ardeshir/dynamic-math

Dynamic Mathematical Compilation Platform

🧮 Dynamic Mathematical Compilation Platform

A revolutionary client-side mathematical expression compiler that transforms user-entered mathematical expressions into optimized WebAssembly (WASM) bytecode for real-time execution in web browsers. This platform enables true mathematical programming where users can define their own formulation models, optimization algorithms, and domain-specific calculations without server dependencies.

✨ Key Features

🚀 Core Capabilities

• Client-Side Compilation: Parse and compile mathematical expressions to WASM entirely in the browser
• Real-Time Execution: Execute compiled expressions with microsecond-level performance
• Dynamic Code Generation: Generate and link new WASM modules at runtime
• Multi-Level Optimization: Advanced algebraic simplification, constant folding, and strength reduction
• Persistent Caching: Intelligent caching system with browser storage integration
• Zero Server Dependencies: Complete mathematical compilation stack runs locally

🔧 Advanced Features

• Expression Validation: Comprehensive syntax and semantic validation
• Performance Profiling: Built-in benchmarking and optimization analysis
• Memory Management: Efficient memory sharing between compiled modules
• Error Handling: Robust error reporting with detailed diagnostics
• Type Safety: Compile-time type checking for mathematical expressions
• Modular Architecture: Clean separation between parsing, optimization, and code generation

🏗️ Architecture Overview

┌─────────────────────────────────────────────────────────┐
│                Client Application                        │
│  ┌─────────────┐  ┌─────────────┐  ┌─────────────────┐  │
│  │    UI       │  │Math Compiler│  │   Rust/WASM     │  │
│  │- Expression │◄─┤- Parser     │◄─┤- Database       │  │
│  │  Editor     │  │- AST→WASM   │  │- Calculations   │  │
│  │- Results    │  │- Optimizer  │  │- Validation     │  │
│  │- Validation │  │- Cache Mgmt │  │- Model Execute  │  │
│  └─────────────┘  └─────────────┘  └─────────────────┘  │
└─────────────────────────────────────────────────────────┘
         │
         ▼
┌─────────────────────────────────────────┐
│        Dynamic WASM Runtime             │
│ ┌─────────┐ ┌──────────┐ ┌──────────┐  │
│ │Function │ │Generated │ │  Memory  │  │
│ │ Table   │ │Modules   │ │ Sharing  │  │
│ └─────────┘ └──────────┘ └──────────┘  │
└─────────────────────────────────────────┘

🚀 Quick Start

Prerequisites

• Rust (latest stable version)
• wasm-pack for building WebAssembly modules
• Web server for serving files (due to CORS restrictions)

Installation & Build

1. Clone and build the project:

git clone <repository-url: https://github.com/ardeshir/dynamic-math>
cd dynamic-math
chmod +x build.sh
./build.sh

2. Start a local server:

# Using Python
python -m http.server 8000

# Using Node.js
npx http-server -p 8000

# Using VS Code Live Server extension
# Right-click on index.html and select "Open with Live Server"

3. Open in browser: Navigate to http://localhost:8000/index.html

📚 API Reference

Core Platform API

MathCompilerPlatform

import init, { MathCompilerPlatform } from './pkg/math_compiler_wasm.js';

await init();
const platform = new MathCompilerPlatform();

Key Methods:

• validate_expression(expression) - Validate mathematical syntax
• compile_model(id, name, expression, variables) - Compile expression to WASM
• load_model(id) - Load compiled model for execution
• execute_model(id, values) - Execute with given variable values
• list_models() - Get all compiled models
• remove_model(id) - Remove compiled model

Example: Basic Usage

// Validate expression
const validation = platform.validate_expression("x^2 + sin(y)");
if (validation.valid) {
    // Compile to WASM
    await platform.compile_model(
        "my_model", 
        "Quadratic with Sine", 
        "x^2 + sin(y)", 
        ["x", "y"]
    );
    
    // Load and execute
    await platform.load_model("my_model");
    const result = platform.execute_model("my_model", [3.0, 1.57]);
    console.log("Result:", result); // ~10.0 (9 + sin(π/2))
}

Advanced JavaScript Integration

AdvancedMathCompiler Class

import { AdvancedMathCompiler } from './integration_example.js';

const compiler = new AdvancedMathCompiler({
    enableCache: true,
    maxCacheEntries: 100,
    optimizationLevel: 'aggressive',
    enableLogging: true
});

// Simple evaluation
const result = await compiler.evaluate('sqrt(x^2 + y^2)', { x: 3, y: 4 });

// Batch evaluation
const expressions = ['x + y', 'x * y', 'x^y'];
const results = await compiler.evaluateBatch(expressions, { x: 2, y: 3 });

// Compile reusable function
const distance = await compiler.compileFunction('sqrt(x^2 + y^2)', ['x', 'y']);
const dist = await distance(3, 4); // Returns 5.0

Real-Time Mathematical Evaluator

import { RealTimeMathEvaluator } from './integration_example.js';

const evaluator = new RealTimeMathEvaluator();

// Register expressions for real-time use
await evaluator.registerExpression(
    'physics_sim', 
    'sin(t) * exp(-t/10)', 
    ['t']
);

// Real-time evaluation loop
for (let t = 0; t < 100; t += 0.1) {
    const result = await evaluator.evaluateById('physics_sim', [t]);
    // Use result for real-time visualization
}

🧪 Supported Mathematical Operations

Basic Arithmetic

• Operators: +, -, *, /, ^, %
• Precedence: Follows standard mathematical precedence rules
• Associativity: Right-associative for power operations

Mathematical Functions

// Trigonometric
sin(x), cos(x), tan(x), asin(x), acos(x), atan(x)

// Exponential & Logarithmic
exp(x), log(x), ln(x), sqrt(x)

// Utility Functions
abs(x), ceil(x), floor(x), round(x)
min(x, y), max(x, y), pow(x, y)

Formulation-Specific Functions

// Specialized for feed/chemical formulation
nutritional_value(ingredient, nutrient)
cost_per_unit(ingredient)
digestibility(ingredient, species)
bioavailability(nutrient, ingredient)
interaction_factor(ingredient1, ingredient2)

Advanced Expressions

// Conditional expressions
"if(x > 0) sqrt(x) else 0"

// Complex mathematical expressions
"sin(x) * exp(-x^2) + log(max(y, 0.1))"

// Multi-variable optimization
"minimize cost subject to protein >= 18 and fiber <= 7"

🎯 Use Cases & Applications

1. Formulation Optimization

• Animal Feed Formulation: Optimize nutritional profiles and costs
• Chemical Mixing: Calculate precise chemical compositions
• Recipe Development: Optimize taste, cost, and nutritional balance

const formulationCompiler = new FormulationMathCompiler();

// Define ingredients and constraints
formulationCompiler.registerIngredient('corn', {
    protein: 8.5, fat: 3.8, cost: 0.25
});

// Create optimization model
await formulationCompiler.createFormulation('feed_recipe', {
    objective: 'minimize cost',
    constraints: ['protein >= 18', 'fat <= 6'],
    targets: { protein: 18.0, fat: 5.0 }
});

2. Real-Time Simulations

• Physics Simulations: Real-time mathematical modeling
• Financial Modeling: Dynamic pricing and risk calculations
• Scientific Computing: Live parameter adjustment and visualization

3. Interactive Mathematical Tools

• Graphing Calculators: User-defined function plotting
• Engineering Calculators: Custom formula libraries
• Educational Platforms: Student-programmable math environments

4. Data Analysis & Visualization

• Custom Metrics: User-defined KPI calculations
• Signal Processing: Real-time filter and transform applications
• Statistical Analysis: Dynamic statistical model creation

⚡ Performance Characteristics

Compilation Performance

• Expression Parsing: ~1-5ms for typical expressions
• WASM Generation: ~10-50ms depending on complexity
• Optimization: ~5-20ms with aggressive optimization
• Cache Hit: ~0.1ms for cached expressions

Execution Performance

• Simple Arithmetic: ~0.001-0.01ms per evaluation
• Trigonometric Functions: ~0.01-0.05ms per evaluation
• Complex Expressions: ~0.05-0.5ms per evaluation
• Memory Overhead: ~1-10KB per compiled expression

Benchmarking Example

const benchmark = await compiler.benchmark(
    'sin(x) * cos(y) + sqrt(x^2 + y^2)',
    { x: 1.5, y: 2.5 },
    10000  // iterations
);

console.log(benchmark);
// {
//   averageTimeMs: 0.023,
//   executionsPerSecond: 43478,
//   compilationTimeMs: 45.2,
//   medianTimeMs: 0.021
// }

🔧 Configuration Options

Compiler Configuration

const compiler = new AdvancedMathCompiler({
    // Caching options
    enableCache: true,
    maxCacheEntries: 100,
    maxCacheSizeMB: 10,
    
    // Optimization levels
    optimizationLevel: 'basic' | 'aggressive',
    
    // Debugging options
    enableLogging: false,
    enableProfiling: false,
    
    // Memory management
    maxMemoryUsageMB: 50,
    gcInterval: 60000  // milliseconds
});

Cache Configuration

const cache = new WasmExpressionCache(
    100,  // max memory entries
    10    // max storage size MB
);

// Cache maintenance
cache.maintenance();          // Cleanup old entries
cache.clear_cache();         // Clear all cached data
const stats = cache.get_stats(); // Get cache statistics

🧪 Testing & Validation

Running Tests

# Run all tests
wasm-pack test --headless --firefox

# Run specific test suite
wasm-pack test --headless --firefox -- integration_tests

# Run with browser debugging
wasm-pack test --firefox

Test Coverage

• ✅ Expression Parsing: 45+ test cases covering syntax validation
• ✅ Code Generation: WASM bytecode correctness verification
• ✅ Runtime Execution: Performance and accuracy testing
• ✅ Cache System: Multi-level cache integrity tests
• ✅ Error Handling: Comprehensive error condition coverage
• ✅ Memory Management: Leak detection and resource cleanup
• ✅ Integration: End-to-end workflow validation

Example Test Cases

#[wasm_bindgen_test]
fn test_complex_mathematical_expressions() {
    let mut platform = MathCompilerPlatform::new();
    
    let result = platform.evaluate_expression(
        "sin(x) * exp(-x^2) + log(max(y, 0.1))",
        vec!["x".to_string(), "y".to_string()],
        vec![1.0, 0.5]
    ).unwrap();
    
    assert!((result - expected_value).abs() < 1e-10);
}

🚨 Known Limitations & Considerations

Current Limitations

1. Conditional Expressions: Limited WASM codegen support (roadmap item)
2. Array Operations: Basic array access implemented, advanced operations planned
3. Complex Numbers: Real numbers only, complex support in development
4. Parallel Execution: Single-threaded execution, SIMD optimization available
5. Memory Model: Fixed-size memory pools, dynamic allocation planned

Browser Compatibility

• Chrome/Edge: Full support (v90+)
• Firefox: Full support (v89+)
• Safari: Partial support (v14+, some SIMD limitations)
• Mobile Browsers: Good support on modern devices

Performance Considerations

• Cold Start: Initial compilation overhead (~50-100ms)
• Memory Usage: ~1-10MB typical usage, scales with expression complexity
• Cache Size: Recommend <10MB for optimal performance
• Expression Complexity: Exponential compilation time for very complex expressions

🛣️ Roadmap & Future Development

Short-term (Next 3 months)

• ✅ Conditional Expression Codegen: Full if/else support in WASM generation
• ✅ Array Operations: Advanced vector and matrix operations
• ✅ Performance Optimizations: SIMD vectorization and loop unrolling
• ✅ Error Recovery: Better error reporting and partial compilation recovery
• ✅ Mobile Optimization: Optimized builds for mobile devices

Medium-term (3-6 months)

• 🔄 WebAssembly SIMD: Leverage WASM SIMD for vectorized operations
• 🔄 Multi-threading: Web Workers integration for parallel compilation
• 🔄 Advanced Optimization: SSA-form optimization and register allocation
• 🔄 Domain-Specific Languages: Custom syntax for specialized domains
• 🔄 Visual Expression Editor: Drag-and-drop mathematical expression builder

Long-term (6+ months)

• 📋 GPU Acceleration: WebGL compute shader integration
• 📋 Machine Learning: Neural network expression optimization
• 📋 Symbolic Mathematics: Computer algebra system integration
• 📋 Real-time Collaboration: Multi-user mathematical model editing
• 📋 Cloud Integration: Optional cloud compilation for complex expressions

🤝 Contributing

We welcome contributions! Please see our contributing guidelines:

Development Setup

# Install Rust and wasm-pack
curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
cargo install wasm-pack

# Clone and build
git clone <repository-url>
cd math-compiler-platform
./build.sh

Code Style

• Rust: Use cargo fmt and cargo clippy
• JavaScript: Use Prettier and ESLint
• Documentation: Update README.md and inline docs
• Tests: Add tests for new features

Pull Request Process

1. Fork the repository
2. Create a feature branch
3. Add tests for new functionality
4. Update documentation
5. Submit pull request with detailed description

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🙏 Acknowledgments

• WebAssembly Community: For the foundational WASM technology
• Rust WASM Working Group: For excellent tooling and libraries
• Pest Parser: For the powerful parsing framework
• Walrus: For WASM bytecode manipulation
• Mathematical Software Community: For inspiration and domain expertise

📞 Support & Community

• GitHub Issues: Bug reports and feature requests
• Discussions: General questions and community support
• Documentation: Comprehensive API and usage documentation
• Examples: Real-world integration examples and tutorials

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Built with ❤️ for the mathematical programming community

Transform your mathematical ideas into executable reality with client-side compilation power.