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good news: testing some fractal perturbation algorithms with single precision shows it still works (no need to use double precision, at least for precision purposes). regular perturbed iterations go to zoom 1e30 or so and rescaled iterations go to 1eLARGE where large is logBase 10 (2^(2^31 - 1)). this is good because single precision takes half the memory and computes a bit faster (about 30%-50% faster in various Mandelbrot power 2 tests using OpenCL on both GPU and CPU).

bad news: the smaller range of single precision float means "deep needle" Burning Ship iterations are considered to be "close to 0" much more often, meaning rescaled single precision float can be significantly slower than rescaled double: 40 seconds vs 3.0 seconds in one test on CPU.

this makes automatically choosing the best number type a bit tricky: it depends on the fractal type, location in the fractal, and the available hardware / drivers / etc

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