def synthetic_pattern_variable_program(include_types=True):
"""A program that tests product types.
Args:
include_types: If False, we omit types on the variables, requiring a type
inference pass.
Returns:
program: `instructions.Program`.
"""
block = instructions.Block([
instructions.prim_op(["inp"], "many", lambda x: (x + 1,
(x + 2, x + 3))),
instructions.prim_op(["many"], ["one", "two"], lambda x: x),
], instructions.halt_op())
leaf = instructions.TensorType(np.int64, ())
the_vars = {
"inp": instructions.Type(leaf),
"many": instructions.Type((leaf, (leaf, leaf))),
"one": instructions.Type(leaf),
"two": instructions.Type((leaf, leaf)),
}
if not include_types:
_strip_types(the_vars)
return instructions.Program(instructions.ControlFlowGraph([block]), [],
the_vars, ["inp"], "two")
def single_if_program():
"""Single if program: 'if (input > 1) ans = 2; else ans = 0; return ans;'.
Returns:
program: `instructions.Program` with a simple conditional.
"""
entry = instructions.Block()
then_ = instructions.Block()
else_ = instructions.Block()
entry.assign_instructions([
instructions.prim_op(["input"], "cond", lambda n: n > 1),
instructions.BranchOp("cond", then_, else_),
])
then_.assign_instructions([
instructions.prim_op([], "answer", lambda: 2),
instructions.halt_op(),
])
else_.assign_instructions([
instructions.prim_op([], "answer", lambda: 0),
instructions.halt_op(),
])
single_if_blocks = [entry, then_, else_]
# pylint: disable=bad-whitespace
single_if_vars = {
"input": instructions.single_type(np.int64, ()),
"cond": instructions.single_type(np.bool, ()),
"answer": instructions.single_type(np.int64, ()),
}
return instructions.Program(
instructions.ControlFlowGraph(single_if_blocks), [], single_if_vars,
["input"], "answer")
def _invoke_fun(program, mask, backend, block_code_cache, function, inputs):
# TODO(axch): program_for_function computation is copied from instructions.py
program_for_function = inst.Program(function.graph, program.functions,
program.var_defs, function.vars_in,
function.vars_out, program.var_alloc)
return _interpret(program_for_function, mask, backend, block_code_cache,
*inputs)
def select_block_priority(program):
"""Order `Block`s in `program` by execution priority."""
msg = 'TODO(axch): Implement block strategy selection for Functions.'
assert not program.functions, msg
def sync_weight(block):
# Sort all "trivial" blocks that don't call user-land operations ahead of
# all others. This critically relies on `sorted` being stable to work
# correctly.
# TODO(b/118911579): Respect user-specified sync priority when that happens.
for op in block.instructions:
if isinstance(op, (inst.PrimOp, inst.FunctionCallOp)):
return 1
return 0
# Have to keep the first block because that's where control enters.
# This is unfortunate if that block is over-heavy.
# Could be fixed by
# - Adding a field to Program for the initial value of the program counter, or
# - Ensuring that the first block is an empty indirection block
new_blocks = ([program.graph.block(0)] +
sorted(program.graph.blocks[1:], key=sync_weight))
new_graph = inst.ControlFlowGraph(new_blocks)
return inst.Program(new_graph, [], program.var_defs, program.vars_in,
program.vars_out, program.var_alloc)
def shape_sequence_program(shape_sequence):
"""Program that writes into `answer` zeros having a sequence of shapes.
This enables us to test that the final inferred shape is the broadcast of all
intermediate shapes.
Args:
shape_sequence: The sequence of intermediate shapes.
Returns:
program: `instructions.Program` which returns an arbitrary value.
"""
block_ops = []
def op(shape, ans):
return np.zeros(shape, dtype=np.array(ans).dtype),
for shape in shape_sequence:
# We use a partial instead of a lambda in order to capture a copy of shape.
block_ops.append(
instructions.prim_op(['ans'], ['ans'],
functools.partial(op, shape)))
shape_seq_block = instructions.Block(block_ops, instructions.halt_op())
shape_seq_vars = {
'ans': instructions.Type(None),
instructions.pc_var: instructions.single_type(np.int64, ()),
}
return instructions.Program(
instructions.ControlFlowGraph([shape_seq_block]), [], shape_seq_vars,
['ans'], ['ans'])
def constant_program():
"""Constant program: 'ans=1; ans=2; return ans;'.
Returns:
program: `instructions.Program` which returns a constant value.
"""
constant_block = instructions.Block([
instructions.prim_op([], "answer", lambda: 1),
instructions.prim_op([], "answer", lambda: 2),
], instructions.halt_op())
constant_vars = {
"answer": instructions.single_type(np.int64, ()),
}
return instructions.Program(
instructions.ControlFlowGraph([constant_block]), [], constant_vars,
["answer"], "answer")
def synthetic_pattern_program():
"""A program that tests pattern matching of `PrimOp` outputs.
Returns:
program: `instructions.Program`.
"""
block = instructions.Block([
instructions.prim_op([], ("one", ("five", "three")), lambda: (1,
(2, 3))),
instructions.prim_op([], (("four", "five"), "six"), lambda:
((4, 5), 6)),
], instructions.halt_op())
the_vars = {
"one": instructions.single_type(np.int64, ()),
"three": instructions.single_type(np.int64, ()),
"four": instructions.single_type(np.int64, ()),
"five": instructions.single_type(np.int64, ()),
"six": instructions.single_type(np.int64, ()),
}
return instructions.Program(instructions.ControlFlowGraph([block]), [],
the_vars, [],
(("one", "three"), "four", ("five", "six")))
def pea_nuts_program(latent_shape, choose_depth, step_state):
"""Synthetic program usable for benchmarking VM performance.
This program is intended to resemble the control flow and scaling
parameters of the NUTS algorithm, without any of the complexity.
Hence the name.
Each batch member looks like:
state = ... # shape latent_shape
def recur(depth, state):
if depth > 1:
state1 = recur(depth - 1, state)
state2 = state1 + 1
state3 = recur(depth - 1, state2)
ans = state3 + 1
else:
ans = step_state(state) # To simulate NUTS, something heavy
return ans
while count > 0:
count = count - 1
depth = choose_depth(count)
state = recur(depth, state)
Args:
latent_shape: Python `tuple` of `int` giving the event shape of the
latent state.
choose_depth: Python `Tensor -> Tensor` callable. The input
`Tensor` will have shape `[batch_size]` (i.e., scalar event
shape), and give the iteration of the outer while loop the
thread is in. The `choose_depth` function must return a `Tensor`
of shape `[batch_size]` giving the depth, for each thread,
to which to call `recur` in this iteration.
step_state: Python `Tensor -> Tensor` callable. The input and
output `Tensor`s will have shape `[batch_size] + latent_shape`.
This function is expected to update the state, and represents
the "real work" versus which the VM overhead is being measured.
Returns:
program: `instructions.Program` that runs the above benchmark.
"""
entry = instructions.Block()
top_body = instructions.Block()
finish_body = instructions.Block()
enter_recur = instructions.Block()
recur_body_1 = instructions.Block()
recur_body_2 = instructions.Block()
recur_body_3 = instructions.Block()
recur_base_case = instructions.Block()
# pylint: disable=bad-whitespace
entry.assign_instructions([
instructions.prim_op(["count"], "cond",
lambda count: count > 0), # cond = count > 0
instructions.BranchOp("cond", top_body,
instructions.halt()), # if cond
])
top_body.assign_instructions([
instructions.PopOp(["cond"]), # done with cond now
instructions.prim_op(["count"], "ctm1",
lambda count: count - 1), # ctm1 = count - 1
instructions.PopOp(["count"]), # done with count now
instructions.push_op(["ctm1"], ["count"]), # count = ctm1
instructions.PopOp(["ctm1"]), # done with ctm1
instructions.prim_op(["count"], "depth",
choose_depth), # depth = choose_depth(count)
instructions.push_op(
["depth", "state"],
["depth", "state"]), # state = recur(depth, state)
instructions.PopOp(["depth", "state"]), # done with depth, state
instructions.PushGotoOp(finish_body, enter_recur),
])
finish_body.assign_instructions([
instructions.push_op(["ans"], ["state"]), # ...
instructions.PopOp(["ans"]), # pop callee's "ans"
instructions.GotoOp(entry), # end of while body
])
# Definition of recur begins here
enter_recur.assign_instructions([
instructions.prim_op(["depth"], "cond1",
lambda depth: depth > 0), # cond1 = depth > 0
instructions.BranchOp("cond1", recur_body_1,
recur_base_case), # if cond1
])
recur_body_1.assign_instructions([
instructions.PopOp(["cond1"]), # done with cond1 now
instructions.prim_op(["depth"], "dm1",
lambda depth: depth - 1), # dm1 = depth - 1
instructions.PopOp(["depth"]), # done with depth
instructions.push_op(
["dm1", "state"],
["depth", "state"]), # state1 = recur(dm1, state)
instructions.PopOp(["state"]), # done with state
instructions.PushGotoOp(recur_body_2, enter_recur),
])
recur_body_2.assign_instructions([
instructions.push_op(["ans"], ["state1"]), # ...
instructions.PopOp(["ans"]), # pop callee's "ans"
instructions.prim_op(["state1"], "state2",
lambda state: state + 1), # state2 = state1 + 1
instructions.PopOp(["state1"]), # done with state1
instructions.push_op(
["dm1", "state2"],
["depth", "state"]), # state3 = recur(dm1, state2)
instructions.PopOp(["dm1", "state2"]), # done with dm1, state2
instructions.PushGotoOp(recur_body_3, enter_recur),
])
recur_body_3.assign_instructions([
instructions.push_op(["ans"], ["state3"]), # ...
instructions.PopOp(["ans"]), # pop callee's "ans"
instructions.prim_op(["state3"], "ans",
lambda state: state + 1), # ans = state3 + 1
instructions.PopOp(["state3"]), # done with state3
instructions.IndirectGotoOp(), # return ans
])
recur_base_case.assign_instructions([
instructions.PopOp(["cond1", "depth"]), # done with cond1, depth
instructions.prim_op(["state"], "ans",
step_state), # ans = step_state(state)
instructions.PopOp(["state"]), # done with state
instructions.IndirectGotoOp(), # return ans
])
pea_nuts_graph = instructions.ControlFlowGraph([
entry,
top_body,
finish_body,
enter_recur,
recur_body_1,
recur_body_2,
recur_body_3,
recur_base_case,
])
# pylint: disable=bad-whitespace
pea_nuts_vars = {
"count": instructions.single_type(np.int64, ()),
"cond": instructions.single_type(np.bool, ()),
"cond1": instructions.single_type(np.bool, ()),
"ctm1": instructions.single_type(np.int64, ()),
"depth": instructions.single_type(np.int64, ()),
"dm1": instructions.single_type(np.int64, ()),
"state": instructions.single_type(np.float32, latent_shape),
"state1": instructions.single_type(np.float32, latent_shape),
"state2": instructions.single_type(np.float32, latent_shape),
"state3": instructions.single_type(np.float32, latent_shape),
"ans": instructions.single_type(np.float32, latent_shape),
}
return instructions.Program(pea_nuts_graph, [], pea_nuts_vars,
["count", "state"], "state")
def fibonacci_function_calls(include_types=True, dtype=np.int64):
"""The Fibonacci program again, but with `instructions.FunctionCallOp`.
Computes fib(n): fib(0) = fib(1) = 1.
Args:
include_types: If False, we omit types on the variables, requiring a type
inference pass.
dtype: The dtype to use for `n`-like internal state variables.
Returns:
program: Full-powered `instructions.Program` that computes fib(n).
"""
enter_fib = instructions.Block(name="enter_fib")
recur = instructions.Block(name="recur")
finish = instructions.Block(name="finish")
fibonacci_type = lambda types: types[0]
fibonacci_func = instructions.Function(None, ["n"],
"ans",
fibonacci_type,
name="fibonacci")
# pylint: disable=bad-whitespace
# Definition of fibonacci function
enter_fib.assign_instructions([
instructions.prim_op(["n"], "cond", lambda n: n > 1), # cond = n > 1
instructions.BranchOp("cond", recur, finish), # if cond
])
recur.assign_instructions([
instructions.prim_op(["n"], "nm1", lambda n: n - 1), # nm1 = n - 1
instructions.FunctionCallOp(fibonacci_func, ["nm1"],
"fibm1"), # fibm1 = fibonacci(nm1)
instructions.prim_op(["n"], "nm2", lambda n: n - 2), # nm2 = n - 2
instructions.FunctionCallOp(fibonacci_func, ["nm2"],
"fibm2"), # fibm2 = fibonacci(nm2)
instructions.prim_op(["fibm1", "fibm2"], "ans",
lambda x, y: x + y), # ans = fibm1 + fibm2
instructions.halt_op(), # return ans
])
finish.assign_instructions([ # else:
instructions.prim_op([], "ans", lambda: 1), # ans = 1
instructions.halt_op(), # return ans
])
fibonacci_blocks = [enter_fib, recur, finish]
fibonacci_func.graph = instructions.ControlFlowGraph(fibonacci_blocks)
fibonacci_main_blocks = [
instructions.Block([
instructions.FunctionCallOp(fibonacci_func, ["n1"], "ans"),
],
instructions.halt_op(),
name="main_entry"),
]
# pylint: disable=bad-whitespace
fibonacci_vars = {
"n": instructions.single_type(dtype, ()),
"n1": instructions.single_type(dtype, ()),
"cond": instructions.single_type(np.bool, ()),
"nm1": instructions.single_type(dtype, ()),
"fibm1": instructions.single_type(dtype, ()),
"nm2": instructions.single_type(dtype, ()),
"fibm2": instructions.single_type(dtype, ()),
"ans": instructions.single_type(dtype, ()),
}
if not include_types:
_strip_types(fibonacci_vars)
return instructions.Program(
instructions.ControlFlowGraph(fibonacci_main_blocks), [fibonacci_func],
fibonacci_vars, ["n1"], "ans")
def is_even_function_calls(include_types=True, dtype=np.int64):
"""The is-even program, via "even-odd" recursion.
Computes True if the input is even, False if the input is odd, by a pair of
mutually recursive functions is_even and is_odd, which return True and False
respectively for <1-valued inputs.
Tests out mutual recursion.
Args:
include_types: If False, we omit types on the variables, requiring a type
inference pass.
dtype: The dtype to use for `n`-like internal state variables.
Returns:
program: Full-powered `instructions.Program` that computes is_even(n).
"""
def pred_type(t):
return instructions.TensorType(np.bool, t[0].shape)
# Forward declaration of is_odd.
is_odd_func = instructions.Function(None, ["n"], "ans", pred_type)
enter_is_even = instructions.Block()
finish_is_even = instructions.Block()
recur_is_even = instructions.Block()
is_even_func = instructions.Function(None, ["n"], "ans", pred_type)
# pylint: disable=bad-whitespace
# Definition of is_even function
enter_is_even.assign_instructions([
instructions.prim_op(["n"], "cond", lambda n: n < 1), # cond = n < 1
instructions.BranchOp("cond", finish_is_even,
recur_is_even), # if cond
])
finish_is_even.assign_instructions([
instructions.PopOp(["n", "cond"]), # done with n, cond
instructions.prim_op([], "ans", lambda: True), # ans = True
instructions.halt_op(), # return ans
])
recur_is_even.assign_instructions([ # else
instructions.PopOp(["cond"]), # done with cond now
instructions.prim_op(["n"], "nm1", lambda n: n - 1), # nm1 = n - 1
instructions.PopOp(["n"]), # done with n
instructions.FunctionCallOp(is_odd_func, ["nm1"],
"ans"), # ans = is_odd(nm1)
instructions.PopOp(["nm1"]), # done with nm1
instructions.halt_op(), # return ans
])
is_even_blocks = [enter_is_even, finish_is_even, recur_is_even]
is_even_func.graph = instructions.ControlFlowGraph(is_even_blocks)
enter_is_odd = instructions.Block()
finish_is_odd = instructions.Block()
recur_is_odd = instructions.Block()
# pylint: disable=bad-whitespace
# Definition of is_odd function
enter_is_odd.assign_instructions([
instructions.prim_op(["n"], "cond", lambda n: n < 1), # cond = n < 1
instructions.BranchOp("cond", finish_is_odd, recur_is_odd), # if cond
])
finish_is_odd.assign_instructions([
instructions.PopOp(["n", "cond"]), # done with n, cond
instructions.prim_op([], "ans", lambda: False), # ans = False
instructions.halt_op(), # return ans
])
recur_is_odd.assign_instructions([ # else
instructions.PopOp(["cond"]), # done with cond now
instructions.prim_op(["n"], "nm1", lambda n: n - 1), # nm1 = n - 1
instructions.PopOp(["n"]), # done with n
instructions.FunctionCallOp(is_even_func, ["nm1"],
"ans"), # ans = is_even(nm1)
instructions.PopOp(["nm1"]), # done with nm1
instructions.halt_op(), # return ans
])
is_odd_blocks = [enter_is_odd, finish_is_odd, recur_is_odd]
is_odd_func.graph = instructions.ControlFlowGraph(is_odd_blocks)
is_even_main_blocks = [
instructions.Block([
instructions.FunctionCallOp(is_even_func, ["n1"], "ans"),
], instructions.halt_op()),
]
# pylint: disable=bad-whitespace
is_even_vars = {
"n": instructions.single_type(dtype, ()),
"n1": instructions.single_type(dtype, ()),
"cond": instructions.single_type(np.bool, ()),
"nm1": instructions.single_type(dtype, ()),
"ans": instructions.single_type(np.bool, ()),
}
if not include_types:
_strip_types(is_even_vars)
return instructions.Program(
instructions.ControlFlowGraph(is_even_main_blocks),
[is_even_func, is_odd_func], is_even_vars, ["n1"], "ans")
def fibonacci_program():
"""More complicated, fibonacci program: computes fib(n): fib(0) = fib(1) = 1.
Returns:
program: Full-powered `instructions.Program` that computes fib(n).
"""
entry = instructions.Block(name="entry")
enter_fib = instructions.Block(name="enter_fib")
recur1 = instructions.Block(name="recur1")
recur2 = instructions.Block(name="recur2")
recur3 = instructions.Block(name="recur3")
finish = instructions.Block(name="finish")
# pylint: disable=bad-whitespace
entry.assign_instructions([
instructions.PushGotoOp(instructions.halt(), enter_fib),
])
# Definition of fibonacci function starts here
enter_fib.assign_instructions([
instructions.prim_op(["n"], "cond", lambda n: n > 1), # cond = n > 1
instructions.BranchOp("cond", recur1, finish), # if cond
])
recur1.assign_instructions([
instructions.PopOp(["cond"]), # done with cond now
instructions.prim_op(["n"], "nm1", lambda n: n - 1), # nm1 = n - 1
instructions.push_op(["nm1"], ["n"]), # fibm1 = fibonacci(nm1)
instructions.PopOp(["nm1"]), # done with nm1
instructions.PushGotoOp(recur2, enter_fib),
])
recur2.assign_instructions([
instructions.push_op(["ans"], ["fibm1"]), # ...
instructions.PopOp(["ans"]), # pop callee's "ans"
instructions.prim_op(["n"], "nm2", lambda n: n - 2), # nm2 = n - 2
instructions.PopOp(["n"]), # done with n
instructions.push_op(["nm2"], ["n"]), # fibm2 = fibonacci(nm2)
instructions.PopOp(["nm2"]), # done with nm2
instructions.PushGotoOp(recur3, enter_fib),
])
recur3.assign_instructions([
instructions.push_op(["ans"], ["fibm2"]), # ...
instructions.PopOp(["ans"]), # pop callee's "ans"
instructions.prim_op(["fibm1", "fibm2"], "ans",
lambda x, y: x + y), # ans = fibm1 + fibm2
instructions.PopOp(["fibm1", "fibm2"]), # done with fibm1, fibm2
instructions.IndirectGotoOp(), # return ans
])
finish.assign_instructions([ # else:
instructions.PopOp(["n", "cond"]), # done with n, cond
instructions.prim_op([], "ans", lambda: 1), # ans = 1
instructions.IndirectGotoOp(), # return ans
])
fibonacci_blocks = [entry, enter_fib, recur1, recur2, recur3, finish]
# pylint: disable=bad-whitespace
fibonacci_vars = {
"n": instructions.single_type(np.int64, ()),
"cond": instructions.single_type(np.bool, ()),
"nm1": instructions.single_type(np.int64, ()),
"fibm1": instructions.single_type(np.int64, ()),
"nm2": instructions.single_type(np.int64, ()),
"fibm2": instructions.single_type(np.int64, ()),
"ans": instructions.single_type(np.int64, ()),
}
return instructions.Program(
instructions.ControlFlowGraph(fibonacci_blocks), [], fibonacci_vars,
["n"], "ans")
def lower_function_calls(program):
"""Lowers a `Program` that may have (recursive) FunctionCallOp instructions.
Mutates the `ControlFlowGraph` of the input program in place. After
lowering, the result CFG
- Has no `FunctionCallOp` instructions
- Obeys a stack discipline
What is the stack discipline? Every function body becomes a CFG
subset that:
- Never transfers control in except to the first block
(corresponding to being called), or to a block stored with
`PushGotoOp` (corresponding to a subroutine returning)
- Never transfers control out except with `IndirectGotoOp`
(corresponding to returning), or with a `PushGotoOp`
(corresponding to calling a subroutine)
- Every path through the graph has the following effect on the
variable stacks:
- The formal parameters receive exactly one net pop
- The return variables receive exactly one net push
- All other variable stacks are left as they are
- No data is read except the top frames of the formal parameter
stacks
Why mutate in place? Because tying the knot in the result seemed
too hard without an explicit indirection between `Block`s and
references thereto in various `Op`s. Specifically, when building a
new CFG to replicate the structure of an existing one, it is
necessary to allocate `Block`s to serve as the targets of all
`BranchOp`, `GotoOp` (and `FunctionCallOp`) before building those
`Op`s, and then correctly reuse those `Block`s when processing said
targets. With an explicit indirection, however, it would have been
possible to reuse the same `Label`s, simply creating a new mapping
from them to `Block`s.
Note that the semantics assumed by this transformation is that the
CFGs being transformed do not use variable stacks internally, but
they will only be used to implement the function sequence when
function calls are lowered. This semantics licenses placing
`PopOp`s to enforce a stack discipline for `FunctionCallOp`s.
Args:
program: A `Program` whose function calls to lower. `Block`s in
the program may be mutated.
Returns:
lowered: A `Program` that defines no `Function`s and does not use the
`FunctionCallOp` instruction. May share structure with the input
`program`.
Raises:
ValueError: If an invalid instruction is encountered, if a live
variable is undefined, if different paths into a `Block` cause
different sets of variables to be defined, or if trying to lower
function calls in a program that already has loops (within a
`Function` body) or `IndirectGotoOp` instructions (they confuse
the liveness analysis).
"""
builder = ControlFlowGraphBuilder()
_lower_function_calls_1(builder,
program.graph,
program.vars_in,
inst.pattern_flatten(program.vars_out),
function=False)
for func in program.functions:
_lower_function_calls_1(builder, func.graph, func.vars_in,
inst.pattern_flatten(func.vars_out))
return inst.Program(builder.control_flow_graph(), [], program.var_defs,
program.vars_in, program.vars_out, program.var_alloc)
