utils.py

import requests
import math
import time

import pandas as pd

def nth_pi(k):
    return (16**(-k))*((4/(8*k+1))-(2/(8*k+4))-(1/(8*k+5))-(1/(8*k+6)))

def pi_google(n, start=0):
    if n > 1000:
        n=1000
    r = requests.get('https://api.pi.delivery/v1/pi?start={}&numberOfDigits={}'.format(start, n))
    return r.json()["content"][2:]

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
    while 1:
        x_old = x
        x = (x + n_one // x) // 2
        if x == x_old:
            break
    return x

def pi_chudnovsky(one=1000000):
    """
    Calculate pi using Chudnovsky's series

    This calculates it in fixed point, using the value for one passed in
    """
    k = 1
    a_k = one
    a_sum = one
    b_sum = 0
    C = 640320
    C3_OVER_24 = C**3 // 24
    while 1:
        a_k *= -(6*k-5)*(2*k-1)*(6*k-1)
        a_k //= k*k*k*C3_OVER_24
        a_sum += a_k
        b_sum += k * a_k
        k += 1
        if a_k == 0:
            break
    total = 13591409*a_sum + 545140134*b_sum
    pi = (426880*sqrt(10005*one, one)*one) // total
    return pi

def count_digits(digits):
    pi_dict = {}
    for n in range(0,10):
        pi_dict[str(n)] = [digits.count(str(n))]

    freq_tbl = pd.DataFrame.from_dict(pi_dict).transpose().reset_index()
    freq_tbl.columns = ["digit", "frequency"]
    freq_tbl["rel_frequency"] = freq_tbl["frequency"]/freq_tbl["frequency"].sum()

    return freq_tbl