def lookup_table_for_inputs_to_negative_constraint(self, function_name,
input_values_set):
"""Translate look-up table to negative constraint for specific inputs.
"""
lookup_table = self.lookup_table_for_function(function_name)
constraint = lambda f: z3p.Or([
z3p.Neq(f(*input_values), output_value)
for input_values, output_value in lookup_table.items()
if set(input_values) in input_values_set
])
return constraint
def lookup_table_to_negative_constraint(self, function_name):
"""Translate look-up table to negative constraint.
Given input variables as z3 variables, translate look-up table
to a constraint that guarantees that the same look-up table will not
be a solution.
"""
lookup_table = self.lookup_table_for_function(function_name)
constraint = lambda f: z3p.Or([
z3p.Neq(f(*input_values), output_value)
for input_values, output_value in lookup_table.items()
])
return constraint
def receiver():
forward_output_channel = z3p.Array('forward_output_channel', z3p.IntSort(),
z3p.IntSort())
backward_input_channel = z3p.Int('backward_input_channel')
receive = z3p.Int('receive')
input_tag = z3p.Int('receiver_tag')
input_data = z3p.Int('receiver_data')
expected_tag = z3p.Int('expected_tag')
transitions = []
transitions.append(
('t0', 'initial', forward_output_channel, z3p.BoolVal(True),
[(input_tag, forward_output_channel[0]),
(input_data, forward_output_channel[1])], 'q0'))
transitions.append(
('t1', 'q0', receive, [input_data], z3p.Eq(input_tag,
expected_tag), [], 'q1'))
transitions.append(
('t2', 'q1', backward_input_channel, [expected_tag],
z3p.BoolVal(True), [(expected_tag,
z3p.If(z3p.Eq(expected_tag, 0), z3p.IntVal(1),
z3p.IntVal(0)))], 'initial'))
transitions.append(('t3', 'q0', z3p.Neq(input_tag,
expected_tag), [], 'q2'))
transitions.append(
('t4', 'q2', backward_input_channel,
[z3p.If(z3p.Eq(expected_tag, 0), z3p.IntVal(1),
z3p.IntVal(0))], z3p.BoolVal(True), [], 'initial'))
return automaton.SymbolicAutomaton(
'receiver', ['initial', 'q0', 'q1', 'q2'],
'initial',
transitions,
input_channels=[forward_output_channel],
output_channels=[receive, backward_input_channel],
variables=[input_tag, input_data, expected_tag],
initial_values=[z3p.IntVal(0),
z3p.IntVal(0),
z3p.IntVal(0)],
variable_ranges={
input_tag: (0, 1),
input_data: (min_value_message, max_value_message),
expected_tag: (0, 1)
},
output_channel_ranges={
receive: (min_value_message, max_value_message),
backward_input_channel: (0, 1)
},
justice=['t3', 't1'])
def guard_enabled(self, state, guard, verbose=0):
if guard.decl().name().startswith('table'):
conditional = self.tables[guard.decl().name()]
expression = z3p.BoolVal(False)
for condition, result in conditional:
expression = z3p.Or(expression, condition if z3p.is_true(result) else z3p.BoolVal(False))
guard = expression
guard_evaluated = util.evaluate_expression(guard, {}, state, self.tables)
if verbose > 0:
print 'Evaluated guard is {}'.format(guard_evaluated)
print 'Simplified guard is {}'.format(z3p.simplify(guard_evaluated))
s = z3p.Solver()
s.add(z3p.Neq(guard_evaluated, True))
if s.check() == z3p.unsat:
return True
else:
return False
def sender():
transitions = []
input_message = z3p.Int('sender_input_message')
sender_tag = z3p.Int('sender_tag')
ack_tag = z3p.Int('ack_tag')
forward_input_channel = z3p.Array('forward_input_channel', z3p.IntSort(),
z3p.IntSort())
backward_output_channel = z3p.Int('backward_output_channel')
send = z3p.Int('send')
timeout = util.new_variable('timeout', 'unit')
transitions.append(('t0', 'initial', send, z3p.BoolVal(True),
[(input_message, send)], 'q0'))
transitions.append(
('t1', 'q0', forward_input_channel, [sender_tag, input_message],
z3p.BoolVal(True), [], 'q1'))
transitions.append(('t2', 'q1', timeout, z3p.BoolVal(True), [], 'q0'))
transitions.append(('t3', 'q1', backward_output_channel, z3p.BoolVal(True),
[(ack_tag, backward_output_channel)], 'q2'))
transitions.append(('t4', 'q2', z3p.Eq(ack_tag, sender_tag), [
(sender_tag, z3p.If(z3p.Eq(sender_tag, 0), z3p.IntVal(1),
z3p.IntVal(0)))
], 'initial'))
transitions.append(('t5', 'q2', z3p.Neq(ack_tag, sender_tag), [], 'q0'))
return automaton.SymbolicAutomaton(
'sender', ['initial', 'q0', 'q1', 'q2'],
'initial',
transitions,
variables=[input_message, sender_tag, ack_tag],
initial_values=[z3p.IntVal(0),
z3p.IntVal(0),
z3p.IntVal(0)],
input_channels=[send, timeout, backward_output_channel],
output_channels=[forward_input_channel],
variable_ranges={
input_message: (min_value_message, max_value_message),
sender_tag: (0, 1),
ack_tag: (0, 1)
},
output_channel_ranges={
forward_input_channel[1]: (min_value_message, max_value_message),
forward_input_channel[0]: (0, 1)
})
def safety_monitor():
safety_data_sent = z3p.Int('safety_data_sent')
safety_data_received = z3p.Int('safety_data_received')
variable_ranges = {
safety_data_sent: (min_value_message, max_value_message),
safety_data_received: (min_value_message, max_value_message)
}
send = z3p.Int('send')
receive = z3p.Int('receive')
transitions = []
transitions.append(('t0', 'waiting_for_send', send, z3p.BoolVal(True),
[(safety_data_sent, send)], 'waiting_for_receive'))
transitions.append(
('t1', 'waiting_for_receive', receive, z3p.BoolVal(True),
[(safety_data_received, receive)], 'check_received_data'))
transitions.append(('t2', 'check_received_data',
z3p.Neq(safety_data_sent,
safety_data_received), [], 'error'))
transitions.append(('t3', 'check_received_data',
z3p.Eq(safety_data_sent,
safety_data_received), [], 'waiting_for_send'))
transitions.append(
('t4', 'waiting_for_send', receive, z3p.BoolVal(True), [], 'error'))
transitions.append(
('t5', 'waiting_for_receive', send, z3p.BoolVal(True), [], 'error'))
transitions.append(('t6', 'error', send, z3p.BoolVal(True), [], 'error'))
transitions.append(
('t6', 'error', receive, z3p.BoolVal(True), [], 'error'))
return automaton.SymbolicAutomaton(
'safety_monitor', [
'waiting_for_send', 'waiting_for_receive', 'error',
'check_received_data'
],
'waiting_for_send',
transitions, [safety_data_sent, safety_data_received],
[z3p.IntVal(0), z3p.IntVal(0)],
input_channels=[send, receive],
variable_ranges=variable_ranges)
def environment(cache_id, directory_id, address_id, num_values):
transitions = []
variables = []
variable_ranges = {}
PendingStore = z3p.Int('pending_store_environment_{}_{}_{}'.format(cache_id, directory_id, address_id))
StoreResult = z3p.Int('store_result_{}_{}_{}'.format(cache_id, directory_id, address_id))
variable_ranges[PendingStore] = (0, num_values - 1)
variable_ranges[StoreResult] = (0, num_values - 1)
variables = [PendingStore, StoreResult]
initial_values = [ZERO, ZERO]
locations = ['Env{}_Initial'.format(cache_id),
'Env{}_PendingLD'.format(cache_id),
'Env{}_PendingST'.format(cache_id),
'Env{}_PendingEV'.format(cache_id),
'Env{}_Error'.format(cache_id)]
# input messages
suffix = '_{}_{}_{}'.format(cache_id, directory_id, address_id)
LDAckMsg = z3p.Int('LDAckMsg' + suffix)
STAckMsg = z3p.Int('STAckMsg' + suffix)
EVAckMsg = util.new_variable('EVAckMsg' + suffix, 'unit')
input_channels = [LDAckMsg, STAckMsg, EVAckMsg]
# input_channels = [LDAckMsg]
LDMsg = util.new_variable('LDMsg' + suffix, 'unit')
STMsg = z3p.Int('STMsg' + suffix)
EVMsg = util.new_variable('EVMsg' + suffix, 'unit')
output_channels = [LDMsg, STMsg, EVMsg]
# output_channels = [LDMsg]
transitions = []
# // Load flow
# Env_Initial send LDMsg[c][d][a] {} -> Env_PendingLD;
# Env_PendingLD on LDAckMsg[c][d][a] (v) {} -> Env_Initial;
transitions.append((None, 'Env{}_Initial'.format(cache_id), LDMsg, [ZERO], TRUE, [], 'Env{}_PendingLD'.format(cache_id)))
transitions.append((None, 'Env{}_PendingLD'.format(cache_id), LDAckMsg, TRUE, [(PendingStore, LDAckMsg)], 'Env{}_Initial'.format(cache_id)))
# // Store flow
# foreach v in ValueType
# Env_Initial send STMsg[c][d][a] (v) { PendingStore := v; } -> Env_PendingST;
# Env_PendingST on STAckMsg[c][d][a]
# if (v = PendingStore) {} -> Env_Initial;
# if (v != PendingStore) {} -> Env_Error;
for v in range(num_values):
transitions.append((None, 'Env{}_Initial'.format(cache_id), STMsg, [z3p.IntVal(v)], TRUE, [(PendingStore, z3p.IntVal(v))], 'Env{}_PendingST'.format(cache_id)))
transitions.append((None, 'Env{}_PendingST'.format(cache_id), STAckMsg, TRUE, [(StoreResult, STAckMsg)], 'Env{}_PendingST2'.format(cache_id)))
transitions.append((None, 'Env{}_PendingST2'.format(cache_id), z3p.Eq(StoreResult, PendingStore), [(StoreResult, ZERO), (PendingStore, ZERO)], 'Env{}_Initial'.format(cache_id)))
transitions.append((None, 'Env{}_PendingST2'.format(cache_id), z3p.Neq(StoreResult, PendingStore), [(StoreResult, ZERO), (PendingStore, ZERO)], 'Env{}_Error'.format(cache_id)))
# // Evict flow
# Env_Initial send EVMsg[c][d][a] {} -> Env_PendingEV;
# Env_PendingEV on EVAckMsg[c][d][a] {} -> Env_Initial;
transitions.append((None, 'Env{}_Initial'.format(cache_id), EVMsg, [ZERO], TRUE, [], 'Env{}_PendingEV'.format(cache_id)))
transitions.append((None, 'Env{}_PendingEV'.format(cache_id), EVAckMsg, TRUE, [], 'Env{}_Initial'.format(cache_id)))
locations.extend(['Env{}_PendingST2'.format(cache_id)])
return automaton.SymbolicAutomaton('enviroment_{}_{}_{}'.format(cache_id, directory_id, address_id),
locations,
'Env{}_Initial'.format(cache_id),
transitions,
variables=variables,
initial_values=initial_values,
input_channels=input_channels,
output_channels=output_channels,
variable_ranges=variable_ranges)
def cache(c, num_caches=1, num_values=1, num_addresses=1, num_directories=1):
transitions = []
variables = []
variable_ranges = {}
DataBlk = z3p.Int('DataBlk_{}'.format(c))
AckCounter = z3p.Int('AckCounter_{}'.format(c))
PendingWrite = z3p.Int('PendingWrite_{}'.format(c))
FwdToCache = z3p.Int('FwdToCache_{}'.format(c))
NumAcksTemp = z3p.Int('NumAcksTemp_{}'.format(c))
variable_ranges = {DataBlk: (0, num_values - 1),
AckCounter: (-num_caches, num_caches),
PendingWrite: (0, num_values - 1),
FwdToCache: (0, num_caches - 1),
NumAcksTemp: (0, num_caches)}
variables = [DataBlk, AckCounter, PendingWrite, FwdToCache, NumAcksTemp]
initial_values = [ZERO, ZERO, ZERO, ZERO, ZERO]
# ??? initial_values
# input messages
input_channels = []
for d in range(num_directories):
for a in range(num_addresses):
input_channels.extend([LDMsg[c][d][a], STMsg[c][d][a], EVMsg[c][d][a], FwdGetXMsgP[c][d][a], FwdGetSMsgP[c][d][a], DataMsgD2CP[c][d][a], WBAckMsgP[c][d][a]])
for c2 in range(num_caches):
if c2 != c:
for d in range(num_directories):
for a in range(num_addresses):
input_channels.extend([DataMsgC2CP[c2][c][d][a], InvAckMsgP[c2][c][d][a]])
# output messages
output_channels = []
for d in range(num_directories):
for a in range(num_addresses):
output_channels.extend([LDAckMsg[c][d][a], STAckMsg[c][d][a], EVAckMsg[c][d][a], UnblockSMsg[c][d][a], UnblockEMsg[c][d][a], GetXMsg[c][d][a], GetSMsg[c][d][a], WBMsg[c][d][a]])
for c2 in range(num_caches):
if c2 != c:
output_channels.extend([DataMsgC2C[c][c2][d][a], InvAckMsg[c][c2][d][a]])
for d in range(num_directories):
for a in range(num_addresses):
# // Transitions from I for Ext events
# C_I on LDMsg[c][d][a] {} -> send GetSMsg[c][d][a] {} -> C_IS;
# C_I on STMsg[c][d][a] (v) { PendingWrite := v; } ->
# send GetXMsg[c][d][a] {} -> C_IM;
# C_I on EVMsg[c][d][a] {} -> send EVAckMsg[c][d][a] -> C_I;
transitions.append((None, 'C_I', LDMsg[c][d][a], TRUE, [], 'C_I2'))
transitions.append((None, 'C_I2', GetSMsg[c][d][a], [], TRUE, [], 'C_IS'))
transitions.append((None, 'C_I', STMsg[c][d][a], TRUE, [(PendingWrite, STMsg[c][d][a])], 'C_I3'))
transitions.append((None, 'C_I3', GetXMsg[c][d][a], [], TRUE, [], 'C_IM'))
transitions.append((None, 'C_I', EVMsg[c][d][a], TRUE, [], 'C_I4'))
transitions.append((None, 'C_I4', EVAckMsg[c][d][a], [], TRUE, [], 'C_I'))
# // Transitions for I on Fwd events
# C_I on FwdGetSMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send InvAckMsg[c][FwdToCache][d][a] { FwdToCache := undef; } -> C_I;
transitions.append((None, 'C_I', FwdGetSMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetSMsgP[c][d][a])], 'C_I5'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_I5', InvAckMsg[c][other_c][d][a], [], z3p.Eq(INT(other_c), FwdToCache), [(FwdToCache, ZERO)], 'C_I'))
# // Transitions from S on Ext Events
# C_S on LDMsg[c][d][a] {} -> send LDAckMsg[c][d][a] (DataBlk) -> C_S;
transitions.append((None, 'C_S', LDMsg[c][d][a], TRUE, [], 'C_S2'))
transitions.append((None, 'C_S2', LDAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_S'))
# C_S on STMsg[c][d][a] (v) { PendingWrite := v; } ->
# send GetXMsg[c][d][a] {} -> C_SM;
transitions.append((None, 'C_S', STMsg[c][d][a], TRUE, [(PendingWrite, STMsg[c][d][a])], 'C_S3'))
transitions.append((None, 'C_S3', GetXMsg[c][d][a], [], TRUE, [], 'C_SM'))
# C_S on EVMsg[c][d][a] {} ->
# send EVAckMsg[c][d][a] { DataBlk := undef; } -> C_I;
transitions.append((None, 'C_S', EVMsg[c][d][a], TRUE, [], 'C_S4'))
transitions.append((None, 'C_S4', EVAckMsg[c][d][a], [], TRUE, [(DataBlk, ZERO)], 'C_I'))
# // Transitions from S on Fwd events
# C_S on FwdGetXMsg[c][d][a] (c2) { FwdToCache := c2; } ->
# send InvAckMsg[c][FwdToCache][d][a] { DataBlk := undef } -> C_I;
transitions.append((None, 'C_S', FwdGetXMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetXMsgP[c][d][a]), (DataBlk, ZERO)], 'C_S5'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_S5', InvAckMsg[c][other_c][d][a], [], z3p.Eq(z3p.IntVal(other_c), FwdToCache), [(FwdToCache, ZERO)], 'C_I'))
# // Transitions from M on Ext events
# C_M on LDMsg[c][d][a] {} -> send LDAckMsg[c][d][a] (DataBlk) {} -> C_M;
transitions.append((None, 'C_M', LDMsg[c][d][a], TRUE, [], 'C_M2'))
transitions.append((None, 'C_M2', LDAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
# C_M on STMsg[c][d][a] (v) { DataBlk := v; } ->
# send STAckMsg[c][d][a] (DataBlk) {} -> C_M;
transitions.append((None, 'C_M', STMsg[c][d][a], TRUE, [(DataBlk, STMsg[c][d][a])], 'C_M3'))
transitions.append((None, 'C_M3', STAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
# C_M on EVMsg[c][d][a] {} -> send WBMsg[c][d][a] (DataBlk) {} -> C_II;
transitions.append((None, 'C_M', EVMsg[c][d][a], TRUE, [], 'C_M4'))
transitions.append((None, 'C_M4', WBMsg[c][d][a], [DataBlk], TRUE, [], 'C_II'))
# // Transitions from M on Fwd events
# C_M on FwdGetSMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send DataMsgC2C[c][FwdToCache][d][a] (DataBlk) { FwdToCache := undef; } -> C_S;
transitions.append((None, 'C_M', FwdGetSMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetSMsgP[c][d][a])], 'C_M5'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_M5', DataMsgC2C[c][other_c][d][a], [DataBlk], z3p.Eq(z3p.IntVal(other_c), FwdToCache), [(FwdToCache, ZERO)], 'C_S'))
# C_M on FwdGetXMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send DataMsgC2C[c][FwdToCache][d][a] (DataBlk)
# { FwdToCache := undef; DataBlk := undef; } -> C_I;
transitions.append((None, 'C_M', FwdGetXMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetXMsgP[c][d][a])], 'C_M6'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_M6', DataMsgC2C[c][other_c][d][a], [DataBlk], z3p.Eq(z3p.IntVal(other_c), FwdToCache), [(FwdToCache, ZERO), (DataBlk, ZERO)], 'C_I'))
# // Transitions from C_IM on Rsp Events
# C_IM on FwdGetXMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send InvAckMsg[c][FwdToCache][d][a] {FwdToCache := undef; } -> C_IM;
transitions.append((None, 'C_IM', FwdGetXMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetXMsgP[c][d][a])], 'C_IM2'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_IM2', InvAckMsg[c][other_c][d][a], [DataBlk], z3p.Eq(INT(other_c), FwdToCache), [(FwdToCache, ZERO)], 'C_IM'))
# // Case when another cache gives me data
# foreach c2 in CacheIDType (!= c2 c) {
# C_IM on DataMsgC2C'[c2][c][d][a] (v) { DataBlk := v; } -> C_M;
# }
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_IM', DataMsgC2CP[other_c][c][d][a], TRUE, [(DataBlk, DataMsgC2CP[other_c][c][d][a])], 'C_M'))
# // Case when data comes from dir ==> Must wait for acks
# C_IM on DataMsgD2C'[c][d][a] (v, NumAcks)
# if (!= AckCounter NumAcks)
# { AckCounter := (- AckCounter NumAcks); DataBlk := v; } -> C_SM;
# if (= AckCounter NumAcks)
# { AckCounter := 0; DataBlk := v; } ->
# send UnblockEMsg[c][d][a] { DataBlk := PendingStore; PendingStore := undef; } -> C_M;
transitions.append((None, 'C_IM', DataMsgD2CP[c][d][a], TRUE, [(DataBlk, DataMsgD2CP[c][d][a][0]), (NumAcksTemp, DataMsgD2CP[c][d][a][1])], 'C_IM3'))
transitions.append((None, 'C_IM3', z3p.Neq(AckCounter, NumAcksTemp), [(AckCounter, AckCounter - NumAcksTemp), (NumAcksTemp, ZERO)], 'C_SM'))
transitions.append((None, 'C_IM3', z3p.Eq(AckCounter, NumAcksTemp), [(AckCounter, ZERO), (NumAcksTemp, ZERO)], 'C_IM4'))
transitions.append((None, 'C_IM4', STAckMsg[c][d][a], [PendingWrite], TRUE, [(DataBlk, PendingWrite), (PendingWrite, ZERO)], 'C_IM5'))
transitions.append((None, 'C_IM5', UnblockEMsg[c][d][a], [ZERO], TRUE, [], 'C_M'))
# foreach c2 in CacheIDType (!= c2 c) {
# C_IM on InvAckMsg[c2][c][d][a] { AckCounter := (+ AckCounter 1); } -> C_IM;
# }
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_IM', InvAckMsgP[other_c][c][d][a], TRUE, [(AckCounter, AckCounter + 1)], 'C_IM'))
# // Transitions from C_SM on Ext Events
# C_SM on LDMsg[c][d][a] {} -> send LDAckMsg[c][d][a] (DataBlk) {} -> C_SM;
transitions.append((None, 'C_SM', LDMsg[c][d][a], TRUE, [], 'C_SM2'))
transitions.append((None, 'C_SM2', LDAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_SM'))
# // Transitions from C_SM on Rsp Events
# C_SM on FwdGetXMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send InvAckMsg[c][FwdToCache][d][a] {} -> C_SM;
transitions.append((None, 'C_SM', FwdGetXMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetXMsgP[c][d][a])], 'C_SM3'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_SM3', InvAckMsg[c][other_c][d][a], [], z3p.Eq(z3p.IntVal(other_c), FwdToCache), [], 'C_IM'))
# // Case where data comes from dir ==> Must wait for acks
# C_SM on DataMsgD2C'[c][d][a] (v, NumAcks)
transitions.append((None, 'C_SM', DataMsgD2CP[c][d][a], TRUE, [(NumAcksTemp, DataMsgD2CP[c][d][a][1])], 'C_SM4'))
# if (= NumAcks AckCounter) { AckCounter := 0; } ->
# send UnblockEMsg[c][d][a] { DataBlk := PendingStore; PendingStore := undef; } ->
# send STAckMsg[c][d][a] (DataBlk) {} -> C_M;
# if (!= NumAcks AckCounter) { AckCounter := (- AckCounter NumAcks) } -> C_SM;
transitions.append((None, 'C_SM4', UnblockEMsg[c][d][a], [ZERO], z3p.Eq(NumAcksTemp, AckCounter), [(DataBlk, PendingWrite), (PendingWrite, ZERO), (NumAcksTemp, ZERO), (AckCounter, ZERO)], 'C_SM5'))
transitions.append((None, 'C_SM5', STAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
transitions.append((None, 'C_SM4', z3p.Neq(NumAcksTemp, AckCounter), [(AckCounter, AckCounter - NumAcksTemp), (NumAcksTemp, ZERO)], 'C_SM'))
# foreach c2 in CacheIDType (!= c2 c) {
# C_SM on InvAckMsg'[c2][c][d][a]
# if (= AckCounter (- 1)) { AckCounter := 0; } ->
# send UnblockEMsg[c][d][a] { DataBlk := PendingStore; PendingStore := undef; } ->
# send STAckMsg[c][d][a] (DataBlk) {} -> C_M;
# if (!= AckCounter (- 1)) { AckCounter := (+ AckCounter 1); } ->
# send UnblockEMsg[c][d][a] { DataBlk := PendingStore; PendingStore := undef; } ->
# send STAckMsg[c][d][a] (DataBlk) {} -> C_M;
# }
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_SM', InvAckMsgP[other_c][c][d][a], z3p.Eq(AckCounter, -ONE), [(AckCounter, ZERO), (DataBlk, PendingWrite), (PendingWrite, ZERO)], 'C_SM6'))
transitions.append((None, 'C_SM6', UnblockEMsg[c][d][a], [DataBlk], TRUE, [], 'C_SM7'))
transitions.append((None, 'C_SM7', STAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
transitions.append((None, 'C_SM', InvAckMsgP[other_c][c][d][a], z3p.Neq(AckCounter, -ONE), [(AckCounter, AckCounter + 1)], 'C_SM'))
# transitions.append((None, 'C_SM6', UnblockEMsg[c][d][a], [DataBlk], TRUE, [], 'C_SM7'))
# transitions.append((None, 'C_SM7', STAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
# transitions.append((None, 'C_SM', InvAckMsgP[other_c][c][d][a], TRUE, [], 'C_SM6'))
# transitions.append((None, 'C_SM6', UnblockEMsg[c][d][a], [ZERO], z3p.Eq(AckCounter, - ONE), [(AckCounter, ZERO), (DataBlk, PendingWrite), (PendingWrite, ZERO)], 'C_SM6'))
# transitions.append((None, 'C_SM7', STAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
# transitions.append((None, 'C_SM6', UnblockEMsg[c][d][a], [], z3p.Neq(AckCounter, ZERO - ONE), [(AckCounter, AckCounter + 1), (DataBlk, PendingWrite), (PendingWrite, ZERO)], 'C_SM7'))
# transitions.append((None, 'C_SM8', STAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_M'))
# // Transitions from IS on Ext Events
# C_IS on FwdGetXMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send InvAckMsg[c][FwdToCache][d][a] {} -> C_IS;
transitions.append((None, 'C_IS', FwdGetXMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetXMsgP[c][d][a])], 'C_IS2'))
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_IS2', InvAckMsg[c][other_c][d][a], [], z3p.Eq(INT(other_c), FwdToCache), [], 'C_IS'))
# // Transitions on IS on Rsp Events
# C_IS on DataMsgD2C'[c][d][a] (v, _) { DataBlk := v; } ->
# send UnblockSMsg[c][d][a] {} -> send LDAckMsg[c][d][a] (DataBlk) {} -> C_S;
transitions.append((None, 'C_IS', DataMsgD2CP[c][d][a], TRUE, [(DataBlk, DataMsgD2CP[c][d][a][0])], 'C_IS3'))
transitions.append((None, 'C_IS3', UnblockSMsg[c][d][a], [ZERO], TRUE, [], 'C_IS4'))
transitions.append((None, 'C_IS4', LDAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_S'))
# foreach c2 in CacheIDType (!= c2 c) {
# C_IS on DataMsgC2C'[c2][c][d][a] (v) -> { DataBlk := v; } ->
# send UnblockSMsg[c][d][a] -> send LDAckMsg[c][d][a] (DataBlk) -> C_S;
# }
for other_c in range(num_caches):
if other_c != c:
transitions.append((None, 'C_IS', DataMsgC2CP[other_c][c][d][a], TRUE, [(DataBlk, DataMsgC2CP[other_c][c][d][a])], 'C_IS3'))
# transitions.append((None, 'C_IS4', UnblockSMsg[c][d][a], [ZERO], TRUE, [], 'C_IS5'))
# transitions.append((None, 'C_IS5', LDAckMsg[c][d][a], [DataBlk], TRUE, [], 'C_S'))
# // Transitions on II on Rsp Events
# C_II on WBAckMsg'[c][d][a] -> C_I;
# send EVAck and then go to C_I
transitions.append((None, 'C_II', WBAckMsgP[c][d][a], TRUE, [], 'C_II2'))
transitions.append((None, 'C_II2', EVAckMsg[c][d][a], [ZERO], TRUE, [], 'C_I'))
# C_II on FwdGetXMsg'[c][d][a] (c2) { FwdToCache := c2; } ->
# send InvAckMsg[c][FwdToCache][d][a] -> C_I;
transitions.append((None, 'C_II', FwdGetXMsgP[c][d][a], TRUE, [(FwdToCache, FwdGetXMsgP[c][d][a])], 'C_I5'))
# for other_c in range(num_caches):
# if other_c != c:
# transitions.append((None, 'C_II2', InvAckMsg[c][other_c][d][a], [], z3p.Eq(FwdToCache, other_c), [(FwdToCache, ZERO)], 'C_I'))
# C_II on FwdGetSMsg'[c][d][a] (_) -> I;
# }
transitions.append((None, 'C_II', FwdGetSMsgP[c][d][a], TRUE, [], 'C_I'))
locations = ['C_I', 'C_S', 'C_M', 'C_IM', 'C_SM', 'C_IS', 'C_II']
locations.extend(['C_I2', 'C_I3', 'C_I4', 'C_I5'])
locations.extend(['C_S2', 'C_S3', 'C_S4', 'C_S5'])
locations.extend(['C_M2', 'C_M3', 'C_M4', 'C_M5', 'C_M6'])
locations.extend(['C_IM2', 'C_IM3', 'C_IM4', 'C_IM5'])
locations.extend(['C_SM2', 'C_SM3', 'C_SM4', 'C_SM5', 'C_SM6', 'C_SM7', 'C_SM8'])
locations.extend(['C_IS2', 'C_IS3', 'C_IS4']) # , 'C_IS5'])
locations.extend(['C_II2'])
return automaton.SymbolicAutomaton('cache{}'.format(c),
locations,
'C_I',
transitions,
variables=variables,
initial_values=initial_values,
input_channels=input_channels,
output_channels=output_channels,
variable_ranges=variable_ranges)
def directory(d, num_caches=2, num_values=1, num_addresses=1):
transitions = []
variables = []
variable_ranges = {}
DataBlk = z3p.Int('DataBlk')
ActiveId = z3p.Int('ActiveId')
Sharers = {}
for cache_id in range(num_caches):
Sharers[cache_id] = z3p.Int('Sharers_{}'.format(cache_id))
NumSharers = z3p.Int('NumSharers')
Owner = z3p.Int('Owner')
variable_ranges = {DataBlk: (0, num_values - 1),
ActiveId: (0, num_caches - 1),
NumSharers: (0, num_caches),
Owner: (0, num_caches - 1)}
for cache_id in range(num_caches):
variable_ranges[Sharers[cache_id]] = (0, 1)
# Do i need numsharers
variables = [DataBlk, ActiveId, NumSharers, Owner] + [Sharers[cache_id] for cache_id in range(num_caches)]
initial_values = [ZERO, ZERO, ZERO, ZERO] + num_caches * [ZERO]
locations = ['D_I', 'D_S', 'D_M', 'D_BUSY', 'D_DATA', 'D_PENDING_UNBLOCK_E', 'D_BUSY_DATA']
# input messages
input_channels = []
for c in range(num_caches):
for a in range(num_addresses):
input_channels.extend([GetXMsgP[c][d][a], GetSMsgP[c][d][a], WBMsgP[c][d][a], UnblockSMsgP[c][d][a], UnblockEMsgP[c][d][a]])
for other_c in range(num_caches):
if other_c != c:
input_channels.append(DataMsgC2CP[c][other_c][d][a])
output_channels = []
# output messages
for c in range(num_caches):
for a in range(num_addresses):
output_channels.extend([FwdGetXMsg[c][d][a], FwdGetSMsg[c][d][a], DataMsgD2C[c][d][a], WBAckMsg[c][d][a]])
for c in range(num_caches):
for a in range(num_addresses):
# // Transitions from I
# D_I on GetXMsg'[c][d][a] { ActiveId := c; } ->
# send DataMsgD2C[c][d][a] (DataBlk, 0) -> D_BUSY;
target = 'D_I2_{}'.format(c)
transitions.append((None, 'D_I', GetXMsgP[c][d][a], TRUE, [(ActiveId, INT(c))], target))
transitions.append((None, target, DataMsgD2C[c][d][a], [DataBlk, ZERO], TRUE, [], 'D_BUSY'))
locations.append(target)
# D_I on GetSMsg'[c][d][a] { ActiveId := c; } ->
# send DataMsgD2C[c][d][a] (DataBlk, 0) -> D_BUSY;
target = 'D_I3_{}'.format(c)
transitions.append((None, 'D_I', GetSMsgP[c][d][a], TRUE, [(ActiveId, INT(c))], target))
transitions.append((None, target, DataMsgD2C[c][d][a], [DataBlk, ZERO], TRUE, [], 'D_BUSY'))
locations.append(target)
# // Transitions from S
# D_S on GetXMsg'[c][d][a] { ActiveId := c; } ->
# send DataMsgD2C[c][d][a] (DataBlk, NumSharers) {} ->
# foreach c2 in CacheIDType {
# if (Sharers[c2]) send FwdGetXMsg[c2][d][a] (c) {};
# if (not Sharers[c2]) pass {};
# } -> D_BUSY;
target = 'D_S2_{}'.format(c)
target2 = 'D_S3_{}'.format(c)
transitions.append((None, 'D_S', GetXMsgP[c][d][a], TRUE, [(ActiveId, INT(c))], target))
transitions.append((None, target, DataMsgD2C[c][d][a], [DataBlk, NumSharers - 1], z3p.Eq(Sharers[c], ONE), [], target2))
transitions.append((None, target, DataMsgD2C[c][d][a], [DataBlk, NumSharers], z3p.Eq(Sharers[c], ZERO), [], target2))
locations.extend([target, target2])
last_state = 'D_S3_{}'.format(c)
other_caches = [other_c for other_c in range(num_caches) if c != other_c]
for i, other_c in enumerate(other_caches):
if other_c != c:
if i + 1 == len(other_caches):
target = 'D_BUSY'
else:
target = 'D_S3_{}_{}'.format(c, other_c)
source = last_state
transitions.append((None, source, FwdGetXMsg[other_c][d][a], [z3p.IntVal(c)], z3p.Eq(Sharers[other_c], ONE), [], target))
transitions.append((None, source, z3p.Neq(Sharers[other_c], ONE), [], target))
locations.extend([target])
last_state = target
# D_S on GetSMsg'[c][d][a] { ActiveId := c; } ->
# send DataMsgD2C[c][d][a] (DataBlk, 0) {} -> D_BUSY;
target = 'D_S4_{}'.format(c)
transitions.append((None, 'D_S', GetSMsgP[c][d][a], TRUE, [(ActiveId, INT(c))], target))
transitions.append((None, target, DataMsgD2C[c][d][a], [DataBlk, ZERO], TRUE, [], 'D_BUSY'))
locations.append(target)
# // Transitions from M
# D_M on GetXMsg'[c][d][a] { ActiveId := c; } ->
# send FwdGetXMsg[Owner][d][a] (ActiveId) {} -> D_BUSY;
target = 'D_M2_{}'.format(c)
transitions.append((None, 'D_M', GetXMsgP[c][d][a], TRUE, [(ActiveId, INT(c))], target))
for c2 in range(num_caches):
transitions.append((None, target, FwdGetXMsg[c2][d][a], [ActiveId], z3p.Eq(INT(c2), Owner), [], 'D_BUSY'))
locations.append(target)
# D_M on GetSMsg'[c][d][a] { ActiveId := c; } ->
# send FwdGetSMsg[Owner][d][a] (ActiveId) {} -> D_BUSY_DATA;
target = 'D_M3_{}'.format(c)
transitions.append((None, 'D_M', GetSMsgP[c][d][a], TRUE, [(ActiveId, INT(c))], target))
for c2 in range(num_caches):
transitions.append((None, target, FwdGetSMsg[c2][d][a], [ActiveId], z3p.Eq(INT(c2), Owner), [], 'D_BUSY_DATA'))
locations.append(target)
# D_M on WBMsg'[c][d][a] (v) { DataBlk := v; Sharers[c] := false; } ->
# send WBAckMsg[c][d][a] {} -> D_I;
target = 'D_M4_{}'.format(c)
transitions.append((None, 'D_M', WBMsgP[c][d][a], z3p.Eq(Sharers[c], ONE), [(DataBlk, WBMsgP[c][d][a]), (Sharers[c], ZERO), (NumSharers, NumSharers - 1)], target))
# debug
transitions.append((None, 'D_M', WBMsgP[c][d][a], z3p.Neq(Sharers[c], ONE), [(DataBlk, WBMsgP[c][d][a])], target))
transitions.append((None, target, WBAckMsg[c][d][a], [ZERO], TRUE, [(ActiveId, ZERO)], 'D_I'))
locations.append(target)
# // Transitions from BUSY
# D_BUSY on WBMsg'[c][d][a] (v)
# if (= c ActiveId) { DataBlk := v; } -> D_PENDING_UNBLOCK_E;
# if (!= c ActiveId) { Sharers[c] := false; DataBlk := v; } ->
# send DataMsgD2C[ActiveId][d][a] (DataBlk, 0) -> D_BUSY;
transitions.append((None, 'D_BUSY', WBMsgP[c][d][a], z3p.Eq(INT(c), ActiveId), [(DataBlk, WBMsgP[c][d][a])], 'D_PENDING_UNBLOCK_E'))
target = 'D_BUSY2_{}'.format(c)
transitions.append((None, 'D_BUSY', WBMsgP[c][d][a], z3p.And(z3p.Neq(INT(c), ActiveId), z3p.Eq(Sharers[c], ONE)), [(Sharers[c], ZERO), (NumSharers, NumSharers - 1), (DataBlk, WBMsgP[c][d][a])], target))
# debug
transitions.append((None, 'D_BUSY', WBMsgP[c][d][a], z3p.And(z3p.Neq(INT(c), ActiveId), z3p.Eq(Sharers[c], ZERO)), [(DataBlk, WBMsgP[c][d][a])], target))
for c2 in range(num_caches):
transitions.append((None, target, DataMsgD2C[c2][d][a], [DataBlk, ONE], z3p.Eq(INT(c2), ActiveId), [], 'D_BUSY'))
locations.append(target)
# D_BUSY on UnblockEMsg'[c][d][a] { Sharers[c] := true; Owner := c; } -> D_M;
transitions.append((None, 'D_BUSY', UnblockEMsgP[c][d][a], TRUE, [(Sharers[c], ONE), (NumSharers, ONE), (Owner, INT(c)), (ActiveId, ZERO)] + [(Sharers[other_c], ZERO) for other_c in range(num_caches) if other_c != c], 'D_M'))
# D_BUSY on UnblockSMsg'[c][d][a] { Sharers[c] := true; Owner := undef; } -> D_S;
transitions.append((None, 'D_BUSY', UnblockSMsgP[c][d][a], z3p.Eq(Sharers[c], ZERO), [(Sharers[c], ONE), (NumSharers, NumSharers + 1), (Owner, ZERO), (ActiveId, ZERO)], 'D_S'))
# debug
transitions.append((None, 'D_BUSY', UnblockSMsgP[c][d][a], z3p.Eq(Sharers[c], ONE), [(Owner, ZERO), (ActiveId, ZERO)], 'D_S'))
# foreach c2 in CacheIDType (!= c2 c) {
# D_BUSY on DataMsgC2C'[c2][c][d][a] (v) { DataBlk := v; } -> S;
# }
for c2 in range(num_caches):
if c2 != c:
transitions.append((None, 'D_BUSY', DataMsgC2CP[c2][c][d][a], TRUE, [(DataBlk, DataMsgC2CP[c2][c][d][a]), (ActiveId, ZERO)], 'D_S'))
# // Transitions from BUSY_DATA
# D_BUSY_DATA on UnblockSMsg'[c][d][a] { Sharers[c] := true; } -> D_BUSY;
# foreach c2 in CacheIDType (!= c2 c) {
# D_BUSY_DATA on DataMsgC2C'[c2][c][d][a] (v) { DataBlk := v; } -> D_BUSY;
# }
transitions.append((None, 'D_BUSY_DATA', UnblockSMsgP[c][d][a], z3p.Eq(Sharers[c], ZERO), [(Sharers[c], ONE), (NumSharers, NumSharers + 1)], 'D_BUSY'))
# debug
transitions.append((None, 'D_BUSY_DATA', UnblockSMsgP[c][d][a], z3p.Eq(Sharers[c], ONE), [], 'D_BUSY'))
for c2 in range(num_caches):
if c2 != c:
transitions.append((None, 'D_BUSY_DATA', DataMsgC2CP[c2][c][d][a], TRUE, [(DataBlk, DataMsgC2CP[c2][c][d][a])], 'D_BUSY'))
# D_BUSY_DATA on WBMsg'[c][d][a] (v)
# if (= c ActiveId) { DataBlk := v; } -> D_PENDING_UNBLOCK_E;
# if (!= c ActiveId) { Sharers[c] := false; DataBlk := v; } ->
# send DataMsgD2C[ActiveId][d][a] (DataBlk, 0) -> D_BUSY;
transitions.append((None, 'D_BUSY_DATA', WBMsgP[c][d][a], z3p.Eq(z3p.IntVal(c), ActiveId), [(DataBlk, WBMsgP[c][d][a])], 'D_PENDING_UNBLOCK_E'))
target = 'D_BUSY2_{}'.format(c)
transitions.append((None, 'D_BUSY_DATA', WBMsgP[c][d][a], z3p.And(z3p.Neq(z3p.IntVal(c), ActiveId), z3p.Eq(Sharers[c], ONE)), [(Sharers[c], ZERO), (NumSharers, NumSharers - 1), (DataBlk, WBMsgP[c][d][a])], target))
# debug
transitions.append((None, 'D_BUSY_DATA', WBMsgP[c][d][a], z3p.And(z3p.Neq(z3p.IntVal(c), ActiveId), z3p.Eq(Sharers[c], ZERO)), [(DataBlk, WBMsgP[c][d][a])], target))
# for c2 in range(num_caches):
# transitions.append((None, 'D_BUSY_DATA2', DataMsgD2C[c2][a], [DataBlk, ZERO], z3p.Eq(z3p.IntVal(c2), ActiveId), [], 'D_BUSY'))
# // Transitions from PENDING_UNBLOCK_E
# D_PENDING_UNBLOCK_E on UnblockEMsg'[c][d][a] { Sharers[c] := false; Owner := undef; } -> D_I;
target = 'D_PENDING_UNBLOCK_E_{}'.format(c)
transitions.append((None, 'D_PENDING_UNBLOCK_E', UnblockEMsgP[c][d][a], z3p.Eq(Sharers[c], ONE), [(Sharers[c], ZERO), (Owner, ZERO), (NumSharers, NumSharers - 1)], target))
#debug
transitions.append((None, 'D_PENDING_UNBLOCK_E', UnblockEMsgP[c][d][a], z3p.Eq(Sharers[c], ZERO), [], target))
transitions.append((None, target, WBAckMsg[c][d][a], [ZERO], TRUE, [], 'D_I'))
locations.append(target)
return automaton.SymbolicAutomaton('directory',
locations,
'D_I',
transitions,
variables=variables,
initial_values=initial_values,
input_channels=input_channels,
output_channels=output_channels,
variable_ranges=variable_ranges)
def transitions_from_state(self, state1, state2, verbose=0):
possible_transitions = dict([(a, []) for a in self.automata])
possible_channels = dict([(a, set([])) for a in self.automata])
possible_internal_transitions = dict([(a, []) for a in self.automata])
transition_channels = {}
for a in self.automata:
if state1[a] == state2[a]:
possible_transitions[a].append(None)
for t in a.edges(data=True):
if a.can_transition(state1[a], state2[a], t):
possible_transitions[a].append(t)
channel = t[2]['channel']
if channel is None:
possible_internal_transitions[a].append(t)
else:
possible_channels[a].add(channel)
for a in self.automata:
for c in list(possible_channels[a]):
assert c in self.readers, "{} not in {}".format(c, self.readers)
assert c in self.writer, "{} not in {}".format(c, self.writer)
automata = self.readers[c] + [self.writer[c]]
if (any(c not in possible_channels[ap]
for ap in automata) or
any(None not in possible_transitions[ap]
for ap in self.automata if ap not in automata)):
possible_channels[a].remove(c)
if any(len(possible_channels[a]) > 0 for a in self.automata):
c = next(list(possible_channels[a])[0] for a in self.automata
if len(possible_channels[a]) > 0)
if verbose > 0:
print "Checking channel {}".format(c)
for t in possible_transitions[self.writer[c]]:
writer_transition = t
if verbose > 0:
print "Checking writer transition {}".format(t)
if t is not None and t[2]['channel'] == c:
channel_expressions = t[2]['channel_expression']
channel_expression_values = [util.evaluate_expression(channel_expression, {}, state1[self.writer[c]], tables=self.writer[c].tables) for channel_expression in channel_expressions]
if verbose > 0:
print 'Writer tables are {}'.format(self.writer[c].tables)
print 'Channel expressions are {}'.format(channel_expressions)
print 'Channel expression values are {}'.format(channel_expression_values)
reader_transitions = [next(t for t in possible_transitions[a]
if t is not None and t[2]['channel'] == c)
for a in self.readers[c]]
writer_matches_readers = True
for rt in reader_transitions:
if verbose > 0:
print "Checking against reader transition {}".format(rt)
ra = rt[2]['automaton']
updates = rt[2]['update']
for update in updates:
if c in z3p.variables_in_expression(update[1]):
if isinstance(c, z3p.ArrayRef):
selects = util.selects_in_expression(update[1])
new_reader_concrete_memory = dict(state1[ra])
for select in selects:
index = select.arg(1)
new_reader_concrete_memory[c[index]] = channel_expression_values[index.as_long()]
if state2[ra][update[0]] != util.evaluate_expression(update[1], {}, new_reader_concrete_memory):
writer_matches_readers = False
else:
new_reader_concrete_memory = dict(state1[ra])
new_reader_concrete_memory[c] = channel_expression_values[0]
s = z3p.Solver()
s.add(z3p.Neq(state2[ra][update[0]], util.evaluate_expression(update[1], {}, new_reader_concrete_memory)))
if s.check() != z3p.unsat:
if verbose:
print "update does not match {}, {}".format(state2[ra][update[0]], util.evaluate_expression(update[1], {}, new_reader_concrete_memory))
writer_matches_readers = False
if writer_matches_readers:
return [writer_transition] + reader_transitions
else:
for a in self.automata:
other_automata = [ap for ap in self.automata if a != ap]
if (len(possible_internal_transitions[a]) > 0 and
all(None in possible_transitions[ap]
for ap in other_automata)):
return [possible_internal_transitions[a]]