CUDA Thread Indexing

When I was learning CUDA programming, I was initially stuck on thread indexing. So I thought to write this blog post to help novices in CUDA programming to understand thread indexing easily. I hope you have the knowledge of CUDA architecture before reading this.

First I’ll introduce the basic terminology in CUDA programming and variables we need to know for thread indexing.

Kernel — GPU function

Grid Architecture

Grid — A kernel (GPU function) is launched as a collection of thread blocks called Grid. A grid is composed of thread blocks.

Grid size is defined using the number of blocks. For example Grid of size 6 contains 6 thread blocks. If the grid is 1D →all 6 blocks are in one dimension (eg: 1x6). If the grid is 2D →6 blocks are in two dimensions (eg: 3x2)

Block — A collection of threads.

Thread — Single execution unit that runs GPU function (kernel) on GPU.

Variables:

I’ll define the variables by giving examples from the following diagram.

Number of blocks in the grid:

gridDim.x — number of blocks in the x dimension of the grid (eg: 3)

gridDim.y — number of blocks in the y dimension of the grid (eg:2)

Number of threads in a block:

blockDim.x — number of threads in the x dimension of the block (eg:4)

blockDim.y — number of threads in the y dimension of the block (eg:3)

Block Index:

blockIdx.x — block’s index in x dimension

blockIdx.y — block’s index in y dimension

eg: block (0,1) — blockIdx.x = 0 , blockIdx.y = 1

Thread Index:

ThreadIdx.x — thread’s index in x dimension

ThreadIdx.y — thread’s index in y dimension

eg: Thread(2,1) — ThreadIdx.x = 2, ThreadIdx.y = 1

Now we can head into the thread indexing. We have to do thread indexing using the above explained variables. By thread indexing we are getting a unique number for each thread and each block in a grid.

1D grid of 1D blocks

Indices given in RED color are the unique numbers for each block and each thread

threadId = (blockIdx.x * blockDim.x) + threadIdx.x

Let’s check the equation for Thread (2,0) in Block (1,0).

Thread ID = (1 * 3) + 2 =3+2 = 5

1D grid of 2D blocks

Here we have various ways for indexing. I’ll show you two methods.

Indices given in RED color are the unique numbers for each block and each thread

threadId = (blockIdx.x * blockDim.x * blockDim.y) + (threadIdx.y * blockDim.x) + threadIdx.x

Let’s check the equation for Thread (2,1) in Block (1,0).

Thread ID = (1*3*2)+(1*3)+2 = 6+3+2 =11

Here (1*3*2) → count threads in block 0

(1*3) →count thread(0,0),(1,0) and (2,0) in block 1

Then add the threadIdx.x of the particular thread.

Here is the second method.

Indices given in RED color are the unique numbers for each block and each thread

threadId = (gridDim.x * blockDim.x * threadIdx.y) + (blockDim.x * blockIdx.x) + threadIdx.x

Let’s check the equation for Thread (2,1) in Block (1,0).

Thread ID = (4 * 3 * 1) +(1 * 3)+2 = 12+3+2 =17

Here (4*3*1) → count thread(0,0),(1,0) and (2,0) in block 0,1,2 and 3

(1*3) →count thread(0,1),(1,1) and (2,1) in block 0

Then add the threadIdx.x of the particular thread.

2D grid of 1D blocks

Indices given in RED color are the unique numbers for each block and each thread

blockId = (gridDim.x * blockIdx.y) + blockIdx.x

threadId = (blockId * blockDim.x) + threadIdx.x

Let’s check the equation for Thread (1,0) in Block (1,1).

blockId = (2*1) + 1 =2+1=3

threadID = (3*3)+1 =9+1=10

2D grid of 2D blocks

Indices given in RED color are the unique numbers for each block and each thread

blockId = (gridDim.x * blockIdx.y) + blockIdx.x

threadId = (blockId * (blockDim.x * blockDim.y)) + (threadIdx.y * blockDim.x) + threadIdx.x

Let’s check the equation for Thread (2,1) in Block (0,1).

block Id = (2 * 1) + 0 = 2

Thread Id = (2 * (3 * 2))+(1*3) + 2 = 12+3+2 = 17

Done ✅ I hope now you can construct the thread indexing equation for 1D grid of 3D blocks, 2D grid of 3D blocks by your own.

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