Zero-Aware Low-Precision RNS Scaling Scheme
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 2<i><sup>k</sup>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/1/5 |
| _version_ | 1797495835616870400 |
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| author | Amir Sabbagh Molahosseini |
| author_facet | Amir Sabbagh Molahosseini |
| author_sort | Amir Sabbagh Molahosseini |
| collection | DOAJ |
| description | 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 2<i><sup>k</sup></i> 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. |
| first_indexed | 2024-03-10T01:55:16Z |
| format | Article |
| id | doaj.art-b42c4d4b6a464913a965435f0b3e678b |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T01:55:16Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b42c4d4b6a464913a965435f0b3e678b2023-11-23T12:58:03ZengMDPI AGAxioms2075-16802021-12-01111510.3390/axioms11010005Zero-Aware Low-Precision RNS Scaling SchemeAmir Sabbagh Molahosseini0School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast BT7 1NN, UKScaling 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 2<i><sup>k</sup></i> 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.https://www.mdpi.com/2075-1680/11/1/5residue number system (RNS)scalingChinese remainder theorem (CRT) |
| spellingShingle | Amir Sabbagh Molahosseini Zero-Aware Low-Precision RNS Scaling Scheme Axioms residue number system (RNS) scaling Chinese remainder theorem (CRT) |
| title | Zero-Aware Low-Precision RNS Scaling Scheme |
| title_full | Zero-Aware Low-Precision RNS Scaling Scheme |
| title_fullStr | Zero-Aware Low-Precision RNS Scaling Scheme |
| title_full_unstemmed | Zero-Aware Low-Precision RNS Scaling Scheme |
| title_short | Zero-Aware Low-Precision RNS Scaling Scheme |
| title_sort | zero aware low precision rns scaling scheme |
| topic | residue number system (RNS) scaling Chinese remainder theorem (CRT) |
| url | https://www.mdpi.com/2075-1680/11/1/5 |
| work_keys_str_mv | AT amirsabbaghmolahosseini zeroawarelowprecisionrnsscalingscheme |