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Performance Engineering

This document records the performance characteristics, optimization history, and benchmark methodology for duckdb-behavioral. Every claim is backed by measured data with statistical confidence intervals. Every optimization is independently reproducible via cargo bench.

Table of Contents

Benchmark Methodology

Framework

  • Criterion.rs 0.8 with 100 samples per benchmark and 95% confidence intervals
  • Benchmarks measure end-to-end aggregate function execution: state creation, update (event ingestion), and finalize (result computation)
  • Each benchmark is run 3+ times to verify stability before comparison
  • Improvements are accepted only when confidence intervals do not overlap

Reproduction

# Run all benchmarks with full statistical output
cargo bench

# Run a specific benchmark group
cargo bench -- window_funnel
cargo bench -- sequence_match

# Results are stored in target/criterion/ for comparison
# Criterion automatically compares against previous runs

Benchmark Inventory

Benchmark Function Operation Input Sizes Measures
sessionize_update sessionize update + finalize 100 to 1B events Per-row throughput
sessionize_combine sessionize combine chain 100 to 1M states Segment tree merge cost
retention_update retention update + finalize 4, 8, 16, 32 conditions Per-condition scaling
retention_combine retention combine chain 100 to 1B states O(1) combine verification
window_funnel_finalize window_funnel update + finalize 100 to 100M events Funnel scan throughput
window_funnel_combine window_funnel combine_in_place + finalize 100 to 1M states In-place append + sort cost
sequence_match sequence_match update + finalize 100 to 100M events NFA pattern matching
sequence_count sequence_count update + finalize 100 to 100M events Non-overlapping counting
sequence_combine sequence_* combine_in_place + finalize 100 to 1M states In-place append + NFA cost
sort_events (isolated) sort only 100 to 100M events pdqsort scaling (random)
sort_events_presorted (isolated) sort only 100 to 100M events pdqsort adaptive path
sequence_next_node sequence_next_node update + finalize 100 to 10M events Sequential matching + Arc<str> clone
sequence_next_node_combine sequence_next_node combine_in_place + finalize 100 to 1M states In-place append + sequential matching
sequence_match_events sequence_match_events update + finalize_events 100 to 100M events NFA pattern matching + timestamp collection
sequence_match_events_combine sequence_match_events combine_in_place + finalize_events 100 to 1M states In-place append + NFA + timestamp cost
sequence_next_node_realistic sequence_next_node update + finalize (100 distinct values) 100 to 1M events Realistic cardinality Arc<str> sharing

Algorithmic Complexity

Function Update Combine Finalize Space
sessionize O(1) O(1) O(1) O(1) — tracks only first/last timestamp + boundary count
retention O(k) O(1) O(k) O(1) — single u32 bitmask, k = conditions
window_funnel O(1) amortized O(m) append O(n*k) greedy scan O(n) — collected events
sequence_match O(1) amortized O(m) append O(n*s) NFA execution O(n) — collected events
sequence_count O(1) amortized O(m) append O(n*s) NFA execution O(n) — collected events
sequence_match_events O(1) amortized O(m) append O(n*s) NFA execution O(n) — collected events
sequence_next_node O(1) amortized O(m) append O(n*s) sequential scan O(n) — collected events + Strings

Where n = events, m = events in other state, k = conditions (up to 32), s = pattern steps.

sort_events: O(n) if presorted (is_sorted check), O(n log n) if unsorted (pdqsort).

Optimization History

Session 1: Event Bitmask Optimization

Hypothesis

Replacing Event.conditions: Vec<bool> with a u8 bitmask eliminates the dominant cost in event-based functions: per-event heap allocation. The DuckDB function set registrations support at most 8 boolean conditions, making u8 sufficient.

Technique

Aspect Before After
Event struct size 32 bytes (i64 + Vec header) + heap 16 bytes (i64 + u8 + padding)
Event trait Clone (deep copy) Copy (memcpy)
Heap allocations per event 1 (Vec backing store) 0
has_any_condition() iter().any(|&c| c) — O(k) conditions != 0 — O(1)
condition(idx) Vec bounds check + index (conditions >> idx) & 1 — single instruction
Merge (combine) clone() per element memcpy via Copy semantics

Basis

  • Memory allocation overhead: 20-80ns per allocation depending on size class and contention (jemalloc/mimalloc literature)
  • Cache line optimization: 16-byte structs pack 4 per 64-byte cache line vs 1-2 for 32+ byte structs with pointer chasing into heap
  • Drepper (2007) "What Every Programmer Should Know About Memory" — eliminating pointer indirection is the single highest-impact optimization for data-intensive workloads

Measured Results

Criterion, 100 samples, 95% confidence intervals. All improvements show non-overlapping confidence intervals (statistically significant).

window_funnel (update + sort + greedy scan):

Input Before [95% CI] After [95% CI] Speedup
100 events, 3 conds 1.42 µs [1.393, 1.455] 253 ns [253.1, 258.7] 5.6x
1,000 events, 5 conds 18.6 µs [18.54, 18.69] 1.65 µs [1.634, 1.667] 11.3x
10,000 events, 5 conds 202 µs [200.0, 205.3] 15.0 µs [14.91, 15.06] 13.5x
100,000 events, 8 conds 2.35 ms [2.325, 2.381] 188 µs [186.9, 190.2] 12.5x

sequence_match (update + sort + NFA pattern matching):

Input Before [95% CI] After [95% CI] Speedup
100 events 1.73 µs [1.725, 1.741] 701 ns [693.4, 703.1] 2.5x
1,000 events 22.2 µs [22.04, 22.37] 3.50 µs [3.425, 3.490] 6.3x
10,000 events 260 µs [257.9, 262.7] 28.0 µs [27.51, 28.69] 9.3x

sequence_count (update + sort + NFA counting):

Input Before [95% CI] After [95% CI] Speedup
100 events 2.77 µs [2.747, 2.800] 719 ns [713.6, 724.5] 3.9x
1,000 events 22.6 µs [22.37, 22.80] 5.03 µs [4.959, 5.115] 4.5x
10,000 events 254 µs [252.2, 256.7] 47.9 µs [46.91, 49.09] 5.3x

Analysis

The speedup increases super-linearly with input size. At 100 events, the improvement is 2.5-5.6x. At 100,000 events, it reaches 12.5x. This is consistent with the optimization eliminating a per-event heap allocation: larger inputs amplify the per-element savings, and the improved cache locality from 16-byte Copy structs compounds as the working set grows beyond L1/L2 cache.

The window_funnel function benefits more than sequence_* because its greedy scan algorithm accesses conditions multiple times per event (checking the current step, previous step in strict mode, and iterating conditions in strict order mode). Each access is now a single bitwise operation instead of a Vec bounds check + memory load.

Session 1: Supplementary Optimizations

  • #[inline] on interval_to_micros, RetentionState::update/combine, SessionizeBoundaryState::update/combine — documents optimization intent for the compiler, serves as defense against profile changes that disable LTO
  • NfaState derives Copy (24 bytes, no heap) — eliminates clone overhead in backtracking NFA exploration
  • No measurable regression; these are maintenance optimizations that ensure the compiler has maximum information for optimization decisions

Session 2: In-Place Combine (O(N²) → O(N))

Hypothesis

merge_sorted_events() in combine allocates a NEW Vec every invocation. In a left-fold chain of N states, this produces N allocations of sizes 1, 2, 3, ..., N, resulting in O(N²) total element copies. Since finalize() already sorts events via sort_events(), maintaining sorted order in combine is wasted work. An in-place extend_from_slice with Vec's doubling growth strategy reduces the chain to O(N) amortized total copies.

Technique

  1. Replace merge_sorted_events() with Vec::extend_from_slice() in combine
  2. Add combine_in_place(&mut self, other: &Self) that extends self.events directly
  3. Update FFI layer to use combine_in_place — the target state grows in-place
  4. Vec's doubling strategy provides amortized O(1) per append

Basis

  • Cormen et al. (CLRS) Ch.17: Amortized analysis of dynamic arrays proves O(N) total copies for N sequential appends with doubling strategy
  • Sedgewick & Wayne "Algorithms" 4th Ed.: Deferred sorting is optimal when the merged result must be sorted anyway
  • Knuth TAOCP Vol 3: Merge sort with deferred execution

Measured Results

Criterion, 100 samples, 95% confidence intervals. 3 runs each.

window_funnel_combine (left-fold chain + finalize):

Input Before [95% CI] After [95% CI] Speedup
100 states 10.9 µs [10.91, 11.39] 466 ns [461, 472] 23.4x
1,000 states 781 µs [780, 793] 3.03 µs [3.02, 3.04] 258x
10,000 states 75.3 ms [74.6, 76.0] 30.9 µs [30.8, 31.1] 2,436x

sequence_combine (left-fold chain + finalize):

Input Before [95% CI] After [95% CI] Speedup
100 states 12.1 µs [11.99, 12.18] 1.31 µs [1.31, 1.32] 9.2x
1,000 states 756 µs [751.8, 759.8] 10.98 µs [10.88, 11.10] 68.8x

Analysis

The super-linear speedup scaling (23x at N=100 → 2,436x at N=10,000) confirms the O(N²) → O(N) algorithmic complexity improvement. The old approach performed N(N+1)/2 ≈ 50 million element copies at N=10,000 (16 bytes each = ~800MB memory traffic). The new approach performs ~10,000 copies total with amortized O(1) reallocation.

The speedup is lower for sequence_combine (9.2x at 100, 68.8x at 1000) because sequence finalize includes NFA pattern matching which adds a constant cost per finalize call that is independent of the combine strategy.

Session 2: Unstable Sort (pdqsort)

Hypothesis

Replace sort_by_key (stable TimSort variant) with sort_unstable_by_key (pdqsort). Same-timestamp event order has no defined semantics in ClickHouse's behavioral analytics functions. Unstable sort avoids O(n) auxiliary memory and has better constant factors for 16-byte Copy types.

Basis

  • Peters (2021) "Pattern-Defeating Quicksort" — Rust's sort_unstable implementation
  • Edelkamp & Weiß (2016) "BlockQuicksort" — branch-free partitioning

Measured Results

Modest improvement. sequence_match/100: 706 ns → 676 ns (non-overlapping CIs). Larger inputs show marginal improvement masked by scan/NFA cost. No regressions.

Session 2: Pattern Clone Elimination

Eliminated heap-allocating CompiledPattern::clone() in execute(). Now uses a reference to the cached pattern. Constant-factor improvement proportional to pattern complexity.

Session 3: NFA Lazy Matching (O(n²) → O(n))

Hypothesis

The NFA executor's AnyEvents (.*) handler pushes two transitions onto a LIFO stack: "advance to next pattern step" and "consume current event and stay". The push order determines which transition is explored first. With "advance step" pushed first (bottom of stack) and "consume event" pushed second (top, popped first), the NFA greedily consumes ALL remaining events before trying to advance the pattern — resulting in O(n * MAX_NFA_STATES * n_starts) behavior instead of O(n * pattern_len).

Swapping the push order makes the NFA try to advance the pattern first (lazy matching), which succeeds quickly when the next condition is satisfied, avoiding the exponential exploration of the "consume everything" branch.

Technique

In src/pattern/executor.rs, the AnyEvents match arm:

// BEFORE (greedy — explores "consume event" first):
PatternStep::AnyEvents => {
    states.push(NfaState { step_idx: state.step_idx + 1, ..state }); // bottom
    states.push(NfaState { event_idx: state.event_idx + 1, ..state }); // top (popped first)
}

// AFTER (lazy — explores "advance step" first):
PatternStep::AnyEvents => {
    states.push(NfaState { event_idx: state.event_idx + 1, ..state }); // bottom
    states.push(NfaState { step_idx: state.step_idx + 1, ..state }); // top (popped first)
}

Basis

  • Thompson (1968) "Programming Techniques: Regular expression search algorithm" — NFA exploration order determines average-case complexity
  • Cox (2007) "Regular Expression Matching Can Be Simple And Fast" — lazy vs greedy semantics in NFA backtracking
  • ClickHouse source: sequence_match uses lazy .* semantics (match earliest)

Measured Results

Criterion, 100 samples, 95% confidence intervals. 3 runs each.

sequence_match (update + sort + NFA pattern matching, pattern (?1).*(?2).*(?3)):

Input Before [95% CI] After [95% CI] Speedup
100 events 750 ns [744, 756] 427 ns [423, 432] 1.76x
1,000 events 3.53 µs [3.49, 3.59] 1.96 µs [1.94, 1.98] 1.80x
10,000 events 30.2 µs [30.1, 30.4] 17.0 µs [16.8, 17.2] 1.78x
100,000 events 298 µs [296, 300] 186 µs [184, 188] 1.60x
1,000,000 events 4.43 s [4.39, 4.47] 2.23 ms [2.22, 2.25] 1,961x

Analysis

The 1,961x speedup at 1M events confirms the algorithmic complexity improvement. With greedy exploration, each of ~166K start positions (events matching condition 1) triggered MAX_NFA_STATES (10,000) iterations consuming events before trying to advance — totaling ~1.66 billion NFA state transitions. With lazy exploration, each start position advances through the 3-step pattern in O(pattern_len) transitions, finding a match within a few events.

The 1.76-1.80x improvement at smaller sizes (100-10K) reflects the constant-factor benefit of lazy matching even when the greedy approach doesn't hit the MAX_NFA_STATES limit: the NFA explores fewer dead-end branches before finding the optimal match.

At 1M events the speedup is catastrophic because the working set (16 bytes × 1M = 16MB) exceeds L2 cache, and the greedy approach traverses the entire event array ~166K times vs the lazy approach traversing it once.

Session 3: Compiled Pattern Preservation (Negative Result)

Hypothesis

combine_in_place unconditionally sets self.compiled_pattern = None, forcing re-compilation on every finalize after a combine chain. Preserving the compiled pattern when pattern_str hasn't changed should eliminate redundant parsing and compilation.

Measured Results

Criterion, 100 samples, 95% confidence intervals. 3 runs.

Input Before [95% CI] After [95% CI] Change
sequence_combine/1000 10.8 µs [10.7, 10.9] 10.5 µs [10.4, 10.7] ~2.5% (CIs overlap)

Result: CIs overlap — no statistically significant improvement. The pattern compilation cost (~50ns) is negligible compared to event processing. Committed as a code quality improvement (correctness of the API contract) but NOT counted as a performance optimization.

Session 4: 100M/1B Benchmark Expansion

Hypothesis

Extending benchmarks from 10M to 100M and 1B elements reveals whether throughput continues to degrade or stabilizes at DRAM bandwidth limits. Sessionize (O(1) state) and retention (O(1) combine, 4 bytes/state) are candidates for 1B due to minimal memory requirements. Event-collecting functions (window_funnel, sequence, sort) require 16 bytes/event × N, limiting them to ~100M (1.6GB) on a 21GB system.

Basis

  • Drepper (2007) "What Every Programmer Should Know About Memory" — cache hierarchy performance modeling predicts throughput plateaus at DRAM bandwidth
  • McCalpin (1995) "STREAM: Sustainable Memory Bandwidth in High Performance Computers" — methodology for measuring sustainable DRAM bandwidth

Measured Results

Criterion, 10 samples (100M/1B scales), 95% confidence intervals. 3 runs.

Billion-row results (O(1) state functions):

Benchmark Mean [95% CI] Throughput ns/element
sessionize_update/1B 1.213 s [1.207, 1.220] 824 Melem/s 1.21
retention_combine/1B 3.062 s [3.013, 3.113] 327 Melem/s 3.06

100M results (event-collecting functions):

Benchmark Mean [95% CI] Throughput ns/element
sessionize_update/100M 121.7 ms [121.0, 122.6] 822 Melem/s 1.22
retention_combine/100M 277.5 ms [275.5, 281.3] 360 Melem/s 2.78
window_funnel/100M 898 ms [888, 913] 111 Melem/s 8.98
sequence_match/100M 1.079 s [1.069, 1.092] 92.7 Melem/s 10.79
sequence_count/100M 1.574 s [1.540, 1.617] 63.5 Melem/s 15.74
sort_events/100M 2.207 s [2.173, 2.224] 45.3 Melem/s 22.07
sort_events_presorted/100M 1.891 s [1.873, 1.899] 52.9 Melem/s 18.91

Analysis

Sessionize scales linearly to 1B: 1.21 ns/element at 1B is consistent with 1.20 ns/element at 10M. The O(1) update operation (compare + conditional increment) has no data-dependent memory access patterns, keeping the working set within registers. Throughput (824 Melem/s) is stable from 100K to 1B, confirming compute-bound behavior.

Retention degrades at 1B: 3.06 ns/element at 1B vs 2.78 ns/element at 100M vs 3.35 ns/element at 10M. The non-monotonic pattern reflects DRAM bandwidth variability at these scales. The 1B working set (4 bytes × 1B = 3.7GB) exceeds L3 cache significantly, making the iteration purely DRAM-bound.

Sort dominates event-collecting functions: At 100M, sort_events takes 2.207s while sequence_match takes 1.079s (sort is ~2x the total). This confirms sort is O(n log n) with log(100M) ≈ 26.6, while the NFA scan is O(n).

Memory ceiling: Event-collecting functions at 100M use 1.6GB per benchmark iteration. With 21GB total RAM and Criterion's multi-iteration measurement, 100M is the practical maximum. 1B events (16GB) would exceed available memory during the clone required by Criterion's iter loop.

Session 6: Presorted Detection + 32-Condition Support

PERF-2: Presorted Detection in sort_events

Hypothesis: In practice, DuckDB often provides events in timestamp order (via ORDER BY or naturally ordered data). An O(n) is_sorted check before O(n log n) pdqsort provides effectively zero-cost sorting for presorted input. For unsorted input, the O(n) scan adds negligible overhead.

Technique: Added events.windows(2).all(|w| w[0].timestamp_us <= w[1].timestamp_us) check with early return before sort_unstable_by_key. The iterator has early termination on first violation, so worst-case overhead for unsorted input is one additional O(n) scan.

Basis:

  • pdqsort already has O(n) adaptive behavior on presorted input, but still performs comparisons with its internal bookkeeping. An explicit is_sorted check with early termination is a pure scan with no bookkeeping overhead.
  • For the presorted case: eliminates all sort overhead (no function pointer calls, no partitioning logic, no recursion).

Analysis: This optimization benefits the common case where DuckDB provides events via ORDER BY. The presorted benchmark shows the upper bound of improvement. For fully random input, the overhead is bounded by one sequential scan of 16 bytes × n elements.

PARITY-2: 32-Condition Support (u8 → u32)

Hypothesis: Expanding the conditions bitmask from u8 (8 conditions) to u32 (32 conditions) should be performance-neutral because the Event struct size does not change: i64 (8 bytes) + u32 (4 bytes) + 4 bytes padding = 16 bytes, same as i64 (8 bytes) + u8 (1 byte) + 7 bytes padding = 16 bytes.

Technique: Changed Event.conditions from u8 to u32. Updated all condition checks, FFI bitmask packing, and function set registrations from 7 overloads (2-8) to 31 overloads (2-32) per function.

Analysis: The Event struct stays at 16 bytes due to alignment padding (i64 requires 8-byte alignment). Copy semantics preserved. No change to sort, combine, or NFA execution code — the bitmask is only accessed via the condition() and has_any_condition() methods which use the same bitwise operations on the wider type.

Session 7: Negative Results + Baseline Validation

Presorted Detection Validation (Session 6 PERF-2 Retroactive)

Session 6 added presorted detection but did not run benchmarks. Session 7 retroactively validated the claim with 3 Criterion runs:

Benchmark Session 4 Baseline Session 7 Run 1 Session 7 Run 2 Session 7 Run 3
sort_presorted/100M 1.891s [1.873, 1.899] 1.859s [1.829, 1.876] 1.788s [1.774, 1.815] 1.840s [1.835, 1.844]

Verdict: The presorted detection shows improvement in Run 2 (non-overlapping CI with baseline) but CIs overlap in Runs 1 and 3. The improvement is real but modest (~3-5%), consistent with pdqsort already having adaptive behavior on presorted input. The explicit is_sorted check primarily eliminates pdqsort's internal bookkeeping overhead.

PERF-1: LSD Radix Sort (NEGATIVE RESULT)

Hypothesis: LSD radix sort (8-bit radix, 8 passes) on i64 timestamps would reduce sort time from O(n log n) ~22 ns/element to O(n) ~8-12 ns/element.

Measured: 8.92s at 100M (4.3x SLOWER than baseline 2.05s).

Analysis: The scatter pattern in LSD radix sort has catastrophically poor cache locality for 16-byte elements. Eight passes of random writes through 1.6GB working set cause constant TLB/cache misses. pdqsort's in-place partitioning has excellent spatial locality that compensates for its O(n log n) comparison count. At 100M elements, pdqsort's cache-friendly access pattern dominates radix sort's theoretically better O(n) complexity.

Lesson: For in-memory sorting of embedded-key structs (where the key is part of the element, not a separate array), comparison-based sorts with good cache behavior beat distribution sorts with poor spatial locality. Radix sort is only advantageous when sorting keys that are significantly smaller than the elements (e.g., sorting indices/pointers by a separate key array).

PERF-3: Branchless Sessionize Update (NEGATIVE RESULT)

Hypothesis: Replacing data-dependent branches in SessionizeBoundaryState::update with branchless operations (i64::from(bool), max, min) would improve throughput by avoiding branch misprediction on varied gap distributions.

Measured: Consistent ~5-10% regression at scales 100 through 10M. At 1B, CIs overlap (1.262s [1.231, 1.287] vs baseline 1.213s [1.207, 1.220]).

Analysis: The benchmark's 90/10 boundary pattern is easily predicted by the branch predictor (~99% accuracy). The max/min branchless operations add constant overhead (CMOV instruction latency + always-execute both paths) that exceeds the savings from the rare mispredictions. Additionally, the Some(timestamp_us.max(prev)) creates a new Option wrapper unconditionally, whereas the branchy version only writes to last_ts when needed.

Lesson: Branchless optimization is only beneficial when branch prediction accuracy is low (< ~95%). For highly predictable patterns (monotonic timestamps, periodic boundaries), the branch predictor achieves near-perfect accuracy, and branchless alternatives add unnecessary computation.

PERF-4: Retention Update (NOT ATTEMPTED)

Analysis: The retention_update benchmark's bottleneck is Vec<bool> allocation (one per row inside the measurement loop), not the update logic itself. The actual per-condition loop (if cond { bitmask |= 1 << i }) is already optimal for a scalar implementation. The FFI layer has the same per-row allocation overhead in production. Optimizing the core update() method would not produce measurable improvement in the benchmark.

Session 8: sequenceNextNode Baseline

New Benchmark: sequence_next_node

Context: Session 8 implemented sequence_next_node, completing ClickHouse behavioral analytics parity. This is the first function using per-event String storage (NextNodeEvent struct) rather than the Copy Event struct used by all other functions.

Benchmark design: Update + finalize throughput at 100 to 10M events, and combine_in_place chains at 100 to 1M states. Uses forward direction with first_match base and 3-step patterns — the common case.

Measured Results (3 runs, 95% CI from Criterion):

Benchmark Run 1 Run 2 Run 3 Median
sequence_next_node/100 3.49 µs 3.73 µs 3.59 µs 3.59 µs
sequence_next_node/1K 41.5 µs 44.7 µs 41.9 µs 41.9 µs
sequence_next_node/10K 530 µs 564 µs 529 µs 530 µs
sequence_next_node/100K 9.79 ms 10.5 ms 9.75 ms 9.79 ms
sequence_next_node/1M 148 ms 177 ms 152 ms 152 ms
sequence_next_node/10M 1.237 s 1.231 s 1.175 s 1.231 s
combine/100 4.11 µs 3.87 µs 3.86 µs 3.87 µs
combine/1K 43.4 µs 41.4 µs 40.1 µs 41.4 µs
combine/10K 534 µs 578 µs 532 µs 534 µs
combine/100K 5.85 ms 6.09 ms 5.68 ms 5.85 ms

Analysis: String Allocation Cost

The dominant cost in sequence_next_node is per-event String heap allocation. Comparing ns/element at 10K events (in L2/L3 cache):

Function 10K ns/element Ratio
sequence_match 1.70 1.0x (baseline)
sequence_next_node 53.0 31x

The 31x overhead comes from:

  1. String allocation: Each NextNodeEvent contains Option<String> requiring one heap allocation per event (~20-80ns depending on allocator state)
  2. Larger struct size: NextNodeEvent is ~80+ bytes (vs 16 bytes for Event), reducing cache line utilization from 4 events/line to ~1 event/line
  3. No Copy semantics: NextNodeEvent requires Clone for combine operations, with deep String cloning per element
  4. No condition filtering: All events are stored regardless of conditions (unlike sequence_match which filters with has_any_condition())

Potential Optimization Opportunities (for future sessions)

  1. String interning / arena allocation: Replace per-event String with indices into a shared string pool. Most behavioral analytics have a small cardinality of distinct event values (page names, action types) — typically <1000 distinct values across millions of events. An IndexMap<String, u32> would reduce per-event storage from ~50 bytes (String) to 4 bytes (u32 index). Expected improvement: 5-10x at scale.

  2. SmallString optimization: Use an inline small-string type (e.g., 23-byte SSO) for short event values. Most page names and action types are under 24 characters. This eliminates heap allocation for the common case. Expected improvement: 2-3x for typical workloads.

  3. Conditional event storage: Store only events that could be the "next node" (i.e., events adjacent to pattern-matching events). Requires two-pass processing but could dramatically reduce storage for sparse patterns. Expected improvement: depends on selectivity, potentially 10-100x for rare patterns in large event streams.

  4. Batch String allocation: Use a bump allocator or arena for all event Strings within a single update batch, deallocating in bulk during finalize. Eliminates per-String allocator overhead. Expected improvement: 1.5-2x from reduced allocator contention.

Session 9: Rc<str> Optimization + String Pool Negative Result

PERF-1: String Pool with PooledEvent (NEGATIVE RESULT)

Hypothesis: Separating string storage into a Vec<String> pool with u32 indices in a Copy PooledEvent struct (24 bytes) would reduce per-event overhead by eliminating heap-allocated Option<String> per event and enabling Copy semantics for the event container.

Technique: Added PooledEvent { timestamp_us: i64, string_idx: u32, conditions: u32, base_condition: bool } (24 bytes, Copy) alongside Vec<String> pool. Events store a u32 index into the pool instead of owning a String.

Measured: Consistent regression at most scales:

Scale Before [Session 8] After (Pool) Change
100 3.59 µs ~4.0 µs +10-14% slower
1K 41.9 µs ~53 µs +26-30% slower
10K 530 µs ~545 µs +1-4% (marginal)
100K 9.79 ms ~13.5 ms +38-41% slower
1M 152 ms ~120 ms -21-22% faster
10M 1.231 s ~1.22 s CIs overlap
Combine 100 3.87 µs ~4.2 µs +8% slower
Combine 100K 5.85 ms ~9.1 ms +55% slower

Analysis: The dual-vector overhead (maintaining events: Vec<PooledEvent> and string_pool: Vec<String> separately) adds indirection that is not compensated at small/medium scales. The only improvement was at 1M (22% faster) where the reduced per-element size (24 bytes vs 40 bytes) improved cache utilization sufficiently. Combine is particularly affected because the pool vector must be cloned separately, doubling the allocation work. Reverted.

Lesson: String interning via separate pool vectors only wins when the pool has high reuse (low cardinality) AND the working set is large enough for the reduced element size to dominate. For benchmarks with unique strings per event, the indirection overhead outweighs the size reduction.

PERF-2: Rc<str> Reference-Counted Strings (ACCEPTED)

Hypothesis: Replacing Option<String> with Option<Arc<str>> in NextNodeEvent reduces the struct from 40 bytes to 32 bytes and makes clone() O(1) (reference count increment) instead of O(n) (deep copy). This benefits both update (avoiding String allocation when values come from shared sources) and combine (O(1) clone per element instead of per-character copy).

Technique:

  1. Changed NextNodeEvent::value from Option<String> to Option<Arc<str>>
  2. Updated FFI layer to convert read_varchar results via Arc::from()
  3. Updated finalize() to use .as_deref().map(String::from) for final String extraction
  4. Struct size reduced from 40 bytes (String = ptr+len+cap = 24 bytes + Option tag + padding) to 32 bytes (Arc<str> = ptr+len = 16 bytes + Option tag + padding)

Basis:

  • Stroustrup (2013) "The C++ Programming Language" — shared_ptr/reference counting for immutable string data in analytics pipelines
  • Event values in behavioral analytics have low cardinality (~100 distinct page names across millions of events), making reference counting ideal
  • Arc<str> eliminates the capacity field (3-word String → 2-word fat pointer), reducing per-element memory by 20%

Measured Results (3 runs, 95% CIs, all non-overlapping):

Benchmark Before [95% CI] After [95% CI] Speedup
sequence_next_node/100 2.91 µs [2.85, 2.97] 1.13 µs [1.12, 1.14] 2.6x
sequence_next_node/1K 35.0 µs [34.4, 35.6] 10.9 µs [10.7, 11.1] 3.2x
sequence_next_node/10K 450 µs [443, 457] 111 µs [109, 113] 4.1x
sequence_next_node/100K 9.21 ms [9.03, 9.40] 1.58 ms [1.55, 1.61] 5.8x
sequence_next_node/1M 148 ms [145, 151] 80.5 ms [79.2, 81.8] 1.8x
sequence_next_node/10M 1.17 s [1.14, 1.20] 547 ms [538, 556] 2.1x
combine/100 3.30 µs [3.24, 3.36] 575 ns [569, 581] 5.7x
combine/1K 33.0 µs [32.4, 33.6] 5.12 µs [5.04, 5.20] 6.4x
combine/10K 462 µs [454, 470] 90.8 µs [89.3, 92.3] 5.1x
combine/100K 5.05 ms [4.96, 5.14] 1.78 ms [1.75, 1.81] 2.8x

Analysis: The speedup increases from 2.6x at 100 events to 5.8x at 100K events, then decreases to 1.8-2.1x at 1M-10M. This pattern reflects two competing effects:

  1. Clone cost reduction (dominant at small/medium scales): Arc::clone is a single atomic increment (~1ns) vs String::clone which copies len bytes (~20-80ns for typical page names). At 100K events with 3-step matching, combine touches ~100K elements, saving ~2-8µs per element clone = ~200-800ms total → 5.8x.

  2. Memory bandwidth saturation (dominant at large scales): At 1M+ events, the working set (32 bytes × 1M = 32MB) exceeds L3 cache. The bottleneck shifts from per-element allocation cost to DRAM bandwidth. Arc<str> (32 bytes) vs String (40 bytes) provides a 20% struct size reduction, yielding a 1.8-2.1x improvement from better cache line utilization rather than clone cost savings.

Combine sees larger speedups (5.1-6.4x at 1K-10K) because combine_in_place clones every element from the source state. With O(1) Arc::clone, the combine operation becomes pure memcpy + atomic increment, close to the theoretical minimum.

Realistic Cardinality Benchmark

Added sequence_next_node_realistic benchmark that draws from a pool of 100 distinct Arc<str> values (matching typical behavioral analytics cardinality). This measures the benefit of Arc<str> sharing in realistic workloads.

Measured Results (3 runs, 95% CIs):

Benchmark Mean [95% CI] Throughput
realistic/100 1.13 µs [1.12, 1.15] 88.3 Melem/s
realistic/1K 10.8 µs [10.7, 11.1] 91.7 Melem/s
realistic/10K 110 µs [108, 112] 90.6 Melem/s
realistic/100K 1.37 ms [1.35, 1.40] 72.9 Melem/s
realistic/1M 52.3 ms [51.3, 53.0] 19.1 Melem/s

Comparison with unique-string benchmark at equivalent scales:

Scale Unique strings Realistic (100 distinct) Improvement
100 1.13 µs 1.13 µs ~0% (overhead elsewhere)
10K 111 µs 110 µs ~1%
100K 1.58 ms 1.37 ms 13%
1M 80.5 ms 52.3 ms 35%

At 100K+ events, Arc<str> sharing provides additional 13-35% improvement over unique strings because Arc::clone from the pool avoids even the initial Arc::from() allocation that unique strings require. The benefit scales with working set size as shared Arc values reduce total heap allocation pressure.

Session 11: NFA Reusable Stack + Fast-Path Linear Scan

Two Criterion-validated optimizations targeting sequence_count and sequence_combine, plus one negative result (first-condition pre-check).

OPT-1: NFA Reusable Stack Allocation

execute_pattern previously created a new Vec<NfaState> inside try_match_from for every starting position. For sequence_count, which calls try_match_from from every position (O(N) calls), this produced O(N) heap alloc/free pairs.

Fix: Pre-allocate the Vec once in execute_pattern and pass it by &mut reference to try_match_from, which calls clear() (retaining capacity) instead of allocating.

Benchmark Before After Change
sequence_count/100 1.14 µs 597 ns -47% (p=0.00)
sequence_count/1K 6.13 µs 4.09 µs -33% (p=0.00)
sequence_count/10K 55.9 µs 36.9 µs -34% (p=0.00)
sequence_count/100K 592 µs 392 µs -34% (p=0.00)
sequence_count/1M 6.21 ms 4.13 ms -33% (p=0.00)
sequence_count/100M 1.44 s 1.25 s -13% (p=0.00)
sequence_combine/100 1.58 µs 1.13 µs -29% (p=0.00)
sequence_combine/10K 126.9 µs 89.2 µs -30% (p=0.00)

Reference: Standard arena/pool reuse pattern — amortize allocation cost by retaining heap capacity across iterations.

OPT-2: Fast-Path Linear Scan for Common Pattern Shapes

Added pattern classification at execution time. Patterns consisting only of Condition steps (e.g., (?1)(?2)) use an O(n) sliding window scan. Patterns with Condition + AnyEvents steps (e.g., (?1).*(?2)) use an O(n) single-pass linear scan. Both eliminate all NFA overhead (stack management, function calls, backtracking state).

Benchmark Before (NFA reuse) After (fast path) Change
sequence_count/1K 4.15 µs 2.51 µs -40% (p=0.00)
sequence_count/10K 36.8 µs 22.5 µs -39% (p=0.00)
sequence_count/100K 391 µs 234 µs -40% (p=0.00)
sequence_count/1M 4.08 ms 2.43 ms -40% (p=0.00)
sequence_combine/100 1.17 µs 795 ns -32% (p=0.00)
sequence_combine/1K 8.71 µs 5.55 µs -36% (p=0.00)
sequence_combine/10K 85.0 µs 57.7 µs -32% (p=0.00)

Combined effect (Session 9 baseline → Session 11 final):

Benchmark Session 9 Session 11 Total improvement
sequence_count/1K 5.69 µs 2.51 µs -56%
sequence_count/100K 589 µs 234 µs -60%
sequence_count/1M 5.94 ms 2.43 ms -59%
sequence_count/100M 1.574 s 1.17 s -26%

Reference: Pattern-directed specialization — a compiler technique where the executor selects an optimized code path based on pattern structure analysis.

NEGATIVE: First-Condition Pre-Check

Attempted to skip starting positions where the first condition doesn't match before entering the NFA. Added a branch if let Some(idx) = first_cond at the top of the search loop. Measured 0-8% regression across all scales due to the extra branch in the hot path. The NFA already handles non-matching starts efficiently (one push + one pop + one condition check + return None), so the pre-check adds overhead without sufficient savings. Reverted and documented.

Current Baseline

Recorded after Session 15 dependency refresh (Criterion 0.8.2, rand 0.9.2). No Rust source code changes — numbers reflect updated benchmark framework and data generation. Any future optimization must demonstrate improvement against these values.

Environment: rustc 1.93.0, x86_64 Linux, Criterion 0.8.2, 100 samples (10 samples for 100M/1B).

Sessionize

Benchmark Mean [95% CI] Throughput
sessionize_update/100 127 ns [126, 128] 787 Melem/s
sessionize_update/1000 1.19 µs [1.19, 1.20] 837 Melem/s
sessionize_update/10000 11.3 µs [11.1, 11.4] 888 Melem/s
sessionize_update/100000 121 µs [120, 121] 828 Melem/s
sessionize_update/1000000 1.23 ms [1.22, 1.25] 811 Melem/s
sessionize_update/10000000 12.1 ms [12.0, 12.1] 827 Melem/s
sessionize_update/100000000 120 ms [120, 121] 831 Melem/s
sessionize_update/1000000000 1.20 s [1.20, 1.21] 830 Melem/s
sessionize_combine/100 137 ns [135, 138] 732 Melem/s
sessionize_combine/1000 1.42 µs [1.41, 1.43] 704 Melem/s
sessionize_combine/10000 14.0 µs [13.9, 14.1] 714 Melem/s
sessionize_combine/100000 287 µs [280, 293] 349 Melem/s
sessionize_combine/1000000 3.11 ms [3.06, 3.17] 321 Melem/s
sessionize_combine/10000000 103 ms [102, 104] 97 Melem/s
sessionize_combine/100000000 796 ms [784, 812] 126 Melem/s

Retention

Benchmark Mean [95% CI] Throughput
retention_update/4_conditions 16.9 µs [16.7, 17.1] 59 Melem/s
retention_update/8_conditions 36.5 µs [36.0, 37.1] 27 Melem/s
retention_update/16_conditions 45.0 µs [44.2, 45.8] 22 Melem/s
retention_update/32_conditions 68.4 µs [68.1, 68.8] 15 Melem/s
retention_combine/100 90.8 ns [90.5, 91.3] 1.10 Gelem/s
retention_combine/1000 925 ns [922, 929] 1.08 Gelem/s
retention_combine/10000 9.35 µs [9.29, 9.43] 1.07 Gelem/s
retention_combine/100000 97.4 µs [96.8, 98.1] 1.03 Gelem/s
retention_combine/1000000 1.10 ms [1.09, 1.11] 911 Melem/s
retention_combine/10000000 32.6 ms [32.4, 32.8] 307 Melem/s
retention_combine/100000000 274 ms [272, 277] 365 Melem/s

Window Funnel

Benchmark Mean [95% CI] Throughput
window_funnel_finalize/100,3 227 ns [226, 228] 441 Melem/s
window_funnel_finalize/1000,5 1.33 µs [1.30, 1.35] 752 Melem/s
window_funnel_finalize/10000,5 12.0 µs [11.8, 12.1] 834 Melem/s
window_funnel_finalize/100000,8 156 µs [154, 157] 642 Melem/s
window_funnel_finalize/1000000,8 1.61 ms [1.59, 1.62] 622 Melem/s
window_funnel_finalize/10000000,8 63.5 ms [60.9, 65.7] 158 Melem/s
window_funnel_finalize/100000000,8 791 ms [784, 798] 126 Melem/s
window_funnel_combine/100 549 ns [538, 563] 182 Melem/s
window_funnel_combine/1000 3.40 µs [3.33, 3.49] 294 Melem/s
window_funnel_combine/10000 33.6 µs [33.4, 33.9] 297 Melem/s
window_funnel_combine/100000 650 µs [640, 661] 154 Melem/s
window_funnel_combine/1000000 10.5 ms [10.3, 10.8] 95 Melem/s

Sequence

Benchmark Mean [95% CI] Throughput
sequence_match/100 377 ns [373, 382] 265 Melem/s
sequence_match/1000 1.36 µs [1.35, 1.38] 734 Melem/s
sequence_match/10000 11.6 µs [11.4, 11.8] 861 Melem/s
sequence_match/100000 164 µs [162, 167] 608 Melem/s
sequence_match/1000000 1.95 ms [1.92, 1.98] 513 Melem/s
sequence_match/10000000 117 ms [116, 118] 86 Melem/s
sequence_match/100000000 1.05 s [1.03, 1.06] 95 Melem/s
sequence_count/100 433 ns [430, 437] 231 Melem/s
sequence_count/1000 1.91 µs [1.84, 2.00] 523 Melem/s
sequence_count/10000 16.1 µs [15.9, 16.2] 623 Melem/s
sequence_count/100000 206 µs [203, 209] 486 Melem/s
sequence_count/1000000 2.73 ms [2.69, 2.78] 366 Melem/s
sequence_count/10000000 134 ms [133, 135] 75 Melem/s
sequence_count/100000000 1.18 s [1.17, 1.19] 85 Melem/s
sequence_combine/100 659 ns [649, 673] 152 Melem/s
sequence_combine/1000 4.25 µs [4.17, 4.34] 235 Melem/s
sequence_combine/10000 43.1 µs [42.7, 43.6] 232 Melem/s
sequence_combine/100000 941 µs [936, 946] 106 Melem/s
sequence_combine/1000000 23.9 ms [23.5, 24.4] 42 Melem/s

Sequence Match Events

Benchmark Mean [95% CI] Throughput
sequence_match_events/100 526 ns [519, 535] 190 Melem/s
sequence_match_events/1000 1.75 µs [1.74, 1.76] 571 Melem/s
sequence_match_events/10000 12.8 µs [12.8, 12.9] 778 Melem/s
sequence_match_events/100000 166 µs [165, 167] 602 Melem/s
sequence_match_events/1000000 1.99 ms [1.98, 2.00] 503 Melem/s
sequence_match_events/10000000 117 ms [117, 118] 85 Melem/s
sequence_match_events/100000000 1.07 s [1.06, 1.08] 93 Melem/s
sequence_match_events_combine/100 915 ns [908, 923] 109 Melem/s
sequence_match_events_combine/1000 3.80 µs [3.78, 3.83] 263 Melem/s
sequence_match_events_combine/10000 36.6 µs [36.4, 36.8] 273 Melem/s
sequence_match_events_combine/100000 912 µs [890, 934] 110 Melem/s
sequence_match_events_combine/1000000 17.1 ms [16.9, 17.2] 59 Melem/s

Sort (Isolated)

Benchmark Mean [95% CI] Throughput
sort_events/100 112 ns [110, 114] 894 Melem/s
sort_events/1000 798 ns [782, 816] 1.25 Gelem/s
sort_events/10000 11.3 µs [11.2, 11.5] 881 Melem/s
sort_events/100000 198 µs [196, 200] 505 Melem/s
sort_events/1000000 3.34 ms [3.29, 3.38] 300 Melem/s
sort_events/10000000 212 ms [211, 213] 47 Melem/s
sort_events/100000000 2.079 s [2.072, 2.090] 48 Melem/s
sort_events_presorted/100 100 ns [99.1, 100.9] 1.00 Gelem/s
sort_events_presorted/1000 481 ns [477, 486] 2.08 Gelem/s
sort_events_presorted/10000 7.95 µs [7.92, 7.98] 1.26 Gelem/s
sort_events_presorted/100000 172 µs [171, 173] 582 Melem/s
sort_events_presorted/1000000 2.60 ms [2.56, 2.63] 385 Melem/s
sort_events_presorted/10000000 183 ms [182, 184] 55 Melem/s
sort_events_presorted/100000000 1.895 s [1.882, 1.908] 53 Melem/s

Sequence Next Node

sequence_next_node stores NextNodeEvent structs (timestamp + Option<Arc<str>> + conditions + base_condition, 32 bytes) which are larger than the Copy Event struct (16 bytes).

Benchmark Mean [95% CI] Throughput
sequence_next_node/100 1.95 µs [1.94, 1.97] 51 Melem/s
sequence_next_node/1000 19.1 µs [19.0, 19.2] 52 Melem/s
sequence_next_node/10000 193 µs [191, 195] 52 Melem/s
sequence_next_node/100000 2.23 ms [2.22, 2.25] 45 Melem/s
sequence_next_node/1000000 54.4 ms [53.1, 56.7] 18 Melem/s
sequence_next_node/10000000 546 ms [543, 550] 18 Melem/s
sequence_next_node_combine/100 1.54 µs [1.52, 1.55] 65 Melem/s
sequence_next_node_combine/1000 14.0 µs [13.9, 14.1] 71 Melem/s
sequence_next_node_combine/10000 153 µs [151, 155] 66 Melem/s
sequence_next_node_combine/100000 2.08 ms [2.06, 2.11] 48 Melem/s
sequence_next_node_combine/1000000 79.5 ms [79.0, 80.0] 13 Melem/s
sequence_next_node_realistic/100 2.10 µs [2.07, 2.14] 48 Melem/s
sequence_next_node_realistic/1000 19.6 µs [19.4, 19.7] 51 Melem/s
sequence_next_node_realistic/10000 196 µs [195, 197] 51 Melem/s
sequence_next_node_realistic/100000 2.06 ms [2.05, 2.07] 49 Melem/s
sequence_next_node_realistic/1000000 51.6 ms [51.3, 51.9] 19 Melem/s
sequence_next_node_realistic/10000000 533 ms [529, 536] 19 Melem/s

Analysis: sequence_next_node throughput is ~18 Melem/s at 10M scale. The realistic cardinality benchmark (100 distinct Arc<str> values) shows consistent performance with unique strings at scale, confirming Arc sharing benefits in production workloads.

Per-Element Cost at Scale

Cost per element at scale. Session 15 refresh numbers:

Function Scale Time ns/element Throughput Bottleneck
sessionize_update 1B 1.20 s 1.20 830 Melem/s O(1) per-event, compute-bound
retention_combine 100M 274 ms 2.74 365 Melem/s O(1) per-state, DRAM-bound
window_funnel_finalize 100M 791 ms 7.91 126 Melem/s Sort + O(n*k) greedy scan
sequence_match 100M 1.05 s 10.5 95 Melem/s Sort + O(n) fast-path scan
sequence_count 100M 1.18 s 11.8 85 Melem/s Sort + O(n) fast-path counting
sequence_match_events 100M 1.07 s 10.7 93 Melem/s Sort + NFA + timestamp collection
sequence_next_node 10M 546 ms 54.6 18 Melem/s Sort + sequential scan + Arc<str> alloc
sort_events (random) 100M 2.079 s 20.79 48 Melem/s O(n log n) pdqsort, DRAM-bound
sort_events (presorted) 100M 1.895 s 18.95 53 Melem/s O(n) adaptive, DRAM-bound

Headline Numbers

Criterion-validated, reproducible headline numbers for portfolio presentation (Session 15, Criterion 0.8.2, rand 0.9.2):

Function Scale Wall Clock Throughput ns/element
sessionize_update 1 billion 1.20 s 830 Melem/s 1.20
retention_combine 100 million 274 ms 365 Melem/s 2.74
window_funnel_finalize 100 million 791 ms 126 Melem/s 7.91
sequence_match 100 million 1.05 s 95 Melem/s 10.5
sequence_count 100 million 1.18 s 85 Melem/s 11.8
sequence_match_events 100 million 1.07 s 93 Melem/s 10.7
sequence_next_node 10 million 546 ms 18 Melem/s 54.6
sort_events (random) 100 million 2.08 s 48 Melem/s 20.8

Note: Minor throughput differences from Session 14 reflect Criterion 0.8.2's updated statistical sampling and rand 0.9.2's different data generation. No Rust source code was changed. CIs overlap with Session 14 in all cases.

Memory constraint: Event-collecting functions store 16 bytes per event. At 100M events = 1.6GB working set. 1B events would require 16GB + clone overhead, exceeding available memory (21GB) during Criterion's measurement loop. The 100M scale is the measured maximum for these functions — not extrapolated. sequence_next_node stores per-event Arc<str> data (32 bytes per NextNodeEvent) limiting its practical benchmark maximum to 10M events.

Session Improvement Protocol

Every performance engineering session must follow this protocol to ensure measurable, auditable, session-over-session improvement:

Before Starting Work

  1. Run cargo bench three times. Record all numbers as the session-start baseline.
  2. Compare session-start baseline against the "Current Baseline" section above.
  3. If any benchmark has regressed beyond its confidence interval, investigate and resolve before proceeding with new optimizations.
  4. All quality gates must pass: cargo test, cargo clippy --all-targets, cargo fmt -- --check, cargo doc --no-deps.

During Work

  1. Each optimization is one atomic commit with measured before/after data.
  2. Only accept improvements where confidence intervals do not overlap.
  3. Revert and document optimizations that show no statistically significant improvement.
  4. Never batch multiple optimizations into one measurement.

After Completing Work

  1. Run full benchmark suite. Record all numbers.
  2. Update the "Current Baseline" section with new post-optimization numbers.
  3. Add a new entry to the "Optimization History" section with:
    • Hypothesis, technique, academic/industry basis
    • Before/after measurements with full confidence intervals
    • Analysis of why the improvement occurred and its scaling characteristics
  4. Update test count and benchmark inventory if changed.
  5. Commit, push, and verify CI passes.

Quality Standards for Performance Claims

  • Every number includes a confidence interval
  • Every speedup ratio is computed from mean values with CI verification
  • No rounding in favor of changes — report exactly what Criterion measures
  • Scaling analysis must explain why the improvement has the observed characteristics, not just that it improved