A parallel processing unit employs an arithmetic logic unit (ALU) having a relatively small footprint, thereby reducing the overall power consumption and circuit area of the processing unit. To support the smaller footprint, the ALU includes multiple stages to execute operations corresponding to a received instruction. The ALU executes at least one operation at a precision indicated by the received instruction, and then reduces the resulting data of the at least one operation to a smaller size before providing the results to another stage of the ALU to continue execution of the instruction.