Abstract
The IEEE 754 and 854 standards regulate the behaviour of real floating-point arithmetic, as implemented in most current hard- and software systems. Although a myriad of libraries for complex floating-point arithmetic is available and in use, there is no general consensus on their implementation. The International C Standard describes in its Annex G guidelines for the implementation of complex arithmetic, in order to achieve a similar behaviour of complex floating-point arithmetic across C-language compliant implementations. In Section 2 we summarize its recommendations and outline the problems inherent to this approach. In Section 3 we describe how the lack of reliability, when computing certain complex-valued expressions, can be overcome. Throughout the discussion the rounding mode is assumed to be round-to-nearest, as in Annex G.
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Backeljauw, F., Cuyt, A. A Constructive Criticism of the C/C++ Proposal for Complex Arithmetic. Reliable Comput 11, 313–319 (2005). https://doi.org/10.1007/s11155-005-6893-9
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DOI: https://doi.org/10.1007/s11155-005-6893-9