Identifying and understanding this PRNG

Question

I have this random number generator, and have had it for quite some time, but despite how much I use it I don't really understand it.

public static int Random(int x)
{
    x = x + seed;
    x = (x << 13) ^ x;
    return (x * (x * x * 15731 + 789221) + 1376312589) & 0x7fffffff;
}

It works really well for my purposes - it takes an integer and just spits out another random integer. It doesn't rely on a state, nor does it rely on its last output like so many linear congruential generators.

What type of generator is this? I'd like some terms that I can google to understand and learn more about it. What family of PRNG does it belong to? How/why does it work?

You shouldn't put images of text in your posts. Always post the code itself so it's easier to copy/paste and to search. I edited your question, you can verify I didn't do any mistake. — Vincent Savard, Jun 23 '16 at 14:24
If you can afford the lower performance, I'd consider using a proper PRF (pseudo-random-function) instead. — CodesInChaos, Jun 23 '16 at 14:51
Can anyone suggest how I could modify this function to accommodate 2 and 3 input integers? — , Jun 23 '16 at 15:48
Combine the integers into one according to your requirements (xor? add? multiply?), then call this function with the result. — jpaugh, Jun 23 '16 at 20:57

Robert Harvey · Accepted Answer · 2016-06-23T14:42:41.283

5

A bit of poking around on Google suggests that this is a Linear Feedback Shift Register or LFSR. It's apparently commonly used to produce noise for shaders.

Further Reading
Noise and Pseudo Random Number Generator in GLSL
Linear-feedback shift register

edited Jun 23 '16 at 14:42

answered Jun 23 '16 at 14:36

Robert Harvey

199,517

@MasonWheeler Depends on the definition you're using. For example one could consider /dev/urandom a PRNG because it's not truly random, but it's not deterministic because it implicitly seeds (and frequently reseeds) itself from various true RNGs. – CodesInChaos Jun 23 '16 at 14:45
@CodesInChaos So what happens when it gets the same seed? – 8bittree Jun 23 '16 at 14:46
1

For perlin noise, you essentially need a hash function, not a stateful PRNG. Since this is cheap hash, it's suitable for that purpose. – CodesInChaos Jun 23 '16 at 14:47
Good links. I think it's important to note that you can imply from the second link that these are not recommended for crypto purposes unless you really know what you are doing. – JimmyJames Jun 23 '16 at 14:50
1

LFSRs are used any time you need a data source that's mostly random at face value, but is still deterministic. If you were developing a wireless transmission protocol for example, an LSFR output is random enough to simulate arbitrary data, but deterministic so that you can debug transmission errors because you know what you should be receiving. – whatsisname Jun 23 '16 at 14:54
Can anyone suggest how I could modify the function to take 2 and 3 input integers? – Jun 23 '16 at 15:49
@user2312610: That doesn't make much sense for an LFSR. – Robert Harvey Jun 23 '16 at 15:57
@whatsisname: as in; how could I get it to do what it currently does, but taking the signature public static float Random(int x, int y, int z) - where it spits out random numbers unique to that combination of 3 numbers – Jun 23 '16 at 15:57
@user2312610 How big is int? If you have an integer type that is quadruple the size, you can make your three ints significant digits of that larger size, but you would have to completely rewrite the function with new constants. – Robert Harvey Jun 23 '16 at 15:59
@RobertHarvey: they're 32 bit integers - and my constants are just large primes I plucked off a graph from memory. How would I encode said significant digits? I can't say I've done much work with bitwise operations before – Jun 23 '16 at 16:02
@user2312610: Sounds like you need a 96 bit LFSR (for three 32-bit integers). According to this table, you can build one using taps at positions 96, 90, 87 and 86. See also http://stackoverflow.com/questions/7830379/how-to-implement-128-bit-linear-feedback-shift-register-with-byte-element-array – Robert Harvey Jun 23 '16 at 16:11
@user2312610: while that doesn't make much sense, in any case, don't change the function, but decide a way to turn your three numbers into a single number then feed that to a LSFR of sufficient size. – whatsisname Jun 23 '16 at 16:13
@whatsisname: The "way" would be x^64 + y^32 + z, assuming you have a data type large enough to put that in. Or simply a 3-element array of 32 bit numbers, and write an LSFR using those. – Robert Harvey Jun 23 '16 at 16:39

JimmyJames · Answer 2 · 2016-06-23T20:18:29.217

4

To be clear, this doesn't produce a random number. What it does (I expect) is produce wildly different numbers for integers that are close to each other. The way it does that is by overflowing the int by creating numbers that are bigger (absolute value) than the 32 bit range can support at least once. The shift and xor appear to expand the input over 32 bits and the multiplications and additions cause it to overflow and improve the distribution. I am not a mathematician but I believe this could be described as a chaotic function.

I ran some numbers through Java with seed of 13. Seems pretty well distributed:

Locally too:

edited Jun 23 '16 at 20:18

answered Jun 23 '16 at 14:43

JimmyJames

27,287

PRNG = Pseudo Random Number Generator. The "pseudo" implies it's not truly random. – 8bittree Jun 23 '16 at 14:45
@8bittree Of that, I am well aware but the comment "takes an integer and just spits out another random integer" suggests to me it's worth pointing out explicitly. – JimmyJames Jun 23 '16 at 14:47
@jimmyjames "random" was just lazy short-hand - i know it's only pseudorandom – Jun 23 '16 at 15:12
1

@user2312610 I figured you did but this often poorly understood and other people could read that and be confused. – JimmyJames Jun 23 '16 at 15:27
Bloody hell - thanks for the graphics and stuff - that's incredible. – Jun 23 '16 at 15:34
@user2312610 cool, glad you liked them. It didn't notice that & 0x7fffffff was stripping off the sign bit until I saw the graph. – JimmyJames Jun 23 '16 at 15:44
@JimmyJames Could you suggest how I might adapt the function to accommodate 2 and 3 input integers? – Jun 23 '16 at 15:50
@user2312610 I can think of some ways but I'm not sure what your goal is. Care to elaborate? – JimmyJames Jun 23 '16 at 15:56
Let us continue this discussion in chat. – Jun 23 '16 at 15:58
@Justin Ha! I made them in Excel how embarrassing is that? – JimmyJames Jun 23 '16 at 17:03
Re, "using x as an exponent": The ^ operator in Java is not exponentiation; it's bit-wise XOR. – Solomon Slow Jun 23 '16 at 20:07
@jameslarge my bad, I'll fix. – JimmyJames Jun 23 '16 at 20:14

Identifying and understanding this PRNG

2 Answers2