Zero-Aware Low-Precision RNS Scaling Scheme

Amir Sabbagh Molahosseini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Scaling is one of the complex operations in the Residue Number System (RNS). This operation is necessary for RNS-based implementations of deep neural networks (DNNs) to prevent overflow. However, the state-of-the-art RNS scalers for special moduli sets consider the 2k modulo as the scaling factor, which results in a high-precision output with a high area and delay. Therefore, low-precision scaling based on multi-moduli scaling factors should be used to improve performance. However, low-precision scaling for numbers less than the scale factor results in zero output, which makes the subsequent operation result faulty. This paper first presents the formulation and hardware architecture of low-precision RNS scaling for four-moduli sets using new Chinese remainder theorem 2 (New CRT-II) based on a two-moduli scaling factor. Next, the low-precision scaler circuits are reused to achieve a high-precision scaler with the minimum overhead. Therefore, the proposed scaler can detect the zero output after low-precision scaling and then transform low-precision scaled residues to high precision to prevent zero output when the input number is not zero.
Original languageEnglish
Article number5
Issue number1
Early online date23 Dec 2021
Publication statusPublished - Jan 2022


  • residue number system (RNS)
  • scaling
  • Chinese remainder theorem (CRT)


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