GPU design trends show that the register file size will continue to increase to enable even more thread level parallelism. As a result register file consumes a large fraction of the total GPU chip power. This paper explores register file data compression for GPUs to improve power efficiency. Compression reduces the width of the register file read and write operations, which in turn reduces dynamic power. This work is motivated by the observation that the register values of threads within the same warp are similar, namely the arithmetic differences between two successive thread registers is small. Compression exploits the value similarity by removing data redundancy of register values. Without decompressing operand values some instructions can be processed inside register file, which enables to further save energy by minimizing data movement and processing in power hungry main execution unit. Evaluation results show that the proposed techniques save 25 percent of the total register file energy consumption and 21 percent of the total execution unit energy consumption with negligible performance impact.