#!/usr/bin/env python3
from random import randint
from math import log2

class lfsr(object):
    def __init__(self, state, taps):
        self.state = state
        self.taps = taps

    # getters and setters (private attributes)
    def get_state(self):
        return self.__state
    def set_state(self, value):
        self.__state = value
    state = property(fget=get_state, fset=set_state, doc="lfsr state (current bits value in lfsr)")

    def get_taps(self):
        return self.__taps
    def set_taps(self, valeur):
        self.__taps = valeur
    taps = property(fget=get_taps, fset=set_taps, doc="lfsr taps (bit positions affecting next state)")

    def shift(self):
        '''
        calculate next state and return the output bit
        '''
        feedback = sum(self.state[tap] for tap in self.taps) % 2
        output = self.state[-1]
        self.state = [feedback] + self.state[:-1]
        return output


def test_lfsr17():
    key = [randint(0, 1) for _ in range(16)] # first 16 bits
    key.append(1)  # prevent initial state from being {0}^17
    taps = [16-0, 16-14]
    lfsr17 = lfsr(key, taps)
    states = [lfsr17.state]
    for _ in range(2**17-2):
        lfsr17.shift()
        states.append(lfsr17.state)
    sorted_states = sorted(states, key=lambda x: tuple(x))
    for i in range(2**17-2):
        if sorted_states[i] == sorted_states[i+1]:  # compare each state with the next state in the sorted list, if 2 states are identical they should be next to each other
            print(f'state {sorted_states[i]} appears at least 2 times')
            return False
    n_state = len(sorted_states)
    n_state_log = log2(n_state+1)
    print(f'all {n_state} = 2^({n_state_log})-1 states are different')
    return True

test_lfsr17()