Harnessing SIMD for Faster Array Operations in Rust

This challenge focuses on understanding and leveraging Rust's auto-vectorization capabilities to significantly speed up common array processing tasks. You will implement a function that performs an element-wise operation on two arrays and observe how Rust's compiler can automatically optimize this for SIMD (Single Instruction, Multiple Data) execution without explicit intrinsics.

Problem Description

Your task is to implement a function that takes two slices of floating-point numbers and performs an element-wise multiplication, storing the results in a new vector. The primary goal is to write the code in a way that allows the Rust compiler to automatically vectorize the operation, utilizing SIMD instructions for performance gains.

Requirements:

1. Function Signature: Implement a function with the signature fn vectorized_multiply(a: &[f32], b: &[f32]) -> Vec<f32>.
2. Element-wise Multiplication: For each corresponding element a[i] and b[i], calculate a[i] * b[i] and store it in the resulting vector.
3. Equal Length Slices: The input slices a and b are guaranteed to have the same length.
4. Return New Vector: The function must return a Vec<f32> containing the results.
5. Auto-Vectorization: Write the code in a idiomatic Rust style that encourages the compiler to apply auto-vectorization. This means avoiding certain patterns that might hinder optimization and favoring simple loop structures.

Expected Behavior:

The function should accurately perform element-wise multiplication. For example, if a = [1.0, 2.0, 3.0] and b = [4.0, 5.0, 6.0], the output should be [4.0, 10.0, 18.0].

Edge Cases:

• Empty Slices: The function should correctly handle empty input slices, returning an empty Vec<f32>.

Examples

Example 1:

Input:
a = [1.0, 2.0, 3.0, 4.0]
b = [5.0, 6.0, 7.0, 8.0]

Output:
[5.0, 12.0, 21.0, 32.0]

Explanation:
1.0 * 5.0 = 5.0
2.0 * 6.0 = 12.0
3.0 * 7.0 = 21.0
4.0 * 8.0 = 32.0

Example 2:

Input:
a = []
b = []

Output:
[]

Explanation:
Input slices are empty, so the output vector is also empty.

Example 3:

Input:
a = [0.5, 1.5]
b = [2.0, 4.0]

Output:
[1.0, 6.0]

Explanation:
0.5 * 2.0 = 1.0
1.5 * 4.0 = 6.0

Constraints

• The length of the input slices a and b will be between 0 and 1,000,000 (inclusive).
• The input slices will contain f32 floating-point numbers.
• The output vector must also contain f32 floating-point numbers.
• For optimal performance, the solution should aim for a time complexity that benefits from vectorization, ideally close to O(N/V) where V is the vector width.

Notes

• Compiler Flags: To observe and verify auto-vectorization, you will likely need to compile with optimization flags (e.g., cargo build --release).
• Verification: You can inspect the generated assembly code (using cargo asm or similar tools) to confirm if SIMD instructions (like mulps, vfmaddps etc.) are being used.
• Idiomatic Rust: Focus on writing clear, straightforward loops. Avoid complex control flow or operations within the loop that might prevent the compiler from vectorizing. For instance, operations that depend on the results of previous iterations within the same loop can be problematic for simple auto-vectorization.
• No Manual Intrinsics: This challenge specifically asks you to rely on auto-vectorization, so do not use explicit SIMD intrinsics (e.g., std::arch).