mirror of
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3dace5fe73
NS_MD.lean: - Added QRResidualWitness structure (Q16_16 fixed-point) - Added residual_bound_ok, basis_size_ok, orthogonality_ok predicates - Extended O_AMMR_Node with qr_witness field - Strengthened O_AMMR_valid: 4 conjuncts (admission + residual + basis + ortho) - lake build: 3300 jobs, 0 errors hash_benchmark.py (240 data points): - Hilbert vs Morton vs xxHash - 5 grid sizes (16^3 to 256^3), 4 trace sizes, 4 patterns Key findings: Morton: 86.5% cache hit rate, 1.08µs p50, 0.512 locality xxHash: 30.3% cache hit rate, 0.96µs p50, 0.342 locality Hilbert: 27.6% cache hit rate, 2.29µs p50, 0.833 locality Morton wins overall for spatial hash grids.
2678 lines
No EOL
72 KiB
JSON
2678 lines
No EOL
72 KiB
JSON
{
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"benchmark": "hash_function_comparison",
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"description": "Hilbert vs Morton vs xxHash spatial hashing benchmark",
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"grid_sizes": [
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16,
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32,
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64,
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128,
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256
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],
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"trace_sizes": [
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1000,
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10000,
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100000,
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1000000
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],
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"hash_functions": [
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"hilbert",
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"morton",
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"xxhash"
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],
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"trace_patterns": [
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"sequential",
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"random",
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"spatial_locality",
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"temporal_locality"
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],
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"metrics": [
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"cache_hit_rate",
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"p50_latency_us",
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"p99_latency_us",
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"memory_bandwidth_mbs",
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"locality_preservation"
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],
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"generated_at": "2026-05-30T20:11:22Z",
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"results": [
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "sequential",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.0,
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"p50_latency_us": 1.82,
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"p99_latency_us": 6.57,
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"memory_bandwidth_mbs": 6.17,
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"locality_preservation": 0.716469
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "sequential",
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"hash_function": "morton",
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"cache_hit_rate": 0.936,
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"p50_latency_us": 0.819,
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"p99_latency_us": 2.19,
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"memory_bandwidth_mbs": 13.78,
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"locality_preservation": 0.0
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "sequential",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.112,
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"p50_latency_us": 0.97,
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"p99_latency_us": 2.9,
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"memory_bandwidth_mbs": 11.53,
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"locality_preservation": 0.008407
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "random",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.112,
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"p50_latency_us": 1.9,
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"p99_latency_us": 4.92,
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"memory_bandwidth_mbs": 6.03,
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"locality_preservation": 0.71932
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "random",
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"hash_function": "morton",
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"cache_hit_rate": 0.936,
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"p50_latency_us": 0.86,
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"p99_latency_us": 1.61,
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"memory_bandwidth_mbs": 13.25,
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"locality_preservation": 0.147023
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "random",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.197,
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"p50_latency_us": 0.75,
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"p99_latency_us": 2.84,
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"memory_bandwidth_mbs": 12.77,
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"locality_preservation": 0.150668
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "spatial_locality",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.147,
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"p50_latency_us": 1.87,
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"p99_latency_us": 5.38,
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"memory_bandwidth_mbs": 6.2,
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"locality_preservation": 0.741935
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "spatial_locality",
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"hash_function": "morton",
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"cache_hit_rate": 0.936,
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"p50_latency_us": 0.85,
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"p99_latency_us": 3.54,
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"memory_bandwidth_mbs": 11.73,
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"locality_preservation": 0.167155
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "spatial_locality",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.221,
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"p50_latency_us": 0.95,
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"p99_latency_us": 2.92,
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"memory_bandwidth_mbs": 11.67,
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"locality_preservation": 0.172043
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "temporal_locality",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.72,
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"p50_latency_us": 1.03,
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"p99_latency_us": 2.34,
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"memory_bandwidth_mbs": 10.81,
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"locality_preservation": 0.955639
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "temporal_locality",
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"hash_function": "morton",
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"cache_hit_rate": 0.937,
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"p50_latency_us": 0.87,
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"p99_latency_us": 2.12,
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"memory_bandwidth_mbs": 12.26,
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"locality_preservation": 0.902658
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},
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{
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"grid_size": 16,
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"trace_size": 1000,
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"trace_pattern": "temporal_locality",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.728,
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"p50_latency_us": 0.47,
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"p99_latency_us": 1.54,
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"memory_bandwidth_mbs": 20.39,
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"locality_preservation": 0.902658
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "sequential",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.5904,
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"p50_latency_us": 1.29,
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"p99_latency_us": 2.85,
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"memory_bandwidth_mbs": 8.09,
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"locality_preservation": 0.745367
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "sequential",
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"hash_function": "morton",
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"cache_hit_rate": 0.9936,
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"p50_latency_us": 0.59,
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"p99_latency_us": 1.67,
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"memory_bandwidth_mbs": 18.06,
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"locality_preservation": 0.253674
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "sequential",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.7385,
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"p50_latency_us": 0.979,
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"p99_latency_us": 2.02,
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"memory_bandwidth_mbs": 11.81,
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"locality_preservation": 0.115335
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "random",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.6255,
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"p50_latency_us": 1.77,
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"p99_latency_us": 3.25,
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"memory_bandwidth_mbs": 6.71,
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"locality_preservation": 0.762647
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "random",
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"hash_function": "morton",
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"cache_hit_rate": 0.9936,
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"p50_latency_us": 0.61,
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"p99_latency_us": 1.02,
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"memory_bandwidth_mbs": 18.64,
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"locality_preservation": 0.316765
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "random",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.7517,
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"p50_latency_us": 1.02,
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"p99_latency_us": 2.17,
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"memory_bandwidth_mbs": 11.28,
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"locality_preservation": 0.171765
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "spatial_locality",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.6451,
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"p50_latency_us": 1.3,
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"p99_latency_us": 2.37,
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"memory_bandwidth_mbs": 8.66,
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"locality_preservation": 0.781142
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "spatial_locality",
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"hash_function": "morton",
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"cache_hit_rate": 0.9936,
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"p50_latency_us": 0.62,
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"p99_latency_us": 1.06,
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"memory_bandwidth_mbs": 18.56,
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"locality_preservation": 0.32699
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "spatial_locality",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.7605,
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"p50_latency_us": 0.97,
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"p99_latency_us": 2.01,
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"memory_bandwidth_mbs": 11.93,
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"locality_preservation": 0.183391
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "temporal_locality",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.7878,
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"p50_latency_us": 1.36,
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"p99_latency_us": 2.96,
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"memory_bandwidth_mbs": 8.09,
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"locality_preservation": 0.893909
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "temporal_locality",
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"hash_function": "morton",
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"cache_hit_rate": 0.9936,
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"p50_latency_us": 1.1,
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"p99_latency_us": 1.88,
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"memory_bandwidth_mbs": 9.77,
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"locality_preservation": 0.700386
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},
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{
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"grid_size": 16,
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"trace_size": 10000,
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"trace_pattern": "temporal_locality",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.8317,
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"p50_latency_us": 0.92,
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"p99_latency_us": 2.09,
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"memory_bandwidth_mbs": 12.22,
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"locality_preservation": 0.625443
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "sequential",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.95904,
|
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"p50_latency_us": 1.31,
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"p99_latency_us": 2.54,
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"memory_bandwidth_mbs": 8.28,
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"locality_preservation": 0.853893
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "sequential",
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"hash_function": "morton",
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"cache_hit_rate": 0.99936,
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"p50_latency_us": 0.62,
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"p99_latency_us": 1.45,
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"memory_bandwidth_mbs": 15.73,
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"locality_preservation": 0.456905
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "sequential",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.97385,
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"p50_latency_us": 0.85,
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"p99_latency_us": 2.07,
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"memory_bandwidth_mbs": 11.99,
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"locality_preservation": 0.15636
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "random",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.95904,
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"p50_latency_us": 1.88,
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"p99_latency_us": 3.419,
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"memory_bandwidth_mbs": 6.22,
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"locality_preservation": 0.824273
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "random",
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"hash_function": "morton",
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"cache_hit_rate": 0.99936,
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"p50_latency_us": 0.69,
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"p99_latency_us": 1.54,
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"memory_bandwidth_mbs": 14.91,
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"locality_preservation": 0.461757
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "random",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.97385,
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"p50_latency_us": 0.74,
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"p99_latency_us": 1.53,
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"memory_bandwidth_mbs": 14.79,
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"locality_preservation": 0.179836
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "spatial_locality",
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"hash_function": "hilbert",
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"cache_hit_rate": 0.95904,
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"p50_latency_us": 1.63,
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"p99_latency_us": 3.84,
|
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"memory_bandwidth_mbs": 6.46,
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"locality_preservation": 0.837229
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
|
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"trace_pattern": "spatial_locality",
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"hash_function": "morton",
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"cache_hit_rate": 0.99936,
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"p50_latency_us": 0.68,
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"p99_latency_us": 1.67,
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"memory_bandwidth_mbs": 14.77,
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"locality_preservation": 0.507937
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},
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{
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"grid_size": 16,
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"trace_size": 100000,
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"trace_pattern": "spatial_locality",
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"hash_function": "xxhash",
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"cache_hit_rate": 0.97385,
|
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"p50_latency_us": 0.96,
|
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"p99_latency_us": 2.11,
|
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"memory_bandwidth_mbs": 11.61,
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"locality_preservation": 0.223088
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},
|
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{
|
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"grid_size": 16,
|
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"trace_size": 100000,
|
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"trace_pattern": "temporal_locality",
|
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"hash_function": "hilbert",
|
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"cache_hit_rate": 0.95904,
|
|
"p50_latency_us": 1.75,
|
|
"p99_latency_us": 3.339,
|
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"memory_bandwidth_mbs": 6.71,
|
|
"locality_preservation": 0.855542
|
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},
|
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{
|
|
"grid_size": 16,
|
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"trace_size": 100000,
|
|
"trace_pattern": "temporal_locality",
|
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"hash_function": "morton",
|
|
"cache_hit_rate": 0.99936,
|
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"p50_latency_us": 0.99,
|
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"p99_latency_us": 1.97,
|
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"memory_bandwidth_mbs": 10.54,
|
|
"locality_preservation": 0.542715
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},
|
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{
|
|
"grid_size": 16,
|
|
"trace_size": 100000,
|
|
"trace_pattern": "temporal_locality",
|
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"hash_function": "xxhash",
|
|
"cache_hit_rate": 0.97385,
|
|
"p50_latency_us": 1.17,
|
|
"p99_latency_us": 2.53,
|
|
"memory_bandwidth_mbs": 9.03,
|
|
"locality_preservation": 0.298132
|
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},
|
|
{
|
|
"grid_size": 16,
|
|
"trace_size": 1000000,
|
|
"trace_pattern": "sequential",
|
|
"hash_function": "hilbert",
|
|
"cache_hit_rate": 0.995904,
|
|
"p50_latency_us": 1.86,
|
|
"p99_latency_us": 3.8,
|
|
"memory_bandwidth_mbs": 6.0,
|
|
"locality_preservation": 0.879824
|
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},
|
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{
|
|
"grid_size": 16,
|
|
"trace_size": 1000000,
|
|
"trace_pattern": "sequential",
|
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"hash_function": "morton",
|
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"cache_hit_rate": 0.999936,
|
|
"p50_latency_us": 0.79,
|
|
"p99_latency_us": 1.78,
|
|
"memory_bandwidth_mbs": 13.33,
|
|
"locality_preservation": 0.579542
|
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},
|
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{
|
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"grid_size": 16,
|
|
"trace_size": 1000000,
|
|
"trace_pattern": "sequential",
|
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"hash_function": "xxhash",
|
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"cache_hit_rate": 0.997385,
|
|
"p50_latency_us": 1.06,
|
|
"p99_latency_us": 2.26,
|
|
"memory_bandwidth_mbs": 10.41,
|
|
"locality_preservation": 0.187637
|
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},
|
|
{
|
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"grid_size": 16,
|
|
"trace_size": 1000000,
|
|
"trace_pattern": "random",
|
|
"hash_function": "hilbert",
|
|
"cache_hit_rate": 0.995904,
|
|
"p50_latency_us": 1.85,
|
|
"p99_latency_us": 3.76,
|
|
"memory_bandwidth_mbs": 6.16,
|
|
"locality_preservation": 0.896838
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