Is the ALU control unit enough to execute all the instructions in a MIPS processor?
So in some (maybe most) processors, ALUs dont have all the required operations as built in commands. I will explain it using the 6502, because I know bunches about its ALU.

Take a look at the 6502 ALU. It only has 5 control lines for performing operations, but can perform operations such as Rotate Left and Subtraction.
It can perform these operations by combining the available operations to create new ones.
For instance, Rotate left can be performed by adding a number to itself.
If you are writing this ALU in some HDL language and are not worried about logic space, I would implement the operations directly in the ALU and not worry about combining operations.