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(Free42) roundoff for complex SQRT
04-11-2018, 09:02 AM (This post was last modified: 04-11-2018 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

Attached File(s)
.pdf  Compensated dot products.pdf (Size: 321.66 KB / Downloads: 21)
.pdf  accurate summation, dot product.pdf (Size: 302.91 KB / Downloads: 16)
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RE: (Free42) roundoff for complex SQRT - Werner - 04-11-2018 09:02 AM

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