python 计算π（pi）到任意的deptth

Posted 2021-05-09

# Author: Muhammad Ahmad Tirmazi
# Date: January 4, 2014
from decimal import *
import math

class PiCalculator(): #Calculates Pi
    def __init__(self, prec):
        getcontext().prec = prec # the precision
        return

    def nilakantha(self, end): # Nilakantha's series
        op = '+'
        x = Decimal(3)
        for n in range(2, end, 2):
            if (op == '-'):
                x -= ( Decimal(4) / Decimal((n * (n+1) * (n+2))) )
                op = '+'
            else:
                x += ( Decimal(4) / Decimal((n * (n+1) * (n+2))) )
                op = '-'
        return x

    def gregory_leibniz(self, end): # Gregory-Leibniz's series
        op = '+'
        x = Decimal(0)
        for n in range(1, end):
            if (op == '-'):
                x -= ( Decimal(4) / Decimal(2*n - 1) )
                op = '+'
            else:
                x += ( Decimal(4) / Decimal(2*n - 1) )
                op = '-'
        return x

    def ramanujan(self, end): # Ramanujan's series
        y = Decimal(0)

        for n in range(0, end):
            y += ( Decimal(math.factorial(4*n)) * Decimal((1103 + 26390*n)) )\
                 / (Decimal(math.pow( Decimal(math.factorial(n)), 4)) \
                    * Decimal(math.pow(396, 4*n)) )
            y *= ( Decimal(2) * Decimal(math.sqrt(2)) ) / Decimal(9801)

        y = Decimal(1/y)
        return y

    def chudnovsky(self, end):
        y = Decimal(0)

        for n in range(0, end):
            y += ( Decimal(math.factorial(6*n)) * \
                   Decimal((13591409 + 545140134*n)) )\
                   / ( Decimal(math.pow( \
                                         Decimal(math.factorial(3*n)) * Decimal(math.factorial(n)), 3)) \
                       * Decimal(math.pow(-640320, 3*n)) )

        y *= ( Decimal(12) / Decimal(math.pow(640320, 1.5)) )

        y = Decimal(1/y)
        return y

    def in_built(self): # Stored Value by Python implementation
        return Decimal(math.pi)