Vol:.(1234567890) Journal of Computational Electronics (2023) 22:570–580 https://doi.org/10.1007/s10825-022-01960-3 1 3 An automatic routing approach for NML circuits Pedro Arthur R. L. Silva 1  · Ruan E. Formigoni 2  · Laysson O. Luz 1  · Ricardo Ferreira 2  · Omar P. Vilela Neto 1  · José Augusto M. Nacif 2 Received: 7 April 2021 / Accepted: 4 September 2022 / Published online: 7 November 2022 © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Nanomagnetic Logic (NML) is an emergent computation model based on the interactions between nanomagnets. However, there are several challenges and open problems in the NML design fow, where clocking schemes and routing play an essential role. We compare the tradeofs between NML synchronized and unsynchronized routing strategies using the A* search in this work. Both algorithms outperform previous work execution times by orders of magnitude, scaling for circuits with more than 1500 logic gates. Furthermore, we compare the synchronized circuits generated by our algorithm with ToPoliNano. For diferent full adders sizes, we outperform their results in terms of number of nanomagnets, absolute area, and clock zones by up to 113 ×, 88 ×, and 1.7 ×, respectively. Keywords Nanocomputing · NML · Routing · EDA 1 Introduction CMOS has been the standard technology for the manufactur- ing of digital devices over the years. However, this technol- ogy is close to its physical limits, while at the same time, reliability and power issues are rising at an alarming pace [12]. Several studies propose new technologies in recent years to overcome these problems and continue increas- ing integration densities, such as Field Coupled Nanotech- nologies (FCN) [1, 4]. One among these is Nanomagnetic Logic (NML), whose circuits are composed of arrays of nanomagnets placed on a plane interacting through the mag- netostatic dipolar coupling. Also, NML is nonvolatile and operates with ultra-low energy dissipation [5, 15]. In NML circuits, the information from one or more input particles propagates in the circuit as antiferromagnetic and ferromagnetic coupling. Particle geometries and position defne their coupling interaction. Therefore, it is possible to tailor the design of the particles in such a way that the shape anisotropy energy (which is magnetostatic) infuences the fnal magnetization direction allowing only two stable states, which are associated with ‘0’ and ‘1’ binary logic states, enabling the implementation of Boolean logic operations. Over the years, as the complexity of the CMOS inte- grated circuits increases, Electronic Design Automation (EDA) teams develop tools capable of providing higher abstraction levels. These tools can perform the design and verifcation of complex integrated circuits and electronic systems. Since CMOS has been the leading technology to build digital electronic devices, the literature presents a well- established set of EDA tools and techniques that address the problem of automatically generating a physical layout for CMOS circuits. Still, NML is not fully mature yet, so there is considerable room for research that aims to use this technology to overcome circuit designing challenges at the nanometric scale. Therefore, the development of tools and techniques that can assist the designer while abstracting low- level details of the NML technology is central. Due to the * Pedro Arthur R. L. Silva pedro.rodrigues@dcc.ufmg.br Ruan E. Formigoni ruan.formigoni@ufv.br Laysson O. Luz layssonluz@dcc.ufmg.br Ricardo Ferreira ricardo@ufv.br Omar P. Vilela Neto omar@dcc.ufmg.br José Augusto M. Nacif jnacif@ufv.br 1 Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil 2 Universidade Federal de Viçosa, Viçosa, MG, Brazil Content courtesy of Springer Nature, terms of use apply. Rights reserved.