: The increasing demand for portable computing has elevated power consumption to be one of the most critical design parameters. A high-level synthesis system, HYPER-LP, is presented for minimizing power consumption in application specific datapath intensive CMOS circuits using a variety of architectural and computational transformations. The synthesis environment consists of high-level estimation of power consumption, a library of transformation primitives, and heuristic/probabilistic optimization search mechanisms for fast and efficient scanning of the design space. Examples with varying degree of computational complexity and structures are optimized and synthesized using the HYPER-LP system. The results indicate that more than an order of magnitude reduction in power can be achieved over current-day design methodologies while maintaining the system throughput; in some cases this can be accomplished while preserving or reducing the implementation area. 1.0 Introduction VLSI research a...

Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast software-level algorithms for exact addition and multiplication of arbitrary precision floating-point values. The second is to propose a technique for adaptive-precision arithmetic that can often speed these algorithms when one wishes to perform multiprecision calculations that do not always require exact arithmetic, but must satisfy some error bound. The third is to provide a practical demonstration of these techniques, in the form of implementations of several common geometric calculations whose required degree of accuracy depends on their inputs. These robust geometric predicates are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines complying with the IEEE 754 standard. The inputs to the predicates may be arbitrary single or double precision floating-point numbers. C code is publicly available for the 2D and 3D orientation and incircle tests, and robust Delaunay triangulation using these tests. Timings of the implementations demonstrate their effectiveness. Supported in part by the Natural Sciences and Engineering Research Council of Canada under a 1967 Science and Engineering Scholarship and by the National Science Foundation under Grant CMS-9318163. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either express or implied, of NSERC, NSF, or the U.S. Government. Keywords: arbitrary precision floating-point arit...

We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixed-precision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next we survey some recent applications of this paradigm. Finally, we outline some basic theory and techniques in this paradigm. 1 This paper will appear as a chapter in the 2nd edition of Computing in Euclidean Geometry, edited by D.-Z. Du and F.K. Hwang, published by World Scientific Press, 1994. 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original mass-produced computers were pocket calculators. Although one's first exposure to computers today is likely to be some non-numerical application, numeri...

High dimensionality of text can be a deterrent in applying complex learners such as Support Vector Machines to the task of text classification. Feature clustering is a powerful alternative to feature selection for reducing the dimensionality of text data. In this paper we propose a new informationtheoretic divisive algorithm for feature/word clustering and apply it to text classification. Existing techniques for such “distributional clustering ” of words are agglomerative in nature and result in (i) sub-optimal word clusters and (ii) high computational cost. In order to explicitly capture the optimality of word clusters in an information theoretic framework, we first derive a global criterion for feature clustering. We then present a fast, divisive algorithm that monotonically decreases this objective function value. We show that our algorithm minimizes the “within-cluster Jensen-Shannon divergence ” while simultaneously maximizing the “between-cluster Jensen-Shannon divergence”. In comparison to the previously proposed agglomerative strategies our divisive algorithm is much faster and achieves comparable or higher classification accuracies. We further show that feature clustering is an effective technique for building smaller class models in hierarchical classification. We present detailed experimental results using Naive Bayes and Support Vector Machines on the 20Newsgroups data set and a 3-level hierarchy of HTML documents collected from the Open Directory project (www.dmoz.org).

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Platt's probabilistic outputs for Support Vector Machines [6] has been popular for applications that require posterior class probabilities. In this note, we propose an improvement which theoretically converges and avoids numerical difficulties. A simpler and ready-to-use pseudo code is included.

Automatic Differentiation is a technique for augmenting computer programs with statements for the computation of derivatives based on the chain rule of differential calculus. The ADIFOR 2.0 system provides automatic differentiation of Fortran 77 programs for first-order derivatives. The ADIFOR 2.0 system consists of three main components: The ADIFOR 2.0 preprocessor, the ADIntrinsics Fortran 77 exception-handling system, and the SparsLinC library. The combination of these tools provides the ability to deal with arbitrary Fortran 77 syntax, to handle codes containing single- and double-precision real- or complex-valued data, to fully support and easily customize the translation of Fortran 77 intrinsics, and to transparently exploit sparsity in derivative computations. ADIFOR 2.0 has been successfully applied to a 60,000-line code, which we believe to be a new record in automatic differentiation.

Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floating-point numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary precision arithmetic that have a strong advantage over other software techniques in computations that manipulate values of extended but small precision. Second, they are adaptive; their running time depends on the degree of uncertainty of the result, and is usually small. These algorithms work on computers whose floating-point arithmetic uses radix two and exact rounding, including machines that comply with the IEEE 754 floating-point standard. Timings of the predicates, in isolation and embedded in 2D and 3D Delaunay triangulation programs, verify their effectiveness. 1 Introduction Algorithms that make decisions based on geometric tests, such as determining which side of a line a point falls on, ...

The sigmoid kernel was quite popular for support vector machines due to its origin from neural networks. However, as the kernel matrix may not be positive semidefinite (PSD), it is not widely used and the behavior is unknown. In this paper, we analyze such non-PSD kernels through the point of view of separability. Based on the investigation of parameters in different ranges, we show that for some parameters, the kernel matrix is conditionally positive definite (CPD), a property which explains its practical viability. Experiments are given to illustrate our analysis. Finally, we discuss how to solve the non-convex dual problems by SMO-type decomposition methods. Suitable modifications for any symmetric non-PSD kernel matrices are proposed with convergence proofs.

Abstract We present a new idea to adapt relational abstract domains to the analysis of IEEE 754-compliant floating-point numbers in order to statically detect, through Abstract Interpretation-based static analyses, potential floating-point run-time exceptions such as overflows or invalid operations. In order to take the non-linearity of rounding into account, expressions are modeled as linear forms with interval coefficients. We show how to extend already existing numerical abstract domains, such as the octagon abstract domain, to efficiently abstract transfer functions based on interval linear forms. We discuss specific fixpoint stabilization techniques and give some experimental results. 1