Click Canvas to Step Through When Paused
- TODO: option to initialize with various seed values to demonstrate tendency to converge towards uniformity (though with suspect quality of randoms) A new PRNG has applications for energy efficient data science, math, finance & physics … This PRNG? Probably not…
- TODO: histogram to demostrate value distribution
- TODO: GPU-friendly method of visualizing entropy and variance in
Parallelized Random Number Generation in the Browser
Yes, the Prison of Zod Effect is Intentional…
This is a basic parallelized random number generator written with
WebGL and ThreeJS. It is, however, a terrible random number generator,
although it could be improved. I’ve used ThreeJS, a javascript
graphics engine built on top of Canvas and WebGL, to seed a texture
from an array containing random floats. The alpha channel of the
texture is one. The PRNG simply adds the values sampled from texture
for the current pixel to the pixels surrounding it with distance 1.
Then, the PRNG runs fract() to get the fractional part of the float
value for that pixels channels. Fract is explained below.
I hope to add some code soon that will verify the uniformity and quality of PRNG distribution, along with allowing the user to modulate parameters for it. I will write some better variations on PRNG’s soon that are based on this concept, but this is a good enough “hello world” for GPU PRNG.
The texture is simply 64x64 so the point can be more easily visualized, but scales to 4096x4096 with no problems at ~30 fps. That’s 30 x 4 x 4096 x 4096 random numbers per second. Even though the quality is suspect, that’s about 2 Gigarands per second. There is no delay from overhead related to WebGL calls and therefore, adding a bit more state and calculation to the shader should not cause delay.
Here’s the shader code for the PRNG. The ThreeJS code to set this up can be found here.
Fragment Shader: computeShaderRandoms
Fragment Shader: shaderStats
Why Is This PRNG Terrible?
Actually, it’s not so bad. If there were major problems with the calculation, there would be noticeible shifts in the output. While the problems with this approach are much more difficult to detect with the human eye, problems with PRNG’s rendered to a texture could leave a discernible color shift.
This PRNG doesn’t provides neither Backtracking Resistance nor Prediction Resistance, so it’s definitely not suitable for security applications. It’s efficency implies it may be more appropriate for other applications dependent on large quantities of random numbers, such as physics, lighting, finance and algorithms using monte carlo. However, since it lacks prediction resistence, it would seem to have deficient quality in randomness. The quality would be greatly improved by
However, this isn’t really a PRNG, as it’s randomness depends solely
on the seeded randoms from javascript’s Math.random() function,
which I used for the input to the initial texture. But what’s great
about sufficiently random seeds is that operating on them in specific
ways should yield sufficiently random output, with limited
state. State is a limiting factor for parallelized PRNG’s, since GPU
handles various forms of memory in different ways. State must not be
mutated by the CPU/GPU in ways prohibitive to many design approaches
for parallel PRNG’s.
This is why the Wallace Transform is useful: it is parallelizable and it’s “good enough” … apparently. The approach in this blog isn’t exactly the Wallace transform, but that was the closest thing in literature that I found that seemed to match the approach most intuitive to me. I didn’t want to look at the studies being done because, to me, the fun is in discovering this stuff myself and so looking is kind of like cheating, in a way. The only reason I looked was because someone tried leading me by the nose to encourage me to give up before completing anything that could be viewed on the web.
I was sent to a mental institution the next day … for reading a bible aloud, in front of a statue of Martin Luther, on the property of a Christian university, and while a track meet of Christian colleges was underway. I still can’t get enough of this shit. I was reading Romans 7 and 8. Don’t judge. Coincidence? I don’t really care.
Thanks Obama. I got TDO’d and someone had to pay a $10,400 bill for me to attend a TDO kangaroo court to have my gun rights disrupted, which prevented me from joining the military. THANKS OBAMA. I was not permitted to have access information that would have helped me make better decisions in the “court” hearing. I was rushed through and had less than a minute to talk to my lawyer, who encouraged me to take a plea deal, which prevented me from having ANY APPEALS RECOURSE. Meanwhile, I am never given credit for any of my strengths, like intelligence, creativity or stubbornness.
I don’t actually know if any of this is Obama’s fault, but holy shit, the government paid $10,400 for me to be in that facility for eight days, which was $10,000 more than I made in 2016! I don’t have to file taxes because I didn’t even make $400 this year! Meanwhile, it appears the government is willing to pay anything to cover its own ass for ruining my life, over and over and over again, all the while interfering with my life.
Anyways, here’s proof that I’m at least somewhat technically competent. Oh an guess what? THIS WAS A “TDO” HEARING, WHICH APPARENTLY NOW SHOWS UP ON MY CRIMINAL RECORD, FOR WHICH I HAD NO RECOURSE, NO REPRESENTATION, AND INADEQUATE MEDICAL EVALUATION FOR TDO – AND IT SHOWS UP ON ANY FUCKING BACKGROUND CHECK. Especially one a military recruiter runs. And honestly, that is the cheapest way to get a background check if you know why they ask the questions they do.
This is why I would make an excellent intellegence analyst. I knew what was wrong with my three minute conversation with the recruiter and I knew exactly what information he was seeing without needing him to tell me. There was nothing wrong with how the recruiter handled the situation: he was exposed to information on my criminal record for which he was trained to handle in a specific way. I’m pissed at the information now on my background check.
Can the Government Get the Fuck Out of My Life?!
Stop pissing all over yourself just for me. It’s not very becoming. And if I could ever get a job without being bullied by the facility security officer (FSO … a role required by the FCL process DSS runs for DoD contracting) then HOLY SHIT I might be so distracted, I wouldn’t even care.
And that’s why I read Joint military doctrine at night. It’s not just to imagine how logistics are applied to manage thousands of people across a large organization. It’s not just because I wanted to join the military. I read this stuff and other assorted government reports because I want to know these people’s decision making processes so that when people lie to me, I know. You see, if you apply a Clausewitzian perspective to my life, you’ll find that, no matter what happens, David Conner gets fucked in the butt. It doesn’t matter how it happens, but that is what happens.
That’s Clauswitz for you. It’s an effects-based paradigm for the philosophy of military tactics that is especially important for judging second-order and third-order effects from the application of ways and means. It’s not how David Conner gets fucked in the butt that matters. It is that, in the end, David Conner gets a good poke in the butt.
And I haven’t even ventured into my understanding of the applictation of the Laplacian to information systems, coupled with an understanding of logistics, employee training and law, which basically means I’m borderline psychic. And damaged goods, psychologically speaking.
The Fract() Function: Floats Zero through One
I need to identify the boundaries for floats, since colors are encoded from one to zero… That way I can xor all the things to my hearts content. Or so I thought…
Fract is a function for OpenGL that truncates floats to return the
value from zero to one. I’m glad I found fract() because otherwise I
was going to need to stomp whoever left bitcrunching functions out of
WebGL. C’est vrai: no GPU bitcrunching for you. Assholes, amiright?
And no, I didn’t actually know what fract() was beforehand.
Here’s some info on identifying floats from zero to one.
[+] Zero
0:00000000 :0000000 00000000 00000000
[-] Zero
1:00000000 :0000000 00000000 00000000
[<] One
0:01111110 :1111111 11111111 11111111
[=] one
0:01111111 :0000000 00000000 00000000
Fract Exclusion Mask
1:10000001 :0000000 00000000 00000000
Fract Inclusion Mask
0:01111110 :1111111 11111111 11111111