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pcwalton's profile
Patrick Walton
Patrick Walton
Patrick Walton
@pcwalton

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Patrick Walton

@pcwalton

Research engineer at Mozilla

San Francisco, CA
pcwalton.github.io
Joined November 2009

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    1. Fiora @ mandatory homestuck!‏ @FioraAeterna 26 Jul 2018
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      Replying to @FioraAeterna @stephentyrone

      (i'm going through all the possible explanations until hopefully one of them hits programmers' brains open)

      1 reply 0 retweets 3 likes
    2. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @FioraAeterna @stephentyrone

      Hmm. Step 1: write a regular prefix sum Step 2: point out that you can do it as a tree with depth O(log(N)) Step 3: that is how they all work

      2 replies 0 retweets 4 likes
    3. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @rygorous @FioraAeterna @stephentyrone

      now looking at a bunch of Wikipedia articles and kind of surprised that https://en.wikipedia.org/wiki/Prefix_sum  doesn't point out that Hillis-Steele is isomorphic to Kogge-Stone and the "work efficient" second algorithm is isomorphic to Brent-Kung

      2 replies 0 retweets 4 likes
    4. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @rygorous @FioraAeterna @stephentyrone

      the associative op for adders is PG(a,b).p = a.p & b.p PG(a,b).g = b.g | (a.g & b.p) for group carry propagate/generate do a scan and you have the group generates for the groups sum[0:1], sum[0:2], sum[0:3], sum[0:4] etc. (left bound incl, right bound excl)

      1 reply 0 retweets 2 likes
    5. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @rygorous @FioraAeterna @stephentyrone

      the group carry generate for the group [0:k] consisting of bits 0,...,k-1 is exactly the carry-in to bit k tree adder architectures are not just similar to parallel scan algorithms, they're the _same_ as a corollary, Harris's taxonomy applies to scan algorithms

      1 reply 0 retweets 0 likes
    6. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @rygorous @FioraAeterna @stephentyrone

      this one http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=DA30EE65FFA4B182C57880CF0FC2D288?doi=10.1.1.78.1106&rep=rep1&type=pdf … that said, most of these design points are not super-relevant for SW algs, since you're generally not directly limited by fan-out or # wiring tracks, or at least can't control them directlypic.twitter.com/MIpv5OK59S

      1 reply 0 retweets 4 likes
    7. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @rygorous @FioraAeterna @stephentyrone

      in SW, usually, the HW engineers have chosen an interconnect network / shuffle unit / whatever with a particular topology for you and you just go for the lowest depth you can achieve. But even when it's not immediately useful, nice to know how the design space looks. :)

      1 reply 0 retweets 1 like
    8. Fabian Giesen‏ @rygorous 26 Jul 2018
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      Replying to @rygorous @FioraAeterna @stephentyrone

      actually re-reading the Harris paper right now and it mentions how this is arbitrary parallel scan and works with any associative op! And it's not full of lingo. So I guess that might be a good answer to Steve's original question. :)

      1 reply 1 retweet 3 likes
    9. Steve Canon‏ @stephentyrone 26 Jul 2018
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      Replying to @rygorous @FioraAeterna

      Yeah, that’s a reasonable suggestion.

      0 replies 0 retweets 0 likes
      Patrick Walton‏ @pcwalton 26 Jul 2018
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      Replying to @johnregehr @stephentyrone and

      One data point: I learned about fast adders from this thread (I feel perpetually guilty about not having an EE background), having long known about the SIMD prefix sum technique. I now mentally have it filed as “oh, OK, it’s like SIMD prefix sums but for single bits”.

      8:48 PM - 26 Jul 2018 from Dogpatch, San Francisco
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      • Tony Garnock-Jones John Regehr Michael Rainey Manish
      2 replies 0 retweets 4 likes
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        2. Patrick Walton‏ @pcwalton 26 Jul 2018
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          Replying to @pcwalton @johnregehr and

          So I guess I’m saying that it might be easiest to teach the general SIMD prefix sum principle first and then mention how fast adders are a specific variation on that technique.

          1 reply 0 retweets 3 likes
        3. Fabian Giesen‏ @rygorous 26 Jul 2018
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          Replying to @pcwalton @johnregehr and

          Fabian Giesen Retweeted Fabian Giesen

          yeah, that's the way I approach it to. :)https://twitter.com/rygorous/status/1022589702598090752 …

          Fabian Giesen added,

          Fabian Giesen @rygorous
          Replying to @FioraAeterna @stephentyrone
          Hmm. Step 1: write a regular prefix sum Step 2: point out that you can do it as a tree with depth O(log(N)) Step 3: that is how they all work
          1 reply 0 retweets 0 likes
        4. 2 more replies
        1. New conversation
        2. Jed Davis  🏳️‍🌈‏ @xlerb 26 Jul 2018
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          Replying to @pcwalton @johnregehr and

          I learned about the prefix sum thing and fast adders many years ago in that order, but separately, and I don't know if I connected them until this thread? (I'm not an EE either, but I was poking at SAT stuff in grad school.)

          1 reply 0 retweets 3 likes
        3. Fabian Giesen‏ @rygorous 26 Jul 2018
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          Replying to @xlerb @pcwalton and

          so the other reason I like the adder thing (and the stuff in the Harris paper) is because in my experience (small sample size though!) a lot of people know about scan algorithms but they either don't know the connection, or don't know there's more than 1 or 2 of these algs

          1 reply 0 retweets 3 likes
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