Realization of an optimal computer arithmetic
Proc. of the symposium on A new approach to scientific computation
Accurate singular values of bidiagonal matrices
SIAM Journal on Scientific and Statistical Computing
IBM RISC System/6000 processor architecture
IBM Journal of Research and Development
Design of the IBM RISC System/6000 floating-point execution unit
IBM Journal of Research and Development
Leading-zero anticipator (LZA) in the IBM RISC System/6000 floating-point execution unit
IBM Journal of Research and Development
Instruction scheduling for the IBM RISC System/6000 processor
IBM Journal of Research and Development
Computation of elementary functions on the IBM RISC System/6000 processor
IBM Journal of Research and Development
The C programming language
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
Computational geometry in C
Matrix computations (3rd ed.)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
SIAM Review
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
The Mathematica Book
Essentials of Numerical Analysis with Pocket Calculator Demonstrations
Essentials of Numerical Analysis with Pocket Calculator Demonstrations
Advanced Basic: Applications and Problems
Advanced Basic: Applications and Problems
A Practical Introduction to Pascal
A Practical Introduction to Pascal
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
IBM Journal of Research and Development
POWER3: the next generation of PowerPC processors
IBM Journal of Research and Development
Analysis and applications of Priest's distillation
ACM Transactions on Mathematical Software (TOMS)
Improving the compensated Horner scheme with a fused multiply and add
Proceedings of the 2006 ACM symposium on Applied computing
Residual iteration and accurate polynomial evaluation for shape-interrogation applications
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
ACM Transactions on Mathematical Software (TOMS)
Error-Free Transformation in Rounding Mode toward Zero
Numerical Validation in Current Hardware Architectures
Challenges for formal verification in industrial setting
FMICS'06/PDMC'06 Proceedings of the 11th international workshop, FMICS 2006 and 5th international workshop, PDMC conference on Formal methods: Applications and technology
Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic
Information and Computation
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Combined with doubly compensated summation, scalar fused multiply-add instructions redefine the concept of floating-point arithmetic, because they allow for the computation of sums of real or complex matrix products accurate to the penultimate digit. Particular cases include complex arithmetic, dot products, cross products, residuals of linear systems, determinants of small matrices, discriminants of quadratic, cubic, or quartic equations, and polynomials.