Vectorized Sum of Squares

Auto-vectorization is a powerful optimization technique where compilers automatically transform scalar operations into parallel operations on vectors, significantly improving performance on modern CPUs with SIMD (Single Instruction, Multiple Data) capabilities. This challenge asks you to implement a simplified form of auto-vectorization in Go to calculate the sum of squares of a slice of floating-point numbers. While Go's compiler already performs some auto-vectorization, this exercise focuses on understanding the underlying principles and implementing a basic, manual vectorization strategy.

Problem Description

You are tasked with writing a Go function SumOfSquaresVectorized that calculates the sum of squares of a slice of float64 values. The function should accept a slice of float64 as input and return the sum of the squares of all elements in the slice. The key requirement is to implement a rudimentary form of auto-vectorization by processing the input slice in chunks of 4 (a common vector size for SIMD operations). This means you should process 4 elements at a time, performing the squaring and summation within a single loop iteration. This will demonstrate a basic understanding of how to leverage parallel processing for improved performance.

Key Requirements:

• The function must accept a slice of float64 as input.
• The function must return a float64 representing the sum of squares.
• The function must process the input slice in chunks of 4 elements.
• The function must handle slices whose length is not a multiple of 4.
• The function should be reasonably efficient, demonstrating the benefits of vectorized processing.

Expected Behavior:

The function should accurately calculate the sum of squares for any valid input slice. It should handle edge cases gracefully, such as empty slices or slices with a length not divisible by 4.

Edge Cases to Consider:

• Empty input slice: Should return 0.0.
• Slice length not divisible by 4: The remaining elements should be processed individually after the main loop.
• Large input slices: The vectorized approach should demonstrate a performance improvement compared to a naive scalar implementation.

Examples

Example 1:

Input: []float64{1.0, 2.0, 3.0, 4.0}
Output: 30.0
Explanation: 1.0^2 + 2.0^2 + 3.0^2 + 4.0^2 = 1 + 4 + 9 + 16 = 30

Example 2:

Input: []float64{1.0, 2.0, 3.0}
Output: 14.0
Explanation: 1.0^2 + 2.0^2 + 3.0^2 = 1 + 4 + 9 = 14

Example 3:

Input: []float64{}
Output: 0.0
Explanation: Empty slice, so the sum of squares is 0.

Constraints

• The input slice will contain only float64 values.
• The length of the input slice can be any non-negative integer.
• The function should be reasonably efficient. While a precise performance target isn't specified, the vectorized approach should demonstrably outperform a simple scalar loop for sufficiently large input slices.
• The chunk size for vectorization is fixed at 4.

Notes

• This is a simplified demonstration of auto-vectorization. Real-world auto-vectorization is significantly more complex and handled by compilers.
• Focus on the logic of processing data in chunks rather than achieving absolute peak performance.
• Consider using a simple loop to iterate through the slice and process elements in groups of 4.
• Remember to handle the remaining elements at the end of the slice if the length is not a multiple of 4.
• You can compare the performance of your vectorized function with a naive scalar implementation to observe the potential benefits.