A method and an apparatus that determine a total number of threads to concurrently execute executable codes compiled from a single source for target processing units in response to an API (Application Programming Interface) request from an application running in a host processing unit are described. The target processing units include GPUs (Graphics Processing Unit) and CPUs (Central Processing Unit). Thread group sizes for the target processing units are determined to partition the total number of threads according to a multi-dimensional global thread number included in the API request. The executable codes are loaded to be executed in thread groups with the determined thread group sizes concurrently in the target processing units.