Size slicing: a hybrid approach to size inference in futhark

We present a shape inference analysis for a purely-functional language, named Futhark, that supports nested parallelism via array combinators such as map, reduce, filter}, and scan}. Our approach is to infer code for computing precise shape information at run-time, which in the most common cases can be effectively optimized by standard compiler optimizations. Instead of restricting the language or sacrificing ease of use, the language allows the occasional shape-dynamic, and even shape-misbehaving, constructs. Inherently shape-dynamic code is treated with a fall-back technique that preserves, asymptotically, the number of operations of the program and that computes and returns the array's shape alongside with its value. This approach leads to a shape-dependent system with existentially-quantified types, where static shape inference corresponds to eliminating existential quantifications from the types of program expressions.

We optimize the common case to negligible overhead via size slicing: a technique that separates the computation of the array's shape from its values. This allows the shape to be calculated in advance and to be used to instantiate the previously existentially-quantified shapes of the value slice. We report negligible overhead, on several mini-benchmarks and three real-world applications.