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In this paper, we propose an implementation of multiple multiplicative inverses modulo \(2^w\) using Intel Advanced Vector Extensions 512 (Intel AVX-512) instructions, where w is the bit width in the integer arithmetic operations. The proposed 52-bit implementation is based on a combination of Newton’s method with quadratic convergence and a variant of Newton’s method with cubic convergence. For multiple modular multiplicative inverses, the proposed 52-bit implementation using Intel AVX-512 instructions is up to approximately 9.95 and 1.92 times faster than a 64-bit implementation based on an inclusive scan using Intel 64 instructions and a 64-bit implementation based on Newton’s method using Intel AVX-512 instructions, respectively, on an Intel Xeon Platinum 8468 processor.

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Implementation of Multiple Multiplicative Inverses Modulo \(2^w\) Using Intel AVX-512 Instructions

  • 会议论文

  • 发表日期：

    2025年

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  • Daisuke Takahashi

摘要

In this paper, we propose an implementation of multiple multiplicative inverses modulo \(2^w\) using Intel Advanced Vector Extensions 512 (Intel AVX-512) instructions, where w is the bit width in the integer arithmetic operations. The proposed 52-bit implementation is based on a combination of Newton’s method with quadratic convergence and a variant of Newton’s method with cubic convergence. For multiple modular multiplicative inverses, the proposed 52-bit implementation using Intel AVX-512 instructions is up to approximately 9.95 and 1.92 times faster than a 64-bit implementation based on an inclusive scan using Intel 64 instructions and a 64-bit implementation based on Newton’s method using Intel AVX-512 instructions, respectively, on an Intel Xeon Platinum 8468 processor.