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Fermat's Library
Fermat's Library
Fermat's Library
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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

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    Fermat's Library‏ @fermatslibrary 28 Mar 2019
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    D. Harvey and Van Der Hoeven claim to have found the first O(nlog n) integer multiplication algorithm. The prevailing 50 year old conjecture has always been that an optimal algorithm is O(n log n) but no one had been able to find it. Discovery Paper: https://hal.archives-ouvertes.fr/hal-02070778/document …pic.twitter.com/Vfi89WDH1Z

    5:41 AM - 28 Mar 2019
    • 378 Retweets
    • 1,257 Likes
    • CT Tanmay Singal Jaime Durán Mi Lia andjedani ( ͡° ͜ʖ ͡°) GargamelAzrael 🐨 MH Manuel Haqiqatkhah
    19 replies 378 retweets 1,257 likes
      1. New conversation
      2. julesh‏ @_julesh_ 28 Mar 2019
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        Replying to @fermatslibrary

        How on earth was it widely conjectured to be O(n log n) if nobody had an algorithm? What constitutes evidence for that?

        2 replies 1 retweet 3 likes
      3. John Carlos Baez‏ @johncarlosbaez 28 Mar 2019
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        Replying to @_julesh_ @fermatslibrary

        I don't know the details, but Arnold Schönhage and Volker Strassen got the time down to O(n log(n) log(log(n))) with fast Fourier transform, and they conjectured that O(n log(n)) was possible. I guess if you almost do something you hope you can do it!

        1 reply 1 retweet 11 likes
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      1.  🐬 🚬 ☕‏ @samwaslow 28 Mar 2019
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        Replying to @fermatslibrary

        hate to break it to you guys, but it only works with numbers containing at least 2^4096 digits..

        0 replies 1 retweet 28 likes
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      1. Joby Otero  📗‏ @JobyOtero 28 Mar 2019
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        Replying to @fermatslibrary @zachbaker

        Fun thread for those trying to digest this.https://www.reddit.com/r/programming/comments/b5avlv/integer_multiplication_in_time_on_log_n_pdf/ …

        0 replies 0 retweets 13 likes
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      1. ⌘‏ @PeterorjustP 28 Mar 2019
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        Replying to @fermatslibrary @paulg

        It took me forever to figure out what this meant (never having heard of BigO before), but here: Multiplication of giant numbers can theoretically be done faster than multiplying each individual digit/bit by all of the digits/bits in the other number.https://www.reddit.com/r/programming/comments/b5avlv/integer_multiplication_in_time_on_log_n_pdf/ …

        0 replies 0 retweets 6 likes
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      1. somebody3830‏ @somebody3830_2 28 Mar 2019
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        Replying to @fermatslibrary @deadalnix

        Finding an O(n log n) algo is easy, but finding one with reasonable memory constraints is difficult

        0 replies 1 retweet 2 likes
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      1. New conversation
      2. Jacques Bensimon‏ @JacqBens 28 Mar 2019
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        Replying to @fermatslibrary

        Yikes, who'd have imagined that an operation as elementary as integer multiplication (even of large numbers) would lend itself to such rich complexity?! Good luck to whoever first tries to implement either one of the two algorithms presented in actual code!

        2 replies 0 retweets 4 likes
      3. möbius‏ @13utters 28 Mar 2019
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        Replying to @JacqBens @fermatslibrary

        Imagine having the ram for it too!

        1 reply 0 retweets 1 like
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      2. David H. Bernstein, Ph.D.‏ @DavidHBernstein 28 Mar 2019
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        Replying to @fermatslibrary

        Fingers crossed 🤞

        1 reply 0 retweets 1 like
      3. Andriy Plokhotnyuk‏ @aplokhotnyuk 28 Mar 2019
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        Replying to @DavidHBernstein @fermatslibrary

        Open archive HAL, is currently down...

        1 reply 0 retweets 2 likes
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