Software Technologies for High-Performance Parallel Signal Processing

ion and Overhead A major goal of PVL is that a reasonably mapped application should be able to achieve performance close to that which can be achieved by native mathematical and message-passing libraries on a given platform. To examine our success in this goal, we measured the amount of overhead PVL adds to an optimized FFT operation. This section describes these performance results in more detail. Understanding the PVL FFT. The use of the PVL FFT can be divided into three phases: declaration, setup, and execution. The distinguishing characteristics of the PVL FFT are that the input vector and the output vector each have a map associated with them that describes how they are distributed, and that, in addition, a computation map is associated with the FFT object that can be different from either the input or the output vector map. The computation map describes how and where the computations take place. Methodology. We measured computation times for out-of-place complex-to-complex vector FFT operations using vectors of length L = 2, n ∈ {8, 9, ..., 14} (i.e., L ranged from 256 to 16,384). These numbers were picked because they reflect a good range of interest for the embedded processing space. Each function of interest was run a given number of iterations and the total time was recorded. The first iteration was not counted because cache effects were likely to be most pronounced the first time the function was called. Measured times considered only the computation portion of the program, and did not include time to create or construct the FFT object, allocate • KEPNER AND LEBAK Software Technologies for High-Performance Parallel Signal Processing 190 LINCOLN LABORATORY JOURNAL VOLUME 14, NUMBER 2, 2003 memory for the vectors, or perform other functions. Computation rates were calculated by assuming 5nL floating-point operations per complex FFT. In all cases we ran the measurement program six times, averaged the time over a thousand iterations each time, and used the minimum of the six results. FIGURE 10. Overhead for PVL fast Fourier transform (FFT) execution time, relative to that of the Fastest Fourier Transform in the West (FFTW) library for vectors of various lengths. In all cases the overhead is less than 2%. FIGURE 11. C++ expression templates. C++ typically requires the use of temporary variables in order to write high-level mathematical expressions. Obtaining high performance from C++ requires technology such as expression templates that eliminate the normal creation of temporary variables in an expression. Performance Results. The PVL FFT object whose performance is measured here used the Fastest Fourier Transform in the West (FFTW) library [5]. Because this library is a collection of self-optimizing FFT routines that has been shown to outperform vendor-optimized libraries in some cases, we can be confident that it represents a well-performing FFT operation. Figure 10 shows the execution time of PVL relative to FFTW. It is clear that PVL adds very little overhead to the underlying FFTW call. Abstraction and Optimizationion and Optimization PVL is implemented by using the C++ programming language, which allows the user to write programs using high-level mathematical constructs such as