Python decimal.InvalidOperation 使用大数时出错

Question

在python中，我编写了一个程序，使用丘德诺夫斯基算法计算圆周率的值。它适用于 800 以下的数字。但是，如果我使用 800 以上的数字，它会 returns 一个 decimal.InvalidOperation 错误。这是我的代码：

from math import factorial
from decimal import Decimal, getcontext

getcontext().prec = 1000

pi_input = input("How Many Digits Of Pi Are To Be Represented: ")
num = int(pi_input)

def cal(n):
    t = Decimal(0)
    pi = Decimal(0)
    deno = Decimal(0)

    for k in range(n):
        t = ((-1) ** k) * (factorial(6 * k)) * (13591409 + 545140134 * k)
        deno = factorial(3 * k) * (factorial(k) ** 3) * (640320 ** (3 * k))
        pi += Decimal(t) / Decimal(deno)
        
    pi = pi * Decimal(12) / Decimal(640320 ** Decimal(1.5))
    pi = 1 / pi

    return round(pi, n)

print(cal(num))

谁能帮帮我？

Answer 1

我不推荐你的方法。尝试像这样使用 gmpy 模块：

import sys
import math
import os.path
from gmpy2 import mpz, sqrt
from time import time, sleep

print_pi = input("Should The Value Of Pi Be Printed: ").lower()
print_pi_bool = 0

if "y" in print_pi:
    print_pi_bool = True
elif "n" in print_pi:
    print_pi = False
else:
    print("Incorrect Input. Please Try Again.")
    sys.exit()

def sqrt(n, one):
    """
    Return the square root of n as a fixed point number with the one
    passed in.  It uses a second order Newton-Raphson convgence.  This
    doubles the number of significant figures on each iteration.
    """
    # Use floating point arithmetic to make an initial guess
    floating_point_precision = 10**16
    n_float = float((n * floating_point_precision) // one) / floating_point_precision
    x = (int(floating_point_precision * math.sqrt(n_float)) * one) // floating_point_precision
    n_one = n * one
    count = 0
    while 1:
        count += 1
        print(count)
        x_old = x
        x = (x + n_one // x) // 2
        if x == x_old:
            break
    return x

def pi_chudnovsky_bs(digits):
    """
    Compute int(pi * 10**digits)

    This is done using Chudnovsky's series with binary splitting
    """
    C = 640320
    C3_OVER_24 = C**3 // 24
    def bs(a, b):
        """
        Computes the terms for binary splitting the Chudnovsky infinite series

        a(a) = +/- (13591409 + 545140134*a)
        p(a) = (6*a-5)*(2*a-1)*(6*a-1)
        b(a) = 1
        q(a) = a*a*a*C3_OVER_24

        returns P(a,b), Q(a,b) and T(a,b)
        """
        if b - a == 1:
            # Directly compute P(a,a+1), Q(a,a+1) and T(a,a+1)
            if a == 0:
                Pab = Qab = mpz(1)
            else:
                Pab = mpz((6*a-5)*(2*a-1)*(6*a-1))
                Qab = mpz(a*a*a*C3_OVER_24)
            Tab = Pab * (13591409 + 545140134*a) # a(a) * p(a)
            if a & 1:
                Tab = -Tab
        else:
            # Recursively compute P(a,b), Q(a,b) and T(a,b)
            # m is the midpoint of a and b
            m = (a + b) // 2
            # Recursively calculate P(a,m), Q(a,m) and T(a,m)
            Pam, Qam, Tam = bs(a, m)
            # Recursively calculate P(m,b), Q(m,b) and T(m,b)
            Pmb, Qmb, Tmb = bs(m, b)
            # Now combine
            Pab = Pam * Pmb
            Qab = Qam * Qmb
            Tab = Qmb * Tam + Pam * Tmb
        return Pab, Qab, Tab
    # how many terms to compute
    DIGITS_PER_TERM = math.log10(C3_OVER_24/6/2/6)
    N = int(digits/DIGITS_PER_TERM + 1)
    # Calclate P(0,N) and Q(0,N)
    P, Q, T = bs(0, N)
    one_squared = mpz(10)**(2*digits)
    sqrtC = sqrt(10005*one_squared, one_squared)
    return (Q*426880*sqrtC) // T

# The last 5 digits or pi for various numbers of digits
check_digits = {
        100 : 70679,
       1000 :  1989,
      10000 : 75678,
     100000 : 24646,
    1000000 : 58151,
   10000000 : 55897,
}

if __name__ == "__main__":
    digits = 100
    pi = pi_chudnovsky_bs(digits)
    #raise SystemExit
    for log10_digits in range(1,11):
        digits = 10**log10_digits
        start =time()
        pi = pi_chudnovsky_bs(digits)
        pi = str(pi)
        pi = pi[:(len(str(pi)) // 2) + 1]
        length = int(len(str(pi))) - 1
        print("Chudnovsky Binary Splitting Using GMPY: Digits",f"{digits:,}","\n--------------",time()-start,"--------------")
        print("Length Of " + f"{length:,}" + " Digits")

第一次回答，希望对你有帮助！

Python decimal.InvalidOperation 使用大数时出错

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