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Extra resources for Portability of Numerical Software: Workshop, Oak Brook, Illinois, June 21–23, 1976

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601-607, (1973). 2. Brown, W. , and Hall, A. , FORTRAN Portability Via Models and Tools, To be published (1977). 3. Brown, W. , and Richman, P. , lhe Choice of Base, Comm. ACM 12, pp. 560-561 (1969). 4. Bus, J. C. , and Dekker, T. , Two Efficient Algorithms With Guaranteed Convergence for Finding a Zero of a Function, AQ~ Transactions on Mathematical Software I, pp. 330-345 (1975). 5. Cody, W. , Desirable Hardware Characteristics for Scientific Computation, SIGNUMNewsletter 6, pp. 16-31 (1971).

S. , real numbers are represented in the form mantissa x base exp°nent' where mantissa is an integer or a pure fraction and exponent an integer, both in a certain machine dependent finite range, and base is an integral constant larger than I. The choice of the base is important, not only for scaling purposes (one can multiply and divide numbers by the base exactly, apart from overfl~ ~ and underflow), but also because the base influences the accuracy of the arithmetic. , a large variation in relative precision (from fleps to fleps x base), cf.

Brown & Richman (3} and Brent {I}. In view of communication with human beings, base i0 has obvious advantages (in particular, no conversion is needed at input and output) and is acceptable, provided one or two guard digits are used in the arithmetic unit. 6. As best possible incorrect values, we suggest: F~ceptional value "undefined" (if available in the system, especially to be reco~m~ended as result of division by 0 and of operations having an exceptional value as argument); giant with appropriate sign (in case of overflow) ; dwarf with appropriate sign or 0 (in case of underflow).

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