Java – is there any reason why languages allow negative modulus?

I'm curious that these languages (Java, C...) ignore the mathematical definition of modular operation

What does it mean to return a negative value in a module operation (by definition, a positive number should be returned)?

Solution

I suspect that the remaining operators are deliberately designed to have these semantics, and I agree that they are not very useful (will you write a calendar program to display the date before the time of Sunday, anti Saturday, anti Friday,..., anti Monday?)

On the contrary, negative remainder is a side effect of defining integer division

A rem B := A - (A div B) * B

If a div B is defined as TRUNC (A / b), you can get the% operator of C If a div B is defined as floor (A / b), you can get Python's% operator Other definitions are possible

So the real question is:

Why do C, Java, c# etc. use truncated integer division?

Because this is the way of C

Why does C use truncation segmentation?

Initially, C did not specify / should handle negative numbers It left it to the hardware

In practice, every important C implementation uses truncation, so in 1999, these semantics officially became part of the C standard

Why does the hardware use truncation partitioning?

Because it is easier to implement in unsigned partition (= cheaper) If (a < 0) XOR (b < 0), only ABS (a) div ABS (b) is calculated and the symbol is flipped If the remaining part is zero, the flooring department will subtract 1.5% from the quotient for additional steps