AADC (Automatic Adjoint Differentiation Compiler) is a just-in-time graph compiler specifically designed for complex repetitive calculations and Automatic Adjoint Differentiation.

Key characteristics:

• Generates optimized binary kernels at runtime
• Leverages AVX2/AVX512 vectorization automatically
• Provides thread-safe multi-core parallelization
• Achieves 6-100x speedup over traditional approaches
• Computes all derivatives with adjoint factor <1

Use cases: XVA calculations, Monte Carlo pricing, real-time risk (Live Risk), model calibration, scenario analysis, stress testing.

Operator overloading with the "idouble" active type allows AADC to extract the valuation graph during a single execution of your analytics.

Process:

1. Execute function once with idouble type (records operations)
2. AADC captures sequence of elementary operations
3. Forms binary instructions that replicate your analytics
4. Generates both forward and adjoint code
5. Optimizes for AVX2/AVX512 vectorization

Advantage: No source code access required - works at runtime with your existing codebase.

AADC is fundamentally different from traditional compilers:

Traditional Compilers (C++, LLVM):

• Work with source code at compile time
• Don't know runtime data patterns
• Can't optimize for specific computational paths
• Too slow for runtime code generation

AADC:

• Executes program for one data sample (e.g., single MC path)
• Captures actual sequence of primitive numerical operations (+, -, exp(), etc.)
• Encodes into optimized assembly for direct CPU execution
• Generates code in milliseconds, not seconds
• Knows exact control flow paths taken at runtime

Result: Better optimization than ahead-of-time compilers because AADC sees the actual execution pattern.

Two Major Benefits: Speed and Ease of Integration

Performance Gains:

• 6-100x faster analytics utilizing native CPU vectorization, multi-threading, and AAD
• Adjoint factor <1: Original + all derivatives faster than original alone
• 23x faster than tape-based Adept for XVA (single core benchmark)
• Linear scaling with number of cores

Why So Fast:

• Runtime optimization more efficient than ahead-of-time compilation
• Full AVX2/AVX512 vectorization (4-8 samples per cycle)
• Optimal memory allocation patterns
• Perfect in-lining based on actual execution flow

Key Advantage: Code in object-oriented style, get data-oriented performance automatically. Adjoint code generation takes less time than code transformation approaches.

Object-oriented code convenience has performance costs that AADC eliminates:

Problems with Traditional OO Code:

• Function call overhead
• Virtual function indirection
• Object-oriented abstractions
• Poor vectorization due to scattered data
• Missed optimization opportunities

AADC Runtime Optimizations:

• Better in-lining: Eliminates all function call overhead
• Optimal memory allocation: Data laid out for vectorization
• Full AVX2/AVX512 vectorization: 4-8 operations per cycle
• Loop unrolling: Reduces branch prediction misses
• Constant folding: Eliminates repeated calculations

Example: Traditional OO Monte Carlo might process 1 path at a time. AADC automatically processes 8 paths simultaneously using AVX512.

Critical Difference: AADC Accelerates Everything, Not Just Risk

Traditional Tape-Based AAD:

• Only accelerates analytical risk calculations
• Actually slows down the original code (tape overhead)
• Adjoint factor 2-5x
• High memory usage (tape storage)
• Cannot accelerate second-order Greeks or scenarios

AADC Code Generation AAD:

• Speeds up risk, pricing, historical VaR, and what-if scenarios
• Adjoint factor <1: Faster than original alone
• Low memory usage
• Accelerates second-order Greeks via bump-and-revalue of AAD deltas
• 5-20x faster than tape-based AAD for organizations already using AAD

Integration: Easier to integrate than tape-based, no tape management complexity

Future-proof: Takes advantage of multi-core hardware automatically; GPU support planned

Technology: Patent-pending approach using specialized JIT compiler

Easy Integration - Initial Results in 2 Weeks

Drop-in Replacement: AADC's active type (idouble) is a drop-in replacement for native double type.

Typical Integration Timeline:

• Week 1-2: Initial integration, first results
• Week 3-4: Expand to key pricing/risk functions
• Week 5-8: Full production integration
• Ongoing: Extend to additional models and products

Semi-Automated Approach: MatLogica's standardized integration methodology delivers results quickly in controlled fashion

No Major Code Changes:

• No template metaprogramming required
• No code transformation needed
• No control flow restrictions
• Works with legacy code

Support: MatLogica provides integration support, debugging tools, and checkpointing toolkit

Third-party functions handled via special wrapper interface:

Two Options:

1. Provide local derivatives: If you know the mathematical derivatives
2. Use bump-and-revalue locally: For black-box components

How It Works:

• Wrap third-party function calls with AADC interface
• AADC maintains AAD chain through the system
• Only the specific third-party component uses alternative method
• Rest of system benefits from full AAD acceleration

Common Use Cases:

• Proprietary vendor pricing libraries
• Legacy Fortran code
• Third-party calibration routines
• External PDE solvers

Performance: Minimal impact - only the wrapped function uses finite differences, everything else gets full AAD

Yes - AADC handles implicit functions almost automatically!

Automated Implicit Function Theorem (IFT): MatLogica's breakthrough technology automates differentiation of calibration routines

What It Means:

• Exact-fit calibration: Fully automated differentiation (e.g., yield curve bootstrap)
• Nearly-exact calibration: Approximate solutions (e.g., volatility surface fitting)
• Solver-based routines: Newton-Raphson, optimization, root-finding

Applications:

• Yield curve calibration with AAD
• Volatility surface fitting with sensitivities
• Model parameter calibration (Heston, SABR, etc.)
• American option pricing with LSM

Benefit: No manual derivative coding for calibration routines - enables Live Risk with real-time recalibration

Read more about Automated IFT for Live Risk

AAD for LSM is fully supported with only 2x memory increase!

Challenge with LSM: Regression at each time step creates data dependencies making straightforward AAD expensive

AADC Solution: Efficient implementation requiring only two-fold memory increase (much better than naive approach)

Applications:

• American option pricing with automatic Greeks
• Bermudan swaption Greeks
• Callable bonds with AAD
• Early exercise features in structured products

Performance: Full AAD speedup maintained despite regression complexity

Ask us for a reference implementation - contact info@matlogica.com

AADC is perfect for scripting languages - best of both worlds!

The Problem with Scripting:

• Flexibility and ease of use (good)
• Severe runtime interpreter penalty (bad)
• No vectorization or optimization (bad)

AADC Solution:

• Write payoffs/models in scripting language
• AADC compiles them at runtime into optimal binary code
• Apply AAD automatically
• No runtime interpreter penalty anymore!

Benefits:

• Traders can define custom payoffs easily
• Get compiled performance without C++ complexity
• Automatic Greeks for custom products
• Rapid product development

Use Cases:

• Custom structured product payoffs
• User-defined trading strategies
• Domain-specific languages (DSLs) for quants
• Python-based analytics with C++ performance

No - external compilers would be way too slow for runtime compilation

Why LLVM/C++ Don't Work:

• LLVM compilation takes seconds to minutes
• Designed for compile-once, run-many-times
• Too slow for changing portfolios or intraday pricing
• Not practical for production Live Risk

MatLogica's Investment: Significant R&D to create really fast streaming compiler specifically for:

• Runtime code generation
• Millisecond compilation times
• Direct machine code emission
• AAD-specific optimizations

Result: Compilation fast enough for practical use - new trades, portfolio changes, intraday recalibration all handled seamlessly

Yes - AADC is designed for secure cloud deployment!

Cloud Deployment Model:

• Send AADC kernels to cloud as encrypted binary code
• Keep data and analytics safe on premises
• Only computational instructions go to cloud
• Nearly impossible to reverse-engineer proprietary models

Benefits:

• Up to 99% cloud cost reduction vs traditional approaches
• Data sovereignty maintained (compliance-friendly)
• Elastic scaling without exposing IP
• Burst compute for stress testing

Architecture: "Guilt-free Live Risk" - get cloud scalability without security compromise

Read full cloud Live Risk architecture guide

Currently Supported Languages:

• C++: Full support, most mature integration
• C#: .NET integration for Windows-based systems
• Python: Bindings for Python-based analytics

Language Integration Patterns:

• Native C++ for maximum performance
• C# for .NET quant libraries
• Python wrappers for data science workflows
• Custom DSL compilation support

More Languages Coming: Additional language support planned for future releases based on customer demand

Mixed-Language Support: Can integrate AADC into systems using multiple languages - common in large financial institutions

GPU support is planned, but CPU performance often beats GPU for quant workloads

Current Status: AADC doesn't generate GPU code yet, but your existing CUDA code can be adapted

Migration Path:

• With minimal changes, existing CUDA code adapts for AADC
• Executes using multi-threading and vectorization on CPU
• Often achieves comparable or better performance than GPU

Why CPU Often Wins for Quant:

• Memory: CPUs have plenty of memory (64GB-512GB+) vs GPU constraints (8-48GB)
• AAD Support: Better suited for adjoint differentiation
• Complex Models: Handle irregular control flow better
• No Data Transfer: Eliminate PCIe bottleneck
• Deployment: Easier in production (no GPU management)

Performance: AVX512 CPU with AADC often matches or exceeds GPU performance for typical quant workloads while supporting larger problem sizes

Future: GPU support planned for specialized use cases where massive parallelism benefits outweigh limitations

No Lock-In - Your Code Remains Yours

Realistic Assessment:

• MatLogica's core product is tech-heavy JIT compiler
• Not many businesses willing to develop their own compilers
• Development, maintenance, and improvement efforts shared across multiple satisfied users
• Lower cost than in-house development

No Vendor Lock-In:

• Run your analytics with or without AADC seamlessly
• Simple compile-time switch to disable AADC
• Code works with native doubles if needed
• Can always go back to the way things were before
• Can switch to alternative AAD tool

Exit Strategy:

1. Your source code is unchanged (just type replacements)
2. Remove idouble, use native double
3. Recompile and run as before
4. Or switch to different AAD library

Risk Mitigation: Many organizations maintain dual-mode capability - can run with or without AADC for validation and business continuity