E. Gallopoulos, B. Philippe, and A. H. Sameh, Parallelism in matrix computations, Scien- tific Computation, Springer, Dordrecht, 2016.E. Gallopoulos, B. Philippe, A. H. Sameh, Parallelism in Matrix Com- putations, Springer, Dordrecht, 2016....
many of the registers keep different values in different threads. In many cases register replication is not a waste at all – any processor would have to keep those values somewhere. So functionally, the plentiful GPU registers can
It is true that the GPU is used for matrix multiplications with batch sizes >= 32 anyways. But for those matrix multiplications most of the runtime goes towards CPU<->GPU data transfers which can be executed in parallel with GPU computations. So it should still help quite a lot. This was...
Although auto-parallelization has been studied for many decades, it has succeeded only in a few application areas such as dense matrix computations. In particular, auto-parallelization of irregular programs, which are organized around large, pointer-based data structures like graphs, has seemed ...
Halo exchange enables each task to perform computations and update the subset of data mapped to that task while having access to any data necessary for such computations that may not be local. • Sparse matrix calculations exploit arrays (e.g., vectors) that are mostly populated with elements...
So an IVar lets you communicate values between parallel Par computations, because you can put a value in the box in one place and get it in another. Once filled, the box stays full; the get operation doesn’t remove the value from the box. It is an error to call put more than once...
Sign in to download full-size image Figure 3.11. Illustration of the _mm256_fmadd_ps(AV,BV,X) intrinsic used in the inner loop of Listing 3.2. Actual execution of our program on an Intel i7-6800K CPU using the matrix dimensions m=1024,l=2048,n=4096 produces the following runtimes: ...
In the remainder of this section, we outline the basic components of AMG in an aggregation context [37] and highlight the necessary sparse matrix computations used in the process. We restrict our attention to aggregation methods because of the flexibility in the construction, however our ...
If we look at the computation in matrix form, it's easy to see how the matrix multiplication can be split between multiple GPUs: If we split the weight matrixAcolumn-wise acrossNGPUs and perform matrix multiplicationsXA_1throughXA_nin parallel, then we will end up withNoutput vectorsY_1,...
The scope of our algorithm is dense matrix computations where the array accesses are affine functions of the loop indices. Our algorithm can handle programs with general nestings of parallel and sequential l oops. We present a mathematical framework that enables us to sys- tematically derive the ...