Automatic source‐to‐source error compensation of floating‐point programs: code synthesis to optimize accuracy and time

Thévenoux, Laurent; Langlois, Philippe; Martel, Matthieu

doi:10.1002/cpe.3953

Cited by 7 publications

(5 citation statements)

References 30 publications

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“…Various applications of compensated summation method have been proposed [9,10]. Thévenoux et al [24] implement an automatic code transformation to derive a compensated programs.…”

Section: Compensated Summation Methodsmentioning

confidence: 99%

An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

Benmouhoub,

Garoche,

Martel

2022

Preprint

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Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. To alleviate this issue, we have introduced a new parallel algorithm for summing a sequence of floating-point numbers. This algorithm which scales up easily with the number of processors, adds numbers of the same exponents first. In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. In order to show the usefulness of our algorithm, we have chosen a set of representative numerical methods which are Simpson, Jacobi, LU factorization and the Iterated power method.

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“…Various applications of compensated summation method have been proposed [9,10]. Thévenoux et al [24] implement an automatic code transformation to derive a compensated programs.…”

Section: Compensated Summation Methodsmentioning

confidence: 99%

An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

Benmouhoub,

Garoche,

Martel

2022

Preprint

Self Cite

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“…e Hall sensor is based on the Hall effect. For the basis of its work, it is used as a Hall switch in electronic products, such as the flip phone to open the bright screen and close the interest screen [20]. Hall effect: connect the current I to the upper and lower ends of the semiconductor block, and then apply a uniform magnetic field with a magnetic field strength of B in the vertical direction of the semiconductor block.…”

Section: Design Of Automated Synthesis Equipmentmentioning

confidence: 99%

Carbon Nanomaterial Manufacturing System and Automatic Synthesis Equipment and Its Control Device and Control Methods

Lou

Cai

2020

Journal of Chemistry

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In recent years, people are committed to developing new technologies and technologies for energy storage and conversion, environmental detection, high-performance sensors and energy security, and other aspects of the increasingly prominent problems in the field of environmental and biosafety. The purpose of this paper is to explore the manufacturing system and automatic synthesis equipment of carbon nanomaterials, understand the control device and control method, and analyze the structure and morphology characteristics of three kinds of carbon nanomaterials produced by carbon nanomaterial manufacturing system by X-ray diffraction and infrared spectroscopy. The results show that the carbon nanomaterial manufacturing system and automatic synthesis system in this paper solve the problems of high cost, low efficiency, and small scale of the existing carbon nanomaterials manufacturing and achieve the precision control of automatic production, so that the productivity is increased by 20%–35%, and the cost is reduced by 15%–30%. Therefore, they are widely used in the fields of science and technology, environmental protection, and intelligent manufacturing broad prospects. Carbon nanotube manufacturing equipment and automatic synthesis equipment have great production advantages, which can greatly improve the quality and efficiency of carbon nanomaterials. UPY, GO, and UGO carbon nanomaterials produced by carbon nanotube manufacturing equipment are not easy to fall off from the materials. When the wavelength is 500 nm, the absorption frequency of the three materials is the largest. With the extension of the spectral wavelength, the absorption frequency of the three materials is reduced by 52%, 33%, and 34.7%, respectively.

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“…CoHD [49] is a source-to-source transformer for C code that automatically compensates for the round-off errors of some basic floating-point operations. SyHD [50] is a C code optimizer that explores a set of programs generated by CoDH and selects the one with the best accuracy and computationtime trade-off. Sardana [36], given a Lustre [12] program, produces a set of equivalent programs with simplified arithmetic expressions.…”

Section: Precision Allocation and Program Optimizationmentioning

confidence: 99%

Automatic generation and verification of test-stable floating-point code

Titolo¹,

Moscato²,

Muñoz³

2020

Preprint

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Test instability in a floating-point program occurs when the control flow of the program diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by the presence of roundoff errors that affect the evaluation of arithmetic expressions occurring in conditional statements. Unstable tests may lead to significant errors in safety-critical applications that depend on numerical computations. Writing programs that take into consideration test instability is a difficult task that requires expertise on finite precision computations and rounding errors. This paper presents a toolchain to automatically generate and verify a provably correct test-stable floating-point program from a functional specification in real arithmetic. The input is a real-valued program written in the Prototype Verification System (PVS) specification language and the output is a transformed floating-point C program annotated with ANSI/ISO C Specification Language (ACSL) contracts. These contracts relate the floating-point program to its functional specification in real arithmetic. The transformed program detects if unstable tests may occur and, in these cases, issues a warning and terminate. An approach that combines the Frama-C analyzer, the PRECiSA round-off error estimator, and PVS is proposed to automatically verify that the generated program code is correct in the sense that, if the program terminates without a warning, it follows the same computational path as its real-valued functional specification.

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Automatic source‐to‐source error compensation of floating‐point programs: code synthesis to optimize accuracy and time

Cited by 7 publications

References 30 publications

An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

Carbon Nanomaterial Manufacturing System and Automatic Synthesis Equipment and Its Control Device and Control Methods

Automatic generation and verification of test-stable floating-point code

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