How do I plan this least-squares computation on a GPU? - opencl

Question

I'm writing a program called PerfectTIN (https://github.com/phma/perfecttin) which does lots of least-squares adjustments of a TIN to fit a point cloud. Each adjustment takes some contiguous group of triangles and adjusts the elevations of up to 8 points, which are corners of the triangles, to fit the dots in the triangles. I have it working on SMP. At the start of processing, it does only one adjustment at a time, so it splits the adjustment into tasks, each of which takes some dots, all of which are in the same triangle. Each thread takes a task from a queue and computes a small square matrix and a small column vector. When they're all ready, the adjustment routine adds up the matrices and the vectors and finishes the least squares computation.
I'd like to process tasks on the GPU as well as the CPU. The data needed for a task are
The three corners of the triangle (x,y,z)
The coordinates of the dots (x,y,z).
The output data are
A symmetric matrix with up to nine nonzero entries (since it's symmetric, I need only compute six numbers)
A column vector with the same number of rows.
The number of dots is a multiple of 1024, except for a few tasks which I can handle in the CPU (the total number of dots in a triangle can be any nonnegative integer). For a fairly large point cloud of 56 million dots, some tasks are larger than 131072 dots.
Here is part of the output of clinfo (if you need other parts, let me know):
Platform Name Clover
Number of devices 1
Device Name Radeon RX 590 Series (POLARIS10, DRM 3.33.0, 5.3.0-7625-generic, LLVM 9.0.0)
Device Vendor AMD
Device Vendor ID 0x1002
Device Version OpenCL 1.1 Mesa 19.2.8
Driver Version 19.2.8
Device OpenCL C Version OpenCL C 1.1
Device Type GPU
Device Profile FULL_PROFILE
Device Available Yes
Compiler Available Yes
Max compute units 36
Max clock frequency 1545MHz
Max work item dimensions 3
Max work item sizes 256x256x256
Max work group size 256
Preferred work group size multiple 64
Preferred / native vector sizes
char 16 / 16
short 8 / 8
int 4 / 4
long 2 / 2
half 8 / 8 (cl_khr_fp16)
float 4 / 4
double 2 / 2 (cl_khr_fp64)
Double-precision Floating-point support (cl_khr_fp64)
Denormals Yes
Infinity and NANs Yes
Round to nearest Yes
Round to zero Yes
Round to infinity Yes
IEEE754-2008 fused multiply-add Yes
Support is emulated in software No
If I understand right, if I put one dot in each core of the GPU, the total number of dots I can process at once is 36×256=9×1024=9216. Could I put four dots in each core, since a work group would then have 1024 dots? In this case I could process 36864 dots at once. How many dots should each core process? What if a task is bigger than the GPU can hold? What if several tasks (possibly from different triangles) fit in the GPU?
Of course I want this code to run on other GPUs than mine. I'm going to use OpenCL for portability. What different GPUs (description rather than name) am I going to encounter?

Answer 1

If I understand right, if I put one dot in each core of the GPU, the total number of dots I can process at once is 36×256=9×1024=9216.
Not quite. The total number of dots is not limited by the maximum work group size. The work group size is the number of GPU threads working synchronously in a group. Within a work group, you can share data via local memory, which can be useful to speed up certain calculations like matrix multiplications for example (cache tiling).
The idea of GPU parallelization is to split the prioblem up into as many independent parts as there are. In C++ something like
void example(float* data, const int N) {
for(int n=0; n<N; n++) {
data[n] += 1.0f;
}
}
in OpenCL becomes this
kernel void example(global float* data ) {
const int n = get_global_id(0) ;
data[n] += 1.0f;
}
where the global range of the kernel is set to N.
Each GPU thread should process only a single dot. The number of threads (global range) can and should be much larger than the number of GPU cores available. If you don't explicitly need local memory (all threads can work independent), you can set the local work group size to either 32, 64, 128 or 256 - it doesn't matter - but there might be some performance difference between these values. However the global range (total number of threads / points) must be a multiple of the work group size.
What if a task is bigger than the GPU can hold?
I assume you mean when your data set does not fit into video memory all at once. In this case you can do the computation in several batches, so exchange the GPU buffers using PCIe transfers. But that comes at a large performance penalty.
Of course I want this code to run on other GPUs than mine. I'm going to use OpenCL for portability. What different GPUs (description rather than name) am I going to encounter?
OpenCL is excellent for portability across devices and operating systems. Other than AMD GPUs and CPUs, you will encounter Nvidia GPUs, which only support OpenCL 1.2, and Intel GPUs and CPUs. If the graphics drivers are installed, your code will run on all of them without issues. Just be aware that the amount of video memory can be vastly different.