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Optimal binary signed-digit representations of integers and the Stern polynomial
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2024-04-02 , DOI: 10.1007/s10623-023-01355-w Laura Monroe
中文翻译:
整数和斯特恩多项式的最佳二进制有符号数字表示
更新日期:2024-04-02
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2024-04-02 , DOI: 10.1007/s10623-023-01355-w Laura Monroe
The binary signed-digit (BSD) representation of integers is used for efficient integer computation in various settings. The Stern polynomial is a polynomial extension of the well-studied Stern diatomic sequence. In this paper, we show previously unknown connections between BSD integer representations and the Stern polynomial. We then exploit these connections to devise a fast algorithm to count optimal BSD representations on a range of integers and calculate their weights.
中文翻译:
整数和斯特恩多项式的最佳二进制有符号数字表示
整数的二进制有符号数字 (BSD) 表示形式用于在各种设置中进行高效的整数计算。斯特恩多项式是经过充分研究的斯特恩双原子序列的多项式扩展。在本文中,我们展示了 BSD 整数表示和 Stern 多项式之间以前未知的联系。然后,我们利用这些连接来设计一种快速算法来计算一系列整数上的最佳 BSD 表示并计算它们的权重。