Stencil computations comprise an important class of kernels in many scientific computing applications.As the diversity of both architectures and programming models grow,autotuning is emerging as a critical strategy for achieving portable performance across a broad range of execution contexts for stencil computations.However,costly tuning overhead is a major obstacle to its popularity.In this work,we propose a fast stencil autotuning framework FAST based on an Optimal-Solution Space(OSS)model to significantly improve tuning speed.It leverages a feature extractor that comprehensively characterizes stencil computation.Using the extracted features,FAST constructs an OSS database to train an off-line model which provides an on-line prediction.We evaluate FAST with five important stencil computation applications on both an Intel Xeon multicore CPU and an NVIDIA Tesla K20c GPU.Compared with state-of-the-art stencil autotuners like Patus and SDSL,FAST improves autotuning speed by $10-2697$ times without any user annotation,while achieving comparable performance.