mod of negative number

[Timon Gehr]

On 9/23/24 21:52, Craig Dillabaugh wrote:
> Why does the following program:
> 
>      \<code>
>          import std.stdio;
> 
>          int main(string[] args) {
>              uint Q = 7681;
>              writeln("Val = ", -1 % Q);
>              return 0;
>          }
>      \</code>
> 
>      Print
>          Val = 5568
> 
> 
> Was hoping for 1.
> 
> I assume it is an integer promotion issue, but I am unsure how to 
> resolve.  I tried replacing the Q with to!int(Q) but this gave me -1, 
> which is closer but not right either.

Yes, what this does is to promote `-1` to `uint.max` and the result you 
are getting is `uint.max % 7686`.

`-1 % 7686` does not work because division rounds towards zero, so the 
result of modulo may be negative.

In general `a%b` will give you a value between `-abs(b)+1` and 
`abs(b)-1`, matching the sign of `a` (and ignoring the sign of `b`).

You can use something like `auto r=a%b; if(r<0) r+=abs(b);` or `auto 
r=(a%b+b)%b;`, depending an your needs (note that those two are not the 
same for negative `b`, but they match for positive `b`).

This implementation is equivalent to `(a%b+b)%b`, if you want to avoid 
the second modulo and the compiler is not smart enough:

```d
int floormod(int a,int b){
     bool sign=(a<0)^(b<0);
     auto r=a%b;
     if(sign&&r!=0) r+=b;
     return r;
}
```

The interpretation of this is to compute the remainder for a division 
that rounds to negative infinity.

Sometimes one might also want `a%0 = a`, but this is a special case that 
has to be checked as the language will give you a division by zero error.