Abstract: The execution engine is a new organization for a digital data processing apparatus, suitable for highly parallel execution of structured fine-grain parallel computations. Possible applications include many types of digital signal processing computations, such as filtering, convolution, and deconvolution, as well as many types of linear algebra operators, such as iterative and direct solvers, singular value decomposition, and constraint optimization. The invention improves energy efficiency of these structured parallel operators as compared to a regular data flow or von Neumann computer.