def op_mod_group(stage, row, operations_tuple):
lhs, op, mul_index = operations_tuple
comp = "add" if op == "+" else "sub"
comp_index = fresh_comp_index(comp)
group_name = CompVar(f"s{stage}_r{row}_op_mod")
op = CompVar(f"{comp}{comp_index}")
reg = CompVar(f"r{lhs}")
mul = CompVar(f"mult_pipe{mul_index}")
mod_pipe = CompVar(f"mod_pipe{row}")
A = CompVar(f"A{row}")
connections = [
Connect(CompPort(reg, "out"), CompPort(op, "left")),
Connect(CompPort(mul, "out"), CompPort(op, "right")),
Connect(CompPort(op, "out"), CompPort(mod_pipe, "left")),
Connect(ConstantPort(input_bitwidth, q), CompPort(mod_pipe, "right")),
Connect(
ConstantPort(1, 1),
CompPort(mod_pipe, "go"),
Not(Atom(CompPort(mod_pipe, "done"))),
),
Connect(CompPort(mod_pipe, "done"), CompPort(A, "write_en")),
Connect(CompPort(mod_pipe, "out_remainder"), CompPort(A, "in")),
Connect(CompPort(A, "done"), HolePort(group_name, "done")),
]
return Group(group_name, connections)
def epilogue_group(row):
group_name = CompVar(f"epilogue_{row}")
A = CompVar(f"A{row}")
connections = [
Connect(ConstantPort(bitwidth, row), CompPort(input, "addr0")),
Connect(ConstantPort(1, 1), CompPort(input, "write_en")),
Connect(CompPort(A, "out"), CompPort(input, "write_data")),
Connect(CompPort(input, "done"), HolePort(group_name, "done")),
]
return Group(group_name, connections)
def consume_pow(i: int) -> Group:
# Write the output of pow{i} to register p{i}.
reg = CompVar(f"p{i}")
group_name = CompVar(f"consume_pow{i}")
connections = [
Connect(ConstantPort(1, 1), CompPort(reg, "write_en")),
Connect(CompPort(CompVar(f"pow{i}"), "out"), CompPort(reg, "in")),
Connect(
ConstantPort(1, 1),
HolePort(group_name, "done"),
CompPort(reg, "done"),
),
]
return Group(group_name, connections, 1)
def final_multiply(register_id: CompVar) -> List[Group]:
# Multiply e^{fractional_value} * e^{integer_value},
# and write it to register `m`.
group_name = CompVar("final_multiply")
mult_pipe = CompVar("mult_pipe1")
reg = CompVar("m")
return [
Group(
id=group_name,
connections=[
Connect(
CompPort(CompVar("pow1"), "out"),
CompPort(mult_pipe, "left"),
),
Connect(
CompPort(CompVar("sum1"), "out"),
CompPort(mult_pipe, "right"),
),
Connect(
ConstantPort(1, 1),
CompPort(mult_pipe, "go"),
Not(Atom(CompPort(mult_pipe, "done"))),
),
Connect(CompPort(mult_pipe, "done"),
CompPort(reg, "write_en")),
Connect(CompPort(mult_pipe, "out"), CompPort(reg, "in")),
Connect(CompPort(reg, "done"),
HolePort(group_name, "done")),
],
)
]
def emit_eval_body_group(s_idx, stmt, b=None):
"""
Returns a string of a group that implements the body
of stmt, a `map` or `reduce` statement. Adds suffix
at the end of the group name, to avoid name collisions
with other `map` or `reduce` statement group implementations.
If this is a `map` expression, b is the banking factor
of the input array. (Otherwise, b is None.)
"""
bank_suffix = "_b" + str(b) if b is not None else ""
mem_offsets = []
name2arr = dict()
for bi in stmt.op.bind:
idx = 0 if isinstance(stmt.op, ast.Map) else 1
name2arr[bi.dest[idx]] = bi.src
src = CompVar(f"{bi.src}{bank_suffix}")
dest = CompVar(f"idx{bank_suffix}_{s_idx}")
mem_offsets.append(
Connect(CompPort(dest, "out"), CompPort(src, "addr0")))
if isinstance(stmt.op, ast.Map):
src = CompVar(f"{stmt.dest}{bank_suffix}")
dest = CompVar(f"idx{bank_suffix}_{s_idx}")
mem_offsets.append(
Connect(CompPort(dest, "out"), CompPort(src, "addr0")))
compute_left_op = emit_compute_op(stmt.op.body.lhs, stmt.op, stmt.dest,
name2arr, s_idx, bank_suffix)
compute_right_op = emit_compute_op(stmt.op.body.rhs, stmt.op, stmt.dest,
name2arr, s_idx, bank_suffix)
if isinstance(stmt.op, ast.Map):
write_to = CompVar(f"{stmt.dest}{bank_suffix}")
adder_op = CompVar(f"adder_op{bank_suffix}_{s_idx}")
write_connection = Connect(CompPort(adder_op, "out"),
CompPort(write_to, "write_data"))
else:
write_connection = Connect(
CompPort(CompVar(f"adder_op{s_idx}"), "out"),
CompPort(CompVar(f"{stmt.dest}"), "in"),
)
group_id = CompVar(f"eval_body{bank_suffix}_{s_idx}")
adder = CompVar(f"adder_op{bank_suffix}_{s_idx}")
dest = CompVar(f"{stmt.dest}{bank_suffix}")
return Group(
id=group_id,
connections=[
Connect(ConstantPort(1, 1), CompPort(dest, "write_en")),
Connect(compute_left_op, CompPort(adder, "left")),
Connect(compute_right_op, CompPort(adder, "right")),
write_connection,
Connect(CompPort(dest, "done"), HolePort(group_id, "done")),
] + mem_offsets,
)
def preamble_group(row):
reg = CompVar(f"r{row}")
phi = CompVar(f"phi{row}")
group_name = CompVar(f"preamble_{row}")
connections = [
Connect(ConstantPort(bitwidth, row), CompPort(input, "addr0")),
Connect(ConstantPort(bitwidth, row), CompPort(phis, "addr0")),
Connect(ConstantPort(1, 1), CompPort(reg, "write_en")),
Connect(CompPort(input, "read_data"), CompPort(reg, "in")),
Connect(ConstantPort(1, 1), CompPort(phi, "write_en")),
Connect(CompPort(phis, "read_data"), CompPort(phi, "in")),
Connect(
ConstantPort(1, 1),
HolePort(group_name, "done"),
And(Atom(CompPort(reg, "done")), Atom(CompPort(phi, "done"))),
),
]
return Group(group_name, connections)
def precursor_group(row):
group_name = CompVar(f"precursor_{row}")
r = CompVar(f"r{row}")
A = CompVar(f"A{row}")
connections = [
Connect(CompPort(A, "out"), CompPort(r, "in")),
Connect(ConstantPort(1, 1), CompPort(r, "write_en")),
Connect(CompPort(r, "done"), HolePort(group_name, "done")),
]
return Group(group_name, connections)
def emit_idx_group(s_idx, b=None):
"""
Emits a group that increments an index.
If the bank number `b` is not None, adds
it (the bank number) as a suffix to each
cell name.
"""
bank_suffix = "_b" + str(b) + "_" if b is not None else ""
group_id = CompVar(f"incr_idx{bank_suffix}{s_idx}")
adder = CompVar(f"adder_idx{bank_suffix}{s_idx}")
idx = CompVar(f"idx{bank_suffix}{s_idx}")
return Group(
id=group_id,
connections=[
Connect(CompPort(idx, "out"), CompPort(adder, "left")),
Connect(ConstantPort(32, 1), CompPort(adder, "right")),
Connect(ConstantPort(1, 1), CompPort(idx, "write_en")),
Connect(CompPort(adder, "out"), CompPort(idx, "in")),
Connect(CompPort(idx, "done"), HolePort(group_id, "done")),
],
)
def mul_group(stage, mul_tuple):
mul_index, k, phi_index = mul_tuple
group_name = CompVar(f"s{stage}_mul{mul_index}")
mult_pipe = CompVar(f"mult_pipe{mul_index}")
phi = CompVar(f"phi{phi_index}")
reg = CompVar(f"r{k}")
connections = [
Connect(CompPort(phi, "out"), CompPort(mult_pipe, "left")),
Connect(CompPort(reg, "out"), CompPort(mult_pipe, "right")),
Connect(ConstantPort(1, 1), CompPort(mult_pipe, "go")),
Connect(CompPort(mult_pipe, "done"), HolePort(group_name, "done")),
]
return Group(group_name, connections)
def emit_compute_op(exp, op, dest, name2arr, suffix, bank_suffix):
"""
Returns a string containing a Calyx implementation of a MrXL
variable or number (exp). op is the type of operation this
expression is used in. dest is the destination of this expression.
name2arr maps statement variable names to the array names they're
accessing elements of, e.g. if we're binding an element of array
`foo` to a variable `a`, `a` maps to `foo`.
"""
if isinstance(exp, ast.VarExpr):
if isinstance(op, ast.Map):
return CompPort(CompVar(f"{name2arr[exp.name]}{bank_suffix}"),
"read_data")
else:
return CompPort(CompVar(f"{dest}"), "out")
else:
return ConstantPort(32, exp.value)
def emit_cond_group(suffix, arr_size, b=None):
"""
Emits a group that checks if an index has reached
arr_size. If the bank number `b` is not None, adds it
to the end of the index cell name.
suffix is added to the end to the end of each cell,
to disambiguate from other `map` or `reduce` implementations.
"""
bank_suffix = f"_b{b}_" if b is not None else ""
group_id = CompVar(f"cond{bank_suffix}{suffix}")
le = CompVar(f"le{bank_suffix}{suffix}")
idx = CompVar(f"idx{bank_suffix}{suffix}")
return CombGroup(
id=group_id,
connections=[
Connect(CompPort(idx, "out"), CompPort(le, "left")),
Connect(ConstantPort(32, arr_size), CompPort(le, "right")),
],
)
def multiply_by_reciprocal_factorial(i: int) -> Group:
# Multiply register p{i} with the reciprocal factorial.
group_name = CompVar(f"mult_by_reciprocal_factorial{i}")
mult_pipe = CompVar(f"mult_pipe{i}")
reg = CompVar(f"p{i}")
product = CompVar(f"product{i}")
reciprocal = CompVar(f"reciprocal_factorial{i}")
connections = [
Connect(CompPort(reg, "out"), CompPort(mult_pipe, "left")),
Connect(CompPort(reciprocal, "out"), CompPort(mult_pipe, "right")),
Connect(
ConstantPort(1, 1),
CompPort(mult_pipe, "go"),
Not(Atom(CompPort(mult_pipe, "done"))),
),
Connect(CompPort(mult_pipe, "done"), CompPort(product,
"write_en")),
Connect(CompPort(mult_pipe, "out"), CompPort(product, "in")),
Connect(CompPort(product, "done"), HolePort(group_name, "done")),
]
return Group(group_name, connections)
def generate_groups(degree: int, width: int, int_width: int,
is_signed: bool) -> List[Structure]:
frac_width = width - int_width
input = CompVar("exponent_value")
init = Group(
id=CompVar("init"),
connections=[
Connect(ConstantPort(1, 1), CompPort(input, "write_en")),
Connect(ThisPort(CompVar("x")), CompPort(input, "in")),
Connect(CompPort(input, "done"), HolePort(CompVar("init"),
"done")),
],
static_delay=1,
)
if is_signed:
mult_pipe = CompVar("mult_pipe1")
negate = Group(
id=CompVar("negate"),
connections=[
Connect(CompPort(input, "out"), CompPort(mult_pipe, "left")),
Connect(
CompPort(CompVar("negative_one"), "out"),
CompPort(mult_pipe, "right"),
),
Connect(
ConstantPort(1, 1),
CompPort(mult_pipe, "go"),
Not(Atom(CompPort(mult_pipe, "done"))),
),
Connect(CompPort(mult_pipe, "done"),
CompPort(input, "write_en")),
Connect(CompPort(mult_pipe, "out"), CompPort(input, "in")),
Connect(CompPort(input, "done"),
HolePort(CompVar("negate"), "done")),
],
)
# Initialization: split up the value `x` into its integer and fractional
# values.
split_bits = Group(
id=CompVar("split_bits"),
connections=[
Connect(
CompPort(CompVar("exponent_value"), "out"),
CompPort(CompVar("and0"), "left"),
),
Connect(
ConstantPort(width, 2**width - 2**frac_width),
CompPort(CompVar("and0"), "right"),
),
Connect(
CompPort(CompVar("and0"), "out"),
CompPort(CompVar("rsh"), "left"),
),
Connect(
ConstantPort(width, frac_width),
CompPort(CompVar("rsh"), "right"),
),
Connect(
CompPort(CompVar("exponent_value"), "out"),
CompPort(CompVar("and1"), "left"),
),
Connect(
ConstantPort(width, (2**frac_width) - 1),
CompPort(CompVar("and1"), "right"),
),
Connect(
ConstantPort(1, 1),
CompPort(CompVar("int_x"), "write_en"),
),
Connect(
ConstantPort(1, 1),
CompPort(CompVar("frac_x"), "write_en"),
),
Connect(
CompPort(CompVar("rsh"), "out"),
CompPort(CompVar("int_x"), "in"),
),
Connect(
CompPort(CompVar("and1"), "out"),
CompPort(CompVar("frac_x"), "in"),
),
Connect(
ConstantPort(1, 1),
HolePort(CompVar("split_bits"), "done"),
And(
Atom(CompPort(CompVar("int_x"), "done")),
Atom(CompPort(CompVar("frac_x"), "done")),
),
),
],
)
def consume_pow(i: int) -> Group:
# Write the output of pow{i} to register p{i}.
reg = CompVar(f"p{i}")
group_name = CompVar(f"consume_pow{i}")
connections = [
Connect(ConstantPort(1, 1), CompPort(reg, "write_en")),
Connect(CompPort(CompVar(f"pow{i}"), "out"), CompPort(reg, "in")),
Connect(
ConstantPort(1, 1),
HolePort(group_name, "done"),
CompPort(reg, "done"),
),
]
return Group(group_name, connections, 1)
def multiply_by_reciprocal_factorial(i: int) -> Group:
# Multiply register p{i} with the reciprocal factorial.
group_name = CompVar(f"mult_by_reciprocal_factorial{i}")
mult_pipe = CompVar(f"mult_pipe{i}")
reg = CompVar(f"p{i}")
product = CompVar(f"product{i}")
reciprocal = CompVar(f"reciprocal_factorial{i}")
connections = [
Connect(CompPort(reg, "out"), CompPort(mult_pipe, "left")),
Connect(CompPort(reciprocal, "out"), CompPort(mult_pipe, "right")),
Connect(
ConstantPort(1, 1),
CompPort(mult_pipe, "go"),
Not(Atom(CompPort(mult_pipe, "done"))),
),
Connect(CompPort(mult_pipe, "done"), CompPort(product,
"write_en")),
Connect(CompPort(mult_pipe, "out"), CompPort(product, "in")),
Connect(CompPort(product, "done"), HolePort(group_name, "done")),
]
return Group(group_name, connections)
def final_multiply(register_id: CompVar) -> List[Group]:
# Multiply e^{fractional_value} * e^{integer_value},
# and write it to register `m`.
group_name = CompVar("final_multiply")
mult_pipe = CompVar("mult_pipe1")
reg = CompVar("m")
return [
Group(
id=group_name,
connections=[
Connect(
CompPort(CompVar("pow1"), "out"),
CompPort(mult_pipe, "left"),
),
Connect(
CompPort(CompVar("sum1"), "out"),
CompPort(mult_pipe, "right"),
),
Connect(
ConstantPort(1, 1),
CompPort(mult_pipe, "go"),
Not(Atom(CompPort(mult_pipe, "done"))),
),
Connect(CompPort(mult_pipe, "done"),
CompPort(reg, "write_en")),
Connect(CompPort(mult_pipe, "out"), CompPort(reg, "in")),
Connect(CompPort(reg, "done"),
HolePort(group_name, "done")),
],
)
]
if is_signed:
# Take the reciprocal, since the initial value was -x.
div_pipe = CompVar("div_pipe")
input = CompVar("m")
reciprocal = Group(
id=CompVar("reciprocal"),
connections=[
Connect(CompPort(CompVar("one"), "out"),
CompPort(div_pipe, "left")),
Connect(CompPort(input, "out"), CompPort(div_pipe, "right")),
Connect(
ConstantPort(1, 1),
CompPort(div_pipe, "go"),
Not(Atom(CompPort(div_pipe, "done"))),
),
Connect(CompPort(div_pipe, "done"),
CompPort(input, "write_en")),
Connect(CompPort(div_pipe, "out_quotient"),
CompPort(input, "in")),
Connect(CompPort(input, "done"),
HolePort(CompVar("reciprocal"), "done")),
],
)
is_negative = CombGroup(id=CompVar("is_negative"),
connections=[
Connect(ThisPort(CompVar("x")),
CompPort(CompVar("lt"), "left")),
Connect(ConstantPort(width, 0),
CompPort(CompVar("lt"), "right")),
])
# Connect final value to the `out` signal of the component.
output_register = CompVar("m")
out = [Connect(CompPort(output_register, "out"), ThisPort(CompVar("out")))]
return (
[init, split_bits] +
([negate, is_negative, reciprocal] if is_signed else []) +
[consume_pow(j) for j in range(2, degree + 1)] +
[multiply_by_reciprocal_factorial(k)
for k in range(2, degree + 1)] + divide_and_conquer_sums(degree) +
final_multiply(output_register) + out)
def divide_and_conquer_sums(degree: int) -> List[Structure]:
"""Returns a list of groups for the sums.
This is done by dividing the groups into
log2(N) different rounds, where N is the `degree`.
These rounds can then be executed in parallel.
For example, with N == 4, we will produce groups:
group sum_round1_1 { ... } # x p2 p3 p4
# \ / \ /
group sum_round1_2 { ... } # sum1 sum2
# \ /
group sum_round2_1 { ... } # sum1
group add_degree_zero { ... } # sum1 + 1
"""
groups = []
sum_count = degree
round = 1
while sum_count > 1:
indices = [i for i in range(1, sum_count + 1)]
register_indices = [(lhs, rhs) for lhs, rhs in zip(
list(filter(lambda x: (x % 2 != 0), indices)),
list(filter(lambda x: (x % 2 == 0), indices)),
)]
for i, (lhs, rhs) in enumerate(register_indices):
group_name = CompVar(f"sum_round{round}_{i + 1}")
adder = CompVar(f"add{i + 1}")
# The first round will accrue its operands
# from the previously calculated products.
register_name = "product" if round == 1 else "sum"
reg_lhs = CompVar(f"{register_name}{lhs}")
reg_rhs = CompVar(f"{register_name}{rhs}")
sum = CompVar(f"sum{i + 1}")
# In the first round and first group, we add the 1st degree, the
# value `x` itself.
lhs = (CompPort(CompVar("frac_x"), "out")
if round == 1 and i == 0 else CompPort(reg_lhs, "out"))
connections = [
Connect(lhs, CompPort(adder, "left")),
Connect(CompPort(reg_rhs, "out"), CompPort(adder, "right")),
Connect(ConstantPort(1, 1), CompPort(sum, "write_en")),
Connect(CompPort(adder, "out"), CompPort(sum, "in")),
Connect(CompPort(sum, "done"), HolePort(group_name, "done")),
]
groups.append(Group(group_name, connections, 1))
sum_count >>= 1
round = round + 1
# Sums the 0th degree value, 1, and the final
# sum of the divide-and-conquer.
group_name = CompVar("add_degree_zero")
adder = CompVar("add1")
reg = CompVar("sum1")
groups.append(
Group(
id=group_name,
connections=[
Connect(CompPort(reg, "out"), CompPort(adder, "left")),
Connect(
CompPort(CompVar("one"), "out"),
CompPort(adder, "right"),
),
Connect(ConstantPort(1, 1), CompPort(reg, "write_en")),
Connect(CompPort(adder, "out"), CompPort(reg, "in")),
Connect(CompPort(reg, "done"), HolePort(group_name, "done")),
],
static_delay=1,
))
return groups
def generate_fp_pow_component(width: int, int_width: int,
is_signed: bool) -> Component:
"""Generates a fixed point `pow` component, which
computes the value x**y, where y must be an integer.
"""
stdlib = Stdlib()
frac_width = width - int_width
pow = CompVar("pow")
count = CompVar("count")
mul = CompVar("mul")
lt = CompVar("lt")
incr = CompVar("incr")
cells = [
Cell(pow, stdlib.register(width)),
Cell(count, stdlib.register(width)),
Cell(
mul,
stdlib.fixed_point_op("mult_pipe",
width,
int_width,
frac_width,
signed=is_signed),
),
Cell(lt, stdlib.op("lt", width, signed=is_signed)),
Cell(incr, stdlib.op("add", width, signed=is_signed)),
]
wires = [
Group(
id=CompVar("init"),
connections=[
Connect(
ConstantPort(
width,
numeric_types.FixedPoint(
"1.0", width, int_width,
is_signed=is_signed).unsigned_integer(),
),
CompPort(pow, "in"),
),
Connect(ConstantPort(1, 1), CompPort(pow, "write_en")),
Connect(ConstantPort(width, 0), CompPort(count, "in")),
Connect(ConstantPort(1, 1), CompPort(count, "write_en")),
Connect(
ConstantPort(1, 1),
HolePort(CompVar("init"), "done"),
And(
Atom(CompPort(pow, "done")),
Atom(CompPort(count, "done")),
),
),
],
),
Group(
id=CompVar("execute_mul"),
connections=[
Connect(ThisPort(CompVar("base")), CompPort(mul, "left")),
Connect(CompPort(pow, "out"), CompPort(mul, "right")),
Connect(
ConstantPort(1, 1),
CompPort(mul, "go"),
Not(Atom(CompPort(mul, "done"))),
),
Connect(CompPort(mul, "done"), CompPort(pow, "write_en")),
Connect(CompPort(mul, "out"), CompPort(pow, "in")),
Connect(
CompPort(pow, "done"),
HolePort(CompVar("execute_mul"), "done"),
),
],
),
Group(
id=CompVar("incr_count"),
connections=[
Connect(ConstantPort(width, 1), CompPort(incr, "left")),
Connect(CompPort(count, "out"), CompPort(incr, "right")),
Connect(CompPort(incr, "out"), CompPort(count, "in")),
Connect(ConstantPort(1, 1), CompPort(count, "write_en")),
Connect(
CompPort(count, "done"),
HolePort(CompVar("incr_count"), "done"),
),
],
),
CombGroup(
id=CompVar("cond"),
connections=[
Connect(CompPort(count, "out"), CompPort(lt, "left")),
Connect(ThisPort(CompVar("integer_exp")),
CompPort(lt, "right")),
],
),
Connect(CompPort(CompVar("pow"), "out"), ThisPort(CompVar("out"))),
]
return Component(
"fp_pow",
inputs=[
PortDef(CompVar("base"), width),
PortDef(CompVar("integer_exp"), width),
],
outputs=[PortDef(CompVar("out"), width)],
structs=cells + wires,
controls=SeqComp([
Enable("init"),
While(
CompPort(lt, "out"),
CompVar("cond"),
ParComp([Enable("execute_mul"),
Enable("incr_count")]),
),
]),
)
Cell(CompVar("t"),
Stdlib().register(width)),
Cell(CompVar("x"),
Stdlib().mem_d1(width, 1, 1),
is_external=True),
Cell(
CompVar("ret"),
Stdlib().mem_d1(width, 1, 1),
is_external=True,
),
Cell(CompVar("e"), CompInst("exp", [])),
Group(
id=CompVar("init"),
connections=[
Connect(
ConstantPort(1, 0),
CompPort(CompVar("x"), "addr0"),
),
Connect(
CompPort(CompVar("x"), "read_data"),
CompPort(CompVar("t"), "in"),
),
Connect(
ConstantPort(1, 1),
CompPort(CompVar("t"), "write_en"),
),
Connect(
CompPort(CompVar("t"), "done"),
HolePort(CompVar("init"), "done"),
),
],