Bound on Run of Zeros and Ones for Images of Floating-Point Numbers by Algebraic FunctionsReport as inadecuate




Bound on Run of Zeros and Ones for Images of Floating-Point Numbers by Algebraic Functions - Download this document for free, or read online. Document in PDF available to download.

1 DECE - Department of Electrical and Computer Engineering 2 ARENAIRE - Computer arithmetic Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l-Informatique du Parallélisme

Abstract : This paper presents upper bounds on the number of zeros and ones after the rounding bit for algebraic functions. These functions include reciprocal, division, square root, and inverse square root, which have been considered in previous work. We here propose simpler proofs for the previously given bounds given and generalize to all algebraic functions. We also determine cases for which the bound is achieved for square root. As is mentioned in the previous work, these bounds are useful for determining the precision required in the computation of approximations in order to be able to perform correct rounding.

Keywords : TABLE MAKER-S DILEMMA CORRECT ROUNDING COMPUTER ARITHMETIC FLOATING-POINT ARITHMETIC ALGEBRAIC FUNCTIONS





Author: Tomas Lang - Jean-Michel Muller -

Source: https://hal.archives-ouvertes.fr/



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