"""Classes and helper functions for PTA and other automata.""" from functions import AnalyticFunction, NormalizationFunction import itertools import numpy as np def _dict_to_list(input_dict: dict) -> list: return [input_dict[x] for x in sorted(input_dict.keys())] def _attribute_to_json(static_value: float, param_function: AnalyticFunction) -> dict: ret = { 'static' : static_value } if param_function: ret['function'] = { 'raw' : param_function._model_str, 'regression_args' : list(param_function._regression_args) } return ret class State: """A single PTA state.""" def __init__(self, name: str, power: float = 0, power_function: AnalyticFunction = None): u""" Create a new PTA state. arguments: name -- state name power -- static state power in µW power_function -- parameterized state power in µW """ self.name = name self.power = power self.power_function = power_function self.outgoing_transitions = {} def add_outgoing_transition(self, new_transition: object): """Add a new outgoing transition.""" self.outgoing_transitions[new_transition.name] = new_transition def get_energy(self, duration: float, param_dict: dict = {}) -> float: u""" Return energy spent in state in pJ. arguments: duration -- duration in µs param_dict -- current parameters """ if self.power_function: return self.power_function.eval(_dict_to_list(param_dict)) * duration return self.power * duration def set_random_energy_model(self, static_model = True): self.power = int(np.random.sample() * 50000) def get_transition(self, transition_name: str) -> object: """Return Transition object for outgoing transtion transition_name.""" return self.outgoing_transitions[transition_name] def has_interrupt_transitions(self) -> bool: """Check whether this state has any outgoing interrupt transitions.""" for trans in self.outgoing_transitions.values(): if trans.is_interrupt: return True return False def get_next_interrupt(self, parameters: dict) -> object: """ Return the outgoing interrupt transition with the lowet timeout. Must only be called if has_interrupt_transitions returned true. arguments: parameters -- current parameter values """ interrupts = filter(lambda x: x.is_interrupt, self.outgoing_transitions.values()) interrupts = sorted(interrupts, key = lambda x: x.get_timeout(parameters)) return interrupts[0] def dfs(self, depth: int, with_arguments: bool = False, trace_filter = None, sleep: int = 0): """ Return a generator object for depth-first search over all outgoing transitions. arguments: depth -- search depth with_arguments -- perform dfs with function+argument transitions instead of just function transitions. trace_filter -- list of lists. Each sub-list is a trace. Only traces matching one of the provided sub-lists are returned. E.g. trace_filter = [['init', 'foo'], ['init', 'bar']] will only return traces with init as first and foo or bar as second element. trace_filter = [['init', 'foo', '$'], ['init', 'bar', '$']] will only return the traces ['init', 'foo'] and ['init', 'bar']. sleep -- if set and non-zero: include sleep pseudo-states with us duration For the [['init', 'foo', '$'], ['init', 'bar', '$']] example above, sleep=10 results in [(None, 10), 'init', (None, 10), 'foo'] and [(None, 10), 'init', (None, 10), 'bar'] """ # A '$' entry in trace_filter indicates that the trace should (successfully) terminate here regardless of `depth`. if trace_filter is not None and next(filter(lambda x: x == '$', map(lambda x: x[0], trace_filter)), None) is not None: yield [] # there may be other entries in trace_filter that still yield results. if depth == 0: for trans in self.outgoing_transitions.values(): if trace_filter is not None and len(list(filter(lambda x: x == trans.name, map(lambda x: x[0], trace_filter)))) == 0: continue if with_arguments: if trans.argument_combination == 'cartesian': for args in itertools.product(*trans.argument_values): if sleep: yield [(None, sleep), (trans, args)] else: yield [(trans, args)] else: for args in zip(*trans.argument_values): if sleep: yield [(None, sleep), (trans, args)] else: yield [(trans, args)] else: if sleep: yield [(None, sleep), (trans,)] else: yield [(trans,)] else: for trans in self.outgoing_transitions.values(): if trace_filter is not None and next(filter(lambda x: x == trans.name, map(lambda x: x[0], trace_filter)), None) is None: continue if trace_filter is not None: new_trace_filter = map(lambda x: x[1:], filter(lambda x: x[0] == trans.name, trace_filter)) new_trace_filter = list(filter(len, new_trace_filter)) if len(new_trace_filter) == 0: new_trace_filter = None else: new_trace_filter = None for suffix in trans.destination.dfs(depth - 1, with_arguments = with_arguments, trace_filter = new_trace_filter, sleep = sleep): if with_arguments: if trans.argument_combination == 'cartesian': for args in itertools.product(*trans.argument_values): if sleep: new_suffix = [(None, sleep), (trans, args)] else: new_suffix = [(trans, args)] new_suffix.extend(suffix) yield new_suffix else: if len(trans.argument_values): arg_values = zip(*trans.argument_values) else: arg_values = [tuple()] for args in arg_values: if sleep: new_suffix = [(None, sleep), (trans, args)] else: new_suffix = [(trans, args)] new_suffix.extend(suffix) yield new_suffix else: if sleep: new_suffix = [(None, sleep), (trans,)] else: new_suffix = [(trans,)] new_suffix.extend(suffix) yield new_suffix def to_json(self) -> dict: """Return JSON encoding of this state object.""" ret = { 'name' : self.name, 'power' : _attribute_to_json(self.power, self.power_function) } return ret class Transition: """A single PTA transition with one origin and one destination state.""" def __init__(self, orig_state: State, dest_state: State, name: str, energy: float = 0, energy_function: AnalyticFunction = None, duration: float = 0, duration_function: AnalyticFunction = None, timeout: float = 0, timeout_function: AnalyticFunction = None, is_interrupt: bool = False, arguments: list = [], argument_values: list = [], argument_combination: str = 'cartesian', # or 'zip' param_update_function = None, arg_to_param_map: dict = None, set_param = None, return_value_handlers: list = []): """ Create a new transition between two PTA states. arguments: orig_state -- origin state dest_state -- destination state name -- transition name, typically the same as a driver/library function name """ self.name = name self.origin = orig_state self.destination = dest_state self.energy = energy self.energy_function = energy_function self.duration = duration self.duration_function = duration_function self.timeout = timeout self.timeout_function = timeout_function self.is_interrupt = is_interrupt self.arguments = arguments.copy() self.argument_values = argument_values.copy() self.argument_combination = argument_combination self.param_update_function = param_update_function self.arg_to_param_map = arg_to_param_map self.set_param = set_param self.return_value_handlers = return_value_handlers for handler in self.return_value_handlers: if 'formula' in handler: handler['formula'] = NormalizationFunction(handler['formula']) def get_duration(self, param_dict: dict = {}, args: list = []) -> float: u""" Return transition duration in µs. arguments: param_dict -- current parameter values args -- function arguments """ if self.duration_function: return self.duration_function.eval(_dict_to_list(param_dict), args) return self.duration def get_energy(self, param_dict: dict = {}, args: list = []) -> float: u""" Return transition energy cost in pJ. arguments: param_dict -- current parameter values args -- function arguments """ if self.energy_function: return self.energy_function.eval(_dict_to_list(param_dict), args) return self.energy def set_random_energy_model(self, static_model = True): self.energy = int(np.random.sample() * 50000) def get_timeout(self, param_dict: dict = {}) -> float: u""" Return transition timeout in µs. Returns 0 if the transition does not have a timeout. arguments: param_dict -- current parameter values args -- function arguments """ if self.timeout_function: return self.timeout_function.eval(_dict_to_list(param_dict)) return self.timeout def get_params_after_transition(self, param_dict: dict, args: list = []) -> dict: """ Return the new parameter dict after taking this transition. parameter values may be affected by this transition's update function, it's argument-to-param map, and its set_param settings. """ if self.param_update_function: return self.param_update_function(param_dict, args) ret = param_dict.copy() if self.arg_to_param_map: for k, v in self.arg_to_param_map.items(): ret[k] = args[v] if self.set_param: for k, v in self.set_param.items(): ret[k] = v return ret def to_json(self) -> dict: """Return JSON encoding of this transition object.""" ret = { 'name' : self.name, 'origin' : self.origin.name, 'destination' : self.destination.name, 'is_interrupt' : self.is_interrupt, 'arguments' : self.arguments, 'argument_values' : self.argument_values, 'argument_combination' : self.argument_combination, 'arg_to_param_map' : self.arg_to_param_map, 'set_param' : self.set_param, 'duration' : _attribute_to_json(self.duration, self.duration_function), 'energy' : _attribute_to_json(self.energy, self.energy_function), 'timeout' : _attribute_to_json(self.timeout, self.timeout_function), } return ret def _json_function_to_analytic_function(base, attribute: str, parameters: list): if attribute in base and 'function' in base[attribute]: base = base[attribute]['function'] return AnalyticFunction(base['raw'], parameters, 0, regression_args = base['regression_args']) return None def _json_get_static(base, attribute: str): if attribute in base: return base[attribute]['static'] return 0 class PTA: """ A parameterized priced timed automaton. All states are accepting. Suitable for simulation, model storage, and (soon) benchmark generation. """ def __init__(self, state_names: list = [], accepting_states: list = None, parameters: list = [], initial_param_values: list = None, codegen: dict = {}, parameter_normalization: dict = None): """ Return a new PTA object. arguments: state_names -- names of PTA states. Note that the PTA always contains an initial UNINITIALIZED state, regardless of the content of state_names. accepting_states -- names of accepting states. By default, all states are accepting parameters -- names of PTA parameters initial_param_values -- initial value for each parameter instance -- class used for generated C++ code header -- header include path for C++ class definition parameter_normalization -- dict mapping driver API parameter values to hardware values, e.g. a bitrate register value to an actual bitrate in kbit/s. Each parameter key has in turn a dict value. Supported entries: `enum`: Mapping of enum descriptors (keys) to parameter values. Note that the mapping is not required to correspond to the driver API. """ self.state = dict([[state_name, State(state_name)] for state_name in state_names]) self.accepting_states = accepting_states.copy() if accepting_states else None self.parameters = parameters.copy() self.parameter_normalization = parameter_normalization self.codegen = codegen if initial_param_values: self.initial_param_values = initial_param_values.copy() else: self.initial_param_values = [None for x in self.parameters] self.transitions = [] if not 'UNINITIALIZED' in state_names: self.state['UNINITIALIZED'] = State('UNINITIALIZED') if self.parameter_normalization: for normalization_spec in self.parameter_normalization.values(): if 'formula' in normalization_spec: normalization_spec['formula'] = NormalizationFunction(normalization_spec['formula']) def normalize_parameters(self, param_dict): if self.parameter_normalization is None: return param_dict.copy() normalized_param = param_dict.copy() for parameter, value in param_dict.items(): if parameter in self.parameter_normalization: if 'enum' in self.parameter_normalization[parameter] and value in self.parameter_normalization[parameter]['enum']: normalized_param[parameter] = self.parameter_normalization[parameter]['enum'][value] if 'formula' in self.parameter_normalization[parameter]: normalization_formula = self.parameter_normalization[parameter]['formula'] normalized_param[parameter] = normalization_formula.eval(value) return normalized_param @classmethod def from_json(cls, json_input: dict): """ Return a PTA created from the provided JSON data. Compatible with the to_json method. """ if 'transition' in json_input: return cls.from_legacy_json(json_input) kwargs = dict() for key in ('state_names', 'parameters', 'initial_param_values', 'accepting_states'): if key in json_input: kwargs[key] = json_input[key] pta = cls(**kwargs) for name, state in json_input['state'].items(): power_function = _json_function_to_analytic_function(state, 'power', pta.parameters) pta.add_state(name, power = _json_get_static(state, 'power'), power_function = power_function) for transition in json_input['transitions']: duration_function = _json_function_to_analytic_function(transition, 'duration', pta.parameters) energy_function = _json_function_to_analytic_function(transition, 'energy', pta.parameters) timeout_function = _json_function_to_analytic_function(transition, 'timeout', pta.parameters) kwargs = dict() for key in ['arg_to_param_map', 'argument_values', 'argument_combination']: if key in transition: kwargs[key] = transition[key] origins = transition['origin'] if type(origins) != list: origins = [origins] for origin in origins: pta.add_transition(origin, transition['destination'], transition['name'], duration = _json_get_static(transition, 'duration'), duration_function = duration_function, energy = _json_get_static(transition, 'energy'), energy_function = energy_function, timeout = _json_get_static(transition, 'timeout'), timeout_function = timeout_function, **kwargs ) return pta @classmethod def from_legacy_json(cls, json_input: dict): """ Return a PTA created from the provided JSON data. Compatible with the legacy dfatool/perl format. """ kwargs = { 'parameters' : list(), 'initial_param_values': list(), } for param in sorted(json_input['parameter'].keys()): kwargs['parameters'].append(param) kwargs['initial_param_values'].append(json_input['parameter'][param]['default']) pta = cls(**kwargs) for name, state in json_input['state'].items(): pta.add_state(name, power = float(state['power']['static'])) for trans_name in sorted(json_input['transition'].keys()): transition = json_input['transition'][trans_name] destination = transition['destination'] arguments = list() argument_values = list() is_interrupt = False if transition['level'] == 'epilogue': is_interrupt = True if type(destination) == list: destination = destination[0] for arg in transition['parameters']: arguments.append(arg['name']) argument_values.append(arg['values']) for origin in transition['origins']: pta.add_transition(origin, destination, trans_name, arguments = arguments, argument_values = argument_values, is_interrupt = is_interrupt) return pta @classmethod def from_yaml(cls, yaml_input: dict): """Return a PTA created from the YAML DFA format (passed as dict).""" kwargs = dict() if 'parameters' in yaml_input: kwargs['parameters'] = yaml_input['parameters'] if 'initial_param_values' in yaml_input: kwargs['initial_param_values'] = yaml_input['initial_param_values'] if 'states' in yaml_input: kwargs['state_names'] = yaml_input['states'] # else: set to UNINITIALIZED by class constructor if 'codegen' in yaml_input: kwargs['codegen'] = yaml_input['codegen'] if 'parameter_normalization' in yaml_input: kwargs['parameter_normalization'] = yaml_input['parameter_normalization'] pta = cls(**kwargs) for trans_name in sorted(yaml_input['transition'].keys()): kwargs = dict() transition = yaml_input['transition'][trans_name] arguments = list() argument_values = list() arg_to_param_map = dict() if 'arguments' in transition: for i, argument in enumerate(transition['arguments']): arguments.append(argument['name']) argument_values.append(argument['values']) if 'parameter' in argument: arg_to_param_map[argument['parameter']] = i if 'argument_combination' in transition: kwargs['argument_combination'] = transition['argument_combination'] if 'set_param' in transition: kwargs['set_param'] = transition['set_param'] if 'is_interrupt' in transition: kwargs['is_interrupt'] = transition['is_interrupt'] if 'return_value' in transition: kwargs['return_value_handlers'] = transition['return_value'] if not 'src' in transition: transition['src'] = ['UNINITIALIZED'] if not 'dst' in transition: transition['dst'] = 'UNINITIALIZED' for origin in transition['src']: pta.add_transition(origin, transition['dst'], trans_name, arguments = arguments, argument_values = argument_values, arg_to_param_map = arg_to_param_map, **kwargs) return pta def to_json(self) -> dict: """ Return JSON encoding of this PTA. Compatible with the from_json method. """ ret = { 'parameters' : self.parameters, 'initial_param_values' : self.initial_param_values, 'state' : dict([[state.name, state.to_json()] for state in self.state.values()]), 'transitions' : [trans.to_json() for trans in self.transitions], 'accepting_states' : self.accepting_states, } return ret def add_state(self, state_name: str, **kwargs): """ Add a new state. See the State() documentation for acceptable arguments. """ if 'power_function' in kwargs and type(kwargs['power_function']) != AnalyticFunction and kwargs['power_function'] != None: kwargs['power_function'] = AnalyticFunction(kwargs['power_function'], self.parameters, 0) self.state[state_name] = State(state_name, **kwargs) def add_transition(self, orig_state: str, dest_state: str, function_name: str, **kwargs): """ Add function_name as new transition from orig_state to dest_state. arguments: orig_state -- origin state name. Must be known to PTA dest_state -- destination state name. Must be known to PTA. function_name -- function name kwargs -- see Transition() documentation """ orig_state = self.state[orig_state] dest_state = self.state[dest_state] for key in ('duration_function', 'energy_function', 'timeout_function'): if key in kwargs and kwargs[key] != None and type(kwargs[key]) != AnalyticFunction: kwargs[key] = AnalyticFunction(kwargs[key], self.parameters, 0) new_transition = Transition(orig_state, dest_state, function_name, **kwargs) self.transitions.append(new_transition) orig_state.add_outgoing_transition(new_transition) def get_transition_id(self, transition: Transition) -> int: """Return PTA-specific ID of transition.""" return self.transitions.index(transition) def get_state_names(self): """Return lexically sorted list of PTA state names.""" return sorted(self.state.keys()) def get_state_id(self, state: State) -> int: """Return PTA-specific ID of state.""" return self.get_state_names().index(state.name) def get_unique_transitions(self): """ Return list of PTA transitions without duplicates. I.e., each transition name only occurs once, even if it has several entries due to multiple origin states and/or overloading. """ seen_transitions = set() ret_transitions = list() for transition in self.transitions: if transition.name not in seen_transitions: ret_transitions.append(transition) seen_transitions.add(transition.name) return ret_transitions def get_unique_transition_id(self, transition: Transition) -> int: """ Return PTA-specific ID of transition in unique transition list. The followinng condition holds: ` max_index = max(map(lambda t: pta.get_unique_transition_id(t), pta.get_unique_transitions())) max_index == len(pta.get_unique_transitions) - 1 ` """ return self.get_unique_transitions().index(transition) def get_initial_param_dict(self): return dict([[self.parameters[i], self.initial_param_values[i]] for i in range(len(self.parameters))]) def set_random_energy_model(self, static_model = True): for state in self.state.values(): state.set_random_energy_model(static_model) for transition in self.transitions: transition.set_random_energy_model(static_model) def _dfs_with_param(self, generator, param_dict): for trace in generator: param = param_dict.copy() ret = list() for elem in trace: transition, arguments = elem if transition is not None: param = transition.get_params_after_transition(param, arguments) ret.append((transition, arguments, self.normalize_parameters(param))) else: # parameters have already been normalized ret.append((transition, arguments, param)) yield ret def dfs(self, depth: int = 10, orig_state: str = 'UNINITIALIZED', param_dict: dict = None, with_parameters: bool = False, **kwargs): """ Return a generator object for depth-first search starting at orig_state. :param depth: search depth :param orig_state: initial state for depth-first search :param param_dict: initial parameter values :param with_arguments: perform dfs with argument values :param with_parameters: include parameters in trace? :param trace_filter: list of lists. Each sub-list is a trace. Only traces matching one of the provided sub-lists are returned. :param sleep: sleep duration between states in us. If None or 0, no sleep pseudo-transitions will be included in the trace. The returned generator emits traces. Each trace consts of a list of tuples describing the corresponding transition and (if enabled) arguments and parameters. When both with_arguments and with_parameters are True, each transition is a (Transition object, argument list, parameter dict) tuple. Note that the parameter dict refers to parameter values _after_ passing the corresponding transition. Although this may seem odd at first, it is useful when analyzing measurements: Properties of the state following this transition may be affected by the parameters set by the transition, so it is useful to have those readily available. """ if with_parameters and not param_dict: param_dict = self.get_initial_param_dict() if with_parameters and not 'with_arguments' in kwargs: raise ValueError("with_parameters = True requires with_arguments = True") if self.accepting_states: generator = filter(lambda x: x[-1][0].destination.name in self.accepting_states, self.state[orig_state].dfs(depth, **kwargs)) else: generator = self.state[orig_state].dfs(depth, **kwargs) if with_parameters: return self._dfs_with_param(generator, param_dict) else: return generator def simulate(self, trace: list, orig_state: str = 'UNINITIALIZED', accounting = None): u""" Simulate a single run through the PTA and return total energy, duration, final state, and resulting parameters. :param trace: list of (function name, arg1, arg2, ...) tuples representing the individual transitions, or list of (Transition, argument tuple, parameter) tuples originating from dfs. The tuple (None, duration) represents a sleep time between states in us :param orig_state: origin state, default UNINITIALIZED :returns (total energy in pJ, total duration in µs, end state, end parameters) """ total_duration = 0. total_energy = 0. state = self.state[orig_state] param_dict = dict([[self.parameters[i], self.initial_param_values[i]] for i in range(len(self.parameters))]) for function in trace: if isinstance(function[0], Transition): function_name = function[0].name function_args = function[1] else: function_name = function[0] function_args = function[1 : ] if function_name is None: duration = function_args[0] total_energy += state.get_energy(duration, param_dict) total_duration += duration if accounting is not None: accounting.sleep(duration) else: transition = state.get_transition(function_name) total_duration += transition.get_duration(param_dict, function_args) total_energy += transition.get_energy(param_dict, function_args) param_dict = transition.get_params_after_transition(param_dict, function_args) state = transition.destination if accounting is not None: accounting.pass_transition(transition) while (state.has_interrupt_transitions()): transition = state.get_next_interrupt(param_dict) duration = transition.get_timeout(param_dict) total_duration += duration total_energy += state.get_energy(duration, param_dict) if accounting is not None: accounting.sleep(duration) accounting.pass_transition(transition) param_dict = transition.get_params_after_transition(param_dict) state = transition.destination return total_energy, total_duration, state, param_dict def update(self, static_model, param_model): for state in self.state.values(): if state.name != 'UNINITIALIZED': state.power = static_model(state.name, 'power') if param_model(state.name, 'power'): state.power_function = param_model(state.name, 'power')['function'] print(state.name, state.power, state.power_function.__dict__)