%0 Unpublished work %T Fast evaluation of some p-adic transcendental functions %+ Institut de Mathématiques de Bordeaux (IMB) %+ Lithe and fast algorithmic number theory (LFANT) %+ Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX) %+ Kobe University %+ XLIM (XLIM) %A Caruso, Xavier %A Mezzarobba, Marc %A Takayama, Nobuki %A Vaccon, Tristan %8 2021-06-16 %D 2021 %Z 2106.09315 %K Algorithms %K p-adic numbers %K differential equations %K binary splitting %Z Computer Science [cs]/Symbolic Computation [cs.SC]Preprints, Working Papers, ... %X We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linearccomplexity with respect to the target precision and most of them are based on an adaptation to the p-adic setting of the binary splitting and bit-burst strategies. %G English %2 https://cnrs.hal.science/hal-03263044/document %2 https://cnrs.hal.science/hal-03263044/file/fasteval.pdf %L hal-03263044 %U https://cnrs.hal.science/hal-03263044 %~ UNILIM %~ X %~ CNRS %~ INRIA %~ LIX %~ INRIA-BORDEAUX %~ XLIM %~ X-LIX %~ X-DEP %~ X-DEP-INFO %~ INRIA_TEST %~ TESTALAIN1 %~ TESTBORDEAUX %~ INRIA2 %~ IP_PARIS %~ IP_PARIS_COPIE %~ TEST-HALCNRS %~ INRIA-JAPON