As CUDA becomes the de facto programming language among data parallel applications such as high-performance computing or machine learning applications, running CUDA on other platforms becomes a compelling option. Although several efforts have attempted to support CUDA on devices other than NVIDIA GPUs, due to extra steps in the translation, the support is always a few years behind CUDA’s latest features. In particular, the new CUDA programming model exposes the warp concept in the programming language, which greatly changes the way the CUDA code should be mapped to CPU programs. In this article, hierarchical collapsing that correctly supports CUDA warp-level functions on CPUs is proposed. To verify hierarchical collapsing , we build a framework, COX , that supports executing CUDA source code on the CPU backend. With hierarchical collapsing , 90% of kernels in CUDA SDK samples can be executed on CPUs, much higher than previous works (68%). We also evaluate the performance with benchmarks for real applications and show that hierarchical collapsing can generate CPU programs with comparable or even higher performance than previous projects in general.