Efficiently initialize and iterate a cyclic prng.
A cyclical PRNG implementation that can provably generate every number in the cycle exactly once before restarting. For more information on why this was built and how it works, see the corresponding natlas documentation.
In short, CyclicPRNG uses a multiplicative cyclic group of prime order, and computes the factorization of the order of the group to obtain possible subgroup orders. CyclicPRNG uses these subgroup orders for generator testing, and finds random generators. CyclicPRNG uses these generators to determine the order to traverse the cycle.
pipenv install cyclicprng
Initializing a Reordering PRNG
from cyclicprng import CyclicPRNG cycle_size = 10 c = CyclicPRNG(cycle_size) first_cycle = [c.get_random() for _ in range(cycle_size)] second_cycle = [c.get_random() for _ in range(cycle_size)] assert first_cycle != second_cycle
Initializing a Consistent PRNG
from cyclicprng import CyclicPRNG cycle_size = 10 c = CyclicPRNG(cycle_size, consistent=True) first_cycle = [c.get_random() for _ in range(cycle_size)] second_cycle = [c.get_random() for _ in range(cycle_size)] assert first_cycle == second_cycle
Registering Event Handlers
CyclicPRNG allows you to register event handlers to receive messages when the PRNG restarts. Optionally, an event handler could be provided at initialization to also receive an
The two events emitted by CyclicPRNG are:
>>> from cyclicprng import CyclicPRNG >>> cycle_size = 5 >>> c = CyclicPRNG(cycle_size, event_handler=print) init >>> for i in range(cycle_size): ... print(c.get_random()) ... 2 3 1 5 restart 4 >>> c.unregister_event_handler(print) >>> c.notify  >>> c.register_event_handler(print) >>> c.notify [<built-in function print>] >>> c.clear_event_handlers() >>> c.notify 
You may notice that the
restart event triggers before the last value is returned. This happens because the cycle automatically restarts when it reaches the final value in the cycle, right before that value is returned to the caller.
The following edge cases exist for CyclicPRNG:
size < 1-> Raise ValueError
size = 1-> Always return 1
size = 2-> The generator is always 2 (equivalent to consistent=true)
I've included these performance numbers based on tests on my development desktop. As such, they may not be indicative of performance on your machine.
On my desktop, CyclicPRNG repeatedly initializes with a size of 2^128 (the size of the IPv6 address space) in 0.03-0.04 seconds. I've included results from 10 sample inits below.
>>> import timeit >>> ip6_timer = timeit.Timer( ... "CyclicPRNG(340282366920938463463374607431768211456)", ... setup="from cyclicprng import CyclicPRNG", ... ) >>> >>> ip6_timer.repeat(10, 1) [0.03722329996526241, 0.0364310999866575, 0.03413929999805987, 0.034686600090935826, 0.03407520009204745, 0.033979699946939945, 0.034076200099661946, 0.03446660004556179, 0.03457159991376102, 0.03437739983201027]
Getting The Next Number
In a similar test, 10 subsequent calls to
get_random() all measured in the range of
7e-6 (3 to 7 microseconds). This would iterate the entire IPv4 address space (2^32) in a little over 8 hours.
>>> random_timer = timeit.Timer( ... "c.get_random()", ... setup="from cyclicprng import CyclicPRNG; c=CyclicPRNG(340282366920938463463374607431768211456)" ... ) >>> random_timer.repeat(10, 1) [5.499925464391708e-06, 7.0999376475811005e-06, 5.600042641162872e-06, 6.4999330788850784e-06, 5.499925464391708e-06, 4.200031980872154e-06, 6.200047209858894e-06, 6.7998189479112625e-06, 5.899928510189056e-06, 3.00002284348011e-06]
CyclicPRNG uses pytest for testing. You can run tests yourself by cloning this repo and setting up like so:
git clone https://github.com/natlas/cyclicprng.git cd cyclicprng/ pipenv install --dev pipenv run pytest tests.py
Copyright 2020 The Natlas Authors Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
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