hakmem/docs/analysis/COMPREHENSIVE_BENCHMARK_ANALYSIS.md

Comprehensive Benchmark Analysis

Bitmap vs Free-List Trade-offs

Date: 2025-10-26 Purpose: Evaluate hakmem's bitmap approach across multiple allocation patterns to identify strengths and weaknesses

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Executive Summary

After discovering that all previous benchmarks were incorrectly measuring glibc (due to Makefile implicit rules), we rebuilt the benchmarking infrastructure and ran comprehensive tests across 6 allocation patterns.

Key Finding: Hakmem's bitmap approach shows relative resistance to random allocation patterns, validating the design for non-sequential workloads, though absolute performance remains 2.6x-8.8x slower than mimalloc.

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Test Methodology

Benchmark Suite: bench_comprehensive.c

6 test patterns × 4 size classes (16B, 32B, 64B, 128B):

1. Sequential LIFO - Allocate 100 blocks, free in reverse order (best case for free-lists)
2. Sequential FIFO - Allocate 100 blocks, free in same order
3. Random Free - Allocate 100 blocks, free in shuffled order (bitmap advantage test)
4. Interleaved - Alternating alloc/free cycles
5. Mixed Sizes - 8B, 16B, 32B, 64B mixed allocation
6. Long-lived vs Short-lived - Keep 50% allocated, churn the rest

Allocators Tested

• hakmem: Bitmap-based with two-tier structure
• glibc malloc: Binned free-list (system default)
• mimalloc: Magazine-based allocator

Verification

All binaries verified with verify_bench.sh:

$ ./verify_bench.sh ./bench_comprehensive_hakmem
✅ hakmem symbols: 119
✅ Binary size: 156KB
✅ Verification PASSED

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Results: 16B Allocations (Representative)

Sequential LIFO (Best case for free-lists)

Allocator	Throughput	Latency	vs hakmem
hakmem	102 M ops/sec	9.8 ns/op	1.0×
glibc	365 M ops/sec	2.7 ns/op	3.6×
mimalloc	942 M ops/sec	1.1 ns/op	9.2×

Random Free (Bitmap advantage test)

Allocator	Throughput	Latency	vs hakmem	Degradation from LIFO
hakmem	68 M ops/sec	14.7 ns/op	1.0×	34%
glibc	138 M ops/sec	7.2 ns/op	2.0×	62%
mimalloc	176 M ops/sec	5.7 ns/op	2.6×	81%

Key Insight: Hakmem degrades the least under random patterns:

• hakmem: 66% of sequential performance
• glibc: 38% of sequential performance
• mimalloc: 19% of sequential performance

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Pattern-by-Pattern Analysis

1. Sequential LIFO

Winner: mimalloc (9.2× faster than hakmem)

Analysis: Free-list allocators excel here because LIFO perfectly matches their intrusive linked list structure. The just-freed block becomes the next allocation with zero cache misses.

Hakmem's bitmap requires:

• Bitmap scan (even if empty-word detection is O(1))
• Bit manipulation
• Pointer arithmetic

2. Sequential FIFO

Winner: mimalloc (8.4× faster than hakmem)

Analysis: Similar to LIFO, though slightly worse for free-lists because FIFO order disrupts cache locality. Hakmem's bitmap is order-independent, so performance is similar to LIFO.

3. Random Free ⭐ Bitmap Advantage

Winner: mimalloc (2.6× faster than hakmem)

Analysis: This is where bitmap shines relatively:

• Hakmem: 34% degradation (66% of LIFO performance)
• glibc: 62% degradation (38% of LIFO performance)
• mimalloc: 81% degradation (19% of LIFO performance)

Why bitmap resists degradation:

• Free order doesn't matter - just flip a bit
• Two-tier bitmap structure: summary bitmap + detail bitmap
• Empty-word detection is still O(1) regardless of fragmentation

Why free-lists degrade badly:

• Random free breaks LIFO order
• List traversal becomes unpredictable
• Cache thrashing on widely scattered allocations

4. Interleaved Alloc/Free

Winner: mimalloc (7.8× faster than hakmem)

Analysis: Frequent switching favors free-lists with hot cache. Bitmap's amortization strategy (batch refill) doesn't help here.

5. Mixed Sizes

Winner: mimalloc (9.1× faster than hakmem)

Analysis: Multiple size classes stress the TLS magazine selection logic. Mimalloc's per-size-class magazines avoid contention.

6. Long-lived vs Short-lived

Winner: mimalloc (8.5× faster than hakmem)

Analysis: Steady-state churning favors free-lists. Hakmem's bitmap doesn't distinguish between long-lived and short-lived allocations.

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Bitmap vs Free-List Trade-offs

Bitmap Advantages ✅

1. Order Independence: Performance doesn't degrade under random allocation patterns
2. Visibility: Bitmap provides instant fragmentation insight for diagnostics
3. Batch Refill: Can amortize bitmap scan across multiple allocations (16 items/scan)
4. Predictability: O(1) empty-word detection regardless of fragmentation
5. Research Value: Easy to instrument and analyze allocation patterns

Free-List Advantages ✅

1. LIFO Fast Path: Just-freed block is next allocation (perfect cache locality)
2. Zero Metadata: Intrusive next-pointer reuses allocated space
3. Simple Push/Pop: Single pointer assignment vs bit manipulation
4. Proven: Battle-tested in production allocators (jemalloc, mimalloc, tcmalloc)

Bitmap Disadvantages ❌

1. Baseline Overhead: Even with empty-word detection, bitmap scan is slower than free-list pop
2. Bit Manipulation Cost: Extract, shift, and combine operations add latency
3. Two-Tier Complexity: Summary + detail bitmap adds indirection
4. Cold Cache: Bitmap memory separate from allocated memory

Free-List Disadvantages ❌

1. Random Pattern Degradation: 62-81% performance loss under random frees
2. Fragmentation Blindness: Can't see allocation patterns without traversal
3. Cache Unpredictability: Scattered allocations break LIFO order

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Performance Gap Analysis

Why is hakmem still 2.6× slower on favorable patterns?

Even on Random Free (bitmap's best case), hakmem is 2.6× slower than mimalloc. The bitmap isn't the only bottleneck:

Potential bottlenecks (requires profiling):

1. TLS Magazine Overhead:

   • 3-tier hierarchy (TLS → Page Mini-Mag → Bitmap)
   • Each tier has bounds checks and fallback logic

2. Statistics Collection:

   • Even batched stats have overhead
   • Consider disabling in release builds

3. Batch Refill Logic:

   • 16-item refill amortizes scan, but adds complexity
   • May not be worth it for bursty workloads

4. Two-Tier Bitmap Traversal:

   • Summary bitmap scan → detail bitmap scan
   • Two levels of indirection

5. Cache Effects:

   • Bitmap memory is separate from allocated memory
   • Free-lists keep everything hot in L1

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Conclusions

Is Bitmap Worth It?

For Research: ✅ Yes

• Visibility and diagnostics are invaluable
• Order-independent performance is a unique advantage
• Easy to instrument and analyze

For Production: ⚠️ Depends

• If workload is random/unpredictable: bitmap degrades less
• If workload is sequential/LIFO: free-list is 9× faster
• If absolute performance matters: mimalloc wins

Next Steps

1. Profile hakmem on Random Free pattern (bench_tiny.c)

   • Identify true bottlenecks beyond bitmap
   • Use perf record -g to find hot paths

2. Consider Hybrid Approach:

   • Free-list for LIFO fast path (top 8-16 items)
   • Bitmap for overflow and diagnostics
   • Best of both worlds?

3. Measure Statistics Overhead:

   • Build with stats disabled
   • Quantify cost of instrumentation

4. Optimize Two-Tier Bitmap:

   • Can we flatten to single tier for small slabs?
   • SIMD instructions for bitmap scan?

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Benchmark Commands

Build

make clean
make bench_comprehensive_hakmem
make bench_comprehensive_system
./verify_bench.sh ./bench_comprehensive_hakmem

Run

# hakmem (bitmap)
./bench_comprehensive_hakmem > results_hakmem.txt

# glibc (system malloc)
./bench_comprehensive_system > results_glibc.txt

# mimalloc (magazine-based)
LD_PRELOAD=/usr/lib/x86_64-linux-gnu/libmimalloc.so.2 \
  ./bench_comprehensive_system > results_mimalloc.txt

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Raw Results (16B allocations)

========================================
hakmem (Bitmap-based)
========================================
Sequential LIFO:   102.00 M ops/sec (9.80 ns/op)
Sequential FIFO:    97.09 M ops/sec (10.30 ns/op)
Random Free:        68.03 M ops/sec (14.70 ns/op)  ← 66% of LIFO
Interleaved:        91.74 M ops/sec (10.90 ns/op)
Mixed Sizes:        99.01 M ops/sec (10.10 ns/op)
Long-lived:         95.24 M ops/sec (10.50 ns/op)

========================================
glibc malloc (Free-list)
========================================
Sequential LIFO:   364.96 M ops/sec (2.74 ns/op)
Sequential FIFO:   357.14 M ops/sec (2.80 ns/op)
Random Free:       138.89 M ops/sec (7.20 ns/op)  ← 38% of LIFO
Interleaved:       333.33 M ops/sec (3.00 ns/op)
Mixed Sizes:       344.83 M ops/sec (2.90 ns/op)
Long-lived:        350.88 M ops/sec (2.85 ns/op)

========================================
mimalloc (Magazine-based)
========================================
Sequential LIFO:   943.40 M ops/sec (1.06 ns/op)
Sequential FIFO:   900.90 M ops/sec (1.11 ns/op)
Random Free:       175.44 M ops/sec (5.70 ns/op)  ← 19% of LIFO
Interleaved:       800.00 M ops/sec (1.25 ns/op)
Mixed Sizes:       909.09 M ops/sec (1.10 ns/op)
Long-lived:        869.57 M ops/sec (1.15 ns/op)

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Appendix: Verification Checklist

Before any benchmark:

1. ✅ make clean
2. ✅ make bench_comprehensive_hakmem
3. ✅ ./verify_bench.sh ./bench_comprehensive_hakmem
   • Expect: 119 hakmem symbols
   • Expect: Binary size > 150KB
4. ✅ Run benchmark
5. ✅ Document results in this file

NEVER rely on make <target> if target doesn't exist in Makefile - it will silently use implicit rules and link with glibc!