text: /*******************************************************************************
  
  "A Collection of Useful C++ Classes for Digital Signal Processing"
   By Vinnie Falco
  
  Official project location:
  https://github.com/vinniefalco/DSPFilters
  
  See Documentation.cpp for contact information, notes, and bibliography.
  
  --------------------------------------------------------------------------------
  
  License: MIT License (http://www.opensource.org/licenses/mit-license.php)
  Copyright (c) 2009 by Vinnie Falco
  
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
  
  The above copyright notice and this permission notice shall be included in
  all copies or substantial portions of the Software.
  
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  THE SOFTWARE.
  
  *******************************************************************************/
  
  #ifndef DSPFILTERS_MATHSUPPLEMENT_H
  #define DSPFILTERS_MATHSUPPLEMENT_H
  
  #include "DspFilters/Common.h"
  
  namespace Dsp {
  
  const double doublePi		=3.1415926535897932384626433832795028841971;
  const double doublePi_2	=1.5707963267948966192313216916397514420986;
  const double doubleLn2  =0.69314718055994530941723212145818;//?????
  const double doubleLn10	=2.3025850929940456840179914546844;//??????
  
  typedef std::complex<double> complex_t;
  typedef std::pair<complex_t, complex_t> complex_pair_t;
  
  template<typename Real>
  inline std::complex<Real> solve_quadratic_1 (Real a, Real b, Real c)
  {
    return (-b + sqrt (std::complex<Real> (b*b - 4*a*c, 0))) / (2. * a);
  }
  
  template<typename Real>
  inline std::complex<Real> solve_quadratic_2 (Real a, Real b, Real c)
  {
    return (-b - sqrt (std::complex<Real> (b*b - 4*a*c, 0))) / (2. * a);
  }
  
  inline const complex_t infinity()
  {
    return complex_t (std::numeric_limits<double>::infinity());
  }
  
  inline const complex_t adjust_imag (const complex_t& c)
  {
    if (fabs (c.imag()) < 1e-30)
      return complex_t (c.real(), 0);
    else
      return c;
  }
  
  template <typename Ty, typename To>
  inline std::complex<Ty> addmul (const std::complex<Ty>& c,
                                  Ty v,
                                  const std::complex<To>& c1)
  {
    return std::complex <Ty> (
      c.real() + v * c1.real(), c.imag() + v * c1.imag());
  }
  
  template <typename Ty>
  inline std::complex<Ty> recip (const std::complex<Ty>& c)
  {
    Ty n = 1.0 / std::norm (c);
    
    return std::complex<Ty> (n * c.real(), n * c.imag());
  }
  
  template <typename Ty>
  inline Ty asinh (Ty x)
  {
    return log (x + std::sqrt (x * x + 1 ));
  }
  
  template <typename Ty>
  inline Ty acosh (Ty x)
  {
    return log (x + std::sqrt (x * x - 1));
  }
  
  template <typename Ty>
  inline bool is_nan (Ty v)
  {
    return !(v == v);
  }
  
  template <>
  inline bool is_nan<complex_t> (complex_t v)
  {
    return Dsp::is_nan (v.real()) || Dsp::is_nan (v.imag());
  }
  
  //------------------------------------------------------------------------------
  
  /*
   * Hack to prevent denormals
   *
   */
  
  //const double anti_denormal_vsa = 1e-16; // doesn't prevent denormals
  //const double anti_denormal_vsa = 0;
  const double anti_denormal_vsa = 1e-8;
  
  class DenormalPrevention
  {
  public:
    DenormalPrevention ()
      : m_v (anti_denormal_vsa)
    {
    }
  
    // small alternating current
    inline double ac ()
    {
      return m_v = -m_v;
    }
  
    // small direct current
    static inline double dc ()
    {
      return anti_denormal_vsa;
    }
  
  private:
    double m_v;
  };
  
  }
  
  #endif
  