(Free42) roundoff for complex SQRT

04112018, 09:02 AM
(This post was last modified: 04112018 10:57 AM by Werner.)
Post: #19




RE: (Free42) roundoff for complex SQRT
Found this (see attachment).
Apparently performing the dot product as before, and carrying along a correction term that can be determined with the FMA (a bit like Kahan summation for sums), results in a dot product as accurate as if it were computed in double precision. Remark that the FMA is only used to determine the correction factor  when FMA's are used for the dot product itself it is much more costly. Also, in this case, the computational penalty is 63% for n=50, and apparently going down to 25% for large n. Keyword to google is 'compensated dot product FMA' Cheers, Werner 

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