Formally certified floating-point filters for homogeneous geometric predicates

Melquiond, Guillaume; Pion, Sylvain

doi:10.1051/ita:2007005

Cited by 15 publications

(12 citation statements)

References 9 publications

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“…But it would have been too much a bore. This automation is currently in progress using the Gappa tool [21]. This should give better bounds on overflow that would also be certified by Coq proofs.…”

Section: Resultsmentioning

confidence: 99%

Kahan's Algorithm for a Correct Discriminant Computation at Last Formally Proven

Boldo

2009

IEEE Trans. Comput.

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Abstract-This article tackles Kahan's algorithm to compute accurately the discriminant. This is a known difficult problem, and this algorithm leads to an error bounded by 2 ulps of the floating-point result. The proofs involved are long and tricky and even trickier than expected as the test involved may give a result different from the result of the same test without rounding. We give here the total demonstration of the validity of this algorithm, and we provide sufficient conditions to guarantee that neither overflow nor underflow will jeopardize the result. The IEEE-754 double-precision program is annotated using the Why platform and the proof obligations are done using the Coq automatic proof checker.

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Section: Resultsmentioning

confidence: 99%

Kahan's Algorithm for a Correct Discriminant Computation at Last Formally Proven

Boldo

2009

IEEE Trans. Comput.

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“…However, we know that all predicates are based on determinant computations, hence polynomial computation, and it is thus sufficient to ensure that intermediate computations are done with a precision sufficiently higher than the precision of the initial data to guarantee the absence of errors introduced by rounding. Thus, the "theoretical" correctness of the algorithm can be preserved in a "practical" sense if one relies on a suitable approach to increase the precision of numeric computations, as in [27,30,20].…”

Section: Resultsmentioning

confidence: 99%

Formal Study of Plane Delaunay Triangulation

Dufourd

Bertot

2010

Lecture Notes in Computer Science

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This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe triangulations, we rely on a combinatorial hypermap specification framework we have been developing for years. We embed hypermaps in the plane by attaching coordinates to elements in a consistent way. We then describe what are legal and illegal Delaunay edges and a flipping operation which we show preserves hypermap, triangulation, and embedding invariants. To prove the termination of the algorithm, we use a generic approach expressing that any non-cyclic relation is well-founded when working on a finite set.

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“…LEDs are widely used in research for visual stimulation to increase the comfortability and reduce visual fatigue [56]. However, existing visual stimulators [52,57,58] based on LEDs have their limitations, as they are limited in their customisation capabilities, are not easy to program and often not possible to control LEDs individually.…”

Section: Related Workmentioning

confidence: 99%

A Configurable, Inexpensive, Portable, Multi-channel, Multi-frequency, Multi-chromatic RGB LED System for SSVEP Stimulation

Mouli

Palaniappan

Sillitoe

2014

Brain-Computer Interfaces

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Steady state visual evoked potential (SSVEP) is extensively used in the research of brain-computer interface (BCI) and require a controllable and configurable light source. SSVEP requires appropriate control of visual stimulus parameters, such as flicker frequency, light intensity, multi-frequency light source and multi-spectral compositions. Light emitting diodes (LEDs) are extensively used as a light source as they are energy efficient, low power, multi-chromatic, have higher contrast, and support wider frequency ranges. Here, we present the design of a compact versatile visual stimulus which is capable of producing simultaneous multiple frequency RGB LED flicker suitable for a wide range of SSVEP paradigms. The hardware is based upon the open source Arduino platform and supports on-the-fly reprogramming with easily configurable user interface via USB. The design provides fourteen independent high output channels with customisable output voltages. The flicker frequencies can be easily customised within the frequency range of 5-50 Hz, using a look-up table. The LED flickers are generated with single RGB LEDs which generate the required colour or frequency combinations for combined multi-frequency flicker with variable duty cycle to generate SSVEP. Electroencephalogram (EEG) signals have been successfully recorded from five subjects using the stimulator for different frequencies, colours, duty cycle, intensity and multiple frequency RGB source, thereby demonstrating the high usability, adaptability and flexibility of the stimulator. Finally we discuss the possible improvements to the stimulator which could provide real time user feedback to reduce visual fatigue and so increase the level of user comfort.

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Formally certified floating-point filters for homogeneous geometric predicates

Cited by 15 publications

References 9 publications

Kahan's Algorithm for a Correct Discriminant Computation at Last Formally Proven

Kahan's Algorithm for a Correct Discriminant Computation at Last Formally Proven

Formal Study of Plane Delaunay Triangulation

A Configurable, Inexpensive, Portable, Multi-channel, Multi-frequency, Multi-chromatic RGB LED System for SSVEP Stimulation

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