How can I auto-vectorize (SIMD) a modular multiplication in Rust?

How can I implement modular multiplication in Rust and optimize it using SIMD (Single Instruction, Multiple Data) to leverage automatic vectorization for improved performance?

Optimizing modular multiplication in Rust using SIMD (Single Instruction, Multiple Data) to leverage auto-vectorization for improved performance involves a few key steps. Here's a high-level overview of the process:

Understanding SIMD and Modular Multiplication: SIMD allows you to process multiple data points with a single instruction, which can significantly speed up operations like modular multiplication.

Using the packed_simd or std::simd Crate: Rust has crates like packed_simd or the more recent std::simd for SIMD operations. These crates provide the necessary tools to work with SIMD vectors.

Implementing Modular Multiplication: First, implement the modular multiplication function in Rust. Ensure that the function can handle large integers and perform the modulo operation efficiently.

Vectorizing the Implementation: Use SIMD vectors to parallelize the multiplication and modulo operations. Load multiple elements into SIMD vectors and perform the operations in parallel.

Handling Overflows and Carry: Ensure that the implementation handles overflows and carry correctly, especially when working with large integers. This might involve additional instructions to manage the carry bits.

Benchmarking and Testing: Test the SIMD implementation to ensure correctness and benchmark its performance against the non-SIMD version. Make adjustments as needed to optimize performance further.