[CupricTea]

Division by zero is mathematically undefined. So two's complement integer division by zero is always undefined.

For floating point there is the interesting property that 0 is signed due to its signed magnitude representation. Mathematically 0 is not signed but in floating point signed magnitude representation, "+0" is equivalent to lim x->0+ x and "-0" is equivalent to lim x->0- x.

This is the only situation where a floating point division by "zero" makes mathematical sense, where a finite number divided by a signed zero will return a signed +/-Inf, and a 0/0 will return a NaN.

Why should 0/0 return a NaN instead of Inf? Because lim x->0 4x/x = 4, NOT Inf.

[nivertech]

OK, but I think it's not up to the programming language designers to define mathematical properties of the operations on specific data types.

I think the most pragmatic solution is to have 2 tiers:

1. use existing standards (i.e. IEEE 754 for FP, de-facto standards for integers, like two's complement, Big-Endian, etc.)

2. fast, native format per each compute device, using different sub-types so you will not be able to mix them in the same expression