CUDA-accelerated 2D Monte Carlo integration with automatic mixed-precision optimization.

• GPU Acceleration with CUDA batch processing
• Mixed Precision: Automatic float/double/long double selection
• Multiple Strategies: Term-wise and region-wise decomposition
• CPU Comparison: OpenMP parallel implementation
• Expression Parser: Supports +, -, *, /, ^, sin, cos, log, ln, exp, sqrt

• CUDA Toolkit (10.0+)
• NVIDIA GPU (compute capability 3.5+)
• G++ with C++17 support
• OpenMP

make

./mci

Input Example:

Expression: x*y + sin(x) + cos(y) x-range [a b]: 0 3.14159 y-range [c d]: 0 3.14159 Total samples: 10000000 

The framework automatically selects optimal precision for each term/region based on:

• Function variance
• Gradient magnitude
• Numerical stability
• Error tolerance (default: 1e-5)

Precision Selection:

• Float: Fast, suitable for smooth functions (~4x faster than double)
• Double: Default for moderate complexity
• Long Double: High precision (CPU only)

The program runs multiple integration strategies:

1. GPU Float Precision
2. GPU Double Precision
3. GPU Mixed Precision (term-wise)
4. GPU Mixed Precision (region-wise)
5. CPU comparisons

Each outputs timing breakdown and integration results.

For function f(x,y) over [a,b] × [c,d]:

Integral ≈ (b-a)(d-c) × (1/N) × Σf(xi, yi) 

Change tolerance:

input.tolerance = 1e-5; // in main()

Adjust OpenMP threads:

omp_set_num_threads(6); // default is 6

• Ferhat Onur Özgan
• Berke Kabasakal