A processor having a reduction unit that sums m input operands plus an accumulator value, with the option of saturating after each addition or wrapping around the result of each addition. The reduction unit also allows the m input operands to be subtracted from the accumulator value by simply inverting the bits of the input operands and setting a carry into each of a plurality of reduction adders to one. The reduction unit can be used in conjunction with m parallel multipliers to quickly perform dot products and other vector operations with either saturating or wrap-around arithmetic.