This project involves the design, implementation, and execution of a CUDA-based program to analyze the 2-point angular correlation function of galaxies. The objective is to determine if the observed distribution of galaxies statistically differs from a random distribution by comparing histograms of galaxy pair angles.

The project includes the following CUDA source files:

1. galaxy_shared_mem.cu: Implements the galaxy distribution analysis using shared memory for optimization.
2. galaxy_no_cache.cu: Implements the analysis without utilizing cache for memory optimization.
3. galaxy_manual.cu: A manual approach to analyzing the galaxy distribution without specific memory optimization techniques.
4. template.cu: A template file setting up the basic environment and defining common functions for the analysis.

• NVIDIA CUDA toolkit
• A GPU-enabled machine
• Access to the real and synthetic galaxy data (available on Moodle)

To compile and run the CUDA programs, use the following commands:

nvcc galaxy_shared_mem.cu -o galaxy_shared_mem
./galaxy_shared_mem real.dat synthetic.dat output.dat

nvcc galaxy_no_cache.cu -o galaxy_no_cache
./galaxy_no_cache real.dat synthetic.dat output.dat

nvcc galaxy_manual.cu -o galaxy_manual
./galaxy_manual real.dat synthetic.dat output.dat

The input consists of two lists of 100,000 galaxy locations: real measured galaxies and synthetic evenly distributed random galaxies. Each list contains the galactic coordinates in the following order:

• Right Ascension (a): in arc minutes
• Declination (d): in arc minutes

These coordinates should be converted to radians by multiplying with $\frac{\pi}{10800} $.

The main task is to compute three histograms representing the 2-point angular correlation function:

• DD: Histogram of angles between pairs of real galaxies.
• DR: Histogram of angles between pairs of real and random galaxies.
• RR: Histogram of angles between pairs of random galaxies.

These histograms cover angles from 0 to 180 degrees with a bin width of 0.25 degrees.

To calculate the angle $( \theta_{12} )$ between two points on a sphere, use the formula:

$$\theta_{12} = \arccos(\sin(d1)\sin(d2) + \cos(d1)\cos(d2)\cos(a1 - a2)) $$

Where:

• $( a )$ is the right ascension converted to radians
• $( d )$ is the declination converted to radians

The scientific measure to determine differences between the distributions is:

$$ w_i(\theta) = \frac{DD_i - 2DR_i + RR_i}{RR_i} $$

Where $DDi, DRi, RRi$ are the values in histogram bin $i$.

If $w_i$ values are close to zero (in the range [-0.5, 0.5]), the distribution of real galaxies is approximately random. If $w_i$ values are significantly different from zero, the distribution is non-random.

• Design threads and thread blocks to efficiently compute pairwise angles.
• Experiment with thread block sizes and workload distribution.
• Synchronize threads as needed and consider atomic operations for histogram updates.

• Compute and store the histograms DD, DR, and RR.
• Plot the histograms to visualize the differences between distributions.
• Compute and analyze the $w_i(\theta)$ values.