2015 IEEE 22nd Symposium on Computer Arithmetic

22-24 June 2015

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Displaying Results 1 - 25 of 36
  • [Front cover]

    Publication Year: 2015, Page(s): C4
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  • [Title page i]

    Publication Year: 2015, Page(s): i
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  • [Title page iii]

    Publication Year: 2015, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2015, Page(s): iv
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  • Table of contents

    Publication Year: 2015, Page(s):v - vii
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  • Foreword

    Publication Year: 2015, Page(s): viii
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  • Organizing Committee

    Publication Year: 2015, Page(s): ix
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  • Program Committee

    Publication Year: 2015, Page(s):x - xi
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  • Steering Committee

    Publication Year: 2015, Page(s): xii
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  • Calculating in floating sexagesimal place value notation, 4000 years ago

    Publication Year: 2015, Page(s): 1
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (131 KB)

    Summary form only given, as follows. The full paper was not made available as part of this conference proceedings. By the end of the third millennium BCE in Mesopotamia an innovation of major significance for the history of mathematics occurred: the sexagesimal place value notation. A sophisticated mathematical culture was subsequently developed by masters attached to the scribal schools that flou... View full abstract»

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  • Low-Cost Duplicate Multiplication

    Publication Year: 2015, Page(s):2 - 9
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (259 KB) | HTML iconHTML

    Rising levels of integration, decreasing component reliabilities, and the ubiquity of computer systems make error protection a rising concern. Meanwhile, the uncertainty of future fault and error modes motivates the design of strong error detection mechanisms that offer fault-agnostic error protection. Current concurrent hardware mechanisms, however, either offer strong error detection coverage at... View full abstract»

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  • Minimizing Energy by Achieving Optimal Sparseness in Parallel Adders

    Publication Year: 2015, Page(s):10 - 17
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (1006 KB) | HTML iconHTML

    Carry tree sparseness is used in high-performance binary adders to achieve better energy-delay trade-off. To determine the energy optimal degree of sparseness, a detailed analysis is performed in this work. An analytical expression for the upper bound of sparseness is derived. The effect of increased sparseness on partial sum block and total energy is explored on 32-, 64-, 128-, and 256-bit adders... View full abstract»

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  • An Efficient Softcore Multiplier Architecture for Xilinx FPGAs

    Publication Year: 2015, Page(s):18 - 25
    Cited by:  Papers (5)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (324 KB) | HTML iconHTML

    This work presents an efficient implementation of a softcore multiplier, i.e., a multiplier architecture which can be efficiently mapped to the slice resources of modern Xilinx FPGAs. Instead of dividing the multiplication into the generation of partial products and the summation using a compressor tree, as done in modern multipliers, an array-like architecture is proposed. Each row of the array g... View full abstract»

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  • Design and Implementation of an Embedded FPGA Floating Point DSP Block

    Publication Year: 2015, Page(s):26 - 33
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (223 KB) | HTML iconHTML

    This paper describes the architecture and implementation, from both the standpoint of target applications as well as circuit design, of an FPGA DSP Block that can efficiently support both fixed and single precision (SP) floating-point (FP) arithmetic. Most contemporary FPGAs embed DSP blocks that provide simple multiply-add-based fixed-point arithmetic cores. Current FP arithmetic FPGA solutions m... View full abstract»

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  • Hardware Implementations of Fixed-Point Atan2

    Publication Year: 2015, Page(s):34 - 41
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (616 KB) | HTML iconHTML

    The atan2 function computes the polar angle arctan(y/x) of a point given by its cartesian coordinates. It is widely used in digital signal processing to recover the phase of a signal. This article studies for this context the implementation of atan2 with fixed-point inputs and outputs. It compares the prevalent CORDIC shift-and-add algorithm to two multiplier-based techniques. The first one comput... View full abstract»

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  • A General-Purpose Method for Faithfully Rounded Floating-Point Function Approximation in FPGAs

    Publication Year: 2015, Page(s):42 - 49
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (255 KB) | HTML iconHTML

    A barrier to wide-spread use of Field Programmable Gate Arrays (FPGAs) has been the complexity of programming, but recent advances in High-Level Synthesis (HLS) have made it possible for non-experts to easily create floating-point numerical accelerators from C-like code. However, HLS users are limited to the set of numerical primitives provided by HLS vendors and designers of floating-point IP cor... View full abstract»

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  • Precise and Fast Computation of Elliptic Integrals and Functions

    Publication Year: 2015, Page(s):50 - 57
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (430 KB) | HTML iconHTML

    Summarized is the recent progress of the new methods to compute Legendre's complete and incomplete elliptic integrals of all three kinds and Jacobian elliptic functions. Also reviewed are the entirely new methods to (i) compute the inverse functions of complete elliptic integrals, (ii) invert a general incomplete elliptic integral numerically, and (iii) evaluate the partial derivatives of the elli... View full abstract»

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  • Semi-Automatic Floating-Point Implementation of Special Functions

    Publication Year: 2015, Page(s):58 - 65
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (689 KB) | HTML iconHTML

    This work introduces an approach to the computer-assisted implementation of mathematical functions geared toward special functions such as those occurring in mathematical physics. The general idea is to start with an exact symbolic representation of a function and automate as much as possible of the process of implementing it. In order to deal with a large class of special functions, our symbolic ... View full abstract»

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  • Code Generators for Mathematical Functions

    Publication Year: 2015, Page(s):66 - 73
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (582 KB) | HTML iconHTML

    A typical floating-point environment includes support for a small set of about 30 mathematical functions such as exponential, logarithm, trigonometric and hyperbolic functions. These functions are provided by mathematical software libraries (libm), typically in IEEE754 single, double and quad precision. This article suggests to replace this libm paradigm by a more general approach: the on-demand g... View full abstract»

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  • The end of numerical error

    Publication Year: 2015, Page(s): 74
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (132 KB)

    Summary form only given, as follows. The full paper was not made available as part of this conference proceedings. It is time to overthrow a century of methods based on floating point arithmetic. Current technical computing is based on the acceptance of rounding error using numerical representations that were invented in 1914, and acceptance of sampling error using algorithms designed for a time w... View full abstract»

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  • Faster FFTs in Medium Precision

    Publication Year: 2015, Page(s):75 - 82
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (266 KB) | HTML iconHTML

    In this paper, we show how to speed up the computation of fast Fourier transforms over complex numbers for "medium" precisions, typically in the range from 100 until 400 bits. On the one hand, such precisions are usually not supported by hardware. On the other hand, asymptotically fast algorithms for multiple precision arithmetic do not pay off yet. The main idea behind our algorithms is to develo... View full abstract»

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  • Efficient Implementation of Elementary Functions in the Medium-Precision Range

    Publication Year: 2015, Page(s):83 - 89
    Cited by:  Papers (5)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (208 KB) | HTML iconHTML

    We describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR library, we achieve a maximum speedup ranging from a factor 3 for cos to 30 for atan. Our implementation uses table-based argument reduction together with rectangular splitting to evaluate Taylor series. We collect denomi... View full abstract»

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  • Efficient Divide-and-Conquer Multiprecision Integer Division

    Publication Year: 2015, Page(s):90 - 95
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (183 KB) | HTML iconHTML

    We present a new divide-and-conquer algorithm for mid-range multiprecision integer division which is typically 20-25% faster than the recent algorithms of Moller and Granlund implemented in the GNU Multi Precision (GMP) library. View full abstract»

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  • Reliable Evaluation of the Worst-Case Peak Gain Matrix in Multiple Precision

    Publication Year: 2015, Page(s):96 - 103
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (223 KB) | HTML iconHTML

    The worst-case peak gain (WCPG) of a linear filter is an important measure for the implementation of signal processing algorithms. It is used in the error propagation analysis for filters, thus a reliable evaluation with controlled precision is required. The WCPG is computed as an infinite sum and has matrix powers in each summand. We propose a direct formula for the lower bound on truncation orde... View full abstract»

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  • Numerical challenges in long term integrations of the solar system

    Publication Year: 2015, Page(s): 104
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (132 KB)

    Summary form only given, as follows. The full paper was not made available as part of this conference proceedings. Long time integrations of the planetary motion in the Solar System has been a challenging work in the past decades. The progress have followed the improvements of computer technology, but also the improvements in the integration algorithms. This quest has led to the development of hig... View full abstract»

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