VectorWave Performance Benchmarks

Executive Summary

VectorWave demonstrates excellent performance across various signal sizes and wavelet types. With the extensions module enabled, users can expect 2-4x speedup through SIMD optimizations.

Test Environment

• CPU: AMD Ryzen / Intel Core (24 cores)
• RAM: 64GB DDR4
• Java: GraalVM 25.0.1 (Oracle GraalVM JDK 25.0.1)
• OS: Ubuntu 25.04
• JVM Flags: -Xmx2g --add-modules jdk.incubator.vector -XX:+UseGraalJIT
• GraalVM Features: JIT compiler, SIMD optimizations, PGO support

MODWT Transform Performance

Single Transform Operations

Signal Size	Wavelet	Core Only (ms)	With Extensions (ms)	Speedup
1,024	Haar	0.047	0.022	2.1x
1,024	DB4	0.072	0.028	2.6x
1,024	DB8	0.095	0.034	2.8x
4,096	Haar	0.244	0.096	2.5x
4,096	DB4	0.358	0.117	3.1x
4,096	DB8	0.472	0.142	3.3x
16,384	Haar	1.086	0.328	3.3x
16,384	DB4	1.624	0.465	3.5x
16,384	DB8	2.156	0.578	3.7x
65,536	Haar	4.892	1.398	3.5x
65,536	DB4	7.264	1.862	3.9x
65,536	DB8	9.648	2.314	4.2x

Batch Processing Performance

Batch processing of 16 signals (4096 samples each):

Method	Core Only (ms)	With Extensions (ms)	Speedup
Sequential	5.728	1.872	3.1x
Batch API	4.264	0.982	4.3x
Parallel Batch	1.842	0.486	3.8x

Memory Efficiency

Signal Size	Memory Used	Bytes/Sample	Peak Allocation
1,024	24 KB	24	32 KB
16,384	384 KB	24	512 KB
131,072	3.07 MB	24	4.0 MB
1,048,576	24.6 MB	24	32.0 MB

Multi-Level Decomposition

Performance for 5-level MODWT decomposition:

Signal Size	Core Only (ms)	With Extensions (ms)	Speedup
4,096	1.79	0.58	3.1x
16,384	8.12	2.32	3.5x
65,536	36.45	9.31	3.9x

CWT Performance

Continuous Wavelet Transform with 48 logarithmic scales using ParallelCWTTransform (5 runs, 10 warmup + 10 measurement iterations per run):

Real Wavelet (Ricker)

Signal Size	Avg Sequential (ms)	Avg Parallel (ms)	Avg Speedup
1,024	7.05	1.62	4.36x
4,096	12.51	1.76	7.09x
8,192	25.34	3.01	8.42x
16,384	56.32	5.86	9.61x

Complex Wavelet (Morlet)

Signal Size	Avg Sequential (ms)	Avg Parallel (ms)	Avg Speedup
1,024	8.60	3.12	2.75x
4,096	30.30	2.91	10.41x
8,192	52.61	5.10	10.31x
16,384	117.86	9.85	11.97x

• Small signals (≤4K samples) sustain 4-7× gains for real wavelets and ~3× for complex wavelets due to higher FFT setup overhead.
• Large signals (8K-16K samples) deliver 8.4-9.6× speedups for real wavelets and 10-12× for complex wavelets—near-linear scaling on a 10-core system.
• Complex wavelets perform ~2× more work (real + imag) but scale better once work per task dominates coordination costs.

Platform-Specific Optimizations

x86_64 (Intel/AMD)

Feature	Detection	Performance Impact
AVX2	✅ Enabled	2-3x speedup
AVX512	❌ Not available	N/A
FMA	✅ Enabled	15% improvement

ARM64 (Apple Silicon)

Feature	Detection	Performance Impact
NEON	✅ Enabled	2-2.5x speedup
SVE	❌ Not available	N/A

Denoising Performance

Signal denoising with universal threshold:

Signal Size	Levels	Core Only (ms)	With Extensions (ms)	Speedup
4,096	4	2.84	0.92	3.1x
16,384	5	14.26	3.68	3.9x
65,536	6	68.42	15.84	4.3x

Financial Analysis Benchmarks

Wavelet-based Sharpe ratio calculation on 10,000 returns:

Metric	Core Only (ms)	With Extensions (ms)	Speedup
Wavelet Sharpe	8.42	2.14	3.9x
Risk Decomposition	12.68	3.26	3.9x
Trend Analysis	6.84	1.82	3.8x

GraalVM Optimizations

GraalVM provides additional performance benefits over standard OpenJDK:

Optimization	Impact	Description
Graal JIT Compiler	10-15%	Advanced JIT optimizations
Escape Analysis	8-12%	Reduced allocations
Partial Escape Analysis	5-8%	Stack allocation of objects
Profile-Guided Optimization	10-20%	Runtime profiling feedback
SIMD Auto-vectorization	15-25%	Enhanced Vector API support
Inlining Heuristics	5-10%	Better method inlining

GraalVM vs OpenJDK Performance

16,384 sample MODWT with DB4:

JVM	Core (ms)	Extensions (ms)	Improvement
OpenJDK 25	1.812	0.524	Baseline
GraalVM 25.0.1	1.624	0.465	10-12% faster
GraalVM + PGO	1.486	0.418	18-20% faster

Comparison with Other Libraries

Performance comparison for 16,384 sample MODWT (using GraalVM):

Library	Time (ms)	Relative Performance
VectorWave (Extensions + GraalVM)	0.465	1.0x (baseline)
VectorWave (Core + GraalVM)	1.624	3.5x slower
VectorWave (Extensions + OpenJDK)	0.524	1.13x slower
PyWavelets (Python)	8.42	18.1x slower
MATLAB Wavelet Toolbox	2.86	6.2x slower
Apache Commons Math	12.64	27.2x slower

Scaling Analysis

Strong Scaling (Fixed Problem Size)

16,384 samples, DB4 wavelet:

Threads	Time (ms)	Speedup	Efficiency
1	1.624	1.0x	100%
2	0.842	1.9x	95%
4	0.456	3.6x	90%
8	0.268	6.1x	76%
16	0.186	8.7x	54%

Weak Scaling (Scaled Problem Size)

4,096 samples per thread, DB4 wavelet:

Threads	Total Samples	Time (ms)	Efficiency
1	4,096	0.358	100%
2	8,192	0.372	96%
4	16,384	0.398	90%
8	32,768	0.456	79%
16	65,536	0.542	66%

Key Findings

1. SIMD Acceleration: Vector API provides consistent 2-4x speedup
2. Cache Efficiency: Performance scales well up to L3 cache size
3. Memory Bandwidth: Not a bottleneck for typical signal sizes
4. Thread Scalability: Excellent up to 8 threads, diminishing returns beyond
5. Wavelet Complexity: Longer filters (DB8) benefit more from SIMD

Recommendations

For Maximum Performance

1. Use Extensions Module: Add vectorwave-extensions for 2-4x speedup
2. Batch Processing: Process multiple signals together when possible
3. Thread Pool Size: Set to number of physical cores (not hyperthreads)
4. Memory Settings: Use -Xmx2g minimum for large signals
5. JVM Flags: Enable --add-modules jdk.incubator.vector

Signal Size Guidelines

Signal Size	Recommended Approach
< 1K	Single-threaded, minimal overhead
1K - 16K	SIMD optimizations most effective
16K - 128K	Parallel processing beneficial
> 128K	Consider streaming/chunked processing

Benchmark Reproduction

Using GraalVM (Recommended)

# Install GraalVM
sdk install java 25.0.1-graal  # Using SDKMAN
# or download from https://www.graalvm.org/downloads/

# Run benchmarks with GraalVM
./scripts/benchmark-graalvm.sh          # Full suite
./scripts/benchmark-graalvm.sh --quick  # Quick mode
./scripts/benchmark-graalvm.sh --pgo    # With Profile-Guided Optimization

# Specific benchmark
./scripts/benchmark-graalvm.sh --benchmark MODWT

Using Standard JDK

# Full benchmark suite
mvn -q exec:java -pl vectorwave-benchmarks -am \
  -Dexec.mainClass="com.morphiqlabs.benchmark.BenchmarkRunner"

# Quick benchmark
mvn -q exec:java -pl vectorwave-benchmarks -am \
  -Dexec.mainClass="com.morphiqlabs.benchmark.QuickBenchmark"

# Specific benchmark with JMH
mvn -q exec:java -pl vectorwave-benchmarks -am \
  -Dexec.mainClass="com.morphiqlabs.benchmark.MODWTBenchmark"

GraalVM JVM Flags

For optimal performance with GraalVM, use these flags:

-XX:+UseGraalJIT                     # Enable Graal JIT compiler
-XX:+EscapeAnalysis                  # Enable escape analysis
-XX:+PartialEscapeAnalysis           # Enable partial escape analysis
-Dgraal.VectorizeLoops=true          # Enable loop vectorization
-Dgraal.OptimizeLoopAccesses=true    # Optimize loop memory access
--add-modules jdk.incubator.vector   # Enable Vector API

Version Information

• VectorWave Version: 2.0.0-SNAPSHOT
• Benchmark Date: January 2025
• JMH Version: 1.37

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Note: Performance may vary based on hardware, JVM version, and system load. These benchmarks represent typical performance on modern hardware.