Expected precision of Fortran FE constant evaluation

[Toon Moene]

On 2/11/19 8:40 PM, Thomas König wrote:

> Hi Salvatore,
> 
>> Right, try this preprint
>> https://www.researchgate.net/publication/298896236_Remark_on_Algorithm_539_Carefully_Computing_the_Euclidean_Norm 
>>
>> Apart from typesetting to an older style it looks essentially the same
> 
> Interesting reading.
> 
> Regarding the algorithm the authors propose, I have one concern.
> The first part of their algorithm is (translating their pseudocode into
> Fortran, resulting errors are mine)
> 
>  Â  real :: sm, s, t
> 
>  Â  sm = 0.
>  Â  s = 0.
>  Â  do i=1, n
>  Â Â Â Â  s = s + x(i)**2
>  Â Â Â Â  t = sm
>  Â Â Â Â  sm = t + s
>  Â Â Â Â  s = s + (t-sm)
>  Â  end do
>  Â  norm2 = sqrt(sm)

Isn't this simply an application of Kahan summation ?

https://en.wikipedia.org/wiki/Kahan_summation_algorithm

...

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Toon Moene - e-mail: toon@moene.org - phone: +31 346 214290
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