Python - 尝试计算 pi 的数字，但无法超过小数点后 48 位数字

Question

我正在尝试编写一个程序来使用Python中的Nilakantha系列来计算pi的数字。每次运行它都不会给我超过 50 位小数。仍在学习 python，因此我们将不胜感激。

# Program using Nilakantha Series to crunch digits of pi
from math import *
from decimal import *

getcontext().prec = 200 # this is not doing anything

# epsilon is how accurate I want to be to pi
EPSILON = 0.000000000000000000000000000000000000000000000000000001

sum = float(3)
step = 0

i = 2

while abs(pi - sum) >= EPSILON:
    step += 1
    print (step)
    if step % 2 == 1:
        sum += 4.0 / (i * (i + 1) * (i + 2))
        i += 2
    else:
        sum -= 4.0 / (i * (i + 1) * (i + 2))
        i += 2

print (Decimal(sum))
print (Decimal(pi))
print ("Total itterations: ", step)
print ("Accurate to: ", EPSILON)

Answer 1

您没有使用 Decimal 类来计算 Pi，而是使用 float 类。

getcontext()

影响 Decimal，而不是 float。

如果您想使用 Decimal，请修改代码以在循环之前转换为 Decimal。请注意，据我所知，Pi 的值在 Python 中不能以十进制形式提供，因此您需要从其他地方获取该值（http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits）。 html）。

Answer 2

这里可以了，但是我对超过30位的数字没有耐心。 200 需要很长很长的时间。

# Program using Nilakantha Series to crunch digits of pi
from math import *
from decimal import *
pr = 24
getcontext().prec = pr+2 # set pi's prec

# epsilon is how accurate I want to be to pi
EPSILON = Decimal(1/10**(pr+1))
from mpmath import mp
def a(n):
   mp.dps=n+1
   return(Decimal(str(mp.pi)))
four = Decimal(4.0)
two = Decimal(2.0) 
x = Decimal(3)
step = 0
p = a(pr) 
print(f"{p}")
i = two

while abs(p - x) >= EPSILON:
    step += 1
    if step%10**6 == 0: 
        w = f"{abs(p-x):.{pr}f}" 
        val = next((index for index,value in enumerate(w[2:]) if value != '0'), None)
        acc = " " * (val+4) + "^" # Accuracy tick mark
        print (f"Iteration {step:,}\npi={p}\nmy={x}\n{acc}")
        
    if step%2:
        x += four / (i * (i + 1) * (i + 2))
        i += two
    else:
        x -= four / (i * (i + 1) * (i + 2))
        i += two

print (f"Calulated={x:.{pr}f}")
print (f"Constant ={p:.{pr}f}")
print (f"Total itterations: {step:,}")
print ("Accurate to: ", EPSILON)

输出为23位：

$ python pi_calc.py 
3.1415926535897932384626
Iteration 1,000,000
pi=3.1415926535897932384626
my=3.14159265358979323871117
                      ^
Iteration 2,000,000
pi=3.1415926535897932384626
my=3.14159265358979323849364
                       ^
Iteration 3,000,000
pi=3.1415926535897932384626
my=3.14159265358979323847099
                        ^
Iteration 4,000,000
pi=3.1415926535897932384626
my=3.14159265358979323846537
                        ^
Iteration 5,000,000
pi=3.1415926535897932384626
my=3.14159265358979323846353
                         ^
Iteration 6,000,000
pi=3.1415926535897932384626
my=3.14159265358979323846267
                         ^
Calulated=3.1415926535897932384626
Constant =3.1415926535897932384626
Total itterations: 6,163,925
Accurate to:  9.999999999999999604346980148993092553230786866765862587503680141039208439934782290947623550891876220703125E-24