(Free42) roundoff for complex SQRT

[BarryMead]

(04-10-2018 05:28 PM)Thomas Okken Wrote:  

(04-10-2018 08:11 AM)Paul Dale Wrote:  If there is a fused multiply add call in Intel's decimal library, then dot products can be made accurate. It is computationally expensive to do so but it's not too difficult.

How would that work?
(I'm not saying I'll do it, but I am curious. And the Intel library does have FMA.)

I found an article that shows how to use fma to do dot product and explains why it is more accurate. The Intel Decimal 128 bit FMA has several internal calculations performed at 256 bit accuracy, this is how it can be
more accurate than separate multiply and add operations.

https://www.quora.com/Floating-Point-How...-computing

Note, however, that the order of the parameters in this example are backwards from those of the Intel Decimal library's FMA: In this article the order is Parameter1 + (Parameter2 * Parameter3), whereas in the
Intel Decimal FMA the order is (Parameter1 * Parameter2) + Parameter3. I don't know if this is helpful or even applicable to your Complex Square Root algorithm, but I thought you might find it worth a look.