Hey all, this is my first post on this forum! I have written a GLSL shader that renders the Mandelbrot/Julia set and I've run into precision problems. I have been able to render fractals on the CPU with arbitrary precision libraries such as GMP. The reason why I switched to rendering on the GPU is that I now have live video orbit traps with shading. I want to keep this and also have the option to do arbitrary precision. Is there any way I can pass an arbitrary precision float to a GLSL shader? Or is there a known way of converting an arbitrary precision float into e.g. a texture or multiple floats?

My ultimate goal is to eventually implement K.I. Martin's perturbation method. I might not understand it correctly, maybe the questions above are invalid due to a misunderstanding of the theory. Here's how I think it works:

1. Pick a Xn
2. Calculate Xn for each n in 0...max iter(?) in arbitrary precision.
3. Calculate An, Bn, and Cn for each n in 0...max iter(?) in arbitrary precision.
4. Send values from 1 and 2 to shader once
5. Calculate delta 0 in single floating-point precision(?)
6. Check whether delta0**3<<delta0**2
7. Calculate delta n
8. Calculate Yn
9. Skip iterations and profit


I hope this is correct. Probably not:) I can't find K.I. Martins superfractalthing website anymore, I'm basing this off an old PDF I had on my computer. I'm unsure which parts are supposed to be done in arbitrary and single floating-point precision.

Programming in C++ is new to me and I wish I had a background in math , but this has been the most interesting and beautiful challenge so far. Any good resource is very welcome! I'm also interested in implementing my own arbitrary precision code if necessary.


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