General decimal arithmetic specification V1.51 by Cowlishaw M.

By Cowlishaw M.

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Extra info for General decimal arithmetic specification V1.51

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When the result is inexact, the cost of exp at precision d is likely to be at least 13×log2(d) times the cost of an inexact multiplication at the same precision (see Multiple-precision zero-finding methods and the complexity of elementary function evaluation by R. P. Brent, in Analytic Computational Complexity pp151–176, Academic Press, York, 1976, and Fast Multiple-Precision Evaluation of Elementary Functions by the same author, in Journal of the ACM (JACM), Vol 23 # 2, pp242–251, ACM, April 1976).

Otherwise, the operands are compared as as though by the compare operation (see page 26). If they are not numerically equal then the minimum (closer to negative infinity) of the two operands is chosen as the result. Otherwise (they are numerically equal): • if the operand signs differ the operand with sign 1 is chosen • if the signs and exponents are equal the operands are identical so either can be chosen • if the signs are both positive, the operand with the minimum exponent is chosen • if the signs are both negative, the operand with the maximum exponent is chosen.

2. A subnormal result is only possible if the working precision is greater than Emax+1. 3. The rules for setting the exponent of the result apply to many operations; they can be used for any operation for which an ideal exponent can be defined. 4. 2. 5. 5). 35 34 35 This rule matches the typical implementations. For example, the square-root of either [0,10,–1] or [0,11,–1] is often calculated by first multiplying the coefficient by ten and reducing the exponent by 1 and then determining the square root.

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