1000 digits of pi in Python

Question

I have been thinking about this issue and I can\'t figure it out. Perhaps you can assist me. The problem is my code isn\'t working to output 1000 digits of pi in the Python

Answer 1

If you don't want to implement your own algorithm, you can use mpmath.

try:
    # import version included with old SymPy
    from sympy.mpmath import mp
except ImportError:
    # import newer version
    from mpmath import mp

mp.dps = 1000  # set number of digits
print(mp.pi)   # print pi to a thousand places

Reference

Update: Code supports older and newer installations of SymPy (see comment).*

Answer 2

wallis formula can get to 3.141592661439964 but a more efficient way is needed to solve this problem.

https://www.youtube.com/watch?v=EZSiQv_G9HM

and now my code

x, y, summing = 2, 3, 4

for count in range (0,100000000):
    summing *= (x/y)
    x += 2
    summing *= (x/y)
    y += 2

print (summing)

Answer 3

I was solved with bellow formula 5-6 years ago.

Machin-like formula

Wikipedia: https://en.wikipedia.org/wiki/Machin-like_formula

Sorry for the code quality. Variable names can be meaningless.

#-*- coding: utf-8 -*-

# Author:    Fatih Mert Doğancan
# Date:      02.12.2014

def arccot(x, u):
    sum = ussu = u // x
    n = 3
    sign = -1
    while 1:
        ussu = ussu // (x*x)
        term = ussu // n
        if not term:
            break
        sum += sign * term
        sign = -sign
        n += 2
    return sum

def pi(basamak):
    u = 10**(basamak+10)
    pi = 4 * (4*arccot(5,u) - arccot(239,u))
    return pi // 10**10

if __name__ == "__main__":
    print pi(1000) # 1000 

Answer 4

Does this do what you want?

i = 0;
pi_str = ""
for x in make_pi():
    pi_str += str(x)
    i += 1
    if i == 1001:
        break

print "pi= %s.%s" % (pi_str[0],pi_str[1:])

Answer 5

Here is a different way I found here --> Python pi calculation? to approximate python based on the Chudnovsky brothers formula for generating Pi which I have sightly modified for my program.

def pifunction():
    numberofdigits = int(input("please enter the number of digits of pi that you want to generate"))
    getcontext().prec = numberofdigits

def calc(n):
    t = Decimal(0)
    pi = Decimal(0)
    deno = Decimal(0)
    k = 0
    for k in range(n):
        t = (Decimal(-1)**k)*(math.factorial(Decimal(6)*k))*(13591409+545140134*k)
        deno = math.factorial(3*k)*(math.factorial(k)**Decimal(3))*(640320**(3*k))
        pi += Decimal(t)/Decimal(deno)
    pi = pi * Decimal(12)/Decimal(640320**Decimal(1.5))
    pi = 1/pi
    return str(pi)
print(calc(1))

I hope this helps as you can generate any number of digits of pi that you wish to generate.

Answer 6

From Fabrice Bellard site: Pi Computation algorithm. Sorry for such a straightforward implementation. 1000 is fast enough (0.1s for me), but 10000 isn't such fast - 71s :-(

import time
from decimal import Decimal, getcontext

def compute(n):
    getcontext().prec = n
    res = Decimal(0)
    for i in range(n):
        a = Decimal(1)/(16**i)
        b = Decimal(4)/(8*i+1)
        c = Decimal(2)/(8*i+4)
        d = Decimal(1)/(8*i+5)
        e = Decimal(1)/(8*i+6)
        r = a*(b-c-d-e)
        res += r
    return res

if __name__ == "__main__":
    t1 = time.time()
    res = compute(1000)
    dt = time.time()-t1
    print(res)
    print(dt)