Generating and Searching Families of FFT Algorithms

A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log n - 6n + 8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Recent work by Van Buskirk et al. demonstrated improvements to the split-radix operation count by using multiplier coefficients or "twiddle factors" that are not n-th roots of unity for a size-n DFT. This paper presents a Boolean Satisfiability-based proof of the lowest operation count for certain classes of DFT algorithms. First, we present a novel way to choose new yet valid twiddle factors for the nodes in flowgraphs generated by common power-of-two fast Fourier transform algorithms, FFTs. With this new technique, we can generate a large family of FFTs realizable by a fixed flowgraph. This solution space of FFTs is cast as a Boolean Satisfiability problem, and a modern Satisfiability Modulo Theory solver is applied to search for FFTs requiring the fewest arithmetic operations. Surprisingly, we find that there are FFTs requiring fewer operations than the split-radix even when all twiddle factors are n-th roots of unity.Comment: Preprint submitted on March 28, 2011, to the Journal on Satisfiability, Boolean Modeling and Computatio

Measurements of vacuum magnetic birefringence using permanent dipole magnets: the PVLAS experiment

The PVLAS collaboration is presently assembling a new apparatus (at the INFN section of Ferrara, Italy) to detect vacuum magnetic birefringence (VMB). VMB is related to the structure of the QED vacuum and is predicted by the Euler-Heisenberg-Weisskopf effective Lagrangian. It can be detected by measuring the ellipticity acquired by a linearly polarised light beam propagating through a strong magnetic field. Using the very same optical technique it is also possible to search for hypothetical low-mass particles interacting with two photons, such as axion-like (ALP) or millicharged particles (MCP). Here we report results of a scaled-down test setup and describe the new PVLAS apparatus. This latter one is in construction and is based on a high-sensitivity ellipsometer with a high-finesse Fabry-Perot cavity ($>4\times 10^5$) and two 0.8 m long 2.5 T rotating permanent dipole magnets. Measurements with the test setup have improved by a factor 2 the previous upper bound on the parameter $A_e$, which determines the strength of the nonlinear terms in the QED Lagrangian: $A_e^{\rm (PVLAS)} < 3.3 \times 10^{-21}$ T$^{-2}$ 95% c.l. Furthermore, new laboratory limits have been put on the inverse coupling constant of ALPs to two photons and confirmation of previous limits on the fractional charge of millicharged particles is given

Integrated testing and verification system for research flight software design document

The NASA Langley Research Center is developing the MUST (Multipurpose User-oriented Software Technology) program to cut the cost of producing research flight software through a system of software support tools. The HAL/S language is the primary subject of the design. Boeing Computer Services Company (BCS) has designed an integrated verification and testing capability as part of MUST. Documentation, verification and test options are provided with special attention on real time, multiprocessing issues. The needs of the entire software production cycle have been considered, with effective management and reduced lifecycle costs as foremost goals. Capabilities have been included in the design for static detection of data flow anomalies involving communicating concurrent processes. Some types of ill formed process synchronization and deadlock also are detected statically