In The Art of Doing Science and Engineering, Hamming gives this amazing sigmoidal formulation for the growth rate of computing power: e^(22(1-e^(-t/20))), with t=0 in 1943. That predicts 2.2 GHz for 2019, with is rather remarkably close to where we are.
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Replying to @patrickc
And also remarkably close to the irritating fact that clock speeds seem to have just barely moved over the past 10 years.
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Replying to @michael_nielsen
There's a lot of what-aboutism in the replies. Saying "but what about parallel computing / pipelining / GPUs / ASICs" etc isn't a response. Ideally, we want faster clock speeds _and_ all those things. Clock speed stagnation isn't something to brush off.
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Replying to @michael_nielsen
We had a huge effort on this at DARPA. A key consideration is clock skew across the device as speeds increase. You end up with "clock domains" that shrink, large overhead in mitigating skew, and what effectively becomes a multicore architecture for fixed die size
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Replying to @MJBiercuk
Interesting! What causes the skew / how do you resync or mitigate it?
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Replying to @michael_nielsen
The skew actually comes from propagation velocities! Clock distribution networks need to be aware and phase shift the clock for synch operation.
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Replying to @MJBiercuk
Interesting. I guess that makes sense - if the signal is propagating say ~3 millimeters (?) even at ~lightspeed it's going to take 1/100 of a nanosecond. At 3 GhZ, that's 1/33rd of a clock cycle. Am I understanding the issue correctly?
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Replying to @michael_nielsen
Broadly. So for a 10 GHz clock and a 2cm die, the propagation delay (ctr to edge) becomes ~1/3 of a clock cycle... Add in rise time distortions and it's a serious issue.
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Replying to @MJBiercuk
I see. Thinking aloud: omitting constants, you want L f << c, where L is the linear dimension of the chip, and f is the clock frequency. If the characteristic size of elements on the chip is d (more or less the feature size), and you want N elements, you have N d^2 = L^2...
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Replying to @michael_nielsen @MJBiercuk
... so the constraint on clock frequency is f << c / [d sqrt(N)]. Pretty interesting constraint.
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"Constraint" isn't really the right word, of course. Something more like "obstacle" is better - you need clever strategies to deal with the drift. I'm sure it can be done, but it'd be a pain.
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Replying to @michael_nielsen
It's true and clock distribution networks are already an essential part of modern SoC design. At some point though you end up trading a huge amount of overhead in space and resources to this vs the performance gain...
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