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This chapter extends the earlier representations of integers
to the equivalent of the real numbers of scientific calculation. It discusses
the basic ideas, especially with reference to the IEEE 754 standard, and
contrasting with descriptions of the IBM S/360 and Burroughs B6700
representations. There is extensive discussion of the requirements of
ideal floating-point representations and the failings of practical implementations. Special mention is made of the requirements of range, precision and rounding. It concludes with examples of straight-forward
calculations which can easily overwhelm many floating-point systems.
Floating-point basics, IEEE 754 standard, Floating-point
precision, Floating-point range, Floating-point rounding, Not a Number
(NaNs), examples of range problems.
The University of Auckland (Retired) New Zealand