Quant mod for CoreTile-A15x2

I'm using the CoreTile-A15x2 to build a low-level system for probability models, stochastic variables, calculus, ML, information theory, statistics, optimziation problem analysis, numerical solvers (ODEs and PDEs), matrix factorizations, and sparse matrix support. This low-level approach deepends the understanding by tackling these topics at their most fundamental and challenging level. So, this is a challenge for myself, of course. But if successful, I would like to utilize it as an tool for solving investment problems.

Core Components

1. Probability Models:

   • Foundational probability distributions (e.g., normal, binomial, Poisson).
   • Bayesian inference and Monte Carlo Simulation methods.
   • Stochasstic processes such as Markov Chains and Brownian Motion.

2. Stochastic Variables and Calculus:

   • Random variable generation and transformation.
   • Stochastic differential equations (SDEs) solvers (e.g., Euler-Maruyama).

3. Machine Learning:

   • Linear models (linear and logistic regression):
   • Algorithms like decision trees and basic neural networks.

4. Information Theory and statistics:

   • Entropy, mutual information, and coding theory algorithms.
   • Descriptive and inferential statistical tools.

5. Optimization Problem analysis:

   • Solvers for both constrained and unconstrained optimization.
   • Gradient-based methods (e.g., L-BFGS) and gradient-free methods (e.g., genetic algorithms).

6. Heavy Equation solving:

   • Numeric solvers for differential equations (ODEs and PDEs).
   • Symbolic math capabilities (e.g., symbolic integrationand SDE solutions).

7. Numerical Linear Algebra:

   • matrix factorizations (LU, QR, SVD).
   • Support for sparse matrices and operations for efficient computation.

8. Low-level Optimziations

   • Hand-tuned assembly routines for critical performance bottlenecks.
   • Use of Cortex-A15's NEON SIMD instructions for vectorized matrix operations.

9. Integration with scheduler:

   • Task scheduling for efficient parallel or sequential computation.
   • Multi-core capabilities leveraging Cortex-A15's architecture for load distribution.

10. Networking capabilities:

    • Protocol support: Develop low-level support for basic networking protocols (TCP/IP stack implementation or lightweight alternatives like LWIP).
    • Real-Time Communication: Support for data exchange and distributed computing tasks.
    • Data Transmission Security: Add encryption mechanisms for secure data communication.
    • Integration with platform: Enable real-time updates or remote access to platform computations.

11. Debugging and profiling tools

    • Basic utilities for debugging, such as memory usage tracking.
    • Performance profiling using Cortex-A15's Performance Monitor Unit (PMU).

12. I/O system

    • Low-level interface for reading/writing datasets directly to memory.
    • Support for real-time data streams.

---> These are the things that I would like to integrate into my project, but reality * time = very unlikely, so for now, this will be purely a inspiration board and nothing else. I would also like to include a sort-of half-roadmap:

Phase 1: Foundation:

1. Environment Setup

   • Setup Cortex-A15 simulation,
   • Configure Barebox bootloader for program loading.

2. Low-Level Framework

   • Develop a custom memory allocator and basic math routines (e.g., floating-point operations).
   • Build a low-level API for matrix and vector operations.

3. Core Computaions:

   • Implement basic probability distributions and statistical methods.
   • Develop random variable generators.

Phase 2: Intermediate Functionality

1. Stochastic Calculus and Optimization

   • Implement stochastic process simulations.
   • Build a library for solving constrained and unconstrained optimization problems.

2. Integration with Machine Learning

   • Add simple models like linear regression and decision trees.
   • Optimize performance using Cortex-A15's hardware features.

3. Equation Solvers

   • Implement numeric solvers for ODEs and PDEs.
   • Add symbolic computation for differentiation and integration.

Phase 3: Advanced capabilities

1. Numerical Linear Algebra:

   • Implement matrix factorizations (LU, QR, SVD).
   • Add sparse matrix operations for efficient computation.

2. Scalability and Performance:

   • Optimize solvers and matrix operations with NEON SIMD instructions.
   • Add multi-core support for parallel computations.

3. Information Theory Tools :

   • Develop entropy-based metrics and mutual information calculations.

4. Debugging and Profiling;:

   • Integrate debugging utilities and performance profiling using Cortex-A15's PMU.

Phase 4: Finalization and Testing

1. Comprehensive Testing

   • Validate implementations with well-known benchmarks.
   • Stress-test the platform with large datasets and high-load scenarios.

2. Documentation

   • Create user documentation and code-level comments.

3. Real-world applications:

   • Test the platform with investment problems and gambling scenarios.

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