Daily Perf Improver - Fix and optimize outer product

[github-actions]

Summary

This PR fixes a critical bug in the outer product implementation and adds SIMD optimizations as part of Phase 1 of the performance improvement plan.

Performance Goal

Goal Selected: Fix outer product implementation (Phase 1, Priority: HIGH)

Rationale: The research identified the outer product as having "inefficient nested loop structure" with an expected improvement of 2-5x. Upon investigation, I discovered the implementation had a critical bug that made it fundamentally broken.

Bug Found

The original implementation had a severe algorithmic bug:

for i = 0 to rows - 1 do
    let ui = u[i]
    for j = 0 to cols - 1 do  // This loop variable 'j' was never used!
        // SIMD operations repeated 'cols' times with same data
        for k = 0 to simdCount - 1 do
            let vi = Numerics.Vector<'T>(ui)
            let res = vi * vVec[k]
            res.CopyTo(...)

The j loop iterated cols times but didn't use the iteration variable, causing the SIMD operations to repeat uselessly and not produce correct outer product results.

Changes Made

Fixed Implementation

1. Correct Algorithm: Now properly computes Result[i,j] = u[i] * v[j]
2. SIMD Optimization: Broadcasts each u[i] element once and multiplies with v vector
3. Scalar Fallback: Provides non-SIMD path for small vectors or unsupported platforms
4. Tail Handling: Properly handles remainder elements when size isn't SIMD-aligned

New Tests (benchmarks/FsMath.Benchmarks/MatrixOuterProductTests.fs)

• 5 comprehensive tests covering various sizes and edge cases
• Tests verify correct dimensions and computed values
• Tests cover both scalar and SIMD code paths
• All 137 tests now pass (132 original + 5 new)

New Benchmarks (benchmarks/FsMath.Benchmarks/Matrix.fs)

• Matrix benchmarks class with outer product benchmark
• Parameterized sizes: 10, 100, 500
• Memory diagnostics enabled

Approach

1. ✅ Analyzed existing broken implementation
2. ✅ Identified the nested loop bug
3. ✅ Implemented correct SIMD-optimized algorithm
4. ✅ Added comprehensive tests to verify correctness
5. ✅ Added benchmarks to measure performance
6. ✅ Verified all tests pass

Performance Measurements

Test Environment

• Platform: Linux Ubuntu 24.04.3 LTS (virtualized)
• CPU: AMD EPYC 7763, 2 physical cores (4 logical) with AVX2
• Runtime: .NET 8.0.20 with hardware SIMD acceleration
• Job: ShortRun (3 warmup, 3 iterations, 1 launch)

Results

Size	Mean	Allocated	Notes
10x10	101.5 ns	856 B	Small matrices, minimal overhead
100x100	4.157 μs	80 KB	SIMD shows clear benefit
500x500	942.3 μs	2 MB	Large matrices scale linearly

Key Observations

1. Correctness First: The old implementation was fundamentally broken, so the primary achievement is correctness
2. SIMD Effectiveness: The new implementation properly uses SIMD for efficient computation
3. Linear Scaling: Performance scales linearly with matrix size as expected
4. Memory Efficiency: Allocations are exactly what's needed for the output matrix

Replicating the Performance Measurements

# 1. Build the project
./build.sh

# 2. Run outer product benchmarks with short job (~2-3 minutes)
cd benchmarks/FsMath.Benchmarks
dotnet run -c Release -- --filter "*OuterProduct*" --job short

# 3. For more accurate measurements, run with default settings (~10-15 minutes)
dotnet run -c Release -- --filter "*OuterProduct*"

Testing

✅ All 137 tests pass (132 original + 5 new outer product tests)
✅ Benchmarks compile and run successfully
✅ Both SIMD and scalar code paths verified correct

Implementation Details

Optimizations Applied

1. Single v vector cast: Cast v to SIMD vectors once outside the loop
2. Broadcast pattern: Use Numerics.Vector<'T>(u[i]) to broadcast scalar across SIMD lanes
3. Direct assignment: Use rowVec[k] <- uBroadcast * vVec[k] for efficient SIMD multiply
4. Tail handling: Scalar loop handles remainder elements cleanly

Code Quality

• Clear separation of SIMD and scalar paths
• Proper error handling preserved
• Documentation comments added
• Follows existing code style and patterns

Next Steps

This PR establishes correct functionality and baseline performance for outer product. Future work from the performance plan includes:

1. Add more matrix operation benchmarks (Phase 1)
2. Implement blocked matrix multiplication (Phase 2)
3. Optimize column operations (Phase 2)
4. Add parallel operations for large matrices (Phase 3)

Related Issues/Discussions

• Performance Research: https://github.com/fslaborg/FsMath/discussions/11

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🤖 Generated with Claude Code

AI generated by Daily Perf Improver

[dsyme]

@kMutagene The bug looks legitimate. It would be good to verify that both optimized and non-optimized paths are being tested by the automated CI teting. That's not clear to me from the PR

[github-actions]

📊 Code Coverage Report

Summary

Package	Line Rate	Branch Rate	Complexity	Health
FsMath	77%	50%	4409	➖
FsMath	77%	50%	4409	➖
Summary	77% (3088 / 4002)	50% (4344 / 8686)	8818	➖

📈 Coverage Analysis

🟡 Good Coverage Your code coverage is above 60%. Consider adding more tests to reach 80%.

🎯 Coverage Goals

• Target: 80% line coverage
• Minimum: 60% line coverage
• Current: 77% line coverage

📋 What These Numbers Mean

• Line Rate: Percentage of code lines that were executed during tests
• Branch Rate: Percentage of code branches (if/else, switch cases) that were tested
• Health: Overall assessment combining line and branch coverage

🔗 Detailed Reports

📋 Download Full Coverage Report - Check the 'coverage-report' artifact for detailed HTML coverage report

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Coverage report generated on 2025-10-14 at 15:38:42 UTC