#!/usr/bin/env python3
# ---------------------------------------
# Project Name : PythonCheatSheet
# File Name : Calculate-Pi-3-Gregory-Leibniz.py
# Created Date : 2023-02-02 12:46:25 UTC+7
# Last Modified: 2023-02-02 12:48:49 UTC+7
# ---------------------------------------
from pytictoc import TicToc
t = TicToc() # create TicToc instance
t.tic() # Start timer
print(f"================================")
# DO SOMETHING
# https://www.mathscareers.org.uk/calculating-pi/
# Gregory-Leibniz:
# Pi/4 = [1 - 1/3 + 1/5 - 1/7 + 1/9 - ...]
def my_pi(p_number: int) -> float:
my_result = 0
for i in range(1, n+1, 1):
if i % 2 == 0: # even
my_result = my_result - 1/(2*i - 1)
else: # odd
my_result = my_result + 1/(2*i - 1)
return my_result*4
n = 1000000
print(f'my_pi({n}): {my_pi(n)}')
print(f"================================")
t.toc() # Print elapsed time: "Elapsed time is <xxx> seconds."
# ---------------------------------------
# REF:
# https://mathshistory.st-andrews.ac.uk/HistTopics/1000_places/
# 3.14159265358979323846264338327950288419716939937510
# RESULT:
# WINDOWS 3900x:
# ================================
# my_pi(1.000.000): 3.1415916535897743
# ================================
# Elapsed time is 0.127023 seconds.
# Linux 3900x:
# ================================
# PI : 3.1415916535897743
# ================================
# Elapsed time is 0.209464 seconds.
# ================================
# PI : 3.1415916535897743
# ================================
# Elapsed time is 0.197258 seconds
# LINUX 5600g:
# n = 100 # 3.1315929035585537
# n = 500 # 3.139592655589785
# n = 700 # 3.1401640828900845
# n = 1.000 # 3.140592653839794
# n = 2.000 # 3.1410926536210413
# n = 3.000 # 3.1412593202657186
# n = 5.000 # 3.141392653591791 - 0.001042 seconds.
# n = 1.000.000 # 3.1415916535897743 - 0.074705 seconds.
# n = 10.000.000 # 3.1415925535897915 - 0.757600 seconds.
# n = 100.000.000 # 3.141592643589326 - 7.646685 seconds.
# n = 1.000.000.000 # 3.1415926525880504 - 81.178900 seconds.
# n = 1.000.000.000 # 3.1415926525880504 - 76.741032 seconds
# n = 10.000.000.000 # 3.141592653488346 - 937.967539 seconds.