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raphlinus's profile
Raph Levien
Raph Levien
Raph Levien
@raphlinus

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Raph Levien

@raphlinus

Rust. Fonts. Graphics. Quaker. Independent. he/him

Berkeley, CA
levien.com
Joined May 2009

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    1. Raph Levien‏ @raphlinus 17 Oct 2018
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      Here's a fairly extreme nerd snipe: what does this do and why? Apologies to those who just can't wrap their head around it. ((x + 0.24999994) + 0.25000006).floor()

      6 replies 7 retweets 28 likes
    2. Eleutheria‏ @EleuEThana 17 Oct 2018
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      Replying to @raphlinus

      I guess the parentheses will lead to different behaviour depending on how big X is, with some loss of precision on the constants when X is big. Not sure why you'd want to do that, though.

      1 reply 0 retweets 0 likes
    3. Raph Levien‏ @raphlinus 17 Oct 2018
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      Replying to @EleuEThana

      So basically that choice of constants is carefully chosen so that it'll round down when x is the next representable number under 0.5, and adding two values near 0.25 avoids rounding up for values like 8388609.0, which you get from (x + 0.5).floor()

      2 replies 0 retweets 4 likes
    4. Yannick Moy‏ @yannick_moy 9 Nov 2018
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      Replying to @raphlinus @EleuEThana

      CVC4 agrees with you that it's correct for 32bits floats, but generates a counterexample for 64bits double: (fp #b0 #b01111111101 #b1111111111111111111111111111111111111111111111111110) IIUC that's the predecessor of the predecessor of 0.5 and indeed I wrote a test and it fails.

      1 reply 0 retweets 0 likes
    5. Raph Levien‏ @raphlinus 9 Nov 2018
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      Replying to @yannick_moy @EleuEThana

      Wow, that's interesting and mysterious. I would have thought that f64 has the same rounding behavior as f32, just more precision, but I guess not. Worth looking into more deeply. Also yay SMT.

      1 reply 0 retweets 0 likes
    6. Yannick Moy‏ @yannick_moy 9 Nov 2018
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      Replying to @raphlinus @EleuEThana

      This seems to work for double: ((x + 0.249999999999995) + 0.250000000000005).floor(). It's proved by CVC4.

      1 reply 0 retweets 0 likes
      Raph Levien‏ @raphlinus 9 Nov 2018
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      Replying to @yannick_moy @EleuEThana

      Ahhhh right, sure. That's what I would expect. It's not the exact constants, it's their relationship with epsilon. Whew.

      1:15 PM - 9 Nov 2018
      1 reply 0 retweets 0 likes
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        2. Yannick Moy‏ @yannick_moy 9 Nov 2018
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          Replying to @raphlinus @EleuEThana

          beautiful floats! :-) and beautiful implementation of float support in CVC4 by Florian Schanda and @ciphernyx, as Z3 does not seem to be able to prove these properties.

          2 replies 0 retweets 1 like
        3. Yannick Moy‏ @yannick_moy 11 Nov 2018
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          Replying to @yannick_moy @raphlinus and

          Looking at the implementation of the float-to-integer conversion in GNAT (in Ada, this conversion does the same round-nearest-tie-to-away), it seems that simply adding the predecessor of 0.5 and then taking floor does the same. Slightly simpler. CVC4 also proves it for 32/64 bits

          1 reply 0 retweets 1 like
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