How to Precisely Spread Numbers?

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1

I want to spread a bunch of integers of primitive type T to a different range, typically T::MIN..=T::MAX. They might be percentages, i.e. add up to 100. Mathematically adjusting their sizes is easy: Say T is u8, then in this case let new = old * 255 / 100. Except the multiplication will overflow, whereas let new = old / 100 * 255 will first truncate to zero.

Obviously let new = old * 2.55 would be the solution, but it is not possible to mix types. Also I can’t generally convert old to float, because, even if we already had f128, floats always have less precision than an equal-sized integer.

I guess I’d need mul_rem<F: {float}>(self, factor: F) -> (Self, F) which would return the floor and the truncated fractional part of the product. (The sum of the floors will often fall short, so I’d then have to adjust: add 1 to some of those with the highest fractional parts.)

I want to do this in const, but I’m beginning to wonder whether this is at all generally possible (i.e. not only on numbers small enough to losslessly fit into float.)

2

Do the multiplication in u16:

 let new = u8::try_from(u16::from(old) * 255 / 100).unwrap();
3

Using the next size up works through u64. For u128 you could adapt this algorithm.

Here's a POC that it can be done in const. Note that I performed zero testing, so you should do your own review and make some test cases etc.

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