[Skeime]

I strongly disagree. I would estimate that in 90% of cases where I use modulo in languages that truncate (instead of flooring), I write (a % b + b) % b, or something similar, just to get the right behaviour. The exceptional cases are those where I can convince myself that negative numbers simply won't come up. (It's never because I actually want the other behaviour for negative numbers.)

- When using modulo to access an array cyclically. (You might get lucky that your language allows using negative numbers to index from the back. In that case, both conventions work.) - When lowering the resolution of integers. If you round to zero, you get strange artifacts around zero, because -b+1, ..., -1, 0, 1, ..., b-1 all go to zero when dividing by b. That's 2b-1 numbers. For every other integer k, there are only b numbers (namely bk, bk+1, ..., bk+b-1).

I have never seen a case where truncation was the right thing to do. (When dealing with integers. Floats are different, of course, but they are not what this is about.)

[cygx]

A common approach (e.g. Cobol, Ada, Common Lisp, Haskell, Clojure, MATLAB, Julia, Kotlin) seems to be to provide two operators: One that uses truncated division, one that uses floored division. By convention, rem truncates, and mod floors.

[TheRealKing]

And first of all, Fortran.

[pwdisswordfishc]

> I have never seen a case where truncation was the right thing to do.

Splitting a quantity into units of differing orders of magnitude. For example, −144 minutes is −2 hours and −24 minutes, not −3 hours and 36 minutes. This is about the only case I know of, though.

[defrost]

In generic numerics work there are two broad cases when you have a sea of sample points (eg: a 2D plane with samples taken all over) and you cast a mesh across the sea to divide the work into cells.

\1 samples have new coords relative to cell left edge and bottom edge.

    We're interested in sample distance from "classic" first quadrant axis.

\2 samples are weighted by distance from cell centre.

    We're pooling, combining channel layers, making representative central 'blobs', we're interested in cell sample positions relative to the centre point of the cell.

Your example is a good one, and falls in the case 2 grouping.

This, of course, generalises to 3D and higher dimensions.

[Skeime]

Oh, that's a somewhat reasonable one. (Though I would expect that you actually want −(2 hours and 24 minutes) in many cases instead, thus needing to handle the negative case separately anyway.)

[ncruces]

Very much this.