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LOZIER, DWU.S. Department of Commerce
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Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered f...
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Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered form of conventional rounded-interval arithmetic. The three forms are compared on the basis of the number of floating-point operations needed to generate error bounds for inner-product accumulation.
A set of arithmetic algorithms is described for operands that are encoded in the ``AN"" error-detecting code with the low-cost check modulus A = 2a - 1. The set includes addition additive inverse (complement...
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A set of arithmetic algorithms is described for operands that are encoded in the ``AN"" error-detecting code with the low-cost check modulus A = 2a - 1. The set includes addition additive inverse (complementation), multiplication, division, roundoff, and two auxiliary algorithms: ``multiply by 2a - 1,"" and ``divide by 2a - 1."" The design of a serial radix-16 processor is presented in which these algorithms are implemented for the low-cost AN code with A = 15. This processor has been constructed for the Jet Propulsion Laboratory STAR computer. The adaptation of ``two"s complement"" arithmetic for an inverse-residue code is also described.
The minimum, maximum and average computing times of the classical Euclidean algorithm are derived. With positive integer inputs of lengths m and n, and with output (greatest common divisor) of length k, m≧n≧km≧n≧k...
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The minimum, maximum and average computing times of the classical Euclidean algorithm are derived. With positive integer inputs of lengths m and n, and with output (greatest common divisor) of length k, m≧n≧k
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