Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!usc!ucsd!ucsdhub!hp-sdd!ncr-sd!ncrcae!hubcap!wen-king
From: wen-king@csvax.caltech.edu (Wen-King Su)
Newsgroups: comp.parallel
Subject: Re: IPSC Communications
Message-ID: <7276@hubcap.clemson.edu>
Date: 1 Dec 89 13:55:02 GMT
Sender: fpst@hubcap.clemson.edu
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Approved: parallel@hubcap.clemson.edu

>From: ran@cs.utah.edu (Ran Ginosar)
<In article <7210@hubcap.clemson.edu> boulder!foobar!grunwald@ncar.UCAR.EDU (Dirk Grunwald) writes:
>
<   In a single phrase, ``fat wires''.  The argument being that 8 wires
>   transmit the info. of 1 at 8x the speed.  Thus, the latency of the
<   *last byte* (not first) decreases because of increased bandwidth. ...
>
<It turns out that, at least in edge-cutting technologies, this is not
>exactly true. The limiting factor in driving N wires OFF CHIP is the
<power-speed product. It takes N times more power to drive N wires off
>the I/O pins of the node-chip than a single one, assuming you're
<driving them as fast as the technology lets you. Given a constant
>amount of power to disipate, it takes N times longer (more slowly!) to
<drive N wires than one. While Dally's constancy factor, bisection
>width, was key to the ongoing discussion, the constant power-speed
<factor was overlooked.

The factor is not N.  If each channel of the cube is 1 bit wide, a
cube router will have a total of 2*log2(n) channel-wires (n is the
number of nodes).  A 2-D grid router, on the other hand will have
8*N wires where N = sqrt(n)/2  ---> a total of 4*sqrt(n) wires.
The wire-count ratio of 2-D grid router to cube router is therefore
2*sqrt(n)/log2(n).  The ratio becomes less than N (and keeps getting
comparatively less) when n is greater than 16.

We also have to take into account that many wires in a cube are long.
We can overcome that difficulty by driving long wires as transmission
lines (pump more than bits into a single wire before the first bit emerge
from the other end of the wire, ie wave length of the data pulses is
shorter than the wire length), but the cost and effort is probably
more than the gain.

/*------------------------------------------------------------------------*\
| Wen-King Su  wen-king@vlsi.caltech.edu  Caltech Corp of Cosmic Engineers |
\*------------------------------------------------------------------------*/


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