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From: mitchalsup@aol.com (MitchAlsup1)
Newsgroups: comp.arch
Subject: Re: Continuations
Date: Mon, 22 Jul 2024 15:01:10 +0000
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On Mon, 22 Jul 2024 11:01:15 +0000, Michael S wrote:

> 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.

There are certain N-R iterations that can be expressed with both::

     NR+1 = F( NR,  SQRT() )
and
     NR+1 = F'(NR, RSQRT() )

Typically the one with RSQRT() converges slightly faster than the
one using SQRT(). How much is slightly::maybe ½-1 more bit per
iteration.