ApexMatch Engine
Deterministic In-Memory Order Matching Core (C++17)
Case 01 Non-Crossing
Limit Order Insertion
Order arrives, evaluates spread, and rests on the active Bid ladder.
Case 02 Aggressive Taker
Market Order Sweep
Aggressive buy order consumes available Ask depth across FIFO queues.
Case 03 Partial Fill
Immediate-Or-Cancel (IOC)
Executes available counterparty volume and cancels residual balance.
Case 04 O(1) Direct Erasure
Hash Index Cancellation
Direct iterator extraction and queue detachment bypassing tree traversal.
Step 1 of 5

Order Allocation in Memory Pool

Speed:
01
Memory Pool
Zero Runtime Malloc
02
Ingress & Validation
OpenMP Multi-Core
03
Matching Core
Deterministic FIFO
04
Telemetry Ring
Lock-Free SPSC
BUY LIMIT
Order #301
45 shares @ $100.5000
Memory Allocated

Execution State

The order acquires a preallocated pointer from the contiguous OrderPool free list. No OS memory allocator primitive (malloc/new) is invoked.

Algorithmic Complexity
O(1) Constant Time
In-Memory Order Book State
Price Priority (std::map)
Bid Ladder (Desc)
Ask Ladder (Asc)
Inverted Order Index Table
std::unordered_map

Maintains direct mappings from OrderID ➔ PriceLevel Iterator to enable constant-time cancellation without scanning.

Live Order Ingress Gateway
Live API
Core ready. Submit an order above to execute live in C++ engine.
Level 2 Depth of Market (DOM)
Price-Time FIFO
Price ($) Aggregated Vol Orders Depth Visual Action
Last Traded Price (LTP)
$100.5000
Execution Audit Tape
Real-time SPSC Feed

    High-Throughput Ingestion Benchmark

    Continuous execution test processing 1,000,000 synthetic multi-threaded limit, market, and cancellation orders through the ingestion pipeline.

    Ingress Throughput
    124,500 orders/sec
    OpenMP Multi-Core Ingestion
    Deterministic Latency
    0.78 ms
    P99 Tail Bound
    Heap Allocation on Path
    0 bytes
    Contiguous Pre-Allocated Storage
    Precision Encoding
    10⁴ Fixed-Pt
    Exact 64-Bit Integer Arithmetic

    Architectural Specification: High-Frequency In-Memory Matching Engine

    Mathematical models and systems design principles for ultra-low latency determinism in modern C++.

    1. Fixed-Point Decimal Quantization ($\mathcal{Q}$)

    Under IEEE-754 floating-point arithmetic, decimal representations accumulate non-deterministic rounding errors ($0.1 + 0.2 \neq 0.3$). Prices are mathematically projected onto scaled 64-bit signed integers:

    $$\mathcal{Q}(P_{\text{market}}) = \left\lfloor P_{\text{market}} \cdot 10^4 + 0.5 \right\rfloor \in \mathbb{Z}$$

    Reconstruction mapping and bounded precision error:

    $$P_{\text{market}} = P_{\text{internal}} \cdot 10^{-4}, \quad \varepsilon \le \frac{1}{2} \cdot 10^{-4} = \$0.00005$$

    Enforces deterministic integer comparisons across all CPU microarchitectures.

    2. Price-Time Priority Strict Ordering Relation ($\succ$)

    For any two orders $O_i = (P_i, t_i, q_i)$ and $O_j = (P_j, t_j, q_j)$ submitted to the engine:

    $$O_i \succ_{\text{Bid}} O_j \iff (P_i > P_j) \;\lor\; \big(P_i = P_j \;\land\; t_i < t_j\big)$$
    $$O_i \succ_{\text{Ask}} O_j \iff (P_i < P_j) \;\lor\; \big(P_i = P_j \;\land\; t_i < t_j\big)$$

    Enforced using sorted Red-Black Trees (std::map) nested with FIFO doubly-linked lists (std::list).

    3. Continuous Double Auction Crossing Invariant

    Let $P_{\text{bid}}^* = \max_{B \in \mathcal{B}} P(B)$ and $P_{\text{ask}}^* = \min_{A \in \mathcal{A}} P(A)$. A continuous trade execution is triggered if and only if the bid-ask spread crosses:

    $$\Delta_{\text{spread}} = P_{\text{ask}}^* - P_{\text{bid}}^* \le 0$$
    $$P_{\text{match}} = P_{\text{maker}}, \quad Q_{\text{match}} = \min\big(Q_{\text{taker}}, Q_{\text{maker}}\big)$$

    Execution price is strictly determined by the resting maker order.

    4. Inverted Hash Index Table $\mathcal{O}(1)$ Cancellation

    Direct hash-indexed iterator dereferencing eliminates tree traversal latency:

    $$\mathcal{M}: \text{OrderID} \to (\text{Side}, \text{Price}, \text{Iterator}_{\text{list}})$$
    $$T_{\text{cancel}} = \mathcal{O}(1) \text{ hash lookup} + \mathcal{O}(1) \text{ list erasure} = \mathcal{O}(1)$$

    Eliminates the $\mathcal{O}(N)$ or $\mathcal{O}(\log N)$ cancellation bottleneck in high-frequency trading.