Chris@49: // Copyright (C) 2008-2011 NICTA (www.nicta.com.au)
Chris@49: // Copyright (C) 2008-2011 Conrad Sanderson
Chris@49: // 
Chris@49: // This Source Code Form is subject to the terms of the Mozilla Public
Chris@49: // License, v. 2.0. If a copy of the MPL was not distributed with this
Chris@49: // file, You can obtain one at http://mozilla.org/MPL/2.0/.
Chris@49: 
Chris@49: 
Chris@49: //! \addtogroup constants_compat
Chris@49: //! @{
Chris@49: 
Chris@49: 
Chris@49: // the Math and Phy classes are kept for compatibility with old code;
Chris@49: // for new code, use the Datum class instead
Chris@49: // eg. instead of math::pi(), use datum::pi
Chris@49: 
Chris@49: 
Chris@49: template<typename eT>
Chris@49: class Math
Chris@49:   {
Chris@49:   public:
Chris@49:   
Chris@49:   // the long lengths of the constants are for future support of "long double"
Chris@49:   // and any smart compiler that does high-precision computation at compile-time
Chris@49:   
Chris@49:   //! ratio of any circle's circumference to its diameter
Chris@49:   static eT pi()        { return eT(3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679); }
Chris@49:   
Chris@49:   //! base of the natural logarithm
Chris@49:   static eT e()         { return eT(2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274); }
Chris@49:   
Chris@49:   //! Euler's constant, aka Euler-Mascheroni constant
Chris@49:   static eT euler()     { return eT(0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495); }
Chris@49:   
Chris@49:   //! golden ratio
Chris@49:   static eT gratio()    { return eT(1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374); }
Chris@49:   
Chris@49:   //! square root of 2
Chris@49:   static eT sqrt2()     { return eT(1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727); }
Chris@49:   
Chris@49:   //! the difference between 1 and the least value greater than 1 that is representable
Chris@49:   static eT eps()       { return std::numeric_limits<eT>::epsilon(); }
Chris@49:   
Chris@49:   //! log of the minimum representable value
Chris@49:   static eT log_min()   { static const eT out = std::log(std::numeric_limits<eT>::min()); return out; }
Chris@49:     
Chris@49:   //! log of the maximum representable value
Chris@49:   static eT log_max()   { static const eT out = std::log(std::numeric_limits<eT>::max()); return out; }
Chris@49:   
Chris@49:   //! "not a number"
Chris@49:   static eT nan()       { return priv::Datum_helper::nan<eT>(); }
Chris@49:   
Chris@49:   //! infinity 
Chris@49:   static eT inf()       { return priv::Datum_helper::inf<eT>(); }
Chris@49:   };
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! Physical constants taken from NIST and WolframAlpha on 2009-06-23
Chris@49: //! http://physics.nist.gov/cuu/Constants
Chris@49: //! http://www.wolframalpha.com
Chris@49: //! See also http://en.wikipedia.org/wiki/Physical_constant
Chris@49: template<typename eT>
Chris@49: class Phy
Chris@49:   {
Chris@49:   public:
Chris@49:   
Chris@49:   //! atomic mass constant (in kg)
Chris@49:   static eT m_u()       {  return eT(1.660538782e-27); }
Chris@49:   
Chris@49:   //! Avogadro constant
Chris@49:   static eT N_A()       {  return eT(6.02214179e23); }
Chris@49:   
Chris@49:   //! Boltzmann constant (in joules per kelvin)
Chris@49:   static eT k()         {  return eT(1.3806504e-23); }
Chris@49:   
Chris@49:   //! Boltzmann constant (in eV/K)
Chris@49:   static eT k_evk()     {  return eT(8.617343e-5); }
Chris@49:   
Chris@49:   //! Bohr radius (in meters)
Chris@49:   static eT a_0()       { return eT(0.52917720859e-10); }
Chris@49:   
Chris@49:   //! Bohr magneton
Chris@49:   static eT mu_B()      { return eT(927.400915e-26); }
Chris@49:   
Chris@49:   //! characteristic impedance of vacuum (in ohms)
Chris@49:   static eT Z_0()       { return eT(3.76730313461771e-2); }
Chris@49:   
Chris@49:   //! conductance quantum (in siemens)
Chris@49:   static eT G_0()       { return eT(7.7480917004e-5); }
Chris@49:   
Chris@49:   //! Coulomb's constant (in meters per farad)
Chris@49:   static eT k_e()       { return eT(8.9875517873681764e9); }
Chris@49:   
Chris@49:   //! electric constant (in farads per meter)
Chris@49:   static eT eps_0()     { return eT(8.85418781762039e-12); }
Chris@49:   
Chris@49:   //! electron mass (in kg)
Chris@49:   static eT m_e()       { return eT(9.10938215e-31); }
Chris@49:   
Chris@49:   //! electron volt (in joules)
Chris@49:   static eT eV()        { return eT(1.602176487e-19); }
Chris@49:   
Chris@49:   //! elementary charge (in coulombs)
Chris@49:   static eT e()         { return eT(1.602176487e-19); }
Chris@49:   
Chris@49:   //! Faraday constant (in coulombs)
Chris@49:   static eT F()         { return eT(96485.3399); }
Chris@49:   
Chris@49:   //! fine-structure constant
Chris@49:   static eT alpha()     { return eT(7.2973525376e-3); }
Chris@49:   
Chris@49:   //! inverse fine-structure constant
Chris@49:   static eT alpha_inv() { return eT(137.035999679); }
Chris@49:   
Chris@49:   //! Josephson constant
Chris@49:   static eT K_J()       { return eT(483597.891e9); }
Chris@49:   
Chris@49:   //! magnetic constant (in henries per meter)
Chris@49:   static eT mu_0()      { return eT(1.25663706143592e-06); }
Chris@49:   
Chris@49:   //! magnetic flux quantum (in webers)
Chris@49:   static eT phi_0()     { return eT(2.067833667e-15); }
Chris@49:   
Chris@49:   //! molar gas constant (in joules per mole kelvin)
Chris@49:   static eT R()         { return eT(8.314472); }
Chris@49:   
Chris@49:   //! Newtonian constant of gravitation (in newton square meters per kilogram squared)
Chris@49:   static eT G()         { return eT(6.67428e-11); }
Chris@49:   
Chris@49:   //! Planck constant (in joule seconds)
Chris@49:   static eT h()         { return eT(6.62606896e-34); }
Chris@49:   
Chris@49:   //! Planck constant over 2 pi, aka reduced Planck constant (in joule seconds)
Chris@49:   static eT h_bar()     { return eT(1.054571628e-34); }
Chris@49:   
Chris@49:   //! proton mass (in kg)
Chris@49:   static eT m_p()       { return eT(1.672621637e-27); }
Chris@49:   
Chris@49:   //! Rydberg constant (in reciprocal meters)
Chris@49:   static eT R_inf()     { return eT(10973731.568527); }
Chris@49:   
Chris@49:   //! speed of light in vacuum (in meters per second)
Chris@49:   static eT c_0()       { return eT(299792458.0); }
Chris@49:   
Chris@49:   //! Stefan-Boltzmann constant
Chris@49:   static eT sigma()     { return eT(5.670400e-8); }
Chris@49:   
Chris@49:   //! von Klitzing constant (in ohms)
Chris@49:   static eT R_k()       { return eT(25812.807557); }
Chris@49:   
Chris@49:   //! Wien wavelength displacement law constant
Chris@49:   static eT b()         { return eT(2.8977685e-3); }
Chris@49:   };
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: typedef Math<float>  fmath;
Chris@49: typedef Math<double> math;
Chris@49: 
Chris@49: typedef Phy<float>   fphy;
Chris@49: typedef Phy<double>  phy;
Chris@49: 
Chris@49: 
Chris@49: 
Chris@49: //! @}