Polynomial and Matrix Computations: Fundamental Algorithms, 1994. ,
Interpretation of IEEE-854 floating-point standard and definition in the HOL system, 1995. ,
Basis for the implementation of a reliable dot product, 1992. ,
Validated roundings of dot products by sticky accumulation, IEEE Transactions on Computers, vol.46, issue.5, pp.623-629, 1997. ,
Exponential: implementation trade-offs for hundred bit precision, Real Numbers and Computers, pp.61-74, 2000. ,
A generic library of floating-point numbers and its application to exact computing, 14th International Conference on Theorem Proving in Higher Order Logics, pp.169-184, 2001. ,
A floating point technique for extending the available precision, Numerische Mathematik, vol.18, issue.3, pp.224-242, 1971. ,
An Introduction to Numerical Methods and Analysis, 2001. ,
Methods of evaluating polynomial approximations in function evaluation routines, Communications of the ACM, vol.10, issue.3, pp.175-178, 1967. ,
A machine-checked theory of floating point arithmetic, 12th International Conference on Theorem Proving in Higher Order Logics, pp.113-130, 1999. ,
Accuracy and stability of numerical algorithms. SIAM, 2002. ,
The Coq proof assistant: a tutorial: version 7.2, 2002. ,
URL : https://hal.archives-ouvertes.fr/inria-00069918
Formal verification of a theory of IEEE rounding, 14th International Conference on Theorem Proving in Higher Order Logics, pp.239-254, 2001. ,
How java's floating-point hurts everyone everywhere, ACM 1998 Workshop on Java for High-Performance Network Computing, vol.81, 1998. ,
The Art of Computer Programming: Seminumerical Algorithms, 1997. ,
, Ropp (powerRZ radix (Zpred (Zpred (Zopp (dExp b
, // Set the residual error Err0 = 0
, // Set the range for the indeterminate XMax
, XMax
, Test the criterion HornerAXPY, issue.0
<< rec_erreur <<, << rec_check << endl ,
, All the steps of Horner's rule were faithful\n, == 0.0) cout <<
, else if (rec_check < 1.0) cout << "The final step of Horner's rule was faithful\n
, else if (rec_check >= 1.0) cout << "Error too large to guarantee that Horner's rule was faithful\n
A simple JAVA test qualifying the accuracy of Horner's rule for polynomials ,
, // Formulas are part of the graduate work of Sylvie BOLDO, 2001.
Faithful rounding without fused multiply and // accumulate, IMACS-GAMM International Symposium on Scientific // Computing, Computer Arithmetic and Validated Numerics, 2002. ,
, Lesser General Public // License along with this library; if not, Suite, vol.330, pp.2111-1307
, class Horner { public static double
, public static double UlpCstIEEE
, public static void main(String[] args) { int lgfr
, Omitted messages
Ulp for (UlpCstIEEE = 1.0, lgfr = 52; lgfr > 0 ,
, // Enter the polynomial Coefficients = new double, vol.9