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IEEE arithmetic

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The IEEE arithmetic is the standard IEEE 754-2008 (or the original IEEE 754-1985) that prescribes how computers should implement binary floating point arithmetic. C++, Java, JavaScript and other computer programming and scripting languages conform to the 1985 version, and in time newer implementations will conform to the 2008 revision. The standard helps computer programmers write more portable programs without worrying that one system running the same program as another might give different results.

The standard calls for two infinities (positive and negative) as well as two zeroes (also positive and negative), making it similar to a 'discretized' version of the extended real numbers The standard is structured in such a way that positive floating point numbers are easily compared (greater than, less than, equal) by interpretation as integers.

Several values can be represented in more than one way, including zero (+0 and –0) and the special value not a number.

  • Jean-Michel Muller, Nicolas Brisebarre, et al, Handbook of Floating-Point Arithmetic. New York: Springer (2009)

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