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The article concerns problems of formulating standard requirements to implementations of mathematical functions working with floating-point numbers and conformance test development for them. Inconsistency and incompleteness of available standards in the domain is demonstrated. Correct rounding requirement is suggested to guarantee preservation of all important properties of functions and to support high level of interoperability between different mathematical libraries and software using them. Conformance test construction method is proposed based on different sources of test data: numbers satisfying specific patterns, boundaries of intervals of uniform function behavior, and points where correct rounding needs much higher precision than in average. Analysis of test results obtained on various implementations of POSIX mathematical library is also presented.