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Calculate the Mandelbrot set for greater accuracy.

Is there any practical way to do calculations, such as those involved in creating a Mandelbrot set for values, to pinpoint what a double or long double can provide? I was thinking about having two variables (two or more long ones), one of which stores a value similar to scientific notation, and the other stores a negative log10 value, but I'm not sure if there really is a way to perform a calculation like this.

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