Vectorized Sum of Squares

Auto-vectorization is a powerful optimization technique where compilers automatically transform scalar code into vectorized code, leveraging SIMD (Single Instruction, Multiple Data) instructions to perform operations on multiple data elements simultaneously. This challenge asks you to implement a function that calculates the sum of squares of a slice of f32 values, and then demonstrate how Rust's compiler can automatically vectorize this function under certain conditions. Understanding how to write code that enables auto-vectorization is crucial for achieving high performance in numerical computations.

Problem Description

You are tasked with implementing a function sum_of_squares that takes a slice of f32 values as input and returns the sum of the squares of those values. The goal is to write this function in a way that allows the Rust compiler to automatically vectorize it, significantly improving performance for large input slices. The function should handle empty slices gracefully, returning 0.0 in that case.

Key Requirements:

The function must accept a slice of f32 (&[f32]) as input.
The function must return an f32 representing the sum of squares.
The code should be written in a way that encourages auto-vectorization by the compiler. Avoid explicit loops where possible, and use operations that are naturally amenable to vectorization.
The function must handle the edge case of an empty input slice.

Expected Behavior:

For a given slice of f32 values, the function should calculate the square of each value and sum the results. The order of summation does not matter.

Edge Cases to Consider:

Empty input slice: Should return 0.0.
Slice containing only zeros: Should return 0.0.
Slice containing very large or very small numbers: Consider potential overflow/underflow issues, although this is less critical for this exercise.

Examples

Example 1:

Input: [1.0, 2.0, 3.0]
Output: 14.0
Explanation: 1.0^2 + 2.0^2 + 3.0^2 = 1.0 + 4.0 + 9.0 = 14.0

Example 2:

Input: [0.0, 0.0, 0.0]
Output: 0.0
Explanation: 0.0^2 + 0.0^2 + 0.0^2 = 0.0

Example 3:

Input: []
Output: 0.0
Explanation: Empty slice, so the sum of squares is 0.0.

Constraints

The input slice will contain only f32 values.
The length of the input slice can be up to 1000000 (1 million) elements. This is to encourage vectorization to be beneficial.
The function must compile and run without panicking.
While not strictly enforced, aim for a solution that demonstrates a good understanding of how to write code that is likely to be auto-vectorized by the Rust compiler. Performance will be evaluated, but clarity and correctness are paramount.

Notes

Rust's compiler often performs auto-vectorization automatically, but it's not guaranteed. Certain code patterns are more conducive to vectorization than others.
Consider using functional programming techniques like map and sum to express the computation concisely.
The #[target(feature = "avx2")] attribute can be used to hint to the compiler that you want to target a specific vectorization feature set. However, for this challenge, focus on writing code that allows the compiler to vectorize, rather than forcing a specific feature set. The compiler should be able to vectorize without this attribute.
Benchmarking your solution with different input sizes is a good way to verify that auto-vectorization is occurring. Use the criterion crate for benchmarking.

Vectorized Sum of Squares

Problem Description

Key Requirements:

The function must accept a slice of f32 (&[f32]) as input.

The function must return an f32 representing the sum of squares.

The code should be written in a way that encourages auto-vectorization by the compiler. Avoid explicit loops where possible, and use operations that are naturally amenable to vectorization.

The function must handle the edge case of an empty input slice.

Expected Behavior:

For a given slice of f32 values, the function should calculate the square of each value and sum the results. The order of summation does not matter.

Edge Cases to Consider:

Empty input slice: Should return 0.0.

Slice containing only zeros: Should return 0.0.

Slice containing very large or very small numbers: Consider potential overflow/underflow issues, although this is less critical for this exercise.

Constraints

The input slice will contain only f32 values.

The length of the input slice can be up to 1000000 (1 million) elements. This is to encourage vectorization to be beneficial.

The function must compile and run without panicking.

While not strictly enforced, aim for a solution that demonstrates a good understanding of how to write code that is likely to be auto-vectorized by the Rust compiler. Performance will be evaluated, but clarity and correctness are paramount.

Notes

Rust's compiler often performs auto-vectorization automatically, but it's not guaranteed. Certain code patterns are more conducive to vectorization than others.

Consider using functional programming techniques like map and sum to express the computation concisely.

The #[target(feature = "avx2")] attribute can be used to hint to the compiler that you want to target a specific vectorization feature set. However, for this challenge, focus on writing code that allows the compiler to vectorize, rather than forcing a specific feature set. The compiler should be able to vectorize without this attribute.

Benchmarking your solution with different input sizes is a good way to verify that auto-vectorization is occurring. Use the criterion crate for benchmarking.