Algorithmic Differentiation of Pragma-Defined Parallel by Michael Förster

By Michael Förster

Numerical courses usually use parallel programming concepts akin to OpenMP to compute the program's output values as effective as attainable. moreover, by-product values of those output values with recognize to sure 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 spinoff values, this paintings introduces numerous source-to-source transformation ideas. those ideas are according to a method referred to as algorithmic differentiation. the focus of this paintings lies at the vital opposite mode of algorithmic differentiation. The inherent data-flow reversal of the opposite mode has to be dealt with correctly through the transformation. the 1st a part of the paintings examines the alterations in a truly common manner for the reason that pragma-based parallel areas take place in lots of other forms akin to OpenMP, OpenACC, and Intel Phi. the second one half describes the transformation principles of an important OpenMP constructs.

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In iteration i, each thread sets first the value of yi and then it sets the component xi to zero. The value of yi depends on the value of xi and therefore it depends on the fact whether or not the assignment that sets xi to zero has been already executed by another thread. The result in yi is decided by a race between read and store operations from different threads. Therefore, this situation at runtime is called a race condition. The reason for this race condition is the critical reference xi that is read and stored by multiple threads.

The original list item becomes defined at the end of the construct if there is an implicit barrier at that point. To avoid race conditions, concurrent reads or updates of the original list item must by synchronized with the update of the original list item that occurs as a result of the lastprivate clause. If the lastprivate clause is used on a construct to which nowait is applied, accesses to the original list item may create a race condition. 1 Citation 33 (p. 103). "The reduction clause specifies an operator and one or more list items.

The residual function is typically nonlinear which means that we have to solve a nonlinear constrained optimization problem. Therefore, we need the first- and second derivative codes of the residual function. These derivative codes are the contribution of dcc. All these codes are compiled into a library which can be accessed through a well defined interface, called equation set object (ESO) [7]. We emphasize two applications that have successfully used such a library. The first application is DyOS9 which is a software tool for the solution of dynamic optimization problems.

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