Tim Wegner:
One little addendum to an earlier message. It may actually be false that Fractint uses IEEE math. In some modes, fractint uses 80 bit "IEEE-like" numbers. I'm not an IEEE math expert, but I'm not entirely sure that 80 bit numbers as used in an Intel Floating Point Unit are legal "IEEE" (though they are very "IEEE-like"). Fractal types in fractint that are implemented 100% in assembler use pure 80 you probably meant "64 bit" ??? """""""
bit floating point math.
In other modes implemented primarily in C, Fractint does an odd mixture - the 64 bit double precision numbers used to implement double types are IEEE, but these are converted to 80 bits briefly when passed to the math coprocessor.
converted by the FPU internally? Intel(-type) Processors IIRC use 80 bit FP numbers for internal calculations and do a conversion back to 64 bit when saving the results to registers.
In my workplace (NASA) this mixed precision behavior on the Intel platform has caused some problems we don't get on machines that use pure IEEE 64 bit doubles consistently.
None of this affects my negative critique of the statement that minbrots are an artifact of IEEE math. That claim is pure unadulterated hogwash.
i agree. Too little precision results in a rectangular or quadrilateral tiling of the image. Little errors that get amplified during iterations (a special feature of fractals) *might* mess up the results (you and others probably knew). a nice example: if one implements the Gauss algorithm for solving linear equations straight out of the book without any clever pivoting strategy the result will be unusable (...my own painful experience...). But even the most sophisticated solver can fail: 64919121 * x1 - 159018721 * x2 = 1 41869520.5 * x1 - 102558961 * x2 = 0 try to reproduce the *exact* results x1=205117922, x2=83739041 with a computer using floating-point math. For example "Waterloo Maple 8" sais x1=100, x2=40.82482904. If "41869520.5" is replaced by "41869520+1/2" Maple uses its arbitrary precision rational numbers and the correct results appear. -- Michael Weitzel ... all work and no play makes Jack a dull boy ...