Multithreaded implicitly dealiased convolutions

Highlights: • Implicit dealiasing is generalized to an arbitrary multiplication operator. • A loop dependency in the implicitly padded Hermitian convolution is removed. • Implicit dealiasing algorithms are parallelized for shared-memory architectures. • An alternate data format enhances cache efficiency and accommodates a Nyquist mode. Implicit dealiasing is a method for computing in-place linear convolutions via fast Fourier transforms that decouples work memory from input data. It offers easier memory management and, for long one-dimensional input sequences, greater efficiency than conventional zero-padding. Furthermore, for convolutions of multidimensional data, the segregation of data and work buffers can be exploited to reduce memory usage and execution time significantly. This is accomplished by processing and discarding data as it is generated, allowing work memory to be reused, for greater data locality and performance. A multithreaded implementation of implicit dealiasing that accepts an arbitrary number of input and output vectors and a general multiplication operator is presented, along with an improved one-dimensional Hermitian convolution that avoids the loop dependency inherent in previous work. An alternate data format that can accommodate a Nyquist mode and enhance cache efficiency is also proposed.