In this paper, we present Amethyst, a generalized on-the-fly de/re-compression framework for GPUs. Our developed framework allows to execute every computational function on every (un)compressed input format and to output the result in an arbitrary (un)compressed format. Thus, our on-the-fly de/re-compression framework approach automatically conducts a decompression on the input side and compression on the output side. To show the feasibility and applicability of our framework, we developed a prototype for integer data types using different integer compression formats. We use this prototype to present exhaustive evaluation results using a great variety of data-intensive operations ranging from simple additions up to compaction and compute-intensive matrix multiplications to validate the efficiency of Amethyst.