By Michael Förster
Numerical courses frequently use parallel programming thoughts akin to OpenMP to compute the program's output values as effective as attainable. additionally, spinoff values of those output values with appreciate to convinced enter values play a very important position. to accomplish code that computes not just the output values at the same time but in addition the by-product values, this paintings introduces a number of source-to-source transformation principles. those ideas are in keeping with a strategy referred to as algorithmic differentiation. the main target of this paintings lies at the very important opposite mode of algorithmic differentiation. The inherent data-flow reversal of the opposite mode needs to be dealt with adequately in the course of the transformation. the 1st a part of the paintings examines the differences in a really normal manner due to the fact that pragma-based parallel areas ensue in lots of other forms akin to OpenMP, OpenACC, and Intel Phi. the second one half describes the transformation ideas of an important OpenMP constructs.
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Extra resources for Algorithmic Differentiation of Pragma-Defined Parallel Regions: Differentiating Computer Programs Containing OpenMP
Throughout this work, we will assume that the used computer architecture is a shared memory multicore machine. Typical home computers are nowadays equipped with two or four computing cores. OpenMP can also be used on these computers but the general use is the domain of high performance computing (HPC). These machines are at this time equipped with up to 64 (SUN T5120) or 128 (Bull BCS) cores and have a maximum of one terabyte of memory. The memory model of OpenMP consist of two types of memory references, shared and private memory references.
1 since it is supported quite well and its features are sufficient for most of the shared memory architectures used nowadays. 1 standard  where we only consider these constructs that later serve as possible input for our source transformation tool. A common introduction into parallel programming with OpenMP can be found in the textbooks  and . For a precise description of the OpenMP constructs, we will cite the original document12 . For the reader who is already familiar with OpenMP, we still recommend to go through the examples because they will later be used as test cases for getting runtime results of the performed source transformation.
20 1 Motivation and Introduction The remaining three combinations to the generation of second derivative code involve at least one application of the adjoint model. Depending on the order in which we apply the forward mode or the reverse mode, we obtain the forwardover-reverse, reverse-over-forward, or the reverse-over-reverse mode. The corre(1) (2) sponding second-order adjoint models are denoted by F(1) , F(2) , and F(1,2) . They all have the same computational complexity of O(n · m) · cost(F) for the accumulation of the whole Hessian.
Algorithmic Differentiation of Pragma-Defined Parallel Regions: Differentiating Computer Programs Containing OpenMP by Michael Förster