By Michael Förster

Numerical courses usually use parallel programming strategies similar to OpenMP to compute the program's output values as effective as attainable. moreover, spinoff values of those output values with admire to yes enter values play a vital function. to accomplish code that computes not just the output values at the same time but in addition the by-product values, this paintings introduces numerous source-to-source transformation ideas. those principles are in response to a strategy known 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 ameliorations in a truly common approach because pragma-based parallel areas take place in lots of other forms similar to OpenMP, OpenACC, and Intel Phi. the second one half describes the transformation principles of crucial OpenMP constructs.

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**Additional resources for Algorithmic Differentiation of Pragma-Defined Parallel Regions: Differentiating Computer Programs Containing OpenMP**

**Sample text**

This model consist of 1488 differential algebraic equations (DAE). The model description in the Modelica format has a size of 4100 lines of code. 000 lines of SL code: 1 v o i d r e s ( d o u b l e ∗ yy , d o u b l e ∗ der_x , d o u b l e ∗ x , 2 d o u b l e ∗ p , i n t &n_x , i n t &n_p ) 3 { 4 ... 18838 #pragma ad e q u a t i o n 18839 { 18840 // s c a l a r e q u a t i o n 1488 18841 yy [ i_E ] = var_Xyl5P_y5_0−var_Xyl5P_11111 ; 18842 i_E = i_E +1; 18843 } 18844 } The important fact of this code is that the function is structured in a way that it contains 1488 equations where the start and the end of the equation are determined by a pragma.

Mathematical models in process engineering become more and more complex and with an increasing complexity the number of equations usually grows as well. With an increasing number of equations there is no way around the approach of letting the equations be calculated simultaneously. To emphasize this, we consider the sizes of the derivative codes from the above listing. Please note that we created the derivative codes of res by ignoring all ad equation pragmas. 000 lines of code. 000 lines of code.

4 Related Work An early approach of coupling AD with OpenMP can be found in [10]. The authors consider a given derivative code Q that implements the tangent-linear model in vector mode. 10). 10) but instead the derivative code computes a Jacobian matrix product. The forward mode in non vector mode augments each assignment in the original code by another assignment that computes one directional derivative value that corresponds to the original assignment. The vector mode on the other side augments the original assignment not by an assignment but by a loop that computes the whole gradient of the original assignment.