Algorithm 719: Multiprecision translation and execution of FORTRAN programs
ACM Transactions on Mathematical Software (TOMS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
ACM Transactions on Mathematical Software (TOMS)
Algorithms for Quad-Double Precision Floating Point Arithmetic
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
SIAM Journal on Scientific Computing
Some Functions Computable with a Fused-Mac
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Hi-index | 0.00 |
Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on a method to improve the accuracy of the polynomial evaluation. It is well known that the use of the Fused Multiply and Add operation available on some microprocessors like Intel Itanium improves slightly the accuracy of the Horner scheme. In this paper, we propose an accurate compensated Horner scheme specially designed to take advantage of the Fused Multiply and Add. We prove that the computed result is as accurate as if computed in twice the working precision. The algorithm we present is fast since it only requires well optimizable floating point operations, performed in the same working precision as the given data.