Download Algorithmic Differentiation of Pragma-Defined Parallel by Michael Förster PDF

By Michael Förster

Numerical courses usually use parallel programming thoughts resembling OpenMP to compute the program's output values as effective as attainable. moreover, by-product values of those output values with appreciate to convinced enter values play a vital function. to accomplish code that computes not just the output values concurrently 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 method known 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 appropriately throughout the transformation. the 1st a part of the paintings examines the alterations in a really normal approach because pragma-based parallel areas ensue 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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Additional info for Algorithmic Differentiation of Pragma-Defined Parallel Regions: Differentiating Computer Programs Containing OpenMP

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In the best case, the compiler gives a warning but this presupposes that the compiler can expect what the developer probably wanted to do, which is often not the case. Example 5. (Wrong OpenMP code) Although at first glance the code below looks fine, the result that elements in y are zero may be surprising. The developer probably wanted to share the work among the threads but instead each thread evaluates the exact same code. 1 #pragma omp p a r a l l e l 2 { 3 int i←0; 4 f o r ( i ← 0 ; i

The code from line 3 to line 15 defines a lower bound (lb) and an upper bound (ub). These boundaries are unique for each thread and define a range of the input data that is processed by a certain thread. The lines 12 and 15 are for adjusting the chunk size and the upper bound for the case that the data cannot be partitioned into equal parts. This is the case when the data size n is not divisible by the number of threads p. 1 #pragma omp p a r a l l e l 2 { 3 int i←0; 4 int tid←0; 5 int lb←0; 6 i n t ub← 0 ; 7 i n t chunk_size←0; 8 t i d ←omp_get_thread_num ( ) ; 9 p←omp_get_num_threads ( ) ; 10 c h u n k _ s i z e ←n/p ; 11 i ← c h u n k _ s i z e ∗p ; 12 i f ( i = n ) { c h u n k _ s i z e ← c h u n k _ s i z e +1; } 13 l b ← t i d ∗ chunk_size ; 14 ub← ( t i d +1)∗ c h u n k _ s i z e −1; 15 i f ( ub ≥ n ) { ub←n −1; } 16 f o r ( i ← l b ; i ≤ ub ; i ++) { 17 y i ←2∗ x i ∗ x i ; 18 xi← 0 .

Once outside the parallel region, once inside the parallel region. The memory model of OpenMP determines that all references defined inside the parallel region are private references and only visible for each individual thread. The column with the header line labeled with ’&x’ displays that the code has three instances of x. One for each thread and one that is accessed only from outside of the parallel region. The latter one is not accessible from inside the parallel region since all references to x are linked to the private instance of x.

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