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The increasing programability and the high computational power of Graphical Processing Units (GPU) make them attractive to general purpose programming. However, taking full benefit of this execution environment is a challenging task. One of these challenges stem from divergences, a phenomenon that occurs when threads that execute in lock-step are forced to take different program paths due to branches in the code. In face of divergences, some threads will have to wait, idly, while their diverging siblings execute. Optimizing the code to avoid divergences is difficult, because this task demands a deep understanding of programs that might be large and convoluted. In order to facilitate the detection of divergences, this paper introduces the divergence map, a data structure that indicates the location and the volume of divergences in a program. We build this map via dynamic profiling techniques, which we have implemented on top of an open source CUDA compiler. To illustrate the importance of the divergence map, we have used it to pin-point the core regions that must be optimized in well known public applications. By hand optimizing some applications, we have added 9-11% speedups onto kernels that have already gone through the sieve of many programmers.