# Parallel Programming with NVIDIA CUDA

Let's develop a sequential version of a vector field calculation algorithm. The input stream is a list of attractors and a list of repulsors, as shown in Figure 2 and without obstacles (Figure 4). The output stream is a matrix called field. The attractors and repulsors are lists of 2-D points that indicate their positions.

A “field” matrix will hold your vector field data structure. Each element field[y][x] will hold a 2-D vector indicating where the robot should move toward when standing at point (x, y). This vector will be the sum of vectors associated with each attractor and repulsor (Figure 5).

When processing each attractor, the associated vector will be pointing from the current point (x, y) toward the attractor's position. When processing each repulsor, the associated vector will be pointing away from the repulsor's position. Note that the plus and minus operators are performing vector addition and subtraction. Sequential pseudo-code:

In Parameters: a list of attractors, a list of repulsors Out Parameters: a zero-initialized vector field calculate_vector_field_cpu(in attractors, in repulsors, out field): for (y = 0 to height): for (x = 0 to width): for (attractor in attractors): vector = attractor - point(x,y) field[y][x] = field[y][x] + vector for (repulsor in repulsors): vector = point(x,y) - repulsor if norm(vector) <= 2: field[y][x] = field[y][x] + vector return

Okay, so the sequential pseudo-code is ready. Now, let's partition the problem in order to use most of the processing cores on the GPU.

The calculation of each vector field element is independent from the calculation of the other elements. You can leverage this property to parallelize your algorithm. You can calculate each element of the vector field matrix in its own thread, effectively dividing the problem into smaller pieces.

Don't worry about the number of threads. Spawning as many threads as possible when developing CUDA algorithms is encouraged by NVIDIA. It will allow the algorithms to scale across several generations of devices, automatically increasing throughput, as NVIDIA adds more and more processing cores to its video cards.

With this in mind, let's develop a parallel version of our previous algorithm. Parallel pseudo-code:

In Parameters: list of attractors, list of repulsors Out Parameters: a zero-initialized vector field calculate_vector_field_gpu(in attractors, in repulsors, out field): x = blockIdx.x * BLOCK_SIZE + threadIdx.x y = blockIdx.y * BLOCK_SIZE + threadIdx.y for (attractor in attractors): vector = attractor - point(x,y) field[y][x] = field[y][x] + vector for (repulsor in repulsors): vector = point(x,y) - repulsor if norm(vector) <= 2:4444444444 field[y][x] = field[y][x] + vector return

Notice I did away with both external for loops, and the points (x, y) are now calculated using a parallel statement.

The new pseudo-code is implemented as a kernel. A kernel is a function that executes on several GPU cores at the same time. Kernels are launched by a host program controlled from the regular CPU that configures the execution environment and supplies the parameters.

How does each thread know what position of the vector field it has to compute? This is where the blockIdx and threadIdx built-in CUDA variables come into place.

As you look at this code, it may not be obvious how this is a parallel implementation, but it's the blockIdx and threadIdx and the CUDA magic associated with them that makes it parallel. When the function is invoked, it actually is invoked multiple times using multiple threads, each thread calculating one part of the result (see the next section).

When the host code sets up an execution environment, it has to determine how the processing cores will be assigned work. As part of its duties, the host must determine how threads will be arranged logically. CUDA allows developers to arrange their threads in a 1-D, 2-D or 3-D structure. It helps developers express design in a natural manner.

Think about the example algorithm. Let's use the GPU to fill a 2-D matrix with data. It would be very convenient if you somehow could assign each thread a “position” in a two-coordinate system, because each thread could use its assigned coordinates to decide which element to compute.

CUDA provides a mechanism through which developers can specify how they want their threads arranged. The compiler takes care of the rest. This feature is available through what is known as a grid of thread blocks. In this example, the host will use a 2-D grid.

You probably are wondering, why a “grid of thread blocks” instead of a “grid of threads”?

Threads do not exist inside grids by themselves, but rather, they are arranged into thread blocks. Each thread is assigned an identifier within its block. Each block, in turn, is assigned an identifier within the grid. The built-in blockIdx and threadIdx variables help determine the current thread and block identifiers. From within a kernel, these identifiers can be seen simply as a C structure containing the thread's x, y and z coordinates.

Using this mechanism, you can have each thread calculate a global thread ID and calculate the x and y variables in your parallel pseudo-code. The pair (x, y) determines which element of the matrix has to be computed. Because each thread will have different values for (x, y), every point of the matrix could, in theory, be computed at the same time if you have enough threads.

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## Comments

## The statement minima[y][x] =

The statement

minima[y][x] = (norm(field[y][x]) < threshold) ? true : false

may incur branching penalty

You can just use the first part

minima[y][x] = (norm(field[y][x]) < threshold)