Exploiting Asymmetry in Booth-Encoded Multipliers for Reduced Energy Multiplication

Booth Encoding is a common technique utilized in the design of high-speed multipliers. These multipliers typically encode just one operand of the multiplier, and this asymmetry results in different power characteristics as each input transitions to the next value in a pipelined design. Relative to the non-encoded input, changes on the Booth-encoded input induce more signal transitions requiring ~73% more multiplier array energy. This paper proposes low-overhead approaches to take advantage of this asymmetric behavior to reduce the energy of multiplication operations in pipelined SIMD architectures like GPUs. Compiler-based approaches that apply constant or uniform inputs to the Booth-encoded input of the multiplier can save 4.8% of multiplier energy on average. An additional 1.5% savings can be achieved with dynamic detection and steering of uniform inputs.