• Stewart Gordon (41/41) Nov 29 2004 The C definitions of the / and % operators (which D mimics) have always

Stewart Gordon <smjg_1998 yahoo.com> writes:

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.