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From: Michael S <already5chosen@yahoo.com>
Newsgroups: comp.arch
Subject: Re: Continuations
Date: Mon, 22 Jul 2024 14:01:15 +0300
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On Fri, 19 Jul 2024 20:55:47 +0200
Terje Mathisen <terje.mathisen@tmsw.no> wrote:

> MitchAlsup1 wrote:
> > On Fri, 19 Jul 2024 14:16:01 +0000, Terje Mathisen wrote:  
> >> Back when I first looked at Invsqrt(), I did so because an
> >> Computation Fluid Chemistry researcher from Sweden asked for help
> >> speeding up his reciprocal calculations
> >> (sqrt(1/(dx^2+dy^2+dz^2))), I found that by combining the 1/x and
> >> the sqrt and doing three of them pipelind together (all the water
> >> molecules having three atoms), his weeklong simulation runs ran in
> >> half the time, on both PentiumPro and Alpha hardware.  
> > 
> > I, personally, have found many Newton-Raphson iterators that
> > converge faster using 1/SQRT(x) than using the SQRT(x) equivalent.  
> 
> Yeah, that was eye-opening to me as well, to the level where I
> consider the invsqrt() NR iteration as a mainstay, it can be useful
> for both sqrt and 1/x as well. :-)
> 
> Terje
> 

What is this "SQRT(x) equivalent" all of you are talking about?
I am not aware of any "direct" (i.e. not via RSQRT) NR-like method for
SQRT that consists only of multiplicationa and additions.
If it exists, I will be very interested to know.