import math
import unittest
import random


def wallis(n):
	a= 1
	while(n):
		a = a*(4*(n**2)/(4*(n**2)-1))
		n-=1
	return 2*a

def monte_carlo(n):
	circle = 0
	sqr = 0
	while(n):
		a,b = random.random(),random.random()
		dist = math.sqrt(a**2 + b**2)
		if dist<1:
			circle+=1
		else:
			sqr +=1
		n-=1
	pi = 4*(circle/(circle+sqr))
	return pi
		

class TestWallis(unittest.TestCase):
    def test_low_iters(self):
        for i in range(0, 5):
            pi = wallis(i)
            self.assertTrue(abs(pi - math.pi) > 0.15, msg=f"Estimate with just {i} iterations is {pi} which is too accurate.\n")
            
    def test_high_iters(self):
        for i in range(500, 600):
            pi = wallis(i)
            self.assertTrue(abs(pi - math.pi) < 0.01, msg=f"Estimate with even {i} iterations is {pi} which is not accurate enough.\n")

class TestMC(unittest.TestCase):
    def test_randomness(self):
        pi0 = monte_carlo(15000)
        pi1 = monte_carlo(15000)
        
        self.assertNotEqual(pi0, pi1, "Two different estimates for PI are exactly the same. This is almost impossible.")

        self.assertFalse(abs(pi0 - pi1) > 0.05, "Two different estimates of PI are too different. This should not happen")

    def test_accuracy(self):
        for i in range(500, 600):
            pi = monte_carlo(i)
            self.assertTrue(abs(pi - math.pi) < 0.4, msg=f"Estimate with even {i} iterations is {pi} which is not accurate enough.\n")

if __name__ == "__main__":
    unittest.main()
