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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: comp.arch
Subject: Re: Continuations
Date: Fri, 19 Jul 2024 13:16:58 -0700
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On 7/19/2024 7:41 AM, Thomas Koenig wrote:
> Terje Mathisen <terje.mathisen@tmsw.no> schrieb:
>> Thomas Koenig wrote:
>>> MitchAlsup1 <mitchalsup@aol.com> schrieb:
>>>
>>>> What I am talking about is to improve their performance until a
>>>> sin() takes about the same number of cycles of FDIV, not 10× more.
>>>
>>> Maybe time for a little story.
>>>
>>> Some unspecified time ago, a colleague did CFD calculations which
>>> included fluid flow (including turbulence modelling and diffusion)
>>> and quite a few chemical reactions together.  So, he evaluated a
>>> huge number of Arrhenius equations,
>>>
>>> k = A * exp(-E_a/(R*T))
>>>
>>> and because some of the reactions he looked at were highly
>>> exothermic or endothermic, he needed tiny relaxation factors (aka
>>> small steps).  His calculaiton spent most of the time evaluating
>>> the Arrhenius equation above many, many, many, many times.
>>>
>>> A single calculation took _months_, and he didn't use weak hardware.
>>>
>>> A fully pipelined evaluation of, let's say, four parallel exp and
>>> four parallel fdiv instructions would have reduced his calculation
>>> time by orders of magnitude, and allowed him to explore the design
>>> space instead of just scratching the surface.
>>
>> 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.
> 
> Not bad.
> 
> Using the square root approximation for 1/x has not yet been
> metiioned, but it is of course quite possible, especially since
> the benchmarks I posted, with -Ofast, do enable this option.

Interesting post:

https://forums.parallax.com/discussion/147522/dog-leg-hypotenuse-approximation

;^)


> 
>>
>>>
>>> (By the way, if I had found a reasonable way to incorporate the
>>> Arrhenius equation into your ISA, I would have done so already :-)
>>>
>>
>> I'm guessing that you would do the exp(-E_a/(R*T)) as
>> exp(-E-a)-exp(R*T), since that should give the same result and now you
>> could interleave the two exp) calculations, and/or hoist the exp(-E_a) term?
> 
> I don't think that formula is correct.