Code Generators for Mathematical Functions

Brunie, Nicolas; Dinechin, Florent de; Kupriianova, Olga; Lauter, Christoph

doi:10.1109/arith.2015.22

Cited by 30 publications

(23 citation statements)

References 22 publications

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“…The implementation of a mathematical function, such as exp(x), sin(x) or atan(x), in the floating-point environment provided by IEEE754-2008 has been extensively studied and described in the literature [4], [5], [6], [7], [8], [9], [10]. Classically, a mathematical function on a floating-point argument is computed in four or five steps.…”

Section: Implementation Of Mathematical Functionsmentioning

confidence: 99%

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A new open-source SIMD vector libm fully implemented with high-level scalar C

Lauter

2016

2016 50th Asilomar Conference on Signals, Systems and Computers

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To cite this version:Christoph Abstract-Systems support mathematical functions like exp, sin, cos through mathematical libraries (libm). With increasingly parallel hardware, scalar libm functions do not suffice; implementations that work on vectors in an element-by-element (SIMD) fashion are required. Only few Open-Source implementations of vector libms exist. They are mostly written in assembly, which hinders portability and maintenance. As they depend on the scalar system libm for special case handling, the existing vector libms may induce a source of non-reproducibility.We present an Open-Source vector libm implemented with high-level scalar C that a modern compiler can translate to SIMD code. The error of all functions does not exceed 8 ulp, while a performance gain of up to 278.5% is obtained. Our library is fully free-standing, i.e. it does not depend on any other system library.

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Section: Implementation Of Mathematical Functionsmentioning

confidence: 99%

“…We have optimized all our polynomials coefficients using the techniques described in [3]. None of our polynomials uses coefficients with higher precision than the working precision, whilst other library tend to use floating-point expansions at least for the coefficients of lower degree [8], [10].…”

Section: A a Bird's Eyes View On The Proposed Algorithmsmentioning

confidence: 99%

A new open-source SIMD vector libm fully implemented with high-level scalar C

Lauter

2016

2016 50th Asilomar Conference on Signals, Systems and Computers

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“…The "middle" and "large" errors are obtained by increasing the bound by one and two orders of magnitude respectively. input: t ∈ [1,3], w ∈ [-5, 5]…”

Section: Appendixmentioning

confidence: 99%

Sound Approximation of Programs with Elementary Functions

Darulová

Volkova

2019

Computer Aided Verification

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Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is, however, not always needed. Unlike arithmetic, where the performance difference between for example single and double precision floating-point arithmetic is relatively small, elementary function calls provide a much richer tradeoff space between accuracy and efficiency. Navigating this space is challenging. First, generating approximations of elementary function calls which are guaranteed to satisfy accuracy error bounds is highly nontrivial. Second, the performance of such approximations generally depends on several parameters which are unintuitive to choose manually, especially for non-experts. We present a fully automated approach and tool which approximates elementary function calls inside small programs while guaranteeing overall user provided error bounds. Our tool leverages existing techniques for roundoff error computation and approximation of individual elementary function calls, and provides automated selection of many parameters. Our experiments show that significant efficiency improvements are possible in exchange for reduced, but guaranteed, accuracy.

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“…In this article, we deal with the vectorized implementation of the logarithm function, log(x), in floating-point arithmetic, with a particular focus on its automation through the MetaLibm framework [1], [2]. It enables to describe the implementation of a function using a meta-language and to generate C codes optimized for different micro-architectures.…”

Section: Meta-implementation Of Vectorized Logarithm Function In Binamentioning

confidence: 99%

Meta-implementation of vectorized logarithm function in binary floating-point arithmetic

Saint-Genies

Brunie

Revy

2018

2018 IEEE 29th International Conference on Application-Specific Systems, Architectures and Processors (ASAP)

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Besides scalar instructions, modern microarchitectures also provide support for vector instructions. They enable to treat packed inputs (typically 4 or 8) in a single instruction. The challenge is now to write vector programs to support mathematical functions like sin, cos, exp, log, • • • which efficiently exploit those vector instructions. This article focuses on the design of vectorized implementation of log(x) function, and more particularly on its automation for different formats and micro-architectures. First it rewrites a classic range reduction in a branchless fashion so as to use at best recent micro-architecture features, like rcp (reciprocal) instruction, and to treat all inputs in the same flow. Second it details rigorously how to achieve "faithfully rounded" implementations. Third it shows how to automate this implementation process using the MetaLibm framework, on SSE/AVX and AVX2 supporting micro-architectures. Finally we illustrate that this process enables to achieve high throughput implementations for the binary32 and binary64 formats in a fully automated way.

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Code Generators for Mathematical Functions

Cited by 30 publications

References 22 publications

A new open-source SIMD vector libm fully implemented with high-level scalar C

A new open-source SIMD vector libm fully implemented with high-level scalar C

Sound Approximation of Programs with Elementary Functions

Meta-implementation of vectorized logarithm function in binary floating-point arithmetic

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