Efficient polynomial L-approximations

Brisebarre, Nicolas; Chevillard, Sylvain

doi:10.1109/arith.2007.17

Cited by 55 publications

(74 citation statements)

References 17 publications

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“…Indeed, this asumption is generally wrong. One may obtain much more accurate polynomials for the same coefficient bit-width using a modified Remez algorithm due to Brisebarre and Chevillard [2] and implemented as the fpminimax command of the Sollya tool. This command inputs a function, an interval and a list of constraints on the coefficient (e.g.…”

Section: Polynomial Approximationmentioning

confidence: 99%

Automatic generation of polynomial-based hardware architectures for function evaluation

Dinechin

Joldeş

Pasca

2010

ASAP 2010 - 21st IEEE International Conference on Application-Specific Systems, Architectures and Processors

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Section: Polynomial Approximationmentioning

confidence: 99%

Automatic generation of polynomial-based hardware architectures for function evaluation

Dinechin

Joldeş

Pasca

2010

ASAP 2010 - 21st IEEE International Conference on Application-Specific Systems, Architectures and Processors

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“…Rounding these coefficients to floating-point numbers entails a loss of accuracy. This problem is solved in [20] by a modified Remez algorithm that finds a minimax-like polynomial among polynomials with floating-point coefficients. These algorithms input f , I and the degree d, and return p and ε approx .…”

Section: A Polynomial Approximationmentioning

confidence: 99%

Code Generators for Mathematical Functions

Brunie¹,

Dinechin

Kupriianova

et al. 2015

2015 IEEE 22nd Symposium on Computer Arithmetic

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Abstract-A typical floating-point environment includes support for a small set of about 30 mathematical functions such as exponential, logarithms and trigonometric 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 generation of numerical function code, on arbitrary domains and with arbitrary accuracies.First, such code generation opens up the libm function space available to programmers. It may capture a much wider set of functions, and may capture even standard functions on nonstandard domains and accuracy/performance points.Second, writing libm code requires fine-tuned instruction selection and scheduling for performance, and sophisticated floatingpoint techniques for accuracy. Automating this task through code generation improves confidence in the code while enabling better design space exploration, and therefore better time to market, even for the libm functions.This article discusses, with examples, the new challenges of this paradigm shift, and presents the current state of open-source function code generators.

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“…As an example, in [8], they reduce the problem of computing machine-efficient polynomial approximations (i. e., having small coefficient sizes) of 1-dimensional functions to CVP under ∞ . The goal in this setting is to generate a high quality approximation that is suitable for hardware implementation or for use in a software library, and hence spending considerable computational resources to generate it is justified.…”

Section: Further Applications and Future Directionsmentioning

confidence: 99%

Lattice Sparsification and the Approximate Closest Vector Problem

Dadush¹,

Kun²

2013

Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

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We give a deterministic algorithm for solving the (1 + ε)-approximate Closest Vector Problem (CVP) on any n-dimensional lattice and in any near-symmetric norm in 2 O(n) (1 + 1/ε) n time and 2 n poly(n) space. Our algorithm builds on the lattice point enumeration techniques of Micciancio and Voulgaris (STOC 2010, SICOMP 2013 and Dadush, Peikert and Vempala (FOCS 2011), and gives an elegant, deterministic alternative to the "AKS Sieve"-based algorithms for (1 + ε)-CVP (Ajtai, Kumar, and Sivakumar; STOC 2001 and CCC 2002). Furthermore, assuming the existence of a poly(n)-space and 2 O(n) -time algorithm for exact CVP in the 2 norm, the space complexity of our algorithm can be reduced to polynomial.Our main technical contribution is a method for "sparsifying" any input lattice while approximately maintaining its metric structure. To this end, we employ the idea of random sublattice restrictions, which was first employed by Khot (FOCS 2003, J. Comp. Syst. Sci.

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Efficient polynomial L-approximations

Cited by 55 publications

References 17 publications

Automatic generation of polynomial-based hardware architectures for function evaluation

Automatic generation of polynomial-based hardware architectures for function evaluation

Code Generators for Mathematical Functions

Lattice Sparsification and the Approximate Closest Vector Problem

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