gpu.js with BigDecimal or float64array possible?

Question

I am writing a mandelbrot-calculator with the help of gpu.js and till now, everything works perfectly fine. The only issue I am facing is, that the GPU only wants to compute 32-Bit floats. Or at least this is what the official docs are telling me.
But when doing the same calculation with python and numba - which also runs on the same GPU - is much more precise when rendering the mandelbrot fractal.
With Python, I am able to get nearly around 1e-15 whereas in Javascript, the image becomes blurry at around 1e-7.

Python Kernel:

@cuda.jit(device=True)
def mandel(x, y, max_iters):
    c = complex(x, y)
    z = 0.0j
    for i in range(max_iters):
        z = z * z + c
        if (z.real * z.real + z.imag * z.imag) >= 4:
            return i

    return max_iters

Javascript Kernel:

const recalculateMandelbrot = gpu.createKernel(function(x_start, x_end, y_start, y_end, iters){
    let c_re = x_start + (x_end - x_start) * this.thread.x / 1024;
    let c_im = y_start + (y_end - y_start) * this.thread.y / 1024;
    let z_re = 0, z_im = 0;
    let z_re_prev = 0;

    for(let i = 0; i < iters; i++) {
        z_re_prev = z_re;
        z_re = z_re * z_re - z_im * z_im + c_re;
        z_im = z_re_prev * z_im + z_re_prev * z_im + c_im;

        if ((z_re * z_re + z_im * z_im) >= 4) {
            return i;
        }
    }
    return iters;
}).setOutput([1024, 1024]).setPrecision('single');

The algorithms are equal to each other, except that in Python, I can use its built-in complex type.

So I thought about using BigDecimal, where I can achieve arbitrary precision (so I can zoom in as far as I want), but I do not know how to add this to my gpu-kernel.

Update:

The reason why python works more precise, is because the complex type consists of two 64-Bit Floats. So the reason why JavaScript is calculation less precise, is because of JavaScript itself.
So my question now focuses on how to add big.js to my gpu-kernel?

Aside: the further you zoom in (on the interesting areas) the more iterations you need. So using a larger type will be a trade-off against speed. — Weather Vane
– Weather Vane, Commented Jun 5, 2022 at 20:42
@WeatherVane I know, and thats totaly fine, just wondering if this is possible — Dominik Lovetinsky
– Dominik Lovetinsky, Commented Jun 6, 2022 at 17:51

huseyin tugrul buyukisik · Accepted Answer · 2022-07-16 14:21:13Z

There is custom kernel test file here: https://github.com/gpujs/gpu.js/blob/1be50c09ed4edb7c7e846b1815414ef504089ab6/test/features/add-custom-native-function.js

with this kernel sample:

const glslDivide = `float divide(float a, float b) {
  return a / b;
}`;

Maybe there can be a way to use "double" in place of "float" and use it in place of simple multiplications and additions.

I don't know how to use glsl but if backend can be attached to glsl somehow, this should work. Also "double" needs glsl 4.0 so it may not work.

Even if it works, it still needs all of the iterations recursive because there is not "state variable" definition for double. Just like calling same function until max-iteration is reached. There should be two function parameters to keep track of imaginary and real parts and two other function parameters to keep track of number of iterations and maybe c value. Considering the depth of recursion is limited, it may not work, again.

Even in webgl backend, https://github.com/gpujs/gpu.js/blob/1be50c09ed4edb7c7e846b1815414ef504089ab6/src/backend/web-gl/fragment-shader.js it looks like you could just edit the string of some functions (like module down there) and use it like multiplication/addition.

You can also read here for an inspiration on multiplying/adding two 64bit values simulated by four 32bit values: https://github.com/visgl/luma.gl/blob/master/modules/shadertools/src/modules/fp64/fp64-arithmetic.glsl.ts

In any way, buffers(between Js environment & GPU driver) may not work at all and you are stuck with 100% functional programming within the kernel (no state handling for 64bit variables).

These are not good options. You should use a library that lets you write native kernel as a string (like this https://github.com/kashif/node-cuda/blob/master/test/test.js) and use it directly from Javascript so that you can do nearly anything you'd do within CUDA/OpenCL.

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