max@0: // Copyright (C) 2008-2011 NICTA (www.nicta.com.au)
max@0: // Copyright (C) 2008-2011 Conrad Sanderson
max@0: // 
max@0: // This file is part of the Armadillo C++ library.
max@0: // It is provided without any warranty of fitness
max@0: // for any purpose. You can redistribute this file
max@0: // and/or modify it under the terms of the GNU
max@0: // Lesser General Public License (LGPL) as published
max@0: // by the Free Software Foundation, either version 3
max@0: // of the License or (at your option) any later version.
max@0: // (see http://www.opensource.org/licenses for more info)
max@0: 
max@0: 
max@0: //! \addtogroup constants
max@0: //! @{
max@0: 
max@0: 
max@0: namespace priv
max@0:   {
max@0:   class Math_helper
max@0:     {
max@0:     public:
max@0:     
max@0:     template<typename eT>
max@0:     static
max@0:     typename arma_float_only<eT>::result
max@0:     nan(typename arma_float_only<eT>::result* junk = 0)
max@0:       {
max@0:       arma_ignore(junk);
max@0:       
max@0:       if(std::numeric_limits<eT>::has_quiet_NaN == true)
max@0:         {
max@0:         return std::numeric_limits<eT>::quiet_NaN();
max@0:         }
max@0:       else
max@0:         {
max@0:         return eT(0);
max@0:         }
max@0:       }
max@0:     
max@0:     
max@0:     template<typename eT>
max@0:     static
max@0:     typename arma_cx_only<eT>::result
max@0:     nan(typename arma_cx_only<eT>::result* junk = 0)
max@0:       {
max@0:       arma_ignore(junk);
max@0:       
max@0:       typedef typename get_pod_type<eT>::result T;
max@0:       
max@0:       return eT( Math_helper::nan<T>(), Math_helper::nan<T>() );
max@0:       }
max@0:     
max@0:     
max@0:     template<typename eT>
max@0:     static
max@0:     typename arma_integral_only<eT>::result
max@0:     nan(typename arma_integral_only<eT>::result* junk = 0)
max@0:       {
max@0:       arma_ignore(junk);
max@0:       
max@0:       return eT(0);
max@0:       }
max@0:     
max@0:     
max@0:     template<typename eT>
max@0:     static
max@0:     typename arma_float_only<eT>::result
max@0:     inf(typename arma_float_only<eT>::result* junk = 0)
max@0:       {
max@0:       arma_ignore(junk);
max@0:       
max@0:       if(std::numeric_limits<eT>::has_infinity == true)
max@0:         {
max@0:         return std::numeric_limits<eT>::infinity();
max@0:         }
max@0:       else
max@0:         {
max@0:         return std::numeric_limits<eT>::max();
max@0:         }
max@0:       }
max@0:     
max@0:     
max@0:     template<typename eT>
max@0:     static
max@0:     typename arma_cx_only<eT>::result
max@0:     inf(typename arma_cx_only<eT>::result* junk = 0)
max@0:       {
max@0:       arma_ignore(junk);
max@0:       
max@0:       typedef typename get_pod_type<eT>::result T;
max@0:       
max@0:       return eT( Math_helper::inf<T>(), Math_helper::inf<T>() );
max@0:       }
max@0:     
max@0: 
max@0:     template<typename eT>
max@0:     static
max@0:     typename arma_integral_only<eT>::result
max@0:     inf(typename arma_integral_only<eT>::result* junk = 0)
max@0:       {
max@0:       arma_ignore(junk);
max@0:       
max@0:       return std::numeric_limits<eT>::max();
max@0:       }
max@0:     
max@0:     };
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: template<typename eT>
max@0: class Math
max@0:   {
max@0:   public:
max@0:   
max@0:   // the long lengths of the constants are for future support of "long double"
max@0:   // and any smart compiler that does high-precision computation at compile-time
max@0:   
max@0:   //! ratio of any circle's circumference to its diameter
max@0:   static eT pi()        { return eT(3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679); }
max@0:   
max@0:   //! base of the natural logarithm
max@0:   static eT e()         { return eT(2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274); }
max@0:   
max@0:   //! Euler's constant, aka Euler-Mascheroni constant
max@0:   static eT euler()     { return eT(0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495); }
max@0:   
max@0:   //! golden ratio
max@0:   static eT gratio()    { return eT(1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374); }
max@0:   
max@0:   //! square root of 2
max@0:   static eT sqrt2()     { return eT(1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727); }
max@0:   
max@0:   //! the difference between 1 and the least value greater than 1 that is representable
max@0:   static eT eps()       { return std::numeric_limits<eT>::epsilon(); }
max@0:   
max@0:   //! log of the minimum representable value
max@0:   static eT log_min()   { static const eT out = std::log(std::numeric_limits<eT>::min()); return out; }
max@0:     
max@0:   //! log of the maximum representable value
max@0:   static eT log_max()   { static const eT out = std::log(std::numeric_limits<eT>::max()); return out; }
max@0:   
max@0:   //! "not a number"
max@0:   static eT nan()       { return priv::Math_helper::nan<eT>(); }
max@0:   
max@0:   //! infinity 
max@0:   static eT inf()       { return priv::Math_helper::inf<eT>(); }
max@0:   };
max@0: 
max@0: 
max@0: 
max@0: //! Physical constants taken from NIST and WolframAlpha on 2009-06-23
max@0: //! http://physics.nist.gov/cuu/Constants
max@0: //! http://www.wolframalpha.com
max@0: //! See also http://en.wikipedia.org/wiki/Physical_constant
max@0: template<typename eT>
max@0: class Phy
max@0:   {
max@0:   public:
max@0:   
max@0:   //! atomic mass constant (in kg)
max@0:   static eT m_u()       {  return eT(1.660538782e-27); }
max@0:   
max@0:   //! Avogadro constant
max@0:   static eT N_A()       {  return eT(6.02214179e23); }
max@0:   
max@0:   //! Boltzmann constant (in joules per kelvin)
max@0:   static eT k()         {  return eT(1.3806504e-23); }
max@0:   
max@0:   //! Boltzmann constant (in eV/K)
max@0:   static eT k_evk()     {  return eT(8.617343e-5); }
max@0:   
max@0:   //! Bohr radius (in meters)
max@0:   static eT a_0()       { return eT(0.52917720859e-10); }
max@0:   
max@0:   //! Bohr magneton
max@0:   static eT mu_B()      { return eT(927.400915e-26); }
max@0:   
max@0:   //! characteristic impedance of vacuum (in ohms)
max@0:   static eT Z_0()       { return eT(3.76730313461771e-2); }
max@0:   
max@0:   //! conductance quantum (in siemens)
max@0:   static eT G_0()       { return eT(7.7480917004e-5); }
max@0:   
max@0:   //! Coulomb's constant (in meters per farad)
max@0:   static eT k_e()       { return eT(8.9875517873681764e9); }
max@0:   
max@0:   //! electric constant (in farads per meter)
max@0:   static eT eps_0()     { return eT(8.85418781762039e-12); }
max@0:   
max@0:   //! electron mass (in kg)
max@0:   static eT m_e()       { return eT(9.10938215e-31); }
max@0:   
max@0:   //! electron volt (in joules)
max@0:   static eT eV()        { return eT(1.602176487e-19); }
max@0:   
max@0:   //! elementary charge (in coulombs)
max@0:   static eT e()         { return eT(1.602176487e-19); }
max@0:   
max@0:   //! Faraday constant (in coulombs)
max@0:   static eT F()         { return eT(96485.3399); }
max@0:   
max@0:   //! fine-structure constant
max@0:   static eT alpha()     { return eT(7.2973525376e-3); }
max@0:   
max@0:   //! inverse fine-structure constant
max@0:   static eT alpha_inv() { return eT(137.035999679); }
max@0:   
max@0:   //! Josephson constant
max@0:   static eT K_J()       { return eT(483597.891e9); }
max@0:   
max@0:   //! magnetic constant (in henries per meter)
max@0:   static eT mu_0()      { return eT(1.25663706143592e-06); }
max@0:   
max@0:   //! magnetic flux quantum (in webers)
max@0:   static eT phi_0()     { return eT(2.067833667e-15); }
max@0:   
max@0:   //! molar gas constant (in joules per mole kelvin)
max@0:   static eT R()         { return eT(8.314472); }
max@0:   
max@0:   //! Newtonian constant of gravitation (in newton square meters per kilogram squared)
max@0:   static eT G()         { return eT(6.67428e-11); }
max@0:   
max@0:   //! Planck constant (in joule seconds)
max@0:   static eT h()         { return eT(6.62606896e-34); }
max@0:   
max@0:   //! Planck constant over 2 pi, aka reduced Planck constant (in joule seconds)
max@0:   static eT h_bar()     { return eT(1.054571628e-34); }
max@0:   
max@0:   //! proton mass (in kg)
max@0:   static eT m_p()       { return eT(1.672621637e-27); }
max@0:   
max@0:   //! Rydberg constant (in reciprocal meters)
max@0:   static eT R_inf()     { return eT(10973731.568527); }
max@0:   
max@0:   //! speed of light in vacuum (in meters per second)
max@0:   static eT c_0()       { return eT(299792458.0); }
max@0:   
max@0:   //! Stefan-Boltzmann constant
max@0:   static eT sigma()     { return eT(5.670400e-8); }
max@0:   
max@0:   //! von Klitzing constant (in ohms)
max@0:   static eT R_k()       { return eT(25812.807557); }
max@0:   
max@0:   //! Wien wavelength displacement law constant
max@0:   static eT b()         { return eT(2.8977685e-3); }
max@0:   };
max@0: 
max@0: 
max@0: 
max@0: typedef Math<float>  fmath;
max@0: typedef Math<double> math;
max@0: 
max@0: typedef Phy<float>   fphy;
max@0: typedef Phy<double>  phy;
max@0: 
max@0: 
max@0: 
max@0: namespace priv
max@0:   {
max@0:   
max@0:   template<typename eT>
max@0:   static
max@0:   arma_inline
max@0:   arma_hot
max@0:   typename arma_float_only<eT>::result
max@0:   most_neg(typename arma_float_only<eT>::result* junk = 0)
max@0:     {
max@0:     arma_ignore(junk);
max@0:     
max@0:     if(std::numeric_limits<eT>::has_infinity == true)
max@0:       {
max@0:       return -(std::numeric_limits<eT>::infinity());
max@0:       }
max@0:     else
max@0:       {
max@0:       return -(std::numeric_limits<eT>::max());
max@0:       }
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   static
max@0:   arma_inline
max@0:   arma_hot
max@0:   typename arma_integral_only<eT>::result
max@0:   most_neg(typename arma_integral_only<eT>::result* junk = 0)
max@0:     {
max@0:     arma_ignore(junk);
max@0:     
max@0:     return std::numeric_limits<eT>::min();
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   static
max@0:   arma_inline
max@0:   arma_hot
max@0:   typename arma_float_only<eT>::result
max@0:   most_pos(typename arma_float_only<eT>::result* junk = 0)
max@0:     {
max@0:     arma_ignore(junk);
max@0:     
max@0:     if(std::numeric_limits<eT>::has_infinity == true)
max@0:       {
max@0:       return std::numeric_limits<eT>::infinity();
max@0:       }
max@0:     else
max@0:       {
max@0:       return std::numeric_limits<eT>::max();
max@0:       }
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   static
max@0:   arma_inline
max@0:   arma_hot
max@0:   typename arma_integral_only<eT>::result
max@0:   most_pos(typename arma_integral_only<eT>::result* junk = 0)
max@0:     {
max@0:     arma_ignore(junk);
max@0:     
max@0:     return std::numeric_limits<eT>::max();
max@0:     }
max@0: 
max@0:   }
max@0: 
max@0: 
max@0: 
max@0: //! @}