PAM: A Piecewise-Linearly-Approximated Floating-Point Multiplier with Unbiasedness and Configurability

Approximate computing is a promising alternative to improve energy efficiency for IoT devices on the edge. This work proposes a piecewise-linearly-approximated and unbiased floating-point approximate multiplier with run-time configurability. We provide a theoretically sound formulation that turns multiplication approximation to an optimization problem. With the formulation and findings, a multi-level architecture is proposed to easily incorporate run-time configurability and module execution parallelism. Finally, the proposed multiplier is further optimized to reduce the circuit implementation complexity, making the multiplier linearly dependent on the precision requirement, instead of quadratically or exponentially as in prior work. When compared to the prior state-of-the-art approximate floating-point multiplier, ApproxLP [1], the proposed multiplier outperforms in all the aspects including accuracy, area, and delay. By replacing a full-precision floating-point multiplier in GPU, the proposed design can improve the energy efficiency for various edge computing tasks. Even with Level 1 approximation, the proposed multiplier improves energy efficiency up to 20x for machine learning on CIFAR-10, with almost negligible accuracy loss.