2017 IEEE 24th Symposium on Computer Arithmetic (ARITH)

24-26 July 2017

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  • [Front cover]

    Publication Year: 2017, Page(s): c1
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  • [Title page i]

    Publication Year: 2017, Page(s): i
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  • [Title page iii]

    Publication Year: 2017, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2017, Page(s): iv
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  • Table of contents

    Publication Year: 2017, Page(s):v - vii
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  • Foreword

    Publication Year: 2017, Page(s):viii - ix
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  • Committees

    Publication Year: 2017, Page(s): x
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  • Program Committee Members

    Publication Year: 2017, Page(s): xi
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  • Steering Committee

    Publication Year: 2017, Page(s): xii
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  • The Rise of Multiprecision Arithmetic

    Publication Year: 2017, Page(s): 1
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (114 KB)

    There is a growing demand for and availability of multiprecision arithmetic: floating point arithmetic supporting multiple, possibly arbitrary, precisions. For an increasing body of applications, including in supernova simulations, electromagnetic scattering theory, and computational number theory, double precision arithmetic is insufficient to provide results of the required accuracy. On the othe... View full abstract»

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  • Multiple Precision Floating-Point Arithmetic on SIMD Processors

    Publication Year: 2017, Page(s):2 - 9
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (266 KB) | HTML iconHTML

    Current general purpose libraries for multiple precision floating-point arithmetic such as MPFR suffer from a large performance penalty with respect to hard-wired instructions. The performance gap tends to become even larger with the advent of wider SIMD arithmetic in both CPUs and GPUs. In this paper, we present efficient algorithms for multiple precision floating- point arithmetic that are suita... View full abstract»

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  • Multiprecision Multiplication on ARMv8

    Publication Year: 2017, Page(s):10 - 17
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (200 KB) | HTML iconHTML

    Multiplication of large integers is a fundamental operation for public key cryptography. In contemporary public key cryptography, the sizes of integers are typically from more than one hundred bits to even several thousands of bits. Because these sizes exceed the bit widths of all general-purpose processors, these multiplications must be performed with a multiprecision multiplication algorithm whi... View full abstract»

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  • Optimized Binary64 and Binary128 Arithmetic with GNU MPFR

    Publication Year: 2017, Page(s):18 - 26
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (261 KB) | HTML iconHTML

    We describe algorithms used to optimize the GNU MPFR library when the operands fit into one or two words. On modern processors, this gives a speedup for a correctly rounded addition, subtraction, multiplication, division or square root in the standard binary64 format (resp. binary128) between 1.8 and 3.5 (resp. between 1.6 and 3.2). We also introduce a new faithful rounding mode, which enables eve... View full abstract»

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  • Implementation and Performance Evaluation of an Extended Precision Floating-Point Arithmetic Library for High-Accuracy Semidefinite Programming

    Publication Year: 2017, Page(s):27 - 34
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (252 KB) | HTML iconHTML

    Semidefinite programming (SDP) is widely used in optimization problems with many applications, however, certain SDP instances are ill-posed and need more precision than the standard double-precision available. Moreover, these problems are large-scale and could benefit from parallelization on specialized architectures such as GPUs. In this article, we implement and evaluate the performance of a flo... View full abstract»

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  • A Parallel Method for the Computation of Matrix Exponential Based on Truncated Neumann Series

    Publication Year: 2017, Page(s):35 - 42
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (254 KB) | HTML iconHTML

    This paper introduces a new method for computing matrix exponential based on truncated Neumann series. The efficiency of the method is based on smart factorizations for evaluation of several Neumann series that can be done in parallel and divided across different processors with low communication overhead. A physical realization on FPGA is provided for proof-of-concept. The method is verified to b... View full abstract»

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  • On Lifting-Based Fixed-Point Complex Multiplications and Rotations

    Publication Year: 2017, Page(s):43 - 49
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (262 KB) | HTML iconHTML

    Lifting-based complex multiplications and rotations are integer invertible, i.e., an integer input value is mapped to the same integer output value when rotating forward and backward. This is an important aspect for lossless transform based source coding, but since the structure only require three real-valued multiplications and three real-valued additions it is also a potentially attractive way t... View full abstract»

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  • A Number System Approach for Adder Topologies

    Publication Year: 2017, Page(s):50 - 57
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (237 KB) | HTML iconHTML

    The design space exploration for fast and power efficient adders is of increasing interest for microprocessors and graphic and digital signal processors. Recently, several methods have been proposed to explore the design space of adders, where well known designs appear as possible instances. These methods are based on the identification of parameters that lead to different hardware structures. In ... View full abstract»

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  • On Improving the Performance Per Area of ASTC with a Multi-output Decoder

    Publication Year: 2017, Page(s):58 - 59
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (268 KB) | HTML iconHTML

    ASTC is an efficient and flexible texture compression format but it is relatively costly to implement in hardware. By outputting multiple texels from a single encoded ASTC block, we will show an performance per area improvement of 25%. View full abstract»

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  • Optimal Streamed Linear Permutations

    Publication Year: 2017, Page(s):60 - 61
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (543 KB) | HTML iconHTML

    We give an overview on optimal circuits to implement linear permutations on FPGAs using only RAM banks and switches. Linear means that the permutation maps linearly the bit representation of the indices, as it is the case with most permutations arising in digital signal processing algorithms including those in fast Fourier transforms, Viterbi decoders, and sorting networks. Additionally, we assume... View full abstract»

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  • Approximate Neumann Series or Exact Matrix Inversion for Massive MIMO?

    Publication Year: 2017, Page(s):62 - 63
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (158 KB) | HTML iconHTML

    Approximate matrix inversion based on Neumann series has seen a recent increased interest motivated by massive MIMO systems. There, the matrices are in many cases diagonally dominant, and, hence, a reasonable approximation can be obtained within a few iterations of a Neumann series. In this work, we clarify that the complexity of exact methods are about the same as when three terms are used for th... View full abstract»

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  • Floating Point Tangent Implementation for FPGAs

    Publication Year: 2017, Page(s):64 - 65
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (130 KB) | HTML iconHTML

    This paper presents an implementation of the floating-point (FP) tangent function, optimized for an FPGA containing hard floating point (HFP) DSP Blocks. This function inputs values in the interval [-π/2,π/2], uses the IEEE-754 single-precision (SP) format, and has an accuracy conforming to OpenCL requirements. The presented architecture is based on a combination of mathematical identities and pro... View full abstract»

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  • The Classical Relative Error Bounds for Computing Sqrt(a^2 + b^2) and c / sqrt(a^2 + b^2) in Binary Floating-Point Arithmetic are Asymptotically Optimal

    Publication Year: 2017, Page(s):66 - 73
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (245 KB) | HTML iconHTML

    We study the accuracy of classical algorithms for evaluating expressions of the form √ (a2+ b2) and c/√ (a2+ b2)in radix-2, precision-p floating-point arithmetic, assuming that the elementary arithmetic operations ±, x, /, '/ are rounded to nearest, and assuming an unbounded exponent range. Classical analyses show that the relative error is bounded by 2u... View full abstract»

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  • Certified Roundoff Error Bounds Using Bernstein Expansions and Sparse Krivine-Stengle Representations

    Publication Year: 2017, Page(s):74 - 81
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (285 KB) | HTML iconHTML

    Floating point error is a notable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary for the validation of critical software. This problem of computing rigorous upper bounds is even more challenging when addressing non-linear programs. In this paper, we propose and compare two new methods based on Bernstein expansions and sparse ... View full abstract»

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  • Round-off Error Analysis of Explicit One-Step Numerical Integration Methods

    Publication Year: 2017, Page(s):82 - 89
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (626 KB) | HTML iconHTML

    Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off... View full abstract»

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  • ULPs and Relative Error

    Publication Year: 2017, Page(s):90 - 97
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (610 KB) | HTML iconHTML

    The paper establishes several simple, but useful relationships between ulp (unit in the last place) errors and the corresponding relative errors. These can be used when converting between the two types of errors, ensuring that the least amount of information is lost in the process. The properties presented here were already useful in IEEE conformance proofs for iterative division and square root a... View full abstract»

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