Simple Lehmer random number generator and Pi calculus. No NumPy, pure Python only.

main.py

#!/usr/bin/env python3
# -*- encoding: utf-8 -*-

from functools import reduce
from math import sqrt
from random import random


class MyRandomizer:

    def __init__(self, m, n):
        assert m < n
        self.m = m
        self.n = n

    def random(self, count):
        seed = int(random() * (self.n - 1)) + 1
        return reduce(lambda x, _: x + [(x[-1] * self.m) % self.n],
                      range(count - 1),
                      [seed])


def test1d(func, randomizer, counts, tries, n):
    for count in counts:
        for _ in range(tries):
            xs = [(2 * x - n) / n for x in randomizer.random(count)]
            ys = map(func, xs)
            area = (2 / count) * sum(ys)
            print('count = %s\tarea = %s' % (count, area))


def test2d(func, randomizer, counts, tries, n):
    for count in counts:
        for _ in range(tries):
            points = ((2 * x - n) / n for x in randomizer.random(2 * count))
            points = zip(*[iter(points)] * 2)
            points_inside = sum(func(x, y) for x, y in points)
            area = 4 * points_inside / count
            print('count = %s\tarea = %s' % (count, area))


def main():
    n = 2 ** 32
    tries = 3
    counts = 4

    badrandomizer = MyRandomizer(3, n)
    goodrandomizer = MyRandomizer(1664525, n)

    counts_list = [10 ** n for n in range(1, counts + 1)]

    # 1-d
    def half_circle(x): return sqrt(1 - x ** 2)

    print('# 1D')
    print()

    print('Bad randomizer (M = 3)')
    test1d(half_circle, badrandomizer, counts_list, tries, n)
    print()
    print('Good randomizer (M = 2^16+3)')
    test1d(half_circle, goodrandomizer, counts_list, tries, n)

    print()

    # 2-d
    def circle_indicator(x, y): return x ** 2 + y ** 2 <= 1

    print('# 2D')
    print()

    print('Bad randomizer (M = 3)')
    test2d(circle_indicator, badrandomizer, counts_list, tries, n)
    print()
    print('Good randomizer (M = 2^16+3)')
    test2d(circle_indicator, goodrandomizer, counts_list, tries, n)


if __name__ == '__main__':
    main()