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Floating-Point Preferred Exponent


The floating-point preferred exponent of a decimal operation in the IEEE 754-2008 standard is the operation-dependent target value of the exponent used to select a floating-point representation of an exact result. If that value cannot represent the result in the destination format, the nearest possible exponent is used.

Writing Q(x) for the exponent of a finite operand x, the preferred exponent is min(Q(x),Q(y)) for addition and subtraction, Q(x)+Q(y) for multiplication, and Q(x)-Q(y) for division (IEEE Computer Society 2008, pp. 18 and 21). Thus preserving the operands' quantum means respecting these operation-dependent rules, rather than keeping each operand's quantum unchanged. For example, 1.2×1.2=1.44 has preferred exponent -2, although each operand has exponent -1.


See also

Arithmetic, Biased Exponent, Floating-Point Algebra, Floating-Point Arithmetic, Floating-Point Exponent, Floating-Point Normal Number, Floating-Point Number, Floating-Point Quantum, Floating-Point Representation, IEEE 754-2008, Interval Arithmetic, NaN, Quiet NaN, Signaling NaN, Significand, Subnormal Number

Portions of this entry contributed by Christopher Stover

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References

IEEE Computer Society. "IEEE Standard for Floating-Point Arithmetic: IEEE Std 754-2008 (Revision of IEEE Std 754-1985)." 2008. https://doi.org/10.1109/IEEESTD.2008.4610935.

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Floating-Point Preferred Exponent

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Floating-Point Preferred Exponent." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Floating-PointPreferredExponent.html

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