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TimSweeneyEpic's profile
Tim Sweeney
Tim Sweeney
Tim Sweeney
@TimSweeneyEpic

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Tim Sweeney

@TimSweeneyEpic

Epic Games founder & CEO

epicgames.com
Joined August 2013

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    1. Tim Sweeney‏ @TimSweeneyEpic Jan 26
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      Another amazing work by Hans Boehm back in 1999: a constructive real number calculator, https://www.hboehm.info/crcalc/ . In a sense, this is "as far as a computer can go" in the hierarchy of accuracy that includes floating-point, exact rational numbers, and then constructive reals.

      6 replies 14 retweets 98 likes
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    2. Tim Sweeney‏ @TimSweeneyEpic Jan 26
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      The idea is: instead of storing digits of a number, we store a lower and upper bound, and a function to refine and add more accuracy to the number. With this, we can compute anything on-demand to arbitrary precision.

      4 replies 0 retweets 24 likes
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      Tim Sweeney‏ @TimSweeneyEpic Jan 26
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      Where this becomes clever is compositionality: the library exposes functions that take constructive reals as input and refine their output on demand. With this, we can do almost anything! BUT...

      3:28 PM - 26 Jan 2020
      • 2 Retweets
      • 9 Likes
      • Khalid_Diaa_Mady Tera UMA Inspire JB Lambie mike🌵black Tanya Degurechaff zooko ADK Aidan 𝒜𝓁𝑒𝓎𝓈𝒾𝒾𝒶 ˳✧༚
      2 replies 2 retweets 9 likes
        1. New conversation
        2. Tim Sweeney‏ @TimSweeneyEpic Jan 26
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          Some seemingly trivial tests like sqrt(2)*sqrt(2)==2 may loop infinitely because they refine a lower and upper bound that approach 2 on both sides without ever reaching it. So it's not a completely usable construct.

          4 replies 0 retweets 23 likes
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        3. Tim Sweeney‏ @TimSweeneyEpic Jan 26
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          In a grand scheme of programming language design, I'd love to have a subtype hierarchy with int64 (64-bit integers) <= int (arbitrary precision integers) <= rational (arbitrary precision rational numbers) <= real (constructive reals).

          8 replies 2 retweets 31 likes
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        4. End of conversation
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        2. Tikhon Jelvis‏ @tikhonjelvis Jan 26
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          Replying to @TimSweeneyEpic

          One way of looking at this is that you can compose a bunch of numbers and operations and choose how much precision you want at the very end, while other approaches force you to choose a level of precision for individual parts of your calculation.

          1 reply 0 retweets 1 like
        3. Tikhon Jelvis‏ @tikhonjelvis Jan 26
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          Replying to @tikhonjelvis @TimSweeneyEpic

          It's a lot like vector graphics vs raster graphics. With vector graphics, you can combine a bunch of different shapes and render to concrete pixels at the end, while with raster graphics you might have components rendered at different resolutions that won't combine nicely.

          1 reply 0 retweets 0 likes
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