Sollya: An Environment for the Development of Numerical Codes

Chevillard, Sylvain; Joldeş, Mioara; Lauter, Christoph

doi:10.1007/978-3-642-15582-6_5

Cited by 83 publications

(69 citation statements)

References 4 publications

(5 reference statements)

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“…Another advantage is that the methods presented in this paper utilize truncated units that have been shown to exhibit lower power requirements [37]. Other similar endeavors, such as the Sollya project, are useful, but are more complex than the algorithm presented in this paper in addition to having different targets [38]. For example, Sollya is a tool for safe floating-point code development, whereas, the novel direct-search methods in this paper provide another approach that is simple and finds a solution to complex error requirements for elementary functions.…”

Section: Polynomial Function Approximationmentioning

confidence: 99%

Optimized Linear, Quadratic and Cubic Interpolators for Elementary Function Hardware Implementations

2016

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This paper presents a method for designing linear, quadratic and cubic interpolators that compute elementary functions using truncated multipliers, squarers and cubers. Initial coefficient values are obtained using a Chebyshev series approximation. A direct search algorithm is then used to optimize the quantized coefficient values to meet a user-specified error constraint. The algorithm minimizes coefficient lengths to reduce lookup table requirements, maximizes the number of truncated columns to reduce the area, delay and power of the arithmetic units, and minimizes the maximum absolute error of the interpolator output. The method can be used to design interpolators to approximate any function to a user-specified accuracy, up to and beyond 53-bits of precision (e.g., IEEE double precision significand). Linear, quadratic and cubic interpolator designs that approximate reciprocal, square root, reciprocal square root and sine are presented and analyzed. Area, delay and power estimates are given for 16, 24 and 32-bit interpolators that compute the reciprocal function, targeting a 65 nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes compared to previously proposed methods. The method can be used to optimize coefficients in other systems while accounting for coefficient quantization as well as truncation and rounding effects of multiple arithmetic units.

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Section: Polynomial Function Approximationmentioning

confidence: 99%

Optimized Linear, Quadratic and Cubic Interpolators for Elementary Function Hardware Implementations

2016

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“…Sollya [26] is a numerical toolbox for libm developers with a focus on safe floating-point computations. In particular it provides state-of-the-art polynomial approximation [20] and safe algorithms to compute ε approx = f − p I ∞ [27].…”

Section: Existing Libm Development Toolsmentioning

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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“…A state-of-the-art implementation of univariate Taylor Models is available in the Sollya tool [12], developed by Mioara Joldeş et al and written in C, but the correctness of this implementation is not formally proved. Roughly speaking, Sollya represents polynomials as arrays of interval coefficients with multiple-precision floating-point bounds and relies on several C libraries such as MPFR or GMP.…”

Section: Benchmarksmentioning

confidence: 99%