7 ms·

> It does not make a difference how wacky or weird f is compared to g below t. It can contain all these crazy memory hierarchy artifacts, it could contain a sho

> It does not make a difference how wacky or weird f is compared to g below t. It can contain all these crazy memory hierarchy artifacts, it could contain a short burst of exponential slowdown, it could contain anything. Yes, but if you continue reading the next post, the author is essentially arguing that the cache hierarchy extends indefinitely due to 1) the speed of light and 2) the amount of information that can fit within a light cone of a certain radius. In that case, cache hierarchy effects aren't 'weird things that happen below t', they represent the asymptotic behavior we can expect due to the laws of physics, no matter how far out to the right we go.

rosalinekarr 10y ago
Worrying about the speed of light in processor caching these days is like putting a spoiler on your cart and horse to reduce drag. It might matter eventually, and that's kind of cool to think about, but it's absurdly negligible with the technology of today. Processors today are orders of magnitude slower than that.
- smallnamespace 10y ago
  That's completely false. The speed of light today already constrains processor design (and by extension, on-CPU caches): http://arstechnica.com/science/2014/08/are-processors-pushing-up-against-the-limits-of-physics/ http://arstechnica.com/science/2014/08/are-processors-pushin... "Even if signals in the chip were moving at the speed of light, a chip running above 5GHz wouldn't be able to transmit information from one side of the chip to the other". Note that a light-nanosecond is about a foot, so I'm assuming this is talking about the propagation delay of electrons in silicon that need to go through gates, which I'm sure is much slower than light in a vacuum. To put this another way, you can view the scaling law as a hard upper bound on the speed of access to data; engineers can only approach that bound from below as technology improves. But given a certain level of technology, it's easier to make a faster L1 cache than an L2 cache, and that will hold even as we approach theoretical limits.
  - creshal 10y ago
    > which I'm sure is much slower than light in a vacuum. Speed of signal in copper is about ⅔c, I suspect silicon will be in a similar ballbark – and the metal layers linking the silicon layers are made of copper anyway. So it's about 8"/ns… and the (three dimensional, 10+ layer) signal routes are anything but a straight line.
    - hamiltonkibbe 10y ago
      And the signals all need to get there at the same time
      - creshal 10y ago
        And that's such a hard problem that you don't even have to go down to CPU scale for it to matter. If you look at mainboards (or some smaller PCBs), the connecting lanes between e.g. RAM and CPU closer to the centre are often zigzagged, to match the lengths – and delays – of the necessarily longer outer lanes. The speed of light is actually really damn slow.
        hamiltonkibbe 10y ago
        > The speed of light is actually really damn slow. I don't think one really appreciates that until they found out that after X hours of place&route they missed timing by some fraction of a nanosecond
        Dylan16807 10y ago
        > you don't even have to go down to CPU scale for it to matter. It's say it's the opposite, really. The longer the wires, the more effort it takes to synchronize their delays within a certain number of picoseconds.
      - klodolph 10y ago
        Well, not entirely. For data signals in general you just need all the lines to resolve to the desired value before the clock. You do need to be very careful about the clock, though.
- aporetics 10y ago
  Spoilers don't reduce drag. They produce downforce to counteract the lift effect of air moving under the car. It is only necessary at very high speeds, and prevents loss of grip in (especially) the rear tires. But, yeah, horse and buggy. I'm with you there.
  - lasc4r 10y ago
    Spoilers reduce drag and provide down force and high speeds.
    - coredog64 10y ago
      Aerospace engineer here: Producing lift in either the up (airplane) or down (spoiler) direction generates induced drag. The amount depends on your design, in that a large real or effective AR can reduce it, but it's going to be there.
      - ScottBurson 10y ago
        I think what happens in automotive designs, which are not always penned with the same attention to aerodynamics as aerospace designs, is that they often have unintentional lift at the rear. Adding a small spoiler, then, doesn't add actual downforce, it just reduces lift -- and therefore reduces drag into the bargain.
  - tankenmate 10y ago
    The downforce isn't there to counteract air under the car (actually fast flowing air under the car produces downforce; read up on ground effect and Bernoulli). The downforce is there so the car can go around corners quicker; the downforce increases the friction (Ff<=mu x Fn), i.e. the force of friction is less than or equal to the coefficient of friction (mu / μ) multiplied by the normal force. In the case of a tire the normal force is the downward force (provided by the wings or spoilers). Therefore the more downward force the higher the friction hence the more the tire can exert lateral force (cornering force). For example a F1 car at high speed can exert approximately 4Gs of lateral force when cornering, or 5Gs of force when breaking (at slower speeds a F1 car can't brake as hard).
reikonomusha 10y ago
I think it's great to make such arguments but a bit more rigor would be appreciated in such theoretical constructions. If the main point to get across is in Part II, and Part I does not support Part II, as a matter of convenience, I would elide Part I.
- zeroer 10y ago
  I wouldn't. It's nice to show these effects in practice. In fact, I would have added a part 1.5 that gave theoretical bounds for how much heat can be dissipated from a volume that contains N bits.
  - smallnamespace 10y ago
    Heat dissipation is proportional to the surface area, so this suggests a reason that information density is (physically) bound by surface area, rather than volume.
    - klodolph 10y ago
      Another factor that gives the same limit in theory is gravity. If you have a volume of space and start shoving hard drives in it, eventually the hard drives will collapse into a black hole, and your information density is limited by the surface area of the black hole—again, giving you O(R^2) bits of storage for a volume with radius R.
      - zeroer 10y ago
        That's explicitly mentioned in the article.
        klodolph 10y ago
        It's mentioned in the second article in the series, not the linked article.
      - deleted 10y ago
        [deleted]

rosalinekarr 10y ago

Worrying about the speed of light in processor caching these days is like putting a spoiler on your cart and horse to reduce drag. It might matter eventually, and that's kind of cool to think about, but it's absurdly negligible with the technology of today. Processors today are orders of magnitude slower than that.

smallnamespace 10y ago
That's completely false. The speed of light today already constrains processor design (and by extension, on-CPU caches): http://arstechnica.com/science/2014/08/are-processors-pushing-up-against-the-limits-of-physics/ http://arstechnica.com/science/2014/08/are-processors-pushin... "Even if signals in the chip were moving at the speed of light, a chip running above 5GHz wouldn't be able to transmit information from one side of the chip to the other". Note that a light-nanosecond is about a foot, so I'm assuming this is talking about the propagation delay of electrons in silicon that need to go through gates, which I'm sure is much slower than light in a vacuum. To put this another way, you can view the scaling law as a hard upper bound on the speed of access to data; engineers can only approach that bound from below as technology improves. But given a certain level of technology, it's easier to make a faster L1 cache than an L2 cache, and that will hold even as we approach theoretical limits.
- creshal 10y ago
  > which I'm sure is much slower than light in a vacuum. Speed of signal in copper is about ⅔c, I suspect silicon will be in a similar ballbark – and the metal layers linking the silicon layers are made of copper anyway. So it's about 8"/ns… and the (three dimensional, 10+ layer) signal routes are anything but a straight line.
  - hamiltonkibbe 10y ago
    And the signals all need to get there at the same time
    - creshal 10y ago
      And that's such a hard problem that you don't even have to go down to CPU scale for it to matter. If you look at mainboards (or some smaller PCBs), the connecting lanes between e.g. RAM and CPU closer to the centre are often zigzagged, to match the lengths – and delays – of the necessarily longer outer lanes. The speed of light is actually really damn slow.
      - hamiltonkibbe 10y ago
        > The speed of light is actually really damn slow. I don't think one really appreciates that until they found out that after X hours of place&route they missed timing by some fraction of a nanosecond
      - Dylan16807 10y ago
        > you don't even have to go down to CPU scale for it to matter. It's say it's the opposite, really. The longer the wires, the more effort it takes to synchronize their delays within a certain number of picoseconds.
    - klodolph 10y ago
      Well, not entirely. For data signals in general you just need all the lines to resolve to the desired value before the clock. You do need to be very careful about the clock, though.
aporetics 10y ago
Spoilers don't reduce drag. They produce downforce to counteract the lift effect of air moving under the car. It is only necessary at very high speeds, and prevents loss of grip in (especially) the rear tires. But, yeah, horse and buggy. I'm with you there.
- lasc4r 10y ago
  Spoilers reduce drag and provide down force and high speeds.
  - coredog64 10y ago
    Aerospace engineer here: Producing lift in either the up (airplane) or down (spoiler) direction generates induced drag. The amount depends on your design, in that a large real or effective AR can reduce it, but it's going to be there.
    - ScottBurson 10y ago
      I think what happens in automotive designs, which are not always penned with the same attention to aerodynamics as aerospace designs, is that they often have unintentional lift at the rear. Adding a small spoiler, then, doesn't add actual downforce, it just reduces lift -- and therefore reduces drag into the bargain.
- tankenmate 10y ago
  The downforce isn't there to counteract air under the car (actually fast flowing air under the car produces downforce; read up on ground effect and Bernoulli). The downforce is there so the car can go around corners quicker; the downforce increases the friction (Ff<=mu x Fn), i.e. the force of friction is less than or equal to the coefficient of friction (mu / μ) multiplied by the normal force. In the case of a tire the normal force is the downward force (provided by the wings or spoilers). Therefore the more downward force the higher the friction hence the more the tire can exert lateral force (cornering force). For example a F1 car at high speed can exert approximately 4Gs of lateral force when cornering, or 5Gs of force when breaking (at slower speeds a F1 car can't brake as hard).

reikonomusha 10y ago

I think it's great to make such arguments but a bit more rigor would be appreciated in such theoretical constructions. If the main point to get across is in Part II, and Part I does not support Part II, as a matter of convenience, I would elide Part I.

zeroer 10y ago
I wouldn't. It's nice to show these effects in practice. In fact, I would have added a part 1.5 that gave theoretical bounds for how much heat can be dissipated from a volume that contains N bits.
- smallnamespace 10y ago
  Heat dissipation is proportional to the surface area, so this suggests a reason that information density is (physically) bound by surface area, rather than volume.
  - klodolph 10y ago
    Another factor that gives the same limit in theory is gravity. If you have a volume of space and start shoving hard drives in it, eventually the hard drives will collapse into a black hole, and your information density is limited by the surface area of the black hole—again, giving you O(R^2) bits of storage for a volume with radius R.
    - zeroer 10y ago
      That's explicitly mentioned in the article.
      - klodolph 10y ago
        It's mentioned in the second article in the series, not the linked article.
    - deleted 10y ago
      [deleted]