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I really like using Fragmentarium to program and view fractals, but it comes up short for deep 2D zooms because the camera position is limited to single-precision. Is there any programmable, fractal renderer that can handle high-precision zooming (at least twice the precision of native doubles) at interactive framerates? CPU-based renderers tend to be pretty slow, so they probably wouldn't be what I'm looking for.

If there's no program out there that's good at this, I suppose I could improve on the gpu-based fractal viewer I'd written a while ago. It supported emulated quad-precision floats, but it had no GUI whatsoever, and only accepted raw glsl code (so none of the modularity that Fragmentarium offers). I gave up on my program because Fragmentarium was so much better, and I don't know the first thing about GUI coding.

Instead of using Fragmentariums built-in camera center and zoom factor, you could store the center position in a vec4 uniform, and then create the quad-float in the shader from these four single precision values. (But mouse control would be lost) 

There is also Henry Thasler's Quad-GLSL Mandelbrot viewer, which might be a possible starting point:
http://www.thasler.org/blog/?p=143

Thanks for the suggestions. I take it that none of the CPU-based fractal renderers are fast enough to really be called interactive?

I've considered using a vec4 uniform to store position, but I always thought it would be too tedious and slow to position the camera.

Henry Thasler's viewer looks pretty nice, but it's written in C++ and Fortran, and I know nothing of either of those two languages (I've only worked with garbage-collected languages like Java and Python).

I'm thinking that adding a basic GUI to my viewer would probably be the simplest way to get all the features I want. That way, I could code and test fractals in Fragmentarium, then copy out the pre-processed glsl code into my program for high-precision zooming.