Read Floating-Point Algorithms and Formal Proofs: A Didactic Tour with Coq - Sylvie Boldo file in PDF
Related searches:
Computer Arithmetic and Formal Proofs: Verifying Floating-point
Floating-Point Algorithms and Formal Proofs: A Didactic Tour with Coq
Computer Arithmetic and Formal Proofs - 1st Edition
Computer Arithmetic and Formal Proofs ScienceDirect
Computer Arithmetic and Formal Proofs - Inria
Computer Arithmetic and Formal Proofs - ISTE
Computer Arithmetic and Formal Proofs: Verifying - Amazon.fr
Floating Point Division and Square Root Algorithms and
Floating point division and square root algorithms and
Formal Verification of C Programs with Floating-Point
Some floating-point algorithms have been used for decades and proved decades ago in radix-2, providing neither underflow, nor overflow occurs.
This paper presents the amd-k7 ieee 754 and x87 compliant floating point division and square root algorithms and implementation. The amd-k7 processor employs an iterative implementation of a series expansion to converge quadratically to the quotient and square root.
30 mar 2012 one of these formal systems is the coq proof assistant [2], which is based on the proving numerous facts on floating-point algorithms.
Has recently experienced algorithmic challenges for which formal methods may contribute to a solution [10,56].
W hile the previous chaptershave made clear that it is common practice to verify floating-point algorithms with pen-and-paper proofs, this practice can lead to subtle bugs.
(1) proving the ieee correctness of these iterative floating-point algorithms, of these algorithms was gained, it became obvious that a formal study and proof.
14 apr 2010 implement high-level floating-point algorithm assuming addition works correctly.
2, accuracy of floating point arithmetic, in the art of computer programming, volume 2, seminumerical algorithms,.
It describes the flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation.
17 mar 2020 if one disregards the floating point rounding, the latches and the output measurement uncertainty, etc) a typical voting algorithm needs to be to get full coverage one can instead of simulation, perform formal veri.
Which can be arbitrarily large if the true inputs and are close. Subtracting nearby numbers in floating-point arithmetic does not always cause catastrophic cancellation, or even any error—by the sterbenz lemma, if the numbers are close enough the floating-point difference is exact.
Flocq is a floating-point formalization for coq, written by sylvie boldo and others. It provides a library of theorems for analyzing arbitrary-precision floating-point arithmetic. Paper: flocq: a unified library for proving floating-point algorithms in coq (sca'11) book: computer arithmetic and formal proofs (elsevier).
Over the years, a variety of floating-point representations have been used in computers. In 1985, the ieee 754 standard for floating-point arithmetic was established, and since the 1990s, the most commonly encountered representations are those defined by the ieee.
We have formal verified a number of algorithms for evaluating transcendental functions in double-extended precision floating point arithmetic in the intel ® ia-64 architecture.
A more realistic example is the following code fragment whoseintent is to compute the square root of c by iterating newton'smethod.
John harrison formal verification: mathematically prove the correctness of a design with respect.
This is a short section as rather few works mix fp arithmetic and formal proofs.
Section 3 presents the renormalization algorithm and the wanted properties. Section 4 explains the formal veri cation of the various levels of the algorithm.
2016 17th international conference on parallel and distributed computing, applications and technologies (pdcat) 51-56.
Roughly speaking, floating-point (fp) arithmetic is the way numerical quantities are handled by the computer. Many different programs rely on fp computations such as control software, weather forecasts, and hybrid systems (embedded systems mixing continuous and discrete behaviors).
Mal verification of fused-multiply-add floating point units (fpus). Our methodology dles for formal algorithms: namely, the multiplier, the alignment shifter that.
Barrett, “formal methods applied to a floating point number of iterative floating-point square root, divide, and remainder algorithms,” intel.
23 apr 2017 we give a formal proof in coq for one of the algorithms used as a basic brick when computing with floating-point expansions, the renormaliza-.
With floating-point arithmetic being at the core of many modern ai chips, and dozens of start-ups involved in the development of ai accelerators, it is crucial to provide easy-to-use formal verification solutions that can enable rigorous, exhaustive verification while also reducing cost and development time.
This chapter describes our work on formal verification of floating-point algorithms using the hol light theorem prover.
The objective of this article is to provide a brief introduction to floating point format. The following description explains terminology and primary details of ieee 754 binary floating point representation. The discussion confines to single and double precision formats.
Computer arithmetic and formal proofs: verifying floating-point algorithms with the coq system (computer engineering) - kindle edition by boldo, sylvie,.
22 apr 2014 digital computers cannot represent all real numbers exactly, so we face new challenges when designing computer algorithms for real numbers.
Note that our formal proof was generalized to ensure this algorithm is correct when computations are done with any even radix.
Hence any fault in such a compiler could result in incorrect software, no matter how carefully the algorithms have been chosen.
Buy computer arithmetic and formal proofs: verifying floating-point algorithms with the coq system (computer engineering) on amazon.
Computer arithmetic and formal proofs: verifying floating-point algorithms with the coq system.
In computing, floating-point arithmetic (fp) is arithmetic using formulaic representation of real in a completely formal way, without dealing with a specific encoding of the significand.
A common way of extending the precision is to use floating-point expansions. As the problems may be critical and as the algorithms used have very complex proofs (many sub-cases), a formal guarantee of correctness is a wish that can now be fulfilled, using interactive theorem proving.
Post Your Comments: