[Libreoffice-bugs] [Bug 137679] Implement a Kahan summation algorithm to reduce the numerical error in the total

[bugzilla-daemon at bugs.documentfoundation.org]

https://bugs.documentfoundation.org/show_bug.cgi?id=137679

--- Comment #69 from b. <newbie-02 at gmx.de> ---
as i'm not familiar with SSE2 ... would that: 

http://blog.zachbjornson.com/2019/08/11/fast-float-summation.html 

and that: 

https://gist.github.com/zbjornson/f90513fcaaee4d6268d26f9c1a0507dd#file-benchmark-cc 

be helpful? 

IMHO that guy knows what he's dealing with ... 

[there might be even more errors in the code, 

(SSE2 is not optimal for Neumaier?)

the calculation of err1 - err4 should be 'dependent on summand size' as in 
        if (std::abs(m_fSum) >= std::abs(x_i))
            m_fError += (m_fSum - t) + x_i;
        else
            m_fError += (x_i - t) + m_fSum;           ??

rows 74-78 should evaluate err2 ?

rows 80-83 should evaluate err4 ?, and calculate a new err3 ?, 

rows 85-88 should evaluate the new err3 ?, and calculate a new err1 ?, 

the new err1 needs to be carried into subsequent calculations ?, either more
input to this sum or into the final result?, 

you had to 'truncate' Neumaier to fit it into SSE2? logically errors will
occur]

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