max@0: // Copyright (C) 2010-2011 NICTA (www.nicta.com.au)
max@0: // Copyright (C) 2010-2011 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 eop_aux
max@0: //! @{
max@0: 
max@0: 
max@0: 
max@0: template<typename eT>
max@0: struct eop_aux_randu
max@0:   {
max@0:   arma_inline
max@0:   operator eT ()
max@0:     {
max@0:     return eT(std::rand()) / eT(RAND_MAX);
max@0:     }
max@0:   };
max@0: 
max@0: 
max@0:   
max@0: template<typename T>
max@0: struct eop_aux_randu< std::complex<T> >
max@0:   {
max@0:   arma_inline
max@0:   operator std::complex<T> ()
max@0:     {
max@0:     return std::complex<T>( T(eop_aux_randu<T>()), T(eop_aux_randu<T>()) );
max@0:     }
max@0:   };
max@0: 
max@0: 
max@0: 
max@0: template<typename eT>
max@0: struct eop_aux_randn
max@0:   {
max@0:   // // rudimentary method, based on the central limit theorem
max@0:   // // http://en.wikipedia.org/wiki/Central_limit_theorem
max@0:   // inline
max@0:   // operator eT () const
max@0:   //   {
max@0:   //   const uword N  = 12;  // N must be >= 12 and an even number
max@0:   //   const uword N2 = N/2;
max@0:   //   
max@0:   //   eT acc = eT(0);
max@0:   //   
max@0:   //   for(uword i=0; i<N2; ++i)
max@0:   //     {
max@0:   //     const eT tmp1 = eT(std::rand()) / eT(RAND_MAX);
max@0:   //     const eT tmp2 = eT(std::rand()) / eT(RAND_MAX);
max@0:   //     acc += tmp1+tmp2;
max@0:   //     }
max@0:   //   
max@0:   //   return acc - eT(N2);
max@0:   //   }
max@0:   
max@0:   
max@0:   // polar form of the Box-Muller transformation
max@0:   // http://en.wikipedia.org/wiki/Box-Muller_transformation
max@0:   // http://en.wikipedia.org/wiki/Marsaglia_polar_method
max@0:   inline
max@0:   operator eT () const
max@0:     {
max@0:     // make sure we are internally using at least floats
max@0:     typedef typename promote_type<eT,float>::result eTp;
max@0:     
max@0:     eTp tmp1;
max@0:     eTp tmp2;
max@0:     eTp w;
max@0:     
max@0:     do
max@0:       {
max@0:       tmp1 = eTp(2) * eTp(std::rand()) / eTp(RAND_MAX) - eTp(1);
max@0:       tmp2 = eTp(2) * eTp(std::rand()) / eTp(RAND_MAX) - eTp(1);
max@0:       w = tmp1*tmp1 + tmp2*tmp2;
max@0:       }
max@0:     while ( w >= eTp(1) );
max@0:     
max@0:     return eT( tmp1 * std::sqrt( (eTp(-2) * std::log(w)) / w) );
max@0:     }
max@0:   
max@0:   
max@0:   // other methods:
max@0:   // http://en.wikipedia.org/wiki/Ziggurat_algorithm
max@0:   //
max@0:   // Marsaglia and Tsang Ziggurat technique to transform from a uniform to a normal distribution.
max@0:   // G. Marsaglia, W.W. Tsang.
max@0:   // "Ziggurat method for generating random variables",
max@0:   // J. Statistical Software, vol 5, 2000.
max@0:   // http://www.jstatsoft.org/v05/i08/
max@0:   };
max@0: 
max@0: 
max@0: 
max@0: template<typename T>
max@0: struct eop_aux_randn< std::complex<T> >
max@0:   {
max@0:   arma_inline
max@0:   operator std::complex<T> () const
max@0:     {
max@0:     return std::complex<T>( T(eop_aux_randn<T>()), T(eop_aux_randn<T>()) );
max@0:     }
max@0: 
max@0:   };
max@0: 
max@0: 
max@0: //! use of the SFINAE approach to work around compiler limitations
max@0: //! http://en.wikipedia.org/wiki/SFINAE
max@0: 
max@0: class eop_aux
max@0:   {
max@0:   public:
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result    acos  (const eT x) { return eT( std::acos(double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result    asin  (const eT x) { return eT( std::asin(double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result    atan  (const eT x) { return eT( std::atan(double(x)) ); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_float_only<eT>::result       acos  (const eT x) { return std::acos(x); }
max@0:   template<typename eT> arma_inline static typename arma_float_only<eT>::result       asin  (const eT x) { return std::asin(x); }
max@0:   template<typename eT> arma_inline static typename arma_float_only<eT>::result       atan  (const eT x) { return std::atan(x); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_cx_only<eT>::result          acos  (const eT x) { return arma_acos(x); }
max@0:   template<typename eT> arma_inline static typename arma_cx_only<eT>::result          asin  (const eT x) { return arma_asin(x); }
max@0:   template<typename eT> arma_inline static typename arma_cx_only<eT>::result          atan  (const eT x) { return arma_atan(x); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result    acosh (const eT x) { return eT( arma_acosh(double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result    asinh (const eT x) { return eT( arma_asinh(double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result    atanh (const eT x) { return eT( arma_atanh(double(x)) ); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result acosh (const eT x) { return arma_acosh(x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result asinh (const eT x) { return arma_asinh(x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result atanh (const eT x) { return arma_atanh(x); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_not_cx<eT>::result conj(const eT               x) { return x;            }
max@0:   template<typename  T> arma_inline static          std::complex<T>         conj(const std::complex<T>& x) { return std::conj(x); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result sqrt  (const eT x) { return eT( std::sqrt (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result log10 (const eT x) { return eT( std::log10(double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result log   (const eT x) { return eT( std::log  (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result exp   (const eT x) { return eT( std::exp  (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result cos   (const eT x) { return eT( std::cos  (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result sin   (const eT x) { return eT( std::sin  (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result tan   (const eT x) { return eT( std::tan  (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result cosh  (const eT x) { return eT( std::cosh (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result sinh  (const eT x) { return eT( std::sinh (double(x)) ); }
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result tanh  (const eT x) { return eT( std::tanh (double(x)) ); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result sqrt  (const eT x) { return std::sqrt (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result log10 (const eT x) { return std::log10(x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result log   (const eT x) { return std::log  (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result exp   (const eT x) { return std::exp  (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result cos   (const eT x) { return std::cos  (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result sin   (const eT x) { return std::sin  (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result tan   (const eT x) { return std::tan  (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result cosh  (const eT x) { return std::cosh (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result sinh  (const eT x) { return std::sinh (x); }
max@0:   template<typename eT> arma_inline static typename arma_float_or_cx_only<eT>::result tanh  (const eT x) { return std::tanh (x); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_unsigned_integral_only<eT>::result neg (const eT x) { return  x; }
max@0:   template<typename eT> arma_inline static typename arma_signed_only<eT>::result            neg (const eT x) { return -x; }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result floor(const eT  x) { return x;                                                }
max@0:   template<typename eT> arma_inline static typename arma_float_only<eT>::result    floor(const eT  x) { return std::floor(x);                                    }
max@0:   template<typename eT> arma_inline static typename arma_cx_only<eT>::result       floor(const eT& x) { return eT( std::floor(x.real()), std::floor(x.imag()) ); }
max@0:   
max@0:   template<typename eT> arma_inline static typename arma_integral_only<eT>::result  ceil(const eT  x) { return x;                                                }
max@0:   template<typename eT> arma_inline static typename arma_float_only<eT>::result     ceil(const eT  x) { return std::ceil(x);                                     }
max@0:   template<typename eT> arma_inline static typename arma_cx_only<eT>::result        ceil(const eT& x) { return eT( std::ceil(x.real()), std::ceil(x.imag()) );   }
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_integral_only<eT>::result
max@0:   log2 (const eT x)
max@0:     {
max@0:     return eT( std::log(double(x))/ double(0.69314718055994530942) );
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_float_or_cx_only<eT>::result
max@0:   log2 (const eT x)
max@0:     {
max@0:     typedef typename get_pod_type<eT>::result T;
max@0:     return std::log(x) / T(0.69314718055994530942);
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_integral_only<eT>::result
max@0:   exp10 (const eT x)
max@0:     {
max@0:     return eT( std::pow(double(10), double(x)) );
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename
max@0:   arma_float_or_cx_only<eT>::result
max@0:   exp10 (const eT x)
max@0:     {
max@0:     typedef typename get_pod_type<eT>::result T;
max@0:     return std::pow( T(10), x);
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_integral_only<eT>::result
max@0:   exp2 (const eT x)
max@0:     {
max@0:     return eT( std::pow(double(2), double(x)) );
max@0:     }
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_float_or_cx_only<eT>::result
max@0:   exp2 (const eT x)
max@0:     {
max@0:     typedef typename get_pod_type<eT>::result T;
max@0:     return std::pow( T(2), x);
max@0:     }
max@0:   
max@0:   
max@0:   template<typename T1, typename T2>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_float_or_cx_only<T1>::result
max@0:   pow(const T1 base, const T2 exponent)
max@0:     {
max@0:     return std::pow(base, exponent);
max@0:     }
max@0:   
max@0:   
max@0:   
max@0:   template<typename T1, typename T2>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_integral_only<T1>::result
max@0:   pow(const T1 base, const T2 exponent)
max@0:     {
max@0:     return T1( std::pow( double(base), double(exponent) ) );
max@0:     }
max@0:   
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   arma_inline
max@0:   static
max@0:   typename arma_integral_only<eT>::result
max@0:   direct_eps(const eT)
max@0:     {
max@0:     return eT(0);
max@0:     }
max@0:   
max@0:   
max@0:   
max@0:   template<typename eT>
max@0:   inline
max@0:   static
max@0:   typename arma_float_only<eT>::result
max@0:   direct_eps(const eT x)
max@0:     {
max@0:     //arma_extra_debug_sigprint();
max@0:     
max@0:     // acording to IEEE Standard for Floating-Point Arithmetic (IEEE 754)
max@0:     // the mantissa length for double is 53 bits = std::numeric_limits<double>::digits
max@0:     // the mantissa length for float  is 24 bits = std::numeric_limits<float >::digits
max@0:     
max@0:     //return std::pow( std::numeric_limits<eT>::radix, (std::floor(std::log10(std::abs(x))/std::log10(std::numeric_limits<eT>::radix))-(std::numeric_limits<eT>::digits-1)) );
max@0:     
max@0:     const eT radix_eT     = eT(std::numeric_limits<eT>::radix);
max@0:     const eT digits_m1_eT = eT(std::numeric_limits<eT>::digits - 1);
max@0:     
max@0:     // return std::pow( radix_eT, eT(std::floor(std::log10(std::abs(x))/std::log10(radix_eT)) - digits_m1_eT) );
max@0:     return eop_aux::pow( radix_eT, eT(std::floor(std::log10(std::abs(x))/std::log10(radix_eT)) - digits_m1_eT) );
max@0:     }
max@0:   
max@0:   
max@0:   
max@0:   template<typename T>
max@0:   inline
max@0:   static
max@0:   typename arma_float_only<T>::result
max@0:   direct_eps(const std::complex<T> x)
max@0:     {
max@0:     //arma_extra_debug_sigprint();
max@0:     
max@0:     //return std::pow( std::numeric_limits<T>::radix, (std::floor(std::log10(std::abs(x))/std::log10(std::numeric_limits<T>::radix))-(std::numeric_limits<T>::digits-1)) );
max@0:     
max@0:     const T radix_T     = T(std::numeric_limits<T>::radix);
max@0:     const T digits_m1_T = T(std::numeric_limits<T>::digits - 1);
max@0:     
max@0:     return std::pow( radix_T, T(std::floor(std::log10(std::abs(x))/std::log10(radix_T)) - digits_m1_T) );
max@0:     }
max@0:   
max@0:   
max@0:   
max@0:   //! work around a bug in GCC 4.4
max@0:   template<typename eT> arma_inline static
max@0:   typename arma_unsigned_integral_only<eT>::result arma_abs(const eT x)              { return x;           }
max@0:   
max@0:   template<typename eT> arma_inline static
max@0:   typename arma_signed_integral_only<eT>::result   arma_abs(const eT x)              { return std::abs(x); }
max@0:   
max@0:   template<typename eT> arma_inline static
max@0:   typename arma_float_only<eT>::result             arma_abs(const eT x)              { return std::abs(x); }
max@0:   
max@0:   template<typename T> arma_inline static
max@0:   typename arma_float_only<T>::result              arma_abs(const std::complex<T> x) { return std::abs(x); }
max@0:   
max@0:   };
max@0: 
max@0: 
max@0: 
max@0: //! @}
max@0: