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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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    Patrick Walton‏ @pcwalton Jan 22
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    Why do we teach floating point as representing numbers in the form “a × 2^b” instead of the easier-to-understand “a/b”, where b is a power of two (i.e. dyadic rationals)? I know they’re the same thing, but rational numbers are a lot easier to intuitively grasp, at least for me…

    3:43 PM - 22 Jan 2020
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    • Jordan Torbiak Jacob Matthews Etienne Cella 🐜 Rob Howard ଘ(੭ˊᵕˋ)੭ Sibelius Seraphini SLEFFY Attila Török Michael Haufe Santiago Tórtora
    9 replies 9 retweets 65 likes
      1. Patrick Walton‏ @pcwalton Jan 22
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        The way it was always taught for me is like “oh, well, floating point is just scientific notation, right? Except it’s binary, not base 10, have fun 🤷‍♂️” Which gives no understanding about the actual numbers floats can represent!

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      2. Sebastian Sylvan‏ @ssylvan Jan 22
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        Replying to @pcwalton

        I like the window + offset analogy. Mantissa identifies a value between two successive powers of two, exponent tells you which "window" you're in.

        1 reply 0 retweets 14 likes
      3. Wes‏ @weskerfoot Jan 22
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        Replying to @ssylvan @pcwalton

        @fabynou

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      1. Wes‏ @weskerfoot Jan 22
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        Replying to @pcwalton

        you could even bring Farey sequences https://en.m.wikipedia.org/wiki/Farey_sequence … into it to better explain it visually

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      1. Sam‏ @lenary Jan 22
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        Replying to @pcwalton

        I think because we teach scientific notation in high school? I was taught floats as “like a * 10^b but binary” but this only tells representation and not limitations.

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      2. Matt Calabrese‏ @CppSage Jan 22
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        Replying to @pcwalton

        I always describe fixed-point as rational numbers with a constant denominator. I've never explained floating point that way though, for no particular reason. I wonder if describing it both ways, stressing the equivalence, might also be helpful for some.

        1 reply 0 retweets 0 likes
      3. Wes‏ @weskerfoot Jan 23
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        Replying to @CppSage @pcwalton

        floats are just like fixed-point, except they're not fixed to any particular point >.>

        0 replies 0 retweets 0 likes
      4. End of conversation
      1. Cor Kalom‏ @1yk0s Jan 23
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        Replying to @pcwalton

        Because it would have to flip between a/b and a*b according to the sign of the exponent. And also because the actual binary representation is less obvious that way.

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      1. _brickner‏ @_brickner Jan 23
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        Replying to @pcwalton

        The mantissa and exponent fields map more directly to a × 2^b. Also, some operations on the scientific notation are a lot easier on paper / in your head. That's my guess.

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      1. isiah meadows  🧢‏ @isiahmeadows1 Jan 23
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        Replying to @pcwalton

        because of how they're spec'd presumably?

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