Re: Continuations

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.

 

>

>
(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.