Standardization and Testing of Mathematical Functions

Kuliamin, Victor V.

doi:10.1007/978-3-642-11486-1_22

Cited by 7 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, we should try to implement our verified algorithms on the virtual computer (for our fix-point arithmetic) available at https://bitbucket.org/ ainoneko/lib_verify/src/ and then test these implementations against selected algebraic values for these functions (for example, sin π 6 = 1 2 , sin π 4 = cos π 4 = √ 2 2 , cos π 6 = √ 3 2 , etc.) in lines with test approach suggested and explained in [12,13]; automatically generated test data computed using Taylor expansions in any language that supports unbounded integer arithmetic; for example, a Lispfunction in Fig. 9 computes approximations for cos in unbounded rational arithmetics with accuracy 10 −8 .…”

Section: Resultsmentioning

confidence: 99%

Platform-independent Specification and Verification of the Standard Mathematical Square Root Function

Shilov

Кондратьев

Anureev

et al. 2018

Model. anal. inf. sist.

View full text Add to dashboard Cite

Research project "Platform-independent approach to formal specification and verification of standard mathematical functions" is aimed onto a development of an incremental combined approach to the specification and verification of the standard mathematical functions like sqrt, cos, sin, etc. Platform-independence means that we attempt to design a relatively simple axiomatization of the computer arithmetic in terms of real, rational, and integer arithmetic (i.e. the fields R and Q of real and rational numbers, the ring Z of integers) but dont specify neither base of the computer arithmetic, nor a format of numbers representation. Incrementality means that we start with the most straightforward specification of the simplest easy to verify algorithm in real numbers and finish with a realistic specification and a verification of an algorithm in computer arithmetic. We call our approach combined because we start with a manual (pen-and-paper) verification of some selected algorithm in real numbers, then use these algorithm and verification as a draft and proof-outlines for the algorithm in computer arithmetic and its manual verification, and finish with a computer-aided validation of our manual proofs with some proof-assistant system (to avoid appeals to "obviousness" that are very common in human-carried proofs). In the paper we present first steps towards a platform-independent incremental combined approach to specification and verification of the standard functions cos and sin that implement mathematical trigonometric functions cos and sin.

show abstract

Section: Resultsmentioning

confidence: 99%

Platform-independent Specification and Verification of the Standard Mathematical Square Root Function

Shilov

Кондратьев

Anureev

et al. 2018

Model. anal. inf. sist.

View full text Add to dashboard Cite

show abstract

“…It is worth to remark that a need for better specification and validation of standard functions is recognized (in principle) by industrial and academic professional community, as well as the problem of conformance of their implementation with the specification [3,10,11,13,14].…”

Section: Discussionmentioning

confidence: 99%

“…The next two papers [10,11] address formal specification and testing of standard mathematical functions. The last two cited papers [13,14] present formal specification and verification of some standard memory management and input-output functions.…”

Section: Discussionmentioning

confidence: 99%

On the Need to Specify and Verify Standard Functions

Shilov¹

2015

bncc.cs

View full text Add to dashboard Cite

Abstract. The problem of validation of standard mathematical functions and libraries is well-recognized by industrial and academic professional community but still is poorly understood by freshmen and inexperienced developers. The paper gives and discusses two examples (from the author's pedagogical experience) when formal specification and verification of standard functions do help and are needed.

show abstract

“…Another test construction method, not using formal specifications, but based on formal investigation of requirements was used to create conformance tests for mathematical functions working with floating-point numbers in POSIX system libraries [12]. The method uses as test data specific floating point values, including numbers having patterns in mantissa (like 0000FFFFAAAA in hexadecimals), boundaries of domains of specific function behavior (such behaviors include monotonicity, sign preservation, well-known asymptotics), and so-called worst cases, numbers, for which correct function calculations requires much more precision than in average.…”

Section: Formal Approachesmentioning

confidence: 99%

Verification of Operating System Components

Kuliamin¹,

Petrenko²,

Хорошилов³

2017

Self Cite

View full text Add to dashboard Cite

The paper concerns recent advances in reaching the goal of industrial operating system (OS) verification. By industrial OS we mean a system actively used in some industrial domain, elaborated and maintained for a significant time, not a proof-of-concept OS developed with mostly research intentions. We consider decomposition of this goal into tasks related with various functional components of OS and various properties under verification, and application of different verification methods to those tasks. This is a trial to explicate and summarize the experience of several projects on various OS components and different OS features verification conducted in ISP RAS.

show abstract

Standardization and Testing of Mathematical Functions

Cited by 7 publications

References 6 publications

Platform-independent Specification and Verification of the Standard Mathematical Square Root Function

Platform-independent Specification and Verification of the Standard Mathematical Square Root Function

On the Need to Specify and Verify Standard Functions

Verification of Operating System Components

Contact Info

Product

Resources

About