Python：计算pi时“long int太大而不能转换为float”

当使用python脚本使用Gauss-Legendre算法计算pi时,我收到此错误.在获得此项之前,您最多只能使用1024次迭代：

    C:\Users\myUsernameHere>python Desktop/piWriter.py
    End iteration: 1025
    Traceback (most recent call last):
      File "Desktop/piWriter.py", line 15, in <module>
        vars()['t' + str(sub)] = vars()['t' + str(i)] - vars()['p' + str(i)] * math.
    pow((vars()['a' + str(i)] - vars()['a' + str(sub)]), 2)
    OverflowError: long int too large to convert to float

这是我的代码：

import math

a0 = 1
b0 = 1/math.sqrt(2)
t0 = .25
p0 = 1

finalIter = input('End iteration: ')
finalIter = int(finalIter)

for i in range(0, finalIter):
        sub = i + 1
        vars()['a' + str(sub)] = (vars()['a' + str(i)] + vars()['b' + str(i)])/ 2
        vars()['b' + str(sub)] = math.sqrt((vars()['a' + str(i)] * vars()['b' + str(i)]))
        vars()['t' + str(sub)] = vars()['t' + str(i)] - vars()['p' + str(i)] * math.pow((vars()['a' + str(i)] - vars()['a' + str(sub)]), 2)
        vars()['p' + str(sub)] = 2 * vars()['p' + str(i)]
        n = i

pi = math.pow((vars()['a' + str(n)] + vars()['b' + str(n)]), 2) / (4 * vars()['t' + str(n)])
print(pi)

理想情况下,我希望能够插入一个非常大的数字作为迭代值,稍后再回来查看结果.

任何帮助赞赏！
谢谢！

解决方法:

浮点数只能表示最大为sys.float_info.max或1.7976931348623157e的数字.一旦你有一个超过308位的int(或左右),你就会陷入困境.当p1024有309位时,您的迭代失败：

179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216L

你必须为pi找到一个不同的算法,一个不需要这么大值的算法.

实际上,你必须小心四处浮动,因为它们只是近似值.如果您修改程序以打印pi的连续近似值,它看起来像这样：

2.914213562373094923430016933707520365715026855468750000000000
3.140579250522168575088244324433617293834686279296875000000000
3.141592646213542838751209274050779640674591064453125000000000
3.141592653589794004176383168669417500495910644531250000000000
3.141592653589794004176383168669417500495910644531250000000000
3.141592653589794004176383168669417500495910644531250000000000
3.141592653589794004176383168669417500495910644531250000000000

换句话说,仅经过4次迭代后,您的近似值就会越来越好.这是由于您使用的浮点数不准确,可能从1 / math.sqrt(2)开始.计算pi的许多数字需要非常仔细地理解数字表示.

标签：python,python-3-x,python-3-3,pi
来源： https://codeday.me/bug/20190620/1246279.html