Davenport, James

In considering the reliability of numerical programs, it is normal to \limitour study to the semantics dealing with numerical precision" (Martel,2005) [Mar05]. On the other hand, there is a great deal of work on thereliability of programs that essentially ignores the numerics. The thesisof this paper is that there is a class of problems that fall between thesetwo, which could be described as \does the low-level arithmetic imple-ment the high-level mathematics". Many of these problems arise becausemathematics, particularly the mathematics of the complex numbers, ismore dicult than expected: for example the complex function log isnot continuous, writing down a program to compute an inverse functionis more complicated than just solving an equation, and many algebraicsimplication rules are not universally valid.The good news is that these problems are theoretically capable of beingsolved, and are practically close to being solved, but not yet solved, inseveral real-world examples. However, there is still a long way to gobefore implementations match the theoretical possibilities

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Program Verification in the presence of complex numbers, functions with branch cuts etc

https://purehost.bath.ac.uk/ws/files/7734533/JHD_SYNASC2012v3.pdf

Program Verification in the presence of complex numbers, functions with branch cuts etc

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