration promotes at least one
# carry to unknown. We need one last iteration to prepare the jaxpr.
carry_uk = carry_init_uk
for _ in range(1 + len(carry_uk)):
body_jaxpr_known, _, carry_out_uk, body_res_avals = pe.partial_eval_jaxpr_nounits( # type: ignore
body_jaxpr, body_consts_uk + carry_uk, instantiate=carry_uk)
if carry_out_uk == carry_uk:
break
else:
carry_uk = _map(operator.or_, carry_uk, carry_out_uk)
else:
assert False, "Fixpoint not reached"
cond_jaxpr_known, _, cond_uk, _ = pe.partial_eval_jaxpr_nounits( # type: ignore
cond_jaxpr, cond_consts_uk + carry_uk, instantiate=False)
if cond_uk[0] or all(not uk for uk in unknowns) or all(unknowns):
# If conditional is unknown, or all inputs are known, or all are unknown,
# just do the default processing.
return trace.default_process_primitive(while_p, tracers, params)
# Run the known part of the while.
in_consts = [t.pval.get_known() for uk, t in
zip(cond_consts_uk + body_consts_uk + carry_uk, tracers)
if not uk]
cond_nconsts_known = len(cond_consts_uk) - sum(cond_consts_uk)
body_nconsts_known = len(body_consts_uk) - sum(body_consts_uk)
num_known_outs = len(carry_uk) - sum(carry_uk)
# TODO(mattjj): use pe.dce_jaxpr to drop res computations and not just outputs
body_jaxpr_known = body_jaxpr_known.replace(
jaxpr=body_jaxpr_known.jaxpr.replace(
outvars=body_jaxpr_known.jaxpr.outvars[:num_known_outs]))
out_known = while_p.bind(
*in_consts, cond_nconsts=cond_nconsts_known, cond_jaxpr=cond_jaxpr_known,
body_nconsts=body_nconsts_known, body_jaxpr=body_jaxpr_known)
del body_jaxpr_known
# Run the whole while_loop to get all the outputs, then merge with known ones
out_tracers_ = trace.default_process_primitive(while_p, tracers, params)
out_tracers = [t for t, uk in zip(out_tracers_, carry_uk) if uk]
return util.merge_lists(carry_uk, out_known, out_tracers)
# TODO(mattjj): de-duplicate code with _while_partial_eval
def _while_partial_eval_custom(saveable, unks_in, inst_in, eqn):
del saveable # We can't save any residuals anyway (w/o dynamic shapes)!
cond_jaxpr = eqn.params['cond_jaxpr']
cond_nconsts = eqn.params['cond_nconsts']
body_jaxpr = eqn.params['body_jaxpr']
body_nconsts = eqn.params['body_nconsts']
cond_consts_uk, body_consts_uk, carry_init_uk = \
split_list(unks_in, [cond_nconsts, body_nconsts])
# Fixpoint to compute known part of the body (trivial on 'inst_in', since we
# make all inputs available as DCE can subsequently prune any unused ones)
carry_uk = carry_init_uk
for _ in range(1 + len(carry_uk)):
body_unks_in = body_consts_uk + carry_uk
jaxpr_known_, _, carry_uk_out, _, num_res = \
pe.partial_eval_jaxpr_custom(
body_jaxpr.jaxpr, in_unknowns=body_unks_in, in_inst=True,
ensure_out_unknowns=carry_uk, ensure_out_inst=True,
saveable=ad_checkpoint.nothing_saveable)
if carry_uk_out == carry_uk:
break
else:
carry_uk = _map(operator.or_, carry_uk, carry_uk_out)
else:
assert False, "Fixpoint not reached"
assert not num_res
body_jaxpr_known = core.ClosedJaxpr(jaxpr_known_, body_jaxpr.consts)
del jaxpr_known_, carry_uk_out, num_res
# Instantiate all inputs (b/c jaxpr_staged will take all inputs).
new_inst = [x for x, inst in zip(eqn.invars, inst_in)
if type(x) is core.Var and not inst]
# Compute the known part of cond_fun (basically pruning inputs on known side).
cond_unks_in = cond_consts_uk + carry_uk
cond_jaxpr_known_, _, [cond_uk], _, _ = \
pe.partial_eval_jaxpr_custom(
cond_jaxpr.jaxpr, cond_unks_in, in_inst=True,
ensure_out_unknowns=False, ensure_out_inst=True,
saveable=ad_checkpoint.nothing_saveable)
# NOTE(mattjj): I think it should be impossible for the condition to be
# unknown, but asserting that caused a test failure in diffrax. So
# we handle it: if it is unknown, stage out the whole cond function.
if cond_uk:
return None, eqn, [True] * len(carry_uk), [True] * len(carry_uk), new_inst
cond_jaxpr_known = core.ClosedJaxpr(cond_jaxpr_known_, cond_jaxpr.consts)
del cond_uk
# Build the known eqn.
ins_known, _ = partition_list(unks_in, eqn.invars)
out_binders_known, _ = partition_list(carry_uk, eqn.outvars)
params_known = dict(cond_jaxpr=cond_jaxpr_known, body_jaxpr=body_jaxpr_known,
cond_nconsts=len(cond_consts_uk) - sum(cond_consts_uk),
body_nconsts=len(body_consts_uk) - sum(body_consts_uk))
effects_known = core.join_effects(cond_jaxpr_known.effects,
body_jaxpr_known.effects)
eqn_known = pe.new_jaxpr_eqn(ins_known, out_binders_known, while_p,
params_known, effects_known, eqn.source_info)
# Staged eqn is same as input eqn.
eqn_staged = eqn
unks_out = carry_uk
inst_out = [True] * len(unks_out)
return eqn_known, eqn_staged, unks_out, inst_out, new_inst
def _while_transpose_error(*_, **kwargs):
raise ValueError("Reverse-mode differentiation does not work for "
"lax.while_loop or lax.fori_loop with dynamic start/stop values. "
"Try using lax.scan, or using fori_loop with static start/stop.")
# For a while loop with ordered effects in the cond, we need a special
# lowering. Fundamentally, we'd like to rewrite a while loop that looks like
# this:
# ```
# while cond(x):
# x = body(x)
# ```
# into something that looks like this:
# ```
# while True:
# token, pred = cond(token, x)
# if not pred:
# break
# token, x = body(token, x)
# ```
# Unfortunately, with a WhileOp we can't (1) return multiple values
# from a `cond` and (2) can't break a while loop. We thus adopt the
# following rewrite strategy:
# ```
# def new_cond(pred, token, x):
# return pred
# token, pred = cond(token, x)
# while new_cond(pred, token, x):
# token, x = body(token, x)
# token, pred = cond(token, x)
# ```
def _while_lowering(ctx, *args, cond_jaxpr, body_jaxpr, cond_nconsts,
body_nconsts):
pred_aval = cond_jaxpr.out_avals[0]
batched = bool(pred_aval.shape)
cond_ordered_effects = effects.ordered_effects.filter_in(cond_jaxpr.effects)
if cond_ordered_effects:
def cond(args):
# Pred can be batched
pred = core.eval_jaxpr(cond_jaxpr.jaxpr, cond_jaxpr.consts, *args)[0]
if batched:
pred = lax._reduce_or(pred, tuple(range(len(pred_aval.shape))))
return pred
def body(args):
return tuple(core.eval_jaxpr(body_jaxpr.jaxpr, body_jaxpr.consts, *args))
def new_cond(pred_args):
pred, _ = pred_args
return pred
def new_body(pred_args):
_, args = pred_args
args = body(args)
pred = cond(args)
return pred, args
def fun(*args):
pred = cond(args)
_, out = while_loop(new_cond, new_body, (pred, args))
return out
return mlir.lower_fun(fun)(ctx, *args)
loop_carry_types = _map(mlir.aval_to_ir_types, ctx.avals_in)
body_effects = effects.ordered_effects.filter_in(body_jaxpr.effects)
num_tokens = len(body_effects)
tokens = [ctx.tokens_in.get(eff) for eff in body_effects]
token_types = [mlir.token_type() for _ in tokens]
loop_carry_types = [*token_types, *loop_carry_types]
flat_loop_carry_types = util.flatten(loop_carry_types)
args = [*tokens, *args]
flat_args = mlir.flatten_lowering_ir_args(args)
while_op = hlo.WhileOp(flat_loop_carry_types, flat_args)
# Loop condition
cond_block = while_op.regions[0].blocks.append(*flat_loop_carry_types)
name_stack = ctx.name_stack.extend('while')
with ir.InsertionPoint(cond_block):
flat_cond_args = [
cond_block.arguments[i] for i in range(len(flat_loop_carry_types))
]
cond_args = util.unflatten(flat_cond_args, _map(len, loop_carry_types))
# Remove tokens from cond args
cond_args = cond_args[num_tokens:]
x, _, z = util.split_list(cond_args, [cond_nconsts, body_nconsts])
cond_consts = [
mlir.ir_constants(xla.canonicalize_dtype(x)) for x in cond_jaxpr.consts
]
cond_name_stack = name_stack.extend('cond')
((pred,),), _ = mlir.jaxpr_subcomp(
ctx.module_context,
cond_jaxpr.jaxpr,
cond_name_stack,
mlir.TokenSet(),
cond_consts,
*(x + z),
dim_var_values=ctx.dim_var_values,
)
if batched:
pred_ctx = mlir.LoweringRuleContext(
module_context=ctx.module_context,
name_stack=cond_name_stack,
primitive=None,
avals_in=[pred_aval],
avals_out=[pred_aval.update(shape=())],
tokens_in=mlir.TokenSet(),
tokens_out=None)
pred, = lax._unary_reduce_lower(
hlo.OrOp,
lambda dtype: np.array(False, dtype),
pred_ctx,
pred,
axes=tuple(range(len(pred_aval.shape))))
hlo.return_([pred])
# Loop body
body_block = while_op.regions[1].blocks.append(*flat_loop_carry_types)
with ir.InsertionPoint(body_block):
flat_body_args = [
body_block.arguments[i] for i in range(len(flat_loop_carry_types))
]
body_args = util.unflatten(flat_body_args, _map(len, loop_carry_types))
# Tokens are at the front of the args list to the while loop
token_args, body_args = util.split_list(body_args, [num_tokens])
tokens_in = mlir.TokenSet(zip(body_effects, token_args))
x, y, z = util.split_list(body_args, [cond_nconsts, body_nconsts])
body_name_stack = name_stack.extend('body')
body_consts = [mlir.ir_constants(xla.canonicalize_dtype(x))
for x in body_jaxpr.consts]
new_z, tokens_out = mlir.jaxpr_subcomp(
ctx.module_context, body_jaxpr.jaxpr, body_name_stack,
tokens_in, body_consts, *(y + z), dim_var_values=ctx.dim_var_values)
out_tokens = [tokens_out.get(eff) for eff in body_effects]
if batched:
body_pred_name_stack = name_stack.extend('body_pred')
cond_consts = [mlir.ir_constants(xla.canonicalize_dtype(x))
for x in cond_jaxpr.consts]
((body_pred,),), _ = mlir.jaxpr_subcomp(
ctx.module_context, cond_jaxpr.jaxpr, body_pred_name_stack,
mlir.TokenSet(), cond_consts, *(x + z),
dim_var_values=ctx.dim_var_values)
new_z = _map(
partial(_pred_bcast_select_hlo, ctx, pred_aval, body_pred), new_z, z,
body_jaxpr.out_avals)
hlo.return_([*util.flatten(out_tokens), *util.flatten(x), *util.flatten(y),
*util.flatten(new_z)])
outputs = util.unflatten(while_op.results, _map(len, loop_carry_types))
tokens, _, _, z = util.split_list(outputs, [num_tokens, cond_nconsts, body_nconsts])
if tokens:
ctx.set_tokens_out(mlir.TokenSet(zip(body_effects, tokens)))
return z
def _while_typecheck(_, *in_atoms, cond_jaxpr, body_jaxpr, cond_nconsts,
body_nconsts):
# TODO(frostig,mattjj): check cond_jaxpr, body_jaxpr types
joined_effects = _join_while_effects(body_jaxpr, cond_jaxpr, body_nconsts,
cond_nconsts)
disallowed_effects = effects.control_flow_allowed_effects.filter_not_in(joined_effects)
if disallowed_effects:
raise NotImplementedError(
f'Effects not supported in `while`: {disallowed_effects}')
return body_jaxpr.out_avals, joined_effects
def _while_discharge_rule(in_avals, out_avals, *args, cond_jaxpr, body_jaxpr,
cond_nconsts, body_nconsts):
# TODO(sharadmv): enable supporting state effects in the cond
if any(isinstance(eff, state.RefEffect) for eff in cond_jaxpr.effects):
raise NotImplementedError
cond_consts, body_consts, carry = split_list(args, [cond_nconsts, body_nconsts])
cond_consts_avals, body_consts_avals, carry_avals = split_list(in_avals,
[cond_nconsts,
body_nconsts])
# There shouldn't be any `Ref`s in the `cond` (because of our check above).
assert not any(isinstance(aval, state.AbstractRef) for aval in cond_consts_avals)
is_ref = [isinstance(aval, state.AbstractRef) for aval in body_consts_avals]
remaining_body_consts, refs = partition_list(is_ref, body_consts)
remaining_body_const_avals, ref_avals = partition_list(is_ref,
body_consts_avals)
num_refs = sum(is_ref)
num_remaining_consts = body_nconsts - num_refs
num_carry = len(in_avals) - body_nconsts - cond_nconsts
body_jaxpr, body_jaxpr_consts = body_jaxpr.jaxpr, body_jaxpr.consts
cond_jaxpr, cond_jaxpr_consts = cond_jaxpr.jaxpr, cond_jaxpr.consts
if body_jaxpr_consts:
raise NotImplementedError("Body jaxpr has consts. If you see this error, "
"please open an issue at "
"https://github.com/google/jax/issues")
# body_jaxpr has the signature (*body_consts, *carry) -> carry.
# Some of these body_consts are actually `Ref`s so when we discharge
# them, they also turn into outputs, effectively turning those consts into
# carries. However this doesn't fit the expected signature for the body_jaxpr.
# Therefore we need to rewrite the jaxpr to shuffle around the `Ref`s so that
# they are part of the carry.
discharged_body_jaxpr, discharged_consts = state_discharge.discharge_state(
body_jaxpr, ())
if discharged_consts: raise NotImplementedError
def new_body(*consts_refs_carry):
consts, refs, carry = split_list(
consts_refs_carry, [num_remaining_consts, num_refs])
consts_and_refs = merge_lists(is_ref, consts, refs)
carry_refs = core.eval_jaxpr(discharged_body_jaxpr, (), *consts_and_refs,
*carry)
carry, refs_out = split_list(carry_refs, [num_carry])
return [*refs_out, *carry]
new_body_jaxpr, _, new_body_consts, () = pe.trace_to_jaxpr_dynamic(
lu.wrap_init(new_body), [*remaining_body_const_avals, *[a.inner_aval for a
in ref_avals],
*carry_avals])
if new_body_consts: raise NotImplementedError
# Since some `Ref`s that were previously consts are now carries, we need to
# deal with them (i.e. ignore them) in the `cond`, so we need to rewrite the
# cond_jaxpr as well.
def new_cond(*consts_refs_carry):
consts, refs, carry = split_list(
consts_refs_carry, [cond_nconsts, num_refs])
del refs # We don't use them here!
return core.eval_jaxpr(cond_jaxpr, cond_jaxpr_consts, *consts, *carry)
new_cond_jaxpr, _, new_cond_consts, () = pe.trace_to_jaxpr_dynamic(
lu.wrap_init(new_cond), [*cond_consts_avals,
*[a.inner_aval for a in ref_avals],
*carry_avals])
if new_cond_consts: raise NotImplementedError
out = while_p.bind(*cond_consts, *remaining_body_consts, *refs, *carry,
body_jaxpr=core.ClosedJaxpr(new_body_jaxpr, ()),
cond_jaxpr=core.ClosedJaxpr(new_cond_jaxpr, ()),
body_nconsts=num_remaining_consts,
cond_nconsts=cond_nconsts)
refs_out, carry_out = split_list(out, [num_refs])
updated_body_consts = merge_lists(is_ref, [None] * num_remaining_consts,
refs_out)
invals_out = [
*[None] * cond_nconsts,
*updated_body_consts,
*[None] * num_carry]
return invals_out, carry_out
while_p = core.AxisPrimitive('while')
while_p.multiple_results = True
while_p.def_impl(partial(dispatch.apply_primitive, while_p))
while_p.def_effectful_abstract_eval(_while_loop_abstract_eval)
ad.primitive_jvps[while_p] = _while_loop_jvp
pe.custom_partial_eval_rules[while_p] = _while_partial_eval
xla.register_initial_style_primitive(while_p)
ad.primitive_transposes[while_p] = _while_transpose_error
batching.axis_primitive_batchers[while_p] = partial(_while_loop_batching_rule, None)
batching.spmd_axis_primitive_batchers[while_p] = _while_loop_batching_rule
pe.partial_eval_jaxpr_custom_rules[while_p] = _while_partial_eval_custom
mlir.register_lowering(while_p, _while_lowering)
core.custom_typechecks[while_p] = _while_typecheck
state_discharge.register_discharge_rule(while_p)(_while_discharge_rule)
def _pred_bcast_select_hlo(ctx,
pred_aval: core.ShapedArray, pred: ir.Value, xs: Sequence[ir.Value],
ys: Sequence[ir.Value], x_y_aval: core.AbstractValue) -> Sequence[ir.Value]:
if x_y_aval is core.abstract_token:
x, = xs
y, = ys
return [hlo.AfterAllOp([x, y]).result]
else:
assert isinstance(x_y_aval, core.ShapedArray), x_y_aval
x, = xs
y, = ys
assert x.type == y.type, (x.type, y.type)
assert (pred_aval.shape == x_y_aval.shape[:len(pred_aval.shape)]), (
pred_aval.shape, x_y_aval)
x_y_aval = core.physical_aval(x_y_aval)
bcast_pred = mlir.broadcast_in_dim(
ctx, pred, core.DShapedArray(x_y_aval.shape, np.dtype(np.bool_)),
broadcast_dimensions=list(range(len(pred_aval.shape))))
return hlo.SelectOp(bcast_pred, x, y).results
### fori_loop
def _fori_cond_fun(loop_carry):
i, upper, _ = loop_carry
return lax.lt(i, upper)
@weakref_lru_cache
def _fori_body_fun(body_fun):
body_fun = weakref.ref(body_fun)
def while_body_fun(loop_carry):
i, upper, x = loop_carry
return lax.add(i, lax._const(i, 1)), upper, body_fun()(i, x)
return while_body_fun
@weakref_lru_cache
def _fori_scan_body_fun(body_fun):
body_fun = weakref.ref(body_fun)
def scanned_fun(loop_carry, _):
i, x = loop_carry
return (i + 1, body_fun()(i, x)), None
return scanned_fun
[docs]
@api_boundary
def fori_loop(lower, upper, body_fun, init_val,
*, unroll: int | bool | None = None):
"""Loop from ``lower`` to ``upper`` by reduction to :func:`jax.lax.while_loop`.
The `Haskell-like type signature`_ in brief is
.. code-block:: haskell
fori_loop :: Int -> Int -> ((Int, a) -> a) -> a -> a
The semantics of ``fori_loop`` are given by this Python implementation::
def fori_loop(lower, upper, body_fun, init_val):
val = init_val
for i in range(lower, upper):
val = body_fun(i, val)
return val
As the Python version suggests, setting ``upper <= lower`` will produce no
iterations. Negative or custom increments are not supported.
Unlike that Python version, ``fori_loop`` is implemented in terms of either a
call to :func:`jax.lax.while_loop` or a call to :func:`jax.lax.scan`. If the
trip count is static (meaning known at tracing time, perhaps because ``lower``
and ``upper`` are Python integer literals) then the ``fori_loop`` is
implemented in terms of :func:`~scan` and reverse-mode autodiff is supported;
otherwise, a ``while_loop`` is used and reverse-mode autodiff is not
supported. See those functions' docstrings for more information.
Also unlike the Python analogue, the loop-carried value ``val`` must hold a
fixed shape and dtype across all iterations (and not just be consistent up to
NumPy rank/shape broadcasting and dtype promotion rules, for example). In
other words, the type ``a`` in the type signature above represents an array
with a fixed shape and dtype (or a nested tuple/list/dict container data
structure with a fixed structure and arrays with fixed shape and dtype at the
leaves).
.. note::
:py:func:`fori_loop` compiles ``body_fun``, so while it can be combined with
:py:func:`jit`, it's usually unnecessary.
Args:
lower: an integer representing the loop index lower bound (inclusive)
upper: an integer representing the loop index upper bound (exclusive)
body_fun: function of type ``(int, a) -> a``.
init_val: initial loop carry value of type ``a``.
unroll: An optional integer or boolean that determines how much to unroll
the loop. If an integer is provided, it determines how many unrolled
loop iterations to run within a single rolled iteration of the loop. If a
boolean is provided, it will determine if the loop is competely unrolled
(i.e. `unroll=True`) or left completely unrolled (i.e. `unroll=False`).
This argument is only applicable if the loop bounds are statically known.
Returns:
Loop value from the final iteration, of type ``a``.
.. _Haskell-like type signature: https://wiki.haskell.org/Type_signature
"""
if not callable(body_fun):
raise TypeError("lax.fori_loop: body_fun argument should be callable.")
# TODO(phawkins): perhaps do more type checking here, better error messages.
lower_dtype = dtypes.canonicalize_dtype(lax.dtype(lower))
upper_dtype = dtypes.canonicalize_dtype(lax.dtype(upper))
if lower_dtype == upper_dtype:
dtype = lower_dtype
else:
# As a special case: allow promotion of weak integers (e.g., Python scalars)
# This improves the ergonomics if one but not both of the loop bounds is a
# scalar.
dtype = None
if (np.issubdtype(lower_dtype, np.signedinteger) and
np.issubdtype(upper_dtype, np.signedinteger)):
lower_weak = dtypes.is_weakly_typed(lower)
upper_weak = dtypes.is_weakly_typed(upper)
if lower_weak and not upper_weak:
dtype = upper_dtype
elif not lower_weak and upper_weak:
dtype = lower_dtype
if dtype is None:
raise TypeError("lower and upper arguments to fori_loop must have equal "
f"types, got {lower_dtype.name} and {upper_dtype.name}")
# If we can specialize on the trip count, call scan instead of a while_loop
# to enable efficient reverse-mode differentiation.
if (isinstance(core.get_aval(lower), ConcreteArray) and
isinstance(core.get_aval(upper), ConcreteArray)):
try:
lower_ = int(lower)
upper_ = int(upper)
except TypeError:
use_scan = False
else:
use_scan = True
else:
use_scan = False
if use_scan:
if unroll is None:
unroll = False
length = max(upper_ - lower_, 0)
if config.disable_jit.value and length == 0:
# non-jit implementation of scan does not support length=0
return init_val
(_, result), _ = scan(
_fori_scan_body_fun(body_fun),
(lower_, init_val),
None,
length=length,
unroll=unroll,
)
return result
if unroll is not None:
raise ValueError("Can only use `unroll` in `fori_loop` if the loop bounds "
"are statically known.")
if lower_dtype != dtype:
lower = lax.convert_element_type(lower, dtype) # type: ignore
if upper_dtype != dtype:
upper = lax.convert_element_type(upper, dtype) # type: ignore
_, _, result = while_loop(_fori_cond_fun, _fori_body_fun(body_fun),
(lower, upper, init_val))
return result
### map and miscellaneous rules
[docs]
@api_boundary
def map(f, xs):
"""Map a function over leading array axes.
Like Python's builtin map, except inputs and outputs are in the form of
stacked arrays. Consider using the :func:`~jax.vmap` transform instead, unless you
need to apply a function element by element for reduced memory usage or
heterogeneous computation with other control flow primitives.
When ``xs`` is an array type, the semantics of :func:`~map` are given by this
Python implementation::
def map(f, xs):
return np.stack([f(x) for x in xs])
Like :func:`~scan`, :func:`~map` is implemented in terms of JAX primitives so
many of the same advantages over a Python loop apply: ``xs`` may be an
arbitrary nested pytree type, and the mapped computation is compiled only
once.
Args:
f: a Python function to apply element-wise over the first axis or axes of
``xs``.
xs: values over which to map along the leading axis.
Returns:
Mapped values.
"""
g = lambda _, x: ((), f(x))
_, ys = scan(g, (), xs)
return ys
def _rng_bit_generator_batching_rule(batched_args, batch_dims, *, shape, dtype, algorithm):
keys, = batched_args
bd, = batch_dims
if bd is batching.not_mapped:
return lax.rng_bit_generator_p.bind(keys, shape=shape, dtype=dtype,
algorithm=algorithm), (None, None)
keys = batching.moveaxis(keys, bd, 0)
batch_size = keys.shape[0]
key = keys[0]
new_key, bits = lax.rng_bit_generator_p.bind(key, shape=(batch_size, *shape),
dtype=dtype, algorithm=algorithm)
new_keys = jax.lax.dynamic_update_index_in_dim(keys, new_key, 0, axis=0)
return (new_keys, bits), (0, 0)
batching.primitive_batchers[lax.rng_bit_generator_p] = _rng_bit_generator_batching_rule # type: ignore
### associative_scan
[docs]
@api_boundary
def associative_scan(fn: Callable, elems, reverse: bool = False, axis: int = 0):
"""Performs a scan with an associative binary operation, in parallel.
For an introduction to associative scans, see [BLE1990]_.
Args:
fn: A Python callable implementing an associative binary operation with
signature ``r = fn(a, b)``. Function `fn` must be associative, i.e., it
must satisfy the equation
``fn(a, fn(b, c)) == fn(fn(a, b), c)``.
The inputs and result are (possibly nested Python tree structures of)
array(s) matching ``elems``. Each array has a dimension in place
of the ``axis`` dimension. `fn` should be applied elementwise over
the ``axis`` dimension (for example, by using :func:`jax.vmap` over the
elementwise function.)
The result ``r`` has the same shape (and structure) as the two inputs
``a`` and ``b``.
elems: A (possibly nested Python tree structure of) array(s), each with
an ``axis`` dimension of size ``num_elems``.
reverse: A boolean stating if the scan should be reversed with respect to
the ``axis`` dimension.
axis: an integer identifying the axis over which the scan should occur.
Returns:
A (possibly nested Python tree structure of) array(s) of the same shape
and structure as ``elems``, in which the ``k``'th element of ``axis`` is the
result of recursively applying ``fn`` to combine the first ``k`` elements
of ``elems`` along ``axis``. For example, given ``elems = [a, b, c, ...]``,
the result would be ``[a, fn(a, b), fn(fn(a, b), c), ...]``.
Example 1: partial sums of an array of numbers:
>>> lax.associative_scan(jnp.add, jnp.arange(0, 4))
Array([0, 1, 3, 6], dtype=int32)
Example 2: partial products of an array of matrices
>>> mats = jax.random.uniform(jax.random.key(0), (4, 2, 2))
>>> partial_prods = lax.associative_scan(jnp.matmul, mats)
>>> partial_prods.shape
(4, 2, 2)
Example 3: reversed partial sums of an array of numbers
>>> lax.associative_scan(jnp.add, jnp.arange(0, 4), reverse=True)
Array([6, 6, 5, 3], dtype=int32)
.. [BLE1990] Blelloch, Guy E. 1990. "Prefix Sums and Their Applications.",
Technical Report CMU-CS-90-190, School of Computer Science, Carnegie Mellon
University.
"""
if not callable(fn):
raise TypeError("lax.associative_scan: fn argument should be callable.")
elems_flat, tree = tree_flatten(elems)
if reverse:
elems_flat = [lax.rev(elem, [axis]) for elem in elems_flat]
def combine(a_flat, b_flat):
# Lower `fn` to operate on flattened sequences of elems.
a = tree_unflatten(tree, a_flat)
b = tree_unflatten(tree, b_flat)
c = fn(a, b)
c_flat, _ = tree_flatten(c)
return c_flat
# Check that all inputs have a consistent leading dimension `num_elems`.
axis = util.canonicalize_axis(axis, elems_flat[0].ndim)
if not core.is_constant_dim(elems_flat[0].shape[axis]):
raise NotImplementedError("associative scan over axis "
f"of non-constant size: {elems_flat[0].shape[axis]}. You may be "
"able to avoid this on TPU. See b/274176030.")
num_elems = int(elems_flat[0].shape[axis])
if not all(int(elem.shape[axis]) == num_elems for elem in elems_flat[1:]):
raise ValueError('Array inputs to associative_scan must have the same '
'first dimension. (saw: {})'
.format([elem.shape for elem in elems_flat]))
# Summary of algorithm:
#
# Consider elements of `_scan(elems)` at odd indices. That's the same as first
# summing successive pairs of elements of `elems` and performing a scan on
# that half sized tensor. We perform the latter scan by recursion.
#
# Now consider the even elements of `_scan(elems)`. These can be computed
# from the odd elements of `_scan(elems)` by adding each odd element of
# `_scan(elems)` to the matching even element in the original `elems`.
#
# We return the odd and even elements interleaved.
#
# For the base case of the recursion we return the first element
# of `elems` followed by the sum of the first two elements computed as
# a (small two-down-to-one) reduction step.
def _scan(elems):
"""Perform scan on `elems`."""
num_elems = elems[0].shape[axis]
if num_elems < 2:
return elems
# Combine adjacent pairs of elements.
reduced_elems = combine(
[slicing.slice_in_dim(elem, 0, -1, stride=2, axis=axis) for elem in elems],
[slicing.slice_in_dim(elem, 1, None, stride=2, axis=axis)
for elem in elems])
# Recursively compute scan for partially reduced tensors.
odd_elems = _scan(reduced_elems)
if num_elems % 2 == 0:
even_elems = combine(
[slicing.slice_in_dim(e, 0, -1, axis=axis) for e in odd_elems],
[slicing.slice_in_dim(e, 2, None, stride=2, axis=axis) for e in elems])
else:
even_elems = combine(
odd_elems,
[slicing.slice_in_dim(e, 2, None, stride=2, axis=axis) for e in elems])
# The first element of a scan is the same as the first element
# of the original `elems`.
even_elems = [
lax.concatenate([slicing.slice_in_dim(elem, 0, 1, axis=axis), result],
dimension=axis)
for (elem, result) in zip(elems, even_elems)]
return list(_map(partial(_interleave, axis=axis), even_elems, odd_elems))
scans = _scan(elems_flat)
if reverse:
scans = [lax.rev(scanned, [axis]) for scanned in scans]
return tree_unflatten(tree, scans)
def _interleave(a, b, axis):
"""Given two Tensors of static shape, interleave them along the first axis."""
assert a.shape[axis] == b.shape[axis] or a.shape[axis] == b.shape[axis] + 1
a_pad = [(0, 0, 0)] * a.ndim
b_pad = [(0, 0, 0)] * b.ndim
a_pad[axis] = (0, 1 if a.shape[axis] == b.shape[axis] else 0, 1)
b_pad[axis] = (1, 0 if a.shape[axis] == b.shape[axis] else 1, 1)
op = lax.bitwise_or if a.dtype == np.bool_ else lax.add
return op(lax.pad(a, lax._const(a, 0), a_pad),
lax.pad(b, lax._const(b, 0), b_pad))
### Cumulative reductions.
[docs]
def cumsum(operand: Array, axis: int = 0, reverse: bool = False) -> Array:
"""Computes a cumulative sum along `axis`."""
return cumsum_p.bind(operand, axis=int(axis), reverse=bool(reverse))
[docs]
def cumprod(operand: Array, axis: int = 0, reverse: bool = False) -> Array:
"""Computes a cumulative product along `axis`."""
return cumprod_p.bind(operand, axis=int(axis), reverse=bool(reverse))
[docs]
def cummax(operand: Array, axis: int = 0, reverse: bool = False) -> Array:
"""Computes a cumulative maximum along `axis`."""
return cummax_p.bind(operand, axis=int(axis), reverse=bool(reverse))
[docs]
def cummin(operand: Array, axis: int = 0, reverse: bool = False) -> Array:
"""Computes a cumulative minimum along `axis`."""
return cummin_p.bind(operand, axis=int(axis), reverse=bool(reverse))
[docs]
def cumlogsumexp(operand: Array, axis: int = 0, reverse: bool = False) -> Array:
"""Computes a cumulative logsumexp along `axis`."""
return cumlogsumexp_p.bind(operand, axis=int(axis), reverse=bool(reverse))
def _cumred_shape_rule(x, *, axis: int, reverse: bool):
if axis < 0:
raise ValueError("XLA operations do not allow negative axes")
elif axis >= x.ndim:
raise ValueError(
f"axis {axis} is out of bounds for array of shape {x.shape}")
return x.shape
def _cumsum_transpose_rule(t, operand, *, axis: int, reverse: bool):
return [cumsum(t, axis=axis, reverse=not reverse)]
def cumred_reduce_window_impl(window_reduce: Callable, x, *, axis: int,
reverse: bool):
n = x.shape[axis]
if n == 0:
return x
padding = [(0, 0)] * x.ndim
padding[axis] = (0, n - 1) if reverse else (n - 1, 0)
strides = [1] * x.ndim
window_dims = [1] * x.ndim
window_dims[axis] = n
return window_reduce(x, window_dims, strides, padding)
def cumred_gpu_impl(window_reduce: Callable, reduce_fn: Callable, x, *,
axis: int, reverse: bool):
# On GPU, reduce_window is executed in a single fusion and associative_scan
# is split into multiple to materialize intermediate calculations.
# On small inputs reduce_window is faster being a single fusion,
# but on larger ones is slower because of O(n^2) complexity.
# This conservative value of the threshold was obtained via benchmarking.
if not core.is_constant_dim(x.shape[axis]):
raise NotImplementedError(
"associative scan reductions not implemented with shape polymorphism "
"and native serialization on GPU")
if x.shape[axis] > 32:
return associative_scan(reduce_fn, x, reverse=reverse, axis=axis)
return cumred_reduce_window_impl(window_reduce, x, axis=axis, reverse=reverse)
def _cumred_batch_rule(prim, batched_args, batch_dims, *, axis: int,
reverse: bool):
operand, = batched_args
bdim, = batch_dims
axis = axis if axis < bdim else axis + 1
return prim.bind(operand, axis=axis, reverse=reverse), bdim
def _cumred_dtype_rule(name, operand, *args, **kw):
if not dtypes.issubdtype(operand.dtype, np.number):
raise TypeError("{} does not accept dtype {}. Accepted dtypes are subtypes "
"of number.".format(name, np.dtype(operand.dtype).name))
return dtypes.canonicalize_dtype(operand.dtype)
def _cumulative_reduction_primitive(name, reduce_fn, reduce_window_fn):
reducer_p = lax.standard_primitive(
_cumred_shape_rule, partial(_cumred_dtype_rule, name),
name)
batching.primitive_batchers[reducer_p] = partial(_cumred_batch_rule,
reducer_p)
def register_lowering(fn, platform=None):
mlir.register_lowering(
reducer_p,
mlir.cache_lowering(mlir.lower_fun(fn, multiple_results=False)),
platform=platform)
# Default for platforms not treated specially below.
register_lowering(partial(associative_scan, reduce_fn))
# On GPU, we choose between window reduction and associative scan
# based on the input size.
for platform in ['cuda', 'rocm']:
register_lowering(
partial(cumred_gpu_impl, reduce_window_fn, reduce_fn), platform)
# On TPU, an implementation using reduce_window is handled specially by the
# compiler and is efficient. On other backends, it is O(n^2).
register_lowering(partial(cumred_reduce_window_impl, reduce_window_fn), 'tpu')
return reducer_p
cumsum_p = _cumulative_reduction_primitive("cumsum", lax.add, windowed_reductions._reduce_window_sum)
ad.deflinear2(cumsum_p, _cumsum_transpose_rule)
cumlogsumexp_p = _cumulative_reduction_primitive(
"cumlogsumexp", logaddexp, windowed_reductions._reduce_window_logaddexp)
cumprod_p = _cumulative_reduction_primitive("cumprod", lax.mul, windowed_reductions._reduce_window_prod)
cummax_p = _cumulative_reduction_primitive("cummax", lax.max, windowed_reductions._reduce_window_max)
cummin_p = _cumulative_reduction_primitive("cummin", lax.min, windowed_reductions._reduce_window_min)
def _cumulative_jvp_rule(primals, tangents, *, axis: int, reverse: bool,
combine_fn: Callable):
# Irrespective of backend, we always use the parallel prefix scan
# implementation when differentiating because reduce_window is not
# arbitrarily differentiable.
return api.jvp(partial(associative_scan, combine_fn, axis=axis,
reverse=reverse),
primals, tangents)
ad.primitive_jvps[cumlogsumexp_p] = partial(_cumulative_jvp_rule, combine_fn=logaddexp)
ad.primitive_jvps[cumprod_p] = partial(_cumulative_jvp_rule, combine_fn=lax.mul)
ad.primitive_jvps[cummin_p] = partial(_cumulative_jvp_rule, combine_fn=lax.min)
ad.primitive_jvps[cummax_p] = partial(_cumulative_jvp_rule, combine_fn=lax.max)
