Abstract: A linear transform such as a Fast Fourier Transform (FFT) is performed on an input data set having a number of points using one or more arrays of concurrent threads that are capable of sharing data with each other. Each thread of one thread array reads two or more of the points, performs an appropriate “butterfly” calculation to generate two or more new points, then stores the new points in a memory location that is accessible to other threads of the array. Each thread determines which points it is to read based at least in part on a unique thread identifier assigned thereto. Multiple transform stages can be handled by a single thread array, or different levels can be handled by different thread arrays.

Abstract: Parallelism in a processor is exploited to permute a data set based on bit reversal of indices associated with data points in the data set. Permuted data can be stored in a memory having entries arranged in banks, where entries in different banks can be accessed in parallel. A destination location in the memory for a particular data point from the data set is determined based on the bit-reversed index associated with that data point. The bit-reversed index can be further modified so that at least some of the destination locations determined by different parallel processes are in different banks, allowing multiple points of the bit-reversed data set to be written in parallel.