The use of floating-point computations for the implementation of critical systems is perceived as increasingly acceptable. Even in modern avionics, one of the most critical domains for software, floating-point numbers are now used, more often than not, instead of fixed-point arithmetic. However, designing and testing floating-point algorithms is significantly more difficult than designing and testing integer algorithms. Acceptance of floating-point computations in the design of critical systems was facilitated by the widespread adoption of significant portions of the IEEE 754 standard for binary floating-point arithmetic: nonetheless, many highly-complex traps and pitfalls remain. In this first webinar on the subject, we will present examples showing how things can go spectacularly wrong with floating-point numbers. We will then introduce the IEEE 754 binary floating-point formats, including NaNs, signed zeroes, infinities and subnormals, along with the reasons they are there. We will illustrate the IEEE 754 rounding modes, with an emphasis on round-to-nearest tails-to-even, and the properties that floating-expressions do and do not possess. After a review of the phenomena that are most often undesirable (NaN generation, overflows, underflows, absorption, cancellation, ...), we will conclude the webinar with a teaser for the second webinar in the series, where we will illustrate how some of the illustrated problems can be solved or mitigated.
ROBERTO BAGNARA , PhD
CTO, Bugseng, Prof. University of Parma, Italy
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Member, ISO/IEC JTC1/SC22/WG14 - C Standardization Working Group
Member, MISRA C Working Group
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