Algorithmic Differentiation of Pragma-Defined Parallel by Michael Förster

By Michael Förster

Numerical courses usually use parallel programming concepts comparable to OpenMP to compute the program's output values as effective as attainable. moreover, spinoff values of those output values with admire to convinced enter values play an important position. to accomplish code that computes not just the output values concurrently but in addition the spinoff values, this paintings introduces numerous source-to-source transformation principles. those ideas are in line with a strategy referred to as algorithmic differentiation. the focus of this paintings lies at the very important opposite mode of algorithmic differentiation. The inherent data-flow reversal of the opposite mode has to be dealt with effectively in the course of the transformation. the 1st a part of the paintings examines the adjustments in a really basic means on the grounds that pragma-based parallel areas take place in lots of other forms reminiscent of OpenMP, OpenACC, and Intel Phi. the second one half describes the transformation ideas of crucial OpenMP constructs.

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The most important construct is the parallel construct which starts the parallel execution. The parallel construct is associated with a sequence of statements that is executed by a team of threads. Each thread in this team has an unique identifier number starting with zero. The thread with the identifier zero is called master or initial thread. Unless otherwise specified, we assume the size of the group of threads to be p. parallel Construct In order to be a close as possible to the description in the standard, we cite the description in the standard instead of repeating in other words.

2 Algorithmic Differentiation 27 For this small example, the gradient of the objective function f (x) and the Jacobian of the constraints g(x) can be deduced by symbolic differentiation. Nevertheless, as we saw in the previous section, it is often the case that the constrained optimization problem consists of many independent equations and all these equations must be differentiated. The symbolic differentiation approach is therefore often not applicable due to the size of the implementation of the objective function.

Example 6. (Implicit data decomposition) This example illustrates the usage of the loop construct of OpenMP. The code implements the same computation as the code from Example 4, or in other words the code from Example 4 and the current code are semantically equivalent. The difference is that in the current implementation the data decomposition is done implicitly by code that is generated by the OpenMP enabled compiler. This means that the data decomposition is handled by the OpenMP runtime system.

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