[Maxima] Increasing the accuracy of Gamma for double float
drdieterkaiser at web.de
Tue Oct 21 13:18:13 CDT 2008
Von: raymond.toy at ericsson.com [mailto:raymond.toy at ericsson.com]
>> I am not really surprised. It is no problem to get any desired precision. But
>> calculating gamma we always need at least 3 to 5 extra digits. In double
>> precision we have no extra digits but lost the 3 to 5 digits we need to
>> calculate gamma.
>How did you arrive at this conclusion? Why does the computation require
>3 to 5 extra digits?
This is not a really strong conclusion. I have played with two different sets of
coefficients for gamma-lanczos which claimed to be accurate within 16 and 32
digits, but I could only reproduce the results of the existing gamma-lanczos
Then I have implemented the gamma-lanczos algorithm in bigfloat arithmetic and
got more accurate results increasing fpprec. Thus I have made the conclusion
that the extra digits are needed to finish the calculation within the desired
Next I have implemented the algorithm of bffac in double float precision. I
tried to get more accurate results as gamma-lanczos. This what not possible, but
we know that bffac can produce any desired accurary. Again I have concluded that
we need extra precision in the calculation for this algorithm.
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