Program transformation for numerical precision
Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics
Formal Methods in System Design
Accurate evaluation of a polynomial and its derivative in Bernstein form
Computers & Mathematics with Applications
Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form
Applied Numerical Mathematics
Accurate evaluation of the k-th derivative of a polynomial and its application
Journal of Computational and Applied Mathematics
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The compensated Horner algorithm improves the accuracy of polynomial evaluation in IEEE-754 floating point arithmetic: the computed result is as accurate as if it was computed with the classic Horner algorithm in twice the working precision. Since the condition number still governs the accuracy of this computation, it may return an arbitrary number of inexact digits. We address here how to compute a faithfully rounded result, that is one of the two floating point neighbors of the exact evaluation. We propose an a priori sufficient condition on the condition number to ensure that the compensated evaluation is faithfully rounded. We also propose a validated and dynamic method to test at the running time if the compensated result is actually faithfully rounded. Numerical experiments illustrate the behavior of these two conditions and that the associated running time over-cost is really interesting.