On Sat, Nov 05, 2022 at 01:37:30AM -0500, James Johnson wrote: > I wrote the attached python (3) code to improve on existing prng functions. > I used the time module for one method, which resulted in > disproportionate odd values, but agreeable means.
First the good news: your random number generator at least is well distributed. We can look at the mean and stdev, and it is about the same as the MT PRNG: >>> import random, time, statistics >>> def rand(n): ... return int(time.time_ns() % n) ... >>> data1 = [rand(10) for i in range(1000000)] >>> data2 = [random.randint(0, 9) for i in range(1000000)] >>> statistics.mean(data1) 4.483424 >>> statistics.mean(data2) 4.498849 >>> statistics.stdev(data1) 2.8723056046255744 >>> statistics.stdev(data2) 2.8734388686467534 There's no real difference there. But let's look at rising and falling sequences. Let's walk through the two runs of random digits, and take a +1 if the value goes up, -1 if it goes down, and 0 if it stays the same. With a *good quality* random sequence, one time in ten you should get the same value twice in a row (on average). And the number of positive steps and negative steps should be roughly the same. We can see that with the MT output: >>> steps_mt = [] >>> for i in range(1, len(data2)): ... a, b = data2[i-1], data2[i] ... if a > b: steps_mt.append(1) ... elif a < b: steps_mt.append(-1) ... else: steps_mt.append(0) ... >>> steps_mt.count(0) 99826 That's quite close to the expected 100,000 zeroes we would expect. And the +1s and -1s almost cancel each other out, with only a small imbalance: >>> sum(steps_mt) 431 The ratio of -ve steps to +ve steps should be 1, and in this sample we get 0.99904 which is pretty close to what we expect. These results correspond to sample probabilities: * Probability of getting the same as the previous number: 0.09983 (theorectical 0.1) * Probability of getting a larger number than the previous: 0.45030 (theoretical 0.45) * Probability of getting a smaller number than the previous: 0.44987 (theoretical 0.45) So pretty close, and it supports the claim that MT is a very good quality RNG. But if we do the same calculation with your random function, we get this: >>> steps.count(0) 96146 >>> sum(steps) -82609 Wow! This gives us probabilities: * Probability of getting the same as the previous number: 0.09615 (theorectical 0.1) * Probability of getting a larger number than the previous: 0.41062 (theoretical 0.45) * Probability of getting a smaller number than the previous: 0.49323 (theoretical 0.45) I ran the numbers again, with a bigger sample size (3 million instead of 1 million) and the bias got much worse. The ratio of -ve steps to +ve steps, instead of being close to 1, was 1.21908. That's a 20% bias. The bottom line here is that your random numbers, generated using the time, have strong correlations between values. And that makes it a much poorer choice for a PRNG. -- Steve _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/D6SV3NQ6OHAPKBGM27UBF5KUMUHABDP5/ Code of Conduct: http://python.org/psf/codeofconduct/
