# Thread Hierarchy in CUDA Programming

__Basic of CUDA Programming: Part 6__

__Thread Hierarchy in CUDA Programming__For convenience, threadIdx is a 3-component vector, so that threads can be identified using a one-dimensional, two-dimensional, or three-dimensional thread index, forming a one-dimensional, two-dimensional, or three-dimensional thread block. This provides a natural way to invoke computation across the elements in a domain such as a vector, matrix, or volume.

The index of a thread and its thread ID relate to each other in a straightforward way: For a one-dimensional block, they are the same; for a two-dimensional block of size (Dx, Dy), the thread ID of a thread of index (x, y) is (x + y Dx); for a three-dimensional block of size (Dx, Dy, Dz), the thread ID of a thread of index (x, y, z) is (x + y Dx + z Dx Dy).

As an example, the following code adds two matrices A and B of size NxN and stores the result into matrix C:

// Kernel definition

__global__ void MatAdd(float A[N][N], float B[N][N], float C[N][N])

{

int i = threadIdx.x;

int j = threadIdx.y;

C[i][j] = A[i][j] + B[i][j];

}

int main()

{

... // Kernel invocation with one block of N * N * 1 threads

int numBlocks = 1;

dim3 threadsPerBlock(N, N);

MatAdd<<<numBlocks, threadsPerBlock>>>(A, B, C);

...

}

There is a limit to the number of threads per block (Know about this limit, click here), since all threads of a block are expected to reside on the same processor core and must share the limited memory resources of that core. On current GPUs, a thread block may contain up to 1024 threads.

However, a kernel can be executed by multiple equally-shaped thread blocks, so that the total number of threads is equal to the number of threads per block times the number of blocks.

Blocks are organized into a one-dimensional, two-dimensional, or three-dimensional grid of thread blocks as illustrated by

**Figures**The number of thread blocks in a grid is usually dictated by the size of the data being processed or the number of processors in the system, which it can greatly exceed.

The number of threads per block and the number of blocks per grid specified in the <<<…>>> syntax can be of type int or dim3. Two-dimensional blocks or grids can be specified as in the example above.

Each block within the grid can be identified by a one-dimensional, two-dimensional, or three-dimensional index accessible within the kernel through the built-in blockIdx variable. The dimension of the thread block is accessible within the kernel through the built-in blockDim variable.

Extending the previous MatAdd() example to handle multiple blocks, the code becomes as follows.

// Kernel definition

__global__ void MatAdd(float A[N][N], float B[N][N], float C[N][N])

{

**int i = blockIdx.x * blockDim.x + threadIdx.x;**

**int j = blockIdx.y * blockDim.y + threadIdx.y;**

if (i < N && j < N)

C[i][j] = A[i][j] + B[i][j];

}

int main()

{

...

// Kernel invocation

**dim3 threadsPerBlock(16, 16);**

**dim3 numBlocks(N / threadsPerBlock.x, N / threadsPerBlock.y);**

MatAdd<<<numBlocks, threadsPerBlock>>>(A, B, C);

...

}

A thread block size of 16x16 (256 threads), although arbitrary in this case, is a common choice. The grid is created with enough blocks to have one thread per matrix element as before. For simplicity, this example assumes that the number of threads per grid in each dimension is evenly divisible by the number of threads per block in that dimension, although that need not be the case.

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References

CUDA C Programming Guide

CUDA; Nvidia

Wikipedia

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