High-Performance Vector Math with SIMD

Explain the use of high-dimensional vectors and distance metrics (Euclidean, Cosine) for similarity search.

Implement naive C functions to calculate Euclidean distance and Cosine similarity between two vectors.

Explain the concepts of instruction-level parallelism and SIMD (Single Instruction, Multiple Data).

Rewrite the Euclidean distance function using AVX2 SIMD intrinsics to process multiple floats simultaneously.

Implement a function to calculate the dot product of two vectors using AVX2 fused multiply-add (FMA) intrinsics.

Implement a function to calculate the squared L2 norm of a vector using AVX2 intrinsics.

Combine the dot product and L2 norm functions to create a final, SIMD-accelerated Cosine similarity function.

Benchmark the performance difference between naive and SIMD distance calculations.