On the Need to Specify and Verify Standard Functions

Abstract

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.

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

“…Можно, например, сослаться на работы [1,19], в которых всесторонне обсуждается проблема спецификации и тестирования стандартных математических функций, причём во внимание принимается не только точность вычислений (ошибка или невязка), но и такие алгебраические свойства стандартных функций, как, например, чётность и нечётность (cos и sin), нормализация (sin 2 x + cos 2 x = 1). Образовательное значение проблемы спецификации и верификации стандартных функций также нашло отражение в литературе [24,25].…”

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

“…The following fabulous story is a quotation from the paper [17] that was a position paper motivating a need for better specification and verification of the standard mathematical function.…”

“…Imagine the embarrassment of the instructor when each of 25 students in the class got 10 times the value 4.000000 as an approximation for π! Please refer papers [17,18] for detailed discussion what was wrong with the described 25 computational experiments and for a human "proof" that π is 4.000000 indeed. But we have to rule the idea to compute π using Monte Carlo methods because of impossibility to generate random numbers (but pseudorandom only) that are used in the method.…”

“…Our present paper is a next one in a series of our papers devoted to the development of a platform-independent incremental combined approach to specification and verification of the standard mathematical functions [17,18,19,20]. Position papers [17,18] have stated our concern regarding a need of better specification and incremental combined platform-independent verification of standard functions, introduction and standardization of a certification process for the standard functions,…”

Operational Semantics of Reflex

“…However, correctly defining the semantics of common implementations of floating-point is tricky, because semantics may change with many factors beyond source-code level, such as choices made by compilers [12]. Therefore, we plan to modify operational semantics rules for arithmetical operations based on the platform-independent approach to specification and verification of arithmetical operations and standard mathematical functions [13][14][15].…”