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PLAM: A Posit Logarithm-Approximate Multiplier [PDF]
IEEE Transactions on Emerging Topics in Computing, 2021 The Posit™ Number System was introduced in 2017 as a replacement for floating-point numbers. Since then, the community has explored its application in several areas, such as deep learning, and produced some unit designs which are still far from being ...
Raul Murillo +5 more
semanticscholar +1 more source
Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment [PDF]
IACR Cryptology ePrint Archive, 2020 We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorization of RSA-768 in 2009 and a 768-bit discrete logarithm computation in 2016.
Fabrice Boudot +5 more
semanticscholar +1 more source
Next-to-Next-to-Next-to-Leading Order Pressure of Cold Quark Matter: Leading Logarithm. [PDF]
Physical Review Letters, 2018 At high baryon chemical potential μ_{B}, the equation of state of QCD allows a weak-coupling expansion in the QCD coupling α_{s}. The result is currently known up to and including the full next-to-next-to-leading order α_{s}^{2}.
Tyler Gorda +4 more
semanticscholar +1 more source
Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law [PDF]
The Annals of Applied Probability, 2017 We show two Freidlin-Wentzell type Large Deviations Principles (LDP) in path space topologies (uniform and Holder) for the solution process of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) using techniques which directly address the presence ...
G. Reis, William Salkeld, Julian Tugaut
semanticscholar +1 more source
Semidefinite Approximations of the Matrix Logarithm [PDF]
Foundations of Computational Mathematics, 2017 The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix functions, many of
Hamza Fawzi, J. Saunderson, P. Parrilo
semanticscholar +1 more source
Factorization for groomed jet substructure beyond the next-to-leading logarithm [PDF]
Journal of High Energy Physics, 2016 Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple ...
C. Frye +3 more
semanticscholar +1 more source
A Kilobit Hidden SNFS Discrete Logarithm Computation [PDF]
International Conference on the Theory and Application of Cryptographic Techniques, 2016 We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields.
Joshua Fried +3 more
semanticscholar +1 more source
A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric [PDF]
SIAM Journal on Matrix Analysis and Applications, 2016 We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic perspective.
Ralf Zimmermann
semanticscholar +1 more source
Soft Gluons in Logarithmic Summations [PDF]
, 1999 We demonstrate that all the known single- and double-logarithm summations for a parton distribution function can be unified in the Collins-Soper resummation technique by applying soft approximations appropriate in different kinematic regions to real ...
Li, Hsiang-nan, Lim, Jyh-Liong
core +3 more sources
Discrete logarithms in free groups [PDF]
, 2004 For the free group on n generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.Comment: 9 pages, 1 figure, Corrects a mistake in the Introduction and Section
Communicated Wen-ching Winnie Li +3 more
core +3 more sources