If I make Blender compute a modulo, then it does not work correctly for negative numbers.
In the picture, the part of the rectangular cuboid with a negative abscissa is incorrect.
Here is a render of a rectangular cuboid with a base color of $mod(abscissa,1)$, according to Blender:
How you fix that?
Nowadays, Wrap is a simple way to an all-positive modulo:
Here, on an 8x8 plane. It also allows you to shift 0 without an extra node. There is a vector version, which gives you a sawtooth in any or all dimensions. (A Wave > Sawtooth will also do it in one of them, but the scaling is more fiddly.)
The mod returns negative outputs for negative inputs. One way to get positive outputs is
$$((x \operatorname{mod} m) + m) \operatorname{mod} m$$
The problem you are seeing is because Blender's gray scale is $[0..1]$ and Blender clamps values < 0 to 0 and values > 1 to 1. So all of your negative values come out as black. If you had values > 1 they would all come out as white.
While you can use other approaches, an efficient approach to solving this problem is to use the Map Range node to map your input values into a positive range:
Here I've used a Texture Coordinate node to generate the range $[-1..1]$ and a Map Range node to the resulting range $[0..20]. This will give you 10 iterations through the modulo operator set to 2, or 20 set to 1.
fmodffunction, which has this behavior. See Modulo operation. – scurest Aug 07 '22 at 00:23