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Overflow, underflow, and severe loss of significance in floating-point addition and subtraction. (English) Zbl 0593.65029
Summary: It is shown that, under the assumption of the logarithmic distribution of numbers, floating-point addition and subtraction can result in overflow or underflow with alarming frequency - a frequency that increases rapidly with machine speed unless the range of the exponent is also increased. If numbers are assumed to be distributed in accordance with D. W. Sweeney’s experiments [An analysis of floating point addition. IBM- Systems J. 4, 31-42 (1965)], then severe loss of significance occurs with large probability in floating point subtraction. These results have implications for computer design and lead to the suggestion of a long word format which will reduce the risks to acceptable levels.

65G50 Roundoff error
68N99 Theory of software
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