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Jukka Aho 2cbb382ca8 feat(benchmark): Validate O(n) vs O(1) struct scaling hypothesis 
- Tests 1 to 5000 fields to find crossover point
- Confirms stack copying is O(n) at 0.16 ns/field
- Confirms Dict mutation is O(1) at 7 ns constant
- Crossover at 100 fields (800 bytes) for updates
- Typical FEM elements (20-60 fields) well below crossover
- Immutable wins for access and iteration at ALL sizes
- Generates 5 publication-quality plots
- Exports JSON + CSV with system specs
- System: Intel Xeon Gold 6326, 32 cores, 503 GB RAM
2025-11-09 21:00:51 +02:00

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Precompiling packages...
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65 dependencies successfully precompiled in 87 seconds. 112 already precompiled.
================================================================================
SYSTEM INFORMATION
================================================================================
CPU Model: Intel(R) Xeon(R) Gold 6326 CPU @ 2.90GHz
CPU Cores: 32 threads (32 physical cores)
CPU Speed: 3300 MHz
Julia Version: 1.12.1
OS: Linux x86_64-linux-gnu
Word Size: 64 bits
Approximate CPU Cache Sizes:
L1 Cache: ~32-64 KB per core (typical)
L2 Cache: ~256-512 KB per core (typical)
L3 Cache: ~8-32 MB shared (typical)
Note: Testing up to 8KB structs to exceed L1 cache
================================================================================
SYSTEM INFORMATION
================================================================================
Julia Version: 1.12.1
CPU Model: Intel(R) Xeon(R) Gold 6326 CPU @ 2.90GHz
CPU Cores: 32
Total Memory: 503.35 GB
L1 Cache: 48K
L2 Cache: 1280K
L3 Cache: 24576K
================================================================================
STRUCT SIZE SCALING BENCHMARK
================================================================================
Testing hypothesis: Immutable slows down with struct size, mutable stays constant
Testing struct with 1 Float64 fields (8 bytes)...
Access: Mut=4.62ns Imm=2.02ns Speedup=2.3x
Update: Mut=7.2ns Imm=2.32ns Speedup=3.1x
Iterate: Mut=11.77ns Imm=2.02ns Speedup=5.8x
Copy: 2.02ns
Testing struct with 2 Float64 fields (16 bytes)...
Access: Mut=4.9ns Imm=2.02ns Speedup=2.4x
Update: Mut=7.21ns Imm=2.31ns Speedup=3.1x
Iterate: Mut=14.49ns Imm=2.02ns Speedup=7.2x
Copy: 2.03ns
Testing struct with 5 Float64 fields (40 bytes)...
Access: Mut=4.9ns Imm=2.37ns Speedup=2.1x
Update: Mut=7.2ns Imm=2.6ns Speedup=2.8x
Iterate: Mut=16.71ns Imm=2.31ns Speedup=7.2x
Copy: 2.38ns
Testing struct with 10 Float64 fields (80 bytes)...
Access: Mut=4.62ns Imm=2.03ns Speedup=2.3x
Update: Mut=7.2ns Imm=2.6ns Speedup=2.8x
Iterate: Mut=23.13ns Imm=2.6ns Speedup=8.9x
Copy: 3.31ns
Testing struct with 20 Float64 fields (160 bytes)...
Access: Mut=4.62ns Imm=2.02ns Speedup=2.3x
Update: Mut=7.2ns Imm=3.16ns Speedup=2.3x
Iterate: Mut=63.13ns Imm=5.52ns Speedup=11.4x
Copy: 3.18ns
Testing struct with 50 Float64 fields (400 bytes)...
Access: Mut=4.62ns Imm=2.03ns Speedup=2.3x
Update: Mut=7.2ns Imm=6.02ns Speedup=1.2x
Iterate: Mut=196.85ns Imm=24.78ns Speedup=7.9x
Copy: 6.9ns
Testing struct with 100 Float64 fields (800 bytes)...
Access: Mut=4.62ns Imm=2.02ns Speedup=2.3x
Update: Mut=7.2ns Imm=11.75ns Speedup=0.6x
Iterate: Mut=260.56ns Imm=68.5ns Speedup=3.8x
Copy: 9.48ns
Testing struct with 200 Float64 fields (1600 bytes)...
Access: Mut=4.62ns Imm=2.37ns Speedup=1.9x
Update: Mut=7.41ns Imm=24.63ns Speedup=0.3x
Iterate: Mut=777.91ns Imm=155.16ns Speedup=5.0x
Copy: 20.95ns
Testing struct with 500 Float64 fields (4000 bytes)...
Access: Mut=4.62ns Imm=2.03ns Speedup=2.3x
Update: Mut=7.2ns Imm=80.84ns Speedup=0.1x
Iterate: Mut=1156.3ns Imm=499.36ns Speedup=2.3x
Copy: 58.68ns
Testing struct with 1000 Float64 fields (8000 bytes)...
Access: Mut=4.67ns Imm=2.08ns Speedup=2.2x
Update: Mut=7.2ns Imm=193.26ns Speedup=0.0x
Iterate: Mut=3465.75ns Imm=1100.2ns Speedup=3.2x
Copy: 45.7ns
Testing struct with 2000 Float64 fields (16000 bytes)...
Access: Mut=4.62ns Imm=2.02ns Speedup=2.3x
Update: Mut=7.2ns Imm=410.85ns Speedup=0.0x
Iterate: Mut=4811.71ns Imm=2226.22ns Speedup=2.2x
Copy: 82.95ns
Testing struct with 5000 Float64 fields (40000 bytes)...
Access: Mut=4.62ns Imm=2.08ns Speedup=2.2x
Update: Mut=7.2ns Imm=1936.1ns Speedup=0.0x
Iterate: Mut=33969.0ns Imm=5667.17ns Speedup=6.0x
Copy: 867.04ns
================================================================================
RESULTS SUMMARY
================================================================================
Field Access Performance:
Size (fields) | Bytes | Mutable (ns) | Immutable (ns) | Speedup
----------------------------------------------------------------------
1 | 8 | 4.62 | 2.02 | 2.3x
2 | 16 | 4.90 | 2.02 | 2.4x
5 | 40 | 4.90 | 2.37 | 2.1x
10 | 80 | 4.62 | 2.03 | 2.3x
20 | 160 | 4.62 | 2.02 | 2.3x
50 | 400 | 4.62 | 2.03 | 2.3x
100 | 800 | 4.62 | 2.02 | 2.3x
200 | 1600 | 4.62 | 2.37 | 1.9x
500 | 4000 | 4.62 | 2.03 | 2.3x
1000 | 8000 | 4.67 | 2.08 | 2.2x
2000 | 16000 | 4.62 | 2.02 | 2.3x
5000 | 40000 | 4.62 | 2.08 | 2.2x
Field Update Performance:
Size (fields) | Bytes | Mutable (ns) | Immutable (ns) | Speedup
----------------------------------------------------------------------
1 | 8 | 7.20 | 2.31 | 3.1x
2 | 16 | 7.21 | 2.31 | 3.1x
5 | 40 | 7.20 | 2.60 | 2.8x
10 | 80 | 7.20 | 2.60 | 2.8x
20 | 160 | 7.20 | 3.16 | 2.3x
50 | 400 | 7.20 | 6.02 | 1.2x
100 | 800 | 7.20 | 11.75 | 0.6x
200 | 1600 | 7.41 | 24.63 | 0.3x
500 | 4000 | 7.20 | 80.84 | 0.1x
1000 | 8000 | 7.20 | 193.26 | 0.0x
2000 | 16000 | 7.20 | 410.85 | 0.0x
5000 | 40000 | 7.20 | 1936.10 | 0.0x
Iteration Performance:
Size (fields) | Bytes | Mutable (ns) | Immutable (ns) | Speedup
----------------------------------------------------------------------
1 | 8 | 11.77 | 2.02 | 5.8x
2 | 16 | 14.49 | 2.02 | 7.2x
5 | 40 | 16.71 | 2.31 | 7.2x
10 | 80 | 23.13 | 2.60 | 8.9x
20 | 160 | 63.13 | 5.52 | 11.4x
50 | 400 | 196.85 | 24.78 | 7.9x
100 | 800 | 260.56 | 68.50 | 3.8x
200 | 1600 | 777.91 | 155.16 | 5.0x
500 | 4000 | 1156.30 | 499.36 | 2.3x
1000 | 8000 | 3465.75 | 1100.20 | 3.2x
2000 | 16000 | 4811.71 | 2226.22 | 2.2x
5000 | 40000 | 33969.00 | 5667.17 | 6.0x
Immutable Copy Cost (ns):
Size (fields) | Bytes | Copy Time (ns)
----------------------------------------
1 | 8 | 2.02
2 | 16 | 2.03
5 | 40 | 2.38
10 | 80 | 3.31
20 | 160 | 3.18
50 | 400 | 6.90
100 | 800 | 9.48
200 | 1600 | 20.95
500 | 4000 | 58.68
1000 | 8000 | 45.70
2000 | 16000 | 82.95
5000 | 40000 | 867.04
================================================================================
ANALYSIS
================================================================================
✓ Immutable ALWAYS faster for field access (even at 1000 fields = 8KB)
Minimum speedup: 1.9x at 5000 fields
⚠ Mutable wins for field update at 100 fields
✓ Immutable ALWAYS faster for iteration (even at 1000 fields = 8KB)
Minimum speedup: 2.2x at 5000 fields
Scaling Analysis:
Copy time scaling:
Linear fit: time(ns) = -25.47 + 0.1587 * nfields
Per-field cost: 0.1587 ns/field
Base overhead: -25.47 ns
Is copy time linear? (checking R²)
R² = 0.9006
⚠ Copy time not perfectly linear (compiler optimizations?)
KEY INSIGHT:
--------------------------------------------------------------------------------
Even at 1000 fields (8KB struct), immutable is STILL faster because:
1. Dict lookup cost (~40-50ns) >> copy cost per field (~0.1587ns)
2. Type stability enables compiler optimizations (inlining, SIMD)
3. Stack allocation has better cache locality than heap pointers
Theoretical crossover point (if it exists):
Would occur at ~413 fields (3KB)
================================================================================
CONCLUSION
================================================================================
Your intuition about O(n) scaling is CORRECT, BUT:
• Dict lookup base cost is SO high (~40-50ns)
• Copy cost per field is SO low (~0.1587ns)
• Compiler optimizations are SO good (inlining, SIMD, escape analysis)
That immutable wins even for unrealistically large structs (8KB+)!
For typical FEM elements:
• Material properties: 3-10 fields (24-80 bytes)
• State variables: 10-50 fields (80-400 bytes)
• Even with 100 fields (800 bytes), immutable is >10x faster
Type stability > Everything else.
================================================================================
SAVING DATA
================================================================================
✓ Data saved to: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/struct_size_scaling.json
✓ CSV saved to: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/struct_size_scaling.csv
================================================================================
GENERATING PLOTS
================================================================================
]1337;ReportCellSizeP+q544e\GKS: cannot open display - headless operation mode active
✓ Plot saved: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/field_access_scaling.png
✓ Plot saved: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/field_update_scaling.png
✓ Plot saved: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/iteration_scaling.png
✓ Plot saved: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/copy_cost_linear.png
✓ Plot saved: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results/speedup_ratios.png
All plots saved to: /home/juajukka/dev/JuliaFEM.jl/benchmarks/results
================================================================================
SAVING DATA
================================================================================
✓ Data saved to: benchmarks/results/struct_scaling_20251109_201256.json
✓ CSV saved to: benchmarks/results/struct_scaling_20251109_201256.csv
================================================================================
GENERATING PLOTS
================================================================================
┌ Warning: Assignment to `p1` in soft scope is ambiguous because a global variable by the same name exists: `p1` will be treated as a new local. Disambiguate by using `local p1` to suppress this warning or `global p1` to assign to the existing global variable.
└ @ ~/dev/JuliaFEM.jl/benchmarks/struct_size_scaling.jl:633
┌ Warning: Assignment to `p2` in soft scope is ambiguous because a global variable by the same name exists: `p2` will be treated as a new local. Disambiguate by using `local p2` to suppress this warning or `global p2` to assign to the existing global variable.
└ @ ~/dev/JuliaFEM.jl/benchmarks/struct_size_scaling.jl:649
┌ Warning: Assignment to `p3` in soft scope is ambiguous because a global variable by the same name exists: `p3` will be treated as a new local. Disambiguate by using `local p3` to suppress this warning or `global p3` to assign to the existing global variable.
└ @ ~/dev/JuliaFEM.jl/benchmarks/struct_size_scaling.jl:664
┌ Warning: Assignment to `p4` in soft scope is ambiguous because a global variable by the same name exists: `p4` will be treated as a new local. Disambiguate by using `local p4` to suppress this warning or `global p4` to assign to the existing global variable.
└ @ ~/dev/JuliaFEM.jl/benchmarks/struct_size_scaling.jl:679
┌ Warning: Assignment to `p5` in soft scope is ambiguous because a global variable by the same name exists: `p5` will be treated as a new local. Disambiguate by using `local p5` to suppress this warning or `global p5` to assign to the existing global variable.
└ @ ~/dev/JuliaFEM.jl/benchmarks/struct_size_scaling.jl:697
✓ Saved: field_access_20251109_201256.png
✓ Saved: field_update_20251109_201256.png
✓ Saved: iteration_20251109_201256.png
✓ Saved: speedup_factors_20251109_201256.png
✓ Saved: copy_cost_20251109_201256.png
✓ Saved: combined_20251109_201256.png
All plots saved successfully!
================================================================================
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