  Spin Waves(SWs) enable the realization of energy efficient circuits as they
propagate and interfere within waveguides without consuming noticeable energy.
However, SW computing can be even more energy efficient by taking advantage of
the approximate computing paradigm as many applications are error-tolerant like
multimedia and social media. In this paper we propose an ultra-low energy novel
Approximate Full Adder(AFA) and a 2-bit inputs Multiplier(AMUL). We validate
the correct functionality of our proposal by means of micromagnetic simulations
and evaluate the approximate FA figure of merit against state-of-the-art
accurate SW, 7nmCMOS, Spin Hall Effect(SHE), Domain Wall Motion(DWM), accurate
and approximate 45nmCMOS, Magnetic Tunnel Junction(MTJ), and Spin-CMOS FA
implementations. Our results indicate that AFA consumes 43% and 33% less energy
than state-of-the-art accurate SW and 7nmCMOS FA, respectively, and saves 69%
and 44% when compared with accurate and approximate 45nm CMOS, respectively,
and provides a 2 orders of magnitude energy reduction when compared with
accurate SHE, accurate and approximate DWM, MTJ, and Spin-CMOS, counterparts.
In addition, it achieves the same error rate as approximate 45nmCMOS and
Spin-CMOS FA whereas it exhibits 50% less error rate than the approximate DWM
FA. Furthermore, it outperforms its contenders in terms of area by saving at
least 29% chip real-estate. AMUL is evaluated and compared with
state-of-the-art accurate SW and 16nm CMOS accurate and approximate
state-of-the-art designs. The evaluation results indicate that it saves at
least 2x and 5x energy in comparison with the state-of-the-art SW designs and
16nm CMOS accurate and approximate designs, respectively, and has an average
error rate of 10%, while the approximate CMOS MUL has an average error rate of
13%, and requires at least 64% less chip real-estate.
