 There's this funny thing with fractions where, if you divide 2 by 3, getting 2/3, you can flip the numbers to get the reciprocal 3/2. Now, while a division takes two whole numbers and gives you a fraction, there's no way to get back to two whole numbers again. It's destructive in a way, so I've added this little operator that is basically the opposite of a division, but that is also not a multiplication, taking the fraction 2/3, and giving you 2 and 3. 18 comments
@eris I've tried looking it up and I didn't find a name for it, in the docs I call it "yet unnamed operator", in the program I call it VID(mirror of DIV). I'd love to find the proper name for it, lemme know if you ever hear of one. @neauoire @eris Right, I guess what I'm trying to say is, that if someone where to define reduction as a mathematical function, they would have to define it like your operator. Meaning it would need something like this signature: Q -> (N, N) and not this one: Q -> Q. Because if they would choose the latter and define it such that reduce(4/6) = 2/3, they would just define the identity function, because 4/6 = 2/3.  @neauoire What number representation is used here? It looks like the display format is integer part plus fraction. Are the individual component regular machine words or bignums? @csepp A mixed fraction is a whole number and a portion less than 1 together, like 2 3/4. @neauoire So that's what they are called. But what's the whole number in memory? Like, what's the biggest number it can represent, and what happens in case of an overflow? @csepp it's really rare that I noodling around with numbers higher than 60 thousands, but I might add a warning or something at some point if that starts bothering me. @neauoire A few years ago I came up with a neat algorithm for this for a floating-point number, including support for expressions with square roots and multiples of pi. It works by trying to deduce a repeated fraction for the number (similar to how the golden ratio is constructed). The code is here: https://gist.github.com/nakst/f8a70fd69724b8a239138c3f03dd1b75 I looked around the internet for a while to see if anyone had described this algorithm, but I couldn't find anything :(  @neauoire @RL_Dane I'm slowly walking through the eras of the past as I learn how to draw things more efficiently! @RL_Dane I've implemented the oval bresenham-type algorithm in uxntal a little while ago :) It's pretty clever. |
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@neauoire i wonder if theres a fancy maths name for this ?