Calculate Mandelbrot set for greater precision

Question

Is there any practical way to perform calculations such as those involved in generating the Mandelbrot Set for values for precise that what double or long double can provide? I was thinking of possibly having two variables(either double or long), one storing the value similar to scientific notation and the other storing the negative log10 of the value, but I'm not sure if there would actually be a way to perform the calculation like this.

Malefaction

Sounds like you want a arbitrary precision math library – Ramsgate

Is there a way to use arbitrary precision math libraries in OpenCL kernels from Java? – Malefaction

And what do OpenCL kernels and Java have to do with C++? – Sensate

Have a read of this blog - lots of info: randomascii.wordpress.com/category/fractals – Tyrus

Fixed-point arithmetic can work, because x^2 + y^2 stays < 4 (when 2 is the typical escape value). – Koal

@WeatherVane: if x has a huge number of digits, you still need some calculation mechanism, which is why it is simpler to use an arbitrary precision library (as @Ramsgate mentioned) – Saltish

@Saltish of course you need computation with fixed point, but arbitrary precision floating point libraries implemented in software are less efficient because they must normalise the sigificand. Fixed-point works well here because the maximum value is known. The results differ but the idea is to get pretty pictures as cheaply as possible. Sharp detail near the boundary of the Mset is unachievable anyway, and when zooming is undesirable (as in any dynamic graphic). – Koal