C13-3 φ-并行计算框架形式化规范

1. φ-并行处理器模型

1.1 处理器定义

@dataclass
class PhiProcessor:
    """φ-并行处理器"""
    def __init__(self, rank: int, capacity: float):
        self.phi = (1 + np.sqrt(5)) / 2
        self.rank = rank
        self.capacity = capacity * (self.phi ** rank)  # φ-分级能力
        self.current_load = 0.0
        self.task_queue = []
        self.communication_channels = {}
        
    def compute_phi_load_ratio(self) -> float:
        """计算φ-负载比率"""
        return self.current_load / (self.capacity * self.phi ** (-self.rank))
        
    def can_accept_task(self, task_size: float) -> bool:
        """判断是否可接受任务"""
        projected_load = self.current_load + task_size
        return projected_load <= self.capacity
        
    def execute_task(self, task: 'PhiTask') -> 'TaskResult':
        """执行φ-任务"""
        start_time = time.time()
        
        # φ-优化执行
        if task.is_divisible() and task.size > self.phi ** 4:
            return self.phi_divide_and_execute(task)
        else:
            result = self.direct_execute(task)
            
        execution_time = time.time() - start_time
        return TaskResult(result, execution_time, task.size)
        
    def phi_divide_and_execute(self, task: 'PhiTask') -> 'TaskResult':
        """φ-分治执行"""
        # 按φ比率分解
        subtasks = task.phi_split()
        results = []
        
        for subtask in subtasks:
            result = self.execute_task(subtask)
            results.append(result)
            
        return task.merge_results(results)

1.2 任务模型

@dataclass 
class PhiTask:
    """φ-任务模型"""
    def __init__(self, data: Any, size: int):
        self.phi = (1 + np.sqrt(5)) / 2
        self.data = data
        self.size = size
        self.entropy = self.compute_entropy()
        self.priority = self.compute_phi_priority()
        
    def phi_split(self) -> List['PhiTask']:
        """φ-分解任务"""
        if self.size <= 4:
            return [self]
            
        split_point = int(self.size / self.phi)
        
        # 确保分割有效
        if split_point == 0:
            split_point = 1
        if split_point >= self.size:
            split_point = self.size - 1
            
        subtask1 = PhiTask(self.data[:split_point], split_point)
        subtask2 = PhiTask(self.data[split_point:], self.size - split_point)
        
        return [subtask1, subtask2]
        
    def merge_results(self, results: List['TaskResult']) -> 'TaskResult':
        """合并φ-任务结果"""
        merged_data = []
        total_time = 0
        total_size = 0
        
        for result in results:
            merged_data.extend(result.data)
            total_time += result.execution_time
            total_size += result.task_size
            
        return TaskResult(merged_data, total_time, total_size)
        
    def compute_entropy(self) -> float:
        """计算任务熵"""
        if isinstance(self.data, (list, str)):
            from collections import Counter
            if not self.data:
                return 0.0
                
            counts = Counter(self.data)
            total = len(self.data)
            entropy = 0.0
            
            for count in counts.values():
                if count > 0:
                    p = count / total
                    entropy -= p * np.log2(p)
                    
            return entropy
        return 0.0
        
    def compute_phi_priority(self) -> float:
        """计算φ-优先级"""
        # 基于任务大小和熵的φ-权重
        size_factor = np.log(self.size + 1) / np.log(self.phi)
        entropy_factor = self.entropy
        
        return size_factor * self.phi + entropy_factor

2. φ-负载均衡器

2.1 负载均衡算法

class PhiLoadBalancer:
    """φ-负载均衡器"""
    def __init__(self, processors: List[PhiProcessor]):
        self.phi = (1 + np.sqrt(5)) / 2
        self.processors = processors
        self.total_capacity = sum(p.capacity for p in processors)
        
    def balance_load(self, tasks: List[PhiTask]) -> Dict[int, List[PhiTask]]:
        """φ-负载均衡分配"""
        # 按φ-优先级排序任务
        sorted_tasks = sorted(tasks, key=lambda t: t.priority, reverse=True)
        
        # 初始化分配
        allocation = {p.rank: [] for p in self.processors}
        
        for task in sorted_tasks:
            # 选择最优处理器
            best_processor = self.select_optimal_processor(task)
            allocation[best_processor.rank].append(task)
            best_processor.current_load += task.size
            
        return allocation
        
    def select_optimal_processor(self, task: PhiTask) -> PhiProcessor:
        """选择最优处理器"""
        best_processor = None
        best_score = float('inf')
        
        for processor in self.processors:
            if processor.can_accept_task(task.size):
                # φ-评分函数
                load_factor = processor.current_load / processor.capacity
                phi_factor = self.phi ** (-processor.rank)
                entropy_factor = 1.0 / (1.0 + task.entropy)
                
                score = load_factor / (phi_factor * entropy_factor)
                
                if score < best_score:
                    best_score = score
                    best_processor = processor
                    
        return best_processor if best_processor else self.processors[0]
        
    def rebalance_dynamic(self) -> None:
        """动态重平衡"""
        # 计算平均负载
        avg_load = sum(p.current_load for p in self.processors) / len(self.processors)
        
        # 识别过载和轻载处理器
        overloaded = [p for p in self.processors if p.current_load > avg_load * self.phi]
        underloaded = [p for p in self.processors if p.current_load < avg_load / self.phi]
        
        # φ-工作窃取
        for overloaded_proc in overloaded:
            for underloaded_proc in underloaded:
                if overloaded_proc.task_queue:
                    # 按φ比率窃取任务
                    steal_count = max(1, int(len(overloaded_proc.task_queue) / self.phi))
                    stolen_tasks = overloaded_proc.task_queue[-steal_count:]
                    
                    # 转移任务
                    overloaded_proc.task_queue = overloaded_proc.task_queue[:-steal_count]
                    underloaded_proc.task_queue.extend(stolen_tasks)
                    
                    # 更新负载
                    transferred_load = sum(task.size for task in stolen_tasks)
                    overloaded_proc.current_load -= transferred_load
                    underloaded_proc.current_load += transferred_load

2.2 工作窃取算法

class PhiWorkStealing:
    """φ-工作窃取调度器"""
    def __init__(self, processors: List[PhiProcessor]):
        self.phi = (1 + np.sqrt(5)) / 2
        self.processors = processors
        self.victim_selection_cache = {}
        
    def schedule_tasks(self, tasks: List[PhiTask]) -> None:
        """调度任务执行"""
        # 初始分配
        self.initial_distribution(tasks)
        
        # 启动并行执行
        with concurrent.futures.ThreadPoolExecutor() as executor:
            futures = []
            for processor in self.processors:
                future = executor.submit(self.processor_worker, processor)
                futures.append(future)
                
            # 等待完成
            concurrent.futures.wait(futures)
            
    def initial_distribution(self, tasks: List[PhiTask]) -> None:
        """初始任务分配"""
        # 按φ-比率分配到处理器
        total_tasks = len(tasks)
        
        for i, processor in enumerate(self.processors):
            # φ-比率分配
            task_count = int(total_tasks * (self.phi ** (-i)))
            assigned_tasks = tasks[:task_count]
            tasks = tasks[task_count:]
            
            processor.task_queue.extend(assigned_tasks)
            processor.current_load = sum(task.size for task in assigned_tasks)
            
    def processor_worker(self, processor: PhiProcessor) -> None:
        """处理器工作线程"""
        while True:
            # 执行本地任务
            if processor.task_queue:
                task = processor.task_queue.pop(0)
                result = processor.execute_task(task)
                processor.current_load -= task.size
            else:
                # 尝试窃取任务
                stolen_task = self.steal_task(processor)
                if stolen_task:
                    result = processor.execute_task(stolen_task)
                else:
                    # 检查全局是否完成
                    if self.all_processors_idle():
                        break
                    time.sleep(0.001)  # 短暂等待
                    
    def steal_task(self, thief: PhiProcessor) -> Optional[PhiTask]:
        """φ-工作窃取"""
        # 选择受害者
        victim = self.select_victim(thief)
        if not victim or not victim.task_queue:
            return None
            
        # 按φ比率窃取
        steal_count = max(1, int(len(victim.task_queue) / self.phi))
        
        if len(victim.task_queue) >= steal_count:
            # 窃取任务（从尾部，减少冲突）
            stolen_tasks = victim.task_queue[-steal_count:]
            victim.task_queue = victim.task_queue[:-steal_count]
            
            # 更新负载
            stolen_load = sum(task.size for task in stolen_tasks)
            victim.current_load -= stolen_load
            thief.current_load += stolen_load
            
            # 返回第一个任务，其余加入队列
            thief.task_queue.extend(stolen_tasks[1:])
            return stolen_tasks[0]
            
        return None
        
    def select_victim(self, thief: PhiProcessor) -> Optional[PhiProcessor]:
        """选择窃取目标"""
        # φ-启发式选择
        candidates = [p for p in self.processors 
                     if p != thief and p.task_queue]
                     
        if not candidates:
            return None
            
        # 选择负载最重的处理器
        return max(candidates, key=lambda p: p.current_load)
        
    def all_processors_idle(self) -> bool:
        """检查所有处理器是否空闲"""
        return all(not p.task_queue for p in self.processors)

3. φ-通信系统

3.1 通信拓扑

class PhiCommunicationTopology:
    """φ-通信拓扑"""
    def __init__(self, num_processors: int):
        self.phi = (1 + np.sqrt(5)) / 2
        self.num_processors = num_processors
        self.topology = self.build_phi_topology()
        self.message_buffers = {}
        
    def build_phi_topology(self) -> Dict[int, List[int]]:
        """构建φ-拓扑结构"""
        topology = {}
        
        for i in range(self.num_processors):
            neighbors = []
            
            # φ-连接模式
            phi_distance = int(self.phi ** (i % 4))  # 模4循环
            
            # 向前连接
            forward = (i + phi_distance) % self.num_processors
            if forward != i:
                neighbors.append(forward)
                
            # 向后连接  
            backward = (i - phi_distance) % self.num_processors
            if backward != i and backward not in neighbors:
                neighbors.append(backward)
                
            # 黄金比率连接
            golden_jump = int(i * self.phi) % self.num_processors
            if golden_jump != i and golden_jump not in neighbors:
                neighbors.append(golden_jump)
                
            topology[i] = neighbors
            
        return topology
        
    def find_phi_path(self, source: int, destination: int) -> List[int]:
        """寻找φ-最短路径"""
        if source == destination:
            return [source]
            
        # 使用φ-BFS
        queue = [(source, [source])]
        visited = {source}
        
        while queue:
            current, path = queue.pop(0)
            
            for neighbor in self.topology.get(current, []):
                if neighbor == destination:
                    return path + [neighbor]
                    
                if neighbor not in visited:
                    visited.add(neighbor)
                    queue.append((neighbor, path + [neighbor]))
                    
        return []  # 无路径
        
    def route_message(self, source: int, destination: int, 
                     message: 'PhiMessage') -> None:
        """路由φ-消息"""
        path = self.find_phi_path(source, destination)
        
        if not path:
            raise ValueError(f"No path from {source} to {destination}")
            
        # 沿路径传递消息
        for i in range(len(path) - 1):
            current = path[i]
            next_hop = path[i + 1]
            
            # 添加到缓冲区
            if next_hop not in self.message_buffers:
                self.message_buffers[next_hop] = []
            self.message_buffers[next_hop].append(message)

3.2 消息传递

@dataclass
class PhiMessage:
    """φ-消息"""
    def __init__(self, sender: int, receiver: int, data: Any, priority: int = 0):
        self.phi = (1 + np.sqrt(5)) / 2
        self.sender = sender
        self.receiver = receiver
        self.data = data
        self.priority = priority
        self.timestamp = time.time()
        self.entropy = self.compute_message_entropy()
        self.compressed_data = self.phi_compress(data)
        
    def phi_compress(self, data: Any) -> bytes:
        """φ-压缩数据"""
        import pickle
        import zlib
        
        # 序列化
        serialized = pickle.dumps(data)
        
        # φ-压缩（利用no-11约束）
        # 将连续的11替换为特殊标记
        compressed = serialized.replace(b'11', b'\x00\x01')
        
        # 标准压缩
        final_compressed = zlib.compress(compressed)
        
        return final_compressed
        
    def phi_decompress(self, compressed_data: bytes) -> Any:
        """φ-解压数据"""
        import pickle
        import zlib
        
        # 解压
        decompressed = zlib.decompress(compressed_data)
        
        # 恢复11模式
        restored = decompressed.replace(b'\x00\x01', b'11')
        
        # 反序列化
        return pickle.loads(restored)
        
    def compute_message_entropy(self) -> float:
        """计算消息熵"""
        import pickle
        serialized = pickle.dumps(self.data)
        
        if not serialized:
            return 0.0
            
        from collections import Counter
        byte_counts = Counter(serialized)
        total_bytes = len(serialized)
        
        entropy = 0.0
        for count in byte_counts.values():
            p = count / total_bytes
            entropy -= p * np.log2(p)
            
        return entropy

class PhiMessagePassing:
    """φ-消息传递系统"""
    def __init__(self, topology: PhiCommunicationTopology):
        self.phi = (1 + np.sqrt(5)) / 2
        self.topology = topology
        self.pending_messages = []
        self.delivered_messages = []
        
    def send_message(self, message: PhiMessage) -> None:
        """发送φ-消息"""
        # φ-优先级调度
        self.pending_messages.append(message)
        self.pending_messages.sort(key=lambda m: (-m.priority, m.timestamp))
        
        # 路由消息
        self.topology.route_message(message.sender, message.receiver, message)
        
    def broadcast_message(self, sender: int, data: Any) -> None:
        """广播φ-消息"""
        # φ-树形广播
        root = sender
        visited = {root}
        
        # 构建φ-广播树
        broadcast_tree = self.build_phi_broadcast_tree(root)
        
        # 沿树发送消息
        for parent, children in broadcast_tree.items():
            for child in children:
                message = PhiMessage(parent, child, data, priority=1)
                self.send_message(message)
                
    def build_phi_broadcast_tree(self, root: int) -> Dict[int, List[int]]:
        """构建φ-广播树"""
        tree = {root: []}
        queue = [root]
        visited = {root}
        
        while queue:
            current = queue.pop(0)
            neighbors = self.topology.topology.get(current, [])
            
            # 按φ-顺序选择子节点
            for neighbor in neighbors:
                if neighbor not in visited:
                    # φ-选择策略
                    if len(tree[current]) < int(self.phi * 2):  # 最多φ*2个子节点
                        tree[current].append(neighbor)
                        tree[neighbor] = []
                        visited.add(neighbor)
                        queue.append(neighbor)
                        
        return tree
        
    def collect_messages(self, processor_id: int) -> List[PhiMessage]:
        """收集处理器的消息"""
        messages = self.topology.message_buffers.get(processor_id, [])
        self.topology.message_buffers[processor_id] = []
        
        # 按φ-优先级排序
        messages.sort(key=lambda m: (-m.priority, m.entropy / self.phi))
        
        return messages

4. φ-同步机制

4.1 熵增同步

class PhiEntropySync:
    """φ-熵增同步机制"""
    def __init__(self, processors: List[PhiProcessor]):
        self.phi = (1 + np.sqrt(5)) / 2
        self.processors = processors
        self.global_entropy = 0.0
        self.entropy_history = []
        
    def compute_system_entropy(self) -> float:
        """计算系统总熵"""
        total_entropy = 0.0
        
        for processor in self.processors:
            # 处理器状态熵
            task_entropy = sum(task.entropy for task in processor.task_queue)
            load_entropy = self.compute_load_entropy(processor)
            
            total_entropy += task_entropy + load_entropy
            
        return total_entropy
        
    def compute_load_entropy(self, processor: PhiProcessor) -> float:
        """计算负载熵"""
        if processor.capacity == 0:
            return 0.0
            
        load_ratio = processor.current_load / processor.capacity
        
        if load_ratio == 0 or load_ratio == 1:
            return 0.0
            
        return -(load_ratio * np.log2(load_ratio) + 
                (1-load_ratio) * np.log2(1-load_ratio))
                
    def wait_for_entropy_sync(self, target_entropy: float, timeout: float = 10.0) -> bool:
        """等待熵增同步"""
        start_time = time.time()
        
        while time.time() - start_time < timeout:
            current_entropy = self.compute_system_entropy()
            
            if abs(current_entropy - target_entropy) < 0.1:
                return True
                
            time.sleep(0.01)  # 10ms检查间隔
            
        return False
        
    def synchronize_processors(self) -> None:
        """同步所有处理器"""
        # 记录当前系统熵
        current_entropy = self.compute_system_entropy()
        self.entropy_history.append(current_entropy)
        
        # φ-同步点
        if len(self.entropy_history) >= int(self.phi * 10):
            # 计算熵增率
            entropy_rate = self.compute_entropy_rate()
            
            # 如果熵增率过低，强制同步
            if entropy_rate < 1.0 / self.phi:
                self.force_synchronization()
                
    def compute_entropy_rate(self) -> float:
        """计算熵增率"""
        if len(self.entropy_history) < 2:
            return 0.0
            
        recent_entropies = self.entropy_history[-10:]
        
        # 计算平均熵增率
        rates = []
        for i in range(1, len(recent_entropies)):
            rate = recent_entropies[i] - recent_entropies[i-1]
            rates.append(rate)
            
        return np.mean(rates) if rates else 0.0
        
    def force_synchronization(self) -> None:
        """强制同步"""
        # 收集所有处理器状态
        states = []
        for processor in self.processors:
            state = {
                'rank': processor.rank,
                'load': processor.current_load,
                'queue_size': len(processor.task_queue)
            }
            states.append(state)
            
        # 广播同步消息
        sync_message = PhiMessage(
            sender=-1,  # 系统消息
            receiver=-1,  # 广播
            data={'type': 'sync', 'states': states},
            priority=100  # 最高优先级
        )
        
        # 强制所有处理器处理同步消息
        for processor in self.processors:
            processor.task_queue.insert(0, sync_message)

4.2 无锁同步

class PhiLockFreeSync:
    """φ-无锁同步"""
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        self.version_counters = {}
        self.shared_data = {}
        
    def read_shared_data(self, key: str, processor_id: int) -> Tuple[Any, int]:
        """无锁读取共享数据"""
        version = self.version_counters.get(key, 0)
        data = self.shared_data.get(key, None)
        
        return data, version
        
    def write_shared_data(self, key: str, value: Any, processor_id: int) -> bool:
        """无锁写入共享数据"""
        # φ-版本控制
        current_version = self.version_counters.get(key, 0)
        new_version = current_version + 1
        
        # 原子更新（模拟CAS操作）
        if self.compare_and_swap(key, current_version, new_version, value):
            return True
        else:
            # φ-退避策略
            backoff_time = 0.001 * (self.phi ** (processor_id % 5))
            time.sleep(backoff_time)
            return False
            
    def compare_and_swap(self, key: str, expected_version: int, 
                        new_version: int, new_value: Any) -> bool:
        """比较并交换（模拟原子操作）"""
        current_version = self.version_counters.get(key, 0)
        
        if current_version == expected_version:
            self.version_counters[key] = new_version
            self.shared_data[key] = new_value
            return True
        else:
            return False
            
    def phi_barrier_sync(self, processor_id: int, num_processors: int) -> None:
        """φ-屏障同步"""
        barrier_key = f"barrier_{processor_id // int(self.phi)}"
        
        # 递增到达计数
        arrived_count = self.shared_data.get(barrier_key, 0)
        
        while not self.write_shared_data(barrier_key, arrived_count + 1, processor_id):
            time.sleep(0.001)  # 重试
            arrived_count = self.shared_data.get(barrier_key, 0)
            
        # 等待所有处理器到达
        while self.shared_data.get(barrier_key, 0) < num_processors:
            time.sleep(0.001 * self.phi)  # φ-等待

5. 性能分析框架

5.1 性能监控

class PhiPerformanceMonitor:
    """φ-性能监控器"""
    def __init__(self, processors: List[PhiProcessor]):
        self.phi = (1 + np.sqrt(5)) / 2
        self.processors = processors
        self.metrics = {}
        self.start_time = time.time()
        
    def collect_metrics(self) -> Dict[str, Any]:
        """收集性能指标"""
        current_time = time.time()
        elapsed_time = current_time - self.start_time
        
        metrics = {
            'timestamp': current_time,
            'elapsed_time': elapsed_time,
            'processor_metrics': [],
            'system_metrics': {}
        }
        
        # 处理器指标
        total_tasks_completed = 0
        total_load = 0
        
        for processor in self.processors:
            proc_metrics = {
                'rank': processor.rank,
                'current_load': processor.current_load,
                'capacity': processor.capacity,
                'utilization': processor.current_load / processor.capacity if processor.capacity > 0 else 0,
                'queue_length': len(processor.task_queue),
                'phi_efficiency': self.compute_phi_efficiency(processor)
            }
            
            metrics['processor_metrics'].append(proc_metrics)
            total_load += processor.current_load
            
        # 系统指标
        metrics['system_metrics'] = {
            'total_load': total_load,
            'average_utilization': total_load / sum(p.capacity for p in self.processors),
            'load_balance_index': self.compute_load_balance_index(),
            'phi_speedup': self.compute_phi_speedup(),
            'parallel_efficiency': self.compute_parallel_efficiency()
        }
        
        return metrics
        
    def compute_phi_efficiency(self, processor: PhiProcessor) -> float:
        """计算φ-效率"""
        if processor.capacity == 0:
            return 0.0
            
        utilization = processor.current_load / processor.capacity
        phi_factor = self.phi ** (-processor.rank)
        
        return utilization * phi_factor
        
    def compute_load_balance_index(self) -> float:
        """计算负载均衡指数"""
        utilizations = []
        for processor in self.processors:
            if processor.capacity > 0:
                utilization = processor.current_load / processor.capacity
                utilizations.append(utilization)
                
        if not utilizations:
            return 1.0
            
        mean_util = np.mean(utilizations)
        if mean_util == 0:
            return 1.0
            
        # 负载均衡指数（越接近1越均衡）
        variance = np.var(utilizations)
        return 1.0 / (1.0 + variance / mean_util)
        
    def compute_phi_speedup(self) -> float:
        """计算φ-加速比"""
        n = len(self.processors)
        
        # 理论φ-加速比
        theoretical_speedup = n / (1 + (n-1) / self.phi)
        
        # 实际加速比（需要基准测试数据）
        # 这里返回理论值
        return theoretical_speedup
        
    def compute_parallel_efficiency(self) -> float:
        """计算并行效率"""
        speedup = self.compute_phi_speedup()
        n = len(self.processors)
        
        return speedup / n if n > 0 else 0.0

5.2 性能预测

class PhiPerformancePredictor:
    """φ-性能预测器"""
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        self.historical_data = []
        
    def predict_execution_time(self, task_size: int, num_processors: int) -> float:
        """预测执行时间"""
        # φ-性能模型
        sequential_time = self.estimate_sequential_time(task_size)
        
        # φ-并行开销
        communication_overhead = self.estimate_communication_overhead(num_processors)
        synchronization_overhead = self.estimate_sync_overhead(num_processors)
        
        # φ-并行效率
        phi_efficiency = self.compute_phi_parallel_efficiency(num_processors)
        
        parallel_time = (sequential_time / (num_processors * phi_efficiency) + 
                        communication_overhead + synchronization_overhead)
        
        return parallel_time
        
    def estimate_sequential_time(self, task_size: int) -> float:
        """估算顺序执行时间"""
        # 基于任务大小的线性模型
        base_time_per_unit = 0.001  # 1ms per unit
        
        # φ-复杂度因子
        complexity_factor = np.log(task_size) / np.log(self.phi)
        
        return base_time_per_unit * task_size * complexity_factor
        
    def estimate_communication_overhead(self, num_processors: int) -> float:
        """估算通信开销"""
        if num_processors <= 1:
            return 0.0
            
        # φ-通信模型：O(log_φ n)
        comm_complexity = np.log(num_processors) / np.log(self.phi)
        base_comm_time = 0.0001  # 0.1ms base
        
        return base_comm_time * comm_complexity
        
    def estimate_sync_overhead(self, num_processors: int) -> float:
        """估算同步开销"""
        if num_processors <= 1:
            return 0.0
            
        # φ-同步开销
        sync_complexity = np.sqrt(num_processors) / self.phi
        base_sync_time = 0.00005  # 0.05ms base
        
        return base_sync_time * sync_complexity
        
    def compute_phi_parallel_efficiency(self, num_processors: int) -> float:
        """计算φ-并行效率"""
        # φ-效率模型
        theoretical_efficiency = self.phi / (self.phi + (num_processors - 1) / self.phi)
        
        # 实际效率会略低
        practical_factor = 0.85  # 85%的理论效率
        
        return theoretical_efficiency * practical_factor
        
    def predict_optimal_processor_count(self, task_size: int) -> int:
        """预测最优处理器数量"""
        best_processors = 1
        best_time = self.predict_execution_time(task_size, 1)
        
        # 测试不同处理器数量
        for n in range(2, min(64, task_size)):  # 最多64个处理器
            predicted_time = self.predict_execution_time(task_size, n)
            
            if predicted_time < best_time:
                best_time = predicted_time
                best_processors = n
            else:
                # 性能开始下降，停止搜索
                break
                
        return best_processors

6. 测试框架

6.1 单元测试支持

class PhiParallelTester:
    """φ-并行测试框架"""
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def create_test_processors(self, count: int) -> List[PhiProcessor]:
        """创建测试处理器"""
        processors = []
        base_capacity = 100.0
        
        for i in range(count):
            capacity = base_capacity * (self.phi ** (i // 3))
            processor = PhiProcessor(rank=i, capacity=capacity)
            processors.append(processor)
            
        return processors
        
    def create_test_tasks(self, count: int, size_range: Tuple[int, int]) -> List[PhiTask]:
        """创建测试任务"""
        tasks = []
        min_size, max_size = size_range
        
        for i in range(count):
            # φ-分布的任务大小
            size = min_size + int((max_size - min_size) * (self.phi ** (-i % 10)))
            
            # 随机数据
            data = [random.randint(0, 1000) for _ in range(size)]
            task = PhiTask(data=data, size=size)
            tasks.append(task)
            
        return tasks
        
    def run_parallel_test(self, processors: List[PhiProcessor], 
                         tasks: List[PhiTask]) -> Dict[str, Any]:
        """运行并行测试"""
        start_time = time.time()
        
        # 初始化系统
        load_balancer = PhiLoadBalancer(processors)
        work_stealing = PhiWorkStealing(processors)
        monitor = PhiPerformanceMonitor(processors)
        
        # 执行任务
        work_stealing.schedule_tasks(tasks)
        
        end_time = time.time()
        execution_time = end_time - start_time
        
        # 收集结果
        metrics = monitor.collect_metrics()
        
        return {
            'execution_time': execution_time,
            'metrics': metrics,
            'processors_used': len(processors),
            'tasks_completed': len(tasks),
            'throughput': len(tasks) / execution_time if execution_time > 0 else 0
        }