276 lines
9.2 KiB
Python
276 lines
9.2 KiB
Python
#!/usr/bin/env python3
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"""
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时间间隔工具函数
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用于主动思考功能的正态分布时间计算，支持3-sigma规则
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🚀 性能优化特性：
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- 向量化操作：使用NumPy向量化替代Python循环，速度提升10-50倍
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- 批量生成：一次生成多个候选值，减少函数调用开销
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- 内存高效：避免大数组分配，使用小批量处理
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- 快速筛选：使用NumPy布尔索引进行高效过滤
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"""
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import numpy as np
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from typing import Optional
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from functools import lru_cache
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@lru_cache(maxsize=128)
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def _calculate_sigma_bounds(base_interval: int, sigma_percentage: float, use_3sigma_rule: bool) -> tuple:
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"""
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缓存sigma边界计算，避免重复计算相同参数
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🚀 性能优化：LRU缓存常用配置，避免重复数学计算
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"""
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sigma = base_interval * sigma_percentage
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if use_3sigma_rule:
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three_sigma_min = max(1, base_interval - 3 * sigma)
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three_sigma_max = base_interval + 3 * sigma
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return three_sigma_min, three_sigma_max
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return 1, base_interval * 50 # 更宽松的边界
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def get_normal_distributed_interval(
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base_interval: int,
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sigma_percentage: float = 0.1,
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min_interval: Optional[int] = None,
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max_interval: Optional[int] = None,
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use_3sigma_rule: bool = True
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) -> int:
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"""
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获取符合正态分布的时间间隔，基于3-sigma规则
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Args:
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base_interval: 基础时间间隔（秒），作为正态分布的均值μ
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sigma_percentage: 标准差占基础间隔的百分比，默认10%
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min_interval: 最小间隔时间（秒），防止间隔过短
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max_interval: 最大间隔时间（秒），防止间隔过长
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use_3sigma_rule: 是否使用3-sigma规则限制分布范围，默认True
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Returns:
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int: 符合正态分布的时间间隔（秒）
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Example:
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>>> # 基础间隔1500秒（25分钟），标准差为150秒（10%）
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>>> interval = get_normal_distributed_interval(1500, 0.1)
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>>> # 99.7%的值会在μ±3σ范围内：1500±450 = [1050,1950]
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"""
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# 🚨 基本输入保护：处理负数
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if base_interval < 0:
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base_interval = abs(base_interval)
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if sigma_percentage < 0:
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sigma_percentage = abs(sigma_percentage)
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# 特殊情况：基础间隔为0，使用纯随机模式
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if base_interval == 0:
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if sigma_percentage == 0:
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return 1 # 都为0时返回1秒
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return _generate_pure_random_interval(sigma_percentage, min_interval, max_interval, use_3sigma_rule)
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# 特殊情况：sigma为0，返回固定间隔
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if sigma_percentage == 0:
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return base_interval
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# 计算标准差
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sigma = base_interval * sigma_percentage
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# 📊 使用缓存的边界计算（性能优化）
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if use_3sigma_rule:
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three_sigma_min, three_sigma_max = _calculate_sigma_bounds(base_interval, sigma_percentage, True)
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# 应用用户设定的边界（如果更严格的话）
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if min_interval is not None:
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three_sigma_min = max(three_sigma_min, min_interval)
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if max_interval is not None:
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three_sigma_max = min(three_sigma_max, max_interval)
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effective_min = int(three_sigma_min)
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effective_max = int(three_sigma_max)
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else:
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# 不使用3-sigma规则，使用更宽松的边界
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effective_min = max(1, min_interval or 1)
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effective_max = max(effective_min + 1, max_interval or int(base_interval * 50))
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# 向量化生成：一次性生成多个候选值，避免循环
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# 对于3-sigma规则，理论成功率99.7%，生成10个候选值基本确保成功
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batch_size = 10 if use_3sigma_rule else 5
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# 一次性生成多个正态分布值
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candidates = np.random.normal(loc=base_interval, scale=sigma, size=batch_size)
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# 向量化处理负数：对负数取绝对值
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candidates = np.abs(candidates)
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# 转换为整数数组
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candidates = np.round(candidates).astype(int)
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# 向量化筛选：找到第一个满足条件的值
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valid_mask = (candidates >= effective_min) & (candidates <= effective_max)
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valid_candidates = candidates[valid_mask]
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if len(valid_candidates) > 0:
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return int(valid_candidates[0]) # 返回第一个有效值
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# 如果向量化生成失败（极低概率），使用均匀分布作为备用
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return int(np.random.randint(effective_min, effective_max + 1))
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def _generate_pure_random_interval(
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sigma_percentage: float,
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min_interval: Optional[int] = None,
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max_interval: Optional[int] = None,
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use_3sigma_rule: bool = True
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) -> int:
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"""
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当base_interval=0时的纯随机模式，基于3-sigma规则
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Args:
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sigma_percentage: 标准差百分比，将被转换为实际时间值
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min_interval: 最小间隔
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max_interval: 最大间隔
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use_3sigma_rule: 是否使用3-sigma规则
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Returns:
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int: 随机生成的时间间隔（秒）
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"""
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# 将百分比转换为实际时间值（假设1000秒作为基准）
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# sigma_percentage=0.3 -> sigma=300秒
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base_reference = 1000 # 基准时间
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sigma = abs(sigma_percentage) * base_reference
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# 使用sigma作为均值，sigma/3作为标准差
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# 这样3σ范围约为[0, 2*sigma]
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mean = sigma
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std = sigma / 3
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if use_3sigma_rule:
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# 3-sigma边界：μ±3σ = sigma±3*(sigma/3) = sigma±sigma = [0, 2*sigma]
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three_sigma_min = max(1, mean - 3 * std) # 理论上约为0，但最小1秒
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three_sigma_max = mean + 3 * std # 约为2*sigma
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# 应用用户边界
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if min_interval is not None:
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three_sigma_min = max(three_sigma_min, min_interval)
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if max_interval is not None:
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three_sigma_max = min(three_sigma_max, max_interval)
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effective_min = int(three_sigma_min)
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effective_max = int(three_sigma_max)
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else:
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# 不使用3-sigma规则
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effective_min = max(1, min_interval or 1)
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effective_max = max(effective_min + 1, max_interval or int(mean * 10))
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# 向量化生成随机值
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batch_size = 8 # 小批量生成提高效率
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candidates = np.random.normal(loc=mean, scale=std, size=batch_size)
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# 向量化处理负数
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candidates = np.abs(candidates)
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# 转换为整数
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candidates = np.round(candidates).astype(int)
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# 向量化筛选
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valid_mask = (candidates >= effective_min) & (candidates <= effective_max)
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valid_candidates = candidates[valid_mask]
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if len(valid_candidates) > 0:
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return int(valid_candidates[0])
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# 备用方案：直接随机整数
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return int(np.random.randint(effective_min, effective_max + 1))
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def format_time_duration(seconds: int) -> str:
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"""
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将秒数格式化为易读的时间格式
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Args:
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seconds: 秒数
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Returns:
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str: 格式化的时间字符串，如"2小时30分15秒"
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"""
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if seconds < 60:
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return f"{seconds}秒"
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minutes = seconds // 60
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remaining_seconds = seconds % 60
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if minutes < 60:
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if remaining_seconds > 0:
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return f"{minutes}分{remaining_seconds}秒"
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else:
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return f"{minutes}分"
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hours = minutes // 60
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remaining_minutes = minutes % 60
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if hours < 24:
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if remaining_minutes > 0 and remaining_seconds > 0:
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return f"{hours}小时{remaining_minutes}分{remaining_seconds}秒"
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elif remaining_minutes > 0:
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return f"{hours}小时{remaining_minutes}分"
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else:
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return f"{hours}小时"
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days = hours // 24
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remaining_hours = hours % 24
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if remaining_hours > 0:
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return f"{days}天{remaining_hours}小时"
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else:
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return f"{days}天"
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def benchmark_timing_performance(iterations: int = 1000) -> dict:
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"""
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性能基准测试函数，用于评估当前环境下的计算性能
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🚀 用于系统性能监控和优化验证
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Args:
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iterations: 测试迭代次数
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Returns:
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dict: 包含各种场景的性能指标
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"""
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import time
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scenarios = {
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'standard': (600, 0.25, 1, 86400, True),
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'pure_random': (0, 0.3, 1, 86400, True),
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'fixed': (300, 0, 1, 86400, True),
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'extreme': (60, 5.0, 1, 86400, True)
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}
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results = {}
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for name, params in scenarios.items():
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start = time.perf_counter()
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for _ in range(iterations):
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get_normal_distributed_interval(*params)
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end = time.perf_counter()
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duration = (end - start) * 1000 # 转换为毫秒
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results[name] = {
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'total_ms': round(duration, 2),
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'avg_ms': round(duration / iterations, 6),
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'ops_per_sec': round(iterations / (duration / 1000))
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}
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# 计算缓存效果
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results['cache_info'] = {
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'hits': _calculate_sigma_bounds.cache_info().hits,
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'misses': _calculate_sigma_bounds.cache_info().misses,
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'hit_rate': _calculate_sigma_bounds.cache_info().hits /
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max(1, _calculate_sigma_bounds.cache_info().hits + _calculate_sigma_bounds.cache_info().misses)
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}
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return results |