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Diffstat (limited to 'src/armadillo/include/armadillo_bits/constants.hpp')
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diff --git a/src/armadillo/include/armadillo_bits/constants.hpp b/src/armadillo/include/armadillo_bits/constants.hpp new file mode 100644 index 0000000..9adf9ea --- /dev/null +++ b/src/armadillo/include/armadillo_bits/constants.hpp @@ -0,0 +1,263 @@ +// SPDX-License-Identifier: Apache-2.0 +// +// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au) +// Copyright 2008-2016 National ICT Australia (NICTA) +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. +// ------------------------------------------------------------------------ + + +//! \addtogroup constants +//! @{ + + +namespace priv + { + class Datum_helper + { + public: + + template<typename eT> + static + typename arma_real_only<eT>::result + nan(typename arma_real_only<eT>::result* junk = nullptr) + { + arma_ignore(junk); + + return (std::numeric_limits<eT>::has_quiet_NaN) ? eT(std::numeric_limits<eT>::quiet_NaN()) : eT(0); + } + + + template<typename eT> + static + typename arma_cx_only<eT>::result + nan(typename arma_cx_only<eT>::result* junk = nullptr) + { + arma_ignore(junk); + + typedef typename get_pod_type<eT>::result T; + + return eT( Datum_helper::nan<T>(), Datum_helper::nan<T>() ); + } + + + template<typename eT> + static + typename arma_integral_only<eT>::result + nan(typename arma_integral_only<eT>::result* junk = nullptr) + { + arma_ignore(junk); + + return eT(0); + } + + + template<typename eT> + static + typename arma_real_only<eT>::result + inf(typename arma_real_only<eT>::result* junk = nullptr) + { + arma_ignore(junk); + + return (std::numeric_limits<eT>::has_infinity) ? eT(std::numeric_limits<eT>::infinity()) : eT(std::numeric_limits<eT>::max()); + } + + + template<typename eT> + static + typename arma_cx_only<eT>::result + inf(typename arma_cx_only<eT>::result* junk = nullptr) + { + arma_ignore(junk); + + typedef typename get_pod_type<eT>::result T; + + return eT( Datum_helper::inf<T>(), Datum_helper::inf<T>() ); + } + + + template<typename eT> + static + typename arma_integral_only<eT>::result + inf(typename arma_integral_only<eT>::result* junk = nullptr) + { + arma_ignore(junk); + + return std::numeric_limits<eT>::max(); + } + }; + } + + + +//! various constants. +//! Physical constants taken from NIST 2018 CODATA values, and some from WolframAlpha (values provided as of 2009-06-23) +//! http://physics.nist.gov/cuu/Constants +//! http://www.wolframalpha.com +//! See also http://en.wikipedia.org/wiki/Physical_constant + + +template<typename eT> +class Datum + { + public: + + static const eT pi; //!< ratio of any circle's circumference to its diameter + static const eT tau; //!< ratio of any circle's circumference to its radius (replacement of 2*pi) + static const eT e; //!< base of the natural logarithm + static const eT euler; //!< Euler's constant, aka Euler-Mascheroni constant + static const eT gratio; //!< golden ratio + static const eT sqrt2; //!< square root of 2 + static const eT sqrt2pi; //!< square root of 2*pi + static const eT log_sqrt2pi; //!< log of square root of 2*pi + static const eT eps; //!< the difference between 1 and the least value greater than 1 that is representable + static const eT log_min; //!< log of the minimum representable value + static const eT log_max; //!< log of the maximum representable value + static const eT nan; //!< "not a number" + static const eT inf; //!< infinity + + // + + static const eT m_u; //!< atomic mass constant (in kg) + static const eT N_A; //!< Avogadro constant + static const eT k; //!< Boltzmann constant (in joules per kelvin) + static const eT k_evk; //!< Boltzmann constant (in eV/K) + static const eT a_0; //!< Bohr radius (in meters) + static const eT mu_B; //!< Bohr magneton + static const eT Z_0; //!< characteristic impedance of vacuum (in ohms) + static const eT G_0; //!< conductance quantum (in siemens) + static const eT k_e; //!< Coulomb's constant (in meters per farad) + static const eT eps_0; //!< electric constant (in farads per meter) + static const eT m_e; //!< electron mass (in kg) + static const eT eV; //!< electron volt (in joules) + static const eT ec; //!< elementary charge (in coulombs) + static const eT F; //!< Faraday constant (in coulombs) + static const eT alpha; //!< fine-structure constant + static const eT alpha_inv; //!< inverse fine-structure constant + static const eT K_J; //!< Josephson constant + static const eT mu_0; //!< magnetic constant (in henries per meter) + static const eT phi_0; //!< magnetic flux quantum (in webers) + static const eT R; //!< molar gas constant (in joules per mole kelvin) + static const eT G; //!< Newtonian constant of gravitation (in newton square meters per kilogram squared) + static const eT h; //!< Planck constant (in joule seconds) + static const eT h_bar; //!< Planck constant over 2 pi, aka reduced Planck constant (in joule seconds) + static const eT m_p; //!< proton mass (in kg) + static const eT R_inf; //!< Rydberg constant (in reciprocal meters) + static const eT c_0; //!< speed of light in vacuum (in meters per second) + static const eT sigma; //!< Stefan-Boltzmann constant + static const eT R_k; //!< von Klitzing constant (in ohms) + static const eT b; //!< Wien wavelength displacement law constant + }; + + +// the long lengths of the constants are for future support of "long double" +// and any smart compiler that does high-precision computation at compile-time + +template<typename eT> const eT Datum<eT>::pi = eT(3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679); +template<typename eT> const eT Datum<eT>::tau = eT(6.2831853071795864769252867665590057683943387987502116419498891846156328125724179972560696506842341359); +template<typename eT> const eT Datum<eT>::e = eT(2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274); +template<typename eT> const eT Datum<eT>::euler = eT(0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495); +template<typename eT> const eT Datum<eT>::gratio = eT(1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374); +template<typename eT> const eT Datum<eT>::sqrt2 = eT(1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727); +template<typename eT> const eT Datum<eT>::sqrt2pi = eT(2.5066282746310005024157652848110452530069867406099383166299235763422936546078419749465958383780572661); +template<typename eT> const eT Datum<eT>::log_sqrt2pi = eT(0.9189385332046727417803297364056176398613974736377834128171515404827656959272603976947432986359541976); +template<typename eT> const eT Datum<eT>::eps = std::numeric_limits<eT>::epsilon(); +template<typename eT> const eT Datum<eT>::log_min = std::log(std::numeric_limits<eT>::min()); +template<typename eT> const eT Datum<eT>::log_max = std::log(std::numeric_limits<eT>::max()); +template<typename eT> const eT Datum<eT>::nan = priv::Datum_helper::nan<eT>(); +template<typename eT> const eT Datum<eT>::inf = priv::Datum_helper::inf<eT>(); + +template<typename eT> const eT Datum<eT>::m_u = eT(1.66053906660e-27); +template<typename eT> const eT Datum<eT>::N_A = eT(6.02214076e23); +template<typename eT> const eT Datum<eT>::k = eT(1.380649e-23); +template<typename eT> const eT Datum<eT>::k_evk = eT(8.617333262e-5); +template<typename eT> const eT Datum<eT>::a_0 = eT(5.29177210903e-11); +template<typename eT> const eT Datum<eT>::mu_B = eT(9.2740100783e-24); +template<typename eT> const eT Datum<eT>::Z_0 = eT(376.730313668); +template<typename eT> const eT Datum<eT>::G_0 = eT(7.748091729e-5); +template<typename eT> const eT Datum<eT>::k_e = eT(8.9875517923e9); +template<typename eT> const eT Datum<eT>::eps_0 = eT(8.8541878128e-12); +template<typename eT> const eT Datum<eT>::m_e = eT(9.1093837015e-31); +template<typename eT> const eT Datum<eT>::eV = eT(1.602176634e-19); +template<typename eT> const eT Datum<eT>::ec = eT(1.602176634e-19); +template<typename eT> const eT Datum<eT>::F = eT(96485.33212); +template<typename eT> const eT Datum<eT>::alpha = eT(7.2973525693e-3); +template<typename eT> const eT Datum<eT>::alpha_inv = eT(137.035999084); +template<typename eT> const eT Datum<eT>::K_J = eT(483597.8484e9); +template<typename eT> const eT Datum<eT>::mu_0 = eT(1.25663706212e-6); +template<typename eT> const eT Datum<eT>::phi_0 = eT(2.067833848e-15); +template<typename eT> const eT Datum<eT>::R = eT(8.314462618); +template<typename eT> const eT Datum<eT>::G = eT(6.67430e-11); +template<typename eT> const eT Datum<eT>::h = eT(6.62607015e-34); +template<typename eT> const eT Datum<eT>::h_bar = eT(1.054571817e-34); +template<typename eT> const eT Datum<eT>::m_p = eT(1.67262192369e-27); +template<typename eT> const eT Datum<eT>::R_inf = eT(10973731.568160); +template<typename eT> const eT Datum<eT>::c_0 = eT(299792458.0); +template<typename eT> const eT Datum<eT>::sigma = eT(5.670374419e-8); +template<typename eT> const eT Datum<eT>::R_k = eT(25812.80745); +template<typename eT> const eT Datum<eT>::b = eT(2.897771955e-3); + + + +typedef Datum<float > fdatum; +typedef Datum<double> datum; + + + + +namespace priv + { + + template<typename eT> + static + constexpr + typename arma_real_only<eT>::result + most_neg() + { + return (std::numeric_limits<eT>::has_infinity) ? -(std::numeric_limits<eT>::infinity()) : std::numeric_limits<eT>::lowest(); + } + + + template<typename eT> + static + constexpr + typename arma_integral_only<eT>::result + most_neg() + { + return std::numeric_limits<eT>::lowest(); + } + + + template<typename eT> + static + constexpr + typename arma_real_only<eT>::result + most_pos() + { + return (std::numeric_limits<eT>::has_infinity) ? std::numeric_limits<eT>::infinity() : std::numeric_limits<eT>::max(); + } + + + template<typename eT> + static + constexpr + typename arma_integral_only<eT>::result + most_pos() + { + return std::numeric_limits<eT>::max(); + } + + } + + + +//! @} |