SLEEF - SIMD Library for Evaluating Elementary Functions Most of today’s processors have capabilities to execute SIMD instructions, and we can expect significant speed-ups in various kinds of computation if these instructions are properly used. But, this is technically hard because many popular programming techniques like table look-ups, conditional branches, scattering/gathering operations can easily slow down the computation. With this library, the trigonometric functions(sin, cos, tan, sincos), inverse trigonometric functions(asin, acos, atan, atan2), exponential and logarithmic functions(exp, log, pow, exp2, exp10, expm1, log10, log1p), hyperbolic/inverse hyperbolic functions(sinh, cosh, tanh, asinh, acosh, atanh), and some other functions(cbrt, ilogb, ldexp) can be evaluated in both double precision and single precision without table look-ups, scattering from, or gathering into SIMD registers, or conditional branches using SSE2, AVX, AVX2, FMA4, or ARM NEON instruction sets. (Source:

References in zbMATH (referenced in 41 articles , 1 standard article )

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  1. Higham, Nicholas J.; Pranesh, Srikara: Simulating low precision floating-point arithmetic (2019)
  2. Johansson, B. Tomas: An elementary algorithm to evaluate trigonometric functions to high precision (2018)
  3. Tsitouras, Ch.; Famelis, I. Th.: Bounds for variable degree rational (L_\infty) approximations to the matrix exponential (2018)
  4. Banjac, Bojan; Makragić, Milica; Malešević, Branko: Some notes on a method for proving inequalities by computer (2016)
  5. Muller, Jean-Michel: Elementary functions. Algorithms and implementation (2016)
  6. Auslender, A.; Ferrer, A.; Goberna, M. A.; López, M. A.: Comparative study of RPSALG algorithm for convex semi-infinite programming (2015)
  7. Savard, B.; Xuan, Y.; Bobbitt, B.; Blanquart, G.: A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry (2015)
  8. Doukhnitch, Evgueni; Salamah, Muhammed; Andreev, Andrey: Effective processor architecture for matrix decomposition (2014)
  9. Dwarakanath, Nagarjun C.; Galbraith, Steven D.: Sampling from discrete Gaussians for lattice-based cryptography on a constrained device (2014)
  10. Tsitouras, Ch.; Katsikis, V. N.: Bounds for variable degree rational (L_\infty) approximations to the matrix cosine (2014)
  11. Sanchez-Romero, Jose-Luis; Jimeno-Morenilla, Antonio; Molina-Carmona, Rafael; Perez-Martinez, Jose: An approach to the application of shift-and-add algorithms on engineering and industrial processes (2013) ioport
  12. Sergeyev, Yaroslav D.: Solving ordinary differential equations on the Infinity Computer by working with infinitesimals numerically (2013)
  13. Yakhontov, S. V.: Time- and space-efficient evaluation of the real logarithmic function on Schonhage machine (2013)
  14. Berthé, V.: Numeration and discrete dynamical systems (2012)
  15. Chen, Dongdong; Ko, Seok-Bum: A novel decimal logarithmic converter based on first-order polynomial approximation (2012)
  16. Melquiond, Guillaume: Floating-point arithmetic in the Coq system (2012)
  17. Butler, Jon T.; Frenzen, C. L.; Macaria, Njuguna; Sasao, Tsutomu: A fast segmentation algorithm for piecewise polynomial numeric function generators (2011)
  18. Sergeyev, Yaroslav D.: Higher order numerical differentiation on the infinity computer (2011)
  19. Akbarpour, Behzad; Paulson, Lawrence Charles: MetiTarski: An automatic theorem prover for real-valued special functions (2010)
  20. Frenzen, C. L.; Sasao, Tsutomu; Butler, Jon T.: On the number of segments needed in a piecewise linear approximation (2010)

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