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Numerical programs often use parallel programming techniques such as OpenMP to compute the program's output values as efficient as possible. In addition, derivative values of these output values with respect to certain input values play a crucial role. To achieve code that computes not only the output values simultaneously but also the derivative values, this work introduces several source-to-source transformation rules. These rules are based on a technique called algorithmic differentiation. The main focus of this work lies on the important reverse mode of algorithmic differentiation. The inherent data-flow reversal of the reverse mode must be handled properly during the transformation. The first part of the work examines the transformations in a very general way since pragma-based parallel regions occur in many different kinds such as OpenMP, OpenACC, and Intel Phi. The second part describes the transformation rules of the most important OpenMP constructs. Contents Introduction with Examples from Numerical Optimization Algorithmic Differentiation by Source Transformation Transformation rules for Parallel Code Regions (e.g. OpenMP 3.1) Static Program Analysis Target Groups Lecturers and students of computer science Computer scientists, engineers, mathematicians and numerical analysts The Author Michael Förster is currently Research Associate of the Institute Software and Tools for Computational Engineering, RWTH Aachen University.

Parallel programming (Computer science) --- OpenMP. --- Heterogeneous computing. --- Computer networks. --- OpenMP (Application program interface) --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Heterogeneous processing (Computers) --- High performance computing --- Parallel processing (Electronic computers) --- Computer programming --- Distributed processing --- Open Multi-Processing (Application program interface) --- Computer science. --- Artificial intelligence. --- Engineering mathematics. --- Mathematics of Computing. --- Artificial Intelligence. --- Mathematical and Computational Engineering. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Engineering --- Engineering analysis --- Mathematical analysis --- Informatics --- Science --- Mathematics --- Computer science --- Applied mathematics. --- Mathematics. --- Computer science—Mathematics. --- Computer mathematics --- Mathematical and Computational Engineering Applications. --- Data processing.

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The shares of top income recipients in total pre-tax income have increased in OECD countries in the past three decades, particularly in most of the English-speaking countries but also in some Nordic (from low levels) and Southern European countries. Today, the richest one percent receives between 7% of all pre-tax income in Denmark and the Netherlands up to almost 20% in the United States. This increase is the result of the top 1% capturing a disproportionate share of overall income growth over the past thirty years: around 20 – 25% in Australia and the United Kingdom, up to 37% in Canada and even 47% in the United States. At the same time, tax reforms in almost all OECD countries reduced top personal income tax rates as well as rates of other taxes affecting the highest income earners. Indeed, while top tax rates were equal to or above 70% in half of the countries in the mid-1970s, this rate has been halved in many countries by 2013.

Social Issues/Migration/Health --- Taxation --- Economics