Fast evaluation of elementary mathematical functions with correctly rounded last bit
ACM Transactions on Mathematical Software (TOMS)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers
IEEE Transactions on Computers
Computing Elementary Functions: A New Approach for Achieving High Accuracy and Good Performance
Proceedings of the Symposium on Accurate Scientific Computations
Scientific Computing on Itanium-Based Systems
Scientific Computing on Itanium-Based Systems
Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
SIAM Journal on Scientific Computing
New Results on the Distance between a Segment and Z2. Application to the Exact Rounding
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Towards the Post-Ultimate libm
ARITH '05 Proceedings of the 17th IEEE Symposium on Computer Arithmetic
Assisted verification of elementary functions using Gappa
Proceedings of the 2006 ACM symposium on Applied computing
Elementary Functions: Algorithms and Implementation
Elementary Functions: Algorithms and Implementation
Efficient polynomial L-approximations
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
A Certified Infinite Norm for the Implementation of Elementary Functions
QSIC '07 Proceedings of the Seventh International Conference on Quality Software
Accurate Floating-Point Summation Part I: Faithful Rounding
SIAM Journal on Scientific Computing
An Efficient Rounding Boundary Test for {\rm pow}(x, y) in Double Precision
IEEE Transactions on Computers
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We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.