C. S. Anderson, S. Story, and N. Astafiev, Accurate Math Functions on the Intel IA-32 Architecture: A Performance-Driven Design, 7th Conference on Real Numbers and Computers, pp.93-105, 2006.

D. Javier and . Bruguera, Radix-64 Floating-Point Divider, 25th Symposium on Computer Arithmetic (ARITH-25), pp.87-94, 2018.

N. Brunie, Modified FMA for exact low precision product accumulation, 24th Symposium on Computer Arithmetic (ARITH-24), 2017.

R. Chaurasiya, J. Gustafson, R. Shrestha, J. Neudorfer, S. Nambiar et al., Parameterized Posit Arithmetic Hardware Generator, 36th International Conference on Computer Design (ICCD), pp.334-341, 2018.

W. and C. , Software Manual for the Elementary Functions, 1980.

A. V. Florent-de-dinechin, N. Ershov, and . Gast, Towards the Post-Ultimate libm, 17th Symposium on Computer Arithmetic (ARITH-17), pp.288-295, 2005.

C. Q. Florent-de-dinechin, J. Lauter, and . Muller, Fast and Correctly Rounded Logarithms in Double-Precision, Theoretical Informatics and Applications, vol.41, pp.85-102, 2007.

B. Florent-de-dinechin, O. Pasca, R. Cre?, and . Tudoran, An FPGA-specific Approach to Floating-Point Accumulation and Sum-of-Products, Field-Programmable Technologies, pp.33-40, 2008.

J. Demmel and H. D. Nguyen, Fast Reproducible Floating-Point Summation, 21th Symposium on Computer Arithmetic (ARITH-21), pp.163-172, 2013.

J. W. Demmel, On error analysis in arithmetic with varying relative precision, 8th Symposium on Computer Arithmetic (ARITH-8), 1987.

L. John, . Gustafson, and . Isaac-t-yonemoto, Beating floating point at its own game: Posit arithmetic, Supercomputing Frontiers and Innovations, vol.4, pp.71-86, 2017.

N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2002.

, IEEE Standard for Floating-Point Arithmetic, IEEE, vol.60559, p.754, 2008.

J. J. , Rethinking floating point for deep learning, 2018.

V. Peter-kornerup, N. Lefèvre, J. Louvet, and . Muller, On the computation of correctly-rounded sums, 19th Symposium on Computer Arithmetic (ARITH-19), 2009.

U. W. Kulisch, Advanced Arithmetic for the Digital Computer: Design of Arithmetic Units, 2002.

P. Langlois and N. Louvet, How to Ensure a Faithful Polynomial Evaluation with the Compensated Horner Algorithm, 18th IEEE Symposium on Computer Arithmetic (ARITH-18), pp.141-149, 2007.

P. Lindstrom, S. Lloyd, and J. Hittinger, Universal Coding of the Reals: Alternatives to IEEE Floating Point, CoNGA, Conference on Next Generation Arithmetic, 2018.

. Peter-markstein, IA-64 and Elementary Functions: Speed and Precision, 2000.

S. Matsui and M. Iri, An overflow/underflow free floating-point representation of numbers, Journal of Information Processing, vol.4, pp.123-133, 1981.

O. Møller, Quasi double-precision in floating point addition, BIT Numerical Mathematics, vol.5, pp.37-50, 1965.

J. Muller, Elementary functions, algorithms and implementation, 2016.
URL : https://hal.archives-ouvertes.fr/ensl-00000008

J. Muller, N. Brunie, C. Florent-de-dinechin, M. Jeannerod, V. Joldes et al., Handbook of Floating-Point Arithmetic, 2018.
URL : https://hal.archives-ouvertes.fr/ensl-00379167

C. Kwok and . Ng, Argument reduction for huge arguments: good to the last bit, 1992.

P. Panchekha, A. Sanchez-stern, J. R. Wilcox, and Z. Tatlock, Automatically Improving Accuracy for Floating Point Expressions, Programming Language Design and Implementation, 2015.

A. Podobas and S. Matsuoka, Hardware Implementation of POSITs and Their Application in FPGAs, International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pp.138-145, 2018.

S. M. Rump, T. Ogita, and S. Oishi, Accurate Floating-Point Summation Part I: Faithful Rounding, SIAM Journal on Scientific Computing, vol.31, pp.189-224, 2008.

S. M. Rump, T. Ogita, and S. Oishi, Accurate Floating-point Summation Part II: Sign, K-fold Faithful and Rounding to Nearest, SIAM Journal on Scientific Computing, vol.31, pp.1269-1302, 2008.

H. Hani, E. E. Saleh, and . Swartzlander, A Floating-Point Fused Dot-Product Unit, International Conference on Computer Design (ICCD, pp.426-431, 2008.

P. Tang, Table-Driven Implementation of the Exponential Function in IEEE Floating-Point Arithmetic, ACM Trans. Math. Software, vol.15, pp.144-157, 1989.

M. B. Taylor, Is Dark Silicon Useful? Harnessing the Four Horsemen of the Coming Dark Silicon Apocalypse, Design Automation Conference, 2012.

Y. Uguen, S. Florent-de-dinechin, and . Derrien, Bridging HighLevel Synthesis and Application-Specific Arithmetic: The Case Study of FloatingPoint Summations, Field-Programmable Logic and Applications, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01373954