pyProject/test_ai.py

import math
import tkinter as tk
from tkinter import messagebox, ttk
from decimal import Decimal, getcontext
import threading

# 定义 Chudnovsky 算法计算圆周率的函数
def compute_pi_chudnovsky(iterations, progress_callback):
    # 设置 Decimal 精度，确保足够的有效数字
    getcontext().prec = 250  # 设置更高的精度，确保中间计算的准确性

    # 初始化常量
    C = Decimal(426880) * Decimal(10005).sqrt()
    M = Decimal(1)
    L = Decimal(13591409)
    X = Decimal(-262537412640768000)  # 初始 X
    K = Decimal(6)
    S = Decimal(L)

    total_iterations = iterations
    for i in range(1, total_iterations + 1):  # 从 1 开始迭代
        if i % 10 == 0:
            progress_callback((i / total_iterations) * 100)

        # 计算 M 和 L
        M = (K**3 - 16 * K) * M // Decimal(i**3)
        L += Decimal(545140134)

        # 计算 S
        try:
            S += M * L / X
        except ZeroDivisionError as e:
            raise ValueError(f"除零错误在迭代次数: {i}, X: {X}, M: {M}, L: {L}") from e
        except Exception as e:
            raise ValueError(f"其他错误在迭代次数: {i}, X: {X}, M: {M}, L: {L}, S: {S}") from e

        # 更新 X 和 K
        X *= Decimal(-262537412640768000)
        K += Decimal(12)

    pi = C / S
    return +pi  # 返回正数值

# 定义工作线程函数，用于在后台计算圆周率
def worker(iterations, progress_callback, result_callback):
    try:
        pi_computed = compute_pi_chudnovsky(iterations, progress_callback)
        result_callback(pi_computed)
    except Exception as e:
        result_callback(None, str(e))

# 定义计算按钮点击事件处理函数
def on_calculate():
    try:
        iterations = int(entry_iterations.get())
        if iterations < 1:
            raise ValueError("迭代次数必须大于0")

        # 创建进度窗口
        progress_window = tk.Toplevel(root)
        progress_window.title("计算进度")

        # 初始化进度条变量
        progress_var = tk.DoubleVar()
        # 创建进度条控件
        progress = ttk.Progressbar(progress_window, variable=progress_var, maximum=100)
        progress.pack(pady=20, padx=20, fill='x')
        # 创建进度标签控件
        progress_label = tk.Label(progress_window, text="0%")
        progress_label.pack(pady=10)

        def progress_callback(progress):
            progress_var.set(progress)
            progress_label.config(text=f"{int(progress)}%")
            progress_window.update_idletasks()

        # 定义结果回调函数
        def result_callback(pi_computed, error=None):
            progress_window.destroy()
            if error:
                messagebox.showerror("错误", error)
            else:
                # 获取数学库中的 π 值（这里使用 Decimal 包装）
                pi_math = Decimal(str(math.pi))

                # 计算误差
                difference = abs(pi_computed - pi_math)

                # 格式化显示计算结果和数学库中的 π 值，并用科学计数法显示误差
                pi_computed_str = f"{pi_computed:.200f}".rstrip('0').rstrip('.')
                pi_math_str = f"{pi_math:.200f}".rstrip('0').rstrip('.')
                difference_str = f"{difference:.20e}"

                message = (f"计算得到的π: {pi_computed_str}\n"
                           f"数学库中的π: {pi_math_str}\n"
                           f"差异: {difference_str}")
                messagebox.showinfo("结果", message)

        # 创建并启动线程进行计算
        thread = threading.Thread(target=worker, args=(iterations, progress_callback, result_callback))
        thread.start()
    except ValueError as e:
        messagebox.showerror("错误", str(e))

# 创建主窗口
root = tk.Tk()
root.title("计算圆周率")

# 创建标签和输入框
label_iterations = tk.Label(root, text="迭代次数:")
label_iterations.grid(row=0, column=0, padx=10, pady=10)

entry_iterations = tk.Entry(root)
entry_iterations.grid(row=0, column=1, padx=10, pady=10)

# 创建计算按钮
button_calculate = tk.Button(root, text="计算", command=on_calculate)
button_calculate.grid(row=1, column=0, columnspan=2, pady=10)

# 运行主循环
root.mainloop()