On approximate arithmetic

Approximate arithmetic has been de-facto present in computing systems using fixed-point (non-integer) and floating-point operations. The main goal has been to obtain exact or close to exact results by deploying error mitigation techniques ranging from increasingly sophisticated rounding to interval arithmetic. Errors committed have been considered bad. Lately, however, ideas have emerged how to make errors help reduce delays of operations, power dissipation and energy consumption. Errors, now often seen as helpful, are becoming an intentional feature in the design because of tangible payoffs and application-based error tolerance. We discuss several approaches and results in approximate arithmetic based on our prior work.