[SYSTEMDS-3855] Vector API: Sparse-Sparse Matrix Multiplication Kernels

[Elmanjhg]

This PR completes the missing Vector API (SIMD) implementations for sparse matrix combinations, extending the work done in previous dense/sparse vectorization PR #2423.

Modifications

Replaced the scalar inner loops with the vectorized "vectMultiplyAddScatter" using the JDK 17 Vector API in the following three Sparse-Sparse matrix multiplication kernels within "LibMatrixMult.java":

1. matrixMultSparseSparseMM
2. matrixMultSparseSparseMMSmallRHS
3. matrixMultSparseSparseSparseMM

Testing & Validation

• Component tests (MatrixMultiplyTest) executed successfully (5000 tests passed, 0 failures).

BENCHMARK

Hardware Environment (Linux)

• OS: Ubuntu Linux
• CPU Model: AMD Ryzen 5 PRO 7530U (x86_64)
• Cores/Threads: 6 Cores / 12 Threads (Turbo: 4.54 GHz)
• Vector Capability: 256-bit (AVX2)
• Cache: L1: 384 KiB / L2: 3 MiB / L3: 16 MiB
• Memory: 16 GB

The benchmark uses like the PR Request before the Java Microbenchmark Harness (JMH) framework to measure the performance of the rewritten kernels. The result is the average execution time in microseconds. Each benchmark run consists of 5 warmup iterations followed by 10 measurement iterations (1 second each), executed in a single forked JVM.

Sparse-Sparse Benchmark Result Summary

• The vectorized implementations yield solid performance gains (up to 1.35x) on larger matrices (e.g., 8192x8192).
• Minor performance regressions (dropping to ~0.87x) occur when the right hand sparsity is precisely around 0.01, likely where the overhead of vector preparation and scatter operations slightly outweighs the raw SIMD throughput.

Benchmark Parameters

• m: 1024, 2048, 4096, 8192
• cd: 1
• n: 1024, 2048, 4096, 8192
• Sparsity Left: 0.5, 0.75, 1.0
• Sparsity Right: 0.001, 0.01, 0.1, 0.2
• Total Configs: 192

Top Performance Gains (Speedup > 1.0)

m	n	sparsityLeft	sparsityRight	Speedup
8192	4096	1.0	0.001	1.35x
8192	8192	0.5	0.001	1.35x
8192	8192	0.75	0.001	1.33x
8192	8192	1.0	0.001	1.32x
8192	4096	1.0	0.010	1.22x

Top Performance Losses (Speedup < 1.0)

m	n	sparsityLeft	sparsityRight	Speedup
8192	2048	1.0	0.010	0.87x
1024	2048	0.75	0.010	0.88x
4096	8192	0.75	0.010	0.90x
8192	2048	0.5	0.010	0.91x
2048	4096	1.0	0.010	0.92x

Baseline vs Vectorized Performance plots

Raw Data

runtimeComparisonSYSTEMDSProject.csv