Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

32位MIPS微处理器中乘法器的设计和实现

在Booth算法的基础上,结合MIPS 4KC微处理器中的流水线结构和乘法器的工作过程,提出了一种改进的Booth乘法器的设计方法,并采用全制定方法实现,用这种方法实现的乘法器单元具有面积小、单元电路可重复性好、版图设计工作量小、功耗低等特点.     

A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

On a Question of Phillips

In [5] Phillips proved that one can obtain the additive group of any nonstandard model *? of the ring ? of integers by using a linear mod 1 function h : F ?, where F is the α-dimensional vector space over ? when α is the cardinality of *?. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case.     

Some remarks on the Jensen-Hadamard inequalities and applications

We provide some inequalities and integral inequalities connected to the Jensen-Hadamard inequalities for convex functions. In particular, we give some refinements to these inequalities. Some natural applications and further extensions are given.

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Sunto Forniamo alcune diseguaglianze e diseguaglianze integrali connesse alle dise-gueglianze di Jensen-Hadamard per funzioni convesse. In particolare, diamo qualche miglioramento di queste diseguaglianze. Alcune applicazioni naturali ed ulteriori estensioni sono date.

     

长柱形CsI(Tl)闪烁晶体探测器的能量重建

提出了用于TEXONO实验中双端读出的长柱形CsI(Tl)闪烁晶体探测器的两种粒子能量重建方法———“算术平均值能量重建法”和“几何平均值能量重建法”,讨论了两种算法的理论依据和计算方法,并对两种算法进行了比较     

直接资本化法中自有资本收益率的算法探讨

在分析我国房地产自有资本收益率操作中所存在问题的基础上,论述了自有资本收益率的实质是自有资金直接资本化率,并在房地产持有期小于抵押贷款期以及房地产持有期和土地批租年限相同的两种情况下,推导出了与土地有限期使用制度相适应的房地产资本化率和自有资本收益率的计算方法,提出了利用债务保障比率的取值范围检验资本化率合理性的基本公式.     

The weak pigeonhole principle for function classes in S 12

It is well known that S ¹₂ cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective (dual) weak pigeonhole principle in S ¹₂ for provably weaker function classes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)