Timeline for Efficiency of representations of number
Current License: CC BY-SA 3.0
8 events
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| Jul 12, 2022 at 7:46 | comment | added | Hakanai | To back up the claim of efficiency of base 3, supposedly a team in South Korea made a working design and published its research in July, 2019. Because of ternary's greater efficiency, the design uses less power and can process computations faster than a comparable binary design. | |
| Sep 11, 2017 at 23:34 | comment | added | Aaron Meyerowitz | @AndrejBauer in the early 80's I heard D Mattula talk about fast algorithms that do ok for graph coloring. Over lunch he told me with enthusiasm about his work with "slash arithmetic." I don't know much more. The question was do we know nothing better than fixed point? Some people claim this is better. Maybe they didn't convince many people. I did find papers In the last two years citing the work. Like the Dvorak keyboard, even if it is better, the usual system is entrenched. | |
| Sep 11, 2017 at 22:37 | comment | added | Andrej Bauer | I don't know about theory, but all practical implementations of real number arithmetic seem to use dyadic rationals underneath, i.e., arbitrary precision floating-points. Many years ago people tried rationals, and continued fractions, and those were all quite awful in terms of space usage. | |
| Sep 11, 2017 at 22:34 | comment | added | Aaron Meyerowitz | @AndrejBauer I corrected the language. The question is about the optimality of fixed (and floating) point which approximate reals by dyadic or decimal rationals. The intriguing assertion is that variable numerator and denominator might be preferable for that kind of approximation. | |
| Sep 11, 2017 at 22:24 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Sep 9, 2017 at 23:43 | comment | added | Andrej Bauer | Why would we want to represent the reals as rationals, as opposed to repreenting them as the reals? There are many ways to do it, and using rationals is not one of them. | |
| Sep 9, 2017 at 15:11 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Sep 9, 2017 at 5:01 | history | answered | Aaron Meyerowitz | CC BY-SA 3.0 |