Puzzle 4: 2D Map

Overview

Implement a kernel that adds 10 to each position of 2D square matrix a and stores it in 2D square matrix output.

Note: You have more threads than positions.

2D Matrix Mapping

Key concepts

  • 2D thread indexing
  • Matrix operations on GPU
  • Handling excess threads
  • Memory layout patterns

For each position \((i,j)\): \[\Large output[i,j] = a[i,j] + 10\]

Thread indexing convention

When working with 2D matrices in GPU programming, we follow a natural mapping between thread indices and matrix coordinates:

  • thread_idx.y corresponds to the row index
  • thread_idx.x corresponds to the column index

2D thread indexing

This convention aligns with:

  1. The standard mathematical notation where matrix positions are specified as (row, column)
  2. The visual representation of matrices where rows go top-to-bottom (y-axis) and columns go left-to-right (x-axis)
  3. Common GPU programming patterns where thread blocks are organized in a 2D grid matching the matrix structure

Historical origins

While graphics and image processing typically use \((x,y)\) coordinates, matrix operations in computing have historically used (row, column) indexing. This comes from how early computers stored and processed 2D data: line by line, top to bottom, with each line read left to right. This row-major memory layout proved efficient for both CPUs and GPUs, as it matches how they access memory sequentially. When GPU programming adopted thread blocks for parallel processing, it was natural to map thread_idx.y to rows and thread_idx.x to columns, maintaining consistency with established matrix indexing conventions.

Implementation approaches

🔰 Raw memory approach

Learn how 2D indexing works with manual memory management.

📚 Learn about LayoutTensor

Discover a powerful abstraction that simplifies multi-dimensional array operations and memory management on GPU.

🚀 Modern 2D operations

Put LayoutTensor into practice with natural 2D indexing and automatic bounds checking.

💡 Note: From this puzzle onward, we’ll primarily use LayoutTensor for cleaner, safer GPU code.