The C definitions of the / and % operators (which D mimics) have always seemed to me to be not quite right in their handling of negative operands.  I've just been looking through my archives at this thread on the issue:

http://google.com/groups?threadm=100320001202113511%25yahoo_com@francis.uy

It would therefore be nice to invent a few new operators to do floor-mod and floor-divide.

floor-mod is like the standard % operator (aka trunc-mod) except that the result has the sign of the right operand.  So, while trunc-mod does this

     23 %  5 ==  3
    -23 %  5 == -3
     23 % -5 ==  3
    -23 % -5 == -3

floor-mod would do this

     23 %%  5 ==  3
    -23 %%  5 ==  2
     23 %% -5 == -2
    -23 %% -5 == -3

and hence for a given right operand, be periodic over the entire number line.

floor-divide is simply division always rounded down, rather than towards zero.

     23 /%  5 ==  4
    -23 /%  5 == -5
     23 /% -5 == -5
    -23 /% -5 ==  4

(Maybe we can come up with a nicer-looking symbol for this operation....)

This satisfies the identity

    (x /% y) * y + (x %% y) == x

just as the regular / and % do on integers.

Of course, for floating points, the same floor-mod operator would apply, but I guess floor-divide isn't really applicable to the same extent.  I guess we could debate what /% (or whatever we decide to call it) should mean on floating point types, or if it should be defined at all.

I don't know how many CPUs have built-in floor-mod and floor-divide instructions, but they would be used if compiling for a machine with these available.  Otherwise, the compiler would generate code to implement the operations in terms of available machine instructions.

Of course, the operators would be overloadable - maybe with opFloorMod and opFloorDiv?

Stewart.