Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
NIST Digital Library of Mathematical Functions
Annals of Mathematics and Artificial Intelligence
Efficient and Reliable Multiprecision Implementation of Elementary and Special Functions
SIAM Journal on Scientific Computing
Handbook of Continued Fractions for Special Functions
Handbook of Continued Fractions for Special Functions
Continued Fractions for Special Functions: Handbook and Software
Numerical Validation in Current Hardware Architectures
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Because of the importance of special functions, several books and a large collection of papers have been devoted to the numerical computation of these functions, the most well-known being the Abramowitz and Stegun handbook [1]. But up to this date, no environment offers routines for the provable correct evaluation of these special functions.We point out how series and limit-periodic continued fraction representations of the functions can be helpful in this respect. Our scalable precision technique is mainly based on the use of sharpened a priori truncation and round-off error upper bounds, in case of real arguments. The implementation is validated in the sense that it returns a sharp interval enclosure for the requested function evaluation, at the same cost as the evaluation.