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Please visit my post at http://xxx.soton.ac.uk/abs/cs.DM/0606103 about
the following paper abstract:
A new floating point arithmetic called the precision arithmetic is
developed to track, limit, and reject the accumulation of calculation
errors during floating point calculations, by reinterpreting the
polymorphic representation of the conventional floating point
arithmetic. The validity of this strategy is demonstrated by tracking
the calculation errors and by rejecting the meaningless results of a
few representative algorithms in various conditions. Using this type,
each algorithm seems to have a constant error ratio and a constant
degradation ratio regardless of input data, and the error in
significand seems to propagate very slowly according to a constant
exponential distribution specific to the algorithm. In addition, the
unfaithful artifact of discrete Fourier transformation is discussed.
The main idea here is to use floating-point number itself to track the
error. Suppost the floating-point number is in form of "Significand x
2^exponent". This method treats the error of the number as
+/-"2^exponent", and defines arithmetic based on this representation.
If you are interest, I can provide source code for it.
Also, according to my paper, the discrete Fourier transformation seems
to have some serious flaw which I named unfaithful artifacts. Its math
base is quite simple and straight-forward. I wonder if it is already
covered in other literature.
Thanks,
Regards,
Chengpu Wang
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