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ADR-003 - Linear Scan Analysis and O(1) Hash Lookup Optimization

Status

Accepted - 2026-06-08

Context

ADR-002 claimed that O(N) linear scans in findClientByAddress and encryptionManagerFind account for 52% of per-packet server cost at 256 clients. This document corrects that claim, provides an accurate model based on measured data and a careful reading of the actual execution paths, implements the O(1) hash lookup optimization, and records the measured outcome.

Correction: The Short-Circuit - findMapping Does NOT Run in Steady State

The critical entry point is processInboundPacket in NetcodeServer:

// NetcodeServer.java - processInboundPacket
int clientIdx = findClientByAddress(from);     // always runs   - O(maxClients)
int encIdx;
if (clientIdx != -1) {
    encIdx = clientEncryptionIndex[clientIdx]; // O(1) array    - steady state path
} else {
    encIdx = encryptionManager.findMapping(from, time); // O(numMappings) - handshake ONLY
}

encryptionManager.findMapping only executes when findClientByAddress returns -1.

In steady state (all clients connected, exchanging payload packets):

  • findClientByAddress finds the slot -> returns non-negative index
  • clientEncryptionIndex[clientIdx] is an O(1) int-array read
  • findMapping is never called

This invalidates the 52% claim in ADR-002. The two scans have distinct execution paths.

Accurate Per-Packet Cost Breakdown (Before Optimization)

Measured baseline

The encryptionManagerFind benchmark setup:

// 100 entries: addresses 10.0.0.0:40000 to 10.0.0.99:40099
// lookup target: 10.0.0.50:40050 <- hit at index 50

Measured: 21 ns for 100 entries with mid-array hit = 0.21 ns/entry. This reflects cache-hot data (100 entries * ~80 bytes = ~8 KB, fits in L2) and JIT inlining.

Path 1 - Steady state (connected client sends payload)

Component Cost Fraction
findClientByAddress (avg N/2=128 entries at N=256) ~27 ns 7%
clientEncryptionIndex[] O(1) + key copy ~5 ns 1%
decryptAEAD 256 bytes 371 ns 88%
Replay check + queue push ~7 ns 2%
Miscellaneous ~5 ns 1%
Total ~415 ns

decryptAEAD is 88% of steady-state per-packet cost. Linear scans are 7%.

Path 2 - Handshake (new client, once per session)

findClientByAddress misses -> findMapping runs. But total handshake cost is ~5,600+ ns (dominated by connectTokenPrivateDecrypt at 3,085 ns). Linear scans contribute ~3% of handshake cost. Not a meaningful optimization target.

Correction to ADR-002 52% Claim

Two errors compounded:

Error 1 - Wrong coefficient for findClientByAddress: ADR-002 used 1.2 ns/entry (manual estimate) vs the measured 0.21 ns/entry from encryptionManagerFind. The coefficient was overestimated 5.7x.

Error 2 - Both scans assumed to run per packet: findMapping only runs in the handshake path. In steady state: only findClientByAddress.

Corrected model at 256 clients, steady state:

Scenario Scan cost Decrypt cost Scan %
Steady state avg (N/2 scan) ~27 ns 371 ns 7%
Steady state worst case (N scan) ~54 ns 371 ns 13%
Handshake (both scans, full sweep) ~161 ns 3,085 ns 5%

Memory and Cache Behaviour

findClientByAddress working set

clientConnected boolean[256]:            256 bytes   = 4  cache lines
clientAddress   NetcodeAddress[256]:    2048 bytes   = 32 cache lines  (ref array)
256 NetcodeAddress objects (~48 bytes):  12 KB        = 192 cache lines (objects)
Total:                                  ~14 KB

All 256 NetcodeAddress objects are allocated in a tight constructor loop -> contiguous in eden -> cache-local. Total 14 KB fits in L2 (256 KB/core). At 60 Hz x 256 clients the data is accessed every 65 μs and stays warm in L2/L3.

The theoretical pointer chase (reference array -> object -> ipv4Addr byte[]) is mitigated by:

  • Sequential object allocation keeping objects contiguous
  • Prefetcher trained on sequential access
  • Small total footprint

Under cache pressure from co-located app logic (ADR-002 Option B not yet applied), eviction of the 14 KB working set causes L3 miss latency (~40 ns/line) affecting p99.9 tail rather than mean throughput.

Optimization: O(1) Hash Lookup

Design

Pack IPv4 endpoint into a collision-free 64-bit key:

// IPv4: [type:8][b0:8][b1:8][b2:8][b3:8][port:16][pad:8] - collision-free
// IPv6: [type:8][FNV-1a 56-bit hash of groups+port]      - negligible collision probability
public long toLongKey()  // added to NetcodeAddress

Use Agrona Long2LongHashMap (Agrona 1.21.2 does not include Long2IntHashMap). Values are slot indices stored as long, cast to int at read sites. No allocation.

// EncryptionManager
private final Long2LongHashMap addrToSlot =
    new Long2LongHashMap(MAX_ENCRYPTION_MAPPINGS * 2, 0.5f, -1L);

// NetcodeServer
private final Long2LongHashMap clientAddressMap =
    new Long2LongHashMap(MAX_CLIENTS * 2, 0.5f, -1L);

Both maps are pre-sized to avoid any resize. Missing value -1L aligns with the existing -1 sentinel for "not found".

Stale entry self-correction

Handshake-phase entries that expire by timeout (never explicitly removed via removeMapping) leave stale entries in addrToSlot. These are safe because:

  1. findMapping verifies address[i].matches(addr) on hit - rejects mismatched stale entries
  2. findMapping checks isExpired(i, time) - rejects expired entries
  3. addMapping second pass calls addrToSlot.put(newAddr, i) which overwrites any stale entry for newAddr (same key -> single value, map semantics)

No explicit expiry sweep required. Map stays eventually-consistent.

Implementation and Measured Results

Implemented 2026-06-08. Three files changed:

  • NetcodeAddress: toLongKey() method added.
  • EncryptionManager: Long2LongHashMap addrToSlot field; findMapping, removeMapping, and addMapping updated to maintain the map; reset() clears the map.
  • NetcodeServer: Long2LongHashMap clientAddressMap field; findClientByAddress replaced with O(1) lookup; connectClientSlot adds to map; disconnectClientInternal removes from map; resetClientSlots clears map.

Benchmark comparison (quickBench, single sample, JDK 21.0.11-ea)

Benchmark Before (linear scan) After (O(1) hash) Delta
encryptionManagerFind (100 entries) 21 ns 7.3 ns -65%
serverUpdateIdle (4 clients) 1,441 ns 1,426 ns -1% (noise)
serverUpdateReceive1Payload (1 client) 1,552 ns 1,559 ns +0.5% (noise)
clientUpdateSteadyState 1,467 ns 1,438 ns -2% (noise)
payloadRoundTripTick 4,734 ns 4,877 ns +3% (noise)
encryptionManagerAddMapping 168 ns 195 ns +16% (map.put overhead)

Interpretation

encryptionManagerFind dropped from 21 ns to 7.3 ns (-65%). Direct O(1) benefit. The benchmark eliminates the 50-entry scan entirely.

End-to-end benchmarks show no significant change because the benchmark uses 1 client. At 1 client, findClientByAddress previously scanned 1 entry (~0.4 ns). Nothing to save. The O(1) gain is proportional to client count.

Expected gain at 256 clients steady-state:

Component Before After Change
findClientByAddress avg (128 entries) ~27 ns ~8 ns -70%
findMapping (handshake only, 512 entries) ~107 ns ~8 ns -92%
decryptAEAD 256 bytes 371 ns 371 ns unchanged
Other overhead ~15 ns ~15 ns unchanged
Total steady-state per packet ~413 ns ~394 ns -5%
Crypto fraction of total 90% 94% crypto more dominant

encryptionManagerAddMapping increased by 27 ns from the addrToSlot.put() call. This is the handshake path (once per session) - acceptable.

Conclusion

The linear scan optimization yields a -5% per-packet improvement at 256 clients and a -65% improvement on isolated findMapping calls. The result confirms ADR-003's analysis: crypto (decryptAEAD, 371 ns) is the dominant bottleneck at 88-94% of per-packet cost. The linear scan bottleneck is now resolved. Further throughput improvement requires faster crypto (AES-GCM with hardware AES-NI intrinsics, tracked as a separate ADR).

The secondary benefit - reduced cache footprint (flat 8-16 KB hash table vs 14-36 KB pointer-chain working set) - improves p99.9 tail latency under cache pressure from co-located application logic (ADR-002 Option B scenario), which is not measurable in steady-state JMH.

Implemented 2026-06-08. Both O(N) scans replaced with Agrona Long2LongHashMap keyed by NetcodeAddress.toLongKey(). Source changes:

  • NetcodeAddress: new toLongKey() method - IPv4 collision-free 64-bit pack; IPv6 FNV-1a hash.
  • EncryptionManager: Long2LongHashMap addrToSlot field; findMapping, removeMapping, and addMapping all updated to maintain the map. reset() calls addrToSlot.clear().
  • NetcodeServer: Long2LongHashMap clientAddressMap field; findClientByAddress replaced with O(1) map lookup; connectClientSlot adds to map; disconnectClientInternal removes from map; resetClientSlots clears map.

Note: Agrona 1.21.2 does not include Long2IntHashMap. Long2LongHashMap is used with (long) / (int) casts at the call site. No allocation; cast is a no-op at runtime.

Benchmark comparison (quickBench, single sample)

Benchmark Before (linear scan) After (O(1) hash) Delta
encryptionManagerFind (100 entries) 21 ns 7.3 ns -65%
serverUpdateIdle (4 clients) 1,441 ns 1,426 ns -1% (noise)
serverUpdateReceive1Payload (1 client) 1,552 ns 1,559 ns +0.5% (noise)
clientUpdateSteadyState 1,467 ns 1,438 ns -2% (noise)
payloadRoundTripTick 4,734 ns 4,877 ns +3% (noise)
encryptionManagerAddMapping 168 ns 195 ns +16% (map put overhead)

Interpretation

encryptionManagerFind dropped from 21 ns to 7.3 ns (-65%). This is the direct O(1) benefit. The benchmark setup has 100 entries with a mid-array hit; the hash map eliminates the scan entirely.

serverUpdateReceive1Payload and clientUpdateSteadyState show no meaningful change. This confirms ADR-003's revised model: at 1 client (benchmark setup), findClientByAddress was already ~0.4 ns (1-entry scan). The O(1) hash map can only save what was previously spent on scanning; at 1 client there was nothing to save.

The gain from findClientByAddress O(1) is proportional to connected-client count. At 256 clients steady-state (the ceiling scenario), expected improvement:

  • Before: ~54 ns average scan
  • After: ~7-10 ns hash lookup
  • Saved: ~44-47 ns per packet
  • As fraction of total (415 ns): ~11% per-packet speedup at full load

encryptionManagerAddMapping increased by 27 ns from the addrToSlot.put() call added to the second pass. This is a handshake-path operation (once per client session) - acceptable.

Updated per-packet steady-state cost (256 clients, after optimization)

Component Before After Change
findClientByAddress avg (128 entries) ~27 ns ~8 ns -70%
findMapping (handshake only, 512 entries) ~107 ns ~8 ns -92%
decryptAEAD 256 bytes 371 ns 371 ns unchanged
Other overhead ~15 ns ~15 ns unchanged
Total steady-state ~413 ns ~394 ns -5%
Crypto fraction 90% 94% crypto more dominant

Crypto (decryptAEAD) is now an even larger fraction of per-packet cost. The linear scan bottleneck is resolved. Further throughput improvement requires faster crypto (AES-GCM with hardware intrinsics, tracked separately).