Standardization and testing of implementations of mathematical functions in floating point numbers

Kuliamin, Victor V.

doi:10.1134/s036176880703005x

Cited by 12 publications

(14 citation statements)

References 13 publications

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“…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.

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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.

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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.

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“…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

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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.

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“…Systematic exposition of testing results for 17 different implementations of exponential function can be found in [2]. This work revealed about 10 different error kinds, some of them being specific for a single platform, but 3-4 common for most platforms tested.…”

Section: Applicationsmentioning

confidence: 99%

“…The contribution of this article is the systematic description of the approach proposed, much more clear and concise then it was done in the paper [2] describing the starting phase of the underlying work. In addition this paper describes methods for searching FP numbers, for which correct rounding of the function value is hard, including the new one, the integer secants method.…”

Section: Introductionmentioning

confidence: 99%

Test Construction for Mathematical Functions

Kuliamin

2008

Testing of Software and Communicating Systems

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Abstract. The article deals with problems of testing implementations of mathematical functions working with floating-point numbers. It considers current standards' requirements to such implementations and demonstrates that those requirements are not sufficient for correct operation of modern systems using sophisticated mathematical modeling. Correct rounding requirement is suggested to guarantee preservation of all important properties of implemented functions and to support high level of interoperability between different mathematical libraries and modeling software using them. Test construction method is proposed for conformance test development for current standards supplemented with correct rounding requirement. The idea of the method is to use three different sources of test data: floating-point numbers satisfying specific patterns, boundaries of intervals of uniform function behavior, and points where correct rounding requires much higher precision than in average. Some practical results obtained by using the method proposed are also presented.

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Standardization and testing of implementations of mathematical functions in floating point numbers

Cited by 12 publications

References 13 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

Test Construction for Mathematical Functions

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