303 research outputs found
Faster polynomial multiplication over finite fields
Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two
polynomials in F_p[X] of degree less than n. For n large compared to p, we
establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the
iterated logarithm. This is the first known F\"urer-type complexity bound for
F_p[X], and improves on the previously best known bound M_p(n) = O(n log n log
log n log p)
Correcting soft errors online in fast fourier transform
While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library - one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes; (2) it detects errors in a much more timely manner; and (3) it also has higher numerical stability and better fault coverage
Efficient FPGA implementation of high-throughput mixed radix multipath delay commutator FFT processor for MIMO-OFDM
This article presents and evaluates pipelined architecture designs for an improved high-frequency Fast Fourier
Transform (FFT) processor implemented on Field Programmable Gate Arrays (FPGA) for Multiple Input Multiple Output
Orthogonal Frequency Division Multiplexing (MIMO-OFDM). The architecture presented is a Mixed-Radix Multipath Delay
Commutator. The presented parallel architecture utilizes fewer hardware resources compared to Radix-2 architecture,
while maintaining simple control and butterfly structures inherent to Radix-2 implementations. The high-frequency
design presented allows enhancing system throughput without requiring additional parallel data paths common in
other current approaches, the presented design can process two and four independent data streams in parallel
and is suitable for scaling to any power of two FFT size N. FPGA implementation of the architecture demonstrated
significant resource efficiency and high-throughput in comparison to relevant current approaches within
literature. The proposed architecture designs were realized with Xilinx System Generator (XSG) and evaluated
on both Virtex-5 and Virtex-7 FPGA devices. Post place and route results demonstrated maximum frequency
values over 400 MHz and 470 MHz for Virtex-5 and Virtex-7 FPGA devices respectively
Computing the fast Fourier transform on SIMD microprocessors
This thesis describes how to compute the fast Fourier transform (FFT) of a power-of-two length signal on single-instruction, multiple-data (SIMD) microprocessors faster than or very close to the speed of state of the art libraries such as FFTW (“Fastest Fourier Transform in the West”), SPIRAL and Intel Integrated Performance Primitives (IPP).
The conjugate-pair algorithm has advantages in terms of memory bandwidth, and three implementations of this algorithm, which incorporate latency and spatial locality optimizations, are automatically vectorized at the algorithm level of abstraction. Performance results on 2- way, 4-way and 8-way SIMD machines show that the performance scales much better than FFTW or SPIRAL.
The implementations presented in this thesis are compiled into a high-performance FFT library called SFFT (“Streaming Fast Fourier Trans- form”), and benchmarked against FFTW, SPIRAL, Intel IPP and Apple Accelerate on sixteen x86 machines and two ARM NEON machines, and shown to be, in many cases, faster than these state of the art libraries, but without having to perform extensive machine specific calibration, thus demonstrating that there are good heuristics for predicting the performance of the FFT on SIMD microprocessors (i.e., the need for empirical optimization may be overstated)
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